515 KiB
515 KiB
%matplotlib inline
%load_ext pycodestyle_magic
# display full output, not only last result, except ended with semicolon
from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = 'all';
from IPython.display import Image, SVG
# magic functions that do not work in current ipython --version
#
# auto check each cell, E703 - "statement ends with a semicolon"
# %flake8_on --ignore E703
import importlib
def import_sage(module_name):
importlib.invalidate_caches()
sage_name = module_name + ".sage"
python_name = module_name + ".sage.py"
if os.path.isfile(sage_name):
os.system('sage --preparse {}'.format(sage_name));
os.system('mv {} {}.py'.format(python_name, module_name))
if module_name in sys.modules:
return importlib.reload(sys.modules[module_name])
return importlib.import_module(module_name, package=None)
cs = import_sage('cable_signature')
# sig = import_sage('signature')Other cables
cs = import_sage('cable_signature')
knot_formula = "[[k[0], k[1], k[3]]," + \
" [-k[1], -k[3]]," + \
" [k[2], k[3]]," + \
" [-k[0], -k[2], -k[3]]]"
# q_vector = (3, 5, 7, 13)
q_vector = (3, 5, 7, 11)
template = cs.CableTemplate(knot_formula, q_vector=q_vector, verbose=True)
cable = template.cable
# cable.plot_all_summands()
cable.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 1 pp = -101/11, satellite_part = -4 sigma(T(2, 7; 2, 11)) = -145/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 1 pp = 101/11, satellite_part = 8 sigma(-T(2, 3; 2, 7; 2, 11)) = 189/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -101/11 Satellite part = -4 Sigma = -145/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 101/11 Satellite part = 8 Sigma = 189/11 ********** [0, 0, 1, 1] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 2 pp = -85/11, satellite_part = -4 sigma(T(2, 7; 2, 11)) = -129/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 2 pp = 85/11, satellite_part = 8 sigma(-T(2, 3; 2, 7; 2, 11)) = 173/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -85/11 Satellite part = -4 Sigma = -129/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 85/11 Satellite part = 8 Sigma = 173/11 [0, 0, 2, 2] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 3 pp = -73/11, satellite_part = -8 sigma(T(2, 7; 2, 11)) = -161/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 3 pp = 73/11, satellite_part = 12 sigma(-T(2, 3; 2, 7; 2, 11)) = 205/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -73/11 Satellite part = -8 Sigma = -161/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 73/11 Satellite part = 12 Sigma = 205/11 [0, 0, 3, 3] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 4 pp = -65/11, satellite_part = -12 sigma(T(2, 7; 2, 11)) = -197/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 4 pp = 65/11, satellite_part = 16 sigma(-T(2, 3; 2, 7; 2, 11)) = 241/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -65/11 Satellite part = -12 Sigma = -197/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 65/11 Satellite part = 16 Sigma = 241/11 [0, 0, 4, 4] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 5 pp = -61/11, satellite_part = -12 sigma(T(2, 7; 2, 11)) = -193/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 5 pp = 61/11, satellite_part = 12 sigma(-T(2, 3; 2, 7; 2, 11)) = 193/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -61/11 Satellite part = -12 Sigma = -193/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 61/11 Satellite part = 12 Sigma = 193/11 [0, 0, 5, 5] 0 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 6 pp = -61/11, satellite_part = -12 sigma(T(2, 7; 2, 11)) = -193/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 6 pp = 61/11, satellite_part = 12 sigma(-T(2, 3; 2, 7; 2, 11)) = 193/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -61/11 Satellite part = -12 Sigma = -193/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 61/11 Satellite part = 12 Sigma = 193/11 [0, 0, 6, 6] 0 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 7 pp = -65/11, satellite_part = -12 sigma(T(2, 7; 2, 11)) = -197/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 7 pp = 65/11, satellite_part = 16 sigma(-T(2, 3; 2, 7; 2, 11)) = 241/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -65/11 Satellite part = -12 Sigma = -197/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 65/11 Satellite part = 16 Sigma = 241/11 [0, 0, 7, 7] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 8 pp = -73/11, satellite_part = -8 sigma(T(2, 7; 2, 11)) = -161/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 8 pp = 73/11, satellite_part = 12 sigma(-T(2, 3; 2, 7; 2, 11)) = 205/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -73/11 Satellite part = -8 Sigma = -161/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 73/11 Satellite part = 12 Sigma = 205/11 [0, 0, 8, 8] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 9 pp = -85/11, satellite_part = -4 sigma(T(2, 7; 2, 11)) = -129/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 9 pp = 85/11, satellite_part = 8 sigma(-T(2, 3; 2, 7; 2, 11)) = 173/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -85/11 Satellite part = -4 Sigma = -129/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 85/11 Satellite part = 8 Sigma = 173/11 [0, 0, 9, 9] 4 ########## T(2, 7; 2, 11) ##########
T(2, 7; 2, 11), theta = 10 pp = -101/11, satellite_part = -4 sigma(T(2, 7; 2, 11)) = -145/11 ########## -T(2, 3; 2, 7; 2, 11) ##########
-T(2, 3; 2, 7; 2, 11), theta = 10 pp = 101/11, satellite_part = 8 sigma(-T(2, 3; 2, 7; 2, 11)) = 189/11 **************************************************************************************************** Calculation summary for a cable sum: T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11) 2. T(2, 7; 2, 11) Pattern part = -101/11 Satellite part = -4 Sigma = -145/11 3. -T(2, 3; 2, 7; 2, 11) Pattern part = 101/11 Satellite part = 8 Sigma = 189/11 [0, 0, 10, 10] 4 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
False
Cables with 8 direct summands
formula_1 = "[[k[0], k[5], k[3]], " + \
"[-k[1], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[0], -k[2], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[-k[5], -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[4], -k[6], -k[7]]]"
cable_template_1 = cs.CableTemplate(knot_formula=formula_1)
cable_template_2 = cs.CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2Relatively small cables
q_vector = (5, 13, 19, 41,\
7, 17, 23, 43)
cable_template.fill_q_vector(q_vector=q_vector)
cable = cable_template.cable
print(cable.knot_description)
q_vector_small = (3, 7, 13, 19,\
5, 11, 17, 23)
cable_template.fill_q_vector(q_vector=q_vector)
cable = cable_template.cable
print(cable.knot_description)T(2, 5; 2, 17; 2, 41) # -T(2, 13; 2, 41) # T(2, 19; 2, 41) # -T(2, 5; 2, 19; 2, 41) # T(2, 7; 2, 13; 2, 43) # -T(2, 17; 2, 43) # T(2, 23; 2, 43) # -T(2, 7; 2, 23; 2, 43) T(2, 5; 2, 17; 2, 41) # -T(2, 13; 2, 41) # T(2, 19; 2, 41) # -T(2, 5; 2, 19; 2, 41) # T(2, 7; 2, 13; 2, 43) # -T(2, 17; 2, 43) # T(2, 23; 2, 43) # -T(2, 7; 2, 23; 2, 43)
# cable.is_signature_big_for_all_metabolizers()Slice candidate
cable_template.fill_q_vector()
# print(cable_template.q_vector)
# print(cable_template.knot_formula)
slice_canidate = cable_template.cable
print(slice_canidate.knot_description)
sf = slice_canidate(4,4,4,4,0,0,0,0)
sf = slice_canidate(4,1,1,4,0,0,0,0)
# cable.is_signature_big_for_all_metabolizers()
T(2, 5; 2, 71; 2, 347) # -T(2, 67; 2, 347) # T(2, 61; 2, 347) # -T(2, 5; 2, 61; 2, 347) # T(2, 11; 2, 67; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)
# knot_formula = "[[k[0], k[1], k[4]], [-k[1], -k[3]],\
# [k[2], k[3]], [-k[0], -k[2], -k[4]]]"
# knot_formula = "[[k[3]], [-k[3]],\
# [k[3]], [-k[3]] ]"
# knot_formula = "[[k[3], k[2], k[0]], [-k[2], -k[0]],\
# [k[1], k[0]], [-k[3], -k[1], -k[0]]]"
# knot_formula = "[[k[0], k[1], k[2]], [k[3], k[4]],\
# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
# knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
# [-k[0], -k[1], -k[3]], [-k[2]]]"formula_1 = "[[k[0], k[5], k[3]], " + \
"[-k[1], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[0], -k[2], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[-k[5], -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[4], -k[6], -k[7]]]"
cable_template_1 = cs.CableTemplate(knot_formula=formula_1)
cable_template_2 = cs.CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
cable_template.fill_q_vector()
# print(cable_template.q_vector)
# print(cable_template.knot_formula)
slice_canidate = cable_template.cable
print(slice_canidate.knot_description)
sf = slice_canidate(4,4,4,4,0,0,0,0)
sf = slice_canidate(4,1,1,4,0,0,0,0)
slice_canidate.q_order
# slice_canidate.is_signature_big_for_all_metabolizers()T(2, 5; 2, 71; 2, 347) # -T(2, 67; 2, 347) # T(2, 61; 2, 347) # -T(2, 5; 2, 61; 2, 347) # T(2, 11; 2, 67; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)
127349
formula_1 = "[[k[0], k[5], k[3]], " + \
"[-k[5], -k[3]], " + \
"[k[2], k[3]], " + \
"[-k[4], -k[2], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[-k[1], -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[0], -k[6], -k[7]]]"
cable_template_1 = cs.CableTemplate(knot_formula=formula_1)
cable_template_2 = cs.CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
cable_template.fill_q_vector()
slice_canidate = cable_template.cable
print(slice_canidate.knot_description)
slice_canidate.q_order
# slice_canidate.is_signature_big_for_all_metabolizers()
sigma = slice_canidate.get_sigma_as_function_of_theta()
# sigma((0, 6, 6, 0, 0,0,0,0))
# 13450/83
sigma((9, 9, 9, 9, 0,0,0,0))T(2, 11; 2, 53; 2, 347) # -T(2, 53; 2, 347) # T(2, 61; 2, 347) # -T(2, 7; 2, 61; 2, 347) # T(2, 7; 2, 71; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)
127349
-4
formula_1 = "[[k[0], k[5], k[3]], " + \
"[-k[1], -k[3]], " + \
"[ k[3]], " + \
"[-k[4], -k[6], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[ -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[0], -k[5], -k[7]]]"
cable_template_1 = cs.CableTemplate(knot_formula=formula_1)
cable_template_2 = cs.CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
cable_template.fill_q_vector()
# print(cable_template.q_vector)
# print(cable_template.knot_formula)
slice_canidate = cable_template.cable
print(slice_canidate.knot_description)
sf = slice_canidate(4,4,4,4,0,0,0,0)
sf = slice_canidate(4,1,1,4,0,0,0,0)
# slice_canidate.is_signature_big_for_all_metabolizers()T(2, 11; 2, 71; 2, 313) # -T(2, 61; 2, 313) # T(2, 313) # -T(2, 7; 2, 67; 2, 313) # T(2, 7; 2, 61; 2, 347) # -T(2, 347) # T(2, 67; 2, 347) # -T(2, 11; 2, 71; 2, 347)
formula_1 = " [ [k[5], k[3]], " + \
" [ -k[1], -k[3]], " + \
" [ k[3]], " + \
"[-k[4], -k[6], -k[3]]]"
formula_2 = "[[k[4], k[1], k[7]], " + \
"[ -k[7]], " + \
"[k[6], k[7]], " + \
"[-k[5], -k[7]]]"
cable_template_1 = cs.CableTemplate(knot_formula=formula_1)
cable_template_2 = cs.CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
cable_template.fill_q_vector()
# print(cable_template.q_vector)
# print(cable_template.knot_formula)
slice_canidate = cable_template.cable
print(slice_canidate.knot_description)
sf = slice_canidate(4,4,4,4,0,0,0,0)
sf = slice_canidate(4,1,1,4,0,0,0,0)
slice_canidate.q_order
# slice_canidate.is_signature_big_for_all_metabolizers()
T(2, 43; 2, 191) # -T(2, 37; 2, 191) # T(2, 191) # -T(2, 5; 2, 41; 2, 191) # T(2, 5; 2, 37; 2, 211) # -T(2, 211) # T(2, 41; 2, 211) # -T(2, 43; 2, 211)
40301
sf = slice_canidate()
sf = sf[2]sf.plot()formula_1 = "[ [k[5], k[3]], " + \
"[ -k[1], -k[3]], " + \
"[ k[3]], " + \
"[ -k[6], -k[3]]]"
formula_2 = "[[ k[1], k[7]], " + \
"[ -k[7]], " + \
"[ k[6], k[7]], " + \
"[ -k[5], -k[7]]]"
cable_template_1 = cs.CableTemplate(knot_formula=formula_1)
cable_template_2 = cs.CableTemplate(knot_formula=formula_2)
cable_template = cable_template_1 + cable_template_2
cable_template.fill_q_vector()
# print(cable_template.q_vector)
# print(cable_template.knot_formula)
slice_canidate = cable_template.cable
print(slice_canidate.knot_description)
sf = slice_canidate(4,4,4,4,0,0,0,0)
sf = slice_canidate(4,1,1,4,0,0,0,0)
slice_canidate.q_orderT(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83) # T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)
8549
slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)[0, 0, 2, 2, 0, 0, 0, 0] 0 [0, 0, 3, 3, 0, 0, 0, 0] 0 [0, 0, 4, 4, 0, 0, 0, 0] 4 [0, 0, 5, 5, 0, 0, 0, 0] 4 [0, 0, 6, 6, 0, 0, 0, 0] 4 [0, 0, 7, 7, 0, 0, 0, 0] 4 [0, 0, 8, 8, 0, 0, 0, 0] 4 [0, 0, 9, 9, 0, 0, 0, 0] 4 [0, 0, 10, 10, 0, 0, 0, 0] 8 [0, 2, 2, 0, 0, 0, 0, 0] 0 [0, 3, 3, 0, 0, 0, 0, 0] 0 [0, 4, 4, 0, 0, 0, 0, 0] 4 [0, 5, 5, 0, 0, 0, 0, 0] 4 [0, 6, 6, 0, 0, 0, 0, 0] 4 [0, 7, 7, 0, 0, 0, 0, 0] 4 [0, 8, 8, 0, 0, 0, 0, 0] 4 [0, 9, 9, 0, 0, 0, 0, 0] 4 [0, 10, 10, 0, 0, 0, 0, 0] 4 [0, 11, 11, 0, 0, 0, 0, 0] 4 [0, 12, 12, 0, 0, 0, 0, 0] 8 [0, 4, 4, 0, 0, 0, 0, 0] 4 [0, 6, 6, 0, 0, 0, 0, 0] 4 [0, 8, 8, 0, 0, 0, 0, 0] 4 [0, 10, 10, 0, 0, 0, 0, 0] 4 [0, 12, 12, 0, 0, 0, 0, 0] 8 [0, 6, 6, 0, 0, 0, 0, 0] 4 [0, 9, 9, 0, 0, 0, 0, 0] 4 [0, 12, 12, 0, 0, 0, 0, 0] 8 [0, 8, 8, 0, 0, 0, 0, 0] 4 [0, 12, 12, 0, 0, 0, 0, 0] 8 [0, 10, 10, 0, 0, 0, 0, 0] 4 [0, 15, 15, 0, 0, 0, 0, 0] 8 [0, 12, 12, 0, 0, 0, 0, 0] 8 [0, 14, 14, 0, 0, 0, 0, 0] 8 [0, 16, 16, 0, 0, 0, 0, 0] 8 [0, 18, 18, 0, 0, 0, 0, 0] 8 [0, 20, 20, 0, 0, 0, 0, 0] 12 [0, 22, 22, 0, 0, 0, 0, 0] 12 [2, 0, 0, 2, 0, 0, 0, 0] 0 [3, 0, 0, 3, 0, 0, 0, 0] -4 [4, 0, 0, 4, 0, 0, 0, 0] 0 [5, 0, 0, 5, 0, 0, 0, 0] 0 [6, 0, 0, 6, 0, 0, 0, 0] 0 [7, 0, 0, 7, 0, 0, 0, 0] 0 [8, 0, 0, 8, 0, 0, 0, 0] -4 [9, 0, 0, 9, 0, 0, 0, 0] -4 [10, 0, 0, 10, 0, 0, 0, 0] 0 [11, 0, 0, 11, 0, 0, 0, 0] 0 [12, 0, 0, 12, 0, 0, 0, 0] 0 [13, 0, 0, 13, 0, 0, 0, 0] -4 [14, 0, 0, 14, 0, 0, 0, 0] -4 [15, 0, 0, 15, 0, 0, 0, 0] -4 [16, 0, 0, 16, 0, 0, 0, 0] 0 [17, 0, 0, 17, 0, 0, 0, 0] 0 [18, 0, 0, 18, 0, 0, 0, 0] -4 [19, 0, 0, 19, 0, 0, 0, 0] -4 [20, 0, 0, 20, 0, 0, 0, 0] -4 [21, 0, 0, 21, 0, 0, 0, 0] -4 [22, 0, 0, 22, 0, 0, 0, 0] -8 [2, 2, 0, 0, 0, 0, 0, 0] 0 [3, 3, 0, 0, 0, 0, 0, 0] -4 [4, 4, 0, 0, 0, 0, 0, 0] 0 [5, 5, 0, 0, 0, 0, 0, 0] 0 [6, 6, 0, 0, 0, 0, 0, 0] 0 [7, 7, 0, 0, 0, 0, 0, 0] 0 [8, 8, 0, 0, 0, 0, 0, 0] -4 [9, 9, 0, 0, 0, 0, 0, 0] -4 [10, 10, 0, 0, 0, 0, 0, 0] -4 [11, 11, 0, 0, 0, 0, 0, 0] -4 [12, 12, 0, 0, 0, 0, 0, 0] 0 [13, 13, 0, 0, 0, 0, 0, 0] -4 [14, 14, 0, 0, 0, 0, 0, 0] -4 [15, 15, 0, 0, 0, 0, 0, 0] -4 [16, 16, 0, 0, 0, 0, 0, 0] -4 [17, 17, 0, 0, 0, 0, 0, 0] -4 [18, 18, 0, 0, 0, 0, 0, 0] -8 [2, 2, 2, 2, 0, 0, 0, 0] 0 [3, 3, 3, 3, 0, 0, 0, 0] -4 [4, 4, 4, 4, 0, 0, 0, 0] 4 [5, 5, 5, 5, 0, 0, 0, 0] 4 [6, 6, 6, 6, 0, 0, 0, 0] 4 [7, 7, 7, 7, 0, 0, 0, 0] 4 [8, 8, 8, 8, 0, 0, 0, 0] 0 [9, 9, 9, 9, 0, 0, 0, 0] 0 [10, 10, 10, 10, 0, 0, 0, 0] 4 [11, 11, 11, 11, 0, 0, 0, 0] 4 [12, 12, 12, 12, 0, 0, 0, 0] 8 [13, 13, 13, 13, 0, 0, 0, 0] 4 [14, 14, 14, 14, 0, 0, 0, 0] 4 [15, 15, 15, 15, 0, 0, 0, 0] 4 [16, 16, 16, 16, 0, 0, 0, 0] 8 [17, 17, 17, 17, 0, 0, 0, 0] 8 [18, 18, 18, 18, 0, 0, 0, 0] 4 [19, 19, 19, 19, 0, 0, 0, 0] 8 [20, 20, 20, 20, 0, 0, 0, 0] 8 [21, 21, 21, 21, 0, 0, 0, 0] 8 [22, 22, 22, 22, 0, 0, 0, 0] 4 [23, 23, 23, 23, 0, 0, 0, 0] 8 [24, 24, 24, 24, 0, 0, 0, 0] 8 [25, 25, 25, 25, 0, 0, 0, 0] 8 [26, 26, 26, 26, 0, 0, 0, 0] 8 [27, 27, 27, 27, 0, 0, 0, 0] 8 [28, 28, 28, 28, 0, 0, 0, 0] 8 [29, 29, 29, 29, 0, 0, 0, 0] 12 [2, 4, 4, 2, 0, 0, 0, 0] 4 [3, 6, 6, 3, 0, 0, 0, 0] 0 [4, 8, 8, 4, 0, 0, 0, 0] 4 [5, 10, 10, 5, 0, 0, 0, 0] 4 [6, 12, 12, 6, 0, 0, 0, 0] 8 [7, 14, 14, 7, 0, 0, 0, 0] 8 [8, 16, 16, 8, 0, 0, 0, 0] 4 [9, 18, 18, 9, 0, 0, 0, 0] 4 [10, 20, 20, 10, 0, 0, 0, 0] 12 [2, 6, 6, 2, 0, 0, 0, 0] 4 [3, 9, 9, 3, 0, 0, 0, 0] 0 [4, 12, 12, 4, 0, 0, 0, 0] 8 [5, 15, 15, 5, 0, 0, 0, 0] 8 [6, 18, 18, 6, 0, 0, 0, 0] 8 [7, 21, 21, 7, 0, 0, 0, 0] 12 [2, 8, 8, 2, 0, 0, 0, 0] 4 [3, 12, 12, 3, 0, 0, 0, 0] 4 [4, 16, 16, 4, 0, 0, 0, 0] 8 [5, 20, 20, 5, 0, 0, 0, 0] 12 [2, 10, 10, 2, 0, 0, 0, 0] 4 [3, 15, 15, 3, 0, 0, 0, 0] 4 [4, 20, 20, 4, 0, 0, 0, 0] 12 [2, 12, 12, 2, 0, 0, 0, 0] 8 [3, 18, 18, 3, 0, 0, 0, 0] 4 [4, 24, 24, 4, 0, 0, 0, 0] 12 [2, 14, 14, 2, 0, 0, 0, 0] 8 [3, 21, 21, 3, 0, 0, 0, 0] 8 [4, 28, 28, 4, 0, 0, 0, 0] 16 [2, 16, 16, 2, 0, 0, 0, 0] 8 [3, 24, 24, 3, 0, 0, 0, 0] 8 [4, 32, 32, 4, 0, 0, 0, 0] 16 [2, 18, 18, 2, 0, 0, 0, 0] 8 [3, 27, 27, 3, 0, 0, 0, 0] 12 [2, 20, 20, 2, 0, 0, 0, 0] 12 [2, 22, 22, 2, 0, 0, 0, 0] 12 [2, 24, 24, 2, 0, 0, 0, 0] 12 [2, 26, 26, 2, 0, 0, 0, 0] 12 [2, 28, 28, 2, 0, 0, 0, 0] 16 [2, 30, 30, 2, 0, 0, 0, 0] 16 [2, 32, 32, 2, 0, 0, 0, 0] 16 [2, 34, 34, 2, 0, 0, 0, 0] 20 [2, 36, 36, 2, 0, 0, 0, 0] 20 [4, 4, 0, 0, 0, 0, 0, 0] 0 [6, 6, 0, 0, 0, 0, 0, 0] 0 [8, 8, 0, 0, 0, 0, 0, 0] -4 [10, 10, 0, 0, 0, 0, 0, 0] -4 [12, 12, 0, 0, 0, 0, 0, 0] 0 [14, 14, 0, 0, 0, 0, 0, 0] -4 [16, 16, 0, 0, 0, 0, 0, 0] -4 [18, 18, 0, 0, 0, 0, 0, 0] -8 [4, 4, 2, 2, 0, 0, 0, 0] 0 [6, 6, 3, 3, 0, 0, 0, 0] 0 [8, 8, 4, 4, 0, 0, 0, 0] 0 [10, 10, 5, 5, 0, 0, 0, 0] 0 [12, 12, 6, 6, 0, 0, 0, 0] 4 [14, 14, 7, 7, 0, 0, 0, 0] 0 [16, 16, 8, 8, 0, 0, 0, 0] 0 [18, 18, 9, 9, 0, 0, 0, 0] -4 [20, 20, 10, 10, 0, 0, 0, 0] 4 [22, 22, 11, 11, 0, 0, 0, 0] 0 [24, 24, 12, 12, 0, 0, 0, 0] 0 [26, 26, 13, 13, 0, 0, 0, 0] 0 [28, 28, 14, 14, 0, 0, 0, 0] 0 [30, 30, 15, 15, 0, 0, 0, 0] 0 [32, 32, 16, 16, 0, 0, 0, 0] 0 [34, 34, 17, 17, 0, 0, 0, 0] 4 [36, 36, 18, 18, 0, 0, 0, 0] 4 [38, 38, 19, 19, 0, 0, 0, 0] 0 [40, 40, 20, 20, 0, 0, 0, 0] 0 [42, 42, 21, 21, 0, 0, 0, 0] 0 [44, 44, 22, 22, 0, 0, 0, 0] 0 [46, 46, 23, 23, 0, 0, 0, 0] 4 [48, 48, 24, 24, 0, 0, 0, 0] 8 [50, 50, 25, 25, 0, 0, 0, 0] 4 [52, 52, 26, 26, 0, 0, 0, 0] 8 [54, 54, 27, 27, 0, 0, 0, 0] 8 [56, 56, 28, 28, 0, 0, 0, 0] 8 [58, 58, 29, 29, 0, 0, 0, 0] 12 [4, 48, 36, 2, 0, 0, 0, 0] 20 [4, 66, 32, 2, 0, 0, 0, 0] 20 [4, 74, 22, 2, 0, 0, 0, 0] 20 [4, 76, 28, 2, 0, 0, 0, 0] 28 [6, 6, 0, 0, 0, 0, 0, 0] 0 [9, 9, 0, 0, 0, 0, 0, 0] -4 [12, 12, 0, 0, 0, 0, 0, 0] 0 [15, 15, 0, 0, 0, 0, 0, 0] -4 [18, 18, 0, 0, 0, 0, 0, 0] -8 [6, 6, 2, 2, 0, 0, 0, 0] 0 [9, 9, 3, 3, 0, 0, 0, 0] -4 [12, 12, 4, 4, 0, 0, 0, 0] 4 [15, 15, 5, 5, 0, 0, 0, 0] 0 [18, 18, 6, 6, 0, 0, 0, 0] -4 [21, 21, 7, 7, 0, 0, 0, 0] 0 [24, 24, 8, 8, 0, 0, 0, 0] -4 [27, 27, 9, 9, 0, 0, 0, 0] -4 [30, 30, 10, 10, 0, 0, 0, 0] 0 [33, 33, 11, 11, 0, 0, 0, 0] -4 [36, 36, 12, 12, 0, 0, 0, 0] 0 [39, 39, 13, 13, 0, 0, 0, 0] -4 [42, 42, 14, 14, 0, 0, 0, 0] -4 [45, 45, 15, 15, 0, 0, 0, 0] -4 [48, 48, 16, 16, 0, 0, 0, 0] 4 [51, 51, 17, 17, 0, 0, 0, 0] 0 [54, 54, 18, 18, 0, 0, 0, 0] 4 [57, 57, 19, 19, 0, 0, 0, 0] 4 [60, 60, 20, 20, 0, 0, 0, 0] 4 [63, 63, 21, 21, 0, 0, 0, 0] 8 [66, 66, 22, 22, 0, 0, 0, 0] 8 [69, 69, 23, 23, 0, 0, 0, 0] 12 [6, 20, 6, 2, 0, 0, 0, 0] -4 [9, 30, 9, 3, 0, 0, 0, 0] -4 [12, 40, 12, 4, 0, 0, 0, 0] 8 [15, 50, 15, 5, 0, 0, 0, 0] 8 [18, 60, 18, 6, 0, 0, 0, 0] 12 [6, 22, 28, 2, 0, 0, 0, 0] 20 [6, 44, 24, 2, 0, 0, 0, 0] 16 [6, 56, 38, 2, 0, 0, 0, 0] 24 [6, 58, 26, 2, 0, 0, 0, 0] 16 [6, 62, 34, 2, 0, 0, 0, 0] 24 [8, 8, 0, 0, 0, 0, 0, 0] -4 [12, 12, 0, 0, 0, 0, 0, 0] 0 [16, 16, 0, 0, 0, 0, 0, 0] -4 [20, 20, 0, 0, 0, 0, 0, 0] -4 [24, 24, 0, 0, 0, 0, 0, 0] -8 [8, 8, 2, 2, 0, 0, 0, 0] -4 [12, 12, 3, 3, 0, 0, 0, 0] 0 [16, 16, 4, 4, 0, 0, 0, 0] 0 [20, 20, 5, 5, 0, 0, 0, 0] 0 [24, 24, 6, 6, 0, 0, 0, 0] -4 [28, 28, 7, 7, 0, 0, 0, 0] -4 [32, 32, 8, 8, 0, 0, 0, 0] -8 [36, 36, 9, 9, 0, 0, 0, 0] -4 [40, 40, 10, 10, 0, 0, 0, 0] -4 [44, 44, 11, 11, 0, 0, 0, 0] -4 [48, 48, 12, 12, 0, 0, 0, 0] 0 [52, 52, 13, 13, 0, 0, 0, 0] 0 [56, 56, 14, 14, 0, 0, 0, 0] 0 [60, 60, 15, 15, 0, 0, 0, 0] 0 [64, 64, 16, 16, 0, 0, 0, 0] 8 [68, 68, 17, 17, 0, 0, 0, 0] 8 [72, 72, 18, 18, 0, 0, 0, 0] 8 [76, 76, 19, 19, 0, 0, 0, 0] 12 [8, 16, 14, 2, 0, 0, 0, 0] 8 [12, 24, 21, 3, 0, 0, 0, 0] 16 [8, 34, 10, 2, 0, 0, 0, 0] 0 [12, 51, 15, 3, 0, 0, 0, 0] 8 [16, 68, 20, 4, 0, 0, 0, 0] 24 [8, 50, 38, 2, 0, 0, 0, 0] 20 [8, 72, 12, 2, 0, 0, 0, 0] 8 [12, 108, 18, 3, 0, 0, 0, 0] 112 [10, 10, 0, 0, 0, 0, 0, 0] -4 [15, 15, 0, 0, 0, 0, 0, 0] -4 [20, 20, 0, 0, 0, 0, 0, 0] -4 [25, 25, 0, 0, 0, 0, 0, 0] -8 [10, 10, 2, 2, 0, 0, 0, 0] -4 [15, 15, 3, 3, 0, 0, 0, 0] -4 [20, 20, 4, 4, 0, 0, 0, 0] 0 [25, 25, 5, 5, 0, 0, 0, 0] -4 [30, 30, 6, 6, 0, 0, 0, 0] -4 [35, 35, 7, 7, 0, 0, 0, 0] -4 [40, 40, 8, 8, 0, 0, 0, 0] -8 [45, 45, 9, 9, 0, 0, 0, 0] -8 [50, 50, 10, 10, 0, 0, 0, 0] -4 [55, 55, 11, 11, 0, 0, 0, 0] 0 [60, 60, 12, 12, 0, 0, 0, 0] 0 [65, 65, 13, 13, 0, 0, 0, 0] 0 [70, 70, 14, 14, 0, 0, 0, 0] 4 [75, 75, 15, 15, 0, 0, 0, 0] 4 [80, 80, 16, 16, 0, 0, 0, 0] 8 [85, 85, 17, 17, 0, 0, 0, 0] 12 [10, 14, 10, 2, 0, 0, 0, 0] 8 [15, 21, 15, 3, 0, 0, 0, 0] 12 [10, 34, 8, 2, 0, 0, 0, 0] 0 [15, 51, 12, 3, 0, 0, 0, 0] 4 [20, 68, 16, 4, 0, 0, 0, 0] 20 [10, 46, 32, 2, 0, 0, 0, 0] 24 [10, 74, 20, 2, 0, 0, 0, 0] 24 [10, 78, 26, 2, 0, 0, 0, 0] 36 [12, 12, 0, 0, 0, 0, 0, 0] 0 [18, 18, 0, 0, 0, 0, 0, 0] -8 [12, 12, 2, 2, 0, 0, 0, 0] 0 [18, 18, 3, 3, 0, 0, 0, 0] -8 [24, 24, 4, 4, 0, 0, 0, 0] -4 [30, 30, 5, 5, 0, 0, 0, 0] -4 [36, 36, 6, 6, 0, 0, 0, 0] -4 [42, 42, 7, 7, 0, 0, 0, 0] -8 [48, 48, 8, 8, 0, 0, 0, 0] -4 [54, 54, 9, 9, 0, 0, 0, 0] -4 [60, 60, 10, 10, 0, 0, 0, 0] 0 [66, 66, 11, 11, 0, 0, 0, 0] 4 [72, 72, 12, 12, 0, 0, 0, 0] 4 [78, 78, 13, 13, 0, 0, 0, 0] 8 [84, 84, 14, 14, 0, 0, 0, 0] 8 [90, 90, 15, 15, 0, 0, 0, 0] 8 [96, 96, 16, 16, 0, 0, 0, 0] 8 [102, 102, 17, 17, 0, 0, 0, 0] 8 [108, 108, 18, 18, 0, 0, 0, 0] 4 [114, 114, 19, 19, 0, 0, 0, 0] 4 [120, 120, 20, 20, 0, 0, 0, 0] 0 [126, 126, 21, 21, 0, 0, 0, 0] 0 [132, 132, 22, 22, 0, 0, 0, 0] 4 [138, 138, 23, 23, 0, 0, 0, 0] 8 [144, 144, 24, 24, 0, 0, 0, 0] 8 [150, 150, 25, 25, 0, 0, 0, 0] 12 [12, 54, 28, 2, 0, 0, 0, 0] 24 [12, 58, 30, 2, 0, 0, 0, 0] 24 [12, 72, 8, 2, 0, 0, 0, 0] 8 [18, 108, 12, 3, 0, 0, 0, 0] 104 [12, 76, 18, 2, 0, 0, 0, 0] 28 [14, 14, 0, 0, 0, 0, 0, 0] -4 [21, 21, 0, 0, 0, 0, 0, 0] -4 [28, 28, 0, 0, 0, 0, 0, 0] -8 [14, 14, 2, 2, 0, 0, 0, 0] -4 [21, 21, 3, 3, 0, 0, 0, 0] -4 [28, 28, 4, 4, 0, 0, 0, 0] -4 [35, 35, 5, 5, 0, 0, 0, 0] -4 [42, 42, 6, 6, 0, 0, 0, 0] -8 [49, 49, 7, 7, 0, 0, 0, 0] -4 [56, 56, 8, 8, 0, 0, 0, 0] -4 [63, 63, 9, 9, 0, 0, 0, 0] 0 [70, 70, 10, 10, 0, 0, 0, 0] 4 [77, 77, 11, 11, 0, 0, 0, 0] 8 [84, 84, 12, 12, 0, 0, 0, 0] 8 [91, 91, 13, 13, 0, 0, 0, 0] 4 [98, 98, 14, 14, 0, 0, 0, 0] 4 [105, 105, 15, 15, 0, 0, 0, 0] 0 [112, 112, 16, 16, 0, 0, 0, 0] 4 [119, 119, 17, 17, 0, 0, 0, 0] 4 [126, 126, 18, 18, 0, 0, 0, 0] 0 [133, 133, 19, 19, 0, 0, 0, 0] 0 [140, 140, 20, 20, 0, 0, 0, 0] 4 [147, 147, 21, 21, 0, 0, 0, 0] 8 [154, 154, 22, 22, 0, 0, 0, 0] 12 [14, 16, 8, 2, 0, 0, 0, 0] 4 [21, 24, 12, 3, 0, 0, 0, 0] 8 [28, 32, 16, 4, 0, 0, 0, 0] 12 [14, 38, 16, 2, 0, 0, 0, 0] 12 [14, 42, 24, 2, 0, 0, 0, 0] 20 [14, 48, 28, 2, 0, 0, 0, 0] 24 [14, 54, 20, 2, 0, 0, 0, 0] 16 [14, 72, 26, 2, 0, 0, 0, 0] 28 [16, 16, 0, 0, 0, 0, 0, 0] -4 [24, 24, 0, 0, 0, 0, 0, 0] -8 [16, 16, 2, 2, 0, 0, 0, 0] -4 [24, 24, 3, 3, 0, 0, 0, 0] -8 [32, 32, 4, 4, 0, 0, 0, 0] -8 [40, 40, 5, 5, 0, 0, 0, 0] -8 [48, 48, 6, 6, 0, 0, 0, 0] -4 [56, 56, 7, 7, 0, 0, 0, 0] -4 [64, 64, 8, 8, 0, 0, 0, 0] 0 [72, 72, 9, 9, 0, 0, 0, 0] 0 [80, 80, 10, 10, 0, 0, 0, 0] 4 [88, 88, 11, 11, 0, 0, 0, 0] 8 [96, 96, 12, 12, 0, 0, 0, 0] 4 [104, 104, 13, 13, 0, 0, 0, 0] 4 [112, 112, 14, 14, 0, 0, 0, 0] 0 [120, 120, 15, 15, 0, 0, 0, 0] -4 [128, 128, 16, 16, 0, 0, 0, 0] 0 [136, 136, 17, 17, 0, 0, 0, 0] 4 [144, 144, 18, 18, 0, 0, 0, 0] 4 [152, 152, 19, 19, 0, 0, 0, 0] 8 [160, 160, 20, 20, 0, 0, 0, 0] 12 [16, 24, 18, 2, 0, 0, 0, 0] 16 [16, 38, 14, 2, 0, 0, 0, 0] 12 [16, 50, 16, 2, 0, 0, 0, 0] 12 [16, 60, 32, 2, 0, 0, 0, 0] 28 [16, 66, 28, 2, 0, 0, 0, 0] 28 [16, 74, 24, 2, 0, 0, 0, 0] 32 [18, 2, 4, 2, 0, 0, 0, 0] 12 [18, 18, 0, 0, 0, 0, 0, 0] -8 [18, 18, 2, 2, 0, 0, 0, 0] -8 [27, 27, 3, 3, 0, 0, 0, 0] -8 [36, 36, 4, 4, 0, 0, 0, 0] -4 [45, 45, 5, 5, 0, 0, 0, 0] -8 [54, 54, 6, 6, 0, 0, 0, 0] -4 [63, 63, 7, 7, 0, 0, 0, 0] 0 [72, 72, 8, 8, 0, 0, 0, 0] 0 [81, 81, 9, 9, 0, 0, 0, 0] 4 [90, 90, 10, 10, 0, 0, 0, 0] 8 [99, 99, 11, 11, 0, 0, 0, 0] 4 [108, 108, 12, 12, 0, 0, 0, 0] 0 [117, 117, 13, 13, 0, 0, 0, 0] 0 [126, 126, 14, 14, 0, 0, 0, 0] -4 [135, 135, 15, 15, 0, 0, 0, 0] 0 [144, 144, 16, 16, 0, 0, 0, 0] 4 [153, 153, 17, 17, 0, 0, 0, 0] 8 [162, 162, 18, 18, 0, 0, 0, 0] 12 [18, 24, 16, 2, 0, 0, 0, 0] 12 [18, 48, 18, 2, 0, 0, 0, 0] 16 [18, 76, 12, 2, 0, 0, 0, 0] 20 [18, 78, 28, 2, 0, 0, 0, 0] 40 [20, 10, 6, 2, 0, 0, 0, 0] 8 [30, 15, 9, 3, 0, 0, 0, 0] 8 [40, 20, 12, 4, 0, 0, 0, 0] 8 [50, 25, 15, 5, 0, 0, 0, 0] 8 [60, 30, 18, 6, 0, 0, 0, 0] 12 [20, 20, 0, 0, 0, 0, 0, 0] -4 [30, 30, 0, 0, 0, 0, 0, 0] -8 [20, 20, 2, 2, 0, 0, 0, 0] -4 [30, 30, 3, 3, 0, 0, 0, 0] -8 [40, 40, 4, 4, 0, 0, 0, 0] -8 [50, 50, 5, 5, 0, 0, 0, 0] -8 [60, 60, 6, 6, 0, 0, 0, 0] -4 [70, 70, 7, 7, 0, 0, 0, 0] 0 [80, 80, 8, 8, 0, 0, 0, 0] 0 [90, 90, 9, 9, 0, 0, 0, 0] 4 [100, 100, 10, 10, 0, 0, 0, 0] 4 [110, 110, 11, 11, 0, 0, 0, 0] 0 [120, 120, 12, 12, 0, 0, 0, 0] -4 [130, 130, 13, 13, 0, 0, 0, 0] 0 [140, 140, 14, 14, 0, 0, 0, 0] 0 [150, 150, 15, 15, 0, 0, 0, 0] 4 [160, 160, 16, 16, 0, 0, 0, 0] 12 [20, 54, 14, 2, 0, 0, 0, 0] 12 [20, 68, 24, 2, 0, 0, 0, 0] 28 [20, 74, 10, 2, 0, 0, 0, 0] 16 [20, 76, 20, 2, 0, 0, 0, 0] 32 [22, 22, 0, 0, 0, 0, 0, 0] -8 [22, 22, 2, 2, 0, 0, 0, 0] -8 [33, 33, 3, 3, 0, 0, 0, 0] -12 [22, 26, 14, 2, 0, 0, 0, 0] 8 [33, 39, 21, 3, 0, 0, 0, 0] 16 [22, 36, 22, 2, 0, 0, 0, 0] 20 [22, 74, 4, 2, 0, 0, 0, 0] 4 [33, 111, 6, 3, 0, 0, 0, 0] 108 [24, 16, 4, 2, 0, 0, 0, 0] 0 [36, 24, 6, 3, 0, 0, 0, 0] -4 [48, 32, 8, 4, 0, 0, 0, 0] 0 [60, 40, 10, 5, 0, 0, 0, 0] 4 [72, 48, 12, 6, 0, 0, 0, 0] 4 [84, 56, 14, 7, 0, 0, 0, 0] -8 [96, 64, 16, 8, 0, 0, 0, 0] -44 [24, 24, 0, 0, 0, 0, 0, 0] -8 [24, 24, 2, 2, 0, 0, 0, 0] -8 [36, 36, 3, 3, 0, 0, 0, 0] -8 [48, 48, 4, 4, 0, 0, 0, 0] -4 [60, 60, 5, 5, 0, 0, 0, 0] -4 [72, 72, 6, 6, 0, 0, 0, 0] 0 [84, 84, 7, 7, 0, 0, 0, 0] 4 [96, 96, 8, 8, 0, 0, 0, 0] 0 [108, 108, 9, 9, 0, 0, 0, 0] -4 [120, 120, 10, 10, 0, 0, 0, 0] -4 [132, 132, 11, 11, 0, 0, 0, 0] 0 [144, 144, 12, 12, 0, 0, 0, 0] 0 [156, 156, 13, 13, 0, 0, 0, 0] 4 [168, 168, 14, 14, 0, 0, 0, 0] 8 [180, 180, 15, 15, 0, 0, 0, 0] 4 [192, 192, 16, 16, 0, 0, 0, 0] 4 [204, 204, 17, 17, 0, 0, 0, 0] 0 [216, 216, 18, 18, 0, 0, 0, 0] 0 [228, 228, 19, 19, 0, 0, 0, 0] 8 [240, 240, 20, 20, 0, 0, 0, 0] 8 [252, 252, 21, 21, 0, 0, 0, 0] 8 [264, 264, 22, 22, 0, 0, 0, 0] 8 [276, 276, 23, 23, 0, 0, 0, 0] 8 [288, 288, 24, 24, 0, 0, 0, 0] 4 [300, 300, 25, 25, 0, 0, 0, 0] 4 [312, 312, 26, 26, 0, 0, 0, 0] 12 [24, 42, 14, 2, 0, 0, 0, 0] 12 [24, 44, 6, 2, 0, 0, 0, 0] 0 [36, 66, 9, 3, 0, 0, 0, 0] 4 [48, 88, 12, 4, 0, 0, 0, 0] 44 [24, 68, 20, 2, 0, 0, 0, 0] 24 [24, 74, 16, 2, 0, 0, 0, 0] 24 [26, 22, 12, 2, 0, 0, 0, 0] 12 [26, 26, 0, 0, 0, 0, 0, 0] -8 [26, 26, 2, 2, 0, 0, 0, 0] -8 [39, 39, 3, 3, 0, 0, 0, 0] -12 [26, 34, 22, 2, 0, 0, 0, 0] 24 [26, 58, 6, 2, 0, 0, 0, 0] 0 [39, 87, 9, 3, 0, 0, 0, 0] 32 [26, 70, 24, 2, 0, 0, 0, 0] 32 [26, 72, 14, 2, 0, 0, 0, 0] 20 [26, 78, 10, 2, 0, 0, 0, 0] 24 [28, 22, 6, 2, 0, 0, 0, 0] 0 [42, 33, 9, 3, 0, 0, 0, 0] -4 [56, 44, 12, 4, 0, 0, 0, 0] 8 [70, 55, 15, 5, 0, 0, 0, 0] 8 [84, 66, 18, 6, 0, 0, 0, 0] 0 [98, 77, 21, 7, 0, 0, 0, 0] -32 [28, 28, 0, 0, 0, 0, 0, 0] -8 [28, 28, 2, 2, 0, 0, 0, 0] -8 [42, 42, 3, 3, 0, 0, 0, 0] -12 [28, 48, 14, 2, 0, 0, 0, 0] 12 [28, 54, 12, 2, 0, 0, 0, 0] 8 [42, 81, 18, 3, 0, 0, 0, 0] 28 [28, 66, 16, 2, 0, 0, 0, 0] 16 [28, 76, 4, 2, 0, 0, 0, 0] 8 [42, 114, 6, 3, 0, 0, 0, 0] 116 [28, 78, 18, 2, 0, 0, 0, 0] 32 [30, 30, 0, 0, 0, 0, 0, 0] -8 [30, 30, 2, 2, 0, 0, 0, 0] -8 [45, 45, 3, 3, 0, 0, 0, 0] -12 [30, 36, 20, 2, 0, 0, 0, 0] 20 [30, 58, 12, 2, 0, 0, 0, 0] 8 [45, 87, 18, 3, 0, 0, 0, 0] 44 [32, 32, 0, 0, 0, 0, 0, 0] -12 [32, 32, 2, 2, 0, 0, 0, 0] -12 [32, 46, 10, 2, 0, 0, 0, 0] 4 [48, 69, 15, 3, 0, 0, 0, 0] 16 [32, 50, 22, 2, 0, 0, 0, 0] 16 [32, 60, 16, 2, 0, 0, 0, 0] 12 [32, 66, 4, 2, 0, 0, 0, 0] -4 [48, 99, 6, 3, 0, 0, 0, 0] 64 [32, 80, 20, 2, 0, 0, 0, 0] 32 [34, 34, 0, 0, 0, 0, 0, 0] -8 [34, 34, 2, 2, 0, 0, 0, 0] -8 [51, 51, 3, 3, 0, 0, 0, 0] -12 [34, 36, 12, 2, 0, 0, 0, 0] 8 [51, 54, 18, 3, 0, 0, 0, 0] 12 [34, 56, 18, 2, 0, 0, 0, 0] 16 [34, 62, 6, 2, 0, 0, 0, 0] 0 [51, 93, 9, 3, 0, 0, 0, 0] 48 [36, 32, 8, 2, 0, 0, 0, 0] 0 [54, 48, 12, 3, 0, 0, 0, 0] 8 [72, 64, 16, 4, 0, 0, 0, 0] 16 [36, 34, 14, 2, 0, 0, 0, 0] 12 [36, 36, 2, 2, 0, 0, 0, 0] -8 [54, 54, 3, 3, 0, 0, 0, 0] -8 [72, 72, 4, 4, 0, 0, 0, 0] 0 [90, 90, 5, 5, 0, 0, 0, 0] 4 [108, 108, 6, 6, 0, 0, 0, 0] -4 [126, 126, 7, 7, 0, 0, 0, 0] -8 [144, 144, 8, 8, 0, 0, 0, 0] -4 [162, 162, 9, 9, 0, 0, 0, 0] 4 [180, 180, 10, 10, 0, 0, 0, 0] 4 [198, 198, 11, 11, 0, 0, 0, 0] -4 [216, 216, 12, 12, 0, 0, 0, 0] -4 [234, 234, 13, 13, 0, 0, 0, 0] 4 [252, 252, 14, 14, 0, 0, 0, 0] 4 [270, 270, 15, 15, 0, 0, 0, 0] 4 [288, 288, 16, 16, 0, 0, 0, 0] 0 [306, 306, 17, 17, 0, 0, 0, 0] 4 [324, 324, 18, 18, 0, 0, 0, 0] 8 [342, 342, 19, 19, 0, 0, 0, 0] 8 [360, 360, 20, 20, 0, 0, 0, 0] 4 [378, 378, 21, 21, 0, 0, 0, 0] 0 [396, 396, 22, 22, 0, 0, 0, 0] 8 [414, 414, 23, 23, 0, 0, 0, 0] 16 [36, 48, 4, 2, 0, 0, 0, 0] -4 [54, 72, 6, 3, 0, 0, 0, 0] 4 [72, 96, 8, 4, 0, 0, 0, 0] 60 [36, 78, 12, 2, 0, 0, 0, 0] 24 [38, 38, 0, 0, 0, 0, 0, 0] -12 [38, 38, 2, 2, 0, 0, 0, 0] -12 [38, 42, 18, 2, 0, 0, 0, 0] 12 [38, 50, 8, 2, 0, 0, 0, 0] -4 [57, 75, 12, 3, 0, 0, 0, 0] 20 [38, 56, 6, 2, 0, 0, 0, 0] -4 [57, 84, 9, 3, 0, 0, 0, 0] 28 [38, 68, 14, 2, 0, 0, 0, 0] 12 [40, 40, 0, 0, 0, 0, 0, 0] -12 [40, 40, 2, 2, 0, 0, 0, 0] -12 [40, 54, 18, 2, 0, 0, 0, 0] 12 [40, 62, 16, 2, 0, 0, 0, 0] 12 [40, 76, 14, 2, 0, 0, 0, 0] 20 [42, 38, 4, 2, 0, 0, 0, 0] -8 [63, 57, 6, 3, 0, 0, 0, 0] -4 [84, 76, 8, 4, 0, 0, 0, 0] 0 [105, 95, 10, 5, 0, 0, 0, 0] -28 [42, 42, 0, 0, 0, 0, 0, 0] -12 [42, 42, 2, 2, 0, 0, 0, 0] -12 [42, 74, 8, 2, 0, 0, 0, 0] 8 [63, 111, 12, 3, 0, 0, 0, 0] 120 [42, 80, 18, 2, 0, 0, 0, 0] 28 [44, 44, 2, 2, 0, 0, 0, 0] -12 [44, 66, 10, 2, 0, 0, 0, 0] 4 [66, 99, 15, 3, 0, 0, 0, 0] 80 [44, 68, 6, 2, 0, 0, 0, 0] 0 [66, 102, 9, 3, 0, 0, 0, 0] 84 [44, 80, 22, 2, 0, 0, 0, 0] 32 [44, 82, 12, 2, 0, 0, 0, 0] 24 [46, 46, 2, 2, 0, 0, 0, 0] -12 [46, 58, 16, 2, 0, 0, 0, 0] 8 [69, 87, 24, 3, 0, 0, 0, 0] 52 [46, 64, 18, 2, 0, 0, 0, 0] 16 [48, 18, 4, 2, 0, 0, 0, 0] -4 [72, 27, 6, 3, 0, 0, 0, 0] -4 [96, 36, 8, 4, 0, 0, 0, 0] -52 [48, 26, 6, 2, 0, 0, 0, 0] -4 [72, 39, 9, 3, 0, 0, 0, 0] 0 [96, 52, 12, 4, 0, 0, 0, 0] -48 [48, 28, 12, 2, 0, 0, 0, 0] 8 [72, 42, 18, 3, 0, 0, 0, 0] 12 [48, 36, 18, 2, 0, 0, 0, 0] 16 [48, 48, 2, 2, 0, 0, 0, 0] -8 [72, 72, 3, 3, 0, 0, 0, 0] -4 [96, 96, 4, 4, 0, 0, 0, 0] 0 [120, 120, 5, 5, 0, 0, 0, 0] -8 [144, 144, 6, 6, 0, 0, 0, 0] -4 [168, 168, 7, 7, 0, 0, 0, 0] 4 [192, 192, 8, 8, 0, 0, 0, 0] -4 [216, 216, 9, 9, 0, 0, 0, 0] -8 [240, 240, 10, 10, 0, 0, 0, 0] 4 [264, 264, 11, 11, 0, 0, 0, 0] 4 [288, 288, 12, 12, 0, 0, 0, 0] -4 [312, 312, 13, 13, 0, 0, 0, 0] 4 [336, 336, 14, 14, 0, 0, 0, 0] 8 [360, 360, 15, 15, 0, 0, 0, 0] 0 [384, 384, 16, 16, 0, 0, 0, 0] 4 [408, 408, 17, 17, 0, 0, 0, 0] 12 [48, 58, 20, 2, 0, 0, 0, 0] 16 [48, 66, 8, 2, 0, 0, 0, 0] 4 [72, 99, 12, 3, 0, 0, 0, 0] 72 [50, 30, 8, 2, 0, 0, 0, 0] 0 [75, 45, 12, 3, 0, 0, 0, 0] 0 [100, 60, 16, 4, 0, 0, 0, 0] -52 [50, 40, 10, 2, 0, 0, 0, 0] 4 [75, 60, 15, 3, 0, 0, 0, 0] 4 [100, 80, 20, 4, 0, 0, 0, 0] -32 [50, 50, 2, 2, 0, 0, 0, 0] -12 [50, 74, 18, 2, 0, 0, 0, 0] 24 [52, 36, 16, 2, 0, 0, 0, 0] 16 [52, 52, 2, 2, 0, 0, 0, 0] -8 [78, 78, 3, 3, 0, 0, 0, 0] 0 [104, 104, 4, 4, 0, 0, 0, 0] 0 [130, 130, 5, 5, 0, 0, 0, 0] -4 [156, 156, 6, 6, 0, 0, 0, 0] 0 [182, 182, 7, 7, 0, 0, 0, 0] 0 [208, 208, 8, 8, 0, 0, 0, 0] -8 [234, 234, 9, 9, 0, 0, 0, 0] 0 [260, 260, 10, 10, 0, 0, 0, 0] 4 [286, 286, 11, 11, 0, 0, 0, 0] -4 [312, 312, 12, 12, 0, 0, 0, 0] 4 [338, 338, 13, 13, 0, 0, 0, 0] 8 [364, 364, 14, 14, 0, 0, 0, 0] -4 [390, 390, 15, 15, 0, 0, 0, 0] 0 [416, 416, 16, 16, 0, 0, 0, 0] 12 [52, 64, 20, 2, 0, 0, 0, 0] 24 [52, 78, 8, 2, 0, 0, 0, 0] 20 [54, 20, 12, 2, 0, 0, 0, 0] 12 [54, 28, 14, 2, 0, 0, 0, 0] 12 [54, 40, 4, 2, 0, 0, 0, 0] -4 [81, 60, 6, 3, 0, 0, 0, 0] -12 [54, 54, 2, 2, 0, 0, 0, 0] -8 [81, 81, 3, 3, 0, 0, 0, 0] 0 [108, 108, 4, 4, 0, 0, 0, 0] -4 [135, 135, 5, 5, 0, 0, 0, 0] -4 [162, 162, 6, 6, 0, 0, 0, 0] 4 [189, 189, 7, 7, 0, 0, 0, 0] -4 [216, 216, 8, 8, 0, 0, 0, 0] -8 [243, 243, 9, 9, 0, 0, 0, 0] 4 [270, 270, 10, 10, 0, 0, 0, 0] 4 [297, 297, 11, 11, 0, 0, 0, 0] 0 [324, 324, 12, 12, 0, 0, 0, 0] 4 [351, 351, 13, 13, 0, 0, 0, 0] 4 [378, 378, 14, 14, 0, 0, 0, 0] -4 [405, 405, 15, 15, 0, 0, 0, 0] 4 [432, 432, 16, 16, 0, 0, 0, 0] 8 [459, 459, 17, 17, 0, 0, 0, 0] 0 [486, 486, 18, 18, 0, 0, 0, 0] 12 [56, 24, 10, 2, 0, 0, 0, 0] 4 [84, 36, 15, 3, 0, 0, 0, 0] -4 [112, 48, 20, 4, 0, 0, 0, 0] -96 [56, 34, 4, 2, 0, 0, 0, 0] -4 [84, 51, 6, 3, 0, 0, 0, 0] -20 [56, 56, 2, 2, 0, 0, 0, 0] -8 [84, 84, 3, 3, 0, 0, 0, 0] 0 [112, 112, 4, 4, 0, 0, 0, 0] -4 [140, 140, 5, 5, 0, 0, 0, 0] -4 [168, 168, 6, 6, 0, 0, 0, 0] 4 [196, 196, 7, 7, 0, 0, 0, 0] -4 [224, 224, 8, 8, 0, 0, 0, 0] -4 [252, 252, 9, 9, 0, 0, 0, 0] 0 [280, 280, 10, 10, 0, 0, 0, 0] 0 [308, 308, 11, 11, 0, 0, 0, 0] 0 [336, 336, 12, 12, 0, 0, 0, 0] 8 [364, 364, 13, 13, 0, 0, 0, 0] -4 [392, 392, 14, 14, 0, 0, 0, 0] 0 [420, 420, 15, 15, 0, 0, 0, 0] 8 [448, 448, 16, 16, 0, 0, 0, 0] 0 [476, 476, 17, 17, 0, 0, 0, 0] 4 [504, 504, 18, 18, 0, 0, 0, 0] 12 [58, 30, 14, 2, 0, 0, 0, 0] 12 [58, 42, 8, 2, 0, 0, 0, 0] 4 [87, 63, 12, 3, 0, 0, 0, 0] -16 [58, 58, 2, 2, 0, 0, 0, 0] -8 [87, 87, 3, 3, 0, 0, 0, 0] 0 [116, 116, 4, 4, 0, 0, 0, 0] -8 [145, 145, 5, 5, 0, 0, 0, 0] 0 [174, 174, 6, 6, 0, 0, 0, 0] 0 [203, 203, 7, 7, 0, 0, 0, 0] -8 [232, 232, 8, 8, 0, 0, 0, 0] 0 [261, 261, 9, 9, 0, 0, 0, 0] 4 [290, 290, 10, 10, 0, 0, 0, 0] -4 [319, 319, 11, 11, 0, 0, 0, 0] 4 [348, 348, 12, 12, 0, 0, 0, 0] 4 [377, 377, 13, 13, 0, 0, 0, 0] -4 [406, 406, 14, 14, 0, 0, 0, 0] 4 [435, 435, 15, 15, 0, 0, 0, 0] 4 [464, 464, 16, 16, 0, 0, 0, 0] 4 [493, 493, 17, 17, 0, 0, 0, 0] 12 [58, 62, 22, 2, 0, 0, 0, 0] 24 [58, 78, 20, 2, 0, 0, 0, 0] 36 [60, 48, 6, 2, 0, 0, 0, 0] 0 [90, 72, 9, 3, 0, 0, 0, 0] -24 [60, 58, 10, 2, 0, 0, 0, 0] 4 [90, 87, 15, 3, 0, 0, 0, 0] 12 [60, 60, 2, 2, 0, 0, 0, 0] -8 [90, 90, 3, 3, 0, 0, 0, 0] 0 [120, 120, 4, 4, 0, 0, 0, 0] -8 [150, 150, 5, 5, 0, 0, 0, 0] 0 [180, 180, 6, 6, 0, 0, 0, 0] 0 [210, 210, 7, 7, 0, 0, 0, 0] -8 [240, 240, 8, 8, 0, 0, 0, 0] 0 [270, 270, 9, 9, 0, 0, 0, 0] 0 [300, 300, 10, 10, 0, 0, 0, 0] -4 [330, 330, 11, 11, 0, 0, 0, 0] 8 [360, 360, 12, 12, 0, 0, 0, 0] 0 [390, 390, 13, 13, 0, 0, 0, 0] 0 [420, 420, 14, 14, 0, 0, 0, 0] 8 [450, 450, 15, 15, 0, 0, 0, 0] 0 [480, 480, 16, 16, 0, 0, 0, 0] 4 [510, 510, 17, 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[0, 0, 0, 0, 78, 90, 28, 2] 24 [0, 0, 0, 0, 78, 92, 18, 2] 24 [0, 0, 0, 0, 78, 96, 56, 2] 36 [0, 0, 0, 0, 80, 52, 4, 2] -24 [0, 0, 0, 0, 80, 56, 6, 2] -20 [0, 0, 0, 0, 80, 58, 26, 2] 0 [0, 0, 0, 0, 120, 87, 39, 3] -52 [0, 0, 0, 0, 80, 62, 34, 2] 4 [0, 0, 0, 0, 120, 93, 51, 3] -44 [0, 0, 0, 0, 80, 68, 44, 2] 4 [0, 0, 0, 0, 120, 102, 66, 3] -28 [0, 0, 0, 0, 80, 82, 88, 2] 8 [0, 0, 0, 0, 120, 123, 132, 3] -96 [0, 0, 0, 0, 80, 88, 100, 2] 4 [0, 0, 0, 0, 120, 132, 150, 3] -140 [0, 0, 0, 0, 80, 90, 46, 2] 28 [0, 0, 0, 0, 80, 92, 76, 2] 32 [0, 0, 0, 0, 80, 98, 18, 2] 36 [0, 0, 0, 0, 82, 86, 26, 2] 20 [0, 0, 0, 0, 82, 88, 32, 2] 24 [0, 0, 0, 0, 82, 94, 46, 2] 32 [0, 0, 0, 0, 82, 102, 64, 2] 48 [0, 0, 0, 0, 84, 48, 14, 2] -16 [0, 0, 0, 0, 84, 60, 16, 2] -12 [0, 0, 0, 0, 84, 74, 22, 2] 0 [0, 0, 0, 0, 126, 111, 33, 3] -24 [0, 0, 0, 0, 84, 76, 28, 2] 4 [0, 0, 0, 0, 126, 114, 42, 3] -16 [0, 0, 0, 0, 84, 90, 92, 2] 12 [0, 0, 0, 0, 84, 94, 62, 2] 32 [0, 0, 0, 0, 84, 96, 102, 2] 8 [0, 0, 0, 0, 126, 144, 153, 3] -128 [0, 0, 0, 0, 84, 102, 46, 2] 44 [0, 0, 0, 0, 86, 30, 10, 2] -12 [0, 0, 0, 0, 86, 52, 16, 2] -16 [0, 0, 0, 0, 86, 68, 42, 2] 0 [0, 0, 0, 0, 129, 102, 63, 3] -56 [0, 0, 0, 0, 86, 72, 26, 2] 0 [0, 0, 0, 0, 129, 108, 39, 3] -44 [0, 0, 0, 0, 86, 76, 54, 2] 4 [0, 0, 0, 0, 129, 114, 81, 3] -36 [0, 0, 0, 0, 86, 80, 48, 2] 8 [0, 0, 0, 0, 129, 120, 72, 3] -16 [0, 0, 0, 0, 86, 84, 30, 2] 12 [0, 0, 0, 0, 86, 94, 38, 2] 28 [0, 0, 0, 0, 86, 98, 96, 2] 16 [0, 0, 0, 0, 86, 100, 62, 2] 40 [0, 0, 0, 0, 86, 102, 98, 2] 20 [0, 0, 0, 0, 88, 46, 12, 2] -24 [0, 0, 0, 0, 88, 66, 18, 2] -12 [0, 0, 0, 0, 88, 72, 88, 2] -12 [0, 0, 0, 0, 88, 74, 38, 2] 0 [0, 0, 0, 0, 132, 111, 57, 3] -48 [0, 0, 0, 0, 88, 82, 80, 2] 4 [0, 0, 0, 0, 132, 123, 120, 3] -92 [0, 0, 0, 0, 88, 86, 58, 2] 12 [0, 0, 0, 0, 88, 94, 90, 2] 12 [0, 0, 0, 0, 88, 96, 72, 2] 28 [0, 0, 0, 0, 88, 100, 32, 2] 36 [0, 0, 0, 0, 90, 34, 8, 2] -20 [0, 0, 0, 0, 90, 60, 6, 2] -28 [0, 0, 0, 0, 90, 74, 26, 2] 0 [0, 0, 0, 0, 135, 111, 39, 3] -56 [0, 0, 0, 0, 90, 76, 96, 2] -16 [0, 0, 0, 0, 90, 80, 40, 2] 8 [0, 0, 0, 0, 135, 120, 60, 3] -32 [0, 0, 0, 0, 90, 88, 36, 2] 16 [0, 0, 0, 0, 90, 92, 70, 2] 24 [0, 0, 0, 0, 90, 94, 88, 2] 16 [0, 0, 0, 0, 90, 98, 90, 2] 20 [0, 0, 0, 0, 92, 40, 12, 2] -24 [0, 0, 0, 0, 92, 76, 32, 2] 0 [0, 0, 0, 0, 138, 114, 48, 3] -64 [0, 0, 0, 0, 92, 82, 18, 2] 0 [0, 0, 0, 0, 138, 123, 27, 3] -40 [0, 0, 0, 0, 92, 84, 48, 2] 8 [0, 0, 0, 0, 138, 126, 72, 3] -32 [0, 0, 0, 0, 92, 90, 84, 2] 12 [0, 0, 0, 0, 92, 100, 60, 2] 36 [0, 0, 0, 0, 94, 48, 8, 2] -32 [0, 0, 0, 0, 94, 54, 26, 2] -16 [0, 0, 0, 0, 94, 56, 22, 2] -20 [0, 0, 0, 0, 94, 64, 38, 2] -12 [0, 0, 0, 0, 94, 66, 46, 2] -12 [0, 0, 0, 0, 94, 68, 18, 2] -16 [0, 0, 0, 0, 94, 72, 36, 2] -8 [0, 0, 0, 0, 141, 108, 54, 3] -88 [0, 0, 0, 0, 94, 76, 72, 2] -4 [0, 0, 0, 0, 141, 114, 108, 3] -116 [0, 0, 0, 0, 94, 78, 62, 2] 0 [0, 0, 0, 0, 141, 117, 93, 3] -80 [0, 0, 0, 0, 94, 82, 40, 2] 4 [0, 0, 0, 0, 141, 123, 60, 3] -48 [0, 0, 0, 0, 94, 90, 68, 2] 16 [0, 0, 0, 0, 96, 58, 34, 2] -16 [0, 0, 0, 0, 96, 62, 20, 2] -24 [0, 0, 0, 0, 96, 76, 90, 2] -20 [0, 0, 0, 0, 96, 80, 22, 2] -8 [0, 0, 0, 0, 144, 120, 33, 3] -68 [0, 0, 0, 0, 96, 84, 78, 2] 0 [0, 0, 0, 0, 144, 126, 117, 3] -120 [0, 0, 0, 0, 96, 86, 48, 2] 4 [0, 0, 0, 0, 144, 129, 72, 3] -44 [0, 0, 0, 0, 96, 92, 30, 2] 12 [0, 0, 0, 0, 96, 98, 86, 2] 16 [0, 0, 0, 0, 96, 102, 70, 2] 32 [0, 0, 0, 0, 98, 44, 24, 2] -24 [0, 0, 0, 0, 98, 64, 26, 2] -20 [0, 0, 0, 0, 98, 70, 48, 2] -16 [0, 0, 0, 0, 98, 72, 42, 2] -12 [0, 0, 0, 0, 98, 82, 76, 2] -4 [0, 0, 0, 0, 147, 123, 114, 3] -132 [0, 0, 0, 0, 98, 94, 36, 2] 12 [0, 0, 0, 0, 98, 96, 50, 2] 16 [0, 0, 0, 0, 98, 100, 20, 2] 16 [0, 0, 0, 0, 98, 102, 86, 2] 20 [0, 0, 0, 0, 100, 38, 10, 2] -32 [0, 0, 0, 0, 100, 40, 16, 2] -28 [0, 0, 0, 0, 100, 56, 12, 2] -36 [0, 0, 0, 0, 100, 58, 28, 2] -24 [0, 0, 0, 0, 100, 60, 14, 2] -32 [0, 0, 0, 0, 100, 78, 38, 2] -8 [0, 0, 0, 0, 150, 117, 57, 3] -104 [0, 0, 0, 0, 100, 80, 100, 2] -28 [0, 0, 0, 0, 100, 88, 80, 2] 0 [0, 0, 0, 0, 150, 132, 120, 3] -136 [0, 0, 0, 0, 100, 90, 24, 2] 4 [0, 0, 0, 0, 150, 135, 36, 3] -52 [0, 0, 0, 0, 100, 92, 42, 2] 12 [0, 0, 0, 0, 100, 94, 30, 2] 12 [0, 0, 0, 0, 102, 32, 10, 2] -32 [0, 0, 0, 0, 102, 42, 4, 2] -48 [0, 0, 0, 0, 102, 48, 12, 2] -40 [0, 0, 0, 0, 102, 62, 6, 2] -44 [0, 0, 0, 0, 102, 64, 44, 2] -24 [0, 0, 0, 0, 102, 80, 74, 2] -12 [0, 0, 0, 0, 102, 82, 54, 2] -8 [0, 0, 0, 0, 153, 123, 81, 3] -104 [0, 0, 0, 0, 102, 84, 40, 2] -4 [0, 0, 0, 0, 153, 126, 60, 3] -88 [0, 0, 0, 0, 102, 96, 84, 2] 8 [0, 0, 0, 0, 153, 144, 126, 3] -128 [0, 0, 0, 0, 102, 98, 50, 2] 16 OK
True
slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGNATURE)[0, 0, 2, 2, 0, 0, 0, 0] 2 [0, 0, 3, 3, 0, 0, 0, 0] 2 [0, 0, 4, 4, 0, 0, 0, 0] -6 [0, 0, 5, 5, 0, 0, 0, 0] -6 [0, 0, 6, 6, 0, 0, 0, 0] -6 [0, 0, 7, 7, 0, 0, 0, 0] -8 [0, 2, 2, 0, 0, 0, 0, 0] 2 [0, 3, 3, 0, 0, 0, 0, 0] 2 [0, 4, 4, 0, 0, 0, 0, 0] -6 [0, 5, 5, 0, 0, 0, 0, 0] -6 [0, 6, 6, 0, 0, 0, 0, 0] -6 [0, 7, 7, 0, 0, 0, 0, 0] -6 [0, 8, 8, 0, 0, 0, 0, 0] -8 [0, 4, 4, 0, 0, 0, 0, 0] -6 [0, 6, 6, 0, 0, 0, 0, 0] -6 [0, 8, 8, 0, 0, 0, 0, 0] -8 [0, 6, 6, 0, 0, 0, 0, 0] -6 [0, 9, 9, 0, 0, 0, 0, 0] -8 [0, 8, 8, 0, 0, 0, 0, 0] -8 [0, 10, 10, 0, 0, 0, 0, 0] -8 [0, 12, 12, 0, 0, 0, 0, 0] -10 [0, 14, 14, 0, 0, 0, 0, 0] -10 [2, 0, 0, 2, 0, 0, 0, 0] 4 [3, 0, 0, 3, 0, 0, 0, 0] 8 [2, 2, 0, 0, 0, 0, 0, 0] 4 [3, 3, 0, 0, 0, 0, 0, 0] 8 [2, 2, 2, 2, 0, 0, 0, 0] 6 [3, 3, 3, 3, 0, 0, 0, 0] 10 [2, 4, 4, 2, 0, 0, 0, 0] -10 [2, 6, 6, 2, 0, 0, 0, 0] -10 [4, 4, 0, 0, 0, 0, 0, 0] 4 [6, 6, 0, 0, 0, 0, 0, 0] -4 [8, 8, 0, 0, 0, 0, 0, 0] 8 [4, 4, 2, 2, 0, 0, 0, 0] 6 [6, 6, 3, 3, 0, 0, 0, 0] -6 [8, 8, 4, 4, 0, 0, 0, 0] -6 [10, 10, 5, 5, 0, 0, 0, 0] -6 [12, 12, 6, 6, 0, 0, 0, 0] -8 [14, 14, 7, 7, 0, 0, 0, 0] 8 [16, 16, 8, 8, 0, 0, 0, 0] 6 [18, 18, 9, 9, 0, 0, 0, 0] 10 [8, 8, 0, 0, 0, 0, 0, 0] 8 [8, 8, 2, 2, 0, 0, 0, 0] 8 [12, 12, 3, 3, 0, 0, 0, 0] -6 [16, 16, 4, 4, 0, 0, 0, 0] 8 [20, 20, 5, 5, 0, 0, 0, 0] -8 [24, 24, 6, 6, 0, 0, 0, 0] 10 [10, 10, 0, 0, 0, 0, 0, 0] 8 [10, 10, 2, 2, 0, 0, 0, 0] 8 [15, 15, 3, 3, 0, 0, 0, 0] 10 [12, 12, 0, 0, 0, 0, 0, 0] -4 [18, 18, 0, 0, 0, 0, 0, 0] 8 [12, 12, 2, 2, 0, 0, 0, 0] -6 [18, 18, 3, 3, 0, 0, 0, 0] 10 [14, 14, 0, 0, 0, 0, 0, 0] 8 [14, 14, 2, 2, 0, 0, 0, 0] 10 [16, 16, 2, 2, 0, 0, 0, 0] 10 [24, 24, 0, 0, 0, 0, 0, 0] 8 [24, 24, 2, 2, 0, 0, 0, 0] 10 [52, 58, 0, 2, 0, 0, 0, 0] 10 OK [0, 0, 0, 0, 0, 0, 2, 2] -4 [0, 0, 0, 0, 0, 0, 3, 3] -4 [0, 0, 0, 0, 0, 0, 4, 4] -4 [0, 0, 0, 0, 0, 0, 5, 5] -4 [0, 0, 0, 0, 0, 0, 6, 6] -4 [0, 0, 0, 0, 0, 0, 7, 7] 4 [0, 0, 0, 0, 0, 0, 8, 8] -4 [0, 0, 0, 0, 0, 0, 9, 9] -4 [0, 0, 0, 0, 0, 0, 10, 10] -8 [0, 0, 0, 0, 0, 2, 2, 0] -2 [0, 0, 0, 0, 0, 3, 3, 0] -2 [0, 0, 0, 0, 0, 4, 4, 0] 6 [0, 0, 0, 0, 0, 5, 5, 0] 6 [0, 0, 0, 0, 0, 6, 6, 0] 6 [0, 0, 0, 0, 0, 7, 7, 0] 6 [0, 0, 0, 0, 0, 8, 8, 0] 8 [0, 0, 0, 0, 0, 4, 4, 0] 6 [0, 0, 0, 0, 0, 6, 6, 0] 6 [0, 0, 0, 0, 0, 8, 8, 0] 8 [0, 0, 0, 0, 0, 6, 6, 0] 6 [0, 0, 0, 0, 0, 9, 9, 0] 8 [0, 0, 0, 0, 0, 8, 8, 0] 8 [0, 0, 0, 0, 0, 10, 10, 0] 8 [0, 0, 0, 0, 0, 12, 12, 0] 10 [0, 0, 0, 0, 0, 14, 14, 0] 10 [0, 0, 0, 0, 0, 46, 36, 2] 10 [0, 0, 0, 0, 2, 0, 0, 2] -4 [0, 0, 0, 0, 3, 0, 0, 3] -4 [0, 0, 0, 0, 4, 0, 0, 4] -8 [0, 0, 0, 0, 2, 2, 0, 0] -2 [0, 0, 0, 0, 3, 3, 0, 0] -2 [0, 0, 0, 0, 4, 4, 0, 0] -2 [0, 0, 0, 0, 5, 5, 0, 0] 6 [0, 0, 0, 0, 6, 6, 0, 0] 6 [0, 0, 0, 0, 7, 7, 0, 0] 6 [0, 0, 0, 0, 8, 8, 0, 0] 6 [0, 0, 0, 0, 9, 9, 0, 0] 6 [0, 0, 0, 0, 10, 10, 0, 0] 8 [0, 0, 0, 0, 2, 2, 2, 2] -6 [0, 0, 0, 0, 3, 3, 3, 3] -6 [0, 0, 0, 0, 4, 4, 4, 4] -6 [0, 0, 0, 0, 5, 5, 5, 5] 10 [0, 0, 0, 0, 2, 4, 4, 2] 10 [0, 0, 0, 0, 2, 6, 6, 2] 10 [0, 0, 0, 0, 2, 12, 12, 2] 10 [0, 0, 0, 0, 2, 14, 14, 2] 10 [0, 0, 0, 0, 2, 16, 16, 2] 12 [0, 0, 0, 0, 2, 30, 22, 0] 10 [0, 0, 0, 0, 4, 4, 0, 0] -2 [0, 0, 0, 0, 6, 6, 0, 0] 6 [0, 0, 0, 0, 8, 8, 0, 0] 6 [0, 0, 0, 0, 10, 10, 0, 0] 8 [0, 0, 0, 0, 4, 4, 2, 2] -6 [0, 0, 0, 0, 6, 6, 3, 3] 10 [0, 0, 0, 0, 6, 6, 0, 0] 6 [0, 0, 0, 0, 9, 9, 0, 0] 6 [0, 0, 0, 0, 12, 12, 0, 0] 8 [0, 0, 0, 0, 6, 6, 2, 2] 10 [0, 0, 0, 0, 8, 8, 0, 0] 6 [0, 0, 0, 0, 12, 12, 0, 0] 8 [0, 0, 0, 0, 8, 8, 2, 2] 10 [0, 0, 0, 0, 10, 10, 0, 0] 8 [0, 0, 0, 0, 12, 12, 0, 0] 8 [0, 0, 0, 0, 14, 14, 0, 0] 8 [0, 0, 0, 0, 16, 16, 0, 0] 10 [0, 0, 0, 0, 18, 18, 0, 0] 10 [0, 0, 0, 0, 22, 30, 2, 0] 10 OK
True
sigma = slice_canidate.get_sigma_as_function_of_theta()
sigma((0, 6, 6, 0, 0,0,0,0))
sigma((9, 0, 0, 9, 0,0,0,0))4
-4
_, _, sf = slice_canidate((1, 1, 0, 0, 0,0,0,0))
sf0: 0, 49/2822: -1, 1/34: 2, 61/1826: 1, 117/2822: -1, 1/22: -2, 105/1826: 1, 215/2822: -1, 3/34: 2, 283/2822: -1, 227/1826: 1, 381/2822: -1, 3/22: -2, 5/34: 2, 271/1826: 1, 449/2822: -1, 547/2822: -1, 7/34: 2, 393/1826: 1, 615/2822: -1, 5/22: -2, 437/1826: 1, 713/2822: -1, 9/34: 2, 781/2822: -1, 559/1826: 1, 879/2822: -1, 7/22: -2, 11/34: 2, 603/1826: 1, 947/2822: -1, 1045/2822: -1, 13/34: 2, 1113/2822: -1, 725/1826: 1, 9/22: -2, 769/1826: 1, 1211/2822: -1, 15/34: 2, 1279/2822: -1, 1543/2822: 1, 19/34: -2, 1611/2822: 1, 1057/1826: -1, 13/22: 2, 1101/1826: -1, 1709/2822: 1, 21/34: -2, 1777/2822: 1, 1875/2822: 1, 1223/1826: -1, 23/34: -2, 15/22: 2, 1943/2822: 1, 1267/1826: -1, 2041/2822: 1, 25/34: -2, 2109/2822: 1, 1389/1826: -1, 17/22: 2, 2207/2822: 1, 1433/1826: -1, 27/34: -2, 2275/2822: 1, 2373/2822: 1, 1555/1826: -1, 29/34: -2, 19/22: 2, 2441/2822: 1, 1599/1826: -1, 2539/2822: 1, 31/34: -2, 2607/2822: 1, 1721/1826: -1, 21/22: 2, 2705/2822: 1, 1765/1826: -1, 33/34: -2, 2773/2822: 1, 1: 0.
cs = import_sage('cable_signature')
sg = import_sage('signature')
sg.SignaturePloter.plot(sf)cs = import_sage('cable_signature')
sg = import_sage('signature')
slice_canidate.plot_sum_for_theta_vector([0,4,0,4,0,0,0,0], save_to_dir=True)T_17_83_inv_T_11_83_T_83_inv_T_13_83_T_11_103_inv_T_103_T_13_103_inv_T_17_103
[0;31m---------------------------------------------------------------------------[0m [0;31mTypeError[0m Traceback (most recent call last) [0;32m<ipython-input-22-c4fd4acceb8f>[0m in [0;36m<module>[0;34m()[0m [1;32m 2[0m [0msg[0m [0;34m=[0m [0mimport_sage[0m[0;34m([0m[0;34m'signature'[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [1;32m 3[0m [0;34m[0m[0m [0;32m----> 4[0;31m [0mslice_canidate[0m[0;34m.[0m[0mplot_sum_for_theta_vector[0m[0;34m([0m[0;34m[[0m[0mInteger[0m[0;34m([0m[0;36m0[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m4[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m0[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m4[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m0[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m0[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m0[0m[0;34m)[0m[0;34m,[0m[0mInteger[0m[0;34m([0m[0;36m0[0m[0;34m)[0m[0;34m][0m[0;34m,[0m [0msave_to_dir[0m[0;34m=[0m[0;32mTrue[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m [0;32m/Users/Kasia/signature_function/cable_signature.py[0m in [0;36mplot_sum_for_theta_vector[0;34m(self, thetas, save_to_dir)[0m [1;32m 342[0m [0;34m[0m[0m [1;32m 343[0m [0;32mfor[0m [0mtheta[0m[0;34m,[0m [0mknot[0m [0;32min[0m [0mzip[0m[0;34m([0m[0mthetas[0m[0;34m,[0m [0mself[0m[0;34m.[0m[0mknot_summands[0m[0;34m)[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m--> 344[0;31m [0mknot[0m[0;34m.[0m[0mplot_summand_for_theta[0m[0;34m([0m[0mthetas[0m[0;34m,[0m [0msave_path[0m[0;34m=[0m[0msave_path[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m[1;32m 345[0m [0;34m[0m[0m [1;32m 346[0m [0;31m# pp, sp, sf = self.signature_as_function_of_theta(*thetas)[0m[0;34m[0m[0;34m[0m[0;34m[0m[0m [0;32m/Users/Kasia/signature_function/cable_signature.py[0m in [0;36mplot_summand_for_theta[0;34m(self, theta, save_path)[0m [1;32m 195[0m [0;34m[0m[0m [1;32m 196[0m [0;32mdef[0m [0mplot_summand_for_theta[0m[0;34m([0m[0mself[0m[0;34m,[0m [0mtheta[0m[0;34m,[0m [0msave_path[0m[0;34m=[0m[0;32mNone[0m[0;34m)[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m--> 197[0;31m [0mpp[0m[0;34m,[0m [0msp[0m[0;34m,[0m [0msf[0m [0;34m=[0m [0mself[0m[0;34m.[0m[0msignature_as_function_of_theta[0m[0;34m([0m[0mtheta[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m[1;32m 198[0m [0mtitle[0m [0;34m=[0m [0mself[0m[0;34m.[0m[0mknot_description[0m [0;34m+[0m [0;34m", theta = "[0m [0;34m+[0m [0mstr[0m[0;34m([0m[0mtheta[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [1;32m 199[0m [0;32mif[0m [0msave_path[0m [0;32mis[0m [0;32mnot[0m [0;32mNone[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m/Users/Kasia/signature_function/cable_signature.py[0m in [0;36mget_summand_signture_function[0;34m(theta)[0m [1;32m 161[0m [0;34m[0m[0m [1;32m 162[0m [0;31m# theta should not be larger than k for the pattern.[0m[0;34m[0m[0;34m[0m[0;34m[0m[0m [0;32m--> 163[0;31m [0mtheta[0m [0;34m%=[0m [0;34m([0m[0m_sage_const_2[0m [0;34m*[0m [0mabs[0m[0;34m([0m[0mpatt_k[0m[0;34m)[0m [0;34m+[0m [0m_sage_const_1[0m [0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m[1;32m 164[0m [0mtheta[0m [0;34m=[0m [0mmin[0m[0;34m([0m[0mtheta[0m[0;34m,[0m [0m_sage_const_2[0m [0;34m*[0m [0mabs[0m[0;34m([0m[0mpatt_k[0m[0;34m)[0m [0;34m+[0m [0m_sage_const_1[0m [0;34m-[0m [0mtheta[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [1;32m 165[0m [0;34m[0m[0m [0;32m/Applications/SageMath-9.0.app/Contents/Resources/sage/local/lib/python3.7/site-packages/sage/rings/rational.pyx[0m in [0;36msage.rings.rational.Rational.__mod__ (build/cythonized/sage/rings/rational.c:23158)[0;34m()[0m [1;32m 2815[0m [0mcdef[0m [0mRational[0m [0mrat[0m[0;34m[0m[0;34m[0m[0m [1;32m 2816[0m [0;32mif[0m [0;32mnot[0m [0misinstance[0m[0;34m([0m[0mx[0m[0;34m,[0m [0mRational[0m[0;34m)[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m-> 2817[0;31m [0mrat[0m [0;34m=[0m [0mRational[0m[0;34m([0m[0mx[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m[1;32m 2818[0m [0;32melse[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [1;32m 2819[0m [0mrat[0m [0;34m=[0m [0mx[0m[0;34m[0m[0;34m[0m[0m [0;32m/Applications/SageMath-9.0.app/Contents/Resources/sage/local/lib/python3.7/site-packages/sage/rings/rational.pyx[0m in [0;36msage.rings.rational.Rational.__init__ (build/cythonized/sage/rings/rational.c:6392)[0;34m()[0m [1;32m 527[0m """ [1;32m 528[0m [0;32mif[0m [0mx[0m [0;32mis[0m [0;32mnot[0m [0;32mNone[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m--> 529[0;31m [0mself[0m[0;34m.[0m[0m__set_value[0m[0;34m([0m[0mx[0m[0;34m,[0m [0mbase[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m[1;32m 530[0m [0;34m[0m[0m [1;32m 531[0m [0;32mdef[0m [0m__reduce__[0m[0;34m([0m[0mself[0m[0;34m)[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m/Applications/SageMath-9.0.app/Contents/Resources/sage/local/lib/python3.7/site-packages/sage/rings/rational.pyx[0m in [0;36msage.rings.rational.Rational.__set_value (build/cythonized/sage/rings/rational.c:8515)[0;34m()[0m [1;32m 683[0m [0;34m[0m[0m [1;32m 684[0m [0;32melse[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;32m--> 685[0;31m [0;32mraise[0m [0mTypeError[0m[0;34m([0m[0;34m"unable to convert {!r} to a rational"[0m[0;34m.[0m[0mformat[0m[0;34m([0m[0mx[0m[0;34m)[0m[0;34m)[0m[0;34m[0m[0;34m[0m[0m [0m[1;32m 686[0m [0;34m[0m[0m [1;32m 687[0m [0mcdef[0m [0mvoid[0m [0mset_from_mpq[0m[0;34m([0m[0mRational[0m [0mself[0m[0;34m,[0m [0mmpq_t[0m [0mvalue[0m[0;34m)[0m[0;34m:[0m[0;34m[0m[0;34m[0m[0m [0;31mTypeError[0m: unable to convert [0, 4, 0, 4, 0, 0, 0, 0] to a rational
sf.plot()