Merge branch 'c'

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ltcptgeneral 2019-04-08 09:17:26 -05:00
commit 979c8f7068
11 changed files with 35864 additions and 260 deletions

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@ -1,15 +1,15 @@
#Titan Robotics Team 2022: Data Analysis Module
#Written by Arthur Lu & Jacob Levine
#Notes:
# Titan Robotics Team 2022: Data Analysis Module
# Written by Arthur Lu & Jacob Levine
# Notes:
# this should be imported as a python module using 'import analysis'
# this should be included in the local directory or environment variable
# this module has not been optimized for multhreaded computing
#number of easter eggs: 2
#setup:
# number of easter eggs: 2
# setup:
__version__ = "1.0.8.005"
#changelog should be viewed using print(analysis.__changelog__)
# changelog should be viewed using print(analysis.__changelog__)
__changelog__ = """changelog:
1.0.8.005:
- minor fixes
@ -101,7 +101,7 @@ __changelog__ = """changelog:
__author__ = (
"Arthur Lu <arthurlu@ttic.edu>, "
"Jacob Levine <jlevine@ttic.edu>,"
)
)
__all__ = [
'_init_device',
@ -125,12 +125,12 @@ __all__ = [
'optimize_regression',
'select_best_regression',
'basic_analysis',
#all statistics functions left out due to integration in other functions
]
# all statistics functions left out due to integration in other functions
]
#now back to your regularly scheduled programming:
# now back to your regularly scheduled programming:
#imports (now in alphabetical order! v 1.0.3.006):
# imports (now in alphabetical order! v 1.0.3.006):
from bisect import bisect_left, bisect_right
import collections
@ -149,14 +149,16 @@ import scipy
from scipy.optimize import curve_fit
from scipy import stats
from sklearn import *
#import statistics <-- statistics.py functions have been integrated into analysis.py as of v 1.0.3.002
# import statistics <-- statistics.py functions have been integrated into analysis.py as of v 1.0.3.002
import time
import torch
class error(ValueError):
pass
def _init_device (setting, arg): #initiates computation device for ANNs
def _init_device(setting, arg): # initiates computation device for ANNs
if setting == "cuda":
try:
return torch.device(setting + ":" + str(arg) if torch.cuda.is_available() else "cpu")
@ -170,6 +172,7 @@ def _init_device (setting, arg): #initiates computation device for ANNs
else:
raise error("specified device does not exist")
class c_entities:
c_names = []
@ -190,7 +193,6 @@ class c_entities:
self.c_logic = logic
return None
def append(self, n_name, n_id, n_pos, n_property, n_logic):
self.c_names.append(n_name)
self.c_ids.append(n_id)
@ -232,6 +234,7 @@ class c_entities:
def regurgitate(self):
return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_logic]
class nc_entities:
c_names = []
@ -241,7 +244,7 @@ class nc_entities:
c_effects = []
def debug(self):
print ("nc_entities (non-controlable entities) has attributes names, ids, positions, properties, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of positions, 2d array of properties, and 2d array of effects.")
print("nc_entities (non-controlable entities) has attributes names, ids, positions, properties, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of positions, 2d array of properties, and 2d array of effects.")
return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_effects]
def __init__(self, names, ids, pos, properties, effects):
@ -295,6 +298,7 @@ class nc_entities:
return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_effects]
class obstacles:
c_names = []
@ -351,6 +355,7 @@ class obstacles:
def regurgitate(self):
return[self.c_names, self.c_ids, self.c_perim, self.c_effects]
class objectives:
c_names = []
@ -408,13 +413,16 @@ class objectives:
def regurgitate(self):
return[self.c_names, self.c_ids, self.c_pos, self.c_effects]
def load_csv(filepath):
with open(filepath, newline = '') as csvfile:
with open(filepath, newline='') as csvfile:
file_array = list(csv.reader(csvfile))
csvfile.close()
return file_array
def basic_stats(data, method, arg): # data=array, mode = ['1d':1d_basic_stats, 'column':c_basic_stats, 'row':r_basic_stats], arg for mode 1 or mode 2 for column or row
# data=array, mode = ['1d':1d_basic_stats, 'column':c_basic_stats, 'row':r_basic_stats], arg for mode 1 or mode 2 for column or row
def basic_stats(data, method, arg):
if method == 'debug':
return "basic_stats requires 3 args: data, mode, arg; where data is data to be analyzed, mode is an int from 0 - 2 depending on type of analysis (by column or by row) and is only applicable to 2d arrays (for 1d arrays use mode 1), and arg is row/column number for mode 1 or mode 2; function returns: [mean, median, mode, stdev, variance]"
@ -423,7 +431,7 @@ def basic_stats(data, method, arg): # data=array, mode = ['1d':1d_basic_stats, '
data_t = []
for i in range (0, len(data), 1):
for i in range(0, len(data), 1):
data_t.append(float(data[i]))
_mean = mean(data_t)
@ -498,11 +506,15 @@ def basic_stats(data, method, arg): # data=array, mode = ['1d':1d_basic_stats, '
else:
raise error("method error")
def z_score(point, mean, stdev): #returns z score with inputs of point, mean and standard deviation of spread
score = (point - mean)/stdev
# returns z score with inputs of point, mean and standard deviation of spread
def z_score(point, mean, stdev):
score = (point - mean) / stdev
return score
def z_normalize(x, y, mode): #mode is either 'x' or 'y' or 'both' depending on the variable(s) to be normalized
# mode is either 'x' or 'y' or 'both' depending on the variable(s) to be normalized
def z_normalize(x, y, mode):
x_norm = []
y_norm = []
@ -513,7 +525,7 @@ def z_normalize(x, y, mode): #mode is either 'x' or 'y' or 'both' depending on t
if mode == 'x':
_mean, _median, _mode, _stdev, _variance = basic_stats(x, "1d", 0)
for i in range (0, len(x), 1):
for i in range(0, len(x), 1):
x_norm.append(z_score(x[i], _mean, _stdev))
return x_norm, y
@ -521,7 +533,7 @@ def z_normalize(x, y, mode): #mode is either 'x' or 'y' or 'both' depending on t
if mode == 'y':
_mean, _median, _mode, _stdev, _variance = basic_stats(y, "1d", 0)
for i in range (0, len(y), 1):
for i in range(0, len(y), 1):
y_norm.append(z_score(y[i], _mean, _stdev))
return x, y_norm
@ -529,12 +541,12 @@ def z_normalize(x, y, mode): #mode is either 'x' or 'y' or 'both' depending on t
if mode == 'both':
_mean, _median, _mode, _stdev, _variance = basic_stats(x, "1d", 0)
for i in range (0, len(x), 1):
for i in range(0, len(x), 1):
x_norm.append(z_score(x[i], _mean, _stdev))
_mean, _median, _mode, _stdev, _variance = basic_stats(y, "1d", 0)
for i in range (0, len(y), 1):
for i in range(0, len(y), 1):
y_norm.append(z_score(y[i], _mean, _stdev))
return x_norm, y_norm
@ -543,19 +555,23 @@ def z_normalize(x, y, mode): #mode is either 'x' or 'y' or 'both' depending on t
return error('method error')
def stdev_z_split(mean, stdev, delta, low_bound, high_bound): #returns n-th percentile of spread given mean, standard deviation, lower z-score, and upper z-score
# returns n-th percentile of spread given mean, standard deviation, lower z-score, and upper z-score
def stdev_z_split(mean, stdev, delta, low_bound, high_bound):
z_split = []
i = low_bound
while True:
z_split.append(float((1 / (stdev * math.sqrt(2 * math.pi))) * math.e ** (-0.5 * (((i - mean) / stdev) ** 2))))
z_split.append(float((1 / (stdev * math.sqrt(2 * math.pi))) *
math.e ** (-0.5 * (((i - mean) / stdev) ** 2))))
i = i + delta
if i > high_bound:
break
return z_split
def histo_analysis(hist_data, delta, low_bound, high_bound):
if hist_data == 'debug':
@ -565,12 +581,12 @@ def histo_analysis(hist_data, delta, low_bound, high_bound):
for i in range(0, len(hist_data), 1):
try:
derivative.append(float(hist_data[i - 1]) - float(hist_data [i]))
derivative.append(float(hist_data[i - 1]) - float(hist_data[i]))
except:
pass
derivative_sorted = sorted(derivative, key=int)
mean_derivative = basic_stats(derivative_sorted,"1d", 0)[0]
mean_derivative = basic_stats(derivative_sorted, "1d", 0)[0]
stdev_derivative = basic_stats(derivative_sorted, "1d", 0)[3]
predictions = []
@ -593,23 +609,26 @@ def histo_analysis(hist_data, delta, low_bound, high_bound):
return predictions
def poly_regression(x, y, power):
if x == "null": #if x is 'null', then x will be filled with integer points between 1 and the size of y
if x == "null": # if x is 'null', then x will be filled with integer points between 1 and the size of y
x = []
for i in range(len(y)):
print(i)
x.append(i+1)
x.append(i + 1)
reg_eq = scipy.polyfit(x, y, deg = power)
reg_eq = scipy.polyfit(x, y, deg=power)
eq_str = ""
for i in range(0, len(reg_eq), 1):
if i < len(reg_eq)- 1:
eq_str = eq_str + str(reg_eq[i]) + "*(z**" + str(len(reg_eq) - i - 1) + ")+"
if i < len(reg_eq) - 1:
eq_str = eq_str + str(reg_eq[i]) + \
"*(z**" + str(len(reg_eq) - i - 1) + ")+"
else:
eq_str = eq_str + str(reg_eq[i]) + "*(z**" + str(len(reg_eq) - i - 1) + ")"
eq_str = eq_str + str(reg_eq[i]) + \
"*(z**" + str(len(reg_eq) - i - 1) + ")"
vals = []
@ -626,18 +645,22 @@ def poly_regression(x, y, power):
return [eq_str, _rms, r2_d2]
def log_regression(x, y, base):
x_fit = []
for i in range(len(x)):
try:
x_fit.append(np.log(x[i]) / np.log(base)) #change of base for logs
# change of base for logs
x_fit.append(np.log(x[i]) / np.log(base))
except:
pass
reg_eq = np.polyfit(x_fit, y, 1) # y = reg_eq[0] * log(x, base) + reg_eq[1]
q_str = str(reg_eq[0]) + "* (np.log(z) / np.log(" + str(base) +"))+" + str(reg_eq[1])
# y = reg_eq[0] * log(x, base) + reg_eq[1]
reg_eq = np.polyfit(x_fit, y, 1)
q_str = str(reg_eq[0]) + "* (np.log(z) / np.log(" + \
str(base) + "))+" + str(reg_eq[1])
vals = []
for i in range(len(x)):
@ -653,18 +676,22 @@ def log_regression(x, y, base):
return eq_str, _rms, r2_d2
def exp_regression(x, y, base):
y_fit = []
for i in range(len(y)):
try:
y_fit.append(np.log(y[i]) / np.log(base)) #change of base for logs
# change of base for logs
y_fit.append(np.log(y[i]) / np.log(base))
except:
pass
reg_eq = np.polyfit(x, y_fit, 1, w=np.sqrt(y_fit)) # y = base ^ (reg_eq[0] * x) * base ^ (reg_eq[1])
eq_str = "(" + str(base) + "**(" + str(reg_eq[0]) + "*z))*(" + str(base) + "**(" + str(reg_eq[1]) + "))"
# y = base ^ (reg_eq[0] * x) * base ^ (reg_eq[1])
reg_eq = np.polyfit(x, y_fit, 1, w=np.sqrt(y_fit))
eq_str = "(" + str(base) + "**(" + \
str(reg_eq[0]) + "*z))*(" + str(base) + "**(" + str(reg_eq[1]) + "))"
vals = []
for i in range(len(x)):
@ -680,14 +707,16 @@ def exp_regression(x, y, base):
return eq_str, _rms, r2_d2
def tanh_regression(x, y):
def tanh (x, a, b, c, d):
def tanh(x, a, b, c, d):
return a * np.tanh(b * (x - c)) + d
reg_eq = np.float64(curve_fit(tanh, np.array(x), np.array(y))[0]).tolist()
eq_str = str(reg_eq[0]) + " * np.tanh(" + str(reg_eq[1]) + "*(z - " + str(reg_eq[2]) + ")) + " + str(reg_eq[3])
eq_str = str(reg_eq[0]) + " * np.tanh(" + str(reg_eq[1]) + \
"*(z - " + str(reg_eq[2]) + ")) + " + str(reg_eq[3])
vals = []
for i in range(len(x)):
@ -702,10 +731,12 @@ def tanh_regression(x, y):
return eq_str, _rms, r2_d2
def r_squared(predictions, targets): # assumes equal size inputs
return metrics.r2_score(np.array(targets), np.array(predictions))
def rms(predictions, targets): # assumes equal size inputs
_sum = 0
@ -713,12 +744,13 @@ def rms(predictions, targets): # assumes equal size inputs
for i in range(0, len(targets), 1):
_sum = (targets[i] - predictions[i]) ** 2
return float(math.sqrt(_sum/len(targets)))
return float(math.sqrt(_sum / len(targets)))
def calc_overfit(equation, rms_train, r2_train, x_test, y_test):
#performance overfit = performance(train) - performance(test) where performance is r^2
#error overfit = error(train) - error(test) where error is rms; biased towards smaller values
# performance overfit = performance(train) - performance(test) where performance is r^2
# error overfit = error(train) - error(test) where error is rms; biased towards smaller values
vals = []
@ -733,19 +765,22 @@ def calc_overfit(equation, rms_train, r2_train, x_test, y_test):
return r2_train - r2_test
def strip_data(data, mode):
if mode == "adam": #x is the row number, y are the data
if mode == "adam": # x is the row number, y are the data
pass
if mode == "eve": #x are the data, y is the column number
if mode == "eve": # x are the data, y is the column number
pass
else:
raise error("mode error")
def optimize_regression(x, y, _range, resolution):#_range in poly regression is the range of powers tried, and in log/exp it is the inverse of the stepsize taken from -1000 to 1000
#usage not: for demonstration purpose only, performance is shit
# _range in poly regression is the range of powers tried, and in log/exp it is the inverse of the stepsize taken from -1000 to 1000
def optimize_regression(x, y, _range, resolution):
# usage not: for demonstration purpose only, performance is shit
if type(resolution) != int:
raise error("resolution must be int")
@ -758,7 +793,7 @@ def optimize_regression(x, y, _range, resolution):#_range in poly regression is
x_test = []
y_test = []
for i in range (0, math.floor(len(x) * 0.5), 1):
for i in range(0, math.floor(len(x) * 0.5), 1):
index = random.randint(0, len(x) - 1)
x_test.append(x[index])
@ -774,7 +809,7 @@ def optimize_regression(x, y, _range, resolution):#_range in poly regression is
rmss = []
r2s = []
for i in range (0, _range + 1, 1):
for i in range(0, _range + 1, 1):
try:
x, y, z = poly_regression(x_train, y_train, i)
eqs.append(x)
@ -783,7 +818,7 @@ def optimize_regression(x, y, _range, resolution):#_range in poly regression is
except:
pass
for i in range (1, 100 * resolution + 1):
for i in range(1, 100 * resolution + 1):
try:
x, y, z = exp_regression(x_train, y_train, float(i / resolution))
eqs.append(x)
@ -792,7 +827,7 @@ def optimize_regression(x, y, _range, resolution):#_range in poly regression is
except:
pass
for i in range (1, 100 * resolution + 1):
for i in range(1, 100 * resolution + 1):
try:
x, y, z = log_regression(x_train, y_train, float(i / resolution))
eqs.append(x)
@ -810,13 +845,14 @@ def optimize_regression(x, y, _range, resolution):#_range in poly regression is
except:
pass
for i in range (0, len(eqs), 1): #marks all equations where r2 = 1 as they 95% of the time overfit the data
# marks all equations where r2 = 1 as they 95% of the time overfit the data
for i in range(0, len(eqs), 1):
if r2s[i] == 1:
eqs[i] = ""
rmss[i] = ""
r2s[i] = ""
while True: #removes all equations marked for removal
while True: # removes all equations marked for removal
try:
eqs.remove('')
rmss.remove('')
@ -826,12 +862,13 @@ def optimize_regression(x, y, _range, resolution):#_range in poly regression is
overfit = []
for i in range (0, len(eqs), 1):
for i in range(0, len(eqs), 1):
overfit.append(calc_overfit(eqs[i], rmss[i], r2s[i], x_test, y_test))
return eqs, rmss, r2s, overfit
def select_best_regression(eqs, rmss, r2s, overfit, selector):
b_eq = ""
@ -860,11 +897,14 @@ def select_best_regression(eqs, rmss, r2s, overfit, selector):
return b_eq, b_rms, b_r2, b_overfit
def p_value(x, y): #takes 2 1d arrays
def p_value(x, y): # takes 2 1d arrays
return stats.ttest_ind(x, y)[1]
def basic_analysis(data): #assumes that rows are the independent variable and columns are the dependant. also assumes that time flows from lowest column to highest column.
# assumes that rows are the independent variable and columns are the dependant. also assumes that time flows from lowest column to highest column.
def basic_analysis(data):
row = len(data)
column = []
@ -900,22 +940,25 @@ def benchmark(x, y):
return [(end_g - start_g), (end_a - start_a)]
def generate_data(filename, x, y, low, high):
file = open(filename, "w")
for i in range (0, y, 1):
for i in range(0, y, 1):
temp = ""
for j in range (0, x - 1, 1):
for j in range(0, x - 1, 1):
temp = str(random.uniform(low, high)) + "," + temp
temp = temp + str(random.uniform(low, high))
file.write(temp + "\n")
class StatisticsError(ValueError):
pass
def _sum(data, start=0):
count = 0
n, d = _exact_ratio(start)
@ -924,7 +967,7 @@ def _sum(data, start=0):
T = _coerce(int, type(start))
for typ, values in groupby(data, type):
T = _coerce(T, typ) # or raise TypeError
for n,d in map(_exact_ratio, values):
for n, d in map(_exact_ratio, values):
count += 1
partials[d] = partials_get(d, 0) + n
if None in partials:
@ -936,26 +979,35 @@ def _sum(data, start=0):
total = sum(Fraction(n, d) for d, n in sorted(partials.items()))
return (T, total, count)
def _isfinite(x):
try:
return x.is_finite() # Likely a Decimal.
except AttributeError:
return math.isfinite(x) # Coerces to float first.
def _coerce(T, S):
assert T is not bool, "initial type T is bool"
if T is S: return T
if T is S:
return T
if S is int or S is bool: return T
if T is int: return S
if S is int or S is bool:
return T
if T is int:
return S
if issubclass(S, T): return S
if issubclass(T, S): return T
if issubclass(S, T):
return S
if issubclass(T, S):
return T
if issubclass(T, int): return S
if issubclass(S, int): return T
if issubclass(T, int):
return S
if issubclass(S, int):
return T
if issubclass(T, Fraction) and issubclass(S, float):
return S
@ -965,6 +1017,7 @@ def _coerce(T, S):
msg = "don't know how to coerce %s and %s"
raise TypeError(msg % (T.__name__, S.__name__))
def _exact_ratio(x):
try:
@ -988,6 +1041,7 @@ def _exact_ratio(x):
msg = "can't convert type '{}' to numerator/denominator"
raise TypeError(msg.format(type(x).__name__))
def _convert(value, T):
if type(value) is T:
@ -1000,10 +1054,11 @@ def _convert(value, T):
return T(value)
except TypeError:
if issubclass(T, Decimal):
return T(value.numerator)/T(value.denominator)
return T(value.numerator) / T(value.denominator)
else:
raise
def _counts(data):
table = collections.Counter(iter(data)).most_common()
@ -1029,8 +1084,8 @@ def _find_lteq(a, x):
def _find_rteq(a, l, x):
i = bisect_right(a, x, lo=l)
if i != (len(a)+1) and a[i-1] == x:
return i-1
if i != (len(a) + 1) and a[i - 1] == x:
return i - 1
raise ValueError
@ -1041,6 +1096,7 @@ def _fail_neg(values, errmsg='negative value'):
raise StatisticsError(errmsg)
yield x
def mean(data):
if iter(data) is data:
@ -1050,7 +1106,8 @@ def mean(data):
raise StatisticsError('mean requires at least one data point')
T, total, count = _sum(data)
assert count == n
return _convert(total/n, T)
return _convert(total / n, T)
def median(data):
@ -1058,11 +1115,12 @@ def median(data):
n = len(data)
if n == 0:
raise StatisticsError("no median for empty data")
if n%2 == 1:
return data[n//2]
if n % 2 == 1:
return data[n // 2]
else:
i = n//2
return (data[i - 1] + data[i])/2
i = n // 2
return (data[i - 1] + data[i]) / 2
def mode(data):
@ -1076,18 +1134,20 @@ def mode(data):
else:
raise StatisticsError('no mode for empty data')
def _ss(data, c=None):
if c is None:
c = mean(data)
T, total, count = _sum((x-c)**2 for x in data)
T, total, count = _sum((x - c)**2 for x in data)
U, total2, count2 = _sum((x-c) for x in data)
U, total2, count2 = _sum((x - c) for x in data)
assert T == U and count == count2
total -= total2**2/len(data)
total -= total2**2 / len(data)
assert not total < 0, 'negative sum of square deviations: %f' % total
return (T, total)
def variance(data, xbar=None):
if iter(data) is data:
@ -1096,7 +1156,8 @@ def variance(data, xbar=None):
if n < 2:
raise StatisticsError('variance requires at least two data points')
T, ss = _ss(data, xbar)
return _convert(ss/(n-1), T)
return _convert(ss / (n - 1), T)
def stdev(data, xbar=None):

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@ -0,0 +1,2 @@
python setup.py build_ext --inplace
pause

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@ -0,0 +1,5 @@
from distutils.core import setup
from Cython.Build import cythonize
setup(name='analysis',
ext_modules=cythonize("analysis.py"))

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@ -1,36 +1,36 @@
23,57,61,28,62,31,58,42
35,58,61,39,51,51,42,31,33,70
14,6,9,54,48,36,59,46,30,17,68,38
46,71,40,52,68,57,60,57,60,60,65
65,43,74,59,68,59,75,62,67,55,60,79,86,67,66,77,71,75
56,44,26,50,49,41,33,40,45,44,39,53,74,63,65,70,71
15,49,53,18,53,45,20,55,36,54,49,53,64,71,82,78,67,60,67
27,16,41,64,48,21,65,61,46,68,46,72,67,61
33,51,63,85,39,59,44,45,34,89,55,34,46
42,56,53,50,37,39,52,59,38,43,56,38,42,53
21,22,59,27,33,32,14,36,53,42,58,58
10,54,36,44,40,63,41,31,46
50,45,49,19,55,35,15,33
26,62,45,37,42,29,59,44,40,47,67,42,64,63,54,60,88,76,80,86,78,78,76
14,12,61,24,53,39,32,15,44
47,53,34,48,42,61,34,51,34,45,50,56,46,59,54,47,53,43,62,40,80,66,94,58,64,71,82,78,67,60,67
42,55,36,34,56,46,26,35,52,70
50,17,66,53,32,60,32,39,53
36,45,44,49,49,37,49,36,46
32,45,61,52,34,47,59,62,48,57,71,49,79,50,48,51,55,54,42,55,47,76,43,65,55,104,57,85,55
10,44,49,20,45,32,38,41
58,41,38,64,61,39,42,40,54,66,69,63,34
42,37,62,38,51,44,41,70,41,28
19,55,58,42,22,34,44,45,43,33,45
26,31,41,26,69,34,12,25
39,45,49,44,48,49,37,39
55,45,48,19,53,32,59,56,58,79,50
33,68,12,18,49,36,39,35,49,35,21,38
47,51,64,50,102,40,47,31,57,15,54,50,56,64,51,37,62,60,77,62,44,52,52,72,67
9,55,26,45,33,18,52,30,53,42,58,58
23,57,61,28,62,31,58,42,47,61,52,54,50,68,54,44,53,26,28,68
35,58,61,39,51,51,42,31,33,70,47,55,44,55,62,43,69,69,65,51,46,68,60,78,96,58,63
14,6,9,54,48,36,59,46,30,17,68,38,35,39,48,33,43,68,60,51,53,51,67,59
46,71,40,52,68,57,60,57,60,60,65,79,55,54,47,75,80,72,45,59,64,67,57,63,77,71,72,72,77
65,43,74,59,68,59,75,62,67,55,60,79,86,67,66,77,71,75,68,67,65,41,75,68,86,92,74,64,65,29,60,78,96,58,63
56,44,26,50,49,41,33,40,45,44,39,53,74,63,65,70,71,52,71,54,75,52,61,46,53,53,51,48,55,67,46,58
15,49,53,18,53,45,20,55,36,54,49,53,64,71,82,78,67,60,67,52,52,52,57,55,64,86,71,59,79,84,52,71,85,84,66,63,64
27,16,41,64,48,21,65,61,46,68,46,72,67,61,51,52,65,55,75,54,60,56,75,55,70,55,63,77,71,72,72,77
33,51,63,85,39,59,44,45,34,89,55,34,46,47,74,54,57,52,80,42,92,60,45,81,64,63,77,71,72,72,77
42,56,53,50,37,39,52,59,38,43,56,38,42,53,52,67,52,47,45,57,69,51,63,64,48,30,58,48
21,22,59,27,33,32,14,36,53,42,58,58,67,48,43,38,62,61,42,60,59,26,70,30,46,50
10,54,36,44,40,63,41,31,46,79,40,43,55,55,65,52,74,46,48,41,81,70,70,64
50,45,49,19,55,35,15,33,68,36,48,49,66,61,69,44,60,55,46,49,58,48
26,62,45,37,42,29,59,44,40,47,67,42,64,63,54,60,88,76,80,86,78,78,76,79,69,66,57,57,43,60,60,63,64,70,64,63,76
14,12,61,24,53,39,32,15,44,47,67,48,38,41,57,52,52,53,61,46,52
47,53,34,48,42,61,34,51,34,45,50,56,46,59,54,47,53,43,62,40,80,66,94,58,64,71,82,78,67,60,67,67,58,65,75,66,74,92,65,79,55,83,60,78,96,58,63
42,55,36,34,56,46,26,35,52,70,51,71,54,33,46,57,49,71,60,46,70,30
50,17,66,53,32,60,32,39,53,68,39,43,61,41,64,49,69,52,45,28,64
36,45,44,49,49,37,49,36,46,53,36,66,61,76,80,74,53,60,61,84,68,71,85,84,66,63,64
53,48,48,41,43,54,46,49,65,46,28,57
32,45,61,52,34,47,59,62,48,57,71,49,79,50,48,51,55,54,42,55,47,76,43,65,55,104,57,85,55,75,48,44,49,50,72,71,75,55,81,83,81,70,70,64
10,44,49,20,45,32,38,41,35,69,65,69,46,57,65,53,65,64,70,83,46,50
58,41,38,64,61,39,42,40,54,66,69,63,34,47,74,65,47,43,61,52,56,62,79,63,64,46,50
42,37,62,38,51,44,41,70,41,28,32,61,54,61,66,57,60,52,75,51,65,57
35,71,43,39,76,52,45,63,55,65,41,67,46,58
19,55,58,42,22,34,44,45,43,33,45,75,39,48,39,57,61,86,46,62,64,55,64,58,48
26,31,41,26,69,34,12,25,67,52,44,69,45,61,60,45,53,61,70,49
39,45,49,44,48,49,37,39,75,40,43,41,46,64,42,44,53,64,46,55,71,85,84,66,63,64
55,45,48,19,53,32,59,56,58,79,50,52,58,45,54,76,60,60,52,64,67,64,67,46,58
33,68,12,18,49,36,39,35,49,35,21,38,51,55,48,38,57,54,49,52,51,81,29
47,51,64,50,102,40,47,31,57,15,54,50,56,64,51,37,62,60,77,62,44,52,52,72,67,52,61,43,75,62,47,72,49,62,64,84,49,81,70,70,64
53,40,45,69,50,43,49,56,60,51,55,59
9,55,26,45,33,18,52,30,53,42,58,58,52,36,65,39,55,57,54,69,65,55,63,59,63,76
32,69,45,49,52,54,74,46,74,26,63,52,63,76
47,58,66,33,45,47,46,46,65,45,46,41
32,74,54,54,41,47,65,51,60,55,46,29

1 23,57,61,28,62,31,58,42 23,57,61,28,62,31,58,42,47,61,52,54,50,68,54,44,53,26,28,68
2 35,58,61,39,51,51,42,31,33,70 35,58,61,39,51,51,42,31,33,70,47,55,44,55,62,43,69,69,65,51,46,68,60,78,96,58,63
3 14,6,9,54,48,36,59,46,30,17,68,38 14,6,9,54,48,36,59,46,30,17,68,38,35,39,48,33,43,68,60,51,53,51,67,59
4 46,71,40,52,68,57,60,57,60,60,65 46,71,40,52,68,57,60,57,60,60,65,79,55,54,47,75,80,72,45,59,64,67,57,63,77,71,72,72,77
5 65,43,74,59,68,59,75,62,67,55,60,79,86,67,66,77,71,75 65,43,74,59,68,59,75,62,67,55,60,79,86,67,66,77,71,75,68,67,65,41,75,68,86,92,74,64,65,29,60,78,96,58,63
6 56,44,26,50,49,41,33,40,45,44,39,53,74,63,65,70,71 56,44,26,50,49,41,33,40,45,44,39,53,74,63,65,70,71,52,71,54,75,52,61,46,53,53,51,48,55,67,46,58
7 15,49,53,18,53,45,20,55,36,54,49,53,64,71,82,78,67,60,67 15,49,53,18,53,45,20,55,36,54,49,53,64,71,82,78,67,60,67,52,52,52,57,55,64,86,71,59,79,84,52,71,85,84,66,63,64
8 27,16,41,64,48,21,65,61,46,68,46,72,67,61 27,16,41,64,48,21,65,61,46,68,46,72,67,61,51,52,65,55,75,54,60,56,75,55,70,55,63,77,71,72,72,77
9 33,51,63,85,39,59,44,45,34,89,55,34,46 33,51,63,85,39,59,44,45,34,89,55,34,46,47,74,54,57,52,80,42,92,60,45,81,64,63,77,71,72,72,77
10 42,56,53,50,37,39,52,59,38,43,56,38,42,53 42,56,53,50,37,39,52,59,38,43,56,38,42,53,52,67,52,47,45,57,69,51,63,64,48,30,58,48
11 21,22,59,27,33,32,14,36,53,42,58,58 21,22,59,27,33,32,14,36,53,42,58,58,67,48,43,38,62,61,42,60,59,26,70,30,46,50
12 10,54,36,44,40,63,41,31,46 10,54,36,44,40,63,41,31,46,79,40,43,55,55,65,52,74,46,48,41,81,70,70,64
13 50,45,49,19,55,35,15,33 50,45,49,19,55,35,15,33,68,36,48,49,66,61,69,44,60,55,46,49,58,48
14 26,62,45,37,42,29,59,44,40,47,67,42,64,63,54,60,88,76,80,86,78,78,76 26,62,45,37,42,29,59,44,40,47,67,42,64,63,54,60,88,76,80,86,78,78,76,79,69,66,57,57,43,60,60,63,64,70,64,63,76
15 14,12,61,24,53,39,32,15,44 14,12,61,24,53,39,32,15,44,47,67,48,38,41,57,52,52,53,61,46,52
16 47,53,34,48,42,61,34,51,34,45,50,56,46,59,54,47,53,43,62,40,80,66,94,58,64,71,82,78,67,60,67 47,53,34,48,42,61,34,51,34,45,50,56,46,59,54,47,53,43,62,40,80,66,94,58,64,71,82,78,67,60,67,67,58,65,75,66,74,92,65,79,55,83,60,78,96,58,63
17 42,55,36,34,56,46,26,35,52,70 42,55,36,34,56,46,26,35,52,70,51,71,54,33,46,57,49,71,60,46,70,30
18 50,17,66,53,32,60,32,39,53 50,17,66,53,32,60,32,39,53,68,39,43,61,41,64,49,69,52,45,28,64
19 36,45,44,49,49,37,49,36,46 36,45,44,49,49,37,49,36,46,53,36,66,61,76,80,74,53,60,61,84,68,71,85,84,66,63,64
20 32,45,61,52,34,47,59,62,48,57,71,49,79,50,48,51,55,54,42,55,47,76,43,65,55,104,57,85,55 53,48,48,41,43,54,46,49,65,46,28,57
21 10,44,49,20,45,32,38,41 32,45,61,52,34,47,59,62,48,57,71,49,79,50,48,51,55,54,42,55,47,76,43,65,55,104,57,85,55,75,48,44,49,50,72,71,75,55,81,83,81,70,70,64
22 58,41,38,64,61,39,42,40,54,66,69,63,34 10,44,49,20,45,32,38,41,35,69,65,69,46,57,65,53,65,64,70,83,46,50
23 42,37,62,38,51,44,41,70,41,28 58,41,38,64,61,39,42,40,54,66,69,63,34,47,74,65,47,43,61,52,56,62,79,63,64,46,50
24 19,55,58,42,22,34,44,45,43,33,45 42,37,62,38,51,44,41,70,41,28,32,61,54,61,66,57,60,52,75,51,65,57
25 26,31,41,26,69,34,12,25 35,71,43,39,76,52,45,63,55,65,41,67,46,58
26 39,45,49,44,48,49,37,39 19,55,58,42,22,34,44,45,43,33,45,75,39,48,39,57,61,86,46,62,64,55,64,58,48
27 55,45,48,19,53,32,59,56,58,79,50 26,31,41,26,69,34,12,25,67,52,44,69,45,61,60,45,53,61,70,49
28 33,68,12,18,49,36,39,35,49,35,21,38 39,45,49,44,48,49,37,39,75,40,43,41,46,64,42,44,53,64,46,55,71,85,84,66,63,64
29 47,51,64,50,102,40,47,31,57,15,54,50,56,64,51,37,62,60,77,62,44,52,52,72,67 55,45,48,19,53,32,59,56,58,79,50,52,58,45,54,76,60,60,52,64,67,64,67,46,58
30 9,55,26,45,33,18,52,30,53,42,58,58 33,68,12,18,49,36,39,35,49,35,21,38,51,55,48,38,57,54,49,52,51,81,29
31 47,51,64,50,102,40,47,31,57,15,54,50,56,64,51,37,62,60,77,62,44,52,52,72,67,52,61,43,75,62,47,72,49,62,64,84,49,81,70,70,64
32 53,40,45,69,50,43,49,56,60,51,55,59
33 9,55,26,45,33,18,52,30,53,42,58,58,52,36,65,39,55,57,54,69,65,55,63,59,63,76
34 32,69,45,49,52,54,74,46,74,26,63,52,63,76
35 47,58,66,33,45,47,46,46,65,45,46,41
36 32,74,54,54,41,47,65,51,60,55,46,29