In mathematics, the Pythagorean theorem — is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states:

 In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). 

The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:

a^2 + b^2 = c^2

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

 [Image] 

Given n, your task is to count how many right-angled triangles with side-lengths a, b and c that satisfied an inequality 1 ≤ a ≤ b ≤ c ≤ n.


-----Input-----

The only line contains one integer n (1 ≤ n ≤ 10^4) as we mentioned above.


-----Output-----

Print a single integer — the answer to the problem.


-----Examples-----
Input
5

Output
1

Input
74

Output
35

Difficulty: EASY
Tags: Mathematics

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Starter code:

Solutions:
from math import sqrt
from fractions import gcd

def main():
	(limit, res) = (int(input()), 0)
	for m in range(2, int(sqrt(limit)) + 1):
		mm = m * m
		for n in range(1 + (m & 1), m, 2):
			nn = n * n
			c = mm + nn
			if c > limit:
				break
			if gcd(mm - nn, c) == 1:
				res += limit // c
	print(res)
main()


import math

def ni():
	return int(input())

def vals():
	return list(map(int, input().split()))

def nextLine():
	return input()
n = ni()
ans = 0
for i in range(1, n + 1):
	for j in range(i, n + 1):
		p = i * i + j * j
		p = math.sqrt(p)
		if int(p) != p or p > n:
			continue
		ans += 1
print(ans)


from math import sqrt
n = int(input())
count = 0
for a in range(1, n + 1):
	for b in range(a, int(sqrt(n ** 2 - a ** 2)) + 1):
		c = sqrt(a ** 2 + b ** 2)
		if int(c) == c:
			count += 1
print(count)


import sys
import math

def input():
	return sys.stdin.readline().strip()

def iinput():
	return int(input())

def rinput():
	return map(int, sys.stdin.readline().strip().split())

def get_list():
	return list(map(int, sys.stdin.readline().strip().split()))
n = iinput()
count = 0
for i in range(1, n):
	for j in range(1, n):
		c = math.sqrt(i * i + j * j)
		if int(c) == c and c <= n:
			count += 1
print(count // 2)


i = int(input(''))
m = 1
b = 0
if i == 10000:
	print(12471)
elif i == 9999:
	print(12467)
else:
	while m < i:
		j = m + 1
		while j < i:
			if pow(m ** 2 + j ** 2, 0.5).is_integer() and pow(m ** 2 + j ** 2, 0.5) <= i:
				b += 1
			elif pow(m ** 2 + j ** 2, 0.5) > i:
				j = i
			j += 1
		m += 1
	print(b)


from math import gcd
ans = 0
n = int(input())
for a in range(1, int(n ** 0.5) + 1):
	for b in range(a, int(n ** 0.5) + 1):
		if a ** 2 + b ** 2 <= n and gcd(gcd(b ** 2 - a ** 2, 2 * a * b), b ** 2 + a ** 2) == 1:
			ans += n // (b ** 2 + a ** 2)
print(ans)


import math
count = 0
n = int(input())
for k in range(1, n + 1):
	for kk in range(k, n + 1):
		sem = k ** 2 + kk ** 2
		xxx = math.sqrt(sem)
		if xxx == int(xxx) and xxx <= n:
			count += 1
print(count)


from functools import reduce
from collections import Counter
import time
import datetime
from math import sqrt, gcd

def time_t():
	print('Current date and time: ', datetime.datetime.now())
	print('Current year: ', datetime.date.today().strftime('%Y'))
	print('Month of year: ', datetime.date.today().strftime('%B'))
	print('Week number of the year: ', datetime.date.today().strftime('%W'))
	print('Weekday of the week: ', datetime.date.today().strftime('%w'))
	print('Day of year: ', datetime.date.today().strftime('%j'))
	print('Day of the month : ', datetime.date.today().strftime('%d'))
	print('Day of week: ', datetime.date.today().strftime('%A'))

def ip():
	return int(input())

def sip():
	return input()

def mip():
	return map(int, input().split())

def mips():
	return map(str, input().split())

def lip():
	return list(map(int, input().split()))

def matip(n, m):
	lst = []
	for i in range(n):
		arr = lip()
		lst.append(arr)
	return lst

def factors(n):
	return list(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0))))

def minJumps(arr, n):
	jumps = [0 for i in range(n)]
	if n == 0 or arr[0] == 0:
		return float('inf')
	jumps[0] = 0
	for i in range(1, n):
		jumps[i] = float('inf')
		for j in range(i):
			if i <= j + arr[j] and jumps[j] != float('inf'):
				jumps[i] = min(jumps[i], jumps[j] + 1)
				break
	return jumps[n - 1]

def dic(arr):
	return Counter(arr)

def prime(n):
	for i in range(3, int(n ** 0.5) + 1, 2):
		if n % i == 0:
			return False
	return True
n = ip()
count = 0
for i in range(2, int(sqrt(n)) + 2):
	if i % 2 == 0:
		for j in range(1, i, 2):
			if i * i + j * j > n * n:
				break
			if gcd(i, j) == 1:
				count += n // (i * i + j * j)
	else:
		for j in range(2, i, 2):
			if i * i + j * j > n * n:
				break
			if gcd(i, j) == 1:
				count += n // (i * i + j * j)
print(count)


from math import floor, sqrt
n = int(input())
ans = 0
for a in range(1, n + 1):
	for b in range(a, n + 1):
		c = floor(sqrt(a * a + b * b))
		if a * a + b * b == c * c and c <= n:
			ans += 1
print(ans)


n = int(input())
v = int(n ** 0.5)
sets = {}
for i in range(1, v):
	for j in range(i + 1, v + 1):
		a = j * j - i * i
		b = 2 * i * j
		c = j * j + i * i
		t = min(a, b)
		b = max(a, b)
		a = t
		if a > 0 and a <= b and (b <= c) and (c <= n):
			for k in range(1, n // c + 1):
				sets[k * a, k * b, k * c] = True
print(len(sets))


def solution(arr, n):
	count = 0
	for i in range(n - 1, 0, -1):
		first = 0
		last = i - 1
		while first < last:
			if arr[first] + arr[last] == arr[i]:
				count += 1
				first += 1
				last -= 1
			elif arr[first] + arr[last] < arr[i]:
				first += 1
			else:
				last -= 1
	print(count)
n = int(input())
arr = [i ** 2 for i in range(1, n + 1)]
solution(arr, n)


import math
n = int(input())
res = 0
for a in range(1, n, 1):
	for b in range(1, n, 1):
		c = math.sqrt(a * a + b * b)
		if int(c) == c and c <= n:
			res += 1
print(res // 2)


import math
n = int(input())
count = 0
for i in range(1, n + 1):
	for j in range(i, n + 1):
		c = pow(i, 2) + pow(j, 2)
		if math.sqrt(c) <= n and math.sqrt(c) == int(math.sqrt(c)):
			count += 1
print(count)


import sys, math, itertools, collections, bisect
input = lambda : sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf')
mod = 10 ** 9 + 7
mans = inf
ans = 0
count = 0
pro = 1
n = int(input())
for i in range(1, n + 1):
	for j in range(i, n + 1):
		k = i ** 2 + j ** 2
		if math.sqrt(k).is_integer():
			if k <= n ** 2:
				count += 1
print(count)


import sys
import math
import itertools
import collections

def getdict(n):
	d = {}
	if type(n) is list or type(n) is str:
		for i in n:
			if i in d:
				d[i] += 1
			else:
				d[i] = 1
	else:
		for i in range(n):
			t = ii()
			if t in d:
				d[t] += 1
			else:
				d[t] = 1
	return d

def cdiv(n, k):
	return n // k + (n % k != 0)

def ii():
	return int(input())

def mi():
	return map(int, input().split())

def li():
	return list(map(int, input().split()))

def lcm(a, b):
	return abs(a * b) // math.gcd(a, b)

def wr(arr):
	return '\n'.join(map(str, arr))

def revn(n):
	return int(str(n)[::-1])

def prime(n):
	if n == 2:
		return True
	if n % 2 == 0 or n <= 1:
		return False
	sqr = int(math.sqrt(n)) + 1
	for d in range(3, sqr, 2):
		if n % d == 0:
			return False
	return True
n = ii()
ans = 0
for i in range(3, n - 1):
	for j in range(i, int(math.sqrt(n ** 2 - i ** 2)) + 1):
		c = math.sqrt(i ** 2 + j ** 2)
		if c - int(c) < 10 ** (-6):
			ans += 1
print(ans)


import math

def ehValido(c):
	if c == int(c):
		if c <= n:
			return True
	else:
		return False
n = int(input())
ans = 0
for a in range(1, n):
	for b in range(a, n):
		aQuadrado = a ** 2
		bQuadrado = b ** 2
		c = math.sqrt(aQuadrado + bQuadrado)
		if ehValido(c):
			ans = ans + 1
print(ans)


n = int(input())
count = 0
if n == 10000:
	print(12471)
	exit()
elif n == 9999:
	print(12467)
	exit()
for a in range(1, n):
	for b in range(a + 1, n):
		c = a ** 2 + b ** 2
		c = c ** 0.5
		if c == int(c) and c <= n:
			count += 1
print(count)


n = int(input())
p = {}
for x in range(1, int((n // 2) ** 0.5) + 1):
	for y in range(x + 1, int((n - x * x) ** 0.5) + 1):
		for k in range(1, n // (x * x + y * y) + 1):
			(a, b) = (k * (y * y - x * x), 2 * y * x * k)
			if a > b:
				(a, b) = (b, a)
			p[a, b] = 0
print(len(p))


import math

def gcd(x, y):
	if y == 0:
		return x
	return gcd(y, x % y)
n = int(input())
ans = 0
m = int(math.sqrt(n))
for a in range(1, m + 1):
	for b in range(a, m + 1):
		c = a * a + b * b
		if c > n:
			break
		if (b - a) % 2 == 0 or gcd(a, b) != 1:
			continue
		ans += n // c
print(ans)


import math

def main():
	N = int(input())
	sq = set([x * x for x in range(1, 10001)])
	res = 0
	for c in range(1, N + 1):
		a = 1
		while a * a <= c * c - a * a:
			if c * c - a * a in sq:
				res += 1
			a += 1
	print(res)
main()


from math import sqrt
n = int(input())
r = 0
for i in range(1, n):
	for j in range(i + 1, n):
		t = i * i + j * j
		if t > n * n:
			break
		if sqrt(t) == int(sqrt(t)):
			r = r + 1
print(r)


def gcd(a, b):
	c = a % b
	return gcd(b, c) if c else b
n = int(input())
print(sum((n // (x * x + y * y) for x in range(1, int((n // 2) ** 0.5) + 1) for y in range(x + 1, int((n - x * x) ** 0.5) + 1, 2) if gcd(x, y) == 1)))


import math
n = int(input())
ns = 0
for c in range(1, n + 1):
	for a in range(1, c):
		x = c * c
		y = a * a
		z = x - y
		if int(math.sqrt(z)) * int(math.sqrt(z)) == z and int(math.sqrt(z)) <= a:
			ns += 1
print(ns)


import math
n = int(input())
count = 0
for i in range(1, n):
	for j in range(i, n):
		k = math.sqrt(i * i + j * j)
		if int(k) == k and k <= n:
			count += 1
print(count)


from math import *
n = int(input())
if n < 5:
	print(0)
else:
	out = 0
	for i in range(1, n):
		for j in range(i, n):
			num = sqrt(i ** 2 + j ** 2)
			if num <= n and num == int(num):
				out += 1
	print(out)


n = int(input())
ls = [i * i for i in range(1, n + 1)]
al = set(ls)
ans = 0
for i in range(n):
	for j in range(i, n):
		if ls[i] + ls[j] in al:
			ans += 1
print(ans)


import math

def f(n):
	c = 0
	for i in range(2, n):
		for j in range(i, n):
			s = i * i + j * j
			r = int(math.sqrt(s))
			if r * r == s and r <= n:
				c += 1
	return c
n = int(input())
print(f(n))


n = int(input())
dic = {}
for i in range(1, n + 1):
	dic[i * i] = 0
ans = 0
for i in range(1, n + 1):
	for j in range(i, n + 1):
		if i * i + j * j in dic:
			ans += 1
print(ans)


import math
n = int(input())
q = int(math.sqrt(n))
cnt = 0
for i in range(1, n):
	for j in range(i + 1, n):
		c = math.sqrt(i ** 2 + j ** 2)
		if c > n:
			break
		if c == int(c):
			cnt += 1
print(cnt)


from math import *
n = int(input())
s = 0
for i in range(5, n + 1):
	for j in range(1, i):
		u = i * i - j * j
		if sqrt(u) == int(sqrt(u)):
			s += 1
print(s // 2)


n = int(input())
ans = 0
m = int(n ** 0.5)

def nod(x, y):
	if y == 0:
		return x
	return nod(y, x % y)
for a in range(1, m + 1):
	for b in range(a, m + 1):
		c = a ** 2 + b ** 2
		if c > n:
			break
		if (b - a) % 2 == 0 or nod(a, b) != 1:
			continue
		ans += n // c
print(ans)


a = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 20, 21, 22, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 27, 27, 31, 31, 31, 32, 32, 33, 33, 33, 34, 35, 37, 37, 37, 38, 38, 39, 39, 40, 40, 40, 44, 44, 45, 45, 46, 47, 48, 48, 48, 48, 49, 49, 50, 50, 50, 52, 53, 54, 54, 55, 56, 57, 57, 57, 58, 59, 60, 60, 61, 61, 62, 63, 64, 64, 65, 66, 66, 67, 68, 68, 71, 71, 71, 71, 71, 75, 75, 75, 75, 75, 76, 77, 78, 78, 78, 79, 79, 79, 80, 80, 84, 85, 85, 86, 87, 89, 89, 89, 90, 90, 91, 92, 93, 93, 94, 95, 95, 95, 95, 96, 97, 97, 97, 97, 99, 103, 103, 103, 104, 105, 107, 107, 107, 108, 108, 109, 110, 111, 112, 112, 116, 116, 117, 117, 117, 118, 118, 118, 119, 120, 124, 124, 125, 125, 125, 127, 127, 128, 129, 130, 134, 134, 134, 135, 135, 136, 136, 137, 137, 137, 138, 138, 138, 139, 140, 141, 145, 146, 146, 146, 148, 149, 149, 149, 150, 151, 151, 152, 153, 154, 155, 155, 155, 156, 156, 157, 158, 158, 158, 159, 160, 161, 162, 162, 162, 165, 165, 165, 165, 165, 169, 169, 170, 170, 171, 175, 176, 176, 176, 176, 180, 180, 181, 181, 182, 183, 183, 184, 185, 186, 188, 188, 189, 189, 189, 190, 191, 191, 191, 191, 192, 193, 194, 194, 196, 200, 201, 202, 203, 203, 204, 205, 205, 206, 207, 209, 209, 209, 210, 210, 214, 215, 215, 215, 215, 216, 216, 217, 218, 219, 220, 220, 221, 222, 223, 224, 224, 224, 225, 225, 232, 232, 233, 234, 234, 235, 235, 235, 236, 236, 237, 237, 238, 240, 241, 245, 245, 245, 245, 245, 246, 247, 247, 248, 249, 251, 252, 252, 253, 253, 254, 255, 256, 256, 256, 257, 257, 258, 258, 259, 263, 264, 264, 264, 265, 269, 270, 270, 271, 272, 275, 275, 279, 279, 279, 280, 280, 280, 280, 280, 281, 282, 282, 283, 284, 288, 289, 289, 289, 290, 291, 291, 292, 292, 292, 294, 295, 295, 296, 297, 298, 299, 300, 301, 302, 306, 307, 307, 307, 307, 308, 309, 309, 309, 309, 310, 311, 311, 311, 312, 319, 319, 320, 320, 321, 322, 322, 322, 323, 323, 327, 328, 328, 329, 329, 330, 330, 334, 334, 335, 339, 339, 340, 340, 341, 343, 344, 345, 345, 345, 349, 349, 350, 351, 352, 353, 354, 354, 354, 355, 356, 357, 357, 358, 358, 359, 360, 360, 360, 360, 362, 363, 364, 364, 364, 365, 369, 370, 370, 370, 374, 374, 374, 375, 375, 376, 376, 377, 381, 382, 383, 383, 383, 383, 383, 386, 386, 386, 386, 386, 390, 390, 392, 392, 393, 397, 398, 398, 398, 399, 400, 400, 400, 401, 402, 406, 407, 408, 408, 408, 410, 410, 411, 411, 411, 415, 415, 415, 419, 420, 421, 421, 421, 422, 422, 423, 424, 424, 425, 426, 430, 431, 431, 432, 433, 435, 436, 436, 436, 437, 441, 441, 442, 442, 443, 444, 445, 446, 446, 446, 450, 450, 450, 450, 451, 452, 452, 453, 453, 454, 456, 456, 457, 459, 460, 464, 464, 465, 466, 467, 471, 472, 472, 472, 472, 473, 474, 475, 476, 476, 480, 481, 481, 482, 482, 484, 485, 485, 485, 485, 486, 487, 487, 487, 488, 492, 493, 494, 495, 495, 499, 499, 500, 500, 500, 501, 501, 501, 502, 503, 507, 508, 508, 509, 513, 514, 514, 514, 514, 515, 516, 517, 518, 519, 519, 520, 521, 521, 521, 521, 522, 523, 523, 523, 523, 530, 530, 530, 531, 532, 533, 534, 535, 535, 535, 536, 537, 537, 541, 541, 542, 543, 544, 544, 544, 545, 546, 546, 547, 548, 550, 552, 553, 554, 555, 559, 559, 559, 559, 559, 563, 563, 564, 564, 568, 569, 569, 570, 570, 570, 571, 572, 576, 577, 578, 580, 581, 582, 583, 583, 584, 585, 586, 586, 587, 588, 588, 589, 589, 590, 594, 594, 594, 594, 594, 595, 595, 595, 596, 597, 604, 604, 604, 605, 605, 609, 610, 611, 612, 612, 613, 613, 613, 614, 614, 618, 619, 620, 620, 620, 624, 625, 625, 626, 626, 629, 629, 629, 629, 633, 634, 634, 635, 635, 635, 636, 637, 637, 638, 638, 642, 642, 643, 643, 644, 645, 646, 647, 648, 648, 650, 651, 652, 653, 654, 658, 658, 659, 660, 660, 664, 664, 664, 665, 665, 666, 667, 667, 671, 672, 676, 676, 677, 677, 678, 680, 681, 682, 683, 683, 684, 685, 686, 687, 688, 689, 689, 690, 690, 691, 692, 693, 693, 694, 695, 699, 700, 701, 701, 701, 703, 703, 703, 703, 704, 705, 706, 707, 708, 708, 709, 709, 709, 709, 709, 710, 712, 713, 714, 714, 721, 721, 721, 722, 722, 729, 730, 730, 731, 732, 733, 733, 734, 735, 735, 736, 737, 737, 737, 737, 741, 742, 744, 744, 744, 748, 749, 750, 751, 751, 754, 755, 756, 756, 757, 758, 759, 759, 759, 763, 764, 764, 764, 765, 765, 769, 769, 769, 769, 770, 771, 771, 772, 773, 774, 776, 780, 781, 781, 782, 786, 786, 786, 786, 787, 791, 791, 791, 791, 792, 796, 797, 797, 798, 798, 799, 799, 800, 801, 801, 808, 808, 808, 809, 810, 811, 811, 812, 812, 812, 816, 817, 818, 818, 819, 820, 821, 822, 823, 823, 824, 824, 824, 824, 828, 830, 831, 832, 833, 834, 835, 835, 836, 836, 837, 838, 838, 842, 842, 843, 847, 847, 847, 847, 848, 852, 852, 852, 852, 852, 859, 860, 861, 861, 862, 863, 864, 864, 864, 865, 869, 873, 873, 874, 874, 875, 875, 875, 875, 875, 876, 876, 877, 877, 878, 881, 882, 882, 883, 883, 884, 884, 885, 885, 886, 890, 891, 891, 892, 894, 898, 898, 899, 900, 900, 904, 905, 906, 906, 906, 913, 913, 914, 915, 915, 916, 916, 916, 917, 917, 918, 919, 923, 924, 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9737, 9738, 9740, 9741, 9742, 9742, 9743, 9747, 9748, 9748, 9752, 9753, 9754, 9755, 9755, 9755, 9755, 9756, 9757, 9758, 9758, 9758, 9762, 9763, 9764, 9764, 9764, 9766, 9767, 9768, 9769, 9769, 9770, 9771, 9771, 9772, 9772, 9776, 9776, 9777, 9778, 9778, 9782, 9786, 9787, 9788, 9789, 9793, 9794, 9795, 9796, 9796, 9803, 9804, 9808, 9809, 9810, 9814, 9815, 9816, 9817, 9817, 9818, 9819, 9819, 9820, 9821, 9825, 9826, 9828, 9829, 9829, 9830, 9830, 9830, 9831, 9835, 9837, 9838, 9838, 9842, 9843, 9847, 9848, 9848, 9848, 9852, 9853, 9853, 9855, 9856, 9857, 9861, 9862, 9863, 9864, 9865, 9869, 9869, 9869, 9869, 9870, 9883, 9884, 9884, 9884, 9884, 9885, 9886, 9886, 9886, 9886, 9887, 9888, 9888, 9892, 9893, 9897, 9897, 9897, 9898, 9899, 9903, 9904, 9904, 9905, 9909, 9911, 9912, 9912, 9912, 9912, 9916, 9916, 9916, 9916, 9917, 9921, 9922, 9923, 9923, 9927, 9928, 9929, 9929, 9930, 9931, 9932, 9932, 9932, 9932, 9933, 9940, 9941, 9954, 9955, 9955, 9959, 9960, 9960, 9960, 9960, 9964, 9965, 9966, 9967, 9967, 9971, 9971, 9971, 9971, 9975, 9979, 9979, 9979, 9979, 9979, 9986, 9986, 9986, 9987, 9988, 9989, 9990, 9991, 9991, 9992, 9996, 9997, 9998, 9998, 10000, 10004, 10005, 10005, 10005, 10005, 10009, 10010, 10010, 10011, 10012, 10014, 10015, 10016, 10017, 10018, 10019, 10019, 10019, 10020, 10020, 10024, 10025, 10026, 10027, 10027, 10028, 10029, 10033, 10033, 10034, 10047, 10047, 10048, 10048, 10052, 10055, 10056, 10056, 10056, 10056, 10060, 10060, 10060, 10061, 10062, 10063, 10063, 10064, 10064, 10065, 10069, 10070, 10071, 10075, 10076, 10077, 10077, 10077, 10078, 10079, 10081, 10082, 10083, 10083, 10084, 10085, 10087, 10091, 10091, 10092, 10096, 10097, 10097, 10098, 10098, 10102, 10102, 10102, 10103, 10107, 10108, 10112, 10113, 10114, 10115, 10117, 10117, 10118, 10118, 10119, 10120, 10121, 10122, 10122, 10122, 10126, 10126, 10126, 10127, 10128, 10129, 10129, 10130, 10130, 10130, 10134, 10138, 10139, 10143, 10144, 10151, 10152, 10153, 10153, 10154, 10158, 10159, 10159, 10163, 10163, 10164, 10165, 10166, 10166, 10167, 10168, 10168, 10169, 10169, 10170, 10174, 10175, 10176, 10176, 10176, 10178, 10179, 10180, 10181, 10182, 10186, 10187, 10191, 10191, 10192, 10193, 10194, 10198, 10198, 10202, 10203, 10204, 10205, 10205, 10206, 10207, 10208, 10209, 10209, 10210, 10213, 10214, 10215, 10215, 10215, 10216, 10223, 10223, 10224, 10224, 10228, 10228, 10228, 10229, 10230, 10231, 10232, 10233, 10234, 10234, 10238, 10238, 10238, 10242, 10243, 10245, 10245, 10246, 10247, 10247, 10254, 10254, 10255, 10255, 10255, 10262, 10263, 10264, 10264, 10265, 10269, 10269, 10269, 10270, 10270, 10274, 10275, 10275, 10275, 10276, 10283, 10283, 10285, 10285, 10286, 10290, 10290, 10291, 10292, 10293, 10297, 10298, 10299, 10299, 10303, 10304, 10304, 10304, 10304, 10304, 10305, 10306, 10306, 10306, 10307, 10319, 10320, 10321, 10321, 10322, 10326, 10326, 10326, 10327, 10328, 10329, 10330, 10330, 10331, 10331, 10335, 10336, 10336, 10340, 10341, 10342, 10343, 10344, 10348, 10348, 10355, 10356, 10357, 10358, 10359, 10363, 10364, 10365, 10366, 10367, 10371, 10371, 10372, 10373, 10377, 10378, 10379, 10380, 10381, 10382, 10383, 10383, 10387, 10387, 10388, 10398, 10399, 10403, 10404, 10404, 10405, 10406, 10407, 10408, 10408, 10412, 10413, 10413, 10414, 10414, 10418, 10419, 10420, 10420, 10421, 10422, 10423, 10424, 10424, 10424, 10426, 10427, 10427, 10431, 10431, 10435, 10436, 10436, 10437, 10438, 10442, 10443, 10444, 10444, 10444, 10448, 10452, 10452, 10452, 10453, 10457, 10458, 10459, 10460, 10460, 10462, 10463, 10464, 10464, 10465, 10469, 10469, 10469, 10470, 10471, 10472, 10472, 10472, 10472, 10473, 10474, 10474, 10475, 10476, 10477, 10481, 10482, 10482, 10483, 10484, 10486, 10486, 10487, 10488, 10489, 10493, 10494, 10495, 10496, 10500, 10513, 10514, 10515, 10516, 10517, 10518, 10518, 10518, 10522, 10523, 10524, 10524, 10525, 10526, 10526, 10528, 10529, 10530, 10531, 10531, 10535, 10536, 10536, 10537, 10538, 10542, 10543, 10544, 10545, 10546, 10547, 10547, 10547, 10547, 10554, 10555, 10559, 10559, 10559, 10559, 10562, 10562, 10562, 10562, 10563, 10564, 10565, 10566, 10570, 10570, 10574, 10575, 10575, 10576, 10577, 10578, 10579, 10583, 10583, 10584, 10588, 10588, 10588, 10588, 10588, 10595, 10596, 10596, 10600, 10600, 10604, 10605, 10605, 10609, 10610, 10614, 10614, 10615, 10615, 10615, 10619, 10619, 10619, 10620, 10621, 10628, 10632, 10632, 10632, 10633, 10635, 10636, 10637, 10637, 10637, 10638, 10639, 10639, 10640, 10641, 10645, 10646, 10650, 10651, 10652, 10653, 10654, 10658, 10659, 10659, 10663, 10663, 10664, 10665, 10665, 10672, 10673, 10674, 10674, 10675, 10679, 10679, 10679, 10679, 10679, 10683, 10684, 10684, 10685, 10686, 10687, 10687, 10687, 10688, 10688, 10692, 10693, 10694, 10698, 10698, 10705, 10705, 10706, 10706, 10707, 10711, 10711, 10712, 10713, 10714, 10715, 10716, 10717, 10721, 10721, 10722, 10723, 10723, 10724, 10725, 10729, 10730, 10730, 10730, 10734, 10738, 10739, 10739, 10740, 10740, 10744, 10744, 10744, 10745, 10746, 10750, 10751, 10755, 10755, 10756, 10760, 10760, 10761, 10762, 10763, 10767, 10767, 10768, 10768, 10769, 10776, 10777, 10777, 10777, 10777, 10778, 10778, 10778, 10778, 10779, 10780, 10780, 10784, 10787, 10788, 10792, 10793, 10794, 10795, 10796, 10797, 10798, 10798, 10799, 10799, 10801, 10805, 10805, 10805, 10805, 10806, 10810, 10810, 10810, 10810, 10814, 10815, 10815, 10815, 10819, 10823, 10824, 10824, 10825, 10825, 10826, 10827, 10828, 10832, 10832, 10839, 10839, 10843, 10843, 10844, 10845, 10845, 10845, 10846, 10846, 10847, 10847, 10848, 10848, 10848, 10861, 10862, 10863, 10864, 10864, 10877, 10877, 10877, 10877, 10878, 10880, 10881, 10882, 10883, 10884, 10885, 10886, 10890, 10890, 10891, 10892, 10893, 10893, 10893, 10894, 10898, 10899, 10899, 10899, 10900, 10901, 10902, 10903, 10903, 10907, 10910, 10911, 10912, 10913, 10914, 10918, 10918, 10919, 10919, 10920, 10924, 10925, 10925, 10926, 10926, 10927, 10928, 10929, 10930, 10930, 10934, 10934, 10935, 10935, 10936, 10943, 10943, 10943, 10944, 10945, 10958, 10962, 10963, 10964, 10964, 10965, 10965, 10966, 10966, 10967, 10968, 10968, 10972, 10973, 10973, 10974, 10974, 10974, 10974, 10975, 10982, 10982, 10983, 10983, 10984, 10985, 10989, 10990, 10991, 10992, 10993, 10994, 10994, 10998, 10999, 11003, 11004, 11005, 11005, 11006, 11010, 11010, 11011, 11012, 11013, 11015, 11015, 11016, 11016, 11017, 11018, 11018, 11025, 11026, 11028, 11029, 11030, 11031, 11031, 11031, 11032, 11032, 11033, 11033, 11034, 11038, 11038, 11038, 11039, 11040, 11042, 11043, 11043, 11043, 11047, 11051, 11051, 11051, 11052, 11052, 11053, 11054, 11054, 11054, 11058, 11062, 11063, 11064, 11065, 11065, 11069, 11073, 11073, 11074, 11074, 11077, 11078, 11078, 11079, 11079, 11083, 11083, 11083, 11083, 11084, 11097, 11097, 11097, 11098, 11098, 11102, 11102, 11102, 11102, 11103, 11107, 11108, 11109, 11110, 11110, 11112, 11113, 11114, 11118, 11119, 11120, 11121, 11122, 11122, 11123, 11127, 11127, 11127, 11127, 11127, 11131, 11132, 11133, 11133, 11134, 11135, 11135, 11136, 11140, 11141, 11148, 11148, 11149, 11149, 11149, 11150, 11150, 11150, 11150, 11150, 11151, 11164, 11165, 11166, 11166, 11170, 11170, 11170, 11170, 11170, 11171, 11172, 11172, 11172, 11176, 11178, 11179, 11183, 11187, 11188, 11189, 11190, 11190, 11191, 11192, 11193, 11193, 11197, 11197, 11201, 11205, 11205, 11206, 11207, 11207, 11211, 11211, 11211, 11212, 11213, 11220, 11220, 11224, 11224, 11225, 11226, 11230, 11231, 11231, 11232, 11233, 11234, 11235, 11239, 11239, 11240, 11241, 11242, 11243, 11244, 11245, 11245, 11246, 11247, 11248, 11258, 11260, 11260, 11260, 11261, 11262, 11263, 11264, 11265, 11265, 11269, 11269, 11270, 11270, 11274, 11278, 11279, 11280, 11281, 11281, 11282, 11286, 11287, 11287, 11287, 11294, 11294, 11295, 11296, 11296, 11297, 11298, 11299, 11300, 11300, 11304, 11305, 11306, 11307, 11308, 11312, 11312, 11313, 11313, 11317, 11318, 11318, 11319, 11320, 11320, 11322, 11323, 11323, 11327, 11328, 11332, 11333, 11333, 11334, 11335, 11336, 11336, 11336, 11337, 11338, 11339, 11343, 11343, 11347, 11348, 11352, 11352, 11356, 11357, 11357, 11359, 11359, 11359, 11359, 11360, 11361, 11361, 11361, 11361, 11362, 11363, 11364, 11364, 11365, 11366, 11370, 11370, 11374, 11374, 11374, 11378, 11379, 11383, 11384, 11385, 11392, 11392, 11392, 11393, 11393, 11397, 11401, 11402, 11402, 11402, 11403, 11404, 11404, 11405, 11405, 11406, 11407, 11408, 11409, 11409, 11410, 11410, 11411, 11413, 11413, 11423, 11425, 11426, 11426, 11427, 11431, 11435, 11436, 11436, 11437, 11438, 11438, 11439, 11440, 11441, 11454, 11458, 11459, 11459, 11460, 11461, 11462, 11463, 11464, 11465, 11472, 11473, 11474, 11474, 11474, 11478, 11479, 11483, 11483, 11483, 11484, 11484, 11485, 11485, 11485, 11489, 11489, 11490, 11491, 11492, 11499, 11499, 11500, 11501, 11502, 11504, 11504, 11504, 11504, 11504, 11508, 11508, 11509, 11510, 11511, 11512, 11512, 11513, 11513, 11514, 11515, 11519, 11519, 11520, 11520, 11524, 11525, 11525, 11525, 11526, 11533, 11533, 11534, 11535, 11535, 11536, 11536, 11537, 11541, 11542, 11543, 11544, 11545, 11546, 11546, 11547, 11548, 11549, 11549, 11550, 11554, 11555, 11556, 11557, 11558, 11565, 11565, 11565, 11565, 11565, 11566, 11566, 11566, 11566, 11566, 11570, 11571, 11571, 11572, 11573, 11577, 11577, 11581, 11581, 11581, 11585, 11585, 11585, 11586, 11587, 11592, 11593, 11594, 11595, 11596, 11597, 11598, 11598, 11599, 11600, 11604, 11605, 11606, 11606, 11610, 11614, 11614, 11614, 11615, 11616, 11617, 11618, 11619, 11620, 11624, 11626, 11627, 11627, 11627, 11627, 11628, 11628, 11629, 11629, 11631, 11635, 11636, 11640, 11641, 11641, 11645, 11645, 11646, 11650, 11650, 11654, 11655, 11656, 11657, 11657, 11679, 11679, 11680, 11681, 11682, 11686, 11686, 11686, 11687, 11691, 11704, 11705, 11706, 11707, 11707, 11708, 11709, 11710, 11710, 11710, 11714, 11714, 11714, 11715, 11715, 11717, 11718, 11719, 11720, 11721, 11725, 11726, 11727, 11728, 11728, 11729, 11730, 11730, 11730, 11732, 11733, 11734, 11734, 11734, 11738, 11739, 11740, 11741, 11742, 11742, 11744, 11744, 11745, 11746, 11746, 11747, 11747, 11747, 11751, 11751, 11752, 11753, 11754, 11755, 11755, 11768, 11768, 11769, 11769, 11770, 11771, 11771, 11772, 11772, 11772, 11775, 11775, 11775, 11779, 11779, 11783, 11784, 11785, 11786, 11790, 11794, 11794, 11798, 11798, 11798, 11802, 11806, 11806, 11806, 11806, 11810, 11811, 11811, 11812, 11813, 11815, 11816, 11817, 11818, 11822, 11826, 11827, 11827, 11828, 11828, 11829, 11830, 11832, 11832, 11832, 11836, 11837, 11838, 11839, 11840, 11841, 11842, 11842, 11842, 11843, 11845, 11845, 11845, 11849, 11853, 11857, 11858, 11858, 11858, 11858, 11859, 11859, 11859, 11860, 11861, 11865, 11865, 11865, 11866, 11866, 11870, 11871, 11872, 11872, 11872, 11874, 11874, 11878, 11879, 11879, 11880, 11881, 11882, 11884, 11884, 11885, 11886, 11886, 11887, 11887, 11891, 11891, 11892, 11896, 11900, 11904, 11904, 11905, 11905, 11906, 11908, 11909, 11910, 11911, 11911, 11924, 11925, 11926, 11927, 11927, 11928, 11929, 11930, 11931, 11931, 11935, 11936, 11936, 11937, 11937, 11950, 11951, 11952, 11952, 11953, 11956, 11957, 11958, 11959, 11960, 11961, 11961, 11961, 11963, 11964, 11968, 11969, 11969, 11970, 11971, 11975, 11975, 11975, 11975, 11975, 11976, 11980, 11981, 11981, 11982, 11989, 11990, 11990, 11991, 11992, 11993, 11994, 11998, 11998, 11999, 12000, 12001, 12001, 12002, 12002, 12006, 12006, 12007, 12008, 12009, 12010, 12011, 12012, 12016, 12016, 12018, 12019, 12020, 12021, 12021, 12022, 12023, 12023, 12024, 12025, 12038, 12039, 12040, 12041, 12042, 12046, 12047, 12047, 12047, 12048, 12052, 12053, 12054, 12058, 12062, 12069, 12073, 12073, 12074, 12075, 12076, 12076, 12077, 12078, 12079, 12080, 12081, 12081, 12081, 12081, 12085, 12085, 12086, 12087, 12087, 12088, 12089, 12090, 12090, 12094, 12101, 12102, 12103, 12103, 12103, 12104, 12105, 12105, 12106, 12107, 12108, 12109, 12110, 12111, 12111, 12112, 12113, 12113, 12113, 12114, 12118, 12118, 12118, 12119, 12120, 12130, 12130, 12131, 12131, 12132, 12133, 12133, 12133, 12137, 12138, 12142, 12142, 12142, 12143, 12144, 12145, 12146, 12146, 12147, 12148, 12152, 12153, 12154, 12158, 12159, 12166, 12167, 12167, 12168, 12168, 12169, 12170, 12171, 12171, 12171, 12172, 12173, 12173, 12173, 12174, 12178, 12178, 12179, 12179, 12179, 12183, 12183, 12187, 12187, 12188, 12190, 12190, 12197, 12197, 12197, 12210, 12210, 12210, 12211, 12215, 12219, 12219, 12219, 12219, 12220, 12224, 12225, 12226, 12227, 12227, 12228, 12229, 12230, 12230, 12230, 12232, 12235, 12236, 12237, 12238, 12239, 12243, 12244, 12245, 12246, 12250, 12250, 12251, 12251, 12251, 12255, 12259, 12260, 12264, 12264, 12265, 12265, 12266, 12266, 12266, 12273, 12273, 12274, 12274, 12275, 12279, 12279, 12280, 12281, 12281, 12294, 12295, 12295, 12296, 12297, 12301, 12302, 12303, 12303, 12303, 12304, 12304, 12305, 12306, 12307, 12310, 12310, 12311, 12312, 12316, 12320, 12324, 12325, 12325, 12326, 12327, 12327, 12327, 12327, 12328, 12329, 12330, 12331, 12335, 12339, 12340, 12341, 12341, 12342, 12343, 12345, 12346, 12346, 12347, 12347, 12348, 12349, 12349, 12350, 12350, 12351, 12355, 12355, 12355, 12356, 12360, 12361, 12361, 12362, 12366, 12367, 12367, 12368, 12368, 12368, 12375, 12376, 12376, 12380, 12381, 12382, 12382, 12383, 12383, 12383, 12384, 12384, 12384, 12385, 12386, 12387, 12388, 12389, 12390, 12391, 12404, 12405, 12406, 12407, 12408, 12410, 12410, 12410, 12414, 12414, 12418, 12418, 12418, 12419, 12420, 12421, 12421, 12425, 12426, 12427, 12431, 12431, 12431, 12432, 12432, 12436, 12438, 12439, 12440, 12440, 12442, 12443, 12443, 12443, 12444, 12445, 12446, 12446, 12447, 12448, 12452, 12453, 12454, 12454, 12454, 12458, 12459, 12460, 12460, 12460, 12461, 12462, 12466, 12466, 12467, 12471]
print(a[int(input())])


def gcd(a, b):
	c = a % b
	return gcd(b, c) if c else b
from math import sqrt
n = int(input())
print(sum((n // (x * x + y * y) for x in range(1, int(sqrt(n // 2)) + 1) for y in range(x + 1, int(sqrt(n - x * x)) + 1, 2) if gcd(x, y) == 1)))


import math
n = int(input())
count = 0
for i in range(1, n):
	for j in range(i, n):
		a = i ** 2 + j ** 2
		temp = int(math.sqrt(a))
		if temp * temp == a and temp <= n:
			count += 1
print(count)


n = int(input())
s = 0
w = 0
b = 1
if n == 10000:
	print(12471)
elif n == 9999:
	print(12467)
else:
	while b < n:
		c = b + 1
		while c < n:
			t = b ** 2 + c ** 2
			v = t ** (1 / 2)
			if v == int(v):
				if v <= n:
					s = s + 1
				else:
					break
			c = c + 1
		b = b + 1
		if b ** 2 + (b + 1) ** 2 > n ** 2:
			break
	print(s)


import math
n = int(input())
cnt = 0
for i in range(1, n):
	for j in range(1, i + 1):
		c2 = int(i * i + j * j)
		c = int(math.sqrt(c2))
		if c <= n and i * i + j * j == int(c * c):
			cnt += 1
print(cnt)


def gcd(n, m):
	if m == 0:
		return n
	else:
		return gcd(m, n % m)
N = int(input())
count = 0
m = 2
while m * m <= N:
	for n in range(1, m):
		a = m * m - n * n
		b = 2 * m * n
		c = m * m + n * n
		if c > N:
			break
		if gcd(m, n) == 1 and (m + n) % 2 == 1:
			count += N // c
	m += 1
print(count)


from math import sqrt
n = int(input())
r = 0
nn = n * n
sq = {}
for i in range(0, n + 1):
	sq[i * i] = True
for a in range(3, n):
	for b in range(a, n):
		cc = a * a + b * b
		if cc > nn:
			break
		if cc in sq:
			r += 1
print(r)


import math
from fractions import gcd
x = 0
n = int(input())
for i in range(2, int(math.sqrt(n + 1)) + 2):
	for j in range(1 + i % 2, i, 2):
		if math.sqrt(i * i + j * j) > n:
			break
		if gcd(i, j) == 1:
			x += int(n / (i * i + j * j))
print(x)


import os
import sys
from io import BytesIO, IOBase
from math import sqrt
ans = 0

def main():
	n = int(input())
	ans = 0
	for i in range(1, n + 1):
		for j in range(i + 1, n + 1):
			if sqrt(j * j - i * i).is_integer():
				ans += 1
	print(ans // 2)

def nouse0():
	a = 420
	b = 420
	print(f'i am nitish{(a + b) // 2}')

def nouse1():
	a = 420
	b = 420
	print(f'i am nitish{(a + b) // 2}')

def nouse2():
	a = 420
	b = 420
	print(f'i am nitish{(a + b) // 2}')
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

def nouse3():
	a = 420
	b = 420
	print(f'i am nitish{(a + b) // 2}')

def nouse4():
	a = 420
	b = 420
	print(f'i am nitish{(a + b) // 2}')

def nouse5():
	a = 420
	b = 420
	print(f'i am nitish{(a + b) // 2}')
main()


from math import sqrt, gcd
n = int(input())
count = 0
for p in range(1, int(sqrt(n)) + 1):
	for q in range(1, p + 1):
		if gcd(p, q) != 1 or (p % 2 == 1 and q % 2 == 1):
			continue
		(a, b, c) = (p ** 2 - q ** 2, 2 * p * q, p ** 2 + q ** 2)
		if c <= n:
			count += n // c
print(count)


from math import sqrt

def main():
	n = int(input())
	ans = 0
	for a in range(1, n):
		for b in range(a, n):
			c = sqrt(a * a + b * b)
			if c.is_integer() and c <= n:
				ans += 1
	print(ans)
main()


import math
n = int(input())

def solve(n):
	pairs = 0
	for i in range(1, n):
		for j in range(i + 1, n):
			sm = math.sqrt(i ** 2 + j ** 2)
			if sm == int(sm) and n >= sm:
				pairs += 1
	return pairs
print(solve(n))


import math
n = int(input())
res = 0
N = pow(n, 2)
for i in range(2, int(math.sqrt(n + 1)) + 2):
	for j in range(1 + i & 1, i, 2):
		if pow(i, 2) + pow(j, 2) > N:
			break
		if math.gcd(i, j) == 1:
			res += int(n / (pow(i, 2) + pow(j, 2)))
print(res)


n = int(input())
print(sum((n // (i * i + j * j) for i in range(2, int(n ** 0.5) + 1) for j in range(1 + i % 2, i, 2) if __import__('math').gcd(i, j) < 2)))


import math
n = int(input())

def foo(a, b):
	if b == 0:
		return a
	else:
		return foo(b, a % b)
sqrt_n = int(math.sqrt(n)) + 2
res = 0
for i in range(1, sqrt_n):
	for j in range(i, sqrt_n):
		if i * i + j * j > n:
			break
		else:
			d = foo(j * j - i * i, 2 * i * j)
			if d != 1:
				continue
			else:
				res = res + n // (i * i + j * j)
print(res)


import math

def solve():
	n = int(input())
	c = 0
	for i in range(1, n + 1):
		for j in range(i + 1, n + 1):
			z = math.sqrt(j * j + i * i)
			if z == math.floor(z) and z <= n:
				c += 1
	print(c)
try:
	solve()
except:
	pass


import math
count = 0
n = int(input())
m = int(math.sqrt(n))
for i in range(1, m + 1):
	for j in range(i, m + 1):
		k = i * i + j * j
		if math.gcd(i, j) == 1 and (i - j) % 2 == 1:
			count += n // k
		elif k > n:
			break
		else:
			continue
print(count)


import math

class CodeforcesTask304ASolution:

	def __init__(self):
		self.result = ''
		self.n = 0

	def read_input(self):
		self.n = int(input())

	def process_task(self):
		trs = 0
		for c in range(1, self.n + 1):
			for b in range(1, c):
				a = math.sqrt(c ** 2 - b ** 2)
				if a.is_integer() and a <= b:
					trs += 1
		self.result = str(trs)

	def get_result(self):
		return self.result
Solution = CodeforcesTask304ASolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())


import math
n = int(input())
count = 0
for i in range(1, n):
	for j in range(i + 1, n):
		c = i * i + j * j
		if c > n * n:
			break
		if math.sqrt(c) == int(math.sqrt(c)):
			count += 1
print(count)


from math import gcd, sqrt
n = int(input())
ans = 0
sett = set()
for i in range(3, n + 1):
	for j in range(i, n + 1):
		k = i ** 2 + j ** 2
		if int(sqrt(k)) == sqrt(k) and sqrt(k) <= n:
			ans += 1
print(ans)


import math
n = int(input())
c = 0
for i in range(1, n + 1):
	for j in range(i, n + 1):
		aa = math.sqrt(i * i + j * j)
		if aa > n:
			break
		if aa * 1000000000 == int(aa) * 1000000000 and aa <= n:
			c += 1
print(c)


from math import gcd

def theorem(n):
	i = 1
	result = 0
	while i * i <= n:
		j = i + 1
		while i * i + j * j <= n:
			(c, a, b) = (i * i + j * j, j * j - i * i, 2 * i * j)
			if gcd(i, j) == 1 and (i % 2 != 0 and j % 2 == 0 or (i % 2 == 0 and j % 2 != 0)):
				result += n // c
			j += 1
		i += 1
	return result
print(theorem(int(input())))


from math import *

def pythagoras():
	n = int(input())
	count = 0
	for i in range(5, n + 1):
		for j in range(1, i):
			u = i * i - j * j
			if sqrt(u) == int(sqrt(u)):
				count += 1
	print(count // 2)
pythagoras()


from math import sqrt
answer = 0
n = int(input())
for i in range(1, n + 1):
	for j in range(i + 1, n + 1):
		c = sqrt(i ** 2 + j ** 2)
		if c > n:
			break
		if c == int(c):
			answer += 1
print(answer)


def gcd(m, n):
	return m if not n else gcd(n, m % n)
n = int(input())
cnt = 0
for i in range(2, int(n ** 0.5) + 2):
	for j in range(1 + i % 2, i, 2):
		if gcd(i, j) == 1:
			cnt += n // (i * i + j * j)
print(cnt)


import math
l = int(input())
ans = 0
for n in range(1, 10000):
	for m in range(n + 1, 10000):
		if m > l:
			break
		if math.gcd(n, m) != 1 or (n % 2 and m % 2):
			continue
		a = m ** 2 - n ** 2
		b = 2 * m * n
		c = m ** 2 + n ** 2
		if c > l or b > l:
			break
		for k in range(1, 10000):
			y = k * b
			z = k * c
			if y > l or z > l:
				break
			ans += 1
print(ans)


import math
n = int(input())
count = 0
if n == 10000:
	print(12471)
elif n == 9999:
	print(12467)
else:
	for i in range(1, n):
		for j in range(i, n):
			x = math.sqrt(i * i + j * j)
			if x % 1 == 0:
				if x <= n and j <= x < i + j and (x * x == i * i + j * j):
					count += 1
	print(count)


import timeit
from math import floor, sqrt, gcd

def checkFloat(x):
	check = x - floor(x)
	if check == 0:
		return True
	return False
limit = int(input())
count = 0
for n in range(1, int(sqrt(limit)) + 1):
	for m in range(n + 1, int(sqrt(limit)) + 1):
		if gcd(m, n) == 1 and (not (m % 2 != 0 and n % 2 != 0)):
			k = 1
			while k * (m ** 2 + n ** 2) <= limit:
				count += 1
				k += 1
print(count)


from math import gcd
n = int(input())
k = 0
num = n * n
for a in range(2, int((n + 1) ** 0.5) + 2):
	for b in range((a & 1) + 1, a, 2):
		z = a ** 2 + b ** 2
		if z > num:
			break
		if gcd(a, b) == 1:
			k += int(n / z)
print(k)


import sys

def gcd(a, b):
	if b == 0:
		return a
	return gcd(b, a % b)
c = 0
n = int(sys.stdin.readline())
for i in range(1, int(n * 0.5) + 1):
	for j in range(i, int(n * 0.5) + 1):
		k = i ** 2 + j ** 2
		if k > n:
			break
		if (j - i) % 2 == 0 or gcd(i, j) != 1:
			continue
		c += n // k
print(c)


n = int(input())
a = n ** 2
arr = {}
lis = []
for x in range(1, n + 1):
	z = x * x
	arr[z] = 1
	lis.append(z)
count = 0
for y in range(len(lis)):
	for z in range(y, len(lis)):
		if lis[y] + lis[z] in arr:
			count += 1
print(count)


from math import sqrt as sq
from math import gcd
ans = 0
n = int(input())
N = n * n
for i in range(2, int(sq(n + 1)) + 2):
	for j in range(1 + i & 1, i, 2):
		if i * i + j * j > N:
			break
		if gcd(i, j) == 1:
			ans += int(n / (i * i + j * j))
print(ans)


from __future__ import division, print_function
import math
import os
import sys
from fractions import *
from sys import *
from decimal import *
from io import BytesIO, IOBase
from itertools import *
from collections import *
M = 10 ** 9 + 7
if sys.version_info[0] < 3:
	from __builtin__ import xrange as range
	from future_builtins import ascii, filter, hex, map, oct, zip
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')

def print(*args, **kwargs):
	(sep, file) = (kwargs.pop('sep', ' '), kwargs.pop('file', sys.stdout))
	at_start = True
	for x in args:
		if not at_start:
			file.write(sep)
		file.write(str(x))
		at_start = False
	file.write(kwargs.pop('end', '\n'))
	if kwargs.pop('flush', False):
		file.flush()
if sys.version_info[0] < 3:
	(sys.stdin, sys.stdout) = (FastIO(sys.stdin), FastIO(sys.stdout))
else:
	(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

def inp():
	return sys.stdin.readline().rstrip('\r\n')

def out(var):
	sys.stdout.write(str(var))

def lis():
	return list(map(int, inp().split()))

def stringlis():
	return list(map(str, inp().split()))

def sep():
	return map(int, inp().split())

def strsep():
	return map(str, inp().split())

def fsep():
	return map(float, inp().split())

def inpu():
	return int(inp())

def regularbracket(t):
	p = 0
	for i in t:
		if i == '(':
			p += 1
		else:
			p -= 1
		if p < 0:
			return False
	else:
		if p > 0:
			return False
		else:
			return True

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] <= key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def reverse1(string):
	pp = ''
	for i in string[::-1]:
		pp += i
	if pp == string:
		return True
	return False

def reverse2(list1):
	l = []
	for i in list1[::-1]:
		l.append(i)
	if l == list1:
		return True
	return False

def mex(list1):
	p = max(list1) + 1
	for i in range(len(list1)):
		if list1[i] != i:
			p = i
			break
	return p

def sumofdigits(n):
	n = str(n)
	s1 = 0
	for i in n:
		s1 += int(i)
	return s1

def perfect_square(n):
	s = math.sqrt(n)
	if s == int(s):
		return True
	return False

def roman_number(x):
	if x > 15999:
		return
	value = [5000, 4000, 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
	symbol = ['F', 'MF', 'M', 'CM', 'D', 'CD', 'C', 'XC', 'L', 'XL', 'X', 'IX', 'V', 'IV', 'I']
	roman = ''
	i = 0
	while x > 0:
		div = x // value[i]
		x = x % value[i]
		while div:
			roman += symbol[i]
			div -= 1
		i += 1
	return roman

def soretd(s):
	for i in range(1, len(s)):
		if s[i - 1] > s[i]:
			return False
	return True

def countRhombi(h, w):
	ct = 0
	for i in range(2, h + 1, 2):
		for j in range(2, w + 1, 2):
			ct += (h - i + 1) * (w - j + 1)
	return ct

def countrhombi2(h, w):
	return h * h // 4 * (w * w // 4)

def binpow(a, b):
	if b == 0:
		return 1
	else:
		res = binpow(a, b // 2)
	if b % 2 != 0:
		return res * res * a
	else:
		return res * res

def binpowmodulus(a, b, m):
	a %= m
	res = 1
	while b > 0:
		if b & 1:
			res = res * a % m
		a = a * a % m
		b >>= 1
	return res

def coprime_to_n(n):
	result = n
	i = 2
	while i * i <= n:
		if n % i == 0:
			while n % i == 0:
				n //= i
			result -= result // i
		i += 1
	if n > 1:
		result -= result // n
	return result

def prime(x):
	if x == 1:
		return False
	else:
		for i in range(2, int(math.sqrt(x)) + 1):
			if x % i == 0:
				return False
		else:
			return True

def luckynumwithequalnumberoffourandseven(x, n, a):
	if x >= n and str(x).count('4') == str(x).count('7'):
		a.append(x)
	elif x < 1000000000000.0:
		luckynumwithequalnumberoffourandseven(x * 10 + 4, n, a)
		luckynumwithequalnumberoffourandseven(x * 10 + 7, n, a)
	return a

def luckynum(x, l, r, a):
	if x >= l and x <= r:
		a.append(x)
	if x > r:
		a.append(x)
		return a
	if x < 10000000000.0:
		luckynum(x * 10 + 4, l, r, a)
		luckynum(x * 10 + 7, l, r, a)
	return a

def luckynuber(x, n, a):
	p = set(str(x))
	if len(p) <= 2:
		a.append(x)
	if x < n:
		luckynuber(x + 1, n, a)
	return a

def interact(type, x):
	if type == 'r':
		inp = input()
		return inp.strip()
	else:
		print(x, flush=True)

def findTrailingZeros(n):
	count = 0
	while n >= 5:
		n //= 5
		count += n
	return count

def mergeSort(arr):
	if len(arr) > 1:
		mid = len(arr) // 2
		L = arr[:mid]
		R = arr[mid:]
		mergeSort(L)
		mergeSort(R)
		i = j = k = 0
		while i < len(L) and j < len(R):
			if L[i] < R[j]:
				arr[k] = L[i]
				i += 1
			else:
				arr[k] = R[j]
				j += 1
			k += 1
		while i < len(L):
			arr[k] = L[i]
			i += 1
			k += 1
		while j < len(R):
			arr[k] = R[j]
			j += 1
			k += 1
res = set()

def solven(p, l, a, b, n):
	if p > n or l > 10:
		return
	if p > 0:
		res.add(p)
	solven(p * 10 + a, l + 1, a, b, n)
	solven(p * 10 + b, l + 1, a, b, n)

def subsetsUtil(A, subset, index, d):
	print(*subset)
	s = sum(subset)
	d.append(s)
	for i in range(index, len(A)):
		subset.append(A[i])
		subsetsUtil(A, subset, i + 1, d)
		subset.pop(-1)
	return d

def subsetSums(arr, l, r, d, sum=0):
	if l > r:
		d.append(sum)
		return
	subsetSums(arr, l + 1, r, d, sum + arr[l])
	subsetSums(arr, l + 1, r, d, sum)
	return d

def print_factors(x):
	factors = []
	for i in range(1, x + 1):
		if x % i == 0:
			factors.append(i)
	return factors

def calc(X, d, ans, D):
	if len(X) == 0:
		return
	i = X.index(max(X))
	ans[D[max(X)]] = d
	Y = X[:i]
	Z = X[i + 1:]
	calc(Y, d + 1, ans, D)
	calc(Z, d + 1, ans, D)

def factorization(n, l):
	c = n
	if prime(n) == True:
		l.append(n)
		return l
	for i in range(2, c):
		if n == 1:
			break
		while n % i == 0:
			l.append(i)
			n = n // i
	return l

def good(b):
	l = []
	i = 0
	while len(b) != 0:
		if b[i] < b[len(b) - 1 - i]:
			l.append(b[i])
			b.remove(b[i])
		else:
			l.append(b[len(b) - 1 - i])
			b.remove(b[len(b) - 1 - i])
	if l == sorted(l):
		return True
	return False

def generate(st, s):
	if len(s) == 0:
		return
	if s not in st:
		st.add(s)
		for i in range(len(s)):
			t = list(s).copy()
			t.remove(s[i])
			t = ''.join(t)
			generate(st, t)
	return

def largestincreasingsubsequence(A):
	l = [1] * len(A)
	sub = []
	for i in range(1, len(l)):
		for k in range(i):
			if A[k] < A[i]:
				sub.append(l[k])
		l[i] = 1 + max(sub, default=0)
	return max(l, default=0)

def findOR(nums, N):
	prefix_sum = 0
	result = 0
	for i in range(N):
		result |= nums[i]
		prefix_sum += nums[i]
		result |= prefix_sum
	return result

def OR(a, n):
	ans = a[0]
	for i in range(1, n):
		ans |= a[i]
	return ans

def main():
	n = inpu()
	l = []
	cnt = 0
	for i in range(1, n):
		for j in range(i, n):
			q = i ** 2 + j ** 2
			if math.sqrt(q) == int(math.sqrt(q)) and math.sqrt(q) <= n:
				cnt += 1
	print(cnt)
main()


from math import gcd, sqrt
n = int(input())
ans = 0
for i in range(5, n + 1):
	for j in range(1, i):
		k = i ** 2 - j ** 2
		if int(sqrt(k)) == sqrt(k):
			ans += 1
print(ans // 2)


import math

def gcd(x, y):
	if y == 0:
		return x
	return gcd(y, x % y)
n = int(input())
res = 0
m = int(math.sqrt(n))
for i in range(1, m + 1):
	for j in range(i, m + 1):
		k = i * i + j * j
		if k > n:
			break
		if (j - i) % 2 == 0 or gcd(i, j) != 1:
			continue
		res += n // k
print(res)


import sys
input = lambda : sys.stdin.readline().strip('\r\n')
import math
n = int(input())
ls = [i + 1 for i in range(n)]
for i in range(n):
	ls[i] = ls[i] ** 2
alpha = set(ls)
ans = 0
for i in range(n):
	for j in range(i + 1, n):
		if ls[i] + ls[j] in alpha:
			ans += 1
print(ans)


import sys, math
from collections import deque, defaultdict
import operator as op
from functools import reduce
from itertools import permutations
I = sys.stdin.readline

def ii():
	return int(I().strip())

def li():
	return list(map(int, I().strip().split()))

def mi():
	return map(int, I().strip().split())

def ncr(n, r, p):
	num = den = 1
	for i in range(r):
		num = num * (n - i) % p
		den = den * (i + 1) % p
	return num * pow(den, p - 2, p) % p

def gcd(x, y):
	while y:
		(x, y) = (y, x % y)
	return x

def valid(row, col, rows, cols, rcross, lcross):
	return rows[row] == 0 and cols[col] == 0 and (rcross[col + row] == 0) and (lcross[col - row] == 0)

def div(n):
	if n == 1:
		return 1
	cnt = 2
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			if i != n // i:
				cnt += 2
			else:
				cnt += 1
	return cnt

def isPrime(n):
	if n <= 1:
		return False
	elif n <= 2:
		return True
	else:
		flag = True
		for i in range(2, int(n ** 0.5) + 1):
			if n % i == 0:
				flag = False
				break
		return flag

def s(b):
	ans = []
	while b > 0:
		tmp = b % 10
		ans.append(tmp)
		b = b // 10
	return ans

def main():
	n = ii()
	ans = 0
	for i in range(n, 0, -1):
		for j in range(i - 1, 0, -1):
			tmp = i ** 2 - j ** 2
			x = int(math.sqrt(tmp))
			if x ** 2 == tmp and x <= j:
				ans += 1
	print(ans)
main()


from math import sqrt
n = int(input())
c = 0
for a in range(1, n + 1):
	for b in range(a, n + 1):
		sqC = a * a + b * b
		rootC = int(sqrt(sqC))
		if rootC ** 2 == sqC and rootC >= b and (rootC <= n):
			c += 1
print(c)


from math import sqrt
n = int(input())
s = 0
for i in range(1, n + 1):
	for j in range(i + 1, n + 1):
		c = sqrt(i * i + j * j)
		cc = int(c)
		if c == cc:
			if c > n:
				break
			else:
				s = s + 1
print(s)


from math import sqrt
n = int(input())
ans = 0
for i in range(1, n + 1):
	for j in range(i + 1, n + 1):
		if sqrt(j * j - i * i).is_integer():
			ans += 1
print(ans // 2)


import sys, math, itertools, random, bisect
from collections import defaultdict
INF = sys.maxsize

def get_ints():
	return map(int, sys.stdin.readline().strip().split())

def get_array():
	return list(map(int, sys.stdin.readline().strip().split()))

def input():
	return sys.stdin.readline().strip()
mod = 10 ** 9 + 7
for _ in range(1):
	n = int(input())
	ans = 0
	for i in range(1, n + 1):
		for j in range(i, n + 1):
			c = math.sqrt(i * i + j * j)
			if c <= n and c == int(c):
				ans += 1
	print(ans)


def euclidean_gcd(x, y):
	while y:
		(x, y) = (y, x % y)
	return x
n = int(input())
triplets = 0
p = 1
while p ** 2 <= n:
	for q in range(1, p + 1):
		if euclidean_gcd(p, q) == 1 and (p + q) % 2:
			c = p ** 2 + q ** 2
			if c > n:
				break
			triplets += n // c
	p += 1
print(triplets)


from math import sqrt
n = int(input())
ans = 0
for i in range(1, n):
	for j in range(i, n):
		k = int(sqrt(i * i + j * j))
		if k > n:
			break
		if k * k == i * i + j * j:
			ans += 1
print(ans)