Find the number of positive integral solutions for the equations 
$\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{N!}$

Input Format 

An integer N   

Output Format 

The number of positive integral solutions for the above equation modulo 1000007  

Constraints 

$1\leq N\leq10^6$  

Sample Input00  

1  

Sample Output00  

1

Sample Input01

32327

Sample Output01

656502  

Sample Input02

40921

Sample Output02

686720

Difficulty: MEDIUM
Tags: Number theory

Starter code:

Solutions:
primes = []
a = range(2, 1000001)
while len(a) > 0:
	if a[0] < 1000:
		primes.append(a[0])
		a = [i for i in a if i % a[0] != 0]
	else:
		break
primes = primes + a
n = int(input())
m = 1
for p in primes:
	b = 0
	nn = n // p
	while nn > 0:
		b += nn
		nn //= p
	m *= 1 + 2 * b
	m %= 1000007
print(m)


n = int(input())
pd = {1: 1}
for i in range(2, n // 2 + 1):
	for j in range(2, n // i + 1):
		pd[i * j] = 1
p = [i for i in range(1, n + 1) if pd.get(i, 0) == 0]
rt = 1
for i in p:
	ip = i
	m = n // ip
	pt = m
	while m != 0:
		ip *= i
		m = n // ip
		pt += m
	rt *= (2 * pt + 1) % 1000007
	rt %= 1000007
print(rt)


import sys
N = int(sys.stdin.readline())
primes = {}
sieve = list(range(N + 1))
n = 2
while n < N + 1:
	if sieve[n] > 1:
		primes[n] = 1
		k = 2
		while k * n < N + 1:
			while sieve[k * n] % n == 0:
				sieve[k * n] //= n
				primes[n] += 1
			k += 1
	n += 1
for k in primes:
	primes[k] *= 2
tau = 1
for (k, v) in primes.items():
	tau *= v + 1
print(tau % 1000007)


def prime(a):
	h = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
	for i in h:
		if i < a // 2 + 1:
			if a % i == 0:
				return 0
		else:
			break
	return 1
a = int(input())
v = []
for i in range(2, a + 1):
	if prime(i):
		v.append(i)
s = []
for i in v:
	d = a
	count = 0
	while d // i:
		count += d // i
		d = d // i
	s.append(2 * count + 1)
res = 1
for i in s:
	res *= i
	if res > 1000007:
		res %= 1000007
print(res)


def primes(end):
	p = [2, 3]
	for i in range(5, end + 1):
		for j in p:
			if j * j > i:
				p.append(i)
				break
			if i % j == 0:
				break
	return p
n = int(input())
p = primes(n)
fact = []
for i in p:
	count = 0
	curr = i
	while curr <= n:
		count += n // curr
		curr *= i
	fact.append(count)
prod = 1
for i in fact:
	prod *= 2 * i + 1
	prod %= 1000007
prod %= 1000007
print(prod)


def isprime(n):
	n *= 1.0
	if n % 2 == 0 and n != 2 or (n % 3 == 0 and n != 3):
		return False
	for b in range(1, int((n ** 0.5 + 1) / 6.0 + 1)):
		if n % (6 * b - 1) == 0:
			return False
		if n % (6 * b + 1) == 0:
			return False
	return True

def muliplicity(i, N):
	count = 0
	duplicate = N
	while duplicate != 0:
		count += int(duplicate / i)
		duplicate = int(duplicate / i)
	return 2 * count + 1
N = int(input())
sol = 1
for i in range(2, N + 1):
	if isprime(i):
		m = muliplicity(i, N)
		sol = sol * m
print(sol % 1000007)


def multiplicity(n, p):
	i = 1
	c = 1
	while n // p ** i != 0:
		c += n // p ** i
		i += 1
	return (c - 1) * 2 + 1

def isPrime(n):
	i = 5
	w = 2
	while i * i <= n:
		if n % i == 0:
			return False
		i += w
		w = 6 - w
	return True
n = int(input())
c = multiplicity(n, 2)
c *= multiplicity(n, 3)
c %= 1000007
i = 5
w = 2
while i <= n:
	if isPrime(i):
		c *= multiplicity(n, i)
		c %= 1000007
	i += w
	w = 6 - w
print(c)


M = int(1000000.0 + 7)

def sieve(n):
	cand = [True] * (n + 1)
	for i in range(2, n + 1):
		if cand[i]:
			for j in range(2 * i, n + 1, i):
				cand[j] = False
	return [i for i in range(2, n + 1) if cand[i]]
primes = sieve(int(1000000.0))

def solve(n):
	rv = 1
	for p in primes:
		if p > n:
			break
		temp = n
		factors = 0
		while temp > 0:
			temp //= p
			factors += temp
		rv = rv * (factors * 2 + 1) % M
	return rv
print(solve(int(input())))


def getPrimesUnder(n):
	if n < 3:
		return []
	r = [2]
	n2 = n // 2
	l = list((True for i in range(0, n2)))
	l[0] = False
	for i in range(1, n2):
		if l[i]:
			r.append(2 * i + 1)
			for m in range(2 * i * (i + 1), n2, 2 * i + 1):
				l[m] = False
	return r

def getPrimeMultiplicity(n):
	Ps = getPrimesUnder(n + 1)
	mul = []
	for p in Ps:
		(c, r) = (0, n)
		while r > 1:
			r //= p
			c += r
		mul.append((p, c))
	return mul
N = int(input())
mul = getPrimeMultiplicity(N)
count = 1
for m in mul:
	count *= 2 * m[1] + 1
	count %= 1000007
print(count)


n = int(input())
primes = [1 for i in range(n + 1)]
m = int(pow(n, 0.5)) + 1
for i in range(2, m):
	if primes[i] == 1:
		for j in range(i, n):
			if i * j > n:
				break
			else:
				primes[i * j] = 0
total = 1
for i in range(2, n + 1):
	if primes[i] == 1:
		tmp = n
		e = 0
		while tmp != 0:
			tmp = int(tmp / i)
			e += tmp
		total *= 2 * e + 1
print(total % 1000007)


q = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 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979037, 979061, 979063, 979093, 979103, 979109, 979117, 979159, 979163, 979171, 979177, 979189, 979201, 979207, 979211, 979219, 979229, 979261, 979273, 979283, 979291, 979313, 979327, 979333, 979337, 979343, 979361, 979369, 979373, 979379, 979403, 979423, 979439, 979457, 979471, 979481, 979519, 979529, 979541, 979543, 979549, 979553, 979567, 979651, 979691, 979709, 979717, 979747, 979757, 979787, 979807, 979819, 979831, 979873, 979883, 979889, 979907, 979919, 979921, 979949, 979969, 979987, 980027, 980047, 980069, 980071, 980081, 980107, 980117, 980131, 980137, 980149, 980159, 980173, 980179, 980197, 980219, 980249, 980261, 980293, 980299, 980321, 980327, 980363, 980377, 980393, 980401, 980417, 980423, 980431, 980449, 980459, 980471, 980489, 980491, 980503, 980549, 980557, 980579, 980587, 980591, 980593, 980599, 980621, 980641, 980677, 980687, 980689, 980711, 980717, 980719, 980729, 980731, 980773, 980801, 980803, 980827, 980831, 980851, 980887, 980893, 980897, 980899, 980909, 980911, 980921, 980957, 980963, 980999, 981011, 981017, 981023, 981037, 981049, 981061, 981067, 981073, 981077, 981091, 981133, 981137, 981139, 981151, 981173, 981187, 981199, 981209, 981221, 981241, 981263, 981271, 981283, 981287, 981289, 981301, 981311, 981319, 981373, 981377, 981391, 981397, 981419, 981437, 981439, 981443, 981451, 981467, 981473, 981481, 981493, 981517, 981523, 981527, 981569, 981577, 981587, 981599, 981601, 981623, 981637, 981653, 981683, 981691, 981697, 981703, 981707, 981713, 981731, 981769, 981797, 981809, 981811, 981817, 981823, 981887, 981889, 981913, 981919, 981941, 981947, 981949, 981961, 981979, 981983, 982021, 982057, 982061, 982063, 982067, 982087, 982097, 982099, 982103, 982117, 982133, 982147, 982151, 982171, 982183, 982187, 982211, 982213, 982217, 982231, 982271, 982273, 982301, 982321, 982337, 982339, 982343, 982351, 982363, 982381, 982393, 982403, 982453, 982489, 982493, 982559, 982571, 982573, 982577, 982589, 982603, 982613, 982621, 982633, 982643, 982687, 982693, 982697, 982703, 982741, 982759, 982769, 982777, 982783, 982789, 982801, 982819, 982829, 982841, 982843, 982847, 982867, 982871, 982903, 982909, 982931, 982939, 982967, 982973, 982981, 983063, 983069, 983083, 983113, 983119, 983123, 983131, 983141, 983149, 983153, 983173, 983179, 983189, 983197, 983209, 983233, 983239, 983243, 983261, 983267, 983299, 983317, 983327, 983329, 983347, 983363, 983371, 983377, 983407, 983429, 983431, 983441, 983443, 983447, 983449, 983461, 983491, 983513, 983519, 983527, 983531, 983533, 983557, 983579, 983581, 983597, 983617, 983659, 983699, 983701, 983737, 983771, 983777, 983783, 983789, 983791, 983803, 983809, 983813, 983819, 983849, 983861, 983863, 983881, 983911, 983923, 983929, 983951, 983987, 983993, 984007, 984017, 984037, 984047, 984059, 984083, 984091, 984119, 984121, 984127, 984149, 984167, 984199, 984211, 984241, 984253, 984299, 984301, 984307, 984323, 984329, 984337, 984341, 984349, 984353, 984359, 984367, 984383, 984391, 984397, 984407, 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987979, 987983, 987991, 987997, 988007, 988021, 988033, 988051, 988061, 988067, 988069, 988093, 988109, 988111, 988129, 988147, 988157, 988199, 988213, 988217, 988219, 988231, 988237, 988243, 988271, 988279, 988297, 988313, 988319, 988321, 988343, 988357, 988367, 988409, 988417, 988439, 988453, 988459, 988483, 988489, 988501, 988511, 988541, 988549, 988571, 988577, 988579, 988583, 988591, 988607, 988643, 988649, 988651, 988661, 988681, 988693, 988711, 988727, 988733, 988759, 988763, 988783, 988789, 988829, 988837, 988849, 988859, 988861, 988877, 988901, 988909, 988937, 988951, 988963, 988979, 989011, 989029, 989059, 989071, 989081, 989099, 989119, 989123, 989171, 989173, 989231, 989239, 989249, 989251, 989279, 989293, 989309, 989321, 989323, 989327, 989341, 989347, 989353, 989377, 989381, 989411, 989419, 989423, 989441, 989467, 989477, 989479, 989507, 989533, 989557, 989561, 989579, 989581, 989623, 989629, 989641, 989647, 989663, 989671, 989687, 989719, 989743, 989749, 989753, 989761, 989777, 989783, 989797, 989803, 989827, 989831, 989837, 989839, 989869, 989873, 989887, 989909, 989917, 989921, 989929, 989939, 989951, 989959, 989971, 989977, 989981, 989999, 990001, 990013, 990023, 990037, 990043, 990053, 990137, 990151, 990163, 990169, 990179, 990181, 990211, 990239, 990259, 990277, 990281, 990287, 990289, 990293, 990307, 990313, 990323, 990329, 990331, 990349, 990359, 990361, 990371, 990377, 990383, 990389, 990397, 990463, 990469, 990487, 990497, 990503, 990511, 990523, 990529, 990547, 990559, 990589, 990593, 990599, 990631, 990637, 990643, 990673, 990707, 990719, 990733, 990761, 990767, 990797, 990799, 990809, 990841, 990851, 990881, 990887, 990889, 990893, 990917, 990923, 990953, 990961, 990967, 990973, 990989, 991009, 991027, 991031, 991037, 991043, 991057, 991063, 991069, 991073, 991079, 991091, 991127, 991129, 991147, 991171, 991181, 991187, 991201, 991217, 991223, 991229, 991261, 991273, 991313, 991327, 991343, 991357, 991381, 991387, 991409, 991427, 991429, 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993203, 993211, 993217, 993233, 993241, 993247, 993253, 993269, 993283, 993287, 993319, 993323, 993341, 993367, 993397, 993401, 993407, 993431, 993437, 993451, 993467, 993479, 993481, 993493, 993527, 993541, 993557, 993589, 993611, 993617, 993647, 993679, 993683, 993689, 993703, 993763, 993779, 993781, 993793, 993821, 993823, 993827, 993841, 993851, 993869, 993887, 993893, 993907, 993913, 993919, 993943, 993961, 993977, 993983, 993997, 994013, 994027, 994039, 994051, 994067, 994069, 994073, 994087, 994093, 994141, 994163, 994181, 994183, 994193, 994199, 994229, 994237, 994241, 994247, 994249, 994271, 994297, 994303, 994307, 994309, 994319, 994321, 994337, 994339, 994363, 994369, 994391, 994393, 994417, 994447, 994453, 994457, 994471, 994489, 994501, 994549, 994559, 994561, 994571, 994579, 994583, 994603, 994621, 994657, 994663, 994667, 994691, 994699, 994709, 994711, 994717, 994723, 994751, 994769, 994793, 994811, 994813, 994817, 994831, 994837, 994853, 994867, 994871, 994879, 994901, 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def getScore(x, n):
	temp = int(n / x)
	s = 0
	while temp != 0:
		s += int(temp)
		temp = int(temp / x)
	return s

def main():
	i = 0
	n = int(input())
	s = 1
	while q[i] <= n:
		s = s * (1 + 2 * getScore(q[i], n))
		i += 1
	if s > 1000007:
		s %= 1000007
	print(int(s))
main()


N = int(input())
ret = 1
factors = list(range(N + 1))
for (i, factor) in enumerate(factors):
	if factor > 1:
		tmp = 2
		k = 2
		while k * i <= N:
			while factors[k * i] % i == 0:
				factors[k * i] //= i
				tmp += 2
			k += 1
		ret *= tmp + 1
		ret %= 1000007
print(ret)


import sys
import math
import collections

def product(numbers):
	result = 1
	for number in numbers:
		result *= number
	return result

def prime_factorization(N):
	assert N <= 1000000
	PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]

	def primes(N):
		for prime in PRIMES:
			if not N % prime:
				return (prime, N // prime)
		return (1, N)
	primes_ = collections.defaultdict(int)
	finished = False
	while not finished:
		(i, N) = primes(N)
		if i == 1:
			finished = True
			if N != 1:
				primes_[N] += 1
		else:
			primes_[i] += 1
	return dict(primes_)
N = int(sys.stdin.readline())
factorizations = [prime_factorization(i) for i in range(2, N + 1)]
primes = collections.defaultdict(int)
for factorization in factorizations:
	for prime in factorization:
		primes[prime] += factorization[prime]
print(product([1 + 2 * k for k in primes.values()]) % 1000007)


import time
import collections

def factorize(number):
	factors = []
	org = number
	n = 2
	if org in factorize.MEMORY:
		return factorize.MEMORY[org]
	while True:
		if number in factorize.MEMORY:
			factors.extend(factorize.MEMORY[number])
			factorize.MEMORY[org] = factors
			return factors
		if number < 2:
			factorize.MEMORY[org] = factors
			return factors
		if n > 1 + number ** 0.5:
			factors.append(number)
			factorize.MEMORY[org] = factors
			return factors
		if number % n == 0:
			factors.append(n)
			number = number // n
		else:
			n += 1
factorize.MEMORY = {}

def numOfDivisors(f):
	d = 1
	for t in f:
		d *= 2 * f[t] + 1
	return d

def main():
	N = int(input())
	f = []
	for i in range(1, N + 1):
		f.extend(factorize(i))
	f = collections.Counter(f)
	return numOfDivisors(f) % 1000007
print(main())


modval = 1000007
N = int(input())
import operator
import functools
factors = dict()
j = 2
f_counts = dict()
while j <= N:
	if j not in factors:
		k = j
		while k <= N:
			if k not in factors:
				factors[k] = [[j], k // j]
			else:
				factors[k][0].append(j)
				factors[k][1] //= j
			k += j
	elif factors[j][1] != 1:
		factors[j][0] += factors[factors[j][1]][0]
		factors[j][1] = 1
	for f in factors[j][0]:
		f_counts[f] = f_counts.get(f, 0) + 1
	j += 1
if N < 2:
	print(1)
else:
	print(functools.reduce(operator.mul, [2 * v + 1 for v in f_counts.values()]) % modval)


def primes_up_to(n):

	def prime(n, p):
		for item in p:
			if n % item == 0:
				return False
			if item ** 2 > n:
				return True
		return True
	if n < 2:
		return []
	p = [2]
	i = 3
	while i <= n:
		if prime(i, p):
			p += [i]
		i += 2
	return p

def prime_factors(nfac):
	res = 1
	p = primes_up_to(nfac)
	for prime in p:
		cur_prime = prime
		prime_factor_count = 0
		while cur_prime <= nfac:
			prime_factor_count += nfac // cur_prime
			cur_prime *= prime
		res *= 2 * prime_factor_count + 1
		res = res % 1000007
	return res
print(prime_factors(int(input())))


from collections import Counter
import math

def product(array):
	total = 1
	for element in array:
		total *= element
	return total

def factorization(n):
	step = lambda x: 1 + x * 4 - x // 2 * 2
	maxq = math.floor(math.sqrt(n))
	d = 1
	q = n % 2 == 0 and 2 or 3
	while q <= maxq and n % q != 0:
		q = step(d)
		d += 1
	res = []
	if q <= maxq:
		res.extend(factorization(n // q))
		res.extend(factorization(q))
	else:
		res = [n]
	return res

def find_solutions(n):
	prime_factors = []
	for x in range(2, n + 1):
		prime_factors.extend(factorization(x))
	factor_count = Counter(prime_factors)
	return product((1 + 2 * x[1] for x in factor_count.most_common())) % (10 ** 6 + 7)
print(find_solutions(int(input())))


from math import log
n = int(input())
d = [0 for _ in range(n + 1)]
sieve = [True for _ in range(n + 1)]
sieve[0] = sieve[1] = False
for i in range(2, int(n ** 0.5) + 1):
	if not sieve[i]:
		continue
	for j in range(2 * i, n + 1, i):
		sieve[j] = False
for (i, e) in enumerate(sieve):
	if e:
		for p in range(1, int(log(n, i)) + 1):
			d[i] += n // i ** p
s = 1
for (i, v) in enumerate(d):
	if sieve[i]:
		s *= v * 2 + 1
print(s % 1000007)


from math import factorial
from fractions import *

def my_sieve_count_dividers_factorial(n):
	sv = [1] * (n + 1)
	mult = 1
	for i in range(2, n + 1):
		if sv[i] != 0:
			for j in range(i * i, n + 1, i):
				sv[j] = 0
			sv[i] = 0
			t = n
			while t >= i:
				t //= i
				sv[i] += t
			mult *= 2 * sv[i] + 1
	return mult
modulo = 1000007
n = int(input())
print(my_sieve_count_dividers_factorial(n) % modulo)


import functools

def generate_prime(n):
	primes = [1 for i in range(n + 1)]
	for i in range(2, n):
		if i * i > n:
			break
		elif primes[i] == 1:
			for j in range(i, n):
				if j * i > n:
					break
				else:
					primes[i * j] = 0
	return primes

def get_multiplicities(primes, n):
	sum = 1
	multiplicities = [1 for i in range(len(primes))]
	for i in range(2, len(primes)):
		if primes[i] == 1:
			tmp = n
			e = 0
			while tmp != 0:
				e = e + tmp // i
				tmp = tmp // i
			multiplicities[i] = 2 * e + 1
			sum *= multiplicities[i]
	return sum
n = int(input())
primes = generate_prime(n)
res = get_multiplicities(primes, n)
print(res % 1000007)


import sys
N = int(sys.stdin.readline())
primes = {}
sieve = list(range(N + 1))
n = 2
while n < N + 1:
	if sieve[n] > 1:
		primes[n] = 1
		k = 2
		while k * n < N + 1:
			while sieve[k * n] % n == 0:
				sieve[k * n] //= n
				primes[n] += 1
			k += 1
	n += 1
for k in primes:
	primes[k] *= 2
tau = 1
for (k, v) in primes.items():
	tau *= v + 1
	tau %= 1000007
print(tau)


import sys
N = int(sys.stdin.readline())
primes = {}
sieve = list(range(N + 1))
n = 2
while n < N + 1:
	if sieve[n] > 1:
		primes[n] = 1
		k = 2
		while k * n < N + 1:
			while sieve[k * n] % n == 0:
				sieve[k * n] //= n
				primes[n] += 1
			k += 1
	n += 1
for k in primes:
	primes[k] *= 2
tau = 1
for (k, v) in primes.items():
	tau *= v + 1
	tau %= 1000007
print(tau)


N = int(input())
primes = [2]
is_prime = [True] * (N + 1)
for i in range(3, N + 1, 2):
	if not is_prime[i]:
		continue
	primes.append(i)
	for j in range(i * i, N + 1, i):
		is_prime[j] = False
prime_counts = [0] * len(primes)
for i in range(len(primes)):
	p = primes[i]
	while p <= N:
		prime_counts[i] = (prime_counts[i] + N // p) % 1000007
		p *= primes[i]
total = 1
for c in prime_counts:
	total = total * (1 + 2 * c) % 1000007
print(total)


def prime_list(n):
	is_prime = [True] * n
	for i in range(3, int(n ** 0.5) + 1, 2):
		if is_prime[i]:
			is_prime[i * i::2 * i] = [False] * ((n - i * i - 1) // (2 * i) + 1)
	return [2] + [i for i in range(3, n, 2) if is_prime[i]]
N = int(input())
nbr_divisors = 1
for p in prime_list(N + 1):
	prime_power = p
	val_p = 0
	while prime_power <= N:
		val_p += N // prime_power
		prime_power *= p
	nbr_divisors *= 2 * val_p + 1
print(nbr_divisors % 1000007)


is_prime = [True] * 10 ** 6
is_prime[0] = is_prime[1] = False
for i in range(4, 10 ** 6, 2):
	is_prime[i] = False
for i in range(3, 10 ** 3, 2):
	if is_prime[i]:
		for j in range(i * i, 10 ** 6, i):
			is_prime[j] = False
primes = [i for (i, x) in enumerate(is_prime) if x]

def calculate(powers, mod):
	result = 1
	for power in powers:
		result *= 2 * power + 1
		result %= mod
	return result

def get_power(n, prime):
	result = 0
	while n:
		result += n // prime
		n //= prime
	return result

def get_powers(n):
	for prime in primes:
		yield get_power(n, prime)
print(calculate(get_powers(int(input())), 1000007))


import sys
N = int(sys.stdin.readline())
primes = {}
sieve = list(range(N + 1))
n = 2
while n < N + 1:
	if sieve[n] > 1:
		primes[n] = 1
		k = 2
		while k * n < N + 1:
			while sieve[k * n] % n == 0:
				sieve[k * n] //= n
				primes[n] += 1
			k += 1
	n += 1
for k in primes:
	primes[k] *= 2
tau = 1
for (k, v) in primes.items():
	tau *= v + 1
	tau %= 1000007
print(tau)


import sys
N = int(sys.stdin.readline())
primes = {}
sieve = list(range(N + 1))
n = 2
while n < N + 1:
	if sieve[n] > 1:
		primes[n] = 1
		k = 2
		while k * n < N + 1:
			while sieve[k * n] % n == 0:
				sieve[k * n] //= n
				primes[n] += 1
			k += 1
	n += 1
for k in primes:
	primes[k] *= 2
tau = 1
for (k, v) in primes.items():
	tau *= v + 1
	tau %= 1000007
print(tau)


from functools import reduce
from math import sqrt
from operator import mul
N = int(input())
factors = {}
for n in range(1, N + 1):
	while n % 2 == 0:
		n //= 2
		if 2 not in factors:
			factors[2] = 0
		factors[2] += 1
	i = 3
	while i <= sqrt(n):
		while n % i == 0:
			n //= i
			if i not in factors:
				factors[i] = 0
			factors[i] += 1
		i += 2
	if n == 1:
		continue
	if n not in factors:
		factors[n] = 0
	factors[n] += 1
print(reduce(lambda a, b: a * b % 1000007, [2 * mx + 1 for mx in factors.values()], 1))


MOD = 1000007
MAXN = 1000005
primes = []
s = [0] * MAXN

def sieve():
	lim = 1002
	for i in range(2, lim):
		if s[i] == 0:
			j = 2 * i
			while j < MAXN:
				s[j] = 1
				j += i
	for i in range(2, MAXN):
		if s[i] == 0:
			primes.append(i)

def Calculate_Power(N, p):
	temp = p
	cnt = int(0)
	while 1:
		x = N // temp
		if x == 0:
			break
		cnt += x
		temp = temp * p
	return cnt

def main():
	N = int(input())
	sieve()
	l = len(primes)
	i = int(0)
	ans = int(1)
	while i < l and primes[i] <= N:
		x = Calculate_Power(N, primes[i])
		ans = ans * (2 * x + 1)
		ans %= MOD
		i += 1
	ans %= MOD
	print(ans)
main()


def isP(n):
	if n <= 3:
		return True
	if (n % 2 == 0) | (n % 3 == 0):
		return False
	for d in range(5, int(n ** 0.5) + 1, 6):
		if (n % d == 0) | (n % (d + 2) == 0):
			return False
	return True

def getP(u):
	P = [2]
	for n in range(3, u + 1, 2):
		if isP(n):
			P.append(n)
	return P
N = int(input())
P = getP(int(N))
mod = 10 ** 6 + 7
d = 1
for p in P:
	i = 1
	s = 0
	while True:
		a = N // p ** i
		if a == 0:
			break
		s += a
		i += 1
	d = d * (2 * s + 1) % mod
print(d)


import sys
item = sys.stdin.readlines()[0]
item = int(item)
num_primes = {}
primed = [{}, {}, {2: 1}]
if item > 1:
	factorial_primes = {2: 1}
else:
	factorial_primes = {}
primes = [2]
for num in range(3, item + 1):
	primed.append({})
	is_prime = True
	limit = int(num / 2)
	for prime in primes:
		if prime > limit:
			break
		limit = int(num / prime)
		if num % prime == 0:
			is_prime = False
			primed[num] = {}
			for (key, val) in primed[prime].items():
				factorial_primes[key] = (factorial_primes[key] + val) % 1000007
				primed[num][key] = val
			for (key, val) in primed[int(num / prime)].items():
				if key in primed[num]:
					primed[num][key] = (primed[num][key] + val) % 1000007
				else:
					primed[num][key] = val % 1000007
				factorial_primes[key] = (factorial_primes[key] + val) % 1000007
			break
	if is_prime:
		primed[num] = {num: 1}
		primes.append(num)
		factorial_primes[num] = 1
answer = 1
for (key, val) in factorial_primes.items():
	answer = answer * (val * 2 + 1) % 1000007
print(answer)


from math import sqrt

def rwh_primes1(n):
	sieve = [True] * (n // 2)
	for i in range(3, int(n ** 0.5) + 1, 2):
		if sieve[i // 2]:
			sieve[i * i // 2::i] = [False] * ((n - i * i - 1) // (2 * i) + 1)
	return [2] + [2 * i + 1 for i in range(1, n // 2) if sieve[i]]
N = int(input().strip())
MOD = 7 + 10 ** 6
primes = rwh_primes1(N + 1)

def valuation(N, p):
	v = 0
	while N:
		N //= p
		v += N
	return v
ans = 1
for p in primes:
	ans = ans * (2 * valuation(N, p) + 1) % MOD
print(ans)


n = int(input().strip())
if n == 1:
	print(1)
	exit()

def get_num_factor_in_nsq(n, p):
	ret = 0
	while n > 0:
		n //= p
		ret += n
	return 2 * ret + 1
is_prime = [True for i in range(n + 1)]
ans = get_num_factor_in_nsq(n, 2) % 1000007
for i in range(3, n + 1, 2):
	if is_prime[i]:
		ans *= get_num_factor_in_nsq(n, i)
		ans %= 1000007
		for j in range(i * i, n + 1, 2 * i):
			is_prime[j] = False
print(ans)


def fact_factor(n):
	factors = dict()
	sieve = [True] * (n + 1)
	for k in range(2, n + 1):
		if not sieve[k]:
			continue
		q = k
		k_powers = 0
		while q <= n:
			k_powers += n // q
			q = q * k
		factors[k] = 2 * k_powers
		for m in range(k, n + 1, k):
			sieve[m] = False
	return factors
M = 1000007
N = int(input())
facts = fact_factor(N)
ans = 1
for p in facts:
	ans = ans * (facts[p] + 1) % M
print(ans)


import sys
from time import time

def gcd(a, b):
	while b:
		(a, b) = (b, a % b)
	return a

def solve_bf(n, m):

	def gen(n):
		u = (1, n)
		for i in range(n + 1, 2 * n + 1):
			v = (1, i)
			w = (i - n, i * n)
			g = gcd(w[0], w[1])
			w = (w[0] // g, w[1] // g)
			if w[0] == 1:
				yield (i, w[1])
	f = 1
	for i in range(2, n + 1):
		f *= i
	cnt = 0
	for (a, b) in gen(n):
		g = gcd(a, b)
		(x, y) = (a // g, b // g)
		z = n // y
		print('a=%d b=%d %d:%d' % (a, b, x * z, n), file=sys.stderr)
		cnt += 1
	print(file=sys.stderr)
	return cnt

def primes_gen(n):
	sieve = [True] * n
	for p in range(2, n):
		if sieve[p]:
			yield p
			for i in range(p + p, n, p):
				sieve[i] = False

def factorial_pfs_gen(n, prms):
	for p in prms:
		(u, cnt) = (p, 0)
		while u <= n:
			cnt += n // u
			u *= p
		if cnt:
			yield (p, cnt)

def solve(n, m):
	print('n=%d m=%d' % (n, m), file=sys.stderr)
	prms = primes_gen(n + 1)
	divs = 1
	for (p, cnt) in factorial_pfs_gen(n, prms):
		divs *= 2 * cnt + 1
		divs %= m
	print('divs(%d!^2)=%d' % (n, divs), file=sys.stderr)
	return divs
tm = time()
n = int(input())
print(solve(n, pow(10, 6) + 7))
print('time elapsed: %s' % (time() - tm), file=sys.stderr)


def is_prime(p):
	if p == 2 or p == 3:
		return True
	for j in range(2, int(p ** 0.5) + 1):
		if p % j == 0:
			return False
	return True
(n, res) = (int(input()), 1)
for i in range(2, n + 1):
	if is_prime(i):
		(x, y) = (1, 0)
		while i ** x <= n:
			y += n // i ** x
			x += 1
		res *= 2 * y + 1
print(res % 1000007)


primes = []
sieve = [True] * 1000001
for n in range(2, 1000001):
	if sieve[n]:
		primes.append(n)
		for i in range(n, 1000001, n):
			sieve[i] = False
n = int(input())
r = 1
for p in primes:
	ep = 0
	i = p
	while True:
		e = n // i
		if e == 0:
			break
		ep += e
		i *= p
	r *= 2 * ep + 1
	r %= 1000007
print(r)


mod = 1000007
n = int(input())
rv = 1
X = [a for a in range(2, n + 1)]
for i in range(len(X)):
	a = X[i]
	if a == 1:
		continue
	count = 0
	for j in range(i, len(X), a):
		while X[j] % a == 0:
			count += 1
			X[j] //= a
	rv = rv * (2 * count + 1) % mod
print(rv)


import math

def isprime(p):
	if p < 4 and p > 1:
		return True
	if p % 2 == 0 or p % 3 == 0:
		return False
	else:
		q = int(math.sqrt(p))
		for i in range(5, q + 1):
			if p % i == 0:
				return False
	return True
n = int(input())
sum_ = 1
for i in range(2, n + 1):
	if isprime(i):
		(f, po, sum_i) = (True, 1, 0)
		while f:
			q = int(n / pow(i, po))
			if q:
				sum_i += q
				po += 1
			else:
				f = False
		if sum_i == 0:
			break
		sum_ = sum_ % 1000007 * (2 * sum_i + 1) % 1000007
print(sum_)


import math
N = int(input())
n = N
prime = [True for i in range(n + 1)]
p = 2
while p * p <= n:
	if prime[p] == True:
		for i in range(p * p, n + 1, p):
			prime[i] = False
	p += 1
div = 1
for p in range(2, n + 1):
	if prime[p]:
		t = n // p
		sum = t
		while t != 0:
			t = t // p
			sum = sum + t
		div = div * (2 * sum + 1)
print(div % 1000007)


import math
N = int(input())
n = N
prime = [True for i in range(n + 1)]
p = 2
while p * p <= n:
	if prime[p] == True:
		for i in range(p * p, n + 1, p):
			prime[i] = False
	p += 1
div = 1
for p in range(2, n + 1):
	if prime[p]:
		t = n // p
		sum = t
		while t != 0:
			t = t // p
			sum = sum + t
		div = div * (2 * sum + 1)
print(div % 1000007)


import math
N = int(input())
a = 0
S = [2, 3]
L = []
for i in range(4, N + 1):
	for j in range(2, int(math.sqrt(i)) + 1):
		if i % j == 0:
			break
	else:
		S.append(i)
for i in range(len(S)):
	a = 0
	for j in range(1, int(math.log(N, S[i])) + 2):
		a = a + int(N / S[i] ** j)
	L.append(a)
	a = 0
b = 1
for i in L:
	b = b * (2 * i + 1)
print(b % 1000007)


N = int(input())
pr = 1

def count(p):
	r = 0
	N2 = N
	while N2 > 1:
		r += N2 // p
		N2 //= p
	return r
isprime = [True] * (N + 1)
for i in range(2, N + 1):
	if not isprime[i]:
		continue
	pr = pr * (2 * count(i) + 1) % 1000007
	for j in range(2 * i, N + 1, i):
		isprime[j] = False
print(pr)


import os
import sys
primes = []
sieve = [True] * 1000001
for n in range(2, 1000001):
	if sieve[n]:
		primes.append(n)
		for i in range(2 * n, 1000001, n):
			sieve[i] = False
n = int(input())
r = 1
for p in primes:
	ep = 0
	i = p
	while True:
		e = n // i
		if e == 0:
			break
		ep += e
		i *= p
	r *= 2 * ep + 1
	r %= 1000007
print(r)


from collections import defaultdict
MOD = 1000007

def sieve_decomp_fact(N):
	N += 1
	P = [True] * N
	Decomp = defaultdict(int)
	for i in range(2, N):
		if P[i]:
			m = 1
			for k in range(2 * i, N, i):
				P[k] = False
				l = k // i
				m += 1
				while l % i == 0:
					l //= i
					m += 1
			Decomp[i] += m
	return Decomp
N = int(input())
D = sieve_decomp_fact(N)
res = 1
for p in D:
	res = res * (2 * D[p] + 1) % MOD
print(res)


import math
M = 1000009
vis = [False] * M
l = []
for i in range(2, M):
	if not vis[i]:
		l.append(i)
		for j in range(2 * i, M, i):
			if not vis[j]:
				vis[j] = True
n = int(input())
d = []
i = 0
while n >= l[i]:
	cnt = 0
	t = n
	while t > 1:
		t //= l[i]
		cnt += t
	d.append(cnt)
	i += 1
ans = 1
for i in range(len(d)):
	ans = ans * (2 * d[i] + 1) % 1000007
print(ans)


def primes(end):
	p = [2, 3]
	for i in range(5, end + 1):
		for j in p:
			if j * j > i:
				p.append(i)
				break
			if i % j == 0:
				break
	return p
n = int(input())
p = primes(n)
fact = []
for i in p:
	count = 0
	curr = i
	while curr <= n:
		count += n // curr
		curr *= i
	fact.append(count)
prod = 1
for i in fact:
	prod *= 2 * i + 1
	prod %= 1000007
prod %= 1000007
print(prod)


def primes_method(n):
	out = list()
	sieve = [True] * (n + 1)
	for p in range(2, n + 1):
		if sieve[p]:
			out.append(p)
			for i in range(p, n + 1, p):
				sieve[i] = False
	return out
n = int(input())
primes = primes_method(n)
final = 1
for ab in primes:
	s = 0
	i = ab
	while True:
		check = n // i
		if check == 0:
			break
		s += check
		i *= ab
	final = final * (2 * s + 1) % 1000007
print(final)


def sieve(n):
	lis = []
	for i in range(n + 1):
		lis.append(True)
	p = 2
	while p * p <= n:
		if lis[p]:
			for i in range(p * p, n + 1, p):
				lis[i] = False
		p += 1
	prime = []
	for i in range(2, n + 1):
		if lis[i]:
			prime.append(i)
	return prime

def solve(n):
	lis = sieve(n)
	ans = 1
	for i in lis:
		x = 0
		k = n
		while k != 0:
			x = x + k // i
			k = k // i
		ans *= 2 * x + 1
	return ans % 1000007
print(solve(int(input())))


primes = []
sieve = [True] * 1000001
for n in range(2, 1000001):
	if sieve[n]:
		primes.append(n)
		for i in range(2 * n, 1000001, n):
			sieve[i] = False
n = int(input())
r = 1
for p in primes:
	ep = 0
	i = p
	while True:
		e = n // i
		if e == 0:
			break
		ep += e
		i *= p
	r *= 2 * ep + 1
	r %= 1000007
print(r)


primes = []
sieve = [True] * 1000001
for n in range(2, 1000001):
	if sieve[n]:
		primes.append(n)
		for i in range(2 * n, 1000001, n):
			sieve[i] = False
n = int(input())
r = 1
for p in primes:
	ep = 0
	i = p
	while True:
		e = n // i
		if e == 0:
			break
		ep += e
		i *= p
	r *= 2 * ep + 1
	r %= 1000007
print(r)


import sys
import math
lvl = 10 ** 6 + 100
vis = [0] * lvl
for i in range(lvl):
	vis[i] = 0
vis[0] = vis[1] = 1
for i in range(2, 1000000, 1):
	if vis[i] == 1:
		continue
	for j in range(i ** 2, 1000000, i):
		vis[j] = 1
pr = []
for i in range(0, 1000000, 1):
	if vis[i] == 0:
		pr.append(i)

def solve(n, t):
	ans = 0
	while n > 0:
		ans += n // t
		n = n // t
	return ans
ans = 1
n = int(input())
for i in range(2, n + 1, 1):
	if vis[i] == 0:
		valor = solve(n, i)
		ans *= valor << 1 | 1
		ans = ans % 1000007
print(ans)


import math
from math import factorial
mod = 1000007

def pf(n):
	div = []
	while n % 2 == 0:
		div.append(2)
		n = n // 2
	for i in range(3, int(n ** 0.5) + 1, 2):
		while n % i == 0:
			div.append(i)
			n = n // i
	if n > 2:
		div.append(n)
	return div
n = int(input())
d = {}
for i in range(2, n + 1):
	temp = pf(i)
	for i in temp:
		if i not in d:
			d[i] = 0
			d[i] += 1
		else:
			d[i] += 1
prod = 1
for i in d.keys():
	prod *= 2 * d[i] + 1
print(prod % mod)


import math
from math import factorial
mod = 1000007

def pf(n):
	div = []
	while n % 2 == 0:
		div.append(2)
		n = n // 2
	for i in range(3, int(n ** 0.5) + 1, 2):
		while n % i == 0:
			div.append(i)
			n = n // i
	if n > 2:
		div.append(n)
	return div
n = int(input())
d = {}
for i in range(2, n + 1):
	temp = pf(i)
	for i in temp:
		if i not in d:
			d[i] = 0
			d[i] += 1
		else:
			d[i] += 1
prod = 1
for i in d.keys():
	prod *= 2 * d[i] + 1
print(prod % mod)


n = int(input())
z = []
l = [0 for i in range(n + 1)]
p = 2
q = 1
while p * p <= n:
	if l[p] == 0:
		for i in range(p * p, n + 1, p):
			l[i] = 1
	p += 1
for i in range(2, n + 1):
	if l[i] == 0:
		z.append(i)
count = 0
for i in z:
	temp = n
	c = 0
	while temp:
		temp //= i
		c += temp
	z[count] = 2 * c + 1
	count += 1
for i in z:
	q *= i
print(q % 1000007)


import math
from functools import reduce
allPrimes = []
mod = 1000007

def sieve(n):
	prime = [True] * (n + 1)
	p = 2
	while p * p <= n:
		if prime[p] == True:
			i = p * 2
			while i <= n:
				prime[i] = False
				i += p
		p += 1
	for p in range(2, n + 1):
		if prime[p]:
			allPrimes.append(p)

def _sum(N, p):
	return sum([N // p ** i % mod for i in range(1, int(math.log(N, p)) + 1)])

def solve(n):
	sieve(n)
	res = list(map(lambda x: (1 + 2 * _sum(n, x)) % mod, allPrimes))
	res = reduce(lambda x, y: x * y % mod, res, 1)
	ans = res
	return int(ans) % mod
n = int(input())
result = solve(n)
print(result)