Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <cassert>
#include <cstdio>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <numeric>
#include <algorithm>

using namespace std;
using lint = long long;
constexpr int MOD = 1000000007, INF = 1010101010;
constexpr lint LINF = 1LL << 60;

template <class T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
	for (const auto &e : vec) os << e << (&e == &vec.back() ? "" : " ");
	return os;
}

#ifdef _DEBUG
template <class T>
void dump(const char* str, T &&h) { cerr << str << " = " << h << "\n"; };
template <class Head, class... Tail>
void dump(const char* str, Head &&h, Tail &&... t) {
	while (*str != ',') cerr << *str++; cerr << " = " << h << "\n";
	dump(str + (*(str + 1) == ' ' ? 2 : 1), t...);
}
#define DMP(...) dump(#__VA_ARGS__, __VA_ARGS__)
#else 
#define DMP(...) ((void)0)
#endif

const int N = 10000;
int min_pf[N];
vector<int> prime;

class Prime {
private:
	vector<int> min_pf; // min_pf[i] = minimum prime factor of i
	vector<int> prime;

	// linear sieve https://cp-algorithms.com/algebra/prime-sieve-linear.html
	void sieve(int N) {
		min_pf[0] = min_pf[1] = -1;
		for (int i = 2; i < N; i++) {
			if (min_pf[i] == 0) {
				prime.push_back(i);
				min_pf[i] = i;
			}
			for (int j = 0; j < (int)(prime.size()); ++j) {
				if (prime[j] > min_pf[i] || i * prime[j] >= N) break;
				min_pf[i * prime[j]] = prime[j];
			}
		}
	}

public:
	Prime(int N = 110000000) : min_pf(N + 1) { 
		assert(3 <= N && N < INF);
		sieve(N + 1); 
	}

	vector<pair<lint, int>> factorize(lint n) {

		vector<pair<lint, int>> res;

		for (lint i = 2; i * i <= n; i++) {
			if (n < (lint)min_pf.size()) break;
			int cnt = 0;
			while (n % i == 0) {
				cnt++;
				n /= i;
			}
			if (cnt) res.emplace_back(i, cnt);
		}

		if (n >= (lint)min_pf.size()) res.emplace_back(n, 1);
		else {
			int prev = min_pf[n], cnt = 0;
			while (n != 1) {
				int now = min_pf[n];
				n /= now;
				cnt++;
				if (prev != min_pf[n]) {
					res.emplace_back(prev, cnt);
					cnt = 0;
					prev = min_pf[n];
				}
			}
		}

		return res;
	}

	// verified using boost miller_rabin_test https://wandbox.org/permlink/0jYXgfzOS8Q3GrcL
	bool isPrime(lint n) {
		if (n < (int)(min_pf.size())) return min_pf[n] == n;
		else if (n % 2 == 0 || n % 3 == 0) return false;
		else if (n % 6 != 1 && n % 6 != 5) return false;
		for (lint i = 5; i * i <= n; i += 6) {
			if (n % i == 0) return false;
			if (n % (i + 2) == 0) return false;
		}
		return true;
	}
};

template <class T>
ostream &operator<<(ostream &os, const set<T> &st) {
	for (const auto &e : st) os << e << " ";
	return os;
}

template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
	os << "(" << p.first << "," << p.second << ")";
	return os;
}

template <class T1, class T2>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
	for (const auto &e : mp) os << e << " ";
	return os;
}

template<int Modulo = MOD> struct Mint {

	lint val;
	constexpr Mint(lint v = 0) noexcept : val(v % Modulo) { if (val < 0) v += Modulo; }

	constexpr Mint& operator += (const Mint &r) noexcept {
		val += r.val;
		if (val >= Modulo) val -= Modulo;
		return *this;
	}
	constexpr Mint& operator -= (const Mint &r) noexcept {
		val -= r.val;
		if (val < 0) val += Modulo;
		return *this;
	}
	constexpr Mint& operator *= (const Mint &r) noexcept {
		val = val * r.val % Modulo;
		return *this;
	}
	constexpr Mint& operator /= (const Mint &r) noexcept {
		lint a = r.val, b = Modulo, u = 1, v = 0;
		while (b) {
			lint t = a / b;
			a -= t * b; swap(a, b);
			u -= t * v; swap(u, v);
		}
		val = val * u % Modulo;
		if (val < 0) val += Modulo;
		return *this;
	}

	constexpr Mint operator + (const Mint &r) const noexcept { return Mint(*this) += r; }
	constexpr Mint operator - (const Mint &r) const noexcept { return Mint(*this) -= r; }
	constexpr Mint operator * (const Mint &r) const noexcept { return Mint(*this) *= r; }
	constexpr Mint operator / (const Mint &r) const noexcept { return Mint(*this) /= r; }

	constexpr int getmod() { return Modulo; }
	constexpr Mint operator - () const noexcept { return val ? Modulo - val : 0; }

	constexpr bool operator == (const Mint &r) const noexcept { return val == r.val; }
	constexpr bool operator != (const Mint &r) const noexcept { return val != r.val; }

	friend ostream &operator << (ostream &os, const Mint<Modulo> &x) noexcept { return os << x.val; }
	friend istream &operator >> (istream &is, Mint<Modulo> &x) noexcept {
		lint tmp; is >> tmp;
		x = Mint<Modulo>(tmp);
		return is;
	}
	friend constexpr Mint<Modulo> modpow(const Mint<Modulo> &a, lint n) noexcept {
		Mint res(1), tmp = a;
		while (n > 0) {
			if (n & 1) res *= tmp;
			tmp *= tmp;
			n >>= 1;
		}
		return res;
	}
};

using mint = Mint<>;

int main() {

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	int N;
	cin >> N;

	Prime p(N);
	map<int, int> mp;
	for (int i = 2; i <= N; i++) {
		auto pfact = p.factorize(i);
		for (const auto &e : pfact) mp[e.first] += e.second;
	}

	mint ans = 1;
	for (const auto &e : mp) ans *= e.second + 1;
	cout << ans << "\n";

	return 0;
}