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.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
#include "bits/stdc++.h"
using namespace std;
typedef long long LL;
const LL MOD = 1000000007;
int main() {
	int N;
	cin >> N;
	map<int, int> cnt;
	for (int i = 1; i <= N; i++) {
		int M = i;
		for (int j = 2; j*j <= M; j++) {
			while (M%j == 0) {
				M /= j;
				cnt[j]++;
			}
		}
		if (M != 1) cnt[M]++;
	}
	LL ans = 1;
	for (auto itr = cnt.begin(); itr != cnt.end(); itr++) {
		ans = (ans*(itr->second+1)) % MOD;
	}
	cout << ans << endl;
}