Let's define a function f(p) on a permutation p as follows. Let g_i be the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of length i). Then f(p) is the number of distinct elements among g_1, g_2, ..., g_n.

Let f_{max}(n) be the maximum value of f(p) among all permutations p of integers 1, 2, ..., n.

Given an integers n, count the number of permutations p of integers 1, 2, ..., n, such that f(p) is equal to f_{max}(n). Since the answer may be large, print the remainder of its division by 1000 000 007 = 10^9 + 7.

Input

The only line contains the integer n (2 ≤ n ≤ 10^6) — the length of the permutations.

Output

The only line should contain your answer modulo 10^9+7.

Examples

Input


2


Output


1

Input


3


Output


4

Input


6


Output


120

Note

Consider the second example: these are the permutations of length 3:

  * [1,2,3], f(p)=1. 
  * [1,3,2], f(p)=1. 
  * [2,1,3], f(p)=2. 
  * [2,3,1], f(p)=2. 
  * [3,1,2], f(p)=2. 
  * [3,2,1], f(p)=2. 



The maximum value f_{max}(3) = 2, and there are 4 permutations p such that f(p)=2.
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void amin(T &x, const T &y) {
  if (y < x) x = y;
}
template <class T>
inline void amax(T &x, const T &y) {
  if (x < y) x = y;
}
template <class Iter>
void rprintf(const char *fmt, Iter begin, Iter end) {
  for (bool sp = 0; begin != end; ++begin) {
    if (sp)
      putchar(' ');
    else
      sp = true;
    printf(fmt, *begin);
  }
  putchar('\n');
}
template <unsigned MOD_>
struct ModInt {
  static const unsigned MOD = MOD_;
  unsigned x;
  void undef() { x = (unsigned)-1; }
  bool isnan() const { return x == (unsigned)-1; }
  inline int geti() const { return (int)x; }
  ModInt() { x = 0; }
  ModInt(const ModInt &y) { x = y.x; }
  ModInt(int y) {
    if (y < 0 || (int)MOD <= y) y %= (int)MOD;
    if (y < 0) y += MOD;
    x = y;
  }
  ModInt(unsigned y) {
    if (MOD <= y)
      x = y % MOD;
    else
      x = y;
  }
  ModInt(long long y) {
    if (y < 0 || MOD <= y) y %= MOD;
    if (y < 0) y += MOD;
    x = y;
  }
  ModInt(unsigned long long y) {
    if (MOD <= y)
      x = y % MOD;
    else
      x = y;
  }
  ModInt &operator+=(const ModInt y) {
    if ((x += y.x) >= MOD) x -= MOD;
    return *this;
  }
  ModInt &operator-=(const ModInt y) {
    if ((x -= y.x) & (1u << 31)) x += MOD;
    return *this;
  }
  ModInt &operator*=(const ModInt y) {
    x = (unsigned long long)x * y.x % MOD;
    return *this;
  }
  ModInt &operator/=(const ModInt y) {
    x = (unsigned long long)x * y.inv().x % MOD;
    return *this;
  }
  ModInt operator-() const { return (x ? MOD - x : 0); }
  ModInt inv() const { return pow(MOD - 2); }
  ModInt pow(long long y) const {
    ModInt b = *this, r = 1;
    if (y < 0) {
      b = b.inv();
      y = -y;
    }
    for (; y; y >>= 1) {
      if (y & 1) r *= b;
      b *= b;
    }
    return r;
  }
  ModInt extgcd() const {
    unsigned a = MOD, b = x;
    int u = 0, v = 1;
    while (b) {
      int t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    if (u < 0) u += MOD;
    return ModInt(u);
  }
  friend ModInt operator+(ModInt x, const ModInt y) { return x += y; }
  friend ModInt operator-(ModInt x, const ModInt y) { return x -= y; }
  friend ModInt operator*(ModInt x, const ModInt y) { return x *= y; }
  friend ModInt operator/(ModInt x, const ModInt y) { return x *= y.inv(); }
  friend bool operator<(const ModInt x, const ModInt y) { return x.x < y.x; }
  friend bool operator==(const ModInt x, const ModInt y) { return x.x == y.x; }
  friend bool operator!=(const ModInt x, const ModInt y) { return x.x != y.x; }
};
const long long MOD = 1000000007;
const int MAX = 2000011;
ModInt<MOD> inv[MAX], fact[MAX], fact_inv[MAX];
void init() {
  fact[0] = 1;
  for (int i = 1; i < MAX; i++) fact[i] = fact[i - 1] * i;
  fact_inv[MAX - 1] = fact[MAX - 1].inv();
  for (int i = MAX - 2; i >= 0; i--) fact_inv[i] = fact_inv[i + 1] * (i + 1);
  inv[0] = 0;
  for (int i = 1; i < MAX; i++) inv[i] = fact_inv[i] * fact[i - 1];
}
ModInt<MOD> nCk(int n, int k) {
  return fact[n] * fact_inv[k] * fact_inv[n - k];
}
int N;
int C[1000011];
int val[255];
ModInt<MOD> ans;
int cnt = 0;
vector<int> X;
void rec(int I) {
  X.push_back(val[I]);
  if (I == cnt - 1) {
    X.push_back(N + 1);
    int len = 0;
    ModInt<MOD> tmp = 1;
    for (int i = 0, i_len = (X.size() - 1u); i < i_len; ++i) {
      int add = N / X[i] - N / X[i + 1];
      tmp *= nCk(add + len - 1, len) * fact[add];
      len += add;
    }
    ans += tmp;
    X.pop_back();
  } else {
    for (int j = I + 1; j < cnt; j++)
      if (C[val[I]] + 1 == C[val[j]] && val[j] % val[I] == 0) rec(j);
  }
  X.pop_back();
}
void MAIN() {
  init();
  scanf("%d", &N);
  for (int i = 2; i <= N; i++)
    for (int j = 1; j * i <= N; j++) amax(C[j * i], C[j] + 1);
  int ma = *max_element(C, C + N + 1);
  for (int h = 1; h <= N; h++)
    if (C[h] == ma) {
      cnt = 0;
      for (int i = 1; i <= h; i++)
        if (h % i == 0) {
          val[cnt++] = i;
        }
      rec(0);
    }
  printf("%d\n", ans.geti());
}
int main() {
  int TC = 1;
  for (int tc = 0, tc_len = (TC); tc < tc_len; ++tc) MAIN();
  return 0;
}
