/**
 * File    : F.cpp
 * Author  : Kazune Takahashi
 * Created : 2018-2-27 18:27:15
 * Powered by Visual Studio Code
 */

#include <iostream>
#include <iomanip>   // << fixed << setprecision(xxx)
#include <algorithm> // do { } while ( next_permutation(A, A+xxx) ) ;
#include <vector>
#include <string> // to_string(nnn) // substr(m, n) // stoi(nnn)
#include <complex>
#include <tuple>
#include <queue>
#include <stack>
#include <map> // if (M.find(key) != M.end()) { }
#include <set>
#include <random> // random_device rd; mt19937 mt(rd());
#include <cctype>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
using namespace std;

#define DEBUG 0 // change 0 -> 1 if we need debug.

typedef long long ll;

// const int dx[4] = {1, 0, -1, 0};
// const int dy[4] = {0, 1, 0, -1};

// const int C = 1e6+10;
// const ll M = 1000000007;

const long long MOD = 1000000007;

long long power(long long x, long long n) {
  if (n == 0) {
    return 1;
  } else if (n%2 == 1) {
    return (x * power(x, n-1)) % MOD;
  } else {
    long long half = power(x, n/2);
    return (half * half) % MOD;
  }
}

int f[30000010];

int main()
{
  int S;
  cin >> S;
  vector<int> Y;
  int SQ = sqrt(S) + 10;
  for (int i = 1; i < SQ; i++)
  {
    if (S%i == 0)
    {
      int j = S / i;
      if (i < j)
      {
        Y.push_back(i);
        Y.push_back(j);
      }
      else if (i == j)
      {
        Y.push_back(i);
      }
    }
  }
  ll ans = 0;
  for (auto i = 0; i < 8; i++)
  {
    int lb = power(10, i);
    int ub = min((int)power(10, i + 1), 30000010);
    for (auto j = lb; j < ub; j++)
    {
      f[j] = i+1;
    }
  }
  int lb = 1;
  int ub = 1;
  int sum = 0;
  while (lb < 10000000)
  {
    if (sum == S)
      ans++;
    if (sum <= S)
    {
      sum += f[ub++];
    }
    else
    {
      sum -= f[lb++];
    }
  }
  ans += S / 8;
  for (auto k : Y)
  {
    if (k <= S/8)
    {
      int d = S / k;
      ans += (power(10, d) + MOD - power(10, d - 1) + MOD - S / d) % MOD;
      ans %= MOD;
    }
  }
  cout << ans << endl;
}
### Prompt

Please formulate a cpp solution to the following problem:

For a positive integer n, let us define f(n) as the number of digits in base 10.

You are given an integer S. Count the number of the pairs of positive integers (l, r) (l \leq r) such that f(l) + f(l + 1) + ... + f(r) = S, and find the count modulo 10^9 + 7.

Constraints

* 1 \leq S \leq 10^8

Input

Input is given from Standard Input in the following format:


S


Output

Print the answer.

Examples

Input

1


Output

9


Input

2


Output

98


Input

123


Output

460191684


Input

36018


Output

966522825


Input

1000


Output

184984484

### Response

```cpp
/**
 * File    : F.cpp
 * Author  : Kazune Takahashi
 * Created : 2018-2-27 18:27:15
 * Powered by Visual Studio Code
 */

#include <iostream>
#include <iomanip>   // << fixed << setprecision(xxx)
#include <algorithm> // do { } while ( next_permutation(A, A+xxx) ) ;
#include <vector>
#include <string> // to_string(nnn) // substr(m, n) // stoi(nnn)
#include <complex>
#include <tuple>
#include <queue>
#include <stack>
#include <map> // if (M.find(key) != M.end()) { }
#include <set>
#include <random> // random_device rd; mt19937 mt(rd());
#include <cctype>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
using namespace std;

#define DEBUG 0 // change 0 -> 1 if we need debug.

typedef long long ll;

// const int dx[4] = {1, 0, -1, 0};
// const int dy[4] = {0, 1, 0, -1};

// const int C = 1e6+10;
// const ll M = 1000000007;

const long long MOD = 1000000007;

long long power(long long x, long long n) {
  if (n == 0) {
    return 1;
  } else if (n%2 == 1) {
    return (x * power(x, n-1)) % MOD;
  } else {
    long long half = power(x, n/2);
    return (half * half) % MOD;
  }
}

int f[30000010];

int main()
{
  int S;
  cin >> S;
  vector<int> Y;
  int SQ = sqrt(S) + 10;
  for (int i = 1; i < SQ; i++)
  {
    if (S%i == 0)
    {
      int j = S / i;
      if (i < j)
      {
        Y.push_back(i);
        Y.push_back(j);
      }
      else if (i == j)
      {
        Y.push_back(i);
      }
    }
  }
  ll ans = 0;
  for (auto i = 0; i < 8; i++)
  {
    int lb = power(10, i);
    int ub = min((int)power(10, i + 1), 30000010);
    for (auto j = lb; j < ub; j++)
    {
      f[j] = i+1;
    }
  }
  int lb = 1;
  int ub = 1;
  int sum = 0;
  while (lb < 10000000)
  {
    if (sum == S)
      ans++;
    if (sum <= S)
    {
      sum += f[ub++];
    }
    else
    {
      sum -= f[lb++];
    }
  }
  ans += S / 8;
  for (auto k : Y)
  {
    if (k <= S/8)
    {
      int d = S / k;
      ans += (power(10, d) + MOD - power(10, d - 1) + MOD - S / d) % MOD;
      ans %= MOD;
    }
  }
  cout << ans << endl;
}
```