#include <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
#include <cassert>
#include <bitset>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define index(xs, x) (int)(lower_bound(all(xs), x) - xs.begin())
#define _1 first
#define _2 second
#define pb push_back
#define INF 1145141919LL
#define MOD 1000000007

int modpow(int x, int k) {
  int a = 1;
  while (k > 0) {
    if (k & 1) a = (1LL*a*x) % MOD;
    x = (1LL*x*x) % MOD;
    k >>= 1;
  }
  return a;
}
int gcd(int a, int b) {
  if (a > b) swap(a, b);
  if (a == 0) return b;
  return gcd(b%a, a);
}
int xGCD(int a, int b, int &x, int &y) {
  if(b == 0) {
     x = 1;
     y = 0;
     return a;
  }
  int x1, y1, gcd = xGCD(b, a % b, x1, y1);
  x = y1;
  y = x1 - (a / b) * y1;
  return gcd;
}

int S;
int num[11];
signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  num[1] = 9;
  for (int i=2; i<=10; i++) num[i] = 10LL*num[i-1];

  cin >> S;
  vector<int> ds;
  for (int d=1; d*d<=S; d++) if (S%d == 0) ds.pb(d), ds.pb(S/d);
  sort(all(ds)); uniq(ds);
  int s = 0;
  for (int f : ds) {
    int n = S/f;
    if (f <= 9 && n > num[f]) continue;
    s = (s + 9LL*modpow(10, f-1)+1+MOD-n) % MOD;
  }
  for (int a=10; a<=S; a++) {
    s += (S-1)/a-S/(a+1);
    if (s >= MOD) s -= MOD;
  }

  for (int a=1; a<=10; a++) {
    for (int b=a+1; b<=10; b++) {
      int g = gcd(a, b);
      long long c = S;
      for (int x=a+1; x<=b-1; x++) c -= 1LL*x*num[x];
      if (c <= 0 || c % g) continue;
      int x0, y0;
      xGCD(a, b, x0, y0);
      x0 *= c/g;
      y0 *= c/g;
      assert(a*x0+b*y0==c);
      int a2 = a/g, b2 = b/g;
      int lo = max((INF*b2+b2-x0)/b2, (INF*a2+y0-num[b]+a2-1)/a2)-INF;
      int hi = min((INF*b2+num[a]-x0)/b2, (INF*a2+y0-1)/a2)-INF;
      if (lo <= hi) s = (s+hi-lo+1) % MOD;
    }
  }
  cout << s << "\n";
  return 0;
}

### Prompt

Please create a solution in CPP 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
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
#include <cassert>
#include <bitset>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define index(xs, x) (int)(lower_bound(all(xs), x) - xs.begin())
#define _1 first
#define _2 second
#define pb push_back
#define INF 1145141919LL
#define MOD 1000000007

int modpow(int x, int k) {
  int a = 1;
  while (k > 0) {
    if (k & 1) a = (1LL*a*x) % MOD;
    x = (1LL*x*x) % MOD;
    k >>= 1;
  }
  return a;
}
int gcd(int a, int b) {
  if (a > b) swap(a, b);
  if (a == 0) return b;
  return gcd(b%a, a);
}
int xGCD(int a, int b, int &x, int &y) {
  if(b == 0) {
     x = 1;
     y = 0;
     return a;
  }
  int x1, y1, gcd = xGCD(b, a % b, x1, y1);
  x = y1;
  y = x1 - (a / b) * y1;
  return gcd;
}

int S;
int num[11];
signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  num[1] = 9;
  for (int i=2; i<=10; i++) num[i] = 10LL*num[i-1];

  cin >> S;
  vector<int> ds;
  for (int d=1; d*d<=S; d++) if (S%d == 0) ds.pb(d), ds.pb(S/d);
  sort(all(ds)); uniq(ds);
  int s = 0;
  for (int f : ds) {
    int n = S/f;
    if (f <= 9 && n > num[f]) continue;
    s = (s + 9LL*modpow(10, f-1)+1+MOD-n) % MOD;
  }
  for (int a=10; a<=S; a++) {
    s += (S-1)/a-S/(a+1);
    if (s >= MOD) s -= MOD;
  }

  for (int a=1; a<=10; a++) {
    for (int b=a+1; b<=10; b++) {
      int g = gcd(a, b);
      long long c = S;
      for (int x=a+1; x<=b-1; x++) c -= 1LL*x*num[x];
      if (c <= 0 || c % g) continue;
      int x0, y0;
      xGCD(a, b, x0, y0);
      x0 *= c/g;
      y0 *= c/g;
      assert(a*x0+b*y0==c);
      int a2 = a/g, b2 = b/g;
      int lo = max((INF*b2+b2-x0)/b2, (INF*a2+y0-num[b]+a2-1)/a2)-INF;
      int hi = min((INF*b2+num[a]-x0)/b2, (INF*a2+y0-1)/a2)-INF;
      if (lo <= hi) s = (s+hi-lo+1) % MOD;
    }
  }
  cout << s << "\n";
  return 0;
}

```