#include <bits/stdc++.h>
using namespace std;
const int N = 111, mod = 998244353;
char s[N];
int dig[N], n;
int gcd(int x, int y) { return x ? gcd(y % x, x) : y; }
map<pair<int, int>, int> dp[2][2][10][10];
void add(int& var, int val) {
  var += val;
  if (var >= mod) var -= mod;
}
int to1[10], to2[10];
long long solve(int x, int y) {
  memset(dp, 0, sizeof dp);
  int c = 0, b = 1;
  memset(to1, 0, sizeof to1);
  memset(to2, 0, sizeof to2);
  for (int i = 1; i * y < 10; ++i) {
    to1[i * x] = 1 << (i - 1);
    to2[i * y] = 1 << (i - 1);
  }
  for (int lebih = 0; lebih < 2; ++lebih) {
    for (int l = 0; l < 10; ++l) {
      for (int r = 0; r < 10; ++r) {
        dp[c][lebih][l][r].clear();
      }
    }
  }
  dp[c][0][0][0][{0, 0}] = 1;
  for (int i = 0; i < n; ++i) {
    swap(c, b);
    for (int lebih = 0; lebih < 2; ++lebih) {
      for (int l = 0; l < 10; ++l) {
        for (int r = 0; r < 10; ++r) {
          dp[c][lebih][l][r].clear();
        }
      }
    }
    for (int lebih = 0; lebih < 2; ++lebih) {
      for (int l = 0; l < 10; ++l) {
        for (int r = 0; r < 10; ++r) {
          for (auto it : dp[b][lebih][l][r]) {
            int now = it.second;
            int maska = it.first.first, maskb = it.first.second;
            if (now == 0) continue;
            for (int k = 0; k < 10; ++k) {
              int ll = l + x * k, rr = r + y * k;
              int dl = ll % 10, dr = rr % 10;
              ll /= 10;
              rr /= 10;
              int more = 0;
              if (dr > dig[i])
                more = 1;
              else if (dr == dig[i])
                more = lebih;
              int mmaska = maska, mmaskb = maskb;
              mmaska |= to1[dl];
              mmaskb |= to2[dr];
              add(dp[c][more][ll][rr][{mmaska, mmaskb}], now);
            }
          }
        }
      }
    }
  }
  int ans = 0;
  for (auto it : dp[c][0][0][0]) {
    auto mask = it.first;
    if (mask.first & mask.second) add(ans, it.second);
  }
  return ans;
}
int main() {
  scanf("%s", s);
  n = strlen(s);
  for (int i = 0; i < n; ++i) dig[n - 1 - i] = s[i] - '0';
  dig[n] = 0;
  long long ans = 0;
  for (int x = 1; x <= 9; ++x) {
    for (int y = x; y <= 9; ++y) {
      if (gcd(x, y) != 1) continue;
      long long res = solve(x, y);
      ans = (ans + res) % mod;
      if (x != y) ans = (ans + res) % mod;
    }
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

Let's call a fraction x/y good if there exists at least one another fraction (x')/(y') such that x/y = (x')/(y'), 1 ≤ x', y' ≤ 9, the digit denoting x' is contained in the decimal representation of x, and the digit denoting y' is contained in the decimal representation of y. For example, 26/13 is a good fraction, because 26/13 = 2/1.

You are given an integer number n. Please calculate the number of good fractions x/y such that 1 ≤ x ≤ n and 1 ≤ y ≤ n. The answer may be really large, so print it modulo 998244353.

Input

The only line of the input contains one integer n (1 ≤ n < 10^{100}).

Output

Print the number of good fractions x/y such that 1 ≤ x ≤ n and 1 ≤ y ≤ n. The answer may be really large, so print it modulo 998244353.

Examples

Input


42


Output


150


Input


3141592653589793238462643383279


Output


459925407

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 111, mod = 998244353;
char s[N];
int dig[N], n;
int gcd(int x, int y) { return x ? gcd(y % x, x) : y; }
map<pair<int, int>, int> dp[2][2][10][10];
void add(int& var, int val) {
  var += val;
  if (var >= mod) var -= mod;
}
int to1[10], to2[10];
long long solve(int x, int y) {
  memset(dp, 0, sizeof dp);
  int c = 0, b = 1;
  memset(to1, 0, sizeof to1);
  memset(to2, 0, sizeof to2);
  for (int i = 1; i * y < 10; ++i) {
    to1[i * x] = 1 << (i - 1);
    to2[i * y] = 1 << (i - 1);
  }
  for (int lebih = 0; lebih < 2; ++lebih) {
    for (int l = 0; l < 10; ++l) {
      for (int r = 0; r < 10; ++r) {
        dp[c][lebih][l][r].clear();
      }
    }
  }
  dp[c][0][0][0][{0, 0}] = 1;
  for (int i = 0; i < n; ++i) {
    swap(c, b);
    for (int lebih = 0; lebih < 2; ++lebih) {
      for (int l = 0; l < 10; ++l) {
        for (int r = 0; r < 10; ++r) {
          dp[c][lebih][l][r].clear();
        }
      }
    }
    for (int lebih = 0; lebih < 2; ++lebih) {
      for (int l = 0; l < 10; ++l) {
        for (int r = 0; r < 10; ++r) {
          for (auto it : dp[b][lebih][l][r]) {
            int now = it.second;
            int maska = it.first.first, maskb = it.first.second;
            if (now == 0) continue;
            for (int k = 0; k < 10; ++k) {
              int ll = l + x * k, rr = r + y * k;
              int dl = ll % 10, dr = rr % 10;
              ll /= 10;
              rr /= 10;
              int more = 0;
              if (dr > dig[i])
                more = 1;
              else if (dr == dig[i])
                more = lebih;
              int mmaska = maska, mmaskb = maskb;
              mmaska |= to1[dl];
              mmaskb |= to2[dr];
              add(dp[c][more][ll][rr][{mmaska, mmaskb}], now);
            }
          }
        }
      }
    }
  }
  int ans = 0;
  for (auto it : dp[c][0][0][0]) {
    auto mask = it.first;
    if (mask.first & mask.second) add(ans, it.second);
  }
  return ans;
}
int main() {
  scanf("%s", s);
  n = strlen(s);
  for (int i = 0; i < n; ++i) dig[n - 1 - i] = s[i] - '0';
  dig[n] = 0;
  long long ans = 0;
  for (int x = 1; x <= 9; ++x) {
    for (int y = x; y <= 9; ++y) {
      if (gcd(x, y) != 1) continue;
      long long res = solve(x, y);
      ans = (ans + res) % mod;
      if (x != y) ans = (ans + res) % mod;
    }
  }
  printf("%lld\n", ans);
  return 0;
}

```