#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
const long long MOD = 1000000007;
const int INF = 1000000007;
const long long LINF = 1LL * INF * INF;
const int MAXN = 200047;
const double EPS = 1e-6;
struct Matrix {
  int A[5][5];
  Matrix operator*(const Matrix& B) {
    Matrix res;
    for (int i = (0); i < (5); ++i)
      for (int j = (i); j < (5); ++j) {
        res.A[i][j] = INF;
        for (int k = (i); k < (j + 1); ++k)
          res.A[i][j] = min(res.A[i][j], this->A[i][k] + B.A[k][j]);
      }
    return res;
  }
};
string S;
Matrix T[MAXN << 2], E;
void build(int v, int tl, int tr) {
  if (tl == tr) {
    T[v] = E;
    if (S[tl] == '2') {
      T[v].A[0][0] = 1;
      T[v].A[0][1] = 0;
    }
    if (S[tl] == '0') {
      T[v].A[1][1] = 1;
      T[v].A[1][2] = 0;
    }
    if (S[tl] == '1') {
      T[v].A[2][2] = 1;
      T[v].A[2][3] = 0;
    }
    if (S[tl] == '7') {
      T[v].A[3][3] = 1;
      T[v].A[3][4] = 0;
    }
    if (S[tl] == '6') T[v].A[3][3] = T[v].A[4][4] = 1;
    return;
  }
  int tm = (tl + tr) >> 1;
  build(v << 1, tl, tm);
  build((v << 1) + 1, tm + 1, tr);
  T[v] = T[v << 1] * T[(v << 1) + 1];
}
Matrix query(int v, int tl, int tr, int l, int r) {
  if (l > tr || r < tl) return E;
  if (l == tl && r == tr) return T[v];
  int tm = (tl + tr) >> 1;
  return query(v << 1, tl, tm, l, min(r, tm)) *
         query((v << 1) + 1, tm + 1, tr, max(l, tm + 1), r);
}
int main() {
  int n, q;
  cin >> n >> q >> S;
  for (int i = (0); i < (5); ++i) {
    E.A[i][i] = 0;
    for (int j = (i + 1); j < (5); ++j) E.A[i][j] = INF;
  }
  build(1, 0, n - 1);
  while (q--) {
    int a, b;
    scanf("%d%d", &a, &b);
    int ans = query(1, 0, n - 1, a - 1, b - 1).A[0][4];
    printf("%d\n", ans < INF ? ans : -1);
  }
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

A string t is called nice if a string "2017" occurs in t as a subsequence but a string "2016" doesn't occur in t as a subsequence. For example, strings "203434107" and "9220617" are nice, while strings "20016", "1234" and "20167" aren't nice.

The ugliness of a string is the minimum possible number of characters to remove, in order to obtain a nice string. If it's impossible to make a string nice by removing characters, its ugliness is  - 1.

Limak has a string s of length n, with characters indexed 1 through n. He asks you q queries. In the i-th query you should compute and print the ugliness of a substring (continuous subsequence) of s starting at the index ai and ending at the index bi (inclusive).

Input

The first line of the input contains two integers n and q (4 ≤ n ≤ 200 000, 1 ≤ q ≤ 200 000) — the length of the string s and the number of queries respectively.

The second line contains a string s of length n. Every character is one of digits '0'–'9'.

The i-th of next q lines contains two integers ai and bi (1 ≤ ai ≤ bi ≤ n), describing a substring in the i-th query.

Output

For each query print the ugliness of the given substring.

Examples

Input

8 3
20166766
1 8
1 7
2 8


Output

4
3
-1


Input

15 5
012016662091670
3 4
1 14
4 15
1 13
10 15


Output

-1
2
1
-1
-1


Input

4 2
1234
2 4
1 2


Output

-1
-1

Note

In the first sample:

  * In the first query, ugliness("20166766") = 4 because all four sixes must be removed. 
  * In the second query, ugliness("2016676") = 3 because all three sixes must be removed. 
  * In the third query, ugliness("0166766") = - 1 because it's impossible to remove some digits to get a nice string. 



In the second sample:

  * In the second query, ugliness("01201666209167") = 2. It's optimal to remove the first digit '2' and the last digit '6', what gives a string "010166620917", which is nice. 
  * In the third query, ugliness("016662091670") = 1. It's optimal to remove the last digit '6', what gives a nice string "01666209170". 

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
const long long MOD = 1000000007;
const int INF = 1000000007;
const long long LINF = 1LL * INF * INF;
const int MAXN = 200047;
const double EPS = 1e-6;
struct Matrix {
  int A[5][5];
  Matrix operator*(const Matrix& B) {
    Matrix res;
    for (int i = (0); i < (5); ++i)
      for (int j = (i); j < (5); ++j) {
        res.A[i][j] = INF;
        for (int k = (i); k < (j + 1); ++k)
          res.A[i][j] = min(res.A[i][j], this->A[i][k] + B.A[k][j]);
      }
    return res;
  }
};
string S;
Matrix T[MAXN << 2], E;
void build(int v, int tl, int tr) {
  if (tl == tr) {
    T[v] = E;
    if (S[tl] == '2') {
      T[v].A[0][0] = 1;
      T[v].A[0][1] = 0;
    }
    if (S[tl] == '0') {
      T[v].A[1][1] = 1;
      T[v].A[1][2] = 0;
    }
    if (S[tl] == '1') {
      T[v].A[2][2] = 1;
      T[v].A[2][3] = 0;
    }
    if (S[tl] == '7') {
      T[v].A[3][3] = 1;
      T[v].A[3][4] = 0;
    }
    if (S[tl] == '6') T[v].A[3][3] = T[v].A[4][4] = 1;
    return;
  }
  int tm = (tl + tr) >> 1;
  build(v << 1, tl, tm);
  build((v << 1) + 1, tm + 1, tr);
  T[v] = T[v << 1] * T[(v << 1) + 1];
}
Matrix query(int v, int tl, int tr, int l, int r) {
  if (l > tr || r < tl) return E;
  if (l == tl && r == tr) return T[v];
  int tm = (tl + tr) >> 1;
  return query(v << 1, tl, tm, l, min(r, tm)) *
         query((v << 1) + 1, tm + 1, tr, max(l, tm + 1), r);
}
int main() {
  int n, q;
  cin >> n >> q >> S;
  for (int i = (0); i < (5); ++i) {
    E.A[i][i] = 0;
    for (int j = (i + 1); j < (5); ++j) E.A[i][j] = INF;
  }
  build(1, 0, n - 1);
  while (q--) {
    int a, b;
    scanf("%d%d", &a, &b);
    int ans = query(1, 0, n - 1, a - 1, b - 1).A[0][4];
    printf("%d\n", ans < INF ? ans : -1);
  }
  return 0;
}

```