#include <bits/stdc++.h>
struct itnod {
  int a[5][5];
  itnod operator+(itnod z) {
    itnod res;
    for (int i = 0; i < 5; i++) {
      for (int j = i; j < 5; j++) {
        res.a[i][j] = 99999999;
        for (int k = i; k <= j; k++) {
          if (res.a[i][j] > a[i][k] + z.a[k][j])
            res.a[i][j] = a[i][k] + z.a[k][j];
        }
      }
    }
    return res;
  }
};
itnod it[1 << 19];
int n, q;
char s[200100];
int qry[200100][2];
const int itsz = 1 << 18;
itnod makeitn(int p) {
  itnod res;
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      res.a[i][j] = 99999999;
      if (i == j) res.a[i][j] = 0;
    }
  }
  if (p == 2) {
    res.a[0][1] = 0;
    res.a[0][0] = 1;
  }
  if (p == 0) {
    res.a[1][2] = 0;
    res.a[1][1] = 1;
  }
  if (p == 1) {
    res.a[2][3] = 0;
    res.a[2][2] = 1;
  }
  if (p == 7) {
    res.a[3][4] = 0;
  }
  if (p == 6) {
    res.a[3][3] = 1;
    res.a[4][4] = 1;
  }
  return res;
}
itnod itcalc(int start, int end) {
  start += itsz;
  end += itsz;
  itnod left = makeitn(3);
  itnod right = makeitn(3);
  while (start <= end) {
    if (start % 2 == 1) {
      left = left + it[start];
      start++;
    }
    if (end % 2 == 0) {
      right = it[end] + right;
      end--;
    }
    start /= 2;
    end /= 2;
  }
  return left + right;
}
int main() {
  scanf("%d%d", &n, &q);
  scanf("%s", s);
  for (int i = 0; i < n; i++) {
    it[itsz + i] = makeitn(s[i] - '0');
  }
  for (int i = itsz - 1; i > 0; i--) {
    it[i] = it[i * 2] + it[i * 2 + 1];
  }
  for (int i = 0; i < q; i++) {
    scanf("%d%d", &qry[i][0], &qry[i][1]);
    qry[i][0]--;
    qry[i][1]--;
    itnod res = itcalc(qry[i][0], qry[i][1]);
    if (res.a[0][4] >= 999999) res.a[0][4] = -1;
    printf("%d\n", res.a[0][4]);
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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>
struct itnod {
  int a[5][5];
  itnod operator+(itnod z) {
    itnod res;
    for (int i = 0; i < 5; i++) {
      for (int j = i; j < 5; j++) {
        res.a[i][j] = 99999999;
        for (int k = i; k <= j; k++) {
          if (res.a[i][j] > a[i][k] + z.a[k][j])
            res.a[i][j] = a[i][k] + z.a[k][j];
        }
      }
    }
    return res;
  }
};
itnod it[1 << 19];
int n, q;
char s[200100];
int qry[200100][2];
const int itsz = 1 << 18;
itnod makeitn(int p) {
  itnod res;
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      res.a[i][j] = 99999999;
      if (i == j) res.a[i][j] = 0;
    }
  }
  if (p == 2) {
    res.a[0][1] = 0;
    res.a[0][0] = 1;
  }
  if (p == 0) {
    res.a[1][2] = 0;
    res.a[1][1] = 1;
  }
  if (p == 1) {
    res.a[2][3] = 0;
    res.a[2][2] = 1;
  }
  if (p == 7) {
    res.a[3][4] = 0;
  }
  if (p == 6) {
    res.a[3][3] = 1;
    res.a[4][4] = 1;
  }
  return res;
}
itnod itcalc(int start, int end) {
  start += itsz;
  end += itsz;
  itnod left = makeitn(3);
  itnod right = makeitn(3);
  while (start <= end) {
    if (start % 2 == 1) {
      left = left + it[start];
      start++;
    }
    if (end % 2 == 0) {
      right = it[end] + right;
      end--;
    }
    start /= 2;
    end /= 2;
  }
  return left + right;
}
int main() {
  scanf("%d%d", &n, &q);
  scanf("%s", s);
  for (int i = 0; i < n; i++) {
    it[itsz + i] = makeitn(s[i] - '0');
  }
  for (int i = itsz - 1; i > 0; i--) {
    it[i] = it[i * 2] + it[i * 2 + 1];
  }
  for (int i = 0; i < q; i++) {
    scanf("%d%d", &qry[i][0], &qry[i][1]);
    qry[i][0]--;
    qry[i][1]--;
    itnod res = itcalc(qry[i][0], qry[i][1]);
    if (res.a[0][4] >= 999999) res.a[0][4] = -1;
    printf("%d\n", res.a[0][4]);
  }
  return 0;
}

```