#include <bits/stdc++.h>
using namespace std;
struct Tree {
  int w[5][5];
} IT[262144 + 262144];
int n, Q;
char p[201000], q[5] = "2016";
Tree Merge(Tree c1, Tree c2) {
  int i, j, k;
  Tree tp;
  for (i = 0; i < 5; i++) {
    for (j = i; j < 5; j++) tp.w[i][j] = -1;
    for (j = i; j < 5; j++) {
      if (c1.w[i][j] == -1) continue;
      int t = c1.w[i][j];
      for (k = j; k < 5; k++) {
        if (c2.w[j][k] == -1) continue;
        if (tp.w[i][k] == -1 || tp.w[i][k] > c2.w[j][k] + t)
          tp.w[i][k] = c2.w[j][k] + t;
      }
    }
  }
  return tp;
}
void init(int nd, int b, int e) {
  if (b == e) {
    int i, j;
    for (i = 0; i < 5; i++) {
      for (j = i + 1; j < 5; j++) {
        IT[nd].w[i][j] = -1;
      }
      IT[nd].w[i][i] = 0;
      if (q[i] == p[b]) {
        IT[nd].w[i][i] = 1;
        IT[nd].w[i][i + 1] = 0;
      }
    }
    return;
  }
  int m = (b + e) >> 1;
  init(nd * 2, b, m);
  init(nd * 2 + 1, m + 1, e);
  IT[nd] = Merge(IT[nd * 2], IT[nd * 2 + 1]);
}
Tree Get(int nd, int b, int e, int s, int l) {
  if (b == s && e == l) return IT[nd];
  Tree ret, tp;
  int m = (b + e) >> 1;
  if (s <= m) {
    ret = Get(nd * 2, b, m, s, min(m, l));
  }
  if (l > m) {
    tp = Get(nd * 2 + 1, m + 1, e, max(m + 1, s), l);
    if (s <= m)
      ret = Merge(ret, tp);
    else
      ret = tp;
  }
  return ret;
}
int P[201000], S[201000];
int main() {
  int i, pv = -1, b, e, x;
  Tree tp;
  scanf("%d%d", &n, &Q);
  scanf("%s", p + 1);
  init(1, 1, n);
  for (i = 1; i <= n; i++) {
    if (p[i] == '7') pv = i;
    P[i] = pv;
    S[i] = S[i - 1];
    if (p[i] == '6') S[i]++;
  }
  while (Q--) {
    scanf("%d%d", &b, &e);
    x = P[e];
    if (x < b) {
      printf("-1\n");
      continue;
    }
    tp = Get(1, 1, n, b, x);
    if (tp.w[0][3] == -1) {
      printf("-1\n");
    } else {
      printf("%d\n", tp.w[0][3] + S[e] - S[x]);
    }
  }
}

### Prompt

Construct a cpp code solution to the problem outlined:

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>
using namespace std;
struct Tree {
  int w[5][5];
} IT[262144 + 262144];
int n, Q;
char p[201000], q[5] = "2016";
Tree Merge(Tree c1, Tree c2) {
  int i, j, k;
  Tree tp;
  for (i = 0; i < 5; i++) {
    for (j = i; j < 5; j++) tp.w[i][j] = -1;
    for (j = i; j < 5; j++) {
      if (c1.w[i][j] == -1) continue;
      int t = c1.w[i][j];
      for (k = j; k < 5; k++) {
        if (c2.w[j][k] == -1) continue;
        if (tp.w[i][k] == -1 || tp.w[i][k] > c2.w[j][k] + t)
          tp.w[i][k] = c2.w[j][k] + t;
      }
    }
  }
  return tp;
}
void init(int nd, int b, int e) {
  if (b == e) {
    int i, j;
    for (i = 0; i < 5; i++) {
      for (j = i + 1; j < 5; j++) {
        IT[nd].w[i][j] = -1;
      }
      IT[nd].w[i][i] = 0;
      if (q[i] == p[b]) {
        IT[nd].w[i][i] = 1;
        IT[nd].w[i][i + 1] = 0;
      }
    }
    return;
  }
  int m = (b + e) >> 1;
  init(nd * 2, b, m);
  init(nd * 2 + 1, m + 1, e);
  IT[nd] = Merge(IT[nd * 2], IT[nd * 2 + 1]);
}
Tree Get(int nd, int b, int e, int s, int l) {
  if (b == s && e == l) return IT[nd];
  Tree ret, tp;
  int m = (b + e) >> 1;
  if (s <= m) {
    ret = Get(nd * 2, b, m, s, min(m, l));
  }
  if (l > m) {
    tp = Get(nd * 2 + 1, m + 1, e, max(m + 1, s), l);
    if (s <= m)
      ret = Merge(ret, tp);
    else
      ret = tp;
  }
  return ret;
}
int P[201000], S[201000];
int main() {
  int i, pv = -1, b, e, x;
  Tree tp;
  scanf("%d%d", &n, &Q);
  scanf("%s", p + 1);
  init(1, 1, n);
  for (i = 1; i <= n; i++) {
    if (p[i] == '7') pv = i;
    P[i] = pv;
    S[i] = S[i - 1];
    if (p[i] == '6') S[i]++;
  }
  while (Q--) {
    scanf("%d%d", &b, &e);
    x = P[e];
    if (x < b) {
      printf("-1\n");
      continue;
    }
    tp = Get(1, 1, n, b, x);
    if (tp.w[0][3] == -1) {
      printf("-1\n");
    } else {
      printf("%d\n", tp.w[0][3] + S[e] - S[x]);
    }
  }
}

```