#include <bits/stdc++.h>
using namespace std;
char s[200005];
struct node {
  int nt[5][5];
};
int str[4] = {2, 0, 1, 7};
node st[800005];
node merge(node a, node b) {
  node res;
  for (int i = 0; i <= 4; i++)
    for (int j = 0; j <= 4; j++) res.nt[i][j] = -1e9;
  for (int i = 0; i <= 4; i++) {
    for (int j = i; j <= 4; j++) {
      for (int k = j; k <= 4; k++) {
        res.nt[i][k] = max(res.nt[i][k], a.nt[i][j] + b.nt[j][k]);
      }
    }
  }
  return res;
}
void update(int n, int s, int e, int idx, int v) {
  if (s == e) {
    for (int i = 0; i <= 3; i++) {
      if (v == str[i]) {
        st[n].nt[i][i + 1] = 1;
        st[n].nt[i][i] = 0;
      } else if (i == 3 && v == 6)
        st[n].nt[i][i] = 0;
      else
        st[n].nt[i][i] = 1;
    }
    if (v == 6)
      st[n].nt[4][4] = 0;
    else
      st[n].nt[4][4] = 1;
  } else {
    int mid = (s + e) / 2;
    if (idx <= mid)
      update(n + n, s, mid, idx, v);
    else
      update(n + n + 1, mid + 1, e, idx, v);
    st[n] = merge(st[n + n], st[n + n + 1]);
  }
}
node query(int n, int s, int e, int l, int r) {
  if (s > r || l > e) {
    node res;
    for (int i = 0; i <= 4; i++)
      for (int j = 0; j <= 4; j++) res.nt[i][j] = -1e9;
    for (int i = 0; i <= 4; i++) res.nt[i][i] = 0;
    return res;
  }
  if (l <= s && e <= r) return st[n];
  int mid = (s + e) / 2;
  node q1 = query(n + n, s, mid, l, r);
  node q2 = query(n + n + 1, mid + 1, e, l, r);
  node q = merge(q1, q2);
  return q;
}
int main() {
  for (int i = 1; i <= 800000; i++) {
    for (int j = 0; j <= 4; j++) {
      for (int k = 0; k <= 4; k++) {
        st[i].nt[j][k] = -1e9;
      }
    }
  }
  int n, q;
  scanf("%d%d", &n, &q);
  scanf("%s", s + 1);
  for (int i = 1; i <= n; i++) update(1, 1, n, i, s[i] - '0');
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    node res = query(1, 1, n, l, r);
    if (res.nt[0][4] < 0)
      printf("-1\n");
    else
      printf("%d\n", r - l + 1 - res.nt[0][4]);
  }
}

### Prompt

Please create a solution in Cpp 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>
using namespace std;
char s[200005];
struct node {
  int nt[5][5];
};
int str[4] = {2, 0, 1, 7};
node st[800005];
node merge(node a, node b) {
  node res;
  for (int i = 0; i <= 4; i++)
    for (int j = 0; j <= 4; j++) res.nt[i][j] = -1e9;
  for (int i = 0; i <= 4; i++) {
    for (int j = i; j <= 4; j++) {
      for (int k = j; k <= 4; k++) {
        res.nt[i][k] = max(res.nt[i][k], a.nt[i][j] + b.nt[j][k]);
      }
    }
  }
  return res;
}
void update(int n, int s, int e, int idx, int v) {
  if (s == e) {
    for (int i = 0; i <= 3; i++) {
      if (v == str[i]) {
        st[n].nt[i][i + 1] = 1;
        st[n].nt[i][i] = 0;
      } else if (i == 3 && v == 6)
        st[n].nt[i][i] = 0;
      else
        st[n].nt[i][i] = 1;
    }
    if (v == 6)
      st[n].nt[4][4] = 0;
    else
      st[n].nt[4][4] = 1;
  } else {
    int mid = (s + e) / 2;
    if (idx <= mid)
      update(n + n, s, mid, idx, v);
    else
      update(n + n + 1, mid + 1, e, idx, v);
    st[n] = merge(st[n + n], st[n + n + 1]);
  }
}
node query(int n, int s, int e, int l, int r) {
  if (s > r || l > e) {
    node res;
    for (int i = 0; i <= 4; i++)
      for (int j = 0; j <= 4; j++) res.nt[i][j] = -1e9;
    for (int i = 0; i <= 4; i++) res.nt[i][i] = 0;
    return res;
  }
  if (l <= s && e <= r) return st[n];
  int mid = (s + e) / 2;
  node q1 = query(n + n, s, mid, l, r);
  node q2 = query(n + n + 1, mid + 1, e, l, r);
  node q = merge(q1, q2);
  return q;
}
int main() {
  for (int i = 1; i <= 800000; i++) {
    for (int j = 0; j <= 4; j++) {
      for (int k = 0; k <= 4; k++) {
        st[i].nt[j][k] = -1e9;
      }
    }
  }
  int n, q;
  scanf("%d%d", &n, &q);
  scanf("%s", s + 1);
  for (int i = 1; i <= n; i++) update(1, 1, n, i, s[i] - '0');
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    node res = query(1, 1, n, l, r);
    if (res.nt[0][4] < 0)
      printf("-1\n");
    else
      printf("%d\n", r - l + 1 - res.nt[0][4]);
  }
}

```