#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 10;
const int INF32 = 0x3f3f3f3f;
const long long INF64 = 0x3f3f3f3f3f3f3f3f;
const long long MOD = 1e9 + 7;
const double PI = acos(-1.0);
const double EPS = 1.0e-8;
struct SegTree {
  struct Node {
    int l, r;
    int a[5][5];
    friend Node operator+(Node a, Node b) {
      Node res;
      res.l = a.l, res.r = b.r;
      memset(res.a, INF32, sizeof(res.a));
      for (int i = 0; i <= 4; ++i) {
        for (int j = 0; j <= 4; ++j) {
          for (int k = 0; k <= 4; ++k) {
            res.a[i][j] = min(res.a[i][j], a.a[i][k] + b.a[k][j]);
          }
        }
      }
      return res;
    }
  };
  Node T[MAXN << 2];
  void PushUp(int rt) { T[rt] = T[rt << 1] + T[rt << 1 | 1]; }
  void Build(int l, int r, int rt, char S[]) {
    T[rt].l = l;
    T[rt].r = r;
    int mid = (l + r) >> 1;
    if (l == r) {
      memset(T[rt].a, INF32, sizeof(T[rt].a));
      for (int i = 0; i <= 4; ++i) T[rt].a[i][i] = 0;
      if (S[l] == '2') T[rt].a[0][0] = 1, T[rt].a[0][1] = 0;
      if (S[l] == '0') T[rt].a[1][1] = 1, T[rt].a[1][2] = 0;
      if (S[l] == '1') T[rt].a[2][2] = 1, T[rt].a[2][3] = 0;
      if (S[l] == '7') T[rt].a[3][3] = 1, T[rt].a[3][4] = 0;
      if (S[l] == '6') T[rt].a[3][3] = 1, T[rt].a[4][4] = 1;
      return;
    }
    Build(l, mid, rt << 1, S);
    Build(mid + 1, r, rt << 1 | 1, S);
    PushUp(rt);
  }
  Node Query(int ql, int qr, int rt) {
    if (ql <= T[rt].l && T[rt].r <= qr) return T[rt];
    if (qr <= T[rt << 1].r)
      return Query(ql, qr, rt << 1);
    else if (ql >= T[rt << 1 | 1].l)
      return Query(ql, qr, rt << 1 | 1);
    else
      return Query(ql, qr, rt << 1) + Query(ql, qr, rt << 1 | 1);
  }
};
SegTree Seg;
char S[MAXN];
int n, m;
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", S + 1);
  Seg.Build(1, n, 1, S);
  for (int i = 1; i <= m; ++i) {
    int l, r;
    scanf("%d%d", &l, &r);
    int tmp = (MAXN << 2) - 1;
    Seg.T[tmp] = Seg.Query(l, r, 1);
    printf("%d\n", Seg.T[tmp].a[0][4] == INF32 ? -1 : Seg.T[tmp].a[0][4]);
  }
}

### 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>
using namespace std;
const int MAXN = 2e5 + 10;
const int INF32 = 0x3f3f3f3f;
const long long INF64 = 0x3f3f3f3f3f3f3f3f;
const long long MOD = 1e9 + 7;
const double PI = acos(-1.0);
const double EPS = 1.0e-8;
struct SegTree {
  struct Node {
    int l, r;
    int a[5][5];
    friend Node operator+(Node a, Node b) {
      Node res;
      res.l = a.l, res.r = b.r;
      memset(res.a, INF32, sizeof(res.a));
      for (int i = 0; i <= 4; ++i) {
        for (int j = 0; j <= 4; ++j) {
          for (int k = 0; k <= 4; ++k) {
            res.a[i][j] = min(res.a[i][j], a.a[i][k] + b.a[k][j]);
          }
        }
      }
      return res;
    }
  };
  Node T[MAXN << 2];
  void PushUp(int rt) { T[rt] = T[rt << 1] + T[rt << 1 | 1]; }
  void Build(int l, int r, int rt, char S[]) {
    T[rt].l = l;
    T[rt].r = r;
    int mid = (l + r) >> 1;
    if (l == r) {
      memset(T[rt].a, INF32, sizeof(T[rt].a));
      for (int i = 0; i <= 4; ++i) T[rt].a[i][i] = 0;
      if (S[l] == '2') T[rt].a[0][0] = 1, T[rt].a[0][1] = 0;
      if (S[l] == '0') T[rt].a[1][1] = 1, T[rt].a[1][2] = 0;
      if (S[l] == '1') T[rt].a[2][2] = 1, T[rt].a[2][3] = 0;
      if (S[l] == '7') T[rt].a[3][3] = 1, T[rt].a[3][4] = 0;
      if (S[l] == '6') T[rt].a[3][3] = 1, T[rt].a[4][4] = 1;
      return;
    }
    Build(l, mid, rt << 1, S);
    Build(mid + 1, r, rt << 1 | 1, S);
    PushUp(rt);
  }
  Node Query(int ql, int qr, int rt) {
    if (ql <= T[rt].l && T[rt].r <= qr) return T[rt];
    if (qr <= T[rt << 1].r)
      return Query(ql, qr, rt << 1);
    else if (ql >= T[rt << 1 | 1].l)
      return Query(ql, qr, rt << 1 | 1);
    else
      return Query(ql, qr, rt << 1) + Query(ql, qr, rt << 1 | 1);
  }
};
SegTree Seg;
char S[MAXN];
int n, m;
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", S + 1);
  Seg.Build(1, n, 1, S);
  for (int i = 1; i <= m; ++i) {
    int l, r;
    scanf("%d%d", &l, &r);
    int tmp = (MAXN << 2) - 1;
    Seg.T[tmp] = Seg.Query(l, r, 1);
    printf("%d\n", Seg.T[tmp].a[0][4] == INF32 ? -1 : Seg.T[tmp].a[0][4]);
  }
}

```