#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
const int MX = 2e5 + 233;
int read() {
  char k = getchar();
  int x = 0;
  while (k < '0' || k > '9') k = getchar();
  while (k >= '0' && k <= '9') x = x * 10 + k - '0', k = getchar();
  return x;
}
struct Matrix {
  int A[5][5];
  Matrix() { memset(A, 0x3f, sizeof A); }
  Matrix(int num) {
    memset(A, 0x3f, sizeof A);
    A[0][0] = (num == 2);
    A[1][0] = (num != 2) * INF;
    A[1][1] = (num == 0);
    A[2][1] = (num != 0) * INF;
    A[2][2] = (num == 1);
    A[3][2] = (num != 1) * INF;
    A[3][3] = (num == 6 || num == 7);
    A[4][3] = (num != 7) * INF;
    A[4][4] = (num == 6);
  }
  Matrix operator*(const Matrix &B) const {
    Matrix C;
    for (int i = 0; i < 5; ++i)
      for (int j = 0; j < 5; ++j)
        for (int k = 0; k < 5; ++k)
          C.A[i][j] = min(C.A[i][j], A[i][k] + B.A[k][j]);
    return C;
  }
  void output() {
    for (int i = 0; i < 5; ++i)
      for (int j = 0; j < 5; ++j) printf("%d%c", A[i][j], " \n"[j == 4]);
    puts("||||||||||||||||||||||||||||||||||||||||||");
  }
};
struct node {
  int l, r;
  Matrix s;
  node *lch, *rch;
  node(int _l, int _r, int num, node *L, node *R) {
    s = Matrix(num);
    l = _l, r = _r;
    lch = L, rch = R;
  }
  void pushup() { s = rch->s * lch->s; }
} * root;
node *build(int l, int r, int *A) {
  node *x = nullptr;
  if (l == r)
    x = new node(l, r, A[l], nullptr, nullptr);
  else {
    int mid = (l + r) >> 1;
    node *lch = build(l, mid, A);
    node *rch = build(mid + 1, r, A);
    x = new node(l, r, -1, lch, rch);
    x->pushup();
  }
  return x;
}
void query(node *x, int l, int r, Matrix &Ans) {
  if (l <= x->l && x->r <= r) return Ans = x->s * Ans, void();
  if (l <= x->lch->r) query(x->lch, l, r, Ans);
  if (r > x->lch->r) query(x->rch, l, r, Ans);
}
char str[MX];
int A[MX];
int main() {
  int n = read(), q = read();
  cin >> (str + 1);
  for (int i = 1; i <= n; ++i) {
    A[i] = str[i] - '0';
  }
  root = build(1, n, A);
  while (q--) {
    int l = read(), r = read();
    Matrix Ans = Matrix();
    Ans.A[0][4] = 0;
    query(root, l, r, Ans);
    printf("%d\n", Ans.A[4][4] > n ? -1 : Ans.A[4][4]);
  }
  return 0;
}

### Prompt

Create a solution in Cpp for 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 INF = 1e9;
const int MX = 2e5 + 233;
int read() {
  char k = getchar();
  int x = 0;
  while (k < '0' || k > '9') k = getchar();
  while (k >= '0' && k <= '9') x = x * 10 + k - '0', k = getchar();
  return x;
}
struct Matrix {
  int A[5][5];
  Matrix() { memset(A, 0x3f, sizeof A); }
  Matrix(int num) {
    memset(A, 0x3f, sizeof A);
    A[0][0] = (num == 2);
    A[1][0] = (num != 2) * INF;
    A[1][1] = (num == 0);
    A[2][1] = (num != 0) * INF;
    A[2][2] = (num == 1);
    A[3][2] = (num != 1) * INF;
    A[3][3] = (num == 6 || num == 7);
    A[4][3] = (num != 7) * INF;
    A[4][4] = (num == 6);
  }
  Matrix operator*(const Matrix &B) const {
    Matrix C;
    for (int i = 0; i < 5; ++i)
      for (int j = 0; j < 5; ++j)
        for (int k = 0; k < 5; ++k)
          C.A[i][j] = min(C.A[i][j], A[i][k] + B.A[k][j]);
    return C;
  }
  void output() {
    for (int i = 0; i < 5; ++i)
      for (int j = 0; j < 5; ++j) printf("%d%c", A[i][j], " \n"[j == 4]);
    puts("||||||||||||||||||||||||||||||||||||||||||");
  }
};
struct node {
  int l, r;
  Matrix s;
  node *lch, *rch;
  node(int _l, int _r, int num, node *L, node *R) {
    s = Matrix(num);
    l = _l, r = _r;
    lch = L, rch = R;
  }
  void pushup() { s = rch->s * lch->s; }
} * root;
node *build(int l, int r, int *A) {
  node *x = nullptr;
  if (l == r)
    x = new node(l, r, A[l], nullptr, nullptr);
  else {
    int mid = (l + r) >> 1;
    node *lch = build(l, mid, A);
    node *rch = build(mid + 1, r, A);
    x = new node(l, r, -1, lch, rch);
    x->pushup();
  }
  return x;
}
void query(node *x, int l, int r, Matrix &Ans) {
  if (l <= x->l && x->r <= r) return Ans = x->s * Ans, void();
  if (l <= x->lch->r) query(x->lch, l, r, Ans);
  if (r > x->lch->r) query(x->rch, l, r, Ans);
}
char str[MX];
int A[MX];
int main() {
  int n = read(), q = read();
  cin >> (str + 1);
  for (int i = 1; i <= n; ++i) {
    A[i] = str[i] - '0';
  }
  root = build(1, n, A);
  while (q--) {
    int l = read(), r = read();
    Matrix Ans = Matrix();
    Ans.A[0][4] = 0;
    query(root, l, r, Ans);
    printf("%d\n", Ans.A[4][4] > n ? -1 : Ans.A[4][4]);
  }
  return 0;
}

```