#include <bits/stdc++.h>
using namespace std;
array<array<int, 5>, 5> identidade() {
  array<array<int, 5>, 5> arr;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) arr[i][j] = 100000000, arr[i][i] = 0;
  return arr;
}
array<array<int, 5>, 5> get(char c) {
  array<array<int, 5>, 5> arr = identidade();
  if (c == '2') arr[0][0] = 1, arr[0][1] = 0;
  if (c == '0') arr[1][1] = 1, arr[1][2] = 0;
  if (c == '1') arr[2][2] = 1, arr[2][3] = 0;
  if (c == '7') arr[3][3] = 1, arr[3][4] = 0;
  if (c == '6') arr[4][4] = 1, arr[3][3] = 1;
  return arr;
}
array<array<int, 5>, 5> merge(array<array<int, 5>, 5> a,
                              array<array<int, 5>, 5> b) {
  array<array<int, 5>, 5> arr;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) arr[i][j] = 100000000;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++)
      for (int k = 0; k < 5; k++)
        arr[i][j] = min({arr[i][j], a[i][k] + b[k][j], 100000000});
  return arr;
}
array<array<int, 5>, 5> tree[4 * 200005];
char s[200005];
void build(int node, int a, int b) {
  if (a == b) {
    tree[node] = get(s[a]);
  } else {
    build(node * 2, a, (a + b) / 2);
    build(node * 2 + 1, (a + b) / 2 + 1, b);
    tree[node] = merge(tree[node * 2], tree[node * 2 + 1]);
  }
}
array<array<int, 5>, 5> query(int node, int a, int b, int i, int j) {
  if (j < a || i > b) return identidade();
  if (a >= i && b <= j) return tree[node];
  array<array<int, 5>, 5> l = query(node * 2, a, (a + b) / 2, i, j);
  array<array<int, 5>, 5> r = query(node * 2 + 1, (a + b) / 2 + 1, b, i, j);
  return merge(l, r);
}
int main() {
  int n, q;
  scanf("%d %d", &n, &q);
  scanf("%s", s);
  build(1, 0, n - 1);
  while (q--) {
    int a, b;
    scanf("%d %d", &a, &b);
    a--, b--;
    array<array<int, 5>, 5> node = query(1, 0, n - 1, a, b);
    printf("%d\n", node[0][4] == 100000000 ? -1 : node[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>
using namespace std;
array<array<int, 5>, 5> identidade() {
  array<array<int, 5>, 5> arr;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) arr[i][j] = 100000000, arr[i][i] = 0;
  return arr;
}
array<array<int, 5>, 5> get(char c) {
  array<array<int, 5>, 5> arr = identidade();
  if (c == '2') arr[0][0] = 1, arr[0][1] = 0;
  if (c == '0') arr[1][1] = 1, arr[1][2] = 0;
  if (c == '1') arr[2][2] = 1, arr[2][3] = 0;
  if (c == '7') arr[3][3] = 1, arr[3][4] = 0;
  if (c == '6') arr[4][4] = 1, arr[3][3] = 1;
  return arr;
}
array<array<int, 5>, 5> merge(array<array<int, 5>, 5> a,
                              array<array<int, 5>, 5> b) {
  array<array<int, 5>, 5> arr;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) arr[i][j] = 100000000;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++)
      for (int k = 0; k < 5; k++)
        arr[i][j] = min({arr[i][j], a[i][k] + b[k][j], 100000000});
  return arr;
}
array<array<int, 5>, 5> tree[4 * 200005];
char s[200005];
void build(int node, int a, int b) {
  if (a == b) {
    tree[node] = get(s[a]);
  } else {
    build(node * 2, a, (a + b) / 2);
    build(node * 2 + 1, (a + b) / 2 + 1, b);
    tree[node] = merge(tree[node * 2], tree[node * 2 + 1]);
  }
}
array<array<int, 5>, 5> query(int node, int a, int b, int i, int j) {
  if (j < a || i > b) return identidade();
  if (a >= i && b <= j) return tree[node];
  array<array<int, 5>, 5> l = query(node * 2, a, (a + b) / 2, i, j);
  array<array<int, 5>, 5> r = query(node * 2 + 1, (a + b) / 2 + 1, b, i, j);
  return merge(l, r);
}
int main() {
  int n, q;
  scanf("%d %d", &n, &q);
  scanf("%s", s);
  build(1, 0, n - 1);
  while (q--) {
    int a, b;
    scanf("%d %d", &a, &b);
    a--, b--;
    array<array<int, 5>, 5> node = query(1, 0, n - 1, a, b);
    printf("%d\n", node[0][4] == 100000000 ? -1 : node[0][4]);
  }
  return 0;
}

```