#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int res = 0;
  int neg;
  while (true) {
    char ch = getchar();
    if (ch >= '0' && ch <= '9' || ch == '-') {
      if (ch == '-')
        neg = -1;
      else
        neg = 1, res = ch - '0';
      break;
    }
  }
  while (true) {
    char ch = getchar();
    if (ch >= '0' && ch <= '9')
      res *= 10, res += ch - '0';
    else
      break;
  }
  return res * neg;
}
const int maxn = 200020;
const int maxm = 1000020;
const int MOd = 1e9 + 7;
struct node {
  int n[5][5];
  node(int x = 0) { n[0][0] = x; }
};
int a, b, n;
char ar[maxn];
node segment[maxn * 3];
node merge(node a, node b) {
  if (a.n[0][0] == -1) return b;
  if (b.n[0][0] == -1) return a;
  node t;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++) t.n[i][j] = 1e9;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = j; k < 5; k++)
        t.n[i][k] = min(t.n[i][k], (a.n[i][j] + b.n[j][k]));
  return t;
}
node find(int k, int b, int s, int x, int y) {
  if (b > y || x > s) return node(-1);
  if (x <= b && s <= y) return segment[k];
  return merge(find(k + k, b, (b + s) / 2, x, y),
               find(k + k + 1, (b + s) / 2 + 1, s, x, y));
}
int main() {
  scanf("%d %d", &a, &b);
  scanf(" %s", ar + 1);
  n = 1;
  while (n < a) n <<= 1;
  for (int i = 1; i <= n; i++)
    for (int j = 0; j < 5; j++)
      for (int k = 0; k < 5; k++)
        if (j != k) segment[i + n - 1].n[j][k] = 1e9;
  for (int i = 1; i <= a; i++) {
    node &p = segment[i + n - 1];
    if (ar[i] == '2') p.n[0][0] = 1, p.n[0][1] = 0;
    if (ar[i] == '0') p.n[1][1] = 1, p.n[1][2] = 0;
    if (ar[i] == '1') p.n[2][2] = 1, p.n[2][3] = 0;
    if (ar[i] == '7') p.n[3][3] = 1, p.n[3][4] = 0;
    if (ar[i] == '6') p.n[3][3] = 1, p.n[4][4] = 1;
  }
  for (int i = n - 1; i >= 1; i--)
    segment[i] = merge(segment[i + i], segment[i + i + 1]);
  for (int i = 1, j, k; i <= b; i++) {
    scanf("%d %d", &j, &k);
    node t = find(1, 1, n, j, k);
    if (t.n[0][4] >= 1e9)
      printf("-1\n");
    else
      printf("%d\n", t.n[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;
inline int read() {
  int res = 0;
  int neg;
  while (true) {
    char ch = getchar();
    if (ch >= '0' && ch <= '9' || ch == '-') {
      if (ch == '-')
        neg = -1;
      else
        neg = 1, res = ch - '0';
      break;
    }
  }
  while (true) {
    char ch = getchar();
    if (ch >= '0' && ch <= '9')
      res *= 10, res += ch - '0';
    else
      break;
  }
  return res * neg;
}
const int maxn = 200020;
const int maxm = 1000020;
const int MOd = 1e9 + 7;
struct node {
  int n[5][5];
  node(int x = 0) { n[0][0] = x; }
};
int a, b, n;
char ar[maxn];
node segment[maxn * 3];
node merge(node a, node b) {
  if (a.n[0][0] == -1) return b;
  if (b.n[0][0] == -1) return a;
  node t;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++) t.n[i][j] = 1e9;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = j; k < 5; k++)
        t.n[i][k] = min(t.n[i][k], (a.n[i][j] + b.n[j][k]));
  return t;
}
node find(int k, int b, int s, int x, int y) {
  if (b > y || x > s) return node(-1);
  if (x <= b && s <= y) return segment[k];
  return merge(find(k + k, b, (b + s) / 2, x, y),
               find(k + k + 1, (b + s) / 2 + 1, s, x, y));
}
int main() {
  scanf("%d %d", &a, &b);
  scanf(" %s", ar + 1);
  n = 1;
  while (n < a) n <<= 1;
  for (int i = 1; i <= n; i++)
    for (int j = 0; j < 5; j++)
      for (int k = 0; k < 5; k++)
        if (j != k) segment[i + n - 1].n[j][k] = 1e9;
  for (int i = 1; i <= a; i++) {
    node &p = segment[i + n - 1];
    if (ar[i] == '2') p.n[0][0] = 1, p.n[0][1] = 0;
    if (ar[i] == '0') p.n[1][1] = 1, p.n[1][2] = 0;
    if (ar[i] == '1') p.n[2][2] = 1, p.n[2][3] = 0;
    if (ar[i] == '7') p.n[3][3] = 1, p.n[3][4] = 0;
    if (ar[i] == '6') p.n[3][3] = 1, p.n[4][4] = 1;
  }
  for (int i = n - 1; i >= 1; i--)
    segment[i] = merge(segment[i + i], segment[i + i + 1]);
  for (int i = 1, j, k; i <= b; i++) {
    scanf("%d %d", &j, &k);
    node t = find(1, 1, n, j, k);
    if (t.n[0][4] >= 1e9)
      printf("-1\n");
    else
      printf("%d\n", t.n[0][4]);
  }
  return 0;
}

```