#include <bits/stdc++.h>
using namespace std;
int n, q;
char s[200005];
struct node {
  int x[5][5];
} t[800005];
node operator+(node x, node y) {
  node z;
  memset(z.x, 63, sizeof(z.x));
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++)
      for (int k = 0; k < 5; k++)
        z.x[i][j] = min(z.x[i][j], x.x[i][k] + y.x[k][j]);
  return z;
}
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) x = (x + (x << 2) << 1) + (ch ^ 48);
  return x * f;
}
inline void write(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10);
  putchar(x % 10 ^ 48);
}
void build(int i, int l, int r) {
  if (l == r) {
    for (int j = 0; j < 5; j++) {
      t[i].x[j][j] = 0;
      for (int k = j + 1; k < 5; k++) t[i].x[j][k] = t[i].x[k][j] = 0x3f3f3f3f;
    }
    if (s[l] == 48) t[i].x[1][1] = 1, t[i].x[2][1] = 0;
    if (s[l] == 49) t[i].x[2][2] = 1, t[i].x[3][2] = 0;
    if (s[l] == 50) t[i].x[0][0] = 1, t[i].x[1][0] = 0;
    if (s[l] == 54) t[i].x[3][3] = t[i].x[4][4] = 1;
    if (s[l] == 55) t[i].x[3][3] = 1, t[i].x[4][3] = 0;
    return;
  }
  int mid = l + r >> 1;
  build(i << 1, l, mid), build(i << 1 | 1, mid + 1, r),
      t[i] = t[i << 1 | 1] + t[i << 1];
}
node query(int i, int l, int r, int x, int y) {
  if (x <= l && y >= r) return t[i];
  int mid = l + r >> 1;
  if (y <= mid) return query(i << 1, l, mid, x, y);
  if (x > mid) return query(i << 1 | 1, mid + 1, r, x, y);
  return query(i << 1 | 1, mid + 1, r, x, y) + query(i << 1, l, mid, x, y);
}
int main() {
  scanf("%d%d%s", &n, &q, s + 1);
  build(1, 1, n);
  while (q--) {
    int x = read(), y = read(), ans = query(1, 1, n, x, y).x[4][0];
    write(ans >= 0x3f3f3f3f ? -1 : ans), putchar('\n');
  }
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;
int n, q;
char s[200005];
struct node {
  int x[5][5];
} t[800005];
node operator+(node x, node y) {
  node z;
  memset(z.x, 63, sizeof(z.x));
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++)
      for (int k = 0; k < 5; k++)
        z.x[i][j] = min(z.x[i][j], x.x[i][k] + y.x[k][j]);
  return z;
}
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) x = (x + (x << 2) << 1) + (ch ^ 48);
  return x * f;
}
inline void write(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10);
  putchar(x % 10 ^ 48);
}
void build(int i, int l, int r) {
  if (l == r) {
    for (int j = 0; j < 5; j++) {
      t[i].x[j][j] = 0;
      for (int k = j + 1; k < 5; k++) t[i].x[j][k] = t[i].x[k][j] = 0x3f3f3f3f;
    }
    if (s[l] == 48) t[i].x[1][1] = 1, t[i].x[2][1] = 0;
    if (s[l] == 49) t[i].x[2][2] = 1, t[i].x[3][2] = 0;
    if (s[l] == 50) t[i].x[0][0] = 1, t[i].x[1][0] = 0;
    if (s[l] == 54) t[i].x[3][3] = t[i].x[4][4] = 1;
    if (s[l] == 55) t[i].x[3][3] = 1, t[i].x[4][3] = 0;
    return;
  }
  int mid = l + r >> 1;
  build(i << 1, l, mid), build(i << 1 | 1, mid + 1, r),
      t[i] = t[i << 1 | 1] + t[i << 1];
}
node query(int i, int l, int r, int x, int y) {
  if (x <= l && y >= r) return t[i];
  int mid = l + r >> 1;
  if (y <= mid) return query(i << 1, l, mid, x, y);
  if (x > mid) return query(i << 1 | 1, mid + 1, r, x, y);
  return query(i << 1 | 1, mid + 1, r, x, y) + query(i << 1, l, mid, x, y);
}
int main() {
  scanf("%d%d%s", &n, &q, s + 1);
  build(1, 1, n);
  while (q--) {
    int x = read(), y = read(), ans = query(1, 1, n, x, y).x[4][0];
    write(ans >= 0x3f3f3f3f ? -1 : ans), putchar('\n');
  }
  return 0;
}

```