#include <bits/stdc++.h>
using namespace std;
const double pai = acos(-1);
const long long mod = 1e9 + 7;
const int MX = 2e5 + 5;
const int sz = 5;
int n, q;
string s;
int ma[300];
struct no {
  int m[5][5];
};
no T[MX << 2];
no ff(no x, no y) {
  no re;
  for (int j = 0; j < sz; j++)
    for (int k = 0; k < sz; k++) re.m[j][k] = INT_MAX / 10;
  for (int i = 0; i < sz; i++) {
    for (int j = 0; j < sz; j++) {
      for (int k = 0; k <= j; k++) {
        re.m[i][j] = min(re.m[i][j], x.m[i][k] + y.m[k][j]);
      }
    }
  }
  return re;
}
void pushUp(int rt) { T[rt] = ff(T[rt << 1], T[rt << 1 | 1]); }
void build(int l, int r, int rt) {
  if (l == r) {
    for (int j = 0; j < sz; j++)
      for (int k = 0; k < sz; k++) T[rt].m[j][k] = (k == j) ? 0 : INT_MAX / 10;
    char now = s[l - 1];
    if (now == '2') T[rt].m[0][0] = 1, T[rt].m[0][1] = 0;
    if (now == '0') T[rt].m[1][1] = 1, T[rt].m[1][2] = 0;
    if (now == '1') T[rt].m[2][2] = 1, T[rt].m[2][3] = 0;
    if (now == '7') T[rt].m[3][3] = 1, T[rt].m[3][4] = 0;
    if (now == '6') T[rt].m[4][4] = 1, T[rt].m[3][3] = 1;
    return;
  }
  int mid = (l + r) / 2;
  build(l, mid, rt << 1);
  build(mid + 1, r, rt << 1 | 1);
  pushUp(rt);
}
no query(int L, int R, int l, int r, int rt) {
  if (l >= L && r <= R) return T[rt];
  int m = (l + r) >> 1;
  if (m < L) return query(L, R, m + 1, r, rt << 1 | 1);
  if (m >= R) return query(L, R, l, m, rt << 1);
  return ff(query(L, R, l, m, rt << 1), query(L, R, m + 1, r, rt << 1 | 1));
}
int main() {
  cin >> n >> q;
  cin >> s;
  build(1, n, 1);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    int now = query(l, r, 1, n, 1).m[0][4];
    if (now == INT_MAX / 10)
      puts("-1");
    else
      cout << now << '\n';
  }
  return 0;
}

### Prompt

Your task is to create a cpp solution to 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 double pai = acos(-1);
const long long mod = 1e9 + 7;
const int MX = 2e5 + 5;
const int sz = 5;
int n, q;
string s;
int ma[300];
struct no {
  int m[5][5];
};
no T[MX << 2];
no ff(no x, no y) {
  no re;
  for (int j = 0; j < sz; j++)
    for (int k = 0; k < sz; k++) re.m[j][k] = INT_MAX / 10;
  for (int i = 0; i < sz; i++) {
    for (int j = 0; j < sz; j++) {
      for (int k = 0; k <= j; k++) {
        re.m[i][j] = min(re.m[i][j], x.m[i][k] + y.m[k][j]);
      }
    }
  }
  return re;
}
void pushUp(int rt) { T[rt] = ff(T[rt << 1], T[rt << 1 | 1]); }
void build(int l, int r, int rt) {
  if (l == r) {
    for (int j = 0; j < sz; j++)
      for (int k = 0; k < sz; k++) T[rt].m[j][k] = (k == j) ? 0 : INT_MAX / 10;
    char now = s[l - 1];
    if (now == '2') T[rt].m[0][0] = 1, T[rt].m[0][1] = 0;
    if (now == '0') T[rt].m[1][1] = 1, T[rt].m[1][2] = 0;
    if (now == '1') T[rt].m[2][2] = 1, T[rt].m[2][3] = 0;
    if (now == '7') T[rt].m[3][3] = 1, T[rt].m[3][4] = 0;
    if (now == '6') T[rt].m[4][4] = 1, T[rt].m[3][3] = 1;
    return;
  }
  int mid = (l + r) / 2;
  build(l, mid, rt << 1);
  build(mid + 1, r, rt << 1 | 1);
  pushUp(rt);
}
no query(int L, int R, int l, int r, int rt) {
  if (l >= L && r <= R) return T[rt];
  int m = (l + r) >> 1;
  if (m < L) return query(L, R, m + 1, r, rt << 1 | 1);
  if (m >= R) return query(L, R, l, m, rt << 1);
  return ff(query(L, R, l, m, rt << 1), query(L, R, m + 1, r, rt << 1 | 1));
}
int main() {
  cin >> n >> q;
  cin >> s;
  build(1, n, 1);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    int now = query(l, r, 1, n, 1).m[0][4];
    if (now == INT_MAX / 10)
      puts("-1");
    else
      cout << now << '\n';
  }
  return 0;
}

```