#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 10;
const int INF = 1e8;
struct Node {
  int val[5][5];
  Node() { memset(val, 63, sizeof(val)); }
};
int n, q;
string s;
Node ZZ, weed[4 * MAXN];
Node sprout(Node a, Node b) {
  Node ret;
  for (int i = 0; i < 5; i++)
    for (int j = 0; i + j < 5; j++)
      for (int k = 0; k <= j; k++)
        ret.val[i][j] = min(ret.val[i][j], a.val[i][k] + b.val[i + k][j - k]);
  return ret;
}
void plant(int v, int b, int e) {
  if (e - b == 1) {
    for (int w = 0; w < 5; w++) weed[v].val[w][0] = 1;
    if (s[b] == '2') {
      weed[v].val[0][1] = 0;
      for (int w = 1; w < 5; w++) weed[v].val[w][0] = 0;
    } else if (s[b] == '0') {
      weed[v].val[1][1] = 0;
      for (int w = 0; w < 5; w++)
        if (w ^ 1) weed[v].val[w][0] = 0;
    } else if (s[b] == '1') {
      weed[v].val[2][1] = 0;
      for (int w = 0; w < 5; w++)
        if (w ^ 2) weed[v].val[w][0] = 0;
    } else if (s[b] == '6') {
      for (int w = 0; w < 3; w++) weed[v].val[w][0] = 0;
    } else if (s[b] == '7') {
      weed[v].val[3][1] = 0;
      for (int w = 0; w < 5; w++)
        if (w ^ 3) weed[v].val[w][0] = 0;
    } else
      for (int w = 0; w < 5; w++) weed[v].val[w][0] = 0;
    return;
  }
  int mid = b + e >> 1;
  plant(v << 1, b, mid);
  plant(v << 1 ^ 1, mid, e);
  weed[v] = sprout(weed[v << 1], weed[v << 1 ^ 1]);
}
Node smoke(int v, int b, int e, int l, int r) {
  if (l <= b && e <= r) return weed[v];
  if (r <= b || e <= l) return ZZ;
  int mid = b + e >> 1;
  return sprout(smoke(v << 1, b, mid, l, r), smoke(v << 1 ^ 1, mid, e, l, r));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> q >> s;
  for (int i = 0; i < 5; i++) ZZ.val[i][0] = 0;
  plant(1, 0, n);
  while (q--) {
    int l, r;
    cin >> l >> r, l--;
    int ans = smoke(1, 0, n, l, r).val[0][4];
    if (ans >= INF) ans = -1;
    cout << ans << "\n";
  }
  return 0;
}

### Prompt

Generate 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 int MAXN = 2e5 + 10;
const int INF = 1e8;
struct Node {
  int val[5][5];
  Node() { memset(val, 63, sizeof(val)); }
};
int n, q;
string s;
Node ZZ, weed[4 * MAXN];
Node sprout(Node a, Node b) {
  Node ret;
  for (int i = 0; i < 5; i++)
    for (int j = 0; i + j < 5; j++)
      for (int k = 0; k <= j; k++)
        ret.val[i][j] = min(ret.val[i][j], a.val[i][k] + b.val[i + k][j - k]);
  return ret;
}
void plant(int v, int b, int e) {
  if (e - b == 1) {
    for (int w = 0; w < 5; w++) weed[v].val[w][0] = 1;
    if (s[b] == '2') {
      weed[v].val[0][1] = 0;
      for (int w = 1; w < 5; w++) weed[v].val[w][0] = 0;
    } else if (s[b] == '0') {
      weed[v].val[1][1] = 0;
      for (int w = 0; w < 5; w++)
        if (w ^ 1) weed[v].val[w][0] = 0;
    } else if (s[b] == '1') {
      weed[v].val[2][1] = 0;
      for (int w = 0; w < 5; w++)
        if (w ^ 2) weed[v].val[w][0] = 0;
    } else if (s[b] == '6') {
      for (int w = 0; w < 3; w++) weed[v].val[w][0] = 0;
    } else if (s[b] == '7') {
      weed[v].val[3][1] = 0;
      for (int w = 0; w < 5; w++)
        if (w ^ 3) weed[v].val[w][0] = 0;
    } else
      for (int w = 0; w < 5; w++) weed[v].val[w][0] = 0;
    return;
  }
  int mid = b + e >> 1;
  plant(v << 1, b, mid);
  plant(v << 1 ^ 1, mid, e);
  weed[v] = sprout(weed[v << 1], weed[v << 1 ^ 1]);
}
Node smoke(int v, int b, int e, int l, int r) {
  if (l <= b && e <= r) return weed[v];
  if (r <= b || e <= l) return ZZ;
  int mid = b + e >> 1;
  return sprout(smoke(v << 1, b, mid, l, r), smoke(v << 1 ^ 1, mid, e, l, r));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> q >> s;
  for (int i = 0; i < 5; i++) ZZ.val[i][0] = 0;
  plant(1, 0, n);
  while (q--) {
    int l, r;
    cin >> l >> r, l--;
    int ans = smoke(1, 0, n, l, r).val[0][4];
    if (ans >= INF) ans = -1;
    cout << ans << "\n";
  }
  return 0;
}

```