#include <bits/stdc++.h>
using namespace std;
char str[200000 + 1];
template <class Node>
struct SegTree {
  int size;
  vector<Node> tree;
  SegTree(int n) {
    size = n;
    tree.resize(4 * n + 1);
  }
  SegTree(int n, char* arr) : SegTree(n) { build(arr); }
  inline int left(int node) { return 2 * node; }
  inline int right(int node) { return 2 * node + 1; }
  void build(char* arr, int node, int st, int end) {
    if (st == end) {
      tree[node] = Node(st, arr[st]);
      return;
    }
    build(arr, left(node), st, (st + end) / 2);
    build(arr, right(node), (st + end) / 2 + 1, end);
    tree[node] = tree[left(node)].join(tree[right(node)]);
  }
  Node query(int node, int st, int end, int i, int j) {
    if (j < st || i > end) return Node();
    if (st >= i && end <= j) return tree[node];
    Node p1 = query(left(node), st, (st + end) / 2, i, j);
    Node p2 = query(right(node), (st + end) / 2 + 1, end, i, j);
    return p1.join(p2);
  }
  void build(char* arr) { build(arr, 1, 0, size - 1); }
  Node query(int i, int j) { return query(1, 0, size - 1, i, j); }
};
void printPref(string str, int prefix[5][5]) {
  cerr << "--" << str << "--" << endl;
  for (int i = 0; i < 5; i++) {
    for (int j = 0; j < 5; j++) {
      fprintf(stderr, "%11d ", prefix[i][j]);
    }
    cerr << endl;
  }
  cerr << endl;
}
struct Node {
  int prefix[5][5];
  Node() {
    memset(prefix, 0x3f, sizeof(prefix));
    for (int i = 0; i < 5; i++) prefix[i][i] = 0;
  }
  Node(int idx, char ch) : Node() {
    if (ch == '2') {
      prefix[0][0] = 1;
      prefix[0][1] = 0;
    } else if (ch == '0') {
      prefix[1][1] = 1;
      prefix[1][2] = 0;
    } else if (ch == '1') {
      prefix[2][2] = 1;
      prefix[2][3] = 0;
    } else if (ch == '7') {
      prefix[3][3] = 1;
      prefix[3][4] = 0;
    } else if (ch == '6') {
      prefix[3][3] = 1;
      prefix[4][4] = 1;
    }
  }
  Node join(Node& o) {
    Node n;
    memset(n.prefix, 0x3f, sizeof(n.prefix));
    for (int i = 0; i < 5; i++) {
      for (int j = 0; j < 5; j++) {
        for (int k = 0; k < 5; k++) {
          n.prefix[i][k] = min(n.prefix[i][k], prefix[i][j] + o.prefix[j][k]);
        }
      }
    }
    return n;
  }
};
int main() {
  int n, q;
  scanf("%d %d\n", &n, &q);
  scanf("%s\n", str);
  SegTree<Node> tree(n, str);
  while (q--) {
    int a, b;
    scanf("%d %d\n", &a, &b);
    Node res = tree.query(a - 1, b - 1);
    printf("%d\n", res.prefix[0][4] != 0x3f3f3f3f ? res.prefix[0][4] : -1);
  }
  return 0;
}

### Prompt

Please create a solution in cpp 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;
char str[200000 + 1];
template <class Node>
struct SegTree {
  int size;
  vector<Node> tree;
  SegTree(int n) {
    size = n;
    tree.resize(4 * n + 1);
  }
  SegTree(int n, char* arr) : SegTree(n) { build(arr); }
  inline int left(int node) { return 2 * node; }
  inline int right(int node) { return 2 * node + 1; }
  void build(char* arr, int node, int st, int end) {
    if (st == end) {
      tree[node] = Node(st, arr[st]);
      return;
    }
    build(arr, left(node), st, (st + end) / 2);
    build(arr, right(node), (st + end) / 2 + 1, end);
    tree[node] = tree[left(node)].join(tree[right(node)]);
  }
  Node query(int node, int st, int end, int i, int j) {
    if (j < st || i > end) return Node();
    if (st >= i && end <= j) return tree[node];
    Node p1 = query(left(node), st, (st + end) / 2, i, j);
    Node p2 = query(right(node), (st + end) / 2 + 1, end, i, j);
    return p1.join(p2);
  }
  void build(char* arr) { build(arr, 1, 0, size - 1); }
  Node query(int i, int j) { return query(1, 0, size - 1, i, j); }
};
void printPref(string str, int prefix[5][5]) {
  cerr << "--" << str << "--" << endl;
  for (int i = 0; i < 5; i++) {
    for (int j = 0; j < 5; j++) {
      fprintf(stderr, "%11d ", prefix[i][j]);
    }
    cerr << endl;
  }
  cerr << endl;
}
struct Node {
  int prefix[5][5];
  Node() {
    memset(prefix, 0x3f, sizeof(prefix));
    for (int i = 0; i < 5; i++) prefix[i][i] = 0;
  }
  Node(int idx, char ch) : Node() {
    if (ch == '2') {
      prefix[0][0] = 1;
      prefix[0][1] = 0;
    } else if (ch == '0') {
      prefix[1][1] = 1;
      prefix[1][2] = 0;
    } else if (ch == '1') {
      prefix[2][2] = 1;
      prefix[2][3] = 0;
    } else if (ch == '7') {
      prefix[3][3] = 1;
      prefix[3][4] = 0;
    } else if (ch == '6') {
      prefix[3][3] = 1;
      prefix[4][4] = 1;
    }
  }
  Node join(Node& o) {
    Node n;
    memset(n.prefix, 0x3f, sizeof(n.prefix));
    for (int i = 0; i < 5; i++) {
      for (int j = 0; j < 5; j++) {
        for (int k = 0; k < 5; k++) {
          n.prefix[i][k] = min(n.prefix[i][k], prefix[i][j] + o.prefix[j][k]);
        }
      }
    }
    return n;
  }
};
int main() {
  int n, q;
  scanf("%d %d\n", &n, &q);
  scanf("%s\n", str);
  SegTree<Node> tree(n, str);
  while (q--) {
    int a, b;
    scanf("%d %d\n", &a, &b);
    Node res = tree.query(a - 1, b - 1);
    printf("%d\n", res.prefix[0][4] != 0x3f3f3f3f ? res.prefix[0][4] : -1);
  }
  return 0;
}

```