#include <bits/stdc++.h>
using namespace std;
const int INF = 1 << 29;
const int N = 200009;
char s[N];
struct SegNode {
  int dp[5][5];
  void init() {
    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 5; ++j) {
        dp[i][j] = INF;
      }
    }
  }
};
SegNode seg[N << 2];
void initNode(SegNode &segNode, int v) {
  segNode.init();
  for (int src = 0; src < 5; ++src) {
    segNode.dp[src][src] = 1;
    int des = src;
    if (src == 0 && v == 2) {
      des = 1;
    } else if (src == 1 && v == 0) {
      des = 2;
    } else if (src == 2 && v == 1) {
      des = 3;
    } else if (src == 3 || src == 4) {
      if (v == 6) {
        des = -1;
      } else if (v == 7) {
        des = 4;
      }
    }
    if (des != -1) {
      segNode.dp[src][des] = 0;
    }
  }
}
void mergeNode(SegNode &desNode, SegNode &s1, SegNode &s2) {
  desNode.init();
  for (int i = 0; i < 5; ++i) {
    for (int j = i; j < 5; ++j) {
      for (int k = i; k <= j; ++k) {
        desNode.dp[i][j] = min(desNode.dp[i][j], s1.dp[i][k] + s2.dp[k][j]);
      }
    }
  }
}
void initTree(int id, int left, int right) {
  seg[id].init();
  if (left == right) {
    initNode(seg[id], s[left] - '0');
    return;
  }
  int mid = (left + right) >> 1;
  int lson = id << 1;
  int rson = id << 1 | 1;
  initTree(lson, left, mid);
  initTree(rson, mid + 1, right);
  mergeNode(seg[id], seg[lson], seg[rson]);
}
SegNode query(int id, int curL, int curR, int aimL, int aimR) {
  if (curL == aimL && curR == aimR) {
    return seg[id];
  }
  int mid = (curL + curR) >> 1;
  int lson = id << 1;
  int rson = id << 1 | 1;
  if (mid >= aimR) {
    return query(lson, curL, mid, aimL, aimR);
  } else if (mid < aimL) {
    return query(rson, mid + 1, curR, aimL, aimR);
  } else {
    SegNode lNode = query(lson, curL, mid, aimL, mid);
    SegNode rNode = query(rson, mid + 1, curR, mid + 1, aimR);
    SegNode mergedNode;
    mergeNode(mergedNode, lNode, rNode);
    return mergedNode;
  }
}
int main() {
  int n, q;
  int a, b;
  while (scanf("%d%d", &n, &q) != EOF) {
    scanf("%s", s);
    initTree(1, 0, n - 1);
    while (q--) {
      scanf("%d%d", &a, &b);
      --a;
      --b;
      SegNode res = query(1, 0, n - 1, a, b);
      int ans = res.dp[0][4];
      if (ans == INF) {
        ans = -1;
      }
      printf("%d\n", ans);
    }
  }
  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 int INF = 1 << 29;
const int N = 200009;
char s[N];
struct SegNode {
  int dp[5][5];
  void init() {
    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 5; ++j) {
        dp[i][j] = INF;
      }
    }
  }
};
SegNode seg[N << 2];
void initNode(SegNode &segNode, int v) {
  segNode.init();
  for (int src = 0; src < 5; ++src) {
    segNode.dp[src][src] = 1;
    int des = src;
    if (src == 0 && v == 2) {
      des = 1;
    } else if (src == 1 && v == 0) {
      des = 2;
    } else if (src == 2 && v == 1) {
      des = 3;
    } else if (src == 3 || src == 4) {
      if (v == 6) {
        des = -1;
      } else if (v == 7) {
        des = 4;
      }
    }
    if (des != -1) {
      segNode.dp[src][des] = 0;
    }
  }
}
void mergeNode(SegNode &desNode, SegNode &s1, SegNode &s2) {
  desNode.init();
  for (int i = 0; i < 5; ++i) {
    for (int j = i; j < 5; ++j) {
      for (int k = i; k <= j; ++k) {
        desNode.dp[i][j] = min(desNode.dp[i][j], s1.dp[i][k] + s2.dp[k][j]);
      }
    }
  }
}
void initTree(int id, int left, int right) {
  seg[id].init();
  if (left == right) {
    initNode(seg[id], s[left] - '0');
    return;
  }
  int mid = (left + right) >> 1;
  int lson = id << 1;
  int rson = id << 1 | 1;
  initTree(lson, left, mid);
  initTree(rson, mid + 1, right);
  mergeNode(seg[id], seg[lson], seg[rson]);
}
SegNode query(int id, int curL, int curR, int aimL, int aimR) {
  if (curL == aimL && curR == aimR) {
    return seg[id];
  }
  int mid = (curL + curR) >> 1;
  int lson = id << 1;
  int rson = id << 1 | 1;
  if (mid >= aimR) {
    return query(lson, curL, mid, aimL, aimR);
  } else if (mid < aimL) {
    return query(rson, mid + 1, curR, aimL, aimR);
  } else {
    SegNode lNode = query(lson, curL, mid, aimL, mid);
    SegNode rNode = query(rson, mid + 1, curR, mid + 1, aimR);
    SegNode mergedNode;
    mergeNode(mergedNode, lNode, rNode);
    return mergedNode;
  }
}
int main() {
  int n, q;
  int a, b;
  while (scanf("%d%d", &n, &q) != EOF) {
    scanf("%s", s);
    initTree(1, 0, n - 1);
    while (q--) {
      scanf("%d%d", &a, &b);
      --a;
      --b;
      SegNode res = query(1, 0, n - 1, a, b);
      int ans = res.dp[0][4];
      if (ans == INF) {
        ans = -1;
      }
      printf("%d\n", ans);
    }
  }
  return 0;
}

```