#include <bits/stdc++.h>
using namespace std;
const int iinf = 1e9 + 7;
const long long linf = 1ll << 60;
const double dinf = 1e10;
template <typename T>
inline void scf(T &x) {
  bool f = 0;
  x = 0;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') {
    f = 1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  if (f) x = -x;
  return;
}
template <typename T1, typename T2>
void scf(T1 &x, T2 &y) {
  scf(x);
  return scf(y);
}
template <typename T1, typename T2, typename T3>
void scf(T1 &x, T2 &y, T3 &z) {
  scf(x);
  scf(y);
  return scf(z);
}
template <typename T1, typename T2, typename T3, typename T4>
void scf(T1 &x, T2 &y, T3 &z, T4 &w) {
  scf(x);
  scf(y);
  scf(z);
  return scf(w);
}
const int N = 2e5 + 100;
char c2017[] = {' ', '2', '0', '1', '7'};
struct node {
  int f[5][5];
  node() {
    for (int i = 0; i < (5); i++)
      for (int j = 0; j < (5); j++) f[i][j] = iinf;
  }
  node(char c) {
    for (int i = 0; i < (5); i++) {
      f[i][i] = 0;
      for (int j = (i + 1); j <= (4); j++) f[i][j] = iinf;
    }
    if (c == '6') {
      f[3][3] = 1;
      f[4][4] = 1;
    } else {
      int i = 0;
      for (int _ = (1); _ <= (4); _++)
        if (c2017[_] == c) {
          i = _;
          break;
        }
      if (i) {
        f[i - 1][i] = 0;
        f[i - 1][i - 1] = 1;
      }
    }
  }
  node operator+(const node &a) const {
    node ret;
    for (int i = 0; i < (5); i++)
      for (int j = (i); j <= (4); j++)
        for (int k = (i); k <= (j); k++)
          ret.f[i][j] = min(ret.f[i][j], f[i][k] + a.f[k][j]);
    return ret;
  }
  void out() const {
    for (int i = 0; i < (5); i++)
      for (int j = 0; j < (5); j++)
        printf("%d%c", f[i][j], j == 4 ? '\n' : '\t');
  }
};
int n, q;
char str[N];
namespace seg {
node num[N << 2];
void update(int i) {
  num[i] = num[(i << 1)] + num[((i << 1) | 1)];
  return;
}
void build(int l = 1, int r = n, int k = 1) {
  if (l == r) {
    num[k] = node(str[l]);
    return;
  }
  int mid = l + r >> 1;
  build(l, mid, (k << 1)), build(mid + 1, r, ((k << 1) | 1));
  return update(k);
}
node query(int a, int b, int l = 1, int r = n, int k = 1) {
  if (a == l && b == r) return num[k];
  int mid = l + r >> 1;
  if (a > mid) return query(a, b, mid + 1, r, ((k << 1) | 1));
  if (b <= mid) return query(a, b, l, mid, (k << 1));
  return query(a, mid, l, mid, (k << 1)) +
         query(mid + 1, b, mid + 1, r, ((k << 1) | 1));
}
}  // namespace seg
int main() {
  scf(n, q);
  scanf("%s", str + 1);
  seg::build();
  for (int i = 0; i < (q); i++) {
    int l, r;
    scf(l, r);
    node ans = seg::query(l, r);
    int res = ans.f[0][4];
    if (res == iinf)
      puts("-1");
    else
      printf("%d\n", res);
  }
  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;
const int iinf = 1e9 + 7;
const long long linf = 1ll << 60;
const double dinf = 1e10;
template <typename T>
inline void scf(T &x) {
  bool f = 0;
  x = 0;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') {
    f = 1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  if (f) x = -x;
  return;
}
template <typename T1, typename T2>
void scf(T1 &x, T2 &y) {
  scf(x);
  return scf(y);
}
template <typename T1, typename T2, typename T3>
void scf(T1 &x, T2 &y, T3 &z) {
  scf(x);
  scf(y);
  return scf(z);
}
template <typename T1, typename T2, typename T3, typename T4>
void scf(T1 &x, T2 &y, T3 &z, T4 &w) {
  scf(x);
  scf(y);
  scf(z);
  return scf(w);
}
const int N = 2e5 + 100;
char c2017[] = {' ', '2', '0', '1', '7'};
struct node {
  int f[5][5];
  node() {
    for (int i = 0; i < (5); i++)
      for (int j = 0; j < (5); j++) f[i][j] = iinf;
  }
  node(char c) {
    for (int i = 0; i < (5); i++) {
      f[i][i] = 0;
      for (int j = (i + 1); j <= (4); j++) f[i][j] = iinf;
    }
    if (c == '6') {
      f[3][3] = 1;
      f[4][4] = 1;
    } else {
      int i = 0;
      for (int _ = (1); _ <= (4); _++)
        if (c2017[_] == c) {
          i = _;
          break;
        }
      if (i) {
        f[i - 1][i] = 0;
        f[i - 1][i - 1] = 1;
      }
    }
  }
  node operator+(const node &a) const {
    node ret;
    for (int i = 0; i < (5); i++)
      for (int j = (i); j <= (4); j++)
        for (int k = (i); k <= (j); k++)
          ret.f[i][j] = min(ret.f[i][j], f[i][k] + a.f[k][j]);
    return ret;
  }
  void out() const {
    for (int i = 0; i < (5); i++)
      for (int j = 0; j < (5); j++)
        printf("%d%c", f[i][j], j == 4 ? '\n' : '\t');
  }
};
int n, q;
char str[N];
namespace seg {
node num[N << 2];
void update(int i) {
  num[i] = num[(i << 1)] + num[((i << 1) | 1)];
  return;
}
void build(int l = 1, int r = n, int k = 1) {
  if (l == r) {
    num[k] = node(str[l]);
    return;
  }
  int mid = l + r >> 1;
  build(l, mid, (k << 1)), build(mid + 1, r, ((k << 1) | 1));
  return update(k);
}
node query(int a, int b, int l = 1, int r = n, int k = 1) {
  if (a == l && b == r) return num[k];
  int mid = l + r >> 1;
  if (a > mid) return query(a, b, mid + 1, r, ((k << 1) | 1));
  if (b <= mid) return query(a, b, l, mid, (k << 1));
  return query(a, mid, l, mid, (k << 1)) +
         query(mid + 1, b, mid + 1, r, ((k << 1) | 1));
}
}  // namespace seg
int main() {
  scf(n, q);
  scanf("%s", str + 1);
  seg::build();
  for (int i = 0; i < (q); i++) {
    int l, r;
    scf(l, r);
    node ans = seg::query(l, r);
    int res = ans.f[0][4];
    if (res == iinf)
      puts("-1");
    else
      printf("%d\n", res);
  }
  return 0;
}

```