#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const int MAXN = 200000;
const int NSTATE = 5;
typedef int Mat[NSTATE][NSTATE];
int n, nq;
char s[MAXN + 1];
Mat sval[4 * MAXN];
void scopy(Mat &A, Mat &B) {
  for (int i = (0); i < (NSTATE); ++i)
    for (int j = (i); j < (NSTATE); ++j) A[i][j] = B[i][j];
}
void smult(Mat &A, Mat &B) {
  Mat C;
  for (int i = (0); i < (NSTATE); ++i)
    for (int j = (i); j < (NSTATE); ++j) {
      int cur = INT_MAX;
      for (int k = (i); k <= (j); ++k)
        if (A[i][k] != INT_MAX && B[k][j] != INT_MAX && A[i][k] + B[k][j] < cur)
          cur = A[i][k] + B[k][j];
      C[i][j] = cur;
    }
  scopy(A, C);
}
void sinit(int x, int l, int r) {
  if (l == r) {
    for (int i = (0); i < (NSTATE); ++i)
      for (int j = (0); j < (NSTATE); ++j) sval[x][i][j] = INT_MAX;
    sval[x][0][0] = s[l] == '2' ? 1 : 0;
    if (s[l] == '2') sval[x][0][1] = 0;
    sval[x][1][1] = s[l] == '0' ? 1 : 0;
    if (s[l] == '0') sval[x][1][2] = 0;
    sval[x][2][2] = s[l] == '1' ? 1 : 0;
    if (s[l] == '1') sval[x][2][3] = 0;
    sval[x][3][3] = s[l] == '6' || s[l] == '7' ? 1 : 0;
    if (s[l] == '7') sval[x][3][4] = 0;
    sval[x][4][4] = s[l] == '6' ? 1 : 0;
  } else {
    int m = l + (r - l) / 2;
    sinit(2 * x + 1, l, m);
    sinit(2 * x + 2, m + 1, r);
    scopy(sval[x], sval[2 * x + 1]);
    smult(sval[x], sval[2 * x + 2]);
  }
}
void sget(int x, int l, int r, int L, int R, Mat &RES) {
  if (L <= l && r <= R) {
    smult(RES, sval[x]);
  } else {
    int m = l + (r - l) / 2;
    if (L <= m) sget(2 * x + 1, l, m, L, R, RES);
    if (m + 1 <= R) sget(2 * x + 2, m + 1, r, L, R, RES);
  }
}
void run() {
  scanf("%d%d%s", &n, &nq, s);
  sinit(0, 0, n - 1);
  for (int i = (0); i < (nq); ++i) {
    int l, r;
    scanf("%d%d", &l, &r);
    --l, --r;
    Mat res;
    for (int i = (0); i < (NSTATE); ++i)
      for (int j = (0); j < (NSTATE); ++j) res[i][j] = i == j ? 0 : INT_MAX;
    sget(0, 0, n - 1, l, r, res);
    int ret = res[0][4];
    printf("%d\n", ret == INT_MAX ? -1 : ret);
  }
}
int main() {
  run();
  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;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const int MAXN = 200000;
const int NSTATE = 5;
typedef int Mat[NSTATE][NSTATE];
int n, nq;
char s[MAXN + 1];
Mat sval[4 * MAXN];
void scopy(Mat &A, Mat &B) {
  for (int i = (0); i < (NSTATE); ++i)
    for (int j = (i); j < (NSTATE); ++j) A[i][j] = B[i][j];
}
void smult(Mat &A, Mat &B) {
  Mat C;
  for (int i = (0); i < (NSTATE); ++i)
    for (int j = (i); j < (NSTATE); ++j) {
      int cur = INT_MAX;
      for (int k = (i); k <= (j); ++k)
        if (A[i][k] != INT_MAX && B[k][j] != INT_MAX && A[i][k] + B[k][j] < cur)
          cur = A[i][k] + B[k][j];
      C[i][j] = cur;
    }
  scopy(A, C);
}
void sinit(int x, int l, int r) {
  if (l == r) {
    for (int i = (0); i < (NSTATE); ++i)
      for (int j = (0); j < (NSTATE); ++j) sval[x][i][j] = INT_MAX;
    sval[x][0][0] = s[l] == '2' ? 1 : 0;
    if (s[l] == '2') sval[x][0][1] = 0;
    sval[x][1][1] = s[l] == '0' ? 1 : 0;
    if (s[l] == '0') sval[x][1][2] = 0;
    sval[x][2][2] = s[l] == '1' ? 1 : 0;
    if (s[l] == '1') sval[x][2][3] = 0;
    sval[x][3][3] = s[l] == '6' || s[l] == '7' ? 1 : 0;
    if (s[l] == '7') sval[x][3][4] = 0;
    sval[x][4][4] = s[l] == '6' ? 1 : 0;
  } else {
    int m = l + (r - l) / 2;
    sinit(2 * x + 1, l, m);
    sinit(2 * x + 2, m + 1, r);
    scopy(sval[x], sval[2 * x + 1]);
    smult(sval[x], sval[2 * x + 2]);
  }
}
void sget(int x, int l, int r, int L, int R, Mat &RES) {
  if (L <= l && r <= R) {
    smult(RES, sval[x]);
  } else {
    int m = l + (r - l) / 2;
    if (L <= m) sget(2 * x + 1, l, m, L, R, RES);
    if (m + 1 <= R) sget(2 * x + 2, m + 1, r, L, R, RES);
  }
}
void run() {
  scanf("%d%d%s", &n, &nq, s);
  sinit(0, 0, n - 1);
  for (int i = (0); i < (nq); ++i) {
    int l, r;
    scanf("%d%d", &l, &r);
    --l, --r;
    Mat res;
    for (int i = (0); i < (NSTATE); ++i)
      for (int j = (0); j < (NSTATE); ++j) res[i][j] = i == j ? 0 : INT_MAX;
    sget(0, 0, n - 1, l, r, res);
    int ret = res[0][4];
    printf("%d\n", ret == INT_MAX ? -1 : ret);
  }
}
int main() {
  run();
  return 0;
}

```