A bracket sequence is a string, containing only characters "(", ")", "[" and "]".

A correct bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()[]", "([])" are correct (the resulting expressions are: "(1)+[1]", "([1+1]+1)"), and "](" and "[" are not. The empty string is a correct bracket sequence by definition.

A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (where |s| is the length of string s) is the string slsl + 1... sr. The empty string is a substring of any string by definition.

You are given a bracket sequence, not necessarily correct. Find its substring which is a correct bracket sequence and contains as many opening square brackets «[» as possible.

Input

The first and the only line contains the bracket sequence as a string, consisting only of characters "(", ")", "[" and "]". It is guaranteed that the string is non-empty and its length doesn't exceed 105 characters.

Output

In the first line print a single integer — the number of brackets «[» in the required bracket sequence. In the second line print the optimal sequence. If there are more than one optimal solutions print any of them.

Examples

Input

([])


Output

1
([])


Input

(((


Output

0
#include <bits/stdc++.h>
char op[256];
int n, be, bl, br;
char b[100020];
int st[100020], stop;
int cnt[100020];
int main() {
  int i;
  scanf("%s", b);
  n = strlen(b);
  cnt[0] = (b[0] == '[');
  for (i = 1; i < n; i++) {
    cnt[i] = cnt[i - 1] + (b[i] == '[');
  }
  memset(op, -1, sizeof(op));
  op[(int)')'] = '(';
  op[(int)']'] = '[';
  stop = 0;
  st[stop] = -1;
  be = -1;
  for (i = 0; i < n; i++) {
    if ((b[i] == ']') || (b[i] == ')')) {
      if ((st[stop] == -1) || (op[(int)b[i]] != b[st[stop]])) {
        if (st[stop] + 1 <= i - 1) {
          if (cnt[i - 1] - cnt[st[stop]] > be) {
            be = cnt[i - 1] - cnt[st[stop]];
            bl = st[stop] + 1;
            br = i - 1;
          }
        }
        st[++stop] = i;
      } else
        stop--;
    } else {
      if (st[stop] + 1 <= i - 1) {
        if (cnt[i - 1] - cnt[st[stop]] > be) {
          be = cnt[i - 1] - cnt[st[stop]];
          bl = st[stop] + 1;
          br = i - 1;
        }
      }
      st[++stop] = i;
    }
  }
  i = n;
  if (st[stop] + 1 <= i - 1) {
    if (cnt[i - 1] - cnt[st[stop]] > be) {
      be = cnt[i - 1] - cnt[st[stop]];
      bl = st[stop] + 1;
      br = i - 1;
    }
  }
  if (be == -1) {
    printf("0\n");
  } else {
    printf("%d\n", be);
    for (i = bl; i <= br; i++) printf("%c", b[i]);
    printf("\n");
  }
  return 0;
}
