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>
using namespace std;
char second[222222];
int n;
int mx[222222];
int st[222222], stn, rn;
int kol[222222];
char res[222222];
int main() {
  scanf("%s", &(second[1]));
  second[0] = '*';
  n = strlen(second) - 1;
  int r = -1;
  for (int i = 1; i <= n; ++i) {
    kol[i] = kol[i - 1];
    if (second[i] == '(' || second[i] == '[') {
      st[stn++] = i;
      kol[i] += (second[i] == '[');
    } else if (stn > 0) {
      int p = st[stn - 1];
      if ((second[p] == '(' && second[i] == ')') ||
          (second[p] == '[' && second[i] == ']')) {
        mx[i] = kol[i] - kol[p - 1] + mx[p - 1];
        if (r == -1 || mx[r] < mx[i]) r = i;
        --stn;
      } else
        stn = 0;
    }
  }
  if (r == -1) {
    puts("0");
    return 0;
  }
  printf("%d\n", mx[r]);
  int k = mx[r];
  int cur = 0;
  for (int i = r; i >= 0; --i) {
    if (second[i] == '[') --k;
    if (second[i] == ']' || second[i] == ')')
      ++cur;
    else
      --cur;
    res[rn++] = second[i];
    if (k == 0 && cur == 0) break;
  }
  for (int i = rn - 1; i >= 0; --i) putchar(res[i]);
  puts("");
  return 0;
}
