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 seq[100010];
char res[100010];
bool valid[100010];
int main() {
  vector<pair<char, int> > stk;
  while (scanf("%s", seq) != EOF) {
    stk.clear();
    int count = 0;
    int last = 0;
    int n = strlen(seq);
    for (int i = 0; i < n; ++i) {
      if (seq[i] == '(') {
        stk.push_back(make_pair('(', i));
      } else if (seq[i] == '[') {
        stk.push_back(make_pair('[', i));
      } else if (seq[i] == ')') {
        if (stk.size() && stk.back().first == '(') {
          stk.pop_back();
        } else {
          stk.push_back(make_pair(')', i));
        }
      } else if (seq[i] == ']') {
        if (stk.size() && stk.back().first == '[') {
          stk.pop_back();
        } else {
          stk.push_back(make_pair(']', i));
        }
      }
    }
    memset(valid, 1, sizeof valid);
    for (int i = 0; i < stk.size(); ++i) {
      valid[stk[i].second] = 0;
    }
    int maxv = 0;
    for (int i = 0; i < n; ++i) {
      if (valid[i]) {
        int j = i;
        while (j + 1 < n && valid[j + 1]) ++j;
        int cnt = 0;
        for (int k = i; k <= j; ++k) {
          if (seq[k] == '[') ++cnt;
        }
        if (cnt > maxv) {
          maxv = cnt;
          memcpy(res, seq + i, j - i + 1);
          res[j - i + 1] = '\0';
        }
        i = j;
      }
    }
    printf("%d\n", maxv);
    if (maxv) printf("%s\n", res);
  }
  return 0;
}
