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;
const int MAX = 1e5 + 9;
string s;
int l, r, st[MAX], t = 1, cnt[MAX], ans;
int main() {
  cin >> s;
  s += 's';
  for (int i = s.size(); i >= 1; i--) s[i] = s[i - 1];
  s[0] = ' ';
  for (int i = 1; i < s.size(); i++) {
    cnt[i] = cnt[i - 1] + (s[i] == '[');
    if (s[i] == '[' || s[i] == '(')
      st[t++] = i;
    else if (s[i] == ']' && s[st[t - 1]] != '[' ||
             s[i] == ')' && s[st[t - 1]] != '(')
      t = 0, st[t++] = i;
    else {
      t--;
      if (ans < cnt[i] - cnt[st[t - 1]])
        ans = cnt[i] - cnt[st[t - 1]], l = st[t - 1], r = i;
    }
  }
  cout << ans << '\n' << s.substr(l + 1, r - l);
}
