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;
string second;
int b[150000];
int main() {
  cin >> second;
  stack<pair<char, int> > st;
  for (int i = 0; i < second.size(); i++) {
    if (second[i] == '(' || second[i] == '[') {
      st.push(make_pair(second[i], i));
    } else {
      if (second[i] == ')') {
        if (st.size() && st.top().first == '(') {
          b[st.top().second] = 1;
          b[i] = 1;
          st.pop();
        } else {
          st.push(make_pair(second[i], i));
        }
      }
      if (second[i] == ']') {
        if (st.size() && st.top().first == '[') {
          b[st.top().second] = 1;
          b[i] = 1;
          st.pop();
        } else {
          st.push(make_pair(second[i], i));
        }
      }
    }
  }
  int mx = 0, col = 0;
  string ans = "", w;
  for (int i = 0; i <= second.size(); i++) {
    if (b[i]) {
      if (second[i] == '[') col++;
      w += second[i];
    } else {
      if (mx < col) {
        mx = col;
        ans = w;
      }
      w = "";
      col = 0;
    }
  }
  cout << mx << endl << ans;
  return 0;
}
