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;
stack<pair<char, int> > second;
string word;
pair<int, int> dp[100005];
int main() {
  cin >> word;
  for (int i = 1; i <= word.length(); i++) {
    if (word[i - 1] == '(' || word[i - 1] == '[') {
      second.push(make_pair(word[i - 1], i));
    } else {
      if (word[i - 1] == ')') {
        if (!second.empty()) {
          pair<char, int> top = second.top();
          if (top.first == '(') {
            second.pop();
            dp[i] = make_pair(dp[i - 1].first, dp[i - 1].second + 2);
            if (dp[top.second - 1].second != 0) {
              dp[i].first += dp[top.second - 1].first;
              dp[i].second += dp[top.second - 1].second;
            }
          } else {
            second.push(make_pair(word[i - 1], i));
          }
        } else
          second.push(make_pair(word[i - 1], i));
      } else {
        if (!second.empty()) {
          pair<char, int> top = second.top();
          if (top.first == '[') {
            second.pop();
            dp[i] = make_pair(dp[i - 1].first + 1, dp[i - 1].second + 2);
            if (dp[top.second - 1].second != 0) {
              dp[i].first += dp[top.second - 1].first;
              dp[i].second += dp[top.second - 1].second;
            }
          } else {
            second.push(make_pair(word[i - 1], i));
          }
        } else
          second.push(make_pair(word[i - 1], i));
      }
    }
  }
  int ans = 0, index = -1;
  for (int i = 1; i <= word.length(); i++) {
    if (dp[i].first > ans) {
      ans = dp[i].first;
      index = i;
    }
  }
  printf("%d", ans);
  ;
  printf("\n");
  if (ans) {
    for (int i = index - dp[index].second; i <= index - 1; i++) cout << word[i];
  }
  printf("\n");
  return 0;
}
