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>
#pragma comment(linker, "/STACK:33554432")
using namespace std;
vector<int> cnt;
int res, L, R;
void calc(int _L, int _R) {
  if (_L >= _R) return;
  int tres = cnt[_R] - (_L > 0 ? cnt[_L - 1] : 0);
  if (tres > res) {
    res = tres;
    L = _L;
    R = _R;
  }
}
int main() {
  string s;
  cin >> s;
  stack<pair<char, int> > S;
  res = -1;
  R = L = -1;
  cnt.resize(int((s).size()), 0);
  for (int i = (0); i < (int((s).size())); ++i) {
    if (i) cnt[i] = cnt[i - 1];
    if (s[i] == '[') cnt[i]++;
  }
  for (int i = (0); i < (int((s).size())); ++i) {
    if (int((S).size()) == 0) {
      S.push(make_pair(s[i], i));
      continue;
    }
    if (s[i] == ')') {
      if (S.top().first == '(') {
        S.pop();
        int prev = 0;
        if (int((S).size())) prev = S.top().second + 1;
        calc(prev, i);
        continue;
      }
      calc(S.top().second + 1, i - 1);
      S.push(make_pair(s[i], i));
      continue;
    }
    if (s[i] == ']') {
      if (S.top().first == '[') {
        S.pop();
        int prev = 0;
        if (int((S).size())) prev = S.top().second + 1;
        calc(prev, i);
        continue;
      }
      calc(S.top().second + 1, i - 1);
      S.push(make_pair(s[i], i));
      continue;
    }
    calc(S.top().second + 1, i - 1);
    S.push(make_pair(s[i], i));
    continue;
  }
  if (res < 0) {
    cout << "0\n";
    return 0;
  }
  string sres = s.substr(L, R - L + 1);
  cout << res << endl << sres << endl;
  return 0;
}
