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
import sys
import math
import string
import operator
import functools
import fractions
import collections
sys.setrecursionlimit(10**7)
dX= [-1, 1, 0, 0,-1, 1,-1, 1]
dY= [ 0, 0,-1, 1, 1,-1,-1, 1]
RI=lambda: list(map(int,input().split()))
RS=lambda: input().rstrip().split()
#################################################
s=RS()[0]
st=[]
closeInd=[0]*len(s)
def rev(c):
    return "(["[c==']']
for i in range(len(s)):
    if len(st) and s[i] in ")]" and st[-1][0]==rev(s[i]):
        temp=st[-1]
        st.pop()
        closeInd[temp[1]]=i
    else:
        st.append((s[i],i))
maxSq=0
maxX,maxY=0,0
i=0
while i<len(s):
    sq=0
    start=i
    while i<len(s) and closeInd[i]:
        j=i
        while i<=closeInd[j]:
            if s[i]=='[':
                sq+=1
            i+=1
    else:
        i+=1
    if sq>maxSq:
        maxSq=sq
        maxX=start
        maxY=i-1
print(maxSq, s[maxX:maxY], sep='\n')
