Problem: You are given string s consists of opening and closing brackets of four kinds <>, {}, [], (). There are two types of brackets: opening and closing. You can replace any bracket by another of the same type. For example, you can replace < by the bracket {, but you can't replace it by ) or >.

The following definition of a regular bracket sequence is well-known, so you can be familiar with it.

Let's define a regular bracket sequence (RBS). Empty string is RBS. Let s1 and s2 be a RBS then the strings <s1>s2, {s1}s2, [s1]s2, (s1)s2 are also RBS.

For example the string "[[(){}]<>]" is RBS, but the strings "[)()" and "][()()" are not.

Determine the least number of replaces to make the string s RBS.

Input

The only line contains a non empty string s, consisting of only opening and closing brackets of four kinds. The length of s does not exceed 106.

Output

If it's impossible to get RBS from s print Impossible.

Otherwise print the least number of replaces needed to get RBS from s.

Examples

Input

[&lt;}){}


Output

2

Input

{()}[]


Output

0

Input

]]


Output

Impossible

Solution (in PYTHON3):

Solution:
import math
import sys,string
input=sys.stdin.readline
import random
from collections import deque,defaultdict
import bisect
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
d=defaultdict(int)
s=input().strip()
x=[]
ans=0
for i in range(len(s)):
    if(s[i]=="[" or s[i]=="(" or s[i]=="{" or s[i]=="<"):
        x.append(s[i])
    else:
        if(len(x)==0):
            print("Impossible")
            exit()
        if(s[i]=="]"):
            if(x[-1]=="["):
                if(len(x)==0):
                    print("Impossible")
                    exit()
                x.pop()
            else:
                x.pop()
                ans+=1
        elif(s[i]=="}"):
            if(x[-1]=="{"):
                if(len(x)==0):
                    print("Impossible")
                    exit()
                x.pop()
            else:
                ans+=1
                x.pop()
        elif(s[i]==">"):
            if(x[-1]=="<"):
                if(len(x)==0):
                    print("Impossible")
                    exit()
                x.pop()
            else:
                ans+=1
                x.pop()
        else:
            if(x[-1]=="("):
                if(len(x)==0):
                    print("Impossible")
                    exit()
                x.pop()
            else:
                x.pop()
                ans+=1
if(len(x)!=0):
    print("Impossible")
else:
    print(ans)