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 sys
import math
import collections
import heapq
import decimal
s=input()
n=len(s)
c=0
c1=1
for i in range(n):
    if(s[i] in ['(','<','{','[']):
        c+=1
    else:
        c-=1
    if(c<0):
        c1=0
        break
if(c1==0 or c!=0):
    print("Impossible")
else:
    l=[]
    c1=1
    d={'<':'>','[':']','{':'}','(':')'}
    c=0
    for i in range(n):
        if(s[i] in ['(','<','{','[']):
            l.append(s[i])
        else:
            if(l==[]):
                c1=0
                break
            elif(d[l[-1]]==s[i]):
                l.pop()
            else:
                l.pop()
                c+=1
    if(c1==0):
        print("Impossible")
    else:
        print(c)