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:
# -*- coding: utf-8 -*-
import sys

def fun():
    try:
        str = input()
    except ValueError:
        print('Invalid number')
        return
    S = {"}": "{",")": "(",">": "<","]":"["}
    L = []
    ans = 0
    for c in str:
        if c in S.values():
            L.append(c)
            pass
        else:
            if(len(L) >0 ):
                ans += 0 if S[c] == L.pop() else 1
            else:
                ans = -1
                break
            pass
    if( len(L)> 0 or ans <0):
        print('Impossible')
    else:
        print(ans)
    pass

if __name__ == "__main__":
    fun()
    '''
    for i,v in enumerate(map(int,input().split())):
        print(i,v)
    '''