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:
from collections import deque 
import sys

strv = list(input())

if len(strv) % 2 != 0:
    print ("Impossible")
    sys.exit()

openQ = deque([])

y=0

for brk in strv:
    if brk in ['[','{','(', '<']:
        openQ.append(brk) 
    else: 
        if len(openQ) >= 1:
            lastIn = openQ.pop() 
            if brk=="}":
                if lastIn != "{":
                    y=y+1
            elif brk=="]":
                if lastIn != "[":
                        y=y+1
            elif brk==")":
                if lastIn != "(":
                        y=y+1
            elif brk==">":
                if lastIn != "<":
                        y=y+1
        else:
            y="Impossible"
            break

if len(openQ) == 0 :
    print(y)
else:
    print("Impossible")