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 -*-
"""
Created on Tue Jun 16 19:06:27 2020

@author: Jonathan
"""

import sys

stack = []
count = 0

lr = {')':'(','>':'<',']':'[','}':'{'}


for char in input():

    if char in lr.values():
        stack.append(char)

    elif char in lr.keys():
        if stack == []:
            print("Impossible")
            sys.exit()
          
        if lr[char] != stack.pop():
            
            #print(lr[char])
            count += 1
            
if len(stack)!=0:
    print("Impossible")
    sys.exit()
print(count)