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:
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright © 2016 missingdays <missingdays@missingdays>
#
# Distributed under terms of the MIT license.

"""

"""

opening = {
        "[": "]",
        "<": ">",
        "{": "}",
        "(": ")",
}

closing = {
        "]": "[",
        ">": "<",
        "}": "{",
        ")": "(",
}

s = input()

stack = []

answ = 0

for c in s:
    if c in opening:
        stack.append(c)
    else:
        if len(stack) == 0:
            print("Impossible")
            exit()

        op = stack.pop()

        if c != opening[op]:
            answ += 1

if len(stack) != 0:
    print("Impossible")
    exit()
print(answ)