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 math

s = input().rstrip()
n = len(s)
stack = []
k = 0
D = {'(' : 0, '{' : 2, '[' : 4, '<' : 6,
     ')' : 1, '}' : 3, ']' : 5, '>' : 7}
for i in range(n):
    c = s[i]
    if D[c]%2 == 0:
        stack.append(c)
    elif len(stack) == 0 or D[stack[-1]]%2:
        print('Impossible')
        break
    else:
        k += (D[c] - D[stack[-1]] != 1)
        stack.pop()
else:
    print(k if len(stack) == 0 else 'Impossible')