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 s 1 and s 2 be a RBS then the strings s 1 s 2 , { s 1 } s 2 , [ s 1 ] s 2 , ( s 1 ) s 2 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.

输入描述:

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.

输出描述:

If it's impossible to get RBS from s print Impossible.Otherwise print the least number of replaces needed to get RBS from s.