CF612C.Replace To Make Regular Bracket Sequence

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.

给你一个字符串 $s$，它由四种括号组成：<>、{}、[]、()。括号分为两类：左括号（opening）和右括号（closing）。你可以将任意一个括号替换成同类型的另一个括号。例如，你可以将 < 替换为 {，但不能将其替换为 ) 或 >。

以下是对“正则括号序列”（Regular Bracket Sequence, RBS）的经典定义，你可能已有所了解：

我们定义正则括号序列（RBS）如下：空字符串是 RBS；若 $s_1$ 和 $s_2$ 均为 RBS，则字符串 <s_1>s_2、{s_1}s_2、[s_1]s_2、(s_1)s_2 也均为 RBS。

例如，字符串 "[[(){}]<>" 是 RBS，但字符串 "[)()" 和 "][()()" 不是 RBS。

请确定使字符串 $s$ 成为 RBS 所需的最少替换次数。

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.

仅有一行，包含一个非空字符串 $s$，该字符串仅由四种类型的括号（开括号和闭括号）组成。字符串 $s$ 的长度不超过 $10^6$。

If it's impossible to get RBS from s print Impossible.

Otherwise print the least number of replaces needed to get RBS from s.

如果无法从字符串 $s$ 得到合法括号序列（RBS），则输出 Impossible。

否则，输出将 $s$ 变为合法括号序列（RBS）所需的最少替换次数。