CF1109B · Sasha and One More Name

• 难度：1800
• 标签：constructive algorithms、hashing、strings
• 链接：https://codeforces.com/problemset/problem/1109/B
• 时间限制：1 second　内存限制：256 megabytes
• 出现位置：Day21-字符串综合-hash-二分-构造

英文原题面

Statement

Reading books is one of Sasha's passions. Once while he was reading one book, he became acquainted with an unusual character. The character told about himself like that: "Many are my names in many countries. Mithrandir among the Elves, Tharkûn to the Dwarves, Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not." And at that moment Sasha thought, how would that character be called in the East? In the East all names are palindromes. A string is a palindrome if it reads the same backward as forward. For example, such strings as "kazak", "oo" and "r" are palindromes, but strings "abb" and "ij" are not. Sasha believed that the hero would be named after one of the gods of the East. As long as there couldn't be two equal names, so in the East people did the following: they wrote the original name as a string on a piece of paper, then cut the paper minimum number of times $k$, so they got $k+1$ pieces of paper with substrings of the initial string, and then unite those pieces together to get a new string. Pieces couldn't be turned over, they could be shuffled. In this way, it's possible to achive a string abcdefg from the string f|de|abc|g using $3$ cuts (by swapping papers with substrings f and abc). The string cbadefg can't be received using the same cuts. More formally, Sasha wants for the given palindrome $s$ find such minimum $k$, that you can cut this string into $k + 1$ parts, and then unite them in such a way that the final string will be a palindrome and it won't be equal to the initial string $s$. It there is no answer, then print "Impossible" (without quotes).

Input

The first line contains one string $s$ ($1 \le |s| \le 5\,000$) — the initial name, which consists only of lowercase Latin letters. It is guaranteed that $s$ is a palindrome.

Output

Print one integer $k$ — the minimum number of cuts needed to get a new name, or "Impossible" (without quotes).

样例

样例 1

输入：

nolon

输出：

2

样例 2

输入：

otto

输出：

1

样例 3

输入：

qqqq

输出：

Impossible

样例 4

输入：

kinnikkinnik

输出：

1

样例解释（英文原文）

In the first example, you can cut the string in those positions: no|l|on, and then unite them as follows on|l|no. It can be shown that there is no solution with one cut. In the second example, you can cut the string right in the middle, and swap peaces, so you get toot. In the third example, you can't make a string, that won't be equal to the initial one. In the fourth example, you can cut the suffix nik and add it to the beginning, so you get nikkinnikkin.