括号序列 - 問題

#13227. 括号序列

統計

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

Petya 发现了一个古老的字符串。该字符串仅包含字符 ‘(’、‘)’ 和 ‘?’。 Petya 想要将每个 ‘?’ 替换为 ‘(’ 或 ‘)’，使得该字符串变为合法的（定义如下）。

空字符串是合法的。
如果 $S$ 是合法的，则 $(S)$ 是合法的。
如果 $U, V$ 是合法的，则 $UV$ 是合法的。

请检查替换方案是否唯一确定。

输入格式

输入包含一个字符串 $s_1s_2 \dots s_n$ ($1 \le n \le 10^6$)，仅由 ‘(’、‘)’ 和 ‘?’ 组成。

输出格式

如果存在唯一的方法可以得到一个合法的字符串，输出 “Unique”。如果没有替换方法可以得到合法字符串，输出 “None”。否则，输出 “Many”。

样例

输入 1

??

输出 1

Unique

输入 2

????

输出 2

Many

输入 3

(??

输出 3

None

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