Parenthese sequence

bobo found an ancient string. The string contains only three charaters -- "(", ")" and "?".

bobo would like to replace each "?" with "(" or ")" so that the string is valid (defined as follows). Check if the way of replacement can be uniquely determined.

Note:

An empty string is valid.
If S is valid, (S) is valid.
If U,V are valid, UV is valid.

The input consists of several tests. For each tests:

A string s₁s₂…s_n (1≤n≤10⁶).

For each tests:

If there is unique valid string, print "Unique". If there are no valid strings at all, print "None". Otherwise, print "Many".

??
????
(??

Unique
Many
None

Xiaoxu Guo (ftiasch)

2014 Multi-University Training Contest 5