Migrated from Lutece 793 A Linear Algebra Problem

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Description

God Kufeng is the God of Math. However, Kufeng is not so skilled with linear algebra, especially when dealing with matrixes.

One day, Captain Chen has a problem with matrix, here is the problem:

Given a $n\times n$ matrix $A$, what is the solution of $n\times n$ matrix $X$ for the equation $AX + XA = 2A$?

Captain Chen is a nice Captain, he wants to solve the equation only when A is a diagonal matrix, which means $A_{ij} = 0$ holds for all $i \neq j$ .

“That’s easy!” says Kufeng, “the answer is simply $X = I$, when $I$ is the Identity Matrix.”

“But… is it the only solution for the equation above?” Captain Chen asks.

Kufeng cannot answer this question, can you help him?

Input

The first line of input is a number $n$, giving the size of matrix $A$ and $X$. $(1\leq n\leq 1000)$

Then comes a single line with $n$ numbers, $x_1, x_2, \cdots, x_n$, where $x_i$ is the value of $A_{ii}$. $(-10000\leq x_i\leq 10000)$

Output

If the answer is unique, output UNIQUE, otherwise output NOT UNIQUE

Samples

3
1 2 3

UNIQUE

2
1 -1

NOT UNIQUE

Note

For the second sample input, $A=\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$, there can be more than one possible solutions for $X$, for example, $X=\begin{pmatrix}1 & 0 \\ 0 & 1 \end{pmatrix}$ and $X=\begin{pmatrix}1 & 0 \\ 1 & 1 \end{pmatrix}$ both satisfy the equation, so the answer is not unique.

Resources

the 12th UESTC Programming Contest Preliminary