Competitions

# Graphs Representation

# Checking for an undirected graph

For a given square matrix **n** x **n** of zeros and ones determine whether it can be the adjacency matrix of a simple undirected graph. The simple graph does not contain loops and multiple edges.

#### Input

The first line contains the value of **n** (**1** ≤ **n** ≤ **100**). Each of the next **n** lines contains **n** numbers, describing the adjacency matrix.

#### Output

Print **YES**, if the graph is simple undirected and **NO** otherwise.

Input example #1

3 0 1 1 1 0 1 1 1 0

Output example #1

YES

Input example #2

3 0 1 1 1 0 1 0 1 0

Output example #2

NO