Diagonal Dominance

Macrohard studies diagonally dominant matrices, which are needed to write their new operating system Doors 8. An $n \times n$ matrix $A$ is called a diagonally dominant matrix if all three of the following conditions hold:

1. $A_{i,j} \ge 0$ $(1 \le i,j \le n)$
2. $A_{i,i} \ge \sum_{j=1}^{i-1} A_{i,j} + \sum_{j=i+1}^{n} A_{i,j}$ $(1 \le i \le n)$
3. There exists an $i$ such that $A_{i,i} > \sum_{j=1}^{i-1} A_{i,j} + \sum_{j=i+1}^{n} A_{i,j}$

A diagonal element $A_{i,i}$ is called dominant if

$A_{i,i} > \sum_{j=1}^{i-1} A_{i,j} + \sum_{j=i+1}^{n} A_{i,j}$

Until recently, the Macrohard staff checked matrices by hand with a calculator. Yesterday they went on strike, because they were tired of doing the same operations on large matrices. The Macrohard chief hired you to write a program that automates their tedious calculations. Don't make a mistake!

The first line contains an integer $n$ ($2 \le n \le 1000$), the size of the matrix. Each of the next $n$ lines contains $n$ integers, the elements of the matrix ($0 \le A_{i,j} \le 1000$).

If the matrix is a "beautiful" matrix, print "YES". Otherwise, print "NO". If the matrix is diagonally dominant, print the number of dominant elements on the next line.