so here is a problem :

Okabe needs to renovate the Future Gadget Laboratory after he tried doing some crazy experiments! The lab is represented as an n by n square grid of integers. A good lab is defined as a lab in which every number not equal to 1 can be expressed as the sum of a number in the same row and a number in the same column. In other words, for every x, y such that 1 ≤ x, y ≤ n and ax, y ≠ 1, there should exist two indices s and t so that ax, y = ax, s + at, y, where ai, j denotes the integer in i-th row and j-th column.

Help Okabe determine whether a given lab is good!

Input

The first line of input contains the integer n (1 ≤ n ≤ 50) — the size of the lab.

The next n lines contain n space-separated integers denoting a row of the grid. The j-th integer in the i-th row is ai, j (1 ≤ ai, j ≤ 105).

Output

Print "Yes" if the given lab is good and "No" otherwise.

You can output each letter in upper or lower case.

Examples

input

3

1 1 2

2 3 1

6 4 1

output

Yes

here is my code:

```
from random import randint
x = int(input("number: "))
board = []
for a in range(x):
row = []
for b in range(x):
row.append(str(randint(2,3)))
board.append(row)
def boardy(board):
for x in board:
print(" ".join(x))
boardy(board)
q=int in range(0,x)
r=int in range(0,x)
e=int in range(0,x)
o=int in range(0,x)
if board[q][r]==board[q][e]+board[o][r]:
print(True)
else:
print( False)
```

please help me with answer , i have been stuck in this problem sice yesterday and i am loosing motivation to continue coding as i cant move forward.. thanking you in anticipation