CF821A Okabe and Future Gadget Laboratory

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

The first line of input contains the integer $ n $ ( $ 1

Print "Yes" if the given lab is good and "No" otherwise. You can output each letter in upper or lower case.

In the first sample test, the $ 6 $ in the bottom left corner is valid because it is the sum of the $ 2 $ above it and the $ 4 $ on the right. The same holds for every number not equal to $ 1 $ in this table, so the answer is "Yes". In the second sample test, the $ 5 $ cannot be formed as the sum of an integer in the same row and an integer in the same column. Thus the answer is "No".