AT_abc451_e [ABC451E] Tree Distance

Determine whether there exists a weighted undirected tree with $ N $ vertices satisfying the following condition. - For any two integers $ i $ and $ j $ with $ 1 \le i \lt j \le N $ , the distance between vertices $ i $ and $ j $ is $ A_{i,j} $ . Here, the distance between vertices $ i $ and $ j $ is defined as the sum of the weights of the edges on the unique simple path connecting these two vertices.

The input is given from Standard Input in the following format: > $ N $ $ A_{1, 2} $ $ A_{1, 3} $ $ \ldots $ $ A_{1, N} $ $ A_{2, 3} $ $ \ldots $ $ A_{2, N} $ $ \vdots $ $ A_{N-1,N} $

If a tree satisfying the condition exists, output `Yes`; otherwise, output `No`.

### Sample Explanation 1 For example, the tree with the following edges satisfies the condition. - Edge $ (1, 2) $ has weight $ 2 $ . - Edge $ (2, 3) $ has weight $ 3 $ . - Edge $ (2, 4) $ has weight $ 2 $ . Thus, output `Yes`. ### Sample Explanation 2 No tree satisfying the condition exists. Thus, output `No`. ### Constraints - $ 2 \le N \le 3000 $ - $ 1 \le A_{i,j} \le 9999 $ - All input values are integers.