AT_abc450_b [ABC450B] Split Ticketing

There are $ N $ stations $ 1, 2, \dots, N $ , arranged in a straight line from west to east in this order. The AtCoder Railway train passes through these $ N $ stations and runs from west to east. For any two integers $ i, j $ satisfying $ 1 \leq i \lt j \leq N $ , the cost of boarding the train at station $ i $ and getting off at station $ j $ is $ C_{i,j} $ . Determine whether there exist three integers $ a, b, c $ such that: - $ 1 \leq a \lt b \lt c \leq N $ - The total cost of boarding the train at station $ a $ , getting off at station $ b $ , then boarding the train again at station $ b $ , and getting off at station $ c $ is less than the cost of boarding the train at station $ a $ and getting off at station $ c $ .

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

If there exist three integers $ a, b, c $ satisfying the conditions, output `Yes`; otherwise, output `No`, on a single line.

### Sample Explanation 1 Choosing $ (a, b, c) = (1, 2, 3) $ , $ C_{a,b}+C_{b,c}=C_{1,2}+C_{2,3}=45+45 $ $ C_{a,c}=C_{1,3}=450 $ so the conditions are satisfied. ### Sample Explanation 2 No choice of $ (a, b, c) $ satisfies the conditions. ### Constraints - $ 3 \leq N \leq 100 $ - $ 1 \leq C_{i,j} \leq 10^9 $ - All input values are integers.