CF1691D Max GEQ Sum

You are given an array $ a $ of $ n $ integers. You are asked to find out if the inequality $\max(a_i, a_{i + 1}, \ldots, a_{j - 1}, a_{j}) \geq a_i + a_{i + 1} + \dots + a_{j - 1} + a_{j} $ holds for all pairs of indices $ (i, j) $ , where $ 1 \leq i \leq j \leq n$.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^5 $ ). Description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) — the size of the array. The next line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -10^9 \le a_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, on a new line output "YES" if the condition is satisfied for the given array, and "NO" otherwise. You can print each letter in any case (upper or lower).

In test cases $ 1 $ and $ 2 $ , the given condition is satisfied for all $ (i, j) $ pairs. In test case $ 3 $ , the condition isn't satisfied for the pair $ (1, 2) $ as $ \max(2, 3) < 2 + 3 $ .