Max GEQ Sum

1000ms

262144K

Description:

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$$$.

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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).

Sample Input:

3
4
-1 1 -1 2
5
-1 2 -3 2 -1
3
2 3 -1

Sample Output:

YES
YES
NO

Note:

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 $$$\max(2, 3) < 2 + 3$$$.

Informação

Provedor Codeforces

Código CF1691D