Max GEQ Sum
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 $1 \leq i \leq j \leq n$.
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).
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).
Samples
3
4
-1 1 -1 2
5
-1 2 -3 2 -1
3
2 3 -1
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 $\max(2, 3) < 2 + 3$.