## Greedy Seunghyun

• 문제 ID
• 시간 제한
• 메모리 제한
• 제출 횟수
• 정답 횟수 (비율)
• 출처
• 분류

#### 문제

Jaehyun, who teaches N$N$ children in his kindergarten, decided to give them candies, because it was his birthday! Each child is denoted as an integer number from 0 to N-1$N-1$. Because Jaehyun tends to give freedom to the kids, he let them take candies as much as they want. As a result, child i$i$ (0 \le i < N$0 \le i < N$) took a_{i}$a_{i}$ candies.

Seunghyun, who is denoted as child 0$0$, was disappointed because he couldn't obtain all the candies. After a deep thought, Seunghyun came out with an idea. He gathered all the kids in the kindergarten, and suggested to distribute candies by the following way:

1. Seunghyun chooses an integer k$k$ which is bigger than 0$0$ and smaller than N$N$.
2. Child k$k$ must hand out one candy to each of child 0$0$, child 1$1$, ... child k-1$k-1$. After this, child k$k$ will lose k$k$ candies, and child 0$0$, child 1$1$, \cdots$\cdots$, child k-1$k-1$ will get one candy.

All the children agreed because they thought that it was a great idea! However, as the only purpose of this suggestion was taking all the candies, Seunghyun wants to know whether he could achieve his goal by repeating this process 0 or more times.

You are to write a program which determines whether Seunghyun can get all the candies.

#### 입력

The first line of the input contains the number of test cases T$T$.

Each test case starts with a line containing N$N$ (2 \le N \le 100,000$2 \le N \le 100,000$), the number of children that Jaehyun teaches. The following line contains N$N$ space-separated integers a_{0}, a_{1}, \cdots, a_{N-1}$a_{0}, a_{1}, \cdots, a_{N-1}$, where a_{i}$a_{i}$ (0 \le a_{i} \le 10^{9}$0 \le a_{i} \le 10^{9}$) is the number of candies that child i$i$ has taken.

#### 출력

For each test case, if Seunghyun can take all candies, print "POSSIBLE" (without quotes). If not print "IMPOSSIBLE" (without quotes).

#### 예제 입력

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

#### 예제 출력

POSSIBLE
IMPOSSIBLE
POSSIBLE