Game is one type of competency, and when it befalls by any number its really astonish.

Rifat is very good in mathematics and he always play with numbers . He take few numbers M and sum up on it. Morever he divides the sum up number by the least number of them.

And at a time he become so exhausted. So, your task is to help him. Note Rifat always keep the integer part.

Input

The input consists of several test case T (max 50). The first line of each test Case take a number N (1 ≤ N ≤ 10000). which will illustrate how many number you want to take. The next line contains N integers M (1 ≤ M ≤ 500) separated by spaces.

Output

The output should contain the position. If the result is match the given M numbers, you will print the positions of them. Otherwise it wil be NULL.