#### Little Chef and Sums

Little Chef and Sums : Our little chef is fond of doing additions/sums in his free time. Today, he has an array **A**consisting of **N** positive integers and he will compute prefix and suffix sums over this array.

He first defines two functions **prefixSum(i)** and **suffixSum(i)** for the array as follows. The function **prefixSum(i)** denotes the sum of first **i** numbers of the array. Similarly, he defines **suffixSum(i)** as the sum of last **N – i + 1** numbers of the array.

Little Chef is interested in finding the minimum index **i** for which the value **prefixSum(i) + suffixSum(i)** is the minimum. In other words, first you should minimize the value of **prefixSum(i) + suffixSum(i)**, and then find the least index **i** for which this value is attained.

Since, he is very busy preparing the dishes for the guests, can you help him solve this problem?

### Input

The first line of the input contains an integer **T** denoting the number of test cases.

The first line of each test case contains a single integer **N** denoting the number of integers in the array **A**.

The second line contains **N** space-separated integers **A _{1}**,

**A**, …,

_{2}**A**denoting the array

_{N}**A**.

### Output

For each test case, output a single line containing the answer.

### Constraints

**1**≤**T**≤**10****1**≤**N, A[i]**≤**10**^{5}

### Subtasks

**Subtask #1 : (20 points)****1 ≤ N ≤ 100****Subtask #2 : (80 points)**Original constraints

### Example

Input:2 3 1 2 3 4 2 1 3 1Output:1 2

### Explanation

**Example case 1.** Let’s calculate prefixSum(i) + suffixSum(i) for all indexes **i** in the sample case.

prefixSum(1) + suffixSum(1) = 1 + 6 = 7 prefixSum(2) + suffixSum(2) = 3 + 5 = 8 prefixSum(3) + suffixSum(3) = 6 + 3 = 9

The minimum value of the function is 7, which is attained at index 1, so the answer would be 1.

**Example case 2.** Let’s calculate prefixSum(i) + suffixSum(i) for all indexes **i** in the sample case.

prefixSum(1) + suffixSum(1) = 2 + 7 = 9 prefixSum(2) + suffixSum(2) = 3 + 5 = 8 prefixSum(3) + suffixSum(3) = 6 + 4 = 10 prefixSum(4) + suffixSum(4) = 7 + 1 = 8

The minimum value of the function is 8, which is achieved for indices 2 and 4. The minimum of these two indices 2, 4 is index 2. Hence, the answer will be 2.

### Solution

Hint: Watch your functions (if you are using). Might kill your time Efficiency.