Dwik and his brother Samir both received scholarships from a famous university in India. Their father, Besher, wants to send some money with each of them.
Besher has n coins, the ith coin has a value of ai. He will distribute these coins between his two sons in n steps. In the ith step, he chooses whether to give the ith coin to Dwik or to Samir.
Let xi be the absolute difference between the sum of Dwik's and Samir's coins after the ith step. The unfairness factor of a distribution is max({x1, x2, ..., xn}). Besher wants to minimize the unfairness factor, can you help him?
The first line of the input consists of a single integer t, the number of test cases. Each test case consists of 2 lines:
The first line contains an integer n (1 ≤ n ≤ 100).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100).
Print t lines, ith line containing a single integer, the answer to the ith test case.
In the first sample test, besher has 5 coins (1, 2, 1, 4, 3), he can distribute them in the following way:
*Step 1:* Give the first coin to dwik , d = 1, s = 0 x1 = |1 - 0| = 1
*Step 2:* Give the second coin to samir, d = 1, s = 2 x2 = |1 - 2| = 1
*Step 3:* Give the third coin to samir, d = 1, s = 3 x3 = |1 - 3| = 2
*Step 4:* Give the fourth coin to dwik, d = 5, s = 3 x4 = |5 - 3| = 2
*Step 5:* Give the fifth coin to samir, d = 5, s = 6 x5 = |5 - 6| = 1
max({x1, x2, x3, x4, x5}) = 2
## Input
The first line of the input consists of a single integer t, the number of test cases. Each test case consists of 2 lines: The first line contains an integer n (1 ≤ n ≤ 100). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100).
## Output
Print t lines, ith line containing a single integer, the answer to the ith test case.
[samples]
## Note
In the first sample test, besher has 5 coins (1, 2, 1, 4, 3), he can distribute them in the following way: *Step 1:* Give the first coin to dwik , d = 1, s = 0 x1 = |1 - 0| = 1 *Step 2:* Give the second coin to samir, d = 1, s = 2 x2 = |1 - 2| = 1 *Step 3:* Give the third coin to samir, d = 1, s = 3 x3 = |1 - 3| = 2 *Step 4:* Give the fourth coin to dwik, d = 5, s = 3 x4 = |5 - 3| = 2 *Step 5:* Give the fifth coin to samir, d = 5, s = 6 x5 = |5 - 6| = 1 max({x1, x2, x3, x4, x5}) = 2
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ N_k \in \mathbb{Z} $ be the total number of people in the line.
- Let $ i_k \in \mathbb{Z} $ be the initial position (1-indexed) of the coach.
The metal detector activates alternately: person $ j $ activates it if $ j $ is even, and does not activate it if $ j $ is odd.
People who activate the detector are sent to the end of the line.
**Constraints**
1. $ 1 \le T \le 1000 $
2. $ 1 \le N_k \le 10^9 $
3. $ 1 \le i_k \le N_k $
**Objective**
For each test case $ k $, determine the order $ j_k $ in which the coach passes through the detector **without activating it**, i.e., the $ j_k $-th person to successfully pass (on an odd-numbered turn in the filtered sequence).