B. Parity and Sum
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an array $$$a$$$ of $$$n$$$ positive integers.

In one operation, you can pick any pair of indexes $$$(i, j)$$$ such that $$$a_i$$$ and $$$a_j$$$ have distinct parity, then replace the smaller one with the sum of them. More formally:

  • If $$$a_i < a_j$$$, replace $$$a_i$$$ with $$$a_i + a_j$$$;
  • Otherwise, replace $$$a_j$$$ with $$$a_i + a_j$$$.

Find the minimum number of operations needed to make all elements of the array have the same parity.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the minimum number of operations required.

Example
Input
7
5
1 3 5 7 9
4
4 4 4 4
3
2 3 4
4
3 2 2 8
6
4 3 6 1 2 1
6
3 6 1 2 1 2
5
999999996 999999997 999999998 999999999 1000000000
Output
0
0
2
4
3
3
3
Note

In the first test case, all integers already have the same parity. Therefore, no operation is needed.

In the third test case, we can perform two operations $$$(1, 2)$$$ and $$$(1, 3)$$$. The array $$$a$$$ transforms as follows: $$$a = [\color{red}2, \color{red}3, 4] \longrightarrow [\color{red}5, 3, \color{red}4] \longrightarrow [5, 3, 9]$$$.

In the fourth test case, an example of an optimal sequence of operations is $$$(1, 2)$$$, $$$(1, 3)$$$, $$$(1, 4)$$$, and $$$(1, 4)$$$. The array $$$a$$$ transforms as follows: $$$a = [\color{red}3, \color{red}2, 2, 8] \longrightarrow [\color{red}3, 5, \color{red}2, 8] \longrightarrow [\color{red}3, 5, 5, \color{red}8] \longrightarrow [\color{red}{11}, 5, 5, \color{red}8] \longrightarrow [11, 5, 5, 19]$$$.