CF1807B.Grab the Candies

Mihai and Bianca are playing with bags of candies. They have a row $a$ of $n$ bags of candies. The $i$-th bag has $a_i$ candies. The bags are given to the players in the order from the first bag to the $n$-th bag.

If a bag has an even number of candies, Mihai grabs the bag. Otherwise, Bianca grabs the bag. Once a bag is grabbed, the number of candies in it gets added to the total number of candies of the player that took it.

Mihai wants to show off, so he wants to reorder the array so that at any moment (except at the start when they both have no candies), Mihai will have strictly more candies than Bianca. Help Mihai find out if such a reordering exists.

米海和比安卡正在玩装有糖果的袋子。他们有一排 $n$ 个糖果袋，记为数组 $a$。其中第 $i$ 个袋子含有 $a_i$ 颗糖果。这些袋子将按从第一个袋子到第 $n$ 个袋子的顺序依次分发给两位玩家。

如果某个袋子中的糖果数量为偶数，则由米海拿走该袋子；否则由比安卡拿走。一旦袋子被某位玩家拿走，其中的糖果数量即计入该玩家所拥有的糖果总数。

米海想炫耀一下，因此他希望重新排列数组 $a$，使得在任意时刻（起始时两人糖果数均为 $0$ 的情况除外），米海所拥有的糖果总数都严格大于比安卡所拥有的糖果总数。请帮助米海判断是否存在这样的重排方案。

The first line of the input contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 100$) — the number of bags in the array.

The second line of each test case contains $n$ space-separated integers $a_i$ ($1 \leq a_i \leq 100$) — the number of candies in each bag.

输入的第一行包含一个整数 $t$（$1 \leq t \leq 1000$）—— 表示测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 100$）—— 表示数组中袋子的数量。

每个测试用例的第二行包含 $n$ 个以空格分隔的整数 $a_i$（$1 \leq a_i \leq 100$）—— 表示每个袋子中的糖果数量。

For each test case, output "YES" (without quotes) if such a reordering exists, and "NO" (without quotes) otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).

对于每个测试用例，如果存在这样的重排，则输出 "YES"（不带引号）；否则输出 "NO"（不带引号）。

您可以以任意大小写形式输出答案（例如，字符串 "yEs"、"yes"、"Yes" 和 "YES" 均被视为肯定回答）。

In the first test case, Mihai can reorder the array as follows: $[4, 1, 2, 3]$. Then the process proceeds as follows:

• the first bag has $4$ candies, which is even, so Mihai takes it — Mihai has $4$ candies, and Bianca has $0$.
• the second bag has $1$ candies, which is odd, so Bianca takes it — Mihai has $4$ candies, and Bianca has $1$.
• the third bag has $2$ candies, which is even, so Mihai takes it — Mihai has $6$ candies, and Bianca has $1$.
• the fourth bag has $3$ candies, which is odd, so Bianca takes it — Mihai has $6$ candies, and Bianca has $4$.

Since Mihai always has more candies than Bianca, this reordering works.

在第一个测试用例中，米海可以将数组重新排列为：$[4, 1, 2, 3]$。随后过程如下进行：

• 第一个袋子有 $4$ 颗糖果，为偶数，因此米海拿走它——此时米海有 $4$ 颗糖果，比安卡有 $0$ 颗。
• 第二个袋子有 $1$ 颗糖果，为奇数，因此比安卡拿走它——此时米海有 $4$ 颗糖果，比安卡有 $1$ 颗。
• 第三个袋子有 $2$ 颗糖果，为偶数，因此米海拿走它——此时米海有 $6$ 颗糖果，比安卡有 $1$ 颗。
• 第四个袋子有 $3$ 颗糖果，为奇数，因此比安卡拿走它——此时米海有 $6$ 颗糖果，比安卡有 $4$ 颗。

由于米海始终拥有的糖果数多于比安卡，因此该重排方案可行。