Division by Two and Permutation

题意翻译

有一个长度为 $n$ 的数组 $a$。 你可以对其中的数进行以下操作： * 不断除以 $2$，并向下取整。 求：能否在若干次操作后，使得 $a$ 数组变成一个 $1 \sim n$ 的全排列。

题目描述

You are given an array $ a $ consisting of $ n $ positive integers. You can perform operations on it. In one operation you can replace any element of the array $ a_i $ with $ \lfloor \frac{a_i}{2} \rfloor $ , that is, by an integer part of dividing $ a_i $ by $ 2 $ (rounding down). See if you can apply the operation some number of times (possible $ 0 $ ) to make the array $ a $ become a permutation of numbers from $ 1 $ to $ n $ —that is, so that it contains all numbers from $ 1 $ to $ n $ , each exactly once. For example, if $ a = [1, 8, 25, 2] $ , $ n = 4 $ , then the answer is yes. You could do the following: 1. Replace $ 8 $ with $ \lfloor \frac{8}{2} \rfloor = 4 $ , then $ a = [1, 4, 25, 2] $ . 2. Replace $ 25 $ with $ \lfloor \frac{25}{2} \rfloor = 12 $ , then $ a = [1, 4, 12, 2] $ . 3. Replace $ 12 $ with $ \lfloor \frac{12}{2} \rfloor = 6 $ , then $ a = [1, 4, 6, 2] $ . 4. Replace $ 6 $ with $ \lfloor \frac{6}{2} \rfloor = 3 $ , then $ a = [1, 4, 3, 2] $ .

输入输出格式

输入格式

The first line of input data contains an integer $ t $ ( $ 1 \le t \le 10^4 $ ) —the number of test cases. Each test case contains exactly two lines. The first one contains an integer $ n $ ( $ 1 \le n \le 50 $ ), the second one contains integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ).

输出格式

For each test case, output on a separate line: - YES if you can make the array $ a $ become a permutation of numbers from $ 1 $ to $ n $ , - NO otherwise. You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive response).

输入输出样例

输入样例 #1

6
4
1 8 25 2
2
1 1
9
9 8 3 4 2 7 1 5 6
3
8 2 1
4
24 7 16 7
5
22 6 22 4 22

输出样例 #1

YES
NO
YES
NO
NO
YES

说明

The first test case is explained in the text of the problem statement. In the second test case, it is not possible to get a permutation.