A16133 | Good Arrays

You are given an array of positive integers $a$ of length $n$ .

Let's call an array of positive integers $b$ of length $n$ good if:

1. $a_i \neq b_i$ for all $i$ from $1$ to $n$ ,
2. $a_1 + a_2 +\ldots + a_n = b_1 + b_2 + \ldots + b_n$ .

Does a good array exist?

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

The first line of each test case contains a single integer $n$ ( $1 \le n \le 10^5$ ) — the length of the array $a$ .

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

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

For each test case, output "YES" (without quotes) if there exists a good array, and "NO" (without quotes) otherwise.

You can output the answer in any case (upper or lower). For example, the strings "yEs","yes", "Yes", and "YES" will be recognized as positive responses.