A13987 | New Year's Number

Polycarp remembered the $2020$ -th year, and he is happy with the arrival of the new $2021$ -th year. To remember such a wonderful moment, Polycarp wants to represent the number $n$ as the sum of a certain number of $2020$ and a certain number of $2021$ .

For example, if:

- $n=4041$ , then the number $n$ can be represented as the sum $2020 + 2021$ ;
- $n=4042$ , then the number $n$ can be represented as the sum $2021 + 2021$ ;
- $n=8081$ , then the number $n$ can be represented as the sum $2020 + 2020 + 2020 + 2021$ ;
- $n=8079$ , then the number $n$ cannot be represented as the sum of the numbers $2020$ and $2021$ .

Help Polycarp to find out whether the number $n$ can be represented as the sum of a certain number of numbers $2020$ and a certain number of numbers $2021$ .

The first line contains one integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. Then $t$ test cases follow.

Each test case contains one integer $n$ ( $1 \leq n \leq 10^6$ ) — the number that Polycarp wants to represent as the sum of the numbers $2020$ and $2021$ .

For each test case, output on a separate line:

- "YES" if the number $n$ is representable as the sum of a certain number of $2020$ and a certain number of $2021$ ;
- "NO" otherwise.

You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).