New Year's Number
Description
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).
Input
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 $2021$.
Output
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).
Samples
5
1
4041
4042
8081
8079
NO
YES
YES
YES
NO