B. New Year's Number
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $2021$.

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).

Example
Input
5
1
4041
4042
8081
8079

Output
NO
YES
YES
YES
NO