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B. New Year's Number

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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