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 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

Each test case contains one integer n (1 ≤ n ≤ 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
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for(int i=a; i<=b; i++)
#define repd(i, a, b) for(int i=a; i>=b; i--)
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int,int>
#define pll pair<long long,long long>
#define pb push_back
#define fr first
#define sc second

typedef long long ll;
typedef unsigned long long ull;

struct cmp{
	bool operator()(const pair<int,int> &p1,const pair<int,int> &p2){
		return p1.first>p2.first;
	}
};

ll n;

void solve(){
    if(n%2021==0){
        cout<<"YES\n";
        return;
    }
    for(int i=1;i<=500;i++){
        n-=2020;
        if(n<0) break;
        if(n%2021==0){
            cout<<"YES\n";
            return;
        }
    }
    cout<<"NO\n";
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t=1;
    cin>>t;
    while(t--){
        cin>>n;
        solve();
    }

}
