Hilbert's Hotel is a very unusual hotel since the number of rooms is infinite! In fact, there is exactly one room for every integer, including zero and negative integers. Even stranger, the hotel is currently at full capacity, meaning there is exactly one guest in every room. The hotel's manager, David Hilbert himself, decides he wants to shuffle the guests around because he thinks this will create a vacancy (a room without a guest).

For any integer k and positive integer n, let kmod n denote the remainder when k is divided by n. More formally, r=kmod n is the smallest non-negative integer such that k-r is divisible by n. It always holds that 0≤ kmod n≤ n-1. For example, 100mod 12=4 and (-1337)mod 3=1.

Then the shuffling works as follows. There is an array of n integers a_0,a_1,…,a_{n-1}. Then for each integer k, the guest in room k is moved to room number k+a_{kmod n}.

After this shuffling process, determine if there is still exactly one guest assigned to each room. That is, there are no vacancies or rooms with multiple guests.

Input

Each test consists of multiple test cases. The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases. Next 2t lines contain descriptions of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 2⋅ 10^5) — the length of the array.

The second line of each test case contains n integers a_0,a_1,…,a_{n-1} (-10^9≤ a_i≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2⋅ 10^5.

Output

For each test case, output a single line containing "YES" if there is exactly one guest assigned to each room after the shuffling process, or "NO" otherwise. You can print each letter in any case (upper or lower).

Example

Input


6
1
14
2
1 -1
4
5 5 5 1
3
3 2 1
2
0 1
5
-239 -2 -100 -3 -11


Output


YES
YES
YES
NO
NO
YES

Note

In the first test case, every guest is shifted by 14 rooms, so the assignment is still unique.

In the second test case, even guests move to the right by 1 room, and odd guests move to the left by 1 room. We can show that the assignment is still unique.

In the third test case, every fourth guest moves to the right by 1 room, and the other guests move to the right by 5 rooms. We can show that the assignment is still unique.

In the fourth test case, guests 0 and 1 are both assigned to room 3.

In the fifth test case, guests 1 and 2 are both assigned to room 2.
import javax.swing.text.StyledEditorKit;
import java.io.*;
import java.util.*;

public class TestC {
    public static void main(String[] args) throws IOException {
        OutputStream out = new BufferedOutputStream( System.out );
        FastReader reader = new FastReader();
        int t = reader.nextInt();

        while (t-->0){
            int n = reader.nextInt();
            int[] arr = new int[n];
            boolean flag = false;
            List<Integer> occupiedRoom = new ArrayList<>();
            int newRoom;
            for (int k=0; k<n; k++){
                arr[k] = reader.nextInt();
            }
            for (int i=0; i<n; i++){
                newRoom = i+arr[i];
                newRoom = ((newRoom%n)+n)%n;
                if (occupiedRoom.contains(newRoom)){
                    flag = true;
                    break;
                } else{
                    occupiedRoom.add(newRoom);
                }
            }

            if (flag){
                out.write(("NO"+"\n").getBytes());
            }else{
                out.write(("YES"+"\n").getBytes());
            }
        }
        out.flush();
        reader.close();
    }



    private static class FastReader{
        final private int BUFFER_SIZE = 1 << 16;
        private byte[] buffer;
        private DataInputStream din;
        private int bufferPointer, bytesRead;

        public FastReader(){
            buffer = new byte[BUFFER_SIZE];
            din = new DataInputStream(System.in);
            bufferPointer = bytesRead = 0;
        }

        private String nextLine() throws IOException{
            StringBuilder sb = new StringBuilder();
            byte c;
            while((c = read()) != -1 && c != '\n'){
                sb.appendCodePoint(c);
            }
            return sb.toString();
        }

        private int nextInt() throws IOException{
            int ret = 0;
            byte c = read();
            while(c <= ' '){
                c = read();
            }
            boolean neg = c == '-';
            if(neg){
                c = read();
            }
            while(c >= '0' && c <= '9'){
                ret = ret * 10 + c - '0';
                c = read();
            }
            return (neg) ? -ret : ret;
        }

        private long nextLong() throws IOException{
            long ret = 0;
            byte c = read();
            while(c <= ' '){
                c = read();
            }
            boolean neg = c == '-';
            if(neg){
                c = read();
            }
            while(c >= '0' && c <= '9'){
                ret = ret * 10 + c - '0';
                c = read();
            }
            return (neg) ? -ret : ret;
        }

        private double nextDouble() throws IOException{
            double ret = 0, div = 1;
            byte c = read();
            while(c <= ' '){
                c = read();
            }
            boolean neg = c == '-';
            if(neg){
                c = read();
            }
            while(c >= '0' && c <= '9'){
                ret = ret * 10 + (c - '0');
                c = read();
            }
            if(c == '.'){
                while((c = read()) >= '0' && c <= '9'){
                    ret += (c - '0') / (div *= 10);
                }
            }
            return (neg) ? -ret : ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if(bytesRead == -1){
                buffer[0] = -1;
            }
        }

        private byte read() throws IOException {
            if(bufferPointer == bytesRead){
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }

        private void close() throws IOException{
            if(din != null){
                din.close();
            }
        }

    }

//    private static class Scan
//    {
//        private byte[] buf=new byte[1024];
//        private int index;
//        private InputStream in;
//        private int total;
//        public Scan()
//        {
//            in=System.in;
//        }
//        public int scan()throws IOException
//        {
//            if(total<0)
//                throw new InputMismatchException();
//            if(index>=total)
//            {
//                index=0;
//                total=in.read(buf);
//                if(total<=0)
//                    return -1;
//            }
//            return buf[index++];
//        }
//        public int scanInt()throws IOException
//        {
//            int integer=0;
//            int n=scan();
//            while(isWhiteSpace(n))
//                n=scan();
//            int neg=1;
//            if(n=='-')
//            {
//                neg=-1;
//                n=scan();
//            }
//            while(!isWhiteSpace(n))
//            {
//                if(n>='0'&&n<='9')
//                {
//                    integer*=10;
//                    integer+=n-'0';
//                    n=scan();
//                }
//                else throw new InputMismatchException();
//            }
//            return neg*integer;
//        }
//        public double scanDouble()throws IOException
//        {
//            double doub=0;
//            int n=scan();
//            while(isWhiteSpace(n))
//                n=scan();
//            int neg=1;
//            if(n=='-')
//            {
//                neg=-1;
//                n=scan();
//            }
//            while(!isWhiteSpace(n)&&n!='.')
//            {
//                if(n>='0'&&n<='9')
//                {
//                    doub*=10;
//                    doub+=n-'0';
//                    n=scan();
//                }
//                else throw new InputMismatchException();
//            }
//            if(n=='.')
//            {
//                n=scan();
//                double temp=1;
//                while(!isWhiteSpace(n))
//                {
//                    if(n>='0'&&n<='9')
//                    {
//                        temp/=10;
//                        doub+=(n-'0')*temp;
//                        n=scan();
//                    }
//                    else throw new InputMismatchException();
//                }
//            }
//            return doub*neg;
//        }
//        public String scanString()throws IOException
//        {
//            StringBuilder sb=new StringBuilder();
//            int n=scan();
//            while(isWhiteSpace(n))
//                n=scan();
//            while(!isWhiteSpace(n))
//            {
//                sb.append((char)n);
//                n=scan();
//            }
//            return sb.toString();
//        }
//        private boolean isWhiteSpace(int n)
//        {
//            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
//                return true;
//            return false;
//        }
//    }
}
