Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

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

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in JAVA):

Solution:
// Long Contest 1, Problem L
import java.nio.charset.Charset;
import java.lang.StringBuilder;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) {
		Charset charset = Charset.forName("ascii");
	    FastIO rd = new FastIO(System.in, System.out, charset);
	    
	    int t = rd.readInt();
	    while(t-- > 0) {
	    	int n = rd.readInt();
	    	int h = n/2;
	    	if(h%2 != 0) {
	    		System.out.println("NO");
	    	}
	    	else {
	    		int sum_evens = 0;
	    		int[] evens = new int[h];
	    		int i = 0;
	    		for(int even=2; i < h; i++, even+=2) {
	    			evens[i] = even;
	    			sum_evens += even;
	    		}
	    		
	    		int sum_odds = 0;
	    		int[] odds = new int[h];
	    		i = 0;
	    		for(int odd=1; i < h-1; i++, odd+=2) {
	    			odds[i] = odd;
	    			sum_odds += odd;
	    		}
	    		int odd = sum_evens-sum_odds;
	    		odds[h-1] = odd;
	    		sum_odds += odd;
	    		// for(int odd=1; sum_odds < sum_evens; odd+=2) {
	    		// 	int next = odd+2;
	    		// 	int temp = sum_odds+odd;
	    		// 	int diff = sum_evens - temp;
	    		// 	if(next > diff) {
	    		// 		continue;
	    		// 	}
	    		// 	else {
	    		// 		sum_odds += odd;
	    		// 		odds[i] = odd;
	    		// 		i++;
	    		// 	}
	    		// }
	    		System.out.println("YES");
	    		print_array(evens);
	    		System.out.print(" ");
	    		print_array(odds);
	    		System.out.println();
	    	}
	    }
	}
	public static void print_array(int[] items) {
		System.out.print(items[0]);
		for(int i=1; i < items.length; i++) {
			System.out.print(" "+items[i]);
		}
	}
}


class FastIO {
    public final StringBuilder cache = new StringBuilder(1 << 20);
    private final InputStream is;
    private final OutputStream os;
    private final Charset charset;
    private StringBuilder defaultStringBuf = new StringBuilder(1 << 8);
    private byte[] buf = new byte[1 << 13];
    private int bufLen;
    private int bufOffset;
    private int next;
    
    public FastIO(InputStream is, OutputStream os, Charset charset) {
        this.is = is;
        this.os = os;
        this.charset = charset;
    }
    
    public FastIO(InputStream is, OutputStream os) {
        this(is, os, Charset.forName("ascii"));
    }
    
    private int read() {
        while (bufLen == bufOffset) {
            bufOffset = 0;
            try {
                bufLen = is.read(buf);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            if (bufLen == -1) {
                return -1;
            }
        }
        return buf[bufOffset++];
    }
    
    public void skipBlank() {
        while (next >= 0 && next <= 32) {
            next = read();
        }
    }
    
    public int readInt() {
        int sign = 1;
        
        skipBlank();
        if (next == '+' || next == '-') {
            sign = next == '+' ? 1 : -1;
            next = read();
        }
        
        int val = 0;
        if (sign == 1) {
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
        } else {
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read();
            }
        }
        
        return val;
    }
    
    public long readLong() {
        int sign = 1;
        
        skipBlank();
        if (next == '+' || next == '-') {
            sign = next == '+' ? 1 : -1;
            next = read();
        }
        
        long val = 0;
        if (sign == 1) {
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
        } else {
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read();
            }
        }
        
        return val;
    }
    
    public double readDouble() {
        boolean sign = true;
        skipBlank();
        if (next == '+' || next == '-') {
            sign = next == '+';
            next = read();
        }
        
        long val = 0;
        while (next >= '0' && next <= '9') {
            val = val * 10 + next - '0';
            next = read();
        }
        if (next != '.') {
            return sign ? val : -val;
        }
        next = read();
        long radix = 1;
        long point = 0;
        while (next >= '0' && next <= '9') {
            point = point * 10 + next - '0';
            radix = radix * 10;
            next = read();
        }
        double result = val + (double) point / radix;
        return sign ? result : -result;
    }
    
    public String readString(StringBuilder builder) {
        skipBlank();
        
        while (next > 32) {
            builder.append((char) next);
            next = read();
        }
        
        return builder.toString();
    }
    
    public String readString() {
        defaultStringBuf.setLength(0);
        return readString(defaultStringBuf);
    }
    
    public String readLine() {
        skipBlank();
        String s="";
        int offset = 0;
        while (next != -1 && next != '\n') {
            s += (char) next;
            next = read();
        }
        return s;
    }
    
    public int readString(char[] data, int offset) {
        skipBlank();
        
        int originalOffset = offset;
        while (next > 32) {
            data[offset++] = (char) next;
            next = read();
        }
        
        return offset - originalOffset;
    }
    
    public int readString(byte[] data, int offset) {
        skipBlank();
        
        int originalOffset = offset;
        while (next > 32) {
            data[offset++] = (byte) next;
            next = read();
        }
        
        return offset - originalOffset;
    }
    
    public char readChar() {
        skipBlank();
        char c = (char) next;
        next = read();
        return c;
    }
    
    public void flush() {
        try {
            os.write(cache.toString().getBytes(charset));
            os.flush();
            cache.setLength(0);
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
    
    public boolean hasMore() {
        skipBlank();
        return next != -1;
    }
}