Problem: You are given one integer n (n > 1).

Recall that a permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2, 3, 1, 5, 4] is a permutation of length 5, but [1, 2, 2] is not a permutation (2 appears twice in the array) and [1, 3, 4] is also not a permutation (n = 3 but there is 4 in the array).

Your task is to find a permutation p of length n that there is no index i (1 ≤ i ≤ n) such that p_i = i (so, for all i from 1 to n the condition p_i ≠ i should be satisfied).

You have to answer t independent test cases.

If there are several answers, you can print any. It can be proven that the answer exists for each n > 1.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 100) — the length of the permutation you have to find.

Output

For each test case, print n distinct integers p_1, p_2, …, p_n — a permutation that there is no index i (1 ≤ i ≤ n) such that p_i = i (so, for all i from 1 to n the condition p_i ≠ i should be satisfied).

If there are several answers, you can print any. It can be proven that the answer exists for each n > 1.

Example

Input


2
2
5


Output


2 1
2 1 5 3 4

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    static class MyScanner {
        private final BufferedReader bf;
        private final StreamTokenizer tk;

        public MyScanner() {
            bf = new BufferedReader(new InputStreamReader(System.in));
            tk = new StreamTokenizer(bf);
        }

        public String next() {
            StringBuilder sb = new StringBuilder();
            while (true) {
                try {
                    char c = (char) bf.read();
                    if (c == ' ' || c == '\n') break;
                    sb.append(c);
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return sb.toString();
        }

        public int nextInt() {
            try {
                tk.nextToken();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return (int) tk.nval;
        }

        public String nextLine() {
            try {
                return bf.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return "";
        }

        public char getChar() {
            try {
                return (char) bf.read();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return '\0';
        }
    }

    public static void main(String[] args) {
        Main s = new Main();
        s.solve();
    }

    PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
    MyScanner sc = new MyScanner();
//    Scanner sc = new Scanner(System.in);

    private void solve() {
        int t = sc.nextInt();

        while (t-- > 0) {
            int n = sc.nextInt();
            int[] arr = new int[n + 1];
            for (int i = n; i >= 1; i--) arr[n - i + 1] = i;
            int tmp = arr[1];
            arr[1] = arr[(n + 1) >> 1];
            arr[(n + 1) >> 1] = tmp;
            for (int i = 1; i <= n; i++) {
                if (i != 1) out.print(" ");
                out.print(arr[i]);
            }
            out.println();
        }
        out.flush();
    }



}