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.util.*;

public class SpecialPermutation {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int x = 0; x < t; x++) {
            int n = sc.nextInt();
            if (n > 2) {
                int[] arr = new int[n];
                int k = 0;
                for (int i = n; i >= 1; i--) {
                    arr[k] = i;
                    k++;
                }
                if (n % 2 != 0) {
                    int temp = arr[n / 2];
                    arr[(n / 2)] = 1;
                    arr[n - 1] = temp;
                }
                for (int i = 0; i < n; i++) {
                    System.out.print(arr[i] + " ");
                }
            } else {
                System.out.print(2 + " " + 1);
            }
            System.out.println();
        }
    }
}