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 PYTHON):

Solution:
from __future__ import print_function, division
import sys
from __builtin__ import xrange as range
from future_builtins import ascii, filter, hex, map, oct, zip
input = lambda: sys.stdin.readline().rstrip("\r\n")
from functools import reduce
a = int(input())
i = 0
while i < a :
    b = int(input())
    s = b
    g = ""
    g = g + str(b)
    while ((s-1) > 0) and (b % 2 == 0) :
        s = s - 1
        g = g + " "
        g = g + str(s)
    while ((s-1) > 0) and (b % 2 == 1) :
        s = s - 1
        if s == ((b//2)+1) :
            g = g + " "
            g = g + str(s - 1)
            g = g + " "
            g = g + str(s)
            s = s - 2
        if s == 0 :
            break
        g = g + " "
        g = g + str(s)
    print(g)
    i = i + 1