Problem: Lunar rover finally reached planet X. After landing, he met an obstacle, that contains permutation p of length n. Scientists found out, that to overcome an obstacle, the robot should make p an identity permutation (make p_i = i for all i).

Unfortunately, scientists can't control the robot. Thus the only way to make p an identity permutation is applying the following operation to p multiple times: 

  * Select two indices i and j (i ≠ j), such that p_j = i and swap the values of p_i and p_j. It takes robot (j - i)^2 seconds to do this operation. 

Positions i and j are selected by the robot (scientists can't control it). He will apply this operation while p isn't an identity permutation. We can show that the robot will make no more than n operations regardless of the choice of i and j on each operation.

Scientists asked you to find out the maximum possible time it will take the robot to finish making p an identity permutation (i. e. worst-case scenario), so they can decide whether they should construct a new lunar rover or just rest and wait. They won't believe you without proof, so you should build an example of p and robot's operations that maximizes the answer.

For a better understanding of the statement, read the sample description.

Input

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

Each of next t lines contains the single integer n (2 ≤ n ≤ 10^5) – the length of p.

Note, that p is not given to you. You should find the maximum possible time over all permutations of length n.

It is guaranteed, that the total sum of n over all test cases doesn't exceed 10^5.

Output

For each test case in the first line, print how many seconds will the robot spend in the worst case.

In the next line, print the initial value of p that you used to construct an answer.

In the next line, print the number of operations m ≤ n that the robot makes in your example.

In the each of next m lines print two integers i and j — indices of positions that the robot will swap on this operation. Note that p_j = i must holds (at the time of operation).

Example

Input


3
2
3
3


Output


1
2 1
1
2 1
5
2 3 1
2
1 3
3 2
5
2 3 1
2
1 3
2 3

Note

For n = 2, p can be either [1, 2] or [2, 1]. In the first case p is already identity, otherwise robot will make it an identity permutation in 1 second regardless of choise i and j on the first operation.

For n = 3, p can be equals [2, 3, 1].

  * If robot will select i = 3, j = 2 on the first operation, p will become [2, 1, 3] in one second. Now robot can select only i = 1, j = 2 or i = 2, j = 1. In both cases, p will become identity in one more second (2 seconds in total).
  * If robot will select i = 1, j = 3 on the first operation, p will become [1, 3, 2] in four seconds. Regardless of choise of i and j on the second operation, p will become identity in five seconds. 



We can show, that for permutation of length 3 robot will always finish all operation in no more than 5 seconds.

Solution (in CPP):

Solution:
/*
 * CM 	= March
 * M 	= April
 * IM 	= July
 * GM 	= September
 * IGM	= December
*/

#include <bits/stdc++.h>

#define F first
#define S second

#define pb push_back
#define mp make_pair

typedef long long int lli;

#define pll pair<lli, lli>
#define pil pair<int, lli>
#define pli pair<lli, int>
#define pii pair<int, int>

#define dmx(x, y) x = max(x, y)
#define dmn(x, y) x = min(x, y)

using namespace std;

void setIO() {
	ios_base::sync_with_stdio(0);

	cin.tie(nullptr);
	cout.tie(nullptr);
}

const int MAX = 2e5 + 5;
const int LEN = 55;
const lli MOD = 1e9 + 7;
const lli INF = 9e9;

int _ = 1; // test cases

int n;

void func() {
	cin >> n;

	lli cst = 0;

	vector<pii> res;
	vector<int> prm(n);

	for (int i = 0; i < n; i++)
		prm[i] = i;

	res.pb({0, n - 1});
	swap(prm[0], prm[n - 1]);
	cst += 1ll * (n - 1) * (n - 1);

	for (int i = 1; i < n / 2; i++) {
		res.pb({i, n - 1});
		cst += 1ll * (n - 1 - i) * (n - 1 - i);
		swap(prm[n - 1], prm[i]);
	}
	for (int i = n / 2; i < n - 1; i++) {
		res.pb({i, 0});
		cst += 1ll * (i) * (i);
		swap(prm[0], prm[i]);
	}

	cout << cst << endl;

	for (int i = 0; i < n; i++)
		cout << prm[i] + 1 << " "; cout << "\n";

	cout << n - 1 << "\n";
	for (int i = n - 2; i >= 0; i--)
		cout << res[i].F + 1 << " " << res[i].S + 1 << "\n";
}

int main() {
	setIO();

	cin >> _;
	while (_--) func();

	return 0;
}