Problem: Nezzar designs a brand new game "Hidden Permutations" and shares it with his best friend, Nanako.

At the beginning of the game, Nanako and Nezzar both know integers n and m. The game goes in the following way:

  * Firstly, Nezzar hides two permutations p_1,p_2,…,p_n and q_1,q_2,…,q_n of integers from 1 to n, and Nanako secretly selects m unordered pairs (l_1,r_1),(l_2,r_2),…,(l_m,r_m); 
  * After that, Nanako sends his chosen pairs to Nezzar; 
  * On receiving those m unordered pairs, Nezzar checks if there exists 1 ≤ i ≤ m, such that (p_{l_i}-p_{r_i}) and (q_{l_i}-q_{r_i}) have different signs. If so, Nezzar instantly loses the game and gets a score of -1. Otherwise, the score Nezzar gets is equal to the number of indices 1 ≤ i ≤ n such that p_i ≠ q_i. 



However, Nezzar accidentally knows Nanako's unordered pairs and decides to take advantage of them. Please help Nezzar find out two permutations p and q such that the score is maximized.

Input

The first line contains a single integer t (1 ≤ t ≤ 5 ⋅ 10^5) — the number of test cases.

The first line of each test case contains two integers n,m (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ m ≤ min((n(n-1))/(2),5 ⋅ 10^5)). 

Then m lines follow, i-th of them contains two integers l_i,r_i (1 ≤ l_i,r_i ≤ n, l_i ≠ r_i), describing the i-th unordered pair Nanako chooses. It is guaranteed that all m unordered pairs are distinct.

It is guaranteed that the sum of n for all test cases does not exceed 5 ⋅ 10^5, and the sum of m for all test cases does not exceed 5⋅ 10^5.

Output

For each test case, print two permutations p_1,p_2,…,p_n and q_1,q_2,…,q_n such that the score Nezzar gets is maximized.

Example

Input


3
4 2
1 2
3 4
6 4
1 2
1 3
3 5
3 6
2 1
1 2


Output


1 2 3 4
3 4 1 2
2 3 4 1 6 5
1 4 3 2 5 6
1 2
1 2

Note

For first test case, for each pair given by Nanako:

  * for the first pair (1,2): p_1 - p_2 = 1 - 2 = -1, q_1 - q_2 = 3 - 4 = -1, they have the same sign; 
  * for the second pair (3,4): p_3 - p_4 = 3 - 4 = -1, q_3 - q_4 = 1 - 2 = -1, they have the same sign. 



As Nezzar does not lose instantly, Nezzar gains the score of 4 as p_i ≠ q_i for all 1 ≤ i ≤ 4. Obviously, it is the maximum possible score Nezzar can get.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int inf = 0x3f3f3f3f; 
const int MAXN = 500005;
template <typename T>
void read(T &x) {
	T flag = 1;
	char ch = getchar();
	for (; '0' > ch || ch > '9'; ch = getchar()) if (ch == '-') flag = 1;
	for (x = 0; '0' <= ch && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
	x *= flag;
}
int T; 
int n, m;
set<int> vec[MAXN], s[MAXN];
int p[MAXN], q[MAXN];
int id[MAXN], rt[MAXN], cnt;
int main() {
	read(T);
	while (T--) {
		read(n); read(m);
		cnt = 0;
		for (int i = 1; i <= n; i++) vec[i].clear(), id[i] = 0, rt[i] = 0;
		for (int i = 1; i <= m; i++) {
			int l, r;
			read(l); read(r);
			vec[l].insert(r);
			vec[r].insert(l);
		}
		int num = 0;
		cnt = 0;
		for (int i = 1; i <= n; i++) {
			if (vec[i].size() >= n - 1) {
				p[i] = q[i] = ++num;
				continue;
			}
			if (id[i]) continue;
			int j = 1;
			for (auto y : vec[i]) {
				if (j == i) j++;
				if (y != j) break;
				j++;
				if (j == i) j++;
			}
//			cout << i << " " << j << endl; 
			if (!id[j]) {
				rt[id[i] = id[j] = ++cnt] = i;
				s[cnt].clear();
				s[cnt].insert(i); s[cnt].insert(j);
				continue;
			}
			int pos = id[j];
			if (s[pos].size() == 2 || rt[pos] == j) rt[pos] = j, s[pos].insert(i), id[i] = pos;
			else {
				s[pos].erase(j);
				rt[id[i] = id[j] = ++cnt] = i;
				s[cnt].clear();
				s[cnt].insert(i); s[cnt].insert(j);
			}
		}
//		cout << cnt << endl;
		for (int i = 1; i <= cnt; i++) {
			p[rt[i]] = ++num;
//			cout << rt[i] << " ";
			for (auto j : s[i]) {
				if (j == rt[i]) continue;
//				cout << j << " ";
				q[j] = num;
				p[j] = ++num;
			}// cout << endl;
			q[rt[i]] = num;
		}
		for (int i = 1; i <= n; i++) printf("%d ", p[i]);
		puts("");
		for (int i = 1; i <= n; i++) printf("%d ", q[i]);
		puts("");
	}
	return 0;
}