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>
#define cs const
#define pb push_back
using namespace std;

cs int N = 5e5 + 50; 
int T, n, m, p[N], q[N], fa[N];
vector<int> G[N], e[N];
int fnd(int x){ return x == fa[x] ? x : fa[x] = fnd(fa[x]); }
bool ex[N]; vector<int> S[N];
bool dfs(int u, int f){
	ex[u] = true; 
	for(int o = 0, v; o < e[u].size(); o++)
	if((v = e[u][o]) != f){
		if(dfs(v, u)) S[u].pb(v); 	
	} if(S[u].empty() && !f) 
	S[e[u][0]].pb(u);
	return S[u].empty();
}
void Main(){
	cin >> n >> m;
	for(int i = 1; i <= n; i++)
		G[i].clear(), e[i].clear(), S[i].clear();
	for(int i = 1; i <= n; i++) fa[i] = i, ex[i] = 0; 
	for(int i = 1, u, v; i <= m; i++)
		scanf("%d%d", &u, &v), 
		G[u].pb(v), G[v].pb(u);
	int ind = 0; 
	for(int i = 1; i <= n; i++){
		sort(G[i].begin(), G[i].end());
		int t = 1 + (i == 1), k = 0;
		while(true){
			if(k == G[i].size() || G[i][k] != t) break;
			++k, ++t; if(t == i) ++t; 
		} if(t > n) p[i] = q[i] = ++ind;
		else if(fnd(t) != fnd(i))
		fa[fnd(i)] = fnd(t), e[i].pb(t), e[t].pb(i);
	}
	for(int i = 1; i <= n; i++)
		if(!ex[i] && e[i].size()) dfs(i, 0);
	for(int i = 1; i <= n; i++)
	if(S[i].size()){
		p[i] = ++ind;
		for(int o = 0, v; o < S[i].size(); o++){
			v = S[i][o];
			q[v] = ind, p[v] = ++ind;
		} q[i] = ind;
	}
	for(int i = 1; i <= n; i++)
		cout << p[i] << " "; puts("");
	for(int i = 1; i <= n; i++)
		cout << q[i] << " "; puts("");
}
int main(){
	#ifdef FSYo
	freopen("1.in", "r", stdin);
	#endif
	cin >> T; 
	while(T--) Main();
	return 0;
}