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 <vector>
#include <cstdio>
#include <algorithm>
using namespace std;
const int Maxn=500000;
int n,m,t,d[Maxn+5],vis[Maxn+5],a[Maxn+5],f[Maxn+5],p[Maxn+5],q[Maxn+5];
int Find(int x){
	if(f[x]==0){
		return x;
	}
	return f[x]=Find(f[x]);
}
vector<int> g[Maxn+5],c[Maxn+5],w[Maxn+5];
void dfs(int i,int fa){
	vis[i]=1;
	for(auto j:c[i]){
		if(j!=fa){
			dfs(j,i);
			if(w[j].empty()){
				w[i].push_back(j);
			}
		}
	}
}
int main(){
	scanf("%d",&t);
	while(t--){
		scanf("%d%d",&n,&m);
		for(int i=1;i<=n;i++){
			vis[i]=d[i]=f[i]=0;
			g[i].clear();
			c[i].clear();
			w[i].clear();
		}
		for(int i=1;i<=m;i++){
			int u,v;
			scanf("%d%d",&u,&v);
			d[u]++;
			d[v]++;
			g[u].push_back(v);
			g[v].push_back(u);
		}
		for(int i=1,j;i<=n;i++){
			if(d[i]!=n-1){
				int k=0;
				for(auto it:g[i]){
					a[++k]=it;
				}
				a[++k]=i;
				sort(a+1,a+1+k);
				for(j=1;j<=k;j++){
					if(j!=a[j]){
						break;
					}
				}
				int x=Find(i),y=Find(j);
				if(x!=y){
					f[x]=y;
					c[i].push_back(j);
					c[j].push_back(i);
				}
			}
		}
		for(int i=1;i<=n;i++){
			if(!c[i].empty()&&!vis[i]){
				dfs(i,0);
				if(w[i].empty()){
					w[c[i][0]].push_back(i);
				}
			}
		}
		int k=0;
		for(int i=1;i<=n;i++){
			if(c[i].empty()){
				p[i]=++k;
				q[i]=k;
			}
			else{
				if(!w[i].empty()){
					for(int j=0;j<(int)w[i].size();j++){
						p[w[i][j]]=j+k+1;
					}
					p[i]=w[i].size()+k+1;
					q[i]=k+1;
					for(int j=0;j<(int)w[i].size();j++){
						q[w[i][j]]=j+k+2;
					}
					k+=w[i].size()+1;
				}
			}
		}
		for(int i=1;i<=n;i++){
			printf("%d ",p[i]);
		}
		puts("");
		for(int i=1;i<=n;i++){
			printf("%d ",q[i]);
		}
		puts("");
	}
}