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:
//starusc
#include<bits/stdc++.h>
using namespace std;
inline int read(){
	int x=0,f=1,c=getchar();
	while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
	while(isdigit(c)){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
	return f==1?x:-x;
}
const int N=5e5+4;
int n,m,cn,cou,c[N],rt[N],p[N],q[N];
set<int>s[N];
vector<int>e[N];
inline void upd(int x,int y){
	rt[c[x]=c[y]=++cn]=x;
	s[cn].insert(x);s[cn].insert(y);
}
inline void solve(){
	n=read();m=read();
	for(int i=1,u,v;i<=m;i++){
		u=read();v=read();
		e[u].push_back(v);e[v].push_back(u);
	}
	for(int i=1;i<=n;i++)if((signed)e[i].size()==n-1)p[i]=q[i]=c[i]=++cou;
	for(int i=1,x;i<=n;i++)if(!c[i]){
		x=1;
		sort(e[i].begin(),e[i].end());
		e[i].push_back(n+1);
		for(auto v:e[i]){
			if(i==x)x++;
			if(v==x)x++;
			else break;
		}
		if(!c[x]){upd(i,x);continue;}
		if((signed)s[c[x]].size()==2||rt[c[x]]==x){
			s[c[x]].insert(i);
			rt[c[i]=c[x]]=x;
		}
		else{
			s[c[x]].erase(x);
			upd(i,x);
		}
	}
	for(int i=1;i<=cn;i++){
		p[rt[i]]=++cou;
		q[rt[i]]=cou+(signed)s[i].size()-1;
		for(auto v:s[i])if(v!=rt[i]){
			q[v]=cou;
			p[v]=++cou;
		}
	}
	for(int i=1;i<=n;i++)cout<<p[i]<<" ";puts("");
	for(int i=1;i<=n;i++)cout<<q[i]<<" ";puts("");
	cn=cou=0;
	memset(c,0,sizeof(int)*(n+1));
	for(int i=1;i<=n;i++){s[i].clear();e[i].clear();}
}
int main(){
	for(int T=read();T--;)solve();
	return (0-0);
}