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;
#define maxn 1000010
set<int> edg[maxn],st[maxn];
int in[maxn],rt[maxn],p[maxn],q[maxn],cnt,blg[maxn],tot;
void work(){
	int n,m;
	scanf("%d%d",&n,&m);
	cnt=tot=0;
	for(int i=1;i<=n;i++){
		edg[i].clear();st[i].clear();
		in[i]=p[i]=q[i]=blg[i]=rt[i]=0;
	}
	for(int i=1;i<=m;i++){
		int x,y;
		scanf("%d%d",&x,&y);
		edg[x].insert(y);edg[y].insert(x);
		in[x]++,in[y]++;
	}
	for(int i=1;i<=n;i++){
		if(in[i]==n-1){
			p[i]=q[i]=++cnt;
			continue;
		}
		if(blg[i])continue;
		int v=1;
		for(auto y:edg[i]){
			//cout<<"ass"<<v<<" "<<y<<endl;
			if(v==i)v++;
			if(v!=y)break;
			v++;
		}
		if(v==i)v++;
		//cout<<i<<" "<<v<<endl;
		if(!blg[v]){
			//cout<<i<<" "<<v<<endl;
			++tot;
			rt[tot]=i;blg[i]=blg[v]=tot;
			st[tot].insert(i);st[tot].insert(v);
		}else if(st[blg[v]].size()==2||rt[blg[v]]==v){
			rt[blg[v]]=v;blg[i]=blg[v];
			st[blg[v]].insert(i);
		}else{
			st[blg[v]].erase(v);
			++tot;
			rt[tot]=i;blg[i]=blg[v]=tot;
			st[tot].insert(i);st[tot].insert(v);
		}
	}
	for(int i=1;i<=tot;i++){
	//	cout<<rt[i]<<endl;
		int l=cnt+2,r=cnt+1;
		p[rt[i]]=cnt+1,q[rt[i]]=cnt+st[i].size();
		for(auto y:st[i]){
		//	cout<<y<<" ";
			if(y==rt[i])continue;
			
			p[y]=l;
			q[y]=p[y]-1;
		//	cout<<p[y]<<" "<<q[y]<<" ";
			l++;
		}//cout<<endl;
		cnt+=st[i].size();
	}
	for(int i=1;i<=n;i++)printf("%d ",p[i]);
	puts("");
	for(int i=1;i<=n;i++)printf("%d ",q[i]);
	puts("");
}
int main(){
	int t;
	scanf("%d",&t);
	while(t--)work();
}//zrt ee zyx