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 MAX 1000005
using namespace std;
int t,n,m,cnt,sz;
int p[MAX],q[MAX],gr[MAX],rt[MAX];
set<int> e[MAX],fr[MAX];
int find(int x){
	for(register int i=1;i<=n;i++)
		if(!e[x].count(i)&&i!=x) return i;
}
void merge(int x,int y){
	gr[x]=gr[y]=++sz;
	fr[sz].insert(x),fr[sz].insert(y);
	rt[sz]=x;
}
void work(){
	scanf("%d%d",&n,&m);
	cnt=sz=0;
	for(register int i=1;i<=n;i++){
		e[i].clear();
		fr[i].clear();
		p[i]=q[i]=gr[i]=rt[i]=0;
	}
	for(register int i=1,a,b;i<=m;i++){
		scanf("%d%d",&a,&b);
		e[a].insert(b),e[b].insert(a);
	}
	for(register int i=1;i<=n;i++){
		if(e[i].size()==n-1){
			p[i]=q[i]=++cnt;
			continue;
		}
		if(gr[i]) continue; 
		int tp=find(i);
		if(!gr[tp]) merge(tp,i);
		else if(rt[gr[tp]]==tp){
			gr[i]=gr[tp];
			fr[gr[tp]].insert(i);
		}else if(fr[gr[tp]].size()>2){
			fr[gr[tp]].erase(tp);
			merge(tp,i);
		}else{
			rt[gr[tp]]=tp,fr[gr[tp]].insert(i);
			gr[i]=gr[tp];
		}
	}
	for(register int i=1;i<=sz;i++){
		p[rt[i]]=++cnt;
		for(int y : fr[i])
			if(y!=rt[i]) q[y]=cnt,p[y]=++cnt;
		q[rt[i]]=cnt;
	}
	for(register int i=1;i<=n;i++) printf("%d ",p[i]);printf("\n");
	for(register int i=1;i<=n;i++) printf("%d ",q[i]);printf("\n");
}
int main(){
	scanf("%d",&t);
	while(t--) work();
}//ccpy