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 <iostream>
#include <cstdio>
#include <cctype>
#include <set>
using namespace std;
const int MAXN=5e5+5;
int vis[MAXN],a[MAXN],b[MAXN];
set<int> edge[MAXN],s[MAXN];
inline int read()
{
	int x=0;char ch=getchar();
	while(!isdigit(ch)) ch=getchar();
	while(isdigit(ch)){x=x*10+ch-'0';ch=getchar();}
	return x;
}
inline void solve()
{
	int n=read(),m=read();
	for(int i=1;i<=n;i++)
		s[i].clear(),
		edge[i].clear(),
		vis[i]=a[i]=b[i]=0;
	for(int i=1;i<=m;i++)
	{
		int x=read(),y=read();
		edge[x].insert(y);
		edge[y].insert(x);
	}
	for(int i=1;i<=n;i++)
	{
		int p=1;
		edge[i].insert(i);
		if(vis[i]) continue;
		if(edge[i].size()==n) continue;
		for(auto x:edge[i]) if(x^p) break; else p++;
		if(!vis[p]) vis[p]=vis[i]=i,s[i].insert(p);
		else if(vis[p]==p) vis[i]=p,s[p].insert(i);
		else if(s[vis[p]].size()==1)
			s[vis[p]].erase(p),s[p].insert(vis[p]),
			s[p].insert(i),vis[vis[p]]=p,vis[p]=vis[i]=p;
		else s[vis[p]].erase(p),vis[p]=vis[i]=i,s[i].insert(p);
	}
	int cnt=0;
	for(int i=1;i<=n;i++)
		if(vis[i]==i)
		{
			a[i]=++cnt;
			for(auto x:s[i])
				b[x]=cnt,a[x]=++cnt;
			b[i]=cnt;
		}
	for(int i=1;i<=n;i++)
		if(!a[i]&&!b[i])
			a[i]=b[i]=++cnt;
	for(int i=1;i<=n;i++)
		printf("%d%c",a[i]," \n"[i==n]);
	for(int i=1;i<=n;i++)
		printf("%d%c",b[i]," \n"[i==n]);
}
int main()
{
	int t=read();
	while(t--) solve();
	return 0;
}