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;

int n,T,m,x,y,tot,ansp[500010],ansq[500010],cnt,id[500010];
vector<int> v[500010],e[500010],grp[500010],E[500010];
bool bo[500010];

bool dfs(int x)
{
	bo[x]=1;
	for (int i=0,sz=e[x].size(); i<sz; i++)
		if (!bo[e[x][i]]) 
			if (!dfs(e[x][i]))
			{
				if (!id[x]) id[x]=++tot,grp[tot].push_back(x);
				grp[id[x]].push_back(e[x][i]);
			}
	if (!id[x]) return 0; else return 1;
}

int main()
{
	scanf("%d",&T);
	while (T--)
	{
		scanf("%d%d",&n,&m),tot=0;
		for (int i=1; i<=n; i++) v[i].clear(),e[i].clear(),bo[i]=0,id[i]=0;
		for (int i=1; i<=m; i++)
		{
			scanf("%d%d",&x,&y);
			v[x].push_back(y),v[y].push_back(x);
		}
		for (int i=1; i<=n; i++) 
		{
			int p=0;
			for (int j=0,sz=v[i].size(); j<sz; j++) bo[v[i][j]]=1;
			for (int j=1; j<=n; j++) if (i!=j&&!bo[j]) {p=j; break;}
			if (!p) grp[++tot].push_back(i); else e[i].push_back(p),e[p].push_back(i);
			for (int j=0,sz=v[i].size(); j<sz; j++) bo[v[i][j]]=0;
		}
		for (int i=1; i<=n; i++) if (!bo[i]&&e[i].size())
			if (!dfs(i)) grp[id[e[i][0]]].push_back(i);
		cnt=0;
		for (int i=1; i<=tot; i++) 
		{
			int sz=grp[i].size();
			for (int j=0; j<sz; j++) ansp[grp[i][j]]=cnt+1+j,ansq[grp[i][j]]=cnt+j;
			cnt+=sz,ansq[grp[i][0]]=cnt,grp[i].clear();
		}
		for (int i=1; i<=n; i++) printf("%d ",ansp[i]);puts("");
		for (int i=1; i<=n; i++) printf("%d ",ansq[i]);puts("");
	}
	return 0;
}