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 pc putchar
#define gc() getchar()
#define pb emplace_back
typedef long long LL;
const int N=5e5+5;

int bel[N],pnt[N],P[N],Q[N];
std::set<int> st[N];
std::vector<int> e[N];

inline int read()
{
	int now=0,f=1; char c=gc();
	for(;!isdigit(c);c=='-'&&(f=-1),c=gc());
	for(;isdigit(c);now=now*10+c-48,c=gc());
	return now*f;
}
void Solve()
{
	const int n=read(),m=read();
	for(int i=1,u,v; i<=m; ++i) u=read(),v=read(), e[u].pb(v), e[v].pb(u);
	for(int i=1; i<=n; ++i) std::sort(e[i].begin(),e[i].end());

	int tot=0,now=0;
	for(int x=1; x<=n; ++x)
		if(e[x].size()==n-1) P[x]=Q[x]=++now;
		else if(!bel[x])
		{
			int y=0; e[x].pb(N);
			for(auto v:e[x])
			{
				if(++y==x) ++y;
				if(y!=v) break;
			}
			int bely=bel[y];
			if(!bely)
				bel[x]=bel[y]=++tot, pnt[tot]=x, st[tot].insert(x), st[tot].insert(y);
			else if(pnt[bely]==y||st[bely].size()==2)
				pnt[bely]=y, bel[x]=bely, st[bely].insert(x);
			else
				st[bely].erase(y), bel[x]=bel[y]=++tot, pnt[tot]=x, st[tot].insert(x), st[tot].insert(y);
		}
	for(int i=1; i<=tot; ++i)
	{
		int p=pnt[i]; P[p]=++now;
		for(auto x:st[i])
			if(x!=p) Q[x]=now, P[x]=++now;
		Q[p]=now;
	}
	for(int i=1; i<=n; ++i) printf("%d ",P[i]); pc('\n');
	for(int i=1; i<=n; ++i) printf("%d ",Q[i]); pc('\n');

	for(int i=1; i<=n; ++i) bel[i]=0;
	for(int i=1; i<=tot; ++i) std::set<int>().swap(st[i]);
	for(int i=1; i<=n; ++i) std::vector<int>().swap(e[i]);
}

int main()
{
	for(int T=read(); T--; Solve());
	return 0;
}