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 <cstdio>
#include <cstring>
#include <algorithm>
#include <set>
const int N = 500005;
int t, n, m;
std::set<int> E[N], S[N];
int cnt, d[N], bel[N], rt[N];
int p[N], q[N], tot;
int main(void)
{
	scanf("%d", &t);
	while(t--)
	{
		scanf("%d%d", &n, &m);
		memset(bel, 0, sizeof(int)*(n+5)), cnt = 0;
		memset(d, 0, sizeof(int)*(n+5));
		memset(rt, 0, sizeof(int)*(n+5));
		tot = 0;
		for(int i = 1;i <= n;++i)
			E[i].clear(), S[i].clear();
		for(int i = 1;i <= m;++i)
		{
			int x, y;
			scanf("%d%d", &x, &y);
			E[x].insert(y), E[y].insert(x);
			++d[x], ++d[y];
		} 
		for(int i = 1;i <= n;++i)
		{
			if(d[i] == n-1)
			{
				p[i] = q[i] = ++tot;
				continue;
			}
			if(bel[i])
				continue;
			int to = 1;
			for(std::set<int>::iterator it = E[i].begin();it != E[i].end();++it, ++to)
			{
				if(to == i)
					++to;
				if(*it != to)
					break;
			}
			if(to == i)
				++to;
			if(!bel[to])
			{
				rt[bel[i] = bel[to] = ++cnt] = to;
				S[cnt].insert(i), S[cnt].insert(to);
				continue;
			}
			if(S[bel[to]].size() == 2 || rt[bel[to]] == to)
				rt[bel[to]] = to, S[bel[to]].insert(i), bel[i] = bel[to];
			else
				S[bel[to]].erase(to), rt[bel[i] = bel[to] = ++cnt] = to, S[cnt].insert(i), S[cnt].insert(to);
		}
		for(int i = 1;i <= cnt;++i)
		{
			++tot;
			p[rt[i]] = tot, q[rt[i]] = tot+S[i].size()-1;
			for(std::set<int>::iterator it = S[i].begin();it != S[i].end();++it)
				if(*it != rt[i])
					p[*it] = ++tot, q[*it] = tot-1;
		}
		for(int i = 1;i <= n;++i)
			printf("%d ", p[i]);
		putchar('\n');
		for(int i = 1;i <= n;++i)
			printf("%d ", q[i]);
		putchar('\n'); 
	}
	return 0;
}