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 <cstring>
#include <set>
#define gc getchar()
#define idg(ch) isdigit(ch)
#define N 500050
using namespace std;

inline void read(int &x, int f = 1) {
	x = 0; char ch = gc;
	while (!idg(ch)) f = ch == '-' ? -1 : 1, ch = gc;
	while (idg(ch)) x = (x << 3) + (x << 1) + (ch ^ 48), ch = gc;
	x *= f;
}

int T, n, m, tot, cnt; // ÅÅÁÐtot£¬ ¼¯ºÏcnt 
int id[N], rt[N], p[N], q[N];

set<int>edge[N], S[N];

int find(int x) {
	for (int i = 1; i <= n; i++) if (!edge[x].count(i) && i != x) return i;
	return n + 1;
}

void merge(int x, int y) {
	rt[id[x] = id[y] = ++cnt] = x;
	S[cnt].insert(x), S[cnt].insert(y);
}

void solve() {
	for (int i = 1; i <= n; i++) {
		if (edge[i].size() == n - 1) {p[i] = q[i] = ++tot; continue;}
		if (id[i]) continue;
		int nxt = find(i);
		if (!id[nxt]) merge(i, nxt);
		else if (S[id[nxt]].size() == 2 || rt[id[nxt]] == nxt) S[id[i] = id[nxt]].insert(i), rt[id[i]] = nxt;
		else S[id[nxt]].erase(nxt), merge(i, nxt);
	}
	//±éÀú¼¯ºÏÄÚ²¿ 
	for (int i = 1; i <= cnt; i++) {
		p[rt[i]] = ++tot;
//		printf("set: ");
		for (set<int>::iterator it = S[i].begin(); it != S[i].end(); it++) {
//			printf("%d ", *it);
			if (*it != rt[i]) q[*it] = tot, p[*it] = ++tot;
		}
//		printf("\n");
		q[rt[i]] = tot;
	} 
}

void preset() {
	tot = cnt = 0;
	for (int i = 1; i <= n; i++) {
		S[i].clear(), edge[i].clear(), p[i] = q[i] = id[i] = rt[i] = 0;
	}
}

void init() {
	read(n), read(m);
	preset();
	for (int i = 1, x, y; i <= m; i++) {
		read(x), read(y);
		edge[x].insert(y), edge[y].insert(x);
	}
	solve();
	for (int i = 1; i <= n; i++) printf("%d ", p[i]); printf("\n");
	for (int i = 1; i <= n; i++) printf("%d ", q[i]); printf("\n");
}

signed main() {
	read(T);
	while (T--) {
		init();
	}
}