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;
const int maxN=5e5;
int star_id[maxN],vis[maxN],stars;
vector<int> g[maxN],comp_g[maxN],star[maxN];
bool dfs(int v){
    vis[v]=1;
    for(int c:comp_g[v]){
        if(!vis[c] && dfs(c)){
            if(star_id[v]==-1)
                star[star_id[v]=stars++].push_back(v);
            star[star_id[c]=star_id[v]].push_back(c);
        }
    }
    return star_id[v]==-1;
}
void solve(){
    int n,m;
    cin >> n >> m;
    stars=0;
    for(int i=0;i<n;i++){
        star_id[i]=-1, vis[i]=0;
        g[i].assign(1,i), comp_g[i].clear(), star[i].clear();
    }
    for(int i=0;i<m;i++){
        int u,v;
        cin >> u >> v;
        u--,v--;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    for(int i=0;i<n;i++){
        int x=0;
        for(int x:g[i]) vis[x]=1;
        for(;x<n && vis[x];x++);
        if(x<n){
            comp_g[i].push_back(x);
            comp_g[x].push_back(i);
        }
        else star[star_id[i]=stars++].push_back(i);
        for(int x:g[i]) vis[x]=0;
    }
    for(int i=0;i<n;i++){
        if(!vis[i] && dfs(i))
            star[star_id[i]=star_id[comp_g[i][0]]].push_back(i);
    }
    int p[n],q[n];
    for(int i=0,k=1;i<stars;i++){
        for(int j=0;j<star[i].size();j++)
            p[star[i][j]]=k+j, q[star[i][j]]=k+j-1;
        k+=star[i].size(), q[star[i][0]]=k-1;
    }
    for(int i=0;i<n;i++)
        cout << p[i] << ' ';
    cout << endl;
    for(int i=0;i<n;i++)
        cout << q[i] << ' ';
    cout << endl;
}
int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
	int T;
	cin >> T;
	while(T--)
		solve();
	return 0;
}