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 N = 500000;

set<int> pairs[N], group[N], remain;
int p[N], q[N];
bool head[N];

void dfs(int u, int p = -1) {
  int c = -1, v = -1;
  group[u].clear();
  head[u] = false;
  remain.erase(u);

  while (true) {
    auto it = remain.upper_bound(c);
    if (it == remain.end()) {
      break;
    }

    c = *it;
    if (pairs[u].count(c) == 0) {
      dfs(c, u);
      if (head[c]) {
        v = c;
      } else {
        head[u] = true;
        group[u].insert(c);
      }
    }
  }

  if (!head[u] && p == -1) {
    if (v == -1) {
      head[u] = true;
    } else {
      group[v].insert(u);
    }
  }
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  int t;
  cin >> t;

  while (t--) {
    int n, m;
    cin >> n >> m;

    fill(pairs, pairs + n, set<int>());

    while (m--) {
      int l, r;
      cin >> l >> r;
      --l, --r;
      pairs[l].insert(r);
      pairs[r].insert(l);
    }

    remain.clear();
    for (int i = 0; i < n; ++i) {
      remain.insert(i);
    }

    for (int i = 0; i < n; ++i) {
      if (remain.count(i) > 0) {
        dfs(i);
      }
    }

    int k = 1;
    for (int i = 0; i < n; ++i) {
      if (head[i]) {
        p[i] = k + group[i].size();
        q[i] = k++;
        for (auto j : group[i]) {
          p[j] = k - 1;
          q[j] = k++;
        }
      }
    }

    for (int i = 0; i < n; ++i) {
      cout << p[i] << " ";
    }
    cout << "\n";

    for (int i = 0; i < n; ++i) {
      cout << q[i] << " ";
    }
    cout << "\n";
  }
}