Nezzar and Hidden Permutations

5000ms

524288K

Description:

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 $$$p_1,p_2,\ldots,p_n$$$ and $$$q_1,q_2,\ldots,q_n$$$ of integers from $$$1$$$ to $$$n$$$, and Nanako secretly selects $$$m$$$ unordered pairs $$$(l_1,r_1),(l_2,r_2),\ldots,(l_m,r_m)$$$;
After that, Nanako sends his chosen pairs to Nezzar;
On receiving those $$$m$$$ unordered pairs, Nezzar checks if there exists $$$1 \le i \le m$$$, 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 $$$1 \le i \le n$$$ such that $$$p_i \neq q_i$$$.

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 $$$t$$$ ($$$1 \le t \le 5 \cdot 10^5$$$) — the number of test cases.

The first line of each test case contains two integers $$$n,m$$$ ($$$1 \le n \le 5 \cdot 10^5, 0 \le m \le \min(\frac{n(n-1)}{2},5 \cdot 10^5)$$$).

Then $$$m$$$ lines follow, $$$i$$$-th of them contains two integers $$$l_i,r_i$$$ ($$$1 \le l_i,r_i \le n$$$, $$$l_i \neq r_i$$$), 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 $$$5 \cdot 10^5$$$, and the sum of $$$m$$$ for all test cases does not exceed $$$5\cdot 10^5$$$.

Output:

For each test case, print two permutations $$$p_1,p_2,\ldots,p_n$$$ and $$$q_1,q_2,\ldots,q_n$$$ such that the score Nezzar gets is maximized.

Sample Input:

Sample 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 $$$p_i \neq q_i$$$ for all $$$1 \leq i \leq 4$$$. Obviously, it is the maximum possible score Nezzar can get.

Informação

Provedor Codeforces

Código CF1477D