문제
훈과 찬은 행렬 게임을 하고 있다. 두 사람은 각각 $N \times N$ 행렬 $A = (a_{ij})$와 $B = (b_{ij})$를 가지고 있다. 게임은 $M$개 라운드로 구성되고, 각 라운드에서 훈과 찬은 동시에 각각 숫자 $\alpha$와 $\beta$를 부른다. 여기서, $\alpha$와 $\beta$는 1ドル$과 $N$사이의 정수이다. 그러면 훈과 찬은 각각 $a_{\alpha \beta}$와 $b_{\alpha \beta}$의 점수를 얻는다.
전날 밤 꿈에서, 훈은 찬이 게임의 각 라운드에서 부를 $M$개 숫자 $\beta_1 , \beta_2 , \dots , \beta_M$를 보았다. 따라서 훈은 Diff 가 최대가 되는 $M$개 숫자 $\alpha_1 , \alpha_2 , \dots , \alpha_M$을 선택할 수 있다. 여기서, Diff 는 $\sum_{k=1}^M{\left| a_{\alpha_k \beta_k} - b_{\alpha_k \beta_k} \right|}$로 정의하고, 이것은 둘의 각 라운드 점수의 절대값 차이의 총 합이다.
각 라운드에서 찬이 부르는 $M$개 숫자가 주어지면, 훈이 Diff 를 최대화하는 $M$개 숫자들을 선택할때, Diff 의 최대값을 출력하는 프로그램을 작성하시오.
출력
출력은 표준 출력을 사용한다. 훈이 Diff 를 최대화하는 $M$개 숫자를 선택할 때, Diff 의 최대값을 출력한다.
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