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No.3185 Three Abs

レベル : / AI推定難易度 : 1225 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 76
作問者 : 蜜蜂 / テスター : Mitarushi
お気に入りにしたユーザー ProblemId : 12380 / 自分の提出
問題文最終更新日: 2025-06-15 12:36:05
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yukicoder contest 471 (順位表) の他の問題:

Problem Statement

You are given an integer sequence $A = (A_1, A_2, \cdots, A_N)$ of length $N$. Here, $N \geq 3$ holds.
You choose $2$ integers $i, j$ satisfying $1 \leq i < j < N$. Your score is then $|A_1 + A_2 + \cdots + A_i| + |A_{i + 1} + A_{i + 2} + \cdots + A_j| + |A_{j + 1} + A_{j + 2} + \cdots + A_N|$.

Find the maximum score you can obtain.

You are given $T$ test cases; find the answer for each of them.

Input

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$
Here, $\mathrm{case}_i$ denotes the $i$-th test case, and each test case is given in the following format.
$N$
$A_1\ \ A_2\ \ \cdots A_N$

  • $1 \leq T \leq 10^5$
  • $3 \leq N \leq 2 \times 10^5$
  • $-10^9 \leq A_i \leq 10^9$
  • All input values are integers.
  • In $1$ input file, the sum of $N$ does not exceed $5 \times 10^5$.

Output

For each test case, output the answer on $1$ line, followed by a newline.

Sample

Sample 1
Input
3
6
6 5 -4 3 -2 1
3
0 0 0
5
1 1 1 1 1
Output
17
0
5

  • For the $1$-st test case, choosing $i = 2, j = 3$ as $i, j$ gives a score of $|6 + 5| + |-4| + |3 + (-2) + 1| = 17$. It can be proved that a score of $18$ or more cannot be obtained, so the answer is $17$.
  • For the $2$-nd test case, the only possible choice of $i, j$ is $i = 1, j = 2$. The score in this case is $|0| + |0| + |0| = 0$.
  • For the $3$-rd test case, the score is $5$ regardless of $i, j$.

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