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Time Limit: 1 s Memory Limit: 512 MB Total points: 100

#6268. 指点江山

统计

给定一个序列 $a_1,a_2,\dots,a_n$,你可以进行任意多次如下操作:

  • 选择 $i$,将 $a_i$ 替换成 $-(a_1+a_2+\cdots+a_n)$。

试求,你能得到的字典序最小的 $a$ 序列是什么?

输入格式

第一行输入一个正整数 $n$。

接下来一行输入 $n$ 个整数,从小到大表示 $a_i$。

输出格式

输出一行 $n$ 个整数,表示字典序最小的序列。

样例数据

样例输入

3
2 -3 2

样例输出

-3 -1 2

样例解释

$[2,-3,2] \to [2, -1, 2] \to [-3, -1, 2]$

子任务

对于 $100\%$ 的数据,保证 $1\leq n\leq 10^5$,$|a_i|\leq 10^9$。

对于测试点 $1\sim 4$,保证 $n\leq 5$。

对于测试点 $5\sim 7$,保证 $n\leq 10^3$。

对于测试点 $8\sim 10$,无特殊限制。

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