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Given $n$ integers $a_1, a_2, \cdots , a_n$ . For each $1\le i\le n$ ，the maximum product for $a_i$ is defined to be $p_i = \max _{i\le j\le n} a_i a_j$ . Your job is to calculate the maximum products for all the $n$ integers.

输入格式

Each input file contains one test case. The first line gives a positive integer $n$ ( $\le 10^5$ ). Then $n$ integers follow in the next line, each in the interval $[-10^4, 10^4]$ .

All the numbers in a line are separated by a space.

输出格式

For each test case, print in a line the maximum products of all the given $n$ integers. All the numbers in a line must be separated by 1 space, and there must be no extra space at the beginning or the end of the line.

题目示例数据

4
1 4 -9 6

6 24 81 36