Multiplication Table

Sasha grew up and went to first grade. To celebrate this event her mother bought her a multiplication table M with n rows and n columns such that M_{ij}=a_i ⋅ a_j where a_1, ..., a_n is some sequence of positive integers.

Of course, the girl decided to take it to school with her. But while she was having lunch, hooligan Grisha erased numbers on the main diagonal and threw away the array a_1, ..., a_n. Help Sasha restore the array!

Input

The first line contains a single integer n (3 ⩽ n ⩽ 10^3), the size of the table.

The next n lines contain n integers each. The j-th number of the i-th line contains the number M_{ij} (1 ≤ M_{ij} ≤ 10^9). The table has zeroes on the main diagonal, that is, M_{ii}=0.

Output

In a single line print n integers, the original array a_1, ..., a_n (1 ≤ a_i ≤ 10^9). It is guaranteed that an answer exists. If there are multiple answers, print any.

Examples

Input

5 0 4 6 2 4 4 0 6 2 4 6 6 0 3 6 2 2 3 0 2 4 4 6 2 0

Output

2 2 3 1 2

Input

3 0 99990000 99970002 99990000 0 99980000 99970002 99980000 0

Output

9999 10000 9998

inputFormat

Input

The first line contains a single integer n (3 ⩽ n ⩽ 10^3), the size of the table.

The next n lines contain n integers each. The j-th number of the i-th line contains the number M_{ij} (1 ≤ M_{ij} ≤ 10^9). The table has zeroes on the main diagonal, that is, M_{ii}=0.

outputFormat

Output

In a single line print n integers, the original array a_1, ..., a_n (1 ≤ a_i ≤ 10^9). It is guaranteed that an answer exists. If there are multiple answers, print any.

Examples

Input

5 0 4 6 2 4 4 0 6 2 4 6 6 0 3 6 2 2 3 0 2 4 4 6 2 0

Output

2 2 3 1 2

Input

3 0 99990000 99970002 99990000 0 99980000 99970002 99980000 0

Output

9999 10000 9998

样例

5
0 4 6 2 4
4 0 6 2 4
6 6 0 3 6
2 2 3 0 2
4 4 6 2 0

2 2 3 1 2