Lord of the Ring

Frodo knows all pairwise distances between bushes placed along one straight road, but not their positions. For each data set, reconstruct a valid placement and compute P, the product of the distances between consecutive bushes.

Input

The input contains data sets until end of file. Each begins with the number m of pairwise distances, followed by those m distances in nondecreasing order. Whitespace may occur freely. There are between 2 and 1000 bushes, and a valid product never exceeds 10^9.

Output

For each data set, print P. If the distances do not describe a valid placement, print No solution.

Example

Input:

6
1 2 2 3 3 5
3
1 2 2

Output:

4
No solution