Summing up coins

Given n coins of some value, you are asked to find out all the possible sums you can obtain with those coins.

Input

The first line of the input contains two integers n (1 ≀ n ≀ 100).
The next line contains n space-separated integers (1 ≀ ≀ 1000) the coin values.

Output

The program should first print the number of possible sums one can obtain with those coins on the first line. While the second line of the output should contain all the possible sums in increasing order separated by a space.

Examples

Input
Output
4 2 5 4 2
9 2 4 5 6 7 8 9 11 13
Β 

Constraints

Time limit: 4 seconds

Memory limit: 512 MB

Output limit: 1 MB

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