The Balance

Time Limit: 1000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)


Now you are asked to measure a dose of medicine with a balance and a number of weights. Certainly it is not always achievable. So you should find out the qualities which cannot be measured from the range [1,S]. S is the total quality of all the weights.


The input consists of multiple test cases, and each case begins with a single positive integer N (1<=N<=100) on a line by itself indicating the number of weights you have. Followed by N integers Ai (1<=i<=N), indicating the quality of each weight where 1<=Ai<=100.


For each input set, you should first print a line specifying the number of qualities which cannot be measured. Then print another line which consists all the irrealizable qualities if the number is not zero.

Sample Input

3 1 2 4 3 9 2 1

Sample Output

0 2 4 5




HDU 2007-Spring Programming Contest