8997: Until the Blue Moon Rises

You are given an array A=(A1,A2,…,An)A = (A_1, A_2, \dots, A_n)A=(A1,A2,…,An) of $n$ positive integers.
You can do the following operation any number of times (possibly, zero) on $A$:

• Choose two distinct indices i,ji, ji,j (1≤i,j≤n1 \leq i, j \leq n1≤i,j≤n), then let Ai=Ai+1,Aj=Aj−1A_i = A_i + 1, A_j = A_j - 1Ai=Ai+1,Aj=Aj−1.
  

Determine whether you can make all the integers in the array $A$ prime numbers by applying the operations.
Recall that a prime number is a positive integer greater than $1$ that is not a product of two smaller positive integers.

The first line contains an integer $n$ ($1\le n\le 1000$) — the length of array $A$.
The second line contains $n$ positive integers A1,A2,…,AnA_1, A_2, \dots, A_nA1,A2,…,An (1≤Ai≤1091\leq A_i\leq 10^91≤Ai≤109) — the integers in $A$.

If it is possible to make all the integers in the array $A$ prime numbers, print ‘Yes’ in a single line (without quotes). Otherwise, print ‘No’ (without quotes).