Problem Statement

We have a sequence of $N$ positive integers: $A_1,A_2,\cdots,A_N$. You are to rearrange these integers into another sequence $x_1,x_2,\cdots,x_N$, where $x$ must satisfy the following condition:

• Let us define $y_i=\operatorname{LCM}(x_1,x_2,\cdots,x_i)$, where the function $\operatorname{LCM}$ returns the least common multiple of the given integers. Then, $y$ is strictly increasing. In other words, $y_1<y_2<\cdots<y_N$ holds.

Determine whether it is possible to form a sequence $x$ satisfying the condition, and show one such sequence if it is possible.

Constraints

• $1 \leq N \leq 100$
• $2 \leq A_1 < A_2 \cdots < A_N \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

If it is possible to form a sequence $x$ satisfying the condition, print your answer in the following format:

Yes
x_1 x_2 \cdots x_N

If it is impossible, print No.