201224: [AtCoder]ARC122 E - Increasing LCMs
Memory Limit:1024 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
Score : $800$ points
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
.
Sample Input 1
3 3 4 6
Sample Output 1
Yes 3 6 4
For $x=(3,6,4)$, we have:
- $y_1=\operatorname{LCM}(3)=3$
- $y_2=\operatorname{LCM}(3,6)=6$
- $y_3=\operatorname{LCM}(3,6,4)=12$
Here, $y_1<y_2<y_3$ holds.
Sample Input 2
3 2 3 6
Sample Output 2
No
No permutation of $A$ would satisfy the condition.
Sample Input 3
10 922513 346046618969 3247317977078471 4638516664311857 18332844097865861 81706734998806133 116282391418772039 134115264093375553 156087536381939527 255595307440611247
Sample Output 3
Yes 922513 346046618969 116282391418772039 81706734998806133 255595307440611247 156087536381939527 134115264093375553 18332844097865861 3247317977078471 4638516664311857