E - Increasing LCMs /

### 問題文

• y_i=\operatorname{LCM}(x_1,x_2,\cdots,x_i) と定義する．ここで，\operatorname{LCM} は与えられた整数たちの最小公倍数を返す関数である．このとき，y は狭義単調増加である．つまり，y_1<y_2<\cdots<y_N が成り立つ．

### 制約

• 1 \leq N \leq 100
• 2 \leq A_1 < A_2 \cdots < A_N \leq 10^{18}
• 入力される値はすべて整数である

### 入力

N
A_1 A_2 \cdots A_N


### 出力

Yes
x_1 x_2 \cdots x_N


### 入力例 1

3
3 4 6


### 出力例 1

Yes
3 6 4


x=(3,6,4) のとき，

• y_1=\operatorname{LCM}(3)=3
• y_2=\operatorname{LCM}(3,6)=6
• y_3=\operatorname{LCM}(3,6,4)=12

となり，y_1<y_2<y_3 を満たします．

### 入力例 2

3
2 3 6


### 出力例 2

No


どのように A を並び替えても条件を満たすことができません．

### 入力例 3

10
922513 346046618969 3247317977078471 4638516664311857 18332844097865861 81706734998806133 116282391418772039 134115264093375553 156087536381939527 255595307440611247


### 出力例 3

Yes
922513 346046618969 116282391418772039 81706734998806133 255595307440611247 156087536381939527 134115264093375553 18332844097865861 3247317977078471 4638516664311857


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