Increasing LCMs

AtCoder

IDarc122_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3
3 4 6

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.

Input #2

3
2 3 6

Output #2

No

No permutation of $A$ would satisfy the condition.

Input #3

10
922513 346046618969 3247317977078471 4638516664311857 18332844097865861 81706734998806133 116282391418772039 134115264093375553 156087536381939527 255595307440611247

Output #3

Yes
922513 346046618969 116282391418772039 81706734998806133 255595307440611247 156087536381939527 134115264093375553 18332844097865861 3247317977078471 4638516664311857

API Response (JSON)

{
  "problem": {
    "name": "Increasing LCMs",
    "description": {
      "content": "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: *   ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc122_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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:\n\n*   ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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