Gold and Silver

AtCoder

IDarc128_a

Time2000ms

Memory256MB

Difficulty—

Snuke has $1$ gram of gold and $0$ grams of silver now. He will do trading of gold and silver for the following $N$ days. On each day, he has two choices: do nothing, or make a trade. If he trades on Day $i$ ($1 \leq i \leq N$), the following will happen. * If he has $x$ grams of gold before the trade, exchange all of it for $x \times A_i$ grams of silver. On the other hand, if he has $x$ grams of silver, exchange all of it for $x / A_i$ grams of gold. Snuke's objective is to maximize the amount of gold he has in the end. Find one way to achieve his objective. ## Constraints * $2 \leq N \leq 200000$ * $1 \leq A_i \leq 10^9$ * 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 5 2

Output #1

0 1 1

The optimal sequence of actions is as follows.

*   Day $1$: Do nothing.
    
*   Day $2$: Exchange $1$ gram of gold for $5$ grams of silver.
    
*   Day $3$: Exchange $5$ grams of silver for $2.5$ grams of gold.

Input #2

4
1 1 1 1

Output #2

0 0 0 0

$(v_1,v_2,v_3,v_4)=(1,1,1,1)$, for example, is also considered correct.

Input #3

10
426877385 186049196 624834740 836880476 19698398 709113743 436942115 436942115 436942115 503843678

Output #3

1 1 0 1 1 1 1 0 0 0

API Response (JSON)

{
  "problem": {
    "name": "Gold and Silver",
    "description": {
      "content": "Snuke has $1$ gram of gold and $0$ grams of silver now. He will do trading of gold and silver for the following $N$ days. On each day, he has two choices: do nothing, or make a trade. If he trades on ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc128_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has $1$ gram of gold and $0$ grams of silver now. He will do trading of gold and silver for the following $N$ days. On each day, he has two choices: do nothing, or make a trade. If he trades on ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments