Strange Balls

AtCoder

IDabc240_d

Time2000ms

Memory256MB

Difficulty—

Takahashi has $N$ balls. Each ball has an integer not less than $2$ written on it. He will insert them in a cylinder one by one. The integer written on the $i$\-th ball is $a_i$. The balls are made of special material. When $k$ balls with $k$ $(k \geq 2)$ written on them line up in a row, all these $k$ balls will disappear. For each $i$ $(1 \leq i \leq N)$, find the number of balls after inserting the $i$\-th ball. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $2 \leq a_i \leq 2 \times 10^5 \, (1 \leq i \leq N)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $\ldots$ $a_N$ [samples]

Samples

Input #1

5
3 2 3 2 2

Output #1

1
2
3
4
3

The content of the cylinder changes as follows.

*   After inserting the $1$\-st ball, the cylinder contains the ball with $3$.
*   After inserting the $2$\-nd ball, the cylinder contains $3, 2$ from bottom to top.
*   After inserting the $3$\-rd ball, the cylinder contains $3, 2, 3$ from bottom to top.
*   After inserting the $4$\-th ball, the cylinder contains $3, 2, 3, 2$ from bottom to top.
*   After inserting the $5$\-th ball, the cylinder momentarily has $3, 2, 3, 2, 2$ from bottom to top. The two consecutive balls with $2$ disappear, and the cylinder eventually contains $3, 2, 3$ from bottom to top.

![image](https://img.atcoder.jp/ghi/ABC240D_sample.png)

Input #2

10
2 3 2 3 3 3 2 3 3 2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Strange Balls",
    "description": {
      "content": "Takahashi has $N$ balls. Each ball has an integer not less than $2$ written on it. He will insert them in a cylinder one by one. The integer written on the $i$\\-th ball is $a_i$. The balls are made of",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc240_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $N$ balls. Each ball has an integer not less than $2$ written on it. He will insert them in a cylinder one by one. The integer written on the $i$\\-th ball is $a_i$.\nThe balls are made of...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments