Balance Update Query

AtCoder

IDabc287_g

Time2000ms

Memory256MB

Difficulty—

Takahashi has $10^{100}$ cards of each of $N$ kinds. Initially, the score and quota of the $i$\-th kind of card are set to $a_i$ and $b_i$, respectively. Given $Q$ queries in the following formats, process them in order. * `1 x y`: set the score of the $x$\-th kind of card to $y$. * `2 x y`: set the quota of the $x$\-th kind of card to $y$. * `3 x`: if one can choose $x$ cards subject to the following condition, print the maximum possible sum of the scores of the chosen cards; print `-1` otherwise. * The number of chosen cards of each kind does not exceed its quota. ## Constraints * $1 \leq N,Q \leq 2 \times 10^5$ * $0 \leq a_i \leq 10^9$ * $0 \leq b_i \leq 10^4$ * For each query of the $1$\-st kind, $1 \leq x \leq N$ and $0 \leq y \leq 10^9$. * For each query of the $2$\-nd kind, $1 \leq x \leq N$ and $0 \leq y \leq 10^4$. * For each query of the $3$\-rd kind, $1 \leq x \leq 10^9$. * There is at least one query of the $3$\-rd kind. * All values in the input are integers. ## Input The input is given from Standard Input in the following format, where $\mathrm{query}_i$ denotes the $i$\-th query: $N$ $a_1$ $b_1$ $\vdots$ $a_N$ $b_N$ $Q$ $\mathrm{query}_1$ $\vdots$ $\mathrm{query}_Q$ [samples]

Samples

Input #1

Output #1

11
19
-1
4

For the first query of the $3$\-rd kind, you can choose one card of the $2$\-nd kind and three cards of the $3$\-rd kind for a total score of $11$, which is the maximum.  
For the second such query, you can choose one card of the $1$\-st kind and three cards of the $3$\-rd kind for a total score of $19$, which is the maximum.  
For the third such query, you cannot choose four cards, so `-1` should be printed.  
For the fourth such query, you can choose two cards of the $2$\-nd kind for a total score of $4$, which is the maximum.

API Response (JSON)

{
  "problem": {
    "name": "Balance Update Query",
    "description": {
      "content": "Takahashi has $10^{100}$ cards of each of $N$ kinds. Initially, the score and quota of the $i$\\-th kind of card are set to $a_i$ and $b_i$, respectively. Given $Q$ queries in the following formats, pr",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc287_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $10^{100}$ cards of each of $N$ kinds. Initially, the score and quota of the $i$\\-th kind of card are set to $a_i$ and $b_i$, respectively.\nGiven $Q$ queries in the following formats, pr...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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