Nice Shopping

AtCoder

IDhitachi2020_b

Time2000ms

Memory256MB

Difficulty—

You are visiting a large electronics store to buy a refrigerator and a microwave. The store sells $A$ kinds of refrigerators and $B$ kinds of microwaves. The $i$\-th refrigerator ( $1 \le i \le A$ ) is sold at $a_i$ yen (the currency of Japan), and the $j$\-th microwave ( $1 \le j \le B$ ) is sold at $b_j$ yen. You have $M$ discount tickets. With the $i$\-th ticket ( $1 \le i \le M$ ), you can get a discount of $c_i$ yen from the total price when buying the $x_i$\-th refrigerator and the $y_i$\-th microwave together. Only one ticket can be used at a time. You are planning to buy one refrigerator and one microwave. Find the minimum amount of money required. ## Constraints * All values in input are integers. * $1 \le A \le 10^5$ * $1 \le B \le 10^5$ * $1 \le M \le 10^5$ * $1 \le a_i , b_i , c_i \le 10^5$ * $1 \le x_i \le A$ * $1 \le y_i \le B$ * $c_i \le a_{x_i} + b_{y_i}$ ## Input Input is given from Standard Input in the following format: $A$ $B$ $M$ $a_1$ $a_2$ $...$ $a_A$ $b_1$ $b_2$ $...$ $b_B$ $x_1$ $y_1$ $c_1$ $\vdots$ $x_M$ $y_M$ $c_M$ [samples]

Samples

Input #1

Output #1

5

With the ticket, you can get the $1$\-st refrigerator and the $2$\-nd microwave for $3+3-1=5$ yen.

Input #2

Output #2

10

Note that you cannot use more than one ticket at a time.

Input #3

Output #3

6

You can get the $1$\-st refrigerator and the $1$\-st microwave for $6$ yen, which is the minimum amount to pay in this case. Note that using a ticket is optional.

API Response (JSON)

{
  "problem": {
    "name": "Nice Shopping",
    "description": {
      "content": "You are visiting a large electronics store to buy a refrigerator and a microwave. The store sells $A$ kinds of refrigerators and $B$ kinds of microwaves. The $i$\\-th refrigerator ( $1 \\le i \\le A$ ) i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "hitachi2020_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are visiting a large electronics store to buy a refrigerator and a microwave.\nThe store sells $A$ kinds of refrigerators and $B$ kinds of microwaves. The $i$\\-th refrigerator ( $1 \\le i \\le A$ ) i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments