Cost to Flip

AtCoder

IDarc194_c

Time2000ms

Memory256MB

Difficulty—

You are given two integer sequences of length $N$, $A = (A_1, A_2, \ldots, A_N)$ and $B = (B_1, B_2, \ldots, B_N)$, each consisting of $0$ and $1$. You can perform the following operation on $A$ any number of times (possibly zero): 1. First, choose an integer $i$ satisfying $1 \leq i \leq N$, and flip the value of $A_i$ (if the original value is $0$, change it to $1$; if it is $1$, change it to $0$). 2. Then, pay $\sum_{k=1}^N A_k C_k$ yen as the cost of this operation. Note that the cost calculation in step 2 uses the $A$ after the change in step 1. Print the minimum total cost required to make $A$ identical to $B$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $A_i, B_i \in {0, 1}$ * $1 \leq C_i \leq 10^6$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_N$ $C_1$ $C_2$ $\ldots$ $C_N$ [samples]

Samples

Input #1

Output #1

16

Consider the following procedure:

*   First, flip $A_4$. Now, $A = (0, 1, 1, 0)$. The cost of this operation is $0 \times 4 + 1 \times 6 + 1 \times 2 + 0 \times 9 = 8$ yen.
*   Next, flip $A_2$. Now, $A = (0, 0, 1, 0)$. The cost of this operation is $0 \times 4 + 0 \times 6 + 1 \times 2 + 0 \times 9 = 2$ yen.
*   Finally, flip $A_1$. Now, $A = (1, 0, 1, 0)$, which matches $B$. The cost of this operation is $1 \times 4 + 0 \times 6 + 1 \times 2 + 0 \times 9 = 6$ yen.

In this case, the total cost is $8 + 2 + 6 = 16$ yen, which is the minimum possible.

Input #2

Output #2

0

$A$ and $B$ are already identical initially, so there is no need to perform any operations.

Input #3

20
1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0
0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0
52 73 97 72 54 15 79 67 13 55 65 22 36 90 84 46 1 2 27 8

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Cost to Flip",
    "description": {
      "content": "You are given two integer sequences of length $N$, $A = (A_1, A_2, \\ldots, A_N)$ and $B = (B_1, B_2, \\ldots, B_N)$, each consisting of $0$ and $1$. You can perform the following operation on $A$ any n",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc194_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given two integer sequences of length $N$, $A = (A_1, A_2, \\ldots, A_N)$ and $B = (B_1, B_2, \\ldots, B_N)$, each consisting of $0$ and $1$.\nYou can perform the following operation on $A$ any n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments