Takahashi's Anguish

AtCoder

IDabc256_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ people numbered $1$ through $N$. Takahashi has decided to choose a sequence $P = (P_1, P_2, \dots, P_N)$ that is a permutation of integers from $1$ through $N$, and give a candy to Person $P_1$, Person $P_2$, $\dots$, and Person $P_N$, in this order. Since Person $i$ dislikes Person $X_i$, if Takahashi gives a candy to Person $X_i$ prior to Person $i$, then Person $i$ gains frustration of $C_i$; otherwise, Person $i$'s frustration is $0$. Takahashi may arbitrarily choose $P$. What is the minimum possible sum of their frustration? ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq X_i \leq N$ * $X_i \neq i$ * $1 \leq C_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $X_1$ $X_2$ $\dots$ $X_N$ $C_1$ $C_2$ $\dots$ $C_N$ [samples]

Samples

Input #1

3
2 3 2
1 10 100

Output #1

10

If he lets $P = (1, 3, 2)$, only Person $2$ gains a positive amount of frustration, in which case the sum of their frustration is $10$.  
Since it is impossible to make the sum of frustration smaller, the answer is $10$.

Input #2

8
7 3 5 5 8 4 1 2
36 49 73 38 30 85 27 45

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Takahashi's Anguish",
    "description": {
      "content": "There are $N$ people numbered $1$ through $N$.   Takahashi has decided to choose a sequence $P = (P_1, P_2, \\dots, P_N)$ that is a permutation of integers from $1$ through $N$, and give a candy to Per",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc256_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people numbered $1$ through $N$.  \nTakahashi has decided to choose a sequence $P = (P_1, P_2, \\dots, P_N)$ that is a permutation of integers from $1$ through $N$, and give a candy to Per...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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