Martial artist

AtCoder

IDabc226_c

Time2000ms

Memory256MB

Difficulty—

Takahashi is a martial artist. There are $N$ moves that a martial artist can learn, called Move $1$, $2$, $\ldots$, $N$. For each $1 \leq i \leq N$, it takes $T_i$ minutes of practice to learn Move $i$. Additionally, at the beginning of that practice, all of the Moves $A_{i,1}$, $A_{i,2}$, $\ldots$, $A_{i,K_i}$ must be already learned. Here, it is guaranteed that $A_{i,j} < i$ for each $1 \leq j \leq K_i$. Takahashi has not learned any move at time $0$. He cannot practice for more than one move simultaneously, nor can he stop a practice he has already started. Find the minimum number of minutes needed for Takahashi to learn Move $N$. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq T_i \leq 10^9$ * $0 \leq K_i < i$ * $1 \leq A_{i,j} < i$ * $\sum_{i=1}^N K_i \leq 2\times 10^5$ * $A_{i,1}$, $A_{i,2}$, $\ldots$, $A_{i,K_i}$ are all distinct. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $T_1$ $K_1$ $A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,K_1}$ $T_2$ $K_2$ $A_{2,1}$ $A_{2,2}$ $\ldots$ $A_{2,K_2}$ $\vdots$ $T_N$ $K_N$ $A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,K_N}$ [samples]

Samples

Input #1

Output #1

10

Here is one possible plan for Takahashi.

*   At time $0$, start practicing for Move $1$ to learn Move $1$ at time $3$.
*   Then, at time $3$, start practicing for Move $3$ to learn Move $3$ at time $10$.

Here, Takahashi spends $3+7=10$ minutes to learn Move $3$, which is the fastest possible. Note that he does not need to learn Move $2$ to learn Move $3$.

Input #2

5
1000000000 0
1000000000 0
1000000000 0
1000000000 0
1000000000 4 1 2 3 4

Output #2

5000000000

Note that the answer may not fit into a $32$\-bit integer.

API Response (JSON)

{
  "problem": {
    "name": "Martial artist",
    "description": {
      "content": "Takahashi is a martial artist. There are $N$ moves that a martial artist can learn, called Move $1$, $2$, $\\ldots$, $N$. For each $1 \\leq i \\leq N$, it takes $T_i$ minutes of practice to learn Move $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": "abc226_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is a martial artist. There are $N$ moves that a martial artist can learn, called Move $1$, $2$, $\\ldots$, $N$. For each $1 \\leq i \\leq N$, it takes $T_i$ minutes of practice to learn Move $i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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