Jumping Takahashi 2

AtCoder

IDabc257_d

Time3000ms

Memory256MB

Difficulty—

There are $N$ trampolines on a two-dimensional planar town where Takahashi lives. The $i$\-th trampoline is located at the point $(x_i, y_i)$ and has a power of $P_i$. Takahashi's jumping ability is denoted by $S$. Initially, $S=0$. Every time Takahashi trains, $S$ increases by $1$. Takahashi can jump from the $i$\-th to the $j$\-th trampoline if and only if: * $P_iS\geq |x_i - x_j| +|y_i - y_j|$. Takahashi's objective is to become able to choose a starting trampoline such that he can reach any trampoline from the chosen one with some jumps. At least how many times does he need to train to achieve his objective? ## Constraints * $2 \leq N \leq 200$ * $-10^9 \leq x_i,y_i \leq 10^9$ * $1 \leq P_i \leq 10^9$ * $(x_i, y_i) \neq (x_j,y_j)\ (i\neq j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $P_1$ $\vdots$ $x_N$ $y_N$ $P_N$ [samples]

Samples

Input #1

Output #1

2

If he trains twice, $S=2$, in which case he can reach any trampoline from the $2$\-nd one.
For example, he can reach the $4$\-th trampoline as follows.

*   Jump from the $2$\-nd to the $3$\-rd trampoline. (Since $P_2 S = 10$ and $|x_2-x_3| + |y_2-y_3| = 10$, it holds that $P_2 S \geq |x_2-x_3| + |y_2-y_3|$.)
    
*   Jump from the $3$\-rd to the $4$\-th trampoline. (Since $P_3 S = 2$ and $|x_3-x_4| + |y_3-y_4| = 1$, it holds that $P_3 S \geq |x_3-x_4| + |y_3-y_4|$.)

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Jumping Takahashi 2",
    "description": {
      "content": "There are $N$ trampolines on a two-dimensional planar town where Takahashi lives. The $i$\\-th trampoline is located at the point $(x_i, y_i)$ and has a power of $P_i$. Takahashi's jumping ability is d",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc257_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ trampolines on a two-dimensional planar town where Takahashi lives. The $i$\\-th trampoline is located at the point $(x_i, y_i)$ and has a power of $P_i$. Takahashi's jumping ability is d...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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