Please Sign

AtCoder

IDarc169_a

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A=(A_1,A_2,\cdots,A_N)$ of length $N$, and another integer sequence $P=(P_2,\cdots,P_N)$ of length $N-1$. Note that the index of $P$ starts at $2$. It is guaranteed that $1 \leq P_i < i$ for each $i$. You will now repeat the following operation $10^{100}$ times. * For each $i=2,\cdots,N$, in this order, replace the value of $A_{P_i}$ with $A_{P_i}+A_{i}$. Determine whether $A_1$ will be positive, negative, or zero when all operations are completed. ## Constraints * $2 \leq N \leq 250000$ * $-10^9 \leq A_i \leq 10^9$ * $1 \leq P_i < i$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ $P_2$ $\cdots$ $P_N$ [samples]

Samples

Input #1

4
1 -2 3 -4
1 2 3

Output #1

\-

Shown below are the results of the first few operations.

*   After the first operation:
    *   Before the operation: $A=(1,-2,3,-4)$.
    *   Processing for $i=2$: Replace the value of $A_1$ with $A_1+A_2=1+(-2)=-1$.
    *   Processing for $i=3$: Replace the value of $A_2$ with $A_2+A_3=-2+3=1$.
    *   Processing for $i=4$: Replace the value of $A_3$ with $A_3+A_4=3+(-4)=-1$.
    *   After the operation: $A=(-1,1,-1,-4)$.
*   After the second operation, $A=(0,0,-5,-4)$.
*   After the third operation, $A=(0,-5,-9,-4)$.
*   After the fourth operation, $A=(-5,-14,-13,-4)$.
*   $\vdots$

After $10^{100}$ operations, $A_1$ will be negative. Thus, you should print `-`.

Input #2

3
0 1 -1
1 1

Output #2

Input #3

5
1 -1 1 -1 1
1 1 2 2

Output #3

Input #4

20
568273618 939017124 -32990462 -906026662 403558381 -811698210 56805591 0 436005733 -303345804 96409976 179069924 0 0 0 -626752087 569946496 0 0 0
1 1 1 4 4 6 7 2 2 3 3 8 13 14 9 9 15 18 19

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Please Sign",
    "description": {
      "content": "You are given an integer sequence $A=(A_1,A_2,\\cdots,A_N)$ of length $N$, and another integer sequence $P=(P_2,\\cdots,P_N)$ of length $N-1$. Note that the index of $P$ starts at $2$. It is guaranteed ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc169_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,A_2,\\cdots,A_N)$ of length $N$, and another integer sequence $P=(P_2,\\cdots,P_N)$ of length $N-1$. Note that the index of $P$ starts at $2$. It is guaranteed ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments