human
Captain Fint is involved in another treasure hunt, but have found only one strange problem. The problem may be connected to the treasure's location or may not. That's why captain Flint decided to leave the solving the problem to his crew and offered an absurdly high reward: one day off. The problem itself sounds like this...

There are two arrays a and b of length n. Initially, an ans is equal to 0 and the following operation is defined: 

  1. Choose position i (1 ≤ i ≤ n).

  2. Add a_i to ans.

  3. If b_i ≠ -1 then add a_i to a_{b_i}. 


What is the maximum ans you can get by performing the operation on each i (1 ≤ i ≤ n) exactly once?

Uncle Bogdan is eager to get the reward, so he is asking your help to find the optimal order of positions to perform the operation on them.

Input

The first line contains the integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of arrays a and b.

The second line contains n integers a_1, a_2, …, a_n (−10^6 ≤ a_i ≤ 10^6).

The third line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ n or b_i = -1).

Additional constraint: it's guaranteed that for any i (1 ≤ i ≤ n) the sequence b_i, b_{b_i}, b_{b_{b_i}}, … is not cyclic, in other words it will always end with -1.

Output

In the first line, print the maximum ans you can get.

In the second line, print the order of operations: n different integers p_1, p_2, …, p_n (1 ≤ p_i ≤ n). The p_i is the position which should be chosen at the i-th step. If there are multiple orders, print any of them.

Examples

Input

3
1 2 3
2 3 -1

Output

10
1 2 3 

Input

2
-1 100
2 -1

Output

99
2 1 

Input

10
-10 -1 2 2 5 -2 -3 -4 2 -6
-1 -1 2 2 -1 5 5 7 7 9

Output

-9
3 5 6 1 9 4 10 7 8 2
Solve the task in PYTHON3.
assistant
#Here is Python program to find the optimal order of positions to perform the operation on them.

"""
    Satwik_Tiwari ;) .
    30th july , 2020  - Thursday
"""

#===============================================================================================
#importing some useful libraries.
from __future__ import division, print_function

from fractions import Fraction
import sys
import os
from io import BytesIO, IOBase

from itertools import *
import bisect
from heapq import *
from math import *
from copy import *
from collections import deque
from collections import Counter as counter  # Counter(list)  return a dict with {key: count}
from itertools import combinations as comb # if a = [1,2,3] then print(list(comb(a,2))) -----> [(1, 2), (1, 3), (2, 3)]
from itertools import permutations as permutate
from bisect import bisect_left as bl
#If the element is already present in the list,
# the left most position where element has to be inserted is returned.
from bisect import bisect_right as br
from bisect import bisect
#If the element is already present in the list,
# the right most position where element has to be inserted is returned

#==============================================================================================
#fast I/O region
BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
           ...