One day *n* cells of some array decided to play the following game. Initially each cell contains a number which is equal to it's ordinal number (starting from 1). Also each cell determined it's favourite number. On it's move *i*-th cell can exchange it's value with the value of some other *j*-th cell, if |*i* - *j*| = *d*<sub class="lower-index">*i*</sub>, where *d*<sub class="lower-index">*i*</sub> is a favourite number of *i*-th cell. Cells make moves in any order, the number of moves is unlimited.

The favourite number of each cell will be given to you. You will also be given a permutation of numbers from 1 to *n*. You are to determine whether the game could move to this state.
The first line contains positive integer *n* (1 ≤ *n* ≤ 100) — the number of cells in the array. The second line contains *n* distinct integers from 1 to *n* — permutation. The last line contains *n* integers from 1 to *n* — favourite numbers of the cells.
def psort():
    n = int(input())

    x = input().split(" ")
    permutation = []
    for i in x:
        permutation.append(int(i))

    x = input().split(" ")
    favourite = []
    for i in x:
        favourite.append(int(i))

    link = [[] for _ in range(n)]
    for i in range(n):
        if i - favourite[i] >= 0:
            link[i].append(i - favourite[i])
            link[i - favourite[i]].append(i)
        if i + favourite[i] < n:
            link[i].append(i + favourite[i])
            link[i + favourite[i]].append(i)
    islink(link, n)

    print(link)
    for i, k in zip(permutation, range(n)):
        if i - 1 == k:
            continue
        if i - 1 not in link[k]:
            print("NO")
            return
    print("YES")
    return


def islink(link, n):
    for i in range(n):
        search(link, i, i, 1)

def search(link, i, root, flag):
    for k in link[i]:
        if link[root].count(k) == 0:
            link[root].append(k)
        else:
            if flag == 0:
                continue
        search(link, k, root, 0)
