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 i , where d i 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.

输入描述:

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.

输出描述:

If the given state is reachable in the described game, output YES, otherwise NO.