The match of the century in the game of boulders has just ended. Its result has already been broadcast by all channels around the world. But soon the match of the millennium will begin, and preparations must be made.

As is known, this game uses N piles of boulders, each of which must be in a specific predetermined ratio with all the others. Moreover, it does not matter how many boulders are in each pile; during preparation, it is only necessary to maintain the specified proportion. However, it is not allowed to leave all piles empty!

Unfortunately, the previous players did not clean up after themselves, and this task has been assigned to Vadim. He can remove one boulder from one pile in one minute, and he can also roll one boulder to any pile in one minute. This is an incredibly labor-intensive and time-consuming task, so it needs to be done as quickly as possible. Help Vadim determine the minimum time required to prepare for the match of the millennium.

The first line contains an integer N — the number of piles of boulders in the game (2 ≤ N ≤ 10⁵).

The second line contains N integers s_i — the number of boulders in each pile remaining after the match of the century (1 ≤ s_i ≤ 10⁹).

The third line contains N integers p_i — the required ratio of boulders in each pile to start the game (1 ≤ p_i ≤ 10⁹).

Output a single integer — the minimum time required to prepare the piles for the match of the millennium.

In the example, Vadim needs to roll a boulder to the first pile and then remove one boulder from the second pile. Then the piles will have 22 and 33 boulders respectively, which satisfies the ratio of 2:3.