VK news recommendation system daily selects interesting publications of one of n disjoint categories for each user. Each publication belongs to exactly one category. For each category i batch algorithm selects a_i publications.

The latest A/B test suggests that users are reading recommended publications more actively if each category has a different number of publications within daily recommendations. The targeted algorithm can find a single interesting publication of i-th category within t_i seconds. 

What is the minimum total time necessary to add publications to the result of batch algorithm execution, so all categories have a different number of publications? You can't remove publications recommended by the batch algorithm.

Input

The first line of input consists of single integer n — the number of news categories (1 ≤ n ≤ 200 000).

The second line of input consists of n integers a_i — the number of publications of i-th category selected by the batch algorithm (1 ≤ a_i ≤ 10^9).

The third line of input consists of n integers t_i — time it takes for targeted algorithm to find one new publication of category i (1 ≤ t_i ≤ 10^5).

Output

Print one integer — the minimal required time for the targeted algorithm to get rid of categories with the same size.

Examples

Input


5
3 7 9 7 8
5 2 5 7 5


Output


6


Input


5
1 2 3 4 5
1 1 1 1 1


Output


0

Note

In the first example, it is possible to find three publications of the second type, which will take 6 seconds.

In the second example, all news categories contain a different number of publications.
import heapq

def metod(x):
    if temp [x] == "A":
        cursc = a
    else:
        cursc = b
    for i in range(x + 1, len(temp )-1):
        if temp [i] != temp [i - 1]:
            if temp [i] == "A":
                cursc+=a
            else:
                cursc+=b
    return cursc

 
def morzermorzer():
    n = int(input())
    arr = sorted(list(zip(list(map(int, input().split())), list(map(int, input().split())))))
    
    zet, cursc, morzer, answer = [], 0, 0, 0
    
    while morzer < n:
        
        temp  = arr[morzer][0]
        cursc += arr[morzer][1]
        heapq.heappush(zet, -arr[morzer][1])
        
        while 0 < n - morzer - 1 and arr[morzer][0] == arr[morzer + 1][0]:
            morzer += 1
            cursc += arr[morzer][1]
            heapq.heappush(zet, -arr[morzer][1])
            
        if morzer + 1 == n:
            cur = 1e18
        else:
            cur = arr[morzer + 1][0]
            
        while zet and temp  - cur < 0:
            temp  += 1
            cursc += heapq.heappop(zet)
            answer += cursc
            
        morzer += 1
        
    print(answer)
        
morzermorzer()