We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller. (The operation is the same as the one in Problem D.)

* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.



It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given the sequence a_i. Find the number of times we will perform the above operation.

Constraints

* 2 ≤ N ≤ 50
* 0 ≤ a_i ≤ 10^{16} + 1000

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the number of times the operation will be performed.

Examples

Input

4
3 3 3 3


Output

0


Input

3
1 0 3


Output

1


Input

2
2 2


Output

2


Input

7
27 0 0 0 0 0 0


Output

3


Input

10
1000 193 256 777 0 1 1192 1234567891011 48 425


Output

1234567894848
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N = INT()
a = LIST()
ans = 0
while any([x >= N for x in a]):
	S = sum([x//N for x in a])
	for i in range(N):
		tmp = a[i]//N  # i番目の要素に対する操作回数
		a[i] -= N*tmp
		a[i] += (S-tmp)
		ans += tmp

print(ans)
