You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
VMAX = 10000

def minCostSort(A, n):
	global VMAX
	VMIN = min(A)
	ans = 0
	B = A.copy()
	B.sort()
	T = [0] * (VMAX + 1)
	for i in range(n):
		T[B[i]] = i
	V = [False] * n
	for i in range(n):
		if V[i]:
			pass
		else:
			index = i
			minv = VMAX
			count = 0
			cycleweight = 0
			while 1:
				V[index] = True
				count += 1
				value = A[index]
				minv = min(minv, value)
				cycleweight += value
				index = T[value]
				if V[index]:
					break
			ans += min(cycleweight + (count - 2) * minv, cycleweight + minv + (count + 1) * VMIN)
	return ans


if __name__ == "__main__":
	n = int(input())
	A = list(map(int, input().split()))
	print(minCostSort(A, n))
