We have a directed weighted graph with N vertices. Each vertex has two integers written on it, and the integers written on Vertex i are A_i and B_i.

In this graph, there is an edge from Vertex x to Vertex y for all pairs 1 \leq x,y \leq N, and its weight is {\rm min}(A_x,B_y).

We will consider a directed cycle in this graph that visits every vertex exactly once. Find the minimum total weight of the edges in such a cycle.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 B_1
A_2 B_2
:
A_N B_N


Output

Print the minimum total weight of the edges in such a cycle.

Examples

Input

3
1 5
4 2
6 3


Output

7


Input

4
1 5
2 6
3 7
4 8


Output

10


Input

6
19 92
64 64
78 48
57 33
73 6
95 73


Output

227
# C
from heapq import heappush, heappop

N = int(input())
values = [0]*(2*N)

for i in range(N):
    A, B = map(int, input().split())
    values[i] = A
    values[i+N] = B

def argsort(R_arr):
    N = len(R_arr)
    R_args = [0]*N
    R_vars = [0]*N
    h = []
    for i in range(N):
        heappush(h, (R_arr[i], i))
    for i in range(N):
        a, b = heappop(h)
        R_args[i] = b
        R_vars[i] = a
    return R_vars, R_args

values_sorted, args = argsort(values)

# check for rare case
picked = [0]*N

for i in range(N):
    picked[args[i] % N] = 1
    
if sum(picked) == N:
    if args[N-1] % N == args[N] % N:
        res1 = sum(values_sorted[:(N-1)]) + values_sorted[N+1]
        res2 = sum(values_sorted[:(N+1)]) - values_sorted[N-2]
        res = min(res1, res2)
    else:
        res = sum(values_sorted[:(N-1)]) + values_sorted[N]
    res3 = sum(values[:N])
    res4 = sum(values[N:])
    res = min(res, res3, res4)
else:
    res = sum(values_sorted[:N])

print(res)