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
from sys import stdin
from heapq import heapify, heappop
from itertools import repeat
def main():
    n = int(stdin.readline())
    dat = map(int, stdin.read().split(), repeat(10, 2 * n))
    q = [(x, i) for i, x in enumerate(dat)]
    q.sort()
    d = [0] * n
    ans = min(sum(dat[::2]), sum(dat[1::2]))
    s = 0
    for i in xrange(n):
        s += q[i][0]
        d[q[i][1]/2] |= 1 << (q[i][1] % 2)
    for i in xrange(n):
        p = s
        c = n - 1
        for j in xrange(2):
            if not (d[i] >> j & 1):
                p += dat[i*2+j]
                while q[c][1] / 2 == i:
                    c -= 1
                p -= q[c][0]
                c -= 1
        if ans > p:
            ans = p
    print ans
main()
