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
N = int(input())
import sys

all_list = []
counter = 1
for line in sys.stdin:
    a, b = [int(x) for x in line.strip().split(" ")]
    all_list += [("a", counter, a), ("b", counter, b)]
    counter += 1

all_list = sorted(all_list, key = lambda x : x[2])

sp_c = all_list[N][1]
sp_i_p = all_list[N][2]
sp_i_pp = all_list[N+1][2]

flag = True
ss = sum([i[2] for i in all_list[:N]])
d = set()
temp = None
for ab, c, i in all_list[:N]:
    if temp != None and temp != ab:
        flag = False
    if c in d:
        flag = True
        break
    d.add(c)
    temp = ab
if flag:
    print(ss)
else:
    candidates = []
    for ab, c, i in all_list[:N]:
        if sp_c != c:
            candidates.append(ss - i + sp_i_p)
        else:
            candidates.append(ss - i + sp_i_pp)
    print(min(candidates))
