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())
src = [tuple(map(int,input().split())) for i in range(N)]

suma = sumb = 0
elems = []
for i,(a,b) in enumerate(src):
    suma += a
    sumb += b
    elems.append((a,i))
    elems.append((b,i))
ans = min(suma, sumb)
elems.sort()

sumw = 0
used = [0]*N
dup = False
for w,i in elems[:N]:
    sumw += w
    used[i] += 1
    if used[i] > 1: dup = True

if dup:
    ans = min(ans, sumw)
    print(ans)
    exit()

for i,(a,b) in enumerate(src):
    if a > b:
        a,b = b,a
    neww = elems[N][0] if i != elems[N][1] else elems[N+1][0]
    tmp = sumw - a + neww
    ans = min(ans, tmp)
print(ans)