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
def mincos(n,ab):
    aball=[]
    aball+=[(ab[i][0],i+1,'a') for i in range(n)]
    aball+=[(ab[i][1],i+1,'b') for i in range(n)]
    aball.sort()
    
    ans1=sum([i[0] for i in aball[:n]])

    hen=aball[n][0]
    hen2=aball[n+1][0]
    d=set()
    t=None
    hantei=True
    for i,c,mab in aball[:n]:
        if t!=None and t!=mab:
            hantei=False
        if  c in d:
            print(ans1)
            exit()
        d.add(c)
        t=mab

    if hantei:
        print(ans1)
        exit()

    ans2=[]
    for i,c,aorb in aball[:n]:
        if aball[n][1]!=c:
            ans2+=[ans1-i+hen]
        else:
            ans2+=[ans1-i+hen2]
    print(min(ans2))
    exit()

n=int(input())
print(mincos(n,[list(map(int,input().split())) for i in range(n)]))