A ground-control team operates a ring of communication relay satellites orbiting in a fixed loop. The satellites are numbered 0 to n-1 in the order they appear around the ring, and for each satellite i there is a known laser-link length connecting it to the next satellite (i+1) mod n going around the ring in the fixed direction. Because the ring is circular, any two satellites are connected by two possible arcs (clockwise and counter-clockwise), and the team always routes a signal along whichever arc is shorter.

Given the link lengths and two relay indices, compute the length of the shorter arc between them.

Input format

Line 1: a single integer n, the number of relays. Line 2: n space-separated integers link[0] ... link[n-1], where link[i] is the link length from relay i to relay (i+1) mod n. Line 3: two space-separated integers start and dest, the indices of the two relays to connect.

Output format

Print a single integer: the length of the shorter of the two arcs connecting relay start and relay dest.

Constraints

• 2 <= n <= 100
• 0 <= link[i] <= 100 for every i
• 0 <= start, dest < n
• start != dest

4
1 2 3 4
0 1

1

4
1 2 3 4
0 2

3