A maintenance pipeline has n joints in a row, numbered 0 to n-1, and joint i requires exactly seal[i] units of sealant to be fully sealed. Two robots start sealing the pipeline at the same time from opposite ends: Robot A starts at joint 0 and works rightward (increasing index), while Robot B starts at joint n-1 and works leftward (decreasing index). Robot A carries a canister with capacity capA units of sealant, and Robot B carries one with capacity capB units; both canisters start completely full.

Each robot advances one joint at a time, in lockstep with the other:

• If a robot's canister currently holds at least as much sealant as the next joint needs, it seals that joint directly, and its canister's sealant decreases by that joint's requirement.
• Otherwise, the robot first empties out and completely refills its canister to full capacity (this refill counts toward the answer), and then seals the joint, decreasing its (now-full) canister by that joint's requirement.

If the two robots would seal the very same joint at the same moment (this happens exactly when n is odd and both reach the middle joint together), no refill occurs at that joint even if one or both canisters are running low: whichever robot currently holds strictly more sealant seals that joint alone (ties are broken in favor of Robot A), and that robot's canister decreases by the joint's requirement -- the other robot's canister is left untouched. If n is even, the two robots simply meet in the middle and each finishes their own half without ever sharing a joint.

Determine the total number of refills performed by both robots combined.

Input format

Line 1 contains a single integer n. Line 2 contains n space-separated integers, seal[0] ... seal[n-1]. Line 3 contains two space-separated integers capA and capB.

Output format

Print a single integer: the total number of refills performed by both robots combined.

Constraints

• 1 <= n <= 10^5
• 1 <= seal[i] <= min(capA, capB) for every i
• 1 <= capA, capB <= 10^9

4
2 2 3 3
5 5

1

3
4 4 3
5 6

1