A ski resort operates a chairlift whose chairs each seat at most 4 skiers. Skiers arrive in n waves: customers[i] new skiers join the lift queue immediately before the (i+1)-th chair is dispatched. Every time a chair is dispatched, up to 4 of the skiers currently waiting board it (any skiers who don't fit keep waiting for a later chair); the lift operator earns boardingCost for every skier who actually boards, and spends runningCost to run that single dispatch, regardless of how many skiers boarded on it. The operator keeps dispatching chairs, one at a time, until every skier who has arrived so far has boarded — dispatches may continue past the n given waves as long as skiers are still waiting, but the operator never dispatches once the queue is completely empty and no more skiers will ever arrive. Determine the number of dispatches at which the operator's cumulative profit (total boarding earnings minus total running costs paid so far) first reaches its highest value. If the cumulative profit is never strictly positive at any point, report that operating the lift is never worthwhile.

Input format

• Line 1: a single integer n — the number of arrival waves.
• Line 2: n space-separated integers customers[0] ... customers[n-1] — the number of new skiers arriving right before each of the first n dispatches.
• Line 3: two space-separated integers boardingCost and runningCost.

Output format

A single integer: the smallest number of dispatches at which the cumulative profit reaches its maximum value, if that maximum value is strictly positive; otherwise print -1.

Constraints

• 1 <= n <= 10^5
• 0 <= customers[i] <= 50
• 1 <= boardingCost <= 100
• 1 <= runningCost <= 10^5

3
10 9 6
6 4

7

2
1 1
1 10

-1