Mr. Henry is saving money to buy a new car. His old car gets low gas mileage. Moreover, its fuel efficiency has diminished over time. Presently, it takes one gallon of gasoline to travel one mile.

He needs to drive to his office, which is at a distance D from his home. On his way to the office, there are N gas stations. Each gas station can only sell a specific amount of gasoline (in gallons) based on a government limit. (Assume that in order to keep running, the car must always have some gasoline in it at all times.)

Write an algorithm to help Mr. Henry determine the minimum number of gas stations at which he should stop to successfully reach his office.

If it is not possible to reach the office, output -1.

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Input Format

1. The first line contains an integer num, representing the number of gas stations (N).
2. The second line contains N space-separated integers dis1 dis2 ... disN, where disi represents the distance of the i-th gas station from Mr. Henry's home.
3. The third line contains an integer numS, representing the number of gas stations available (numS = N).
4. The fourth line contains N space-separated integers iGas1 iGas2 ... iGasN, where iGasi represents the gallons of gasoline available at the i-th gas station.
5. The next line contains an integer distance, representing the distance of the office from Mr. Henry's home (D).
6. The next line contains an integer initialGas, representing the initial amount of gasoline in the car (K).

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Output Format

Print a single integer representing the minimum number of gas stations at which Mr. Henry should stop to successfully reach his office.

If reaching the office is impossible, print -1.

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Constraints

• (1 <= N <= 10^4)
• (1 <= dis_i < D <= 10^5)
• (1 <= iGas_i <=10^3)
• (0 <= initialGas <=10^5)

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Example

Input

4
5 7 8 10
4
2 3 15 15
15
5

Output

3

Explanation

• Initially, the car has 5 gallons, allowing it to travel 5 miles, reaching the 1st gas station.
• Refuel there with 2 gallons.
• Later, the car reaches the 2nd gas station and refuels with 3 gallons.
• Finally, it reaches the 3rd gas station, where it refuels with 15 gallons, which is enough to reach the office.

Thus, the minimum number of gas stations visited is:

3