Coins

You have A 500-yen coins, B 100-yen coins and C 50-yen coins (yen is the currency of Japan). In how many ways can we select some of these coins so that they are X yen in total?

Coins of the same kind cannot be distinguished. Two ways to select coins are distinguished when, for some kind of coin, the numbers of that coin are different.

Constraints

• 0 \leq A, B, C \leq 50
• A + B + C \geq 1
• 50 \leq X \leq 20 000
• A, B and C are integers.
• X is a multiple of 50.

Input

Input is given from Standard Input in the following format:

A B C X

Output

Print the number of ways to select coins.

Examples

Input

2 2 2 100

Output

2

Input

5 1 0 150

Output

0

Input

30 40 50 6000

Output

213

inputFormat

Input

Input is given from Standard Input in the following format:

A B C X

outputFormat

Output

Print the number of ways to select coins.

Examples

Input

2 2 2 100

Output

2

Input

5 1 0 150

Output

0

Input

30 40 50 6000

Output

213

样例

2
2
2
100

2