Le Hamburg de Rahul

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Problem

Rahul loves hamburgers very much. He especially adores the hamburgers he makes with his own hands. Rahul thinks that there are only three decent ingredients to make hamburgers from: a bread, sausage and cheese. He writes down the recipe of his favorite "Le Hamburger de Rahul" as a string of letters 'B' (bread), 'S' (sausage) & 'C' (cheese). The ingredients in the recipe go from bottom to top, for example, recipe "ВSCBS" represents the hamburger where the ingredients go from bottom to top as bread, sausage, cheese, bread and sausage again.

Rahul has nb pieces of bread, ns pieces of sausage and nc pieces of cheese in the kitchen. Besides, the shop nearby has all three ingredients, the prices are pb rubles for a piece of bread, ps for a piece of sausage and pc for a piece of cheese.

Rahul has r rubles and he is ready to shop on them. What maximum number of hamburgers can he cook? You can assume that Rahul cannot break or slice any of the pieces of bread, sausage or cheese. Besides, the shop has an unlimited number of pieces of each ingredient.

Input The first line of the input contains a non-empty string that describes the recipe of "Le Hamburger de Rahul". The length of the string doesn't exceed 100, the string contains only letters 'B' (uppercase English B), 'S' (uppercase English S) and 'C' (uppercase English C). The second line contains three integers nb, ns, nc (1 ≤ nb, ns, nc ≤ 100) — the number of the pieces of bread, sausage and cheese on Rahul' kitchen. The third line contains three integers pb, ps, pc (1 ≤ pb, ps, pc ≤ 100) — the price of one piece of bread, sausage and cheese in the shop. Finally, the fourth line contains integer r (1 ≤ r ≤ 1012) — the number of rubles Rahul has.

Output Print the maximum number of hamburgers Rahul can make. If he can't make any hamburger, print 0.

Sample Input
BBBSSC
6 4 1
1 2 3
4
Sample Output
2
Time Limit: 5
Memory Limit: 256
Source Limit:
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