Diamond

You are a big fan of jewelry and gemstones. Recently, a remarkable diamond was put for sale in the jewelry store next to your house. However, its price was also remarkable — $X$ dollars. Unfortunately, you had to admit that this was too expensive for you, no matter how much you liked the diamond itself.

Apparently, other potential buyers felt the same way, because soon the store started an advertising campaign. "Get a $5\%$ discount for each letter in your name!" read the sign at the entrance. This wording was not very clear, so you decided to ask the staff. After talking with them, it turned out that:

• If a letter occurs in your name multiple times, it is counted only once. For example, for the name alexandra, there are $7$ letters for this promotion, not $9$, since $a$ appears three times.

• The $5\%$ discount is multiplied by the number of distinct letters in your name. For alexandra, for example, you would get a $35\%$ discount.

• Discounts greater than $100\%$ are not given, but a full $100\%$ discount is possible (when you asked about this, the staff gave you a strange look).

Of course, it would be a shame not to take advantage of such a generous offer, but maybe you can save even more. By a stroke of luck, you recently met a person who forges passports. His services are paid as follows:

• Forging a passport costs $A$ dollars. The fake passport can use your real name without changes, or you can change it using any number of operations of the following three kinds.

• Inserting a letter at any position costs $B$ dollars.

• Deleting a letter at any position costs $C$ dollars. The resulting name must not be empty.

• Replacing any letter with any other lowercase English letter costs $D$ dollars.

Given $X$, $A$, $B$, $C$, $D$, and your real name $Name$, determine the minimum total amount of money needed to obtain the diamond (including the amount paid for the diamond and for the forged passport, if any). Forging a passport is not required; you may also simply present your real passport with the name $Name$ when buying.