Guild Bounty Levy Tiers

The Hunters' Guild collects a tiered royalty on the bounty gold its hunters earn each season. The royalty schedule is given as m tiers; tier i is described by a cap cap_i and a rate rate_i (a percentage), listed in strictly increasing order of cap. The final tier's cap is guaranteed to be at least as large as any bounty amount you are asked about. The royalty is charged tier by tier, in order:

• The first cap_0 gold earned is charged at rate_0 percent.
• The next cap_1 - cap_0 gold earned (that is, gold earned beyond cap_0 and up to cap_1) is charged at rate_1 percent.
• The next cap_2 - cap_1 gold earned is charged at rate_2 percent.
• ...and so on, tier by tier, until the hunter's entire bounty has been accounted for. If the bounty falls short of filling a tier, only the gold actually earned within that tier is charged at that tier's rate, and no later tier contributes anything.

Given the tier schedule and a hunter's total bounty gold for the season, compute the total royalty owed.

Input format

Line 1: an integer m, the number of tiers. Next m lines: two integers cap_i and rate_i, the cap and royalty percentage of tier i, given in strictly increasing order of cap. Last line: an integer bounty, the hunter's total bounty gold for the season.

Output format

Print a single number: the total royalty owed, printed with exactly 5 digits after the decimal point. An answer within 1e-5 (absolute or relative) of the exact value is accepted.

Constraints

1 <= m <= 500 1 <= cap_i <= 10^9, strictly increasing across tiers 0 <= rate_i <= 100 0 <= bounty <= cap_{m-1} (the cap of the last tier)

3
3 50
7 10
12 25
10

2.65000

1
5 20
5

1.00000