You are given a 0-indexed 2D integer array brackets where brackets[i] = [upperᵢ, percentᵢ] means that the i^(th) tax bracket has an upper bound of upperᵢ and is taxed at a rate of percentᵢ. The brackets are sorted by upper bound (i.e. upperᵢ₋₁ < upperᵢ for 0 < i < brackets.length).

Tax is calculated as follows:

• The first upper₀ dollars earned are taxed at a rate of percent₀.
• The next upper₁ - upper₀ dollars earned are taxed at a rate of percent₁.
• The next upper₂ - upper₁ dollars earned are taxed at a rate of percent₂.
• And so on.

You are given an integer income representing the amount of money you earned. Return the amount of money that you have to pay in taxes. Answers within 10⁻⁵ of the actual answer will be accepted.

Examples

Example 1

Input:  brackets = [[3,50],[7,10],[12,25]], income = 10
Output: 2.65000

Based on your income, you have 3 dollars in the 1^(st) tax bracket, 4 dollars in the 2^(nd) tax bracket, and 3 dollars in the 3^(rd) tax bracket. The tax rate for the three tax brackets is 50%, 10%, and 25%, respectively. In total, you pay $3 * 50% + $4 * 10% + $3 * 25% = $2.65 in taxes.

Example 2

Input:  brackets = [[1,0],[4,25],[5,50]], income = 2
Output: 0.25000

Based on your income, you have 1 dollar in the 1^(st) tax bracket and 1 dollar in the 2^(nd) tax bracket. The tax rate for the two tax brackets is 0% and 25%, respectively. In total, you pay $1 * 0% + $1 * 25% = $0.25 in taxes.

Example 3

Input:  brackets = [[2,50]], income = 0
Output: 0.00000

You have no income to tax, so you have to pay a total of $0 in taxes.

Constraints

• 1 <= brackets.length <= 100
• 1 <= upperᵢ <= 1000
• 0 <= percentᵢ <= 100
• 0 <= income <= 1000
• upperᵢ is sorted in ascending order.
• All the values of upperᵢ are unique.
• The upper bound of the last tax bracket is greater than or equal to income.