A trading firm predicts the stock prices of a commodity for the next n days. A period of consecutive days is considered investable if the maximum price in the period is max_price , and the minimum price in the period is min_price . Find the number of investable periods in the next n days.

More formally, given an array price of length n , find the number of subarrays in which the maximum element is max_price and the minimum element is min_price . Note: A subarray is a sequence of consecutive elements of the array.

Function Description

Complete the function countInvestablePeriods in the editor below.

countInvestablePeriods has the following parameters:

1. int price[n] : the predicted prices for the next n days
2. int max_price : the maximum price of an investable period
3. int min_price : the minimum price of an investable period

Returns

long integer : the number of investable periods

Example 1 :

Input: price = [4, 5, 3, 3, 1], max_price = 5, min_price = 3
Output: 4
Explanation: Here, the periods [4, 5, 3], [4, 5, 3, 3], [5, 3], and [5, 3, 3] are investable.

Example 2 :

Input: price = [2, 2, 1, 5, 1], max_price = 2, min_price = 1
Output: 2
Explanation: The periods [2, 2, 1] and [2, 1] are investable.

Constraints: