E. Outermost Maximumstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYeri has an array of n + 2 non-negative integers : a_0, a_1, ..., a_n, a_{n + 1}.We know that a_0 = a_{n + 1} = 0.She wants to make all the elements of a equal to zero in the minimum number of operations.In one operation she can do one of the following:  Choose the leftmost maximum element and change it to the maximum of the elements on its left. Choose the rightmost maximum element and change it to the maximum of the elements on its right.Help her find the minimum number of operations needed to make all elements of a equal to zero.InputThe first line contains a single integer n (1 \le n \le 2 \cdot 10^5).The second line contains n integers a_1, a_2, \ldots, a_n (0 \le a_i \le n).OutputPrint a single integer  — the minimum number of operations needed to make all elements of a equal to zero.ExamplesInput
6
1 4 2 4 0 2
Output
7
Input
5
1 3 5 4 2
Output
9
Input
4
0 0 0 0
Output
0
NoteIn the first sample, you get \langle 1, \underline{1}, 2, 4, 0, 2 \rangle by performing the first operation and \langle 1, 4, 2, \underline{2}, 0, 2 \rangle by performing the second operation.One way to achieve our goal is shown below. (The underlines show the last change.) \langle 1, 4, 2, 4, 0, 2 \rangle \to \langle 1, 4, 2, \underline{2}, 0, 2 \rangle \to \langle 1, \underline{1}, 2, 2, 0, 2 \rangle \to \langle 1, 1, 2, 2, 0, \underline{0} \rangle \to \langle 1, 1, 2, \underline{0}, 0, 0 \rangle \to \langle 1, 1, \underline{0}, 0, 0, 0 \rangle \to \langle \underline{0}, 1, 0, 0, 0, 0 \rangle \to \langle 0, \underline{0}, 0, 0, 0, 0 \rangle In the third sample each element is already equal to zero so no operations are needed.
6
1 4 2 4 0 2

7 
['data structures', 'greedy', '*3400']