#P1693E. Outermost Maximums

Outermost Maximums

Description

Yeri has an array of n+2n + 2 non-negative integers : a0,a1,...,an,an+1a_0, a_1, ..., a_n, a_{n + 1}.

We know that a0=an+1=0a_0 = a_{n + 1} = 0.

She wants to make all the elements of aa 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 aa equal to zero.

The first line contains a single integer nn (1n21051 \le n \le 2 \cdot 10^5).

The second line contains nn integers a1,a2,,ana_1, a_2, \ldots, a_n (0ain0 \le a_i \le n).

Print a single integer  — the minimum number of operations needed to make all elements of aa equal to zero.

Input

The first line contains a single integer nn (1n21051 \le n \le 2 \cdot 10^5).

The second line contains nn integers a1,a2,,ana_1, a_2, \ldots, a_n (0ain0 \le a_i \le n).

Output

Print a single integer  — the minimum number of operations needed to make all elements of aa equal to zero.

Sample Input 1

6
1 4 2 4 0 2

Sample Output 1

7

Sample Input 2

5
1 3 5 4 2

Sample Output 2

9

Sample Input 3

4
0 0 0 0

Sample Output 3

0

Note

In the first sample, you get 1,1,2,4,0,2\langle 1, \underline{1}, 2, 4, 0, 2 \rangle by performing the first operation and 1,4,2,2,0,2\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.) 1,4,2,4,0,21,4,2,2,0,21,1,2,2,0,21,1,2,2,0,01,1,2,0,0,01,1,0,0,0,00,1,0,0,0,00,0,0,0,0,0\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.