Non-increasing sequence

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Zenyk fulfilled another of Marichka’s whims — he wrote down a sequence of \(n\) numbers \(a_1\), \(a_2\), ..., \(a_n\). Just as Marichka wanted, the numbers in this sequence form a non-decreasing sequence, i.e., each next element is greater than or equal to the previous one. Happy Zenyk ran to his Marichka to present her with this sequence.

Suddenly, Zenyk broke into a cold sweat. Everything stopped inside his soul. He remembered that Marichka wanted to get a non-increasing sequence, not a non-decreasing one. That is, in his sequence, each next element must be less than or equal to the previous one. Now Zenyk wants to fix his mistake as soon as possible. In one minute, Zenyk can choose any number from the current sequence and replace its value with any other. What is the minimum amount of time in which Zenyk can fix his mistake?

Input

The first line contains a single integer \(n\) — the number of elements in the sequence.

The second line contains the non-decreasing sequence \(a_1\), \(a_2\), ..., \(a_n\).

Output

In a single line, print one integer — the minimum number of minutes in which Zenyk can change the sequence to a non-increasing one.

Constraints

\(1 \le n \le 10^5\),

\(0 \le a_i \le 10^9\),

\(a_{i+1} \ge a_i\),

for 40% of the tests, an additional constraint holds: \(n, a_i \le 10^3\).

Samples

Input (stdin) сopy	Output (stdout) сopy
4 1 4 4 7	2

Notes

In the example, you can replace two elements: the first with 7, the last with 2. This forms the sequence [7, 4, 4, 2], which is non-increasing.