problem

Given the sequence $ A $ of length $ N $. The $ i $ item in $ A $ is $ A_i $. You can do the following for this sequence:

• $1 \ leq i \ leq N --Choose the integer i that is 1$. Swap the value of $ A_i $ with the value of $ A_ {i + 1} $.

Find the minimum number of operations required to make $ A $ a sequence of bumps.

A sequence of length $ N $ that satisfies the following conditions is defined as a sequence of irregularities.

• For any $ i $ that satisfies $ 1 <i <N $, ​​$ A_ {i + 1}, A_ {i --1}> A_i $ or $ A_ {i + 1}, A_ {i --1} <A_i Satisfy $.
  Intuitively, increase, decrease, increase ... (decrease, like $1, \ 10, \ 2, \ 30, \ \ dots (10, \ 1, \ 30, \ 2, \ \$ It is a sequence that repeats increase, decrease ...).

output

Output the minimum number of operations required to make a sequence of bumps. Also, output a line break at the end.

Example

Input

5
1 2 3 4 5

Output

2

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