You are standing at position \(1\). From position $$i$$, you can walk to $$i+1$$ or $$i-1$$ with cost \(1\). From position \(i\), you can travel to without any cost to $$p_i$$ (\(p\) is a permutation of numbers \(1 \ldots n\)). You have to reach position \(n\). Determine the minimum possible cost.

Input format

• First line: \(T\) denotes the number of test cases (\(1 \le T \le 10\))
• For each test case:
  • First line: \(n\) (\(1 \le n \le 50\ 000\))
  • Second line: \(n\) integers where the \(i_{th}\) integer is \(p_i\)
    Note: It is guaranteed that \(p\) is a permutation.

Output format
Print the minimum possible cost.