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.