Chef is very adventurous, so he asked Bob to give him a task. Bob gave him a sequence of blocks with heights A1,A2,…,ANA1,A2,…,AN. Chef is at the first block and he has to reach the NN-th block using the minimum number of moves to complete the task. In one move, he can jump from the ii-th block to the jj-th block only if the following conditions are satisfied:- Chef is very adventurous, so he asked Bob to give him a task. Bob gave him a sequence of blocks with heights A1,A2,…,ANA1,A2,…,AN. Chef is at the first block and he has to reach the NN-th block using the minimum number of moves to complete the task. In one move, he can jump from the ii-th block to the jj-th block only if the following conditions are satisfied:

Chef is very adventurous, so he asked Bob to give him a task.

Bob gave him a sequence of blocks with heights A1,A2,,ANA1,A2,…,AN. Chef is at the first block and he has to reach the NN-th block using the minimum number of moves to complete the task.

In one move, he can jump from the ii-th block to the jj-th block only if the following conditions are satisfied:

  • i<ji<j Crossing Blocks solution codechef 
  • AiAjAi≥Aj
  • for all kk (i<k<ji<k<j), AkAjAk≤Aj

You have to find the minimum number of moves Chef needs to perform to reach the last block, or determine that it is impossible.

Input Format Crossing Blocks solution codechef

  • The first line of the input contains a single integer TT denoting the number of test cases. The description of TT test cases follows.
  • The first line of each test case contains a single integer NN.
  • The second line contains NN space-separated integers A1,A2,,ANA1,A2,…,AN.

Output Format

For each test case, print a single line containing one integer — the minimum number of moves or 1−1 if it is impossible to reach the last block.

Constraints

  • 1T1001≤T≤100
  • 2N1052≤N≤105
  • 0Ai1050≤Ai≤105 for each valid ii
  • the sum of NN over all test cases does not exceed 106106

Subtasks Crossing Blocks solution codechef

Subtask #1 (30 points):

  • 2N1,0002≤N≤1,000
  • the sum of NN over all test cases does not exceed 51045⋅104

Subtask #2 (70 points): original constraints

Sample Input 1 

2
5
9 15 8 13 8
9
20 16 13 9 17 11 15 8 7

Sample Output 1  Crossing Blocks solution codechef 

-1
4

Explanation

Example case 1: There is no way to move from the first block (with height 99) to any other block.

Example case 2: The only sequence of 44 moves is 2017158720→17→15→8→7. For example, in the first move, all the heights between 2020 and 1717 do not exceed 1717, so all conditions are satisfied.

Chef is very adventurous, so he asked Bob to give him a task. Bob gave him a sequence of blocks with heights A1,A2,…,ANA1,A2,…,AN. Chef is at the first block and he has to reach the NN-th block using the minimum number of moves to complete the task. In one move, he can jump from the ii-th block to the jj-th block only if the following conditions are satisfied:

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