Strange Sorting

Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

• First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
• Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
• Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).

How many operations are necessary until the permutation is sorted?

Constraints

• 1 ≤ N ≤ 2×10^5
• (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:

N p_1 p_2 ... p_N

Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5 3 5 1 2 4

Output

3

Input

5 5 4 3 2 1

Output

4

Input

10 2 10 5 7 3 6 4 9 8 1

Output

6

inputFormat

Input

Input is given from Standard Input in the following format:

N p_1 p_2 ... p_N

outputFormat

Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5 3 5 1 2 4

Output

3

Input

5 5 4 3 2 1

Output

4

Input

10 2 10 5 7 3 6 4 9 8 1

Output

6

样例

10
2 10 5 7 3 6 4 9 8 1

6