Second Sum

Given is a permutation P of \{1, 2, \ldots, N\}.

For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.

Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Constraints

• 2 \le N \le 10^5
• 1 \le P_i \le N
• P_i \neq P_j (i \neq j)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N P_1 P_2 \ldots P_N

Output

Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Examples

Input

3 2 3 1

Output

5

Input

5 1 2 3 4 5

Output

30

Input

8 8 2 7 3 4 5 6 1

Output

136

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N P_1 P_2 \ldots P_N

outputFormat

Output

Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Examples

Input

3 2 3 1

Output

5

Input

5 1 2 3 4 5

Output

30

Input

8 8 2 7 3 4 5 6 1

Output

136

样例

5
1 2 3 4 5

30