Minimum Sum

One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

Constraints

• 1 ≦ N ≦ 200,000
• (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3 2 1 3

Output

9

Input

4 1 3 2 4

Output

19

Input

8 5 4 8 1 2 6 7 3

Output

85

inputFormat

Input

The input is given from Standard Input in the following format:

N a_1 a_2 ... a_N

outputFormat

Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3 2 1 3

Output

9

Input

4 1 3 2 4

Output

19

Input

8 5 4 8 1 2 6 7 3

Output

85

样例

3
2 1 3

9