Problem

Given an array A of length N that contains the numbers from 1 to N in any order. It is allowed to move from an index i to an index i+1 or index A[i] in one move. You are required to reach to Index N+1 from all Index i with minimum moves and take the sum of these minimum moves. Find and print the required sum.

Note

• You have to consider the minimum number of moves to reach from an index i to an index N+1.
• All the paths to index N+1 go via index N.
• Consider 1 based indexing.

Input Format

The input consists of two lines:

• The first line contains an integer N.
• Next line contains N integers A[i] which is the permutation of length N. The input will be read from the STDIN by the candidate.

Output Format

• Print a number that represents the sum of the minimum moves from all the indexes to reach index N+1.
• The output will be matched to the candidate's output printed on the STDOUT.

Example 1:

Input: 7 3 2 1 7 4 6 5 Output: 4

Explanation:

N=7. A:13217465

• To go from an index i to an index N + 1 - i requires 4 moves.
• Similarly, index 2 to index 8: 4 moves
• index 3 to index 8: 3 moves
• index 4 to index 8: 2 moves
• index 5 to index 8: 3 moves
• index 6 to index 8: 2 moves
• index 7 to index 8: 1 move
• total moves=19