Dorothy has been caught up in a cyclone and has reached the Munichkin kingdom in the magical land of Oz$.$ On her way, she comes across a yellow brick road across which, she can see the towering castle of the great wizard. The brick road, however, requires a test of the mind to cross it$.$ It has been set up by the wizard so that unworthy people may not enter his castle.

The yellow brick road can only be crossed in the following way:

There are N bricks and each brick is labeled with a random number from $0$ to $9.$

Dorothy is on the $1$th brick and needs to reach the Nth brick.

If she is on the ith brick with value V$,$ then she can move to the i$+1$th brick, i$-1$th brick or any brick with the same value V$.$

There are N bricks and each brick is labeled with a random number from $0$ to $9.$

Dorothy is on the $1$th brick and needs to reach the Nth brick.

If she is on the it brick with value V$,$ then she can move to the i$+1$th brick, i$-1$th brick or any brick with the same value V$.$

Help Dorothy cross the golden brick road in the smallest number of moves.

Input format:

Line $1$: N$,$ number of bricks.

Line $2$: Space separated array representing the numbers on each brick.

Output Format:

Your program should print the smallest number of moves to cross the brick road.

Examples:

Example $1$:

Line $1$: $5$

Line $2$:$12341$

Output: $1$

Explanation:

Since the value at Oth position is same as at $4$th position, Dorothy directly moves to the end position. The number of moves is $1.$

Example $2$:

Line $1$: $6$

Line $2$:$123413$

Output: $2$

Explanation:

The shortest path is position $0$th$-4$th$-5$th$.$ The number of moves is $2.$