Description

In this problem, i will give you a integer sequence, you should use the least steps to regulate it to a strictly increase one; and then you should promises that sigma |A[i] - B[i]| is min; assume that the A is origin sequence , B is your obtain sequence, as long as satisfy the condition, B can be arbitrary.

Input

in each case ,first line will be a integer N (1<=N<=5000),which indicate the length of sequence; second line will be the sequence,see the example for clarify.

Output

ouput will be two lines ,first is the min steps,second is the sigma;

Sample Input

4 5 2 3 5

Sample Output

1 4

Source

kscinow@joj