Problem:
Score : 700 points

Problem Statement

There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.

You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.

Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 10^9(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.

Sample Input 1

4
0
1
1
2

Sample Output 1

3

We can make X equal to A as follows:

Choose i=2. X becomes (0,0,1,0).

Choose i=1. X becomes (0,1,1,0).

Choose i=3. X becomes (0,1,1,2).

Sample Input 2

3
1
2
1

Sample Output 2

-1

Sample Input 3

9
0
1
1
0
1
2
2
1
2

Sample Output 3

8

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program test
implicit none
integer(8) :: n,i
integer(8) :: retsu(2*10**5) = 0, imp=0, number=0

read(*,*) n

do i=1,n
	read(*,*) retsu(i)
enddo

if(retsu(1)>0) then
imp = 1
endif

do i=2,n

		if(retsu(i) - retsu(i-1) > 1) then
			imp = 1
		endif
		
		if(retsu(i)==0) then
			number = number
		else if(retsu(i)==1)then
			number = number + 1
		else if(retsu(i) - retsu(i-1) == 1) then
			number = number + 1
		else if(retsu(i) <= retsu(i-1)) then
			number = number + retsu(i)
		endif
			
enddo

if(imp == 1)then
	write(*,*) -1
else
	write(*,*) number
endif

end program