Score : $500$ points

Problem Statement

We have an integer sequence of length $N$: $x=(x_0,x_1,\cdots,x_{N-1})$ (note that its index is $0$-based). Initially, all elements of $x$ are $0$.

You can repeat the following operation any number of times.

• Choose integers $i,k$ ($0 \leq i \leq N-1$, $1 \leq k \leq N$). Then, for every $j$ such that $i \leq j \leq i+k-1$, increase the value of $x_{j\bmod N}$ by $1$.

You are given an integer sequence of length $N$: $A=(A_0,A_1,\cdots,A_{N-1})$. Find the minimum number of operations needed to make $x$ equal $A$.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_0$ $A_1$ $\cdots$ $A_{N-1}$

Output

Print the answer.

4
1 2 1 2

2

We should do the following.

• Initially, we have $x=(0,0,0,0)$.
• Do the operation with $i=1,k=3$, making $x=(0,1,1,1)$.
• Do the operation with $i=3,k=3$, making $x=(1,2,1,2)$.

5
3 1 4 1 5

7

1
1000000000

1000000000