You have a multiset containing several integers. Initially, it contains $a_1$ elements equal to $1$, $a_2$ elements equal to $2$, ..., $a_n$ elements equal to $n$.

You may apply two types of operations:

• choose two integers $l$ and $r$ ($l \le r$), then remove one occurrence of $l$, one occurrence of $l + 1$, ..., one occurrence of $r$ from the multiset. This operation can be applied only if each number from $l$ to $r$ occurs at least once in the multiset;
• choose two integers $i$ and $x$ ($x \ge 1$), then remove $x$ occurrences of $i$ from the multiset. This operation can be applied only if the multiset contains at least $x$ occurrences of $i$.

What is the minimum number of operations required to delete all elements from the multiset?

Input

The first line contains one integer $n$ ($1 \le n \le 5000$).

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($0 \le a_i \le 10^9$).

Output

Print one integer — the minimum number of operations required to delete all elements from the multiset.

见题面 Input 部分

见题面 Output 部分