Problem Statement

Kero-chan, an indigenous god, can create forests.

Kero-chan is trying to create a forest that satisfies the following conditions.

• For every $i(0\leq i\leq N)$, there are exactly $A_i$ vertices of degree $i$
• For $N<i$, the number of vertices of degree $i$ is $0$

Determine whether this is possible. Here, assume that Kero-chan can create any forest.

Note that a graph with no vertices is also considered a forest (when all $A_i$ are $0$, the answer is Yes).

About the red text

• If interpreted as allowing any number of vertices of degree greater than $N$, cases such as $N=1, A=(0, 9)$ would also be Yes, but the intent of the problem when it was written was No
• Without mention of $N<i$ the statement was somewhat ambiguous, so a sentence was added, but it was worded incorrectly at that time, which led to this situation

Input

$N$
$A_0\ A_1\ A_2\ \cdots\ A_N$

• $1\leq N\leq 10^5$
• $0\leq A_i\leq 10^8$
• All inputs are integers

Output

Print Yes if a forest satisfying the conditions can be created, and No otherwise, on $1$ line.

Print a newline at the end.

Sample

3
0 5 1 1

Yes

   o        o
  /         |
 o - o  o - o - o

2
0 0 3

No