The tunnels of Cu Chi are an immense network of underground
tunnels connecting rooms located in the Cu Chi District of Ho
Chi Minh City. The Cu Chi tunnels were the location of several
military campaigns in the 1960s. Nowadays, it is a popular
tourist destination.
There are documents from trusted sources about a private
network of tunnels in this area used by a secret forces unit
but it has not been discovered. According to the documents,
this private network has $N$ rooms (numbered from $1$ to $N$) connected by $N1$ bidirectional tunnels. Room
$1$ is the entry point
from the ground surface to this underground network. From room
$1$, you can follow the
tunnels to go to any of the rooms. The rooms are numbered in
such a way that, if you follow the shortest path from room
$1$ to any room
$X$, the sequence of
visited roomsâ€™ indices will be increasing. The image below
shows a valid map of this network.
The network below is invalid, since the path from
$1$ to $4$ is $1$  $3$  $2$  $4$, which is not increasing:
There is also an old article from an unknown source
mentioning about $D_ i$
which is the number of rooms directly connected to room
$i$.
Given an array $D$ of
size $N$, your task is to
verify if it is possible to have such a network.
Input

The first line contains an integer $N$  the number of rooms in the
network $(2 \leq N \leq 1\,
000)$.

The second line consists of $N$ integers $D_ i$  the number of rooms that
are directly connected to room $i$ $(1 \leq D_ i \leq N  1)$.
Output
Print YES/NO
if it is possible/impossible to have such a network,
respectively.
Sample Input 1 
Sample Output 1 
8
3 2 2 1 1 3 1 1

YES

Sample Input 2 
Sample Output 2 
4
3 3 3 3

NO
