Easy Quest

A young hero is starting his heroic life. A wise wizard gave him an easy first quest. During the quest the hero meets $n$ magical creatures in a fixed order. To help him, the wizard handed him a list of $n$ integers $a_1, a_2, \dots, a_n$.

• If $a_i$ is positive, the $i$-th creature is benevolent and gives the hero one magical item of type $a_i$. The hero may keep several items of the same type.
• If $a_i$ is negative, the $i$-th creature is evil, and defeating it costs one magical item of type $-a_i$. Every magical item is fragile and can be used only once.
• If $a_i$ is zero, the $i$-th creature is a unicorn. It gives the hero a magical item of any type he asks for, but only one item.

Decide whether the hero can defeat every enemy on the way and finish the quest. If he can, decide what to ask each unicorn for.

The first line contains one integer $n$ ($1 \le n \le 1000$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ separated by single spaces ($-1000 \le a_i \le 1000$).

If the hero cannot defeat every enemy, print No.

Otherwise print Yes on the first line. On the second line print the type the hero asks each unicorn for, in the order he meets the unicorns, separated by single spaces. Every type must be an integer between 1 and 1000. If the hero meets no unicorn, print only Yes.

When several sequences of requests work, print the lexicographically smallest one. For two sequences $x$ and $y$ of the same length, $x$ is lexicographically smaller than $y$ when there is a position $j$ with $x_j < y_j$ and $x_i = y_i$ for every $i < j$.