Statues

The mayor of a city wants to place $n$ statues at intersections around the city. The intersections in the city are at all points $(x, y)$ with integer coordinates. Distances between intersections are measured using Manhattan distance, defined as follows:

$\text{distance}((x_1, y_1),(x_2, y_2)) = |x_1 - x_2| + |y_1 - y_2|$.

The city council has provided the following requirements for the placement of the statues:

• The first statue is placed at $(0, 0)$;
• The $n$-th statue is placed at $(a, b)$;
• For $i = 1, \dots , n - 1$, the distance between the $i$-th statue and the $(i + 1)$-th statue is $d_i$.

It is allowed to place multiple statues at the same intersection.

Help the mayor find a valid arrangement of the $n$ statues, or determine that it does not exist.

The first line contains an integer $n$ ($3 ≤ n ≤ 50$) — the number of statues.

The second line contains two integers $a$ and $b$ ($0 ≤ a, b ≤ 10^9$) — the coordinates of the intersection where the $n$-th statue must be placed.

The third line contains $n - 1$ integers $d_1, \dots , d_{n-1}$ ($0 ≤ d_i ≤ 10^9$) — the distance between the $i$-th statue and the $(i + 1)$-th statue.

Print YES if there is a valid arrangement of the $n$ statues. Otherwise, print NO.

If there is a valid arrangement, print a valid arrangement in the following $n$ lines. The $i$-th of these lines must contain two integers $x_i$ and $y_i$ — the coordinates of the intersection where the $i$-th statue is placed. You can print any valid arrangement if multiple exist.