A national beauty pageant is the qualifier for an international beauty pageant, whose evening gown segment is held on a lava lake. Catriona, Emma, and Nadine are the three finalists of this. In preparation for the international pageant's evening gown segment, the night gown segment of this pageant is held on a $16 times 16$ grid of squares, each containing a different sort of liquid.
Exactly one of the squares is a stone that the three contestants start on. Each step consists of walking from a square to the square in front of it, behind it, to its left, or to its right. Each square contains one of three things: lava, water, or lemonade.
Fortunately, all three contestants are fireproof, immune to lava, and can walk on liquids. Unfortunately, the contestants are wearing different colors of gowns, which means they can only walk on liquids that match the colors of their gowns:
Can you find a possible layout of the grid that satisfies this? If there is no such layout, say so.
The first line of input contains $t$, the number of test cases.
Each test case consists of a single line containing three space-separated integers $c$, $e$ and $n$.
For each test case, first output a single line containing either _YES_ or _NO_ denoting whether it is possible. If you printed _YES_, output 16 more lines, each containing 16 characters from the following:
$0 <= t <= 60000$
$9 <= c, e, n <= 111$
*Subtask 1* (4 points):
$t <= 1000$
$c = e = n = 21$
*Subtask 2* (7 points):
$t <= 1000$
$c$, $e$ and $n$ belong to the set ${21, 42}$
*Subtask 3* (8 points):
$t <= 20000$
$c = 16$
$e >= 32$
$n >= e + 16$
*Subtask 4* (18 points):
$t <= 20000$
$21 <= c, e, n <= 42$
*Subtask 5* (42 points):
$c + e + n <= 168$
*Subtask 6* (21 points):
No additional constraints.
## Input
The first line of input contains $t$, the number of test cases.Each test case consists of a single line containing three space-separated integers $c$, $e$ and $n$.
## Output
For each test case, first output a single line containing either _YES_ or _NO_ denoting whether it is possible. If you printed _YES_, output 16 more lines, each containing 16 characters from the following: _S_, which represents the starting stone. _._, which represents lava. _#_, which represents water. _$tilde$_, which represents lemonade.
[samples]
## Scoring
$0 <= t <= 60000$$9 <= c, e, n <= 111$*Subtask 1* (4 points):$t <= 1000$ $c = e = n = 21$ *Subtask 2* (7 points):$t <= 1000$ $c$, $e$ and $n$ belong to the set ${21, 42}$*Subtask 3* (8 points):$t <= 20000$ $c = 16$ $e >= 32$ $n >= e + 16$ *Subtask 4* (18 points):$t <= 20000$ $21 <= c, e, n <= 42$ *Subtask 5* (42 points):$c + e + n <= 168$*Subtask 6* (21 points):No additional constraints.
**Definitions**
Let $ t \in \mathbb{Z} $ be the number of test cases.
For each test case, let $ c, e, n \in \mathbb{Z} $ denote the required number of squares for Catriona, Emma, and Nadine, respectively, such that each contestant may only step on squares assigned to their gown color.
**Constraints**
1. $ 0 \leq t \leq 60000 $
2. $ 9 \leq c, e, n \leq 111 $
3. $ c + e + n \leq 256 $ (since grid has $16 \times 16 = 256$ squares)
4. The grid must contain exactly $ c $ squares of Catriona’s color, $ e $ of Emma’s, $ n $ of Nadine’s, and one stone square (starting position), which is counted within one of the three color groups.
**Objective**
Determine whether there exists a partition of the $16 \times 16$ grid into three disjoint color regions (with sizes $c$, $e$, $n$) such that the entire grid is covered and the stone is placed on one of the squares.
**Output**
For each test case:
- If $ c + e + n \leq 256 $, output "YES" followed by a valid $16 \times 16$ grid coloring.
- Otherwise, output "NO".
Note: The stone is not an additional square — it occupies one of the $c$, $e$, or $n$ squares.