### No.3052 Squaring

レベル : / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / スペシャルジャッジ問題 （複数の解が存在する可能性があります）
タグ : / 解いたユーザー数 3

ProblemId : 2865 / 出題時の順位表 / 自分の提出

#### 入力

$N$
$A_1$ $\cdots$ $A_N$


・$1 \leq N \leq 26$
・$1 \leq A_1 < \cdots < A_N$
・$A_1 ^ 2 + \cdots + A_N ^ 2 \leq 500 ^ 2$

#### 出力

###### 可能な場合：
$L$
$c_{1, 1} \cdots c_{1, L}$
$\vdots$
$c_{L, 1} \cdots c_{L, L}$


・できあがった正方形の一辺の長さを $L$ とする
・並べ方は、縦 $L$ マス、横 $L$ マスの文字配列 $c$ として表現する
・各マスの文字は、全体の正方形のそのマスに相当する部分が $1$ 番目に小さい正方形である場合は 'A' 、$2$ 番目に小さい正方形である場合は 'B' 、……、$26$ 番目に小さい正方形である場合は 'Z' とする

###### 不可能な場合：
-1


#### サンプル

##### サンプル1
###### 入力
1
3

###### 出力
3
AAA
AAA
AAA


##### サンプル2
###### 入力
2
1 3

###### 出力
-1


$2$ 個の正方形の面積の和は $10$ なので、もし正方形にできるとしたらその一辺の長さは $\sqrt{10}$ にならなければいけませんが、そんなことは不可能です。

##### サンプル3
###### 入力
24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

###### 出力
-1


##### サンプル4
###### 入力
23
1 2 3 4 5 7 8 10 12 13 14 15 16 19 21 28 29 31 32 37 38 41 44

###### 出力例
110
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PPPPPPPPPPPPPPPPPPPPPPPPPPPPMMMMMMMMMMMMMMMMLLLLLLLLLLLLLLLNNNNNNNNNNNNNNNNNNNSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
PPPPPPPPPPPPPPPPPPPPPPPPPPPPMMMMMMMMMMMMMMMMLLLLLLLLLLLLLLLNNNNNNNNNNNNNNNNNNNSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
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