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Chopsticks

ด ๋ฌธ œ๋Š”

ธฐ๋„:B(A,B,C), „ณต๋ฅ :๋ณด†ต(๋‚ฎŒ,๋ณด†ต,๋†’Œ), ๋ ˆ๋ฒจ:3(1~4)

About Chopsticks

‘ตญ—„œ๋Š” Œ‹„ ๋จน„•Œ  “ฐ€๋ฝ ๋‘ œ๋ฅผ “ฐง€๋งŒ, L”จ๋Š” กฐธˆ ๋‹ค๋ฅด๋‹ค. ธ๋Š”  “ฐ€๋„œ๋ฅผ ‚ฌšฉ•œ‹ค. …‹ ‘ •˜๋‚˜๋Š” ธด  “ฐ€๋œผ๋กœ, Œ‹„ ฟก ฐ–ด๋จนธฐ œ„•œ šฉ๋„๋กœ “ฐธ๋‹ค. ๋‘ œ˜ ผ๋ฐ˜  “ฐ€๋˜ ธธด๋Š” œ๋Œ€•œ ๋น„Š•••˜ง€๋งŒ ๋‚˜๋จธง€ •˜๋‚˜๋Š” ๋ฌดกฐฑด  œธธธฐ๋งŒ •˜๋ฉด ๋œ‹ค. ธธฐ€ ฐฐ A, B, C(A<=B<=C)์ธ ์„ธ ๊ฐœ์˜ ์ “๊ฐ€๋ฝ์ด ์žˆ์„ ๋•Œ (A-B)^2์„ ๊ณ„์‚ฐํ•˜๋ฉด ๋‘ ์ “๊ฐ€๋ฝ์ด ์ง์ด ์•ˆ ๋งž๋Š” ์ •๋„๋ฅผ ๊ตฌํ•  ์ˆ˜ ์žˆ๋‹ค.

L”จ๋Š” ˜ ƒŒŒ‹— K๋ช…˜ †๋‹˜„ ดˆ๋Œ€–ˆ๋Š”๋ฐ, ˜ Šน•œ  “ฐ€๋งˆ ๋ฐฉ๋ฒ•„ †Œœ•˜  ‹–ด„œ •ˆ๋‹ด ๋‚˜ žˆ๋‹ค.  “ฐ€๋„ K+8„Šธ(L”จ ž‹ , ๋ถ€ธ, •„๋“ค, ๋”ธ, –ด๋จธ๋‹˜, •„๋ฒ„‹˜, žฅ๋ชจ๋‹˜, žฅ–ด๋ฅธ, ธ๋ฆฌ  K๋ช…˜ †๋‹˜)๋ฅผ ค€๋น„•••œ‹ค. •˜ง€๋งŒ L”จ๋„‘— žˆ๋Š”  “ฐ€๋ฝ๋“ค ‘—๋Š” ธธฐ€ ๋‹ค๋ฅธ ฒƒด ๋งŽ๋‹ค.  “ฐ€๋ฝ๋“ค˜ ธธฐ€ ฃผ–ดกŒ„•Œ, ฐ „Šธ˜ •ˆ ๋งž๋Š”  •๋„๋ฅผ œ†Œ™”•˜๋ฉด„œ K+8„Šธ๋ฅผ ๋งŒ๋“ค–ด๋‚ด๋Š” ๋ฐฉ๋ฒ•„ ฐพ•„••œ‹ค.

Input

ฒซงธ „—๋Š” …ŒŠคŠธ ผ€Šค˜ œˆ˜๋ฅผ ๋‚˜ƒ€๋‚ด๋Š”  •ˆ˜ T(1<=T<=20)๊ฐ€ ์ž…๋ ฅ๋œ๋‹ค. ๊ฐ ํ…Œ์ŠคํŠธ ์ผ€์ด์Šค์˜ ์ฒซ์งธ์ค„์—๋Š” ์†๋‹˜ ์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ด๋Š” ์ •์ˆ˜(0<=K<=1,000)์™€ ์ “๊ฐ€๋ฝ์˜ ๊ฐœ์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ด๋Š” ์ •์ˆ˜ N(3K+24<=N<=5,000)์ด ์ž…๋ ฅ๋œ๋‹ค. ๊ทธ ๋ฐ‘์œผ๋กœ๋Š” ๊ฐ ์ “๊ฐ€๋ฝ์˜ ๊ธธ์ด๋ฅผ ๋‚˜ํƒ€๋‚ด๋Š” N๊ฐœ์˜ ์–‘์˜ ์ •์ˆ˜ Li(1 <= Li <= 32,000)๊ฐ€ ์˜ค๋ฆ„์ฐจ์ˆœ์œผ๋กœ ์ž…๋ ฅ๋œ๋‹ค.

output

ž…๋ ฅ๋œ ฐ …ŒŠคŠธ ผ€Šค— ๋Œ€••œ „— •˜๋‚˜”ฉ, ๋ชจ๋“   “ฐ€๋„Šธ˜ •ˆ ๋งž๋Š”  •๋„˜ •ฐ€ง€๋Š” œ†Œ ฐ’„ œ •œ‹ค.

Sample Input

~cpp 
1
1 40
1 8 10 16 19 22 27 33 36 40 47 52 56 61 63 71 72 75 81 81 84 88 96 98 103 110 113 118 124 128 129 134 134 139 148 157 157 160 162 164

Sample Output

~cpp 
23

Note

œ„˜ ž…๋ ˜ˆ— ๋Œ€•„œ‹Œณผ ฐ™€ ‹œผ๋กœ  “ฐ€๋„Šธ๋ฅผ ตฌ„•  ˆ˜ žˆ๋‹ค.
8,10,16 ; 19,22,27; 61,63,75; 71,72,88; 81,81,84; 96,98,103; 128,129,148; 134,134,139; 157,157,160

’€

ž‘„ž ‚ฌšฉ–ธ–ด œ๋ฐœ‹œ„ ฝ”๋“œ
๋ฌธ๋ณดฐฝ C++ 4‹œ„ Chopsticks/๋ฌธ๋ณดฐฝ

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