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Retaining Water

Statement

 Goal

François designs above-ground swimming pools for the bourgeoisie. His designs are represented by an NxN grid of letters, with heights ranging from A=1 to Z=26. Find the volume of water each pool can hold.
Input
Line 1: The size N of the grid.
Next N lines: The grid values.
Output
The volume of water that the pool can hold. Outside the pool the height is 0, so no water is held on the cells at the edge of the pool. The water does not leak diagonally. You can think of the puzzle as a bunch of blocks, take a look at the cover picture for illustration.
Constraints
10 ≤ N ≤ 40
Example
Input
10
ZZZZZZZZZZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZAAAAAAAAZ
ZZZZZZZZZZ
Output
1600

Tags

Difficulty
Easy

Test cases
Test 1 Test
Input
10 ZZZZZZZZZZ ZAAAAAAAAZ ZAAAAAAAAZ ZAAAAAAAAZ ZAAAAAAAAZ ZAAAAAAAAZ ZAAAAAAAAZ ZAAAAAAAAZ ZAAAAAAAAZ ZZZZZZZZZZ
Output
1600

Validator 1 Validator
Input
10 ZZZZZZZZZZ RAAAAZEEEZ RAAAAZEEEZ RAAAAZEEEZ RAAAAZEEEZ RAAAAAEEEZ RAAAAZEEEZ RAAAAZEEEZ QAAAAZEEEZ ZZZZZZZZZZ
Output
816

Test 2 Test
Input
10 ZZZZZZZZZZ ZRRRRRRRRZ ZRRRRRRRRZ ZRRRRRRRRZ ZFFFFFFFFZ ZDDDDDDDDZ ZDDDDDDDDZ ZDDDDDDDDZ ZDDDDDDDDZ ZZZZZZZZZZ
Output
1056

Validator 2 Validator
Input
10 FFFFFFFFFF FRRRRRRRRF FRRRRRRRRF FRRRRRRRRF FFFFFFFFFF FDDDDDDDDF FDDDDDDDDF FDDDDDDDDF FDDDDDDDDF FFFFFFFFFF
Output
64

Test 3 Test
Input
10 XXXXXXXXXX XSSSSRAAAX XSSSSRAAAX XSSSSRAAAX XXXXXCXXXX XSSSSCBBBX XSSSSCBBBX RSSSSCBBBX XSSSSCBBBX XXXXXXXXXX
Output
449

Validator 3 Validator
Input
10 GGGGGGGGGG GAAAAAAAAG GEEEEEEEEG GFFFFFFFFG GGGGGCGGGG GDDDDDDDDG GCCCCCCCCG GBBBBBBBBG GAAAAAAAAG GGGGGGGGGG
Output
220

Test 4 Test
Input
20 DDDDDDDDDDDDDDDDDDDD DAAAAAAAAAAAABBBCCCC DAAAAAAAAAAAABBBDDDD DAAAAAAAAAAAABBBDDDD DAAAAAAAAAAAABBBEEFF GGGGGGGGGHHHIIJJEEFF GGGGGGGGGHHHIIJJEEFF KKKKKLLLLHHHIIJJMMMM KKKKKLLLLNNOOPPPMMMM QQQQRRSSSNNOOPPPTTTT QQQQRRSSSNNOOUUUTTTT VVVVRRWWWNNXXUUUYYYY VVVVRRWWWZZXXAAAYYYY VVVVBBBBBZZXXAAAYYYY VVVVBBBBBZZCCCDDEEFR GGGHHHIIIJJCCCDDEEFR GGGHHHIIIJJKKKDDEEFR GGGHHHIIIJJKKKDDEEFR LLLLLLLLLLLLLMMMMNNR FFFFFFFFFFFFFFFFFFFF
Output
368

Validator 4 Validator
Input
20 SSSSSSSSSSSSSSSSSSSS SAAAAAAAAAAAAAAAAAAS SAAAAAAAAAAAAAAAAAAS UBCCDDEEFFFGGGGHHHII UBCCDDEEFFFGGGGHHHII UBCCDDEEJJJKKKKLLLII UBCCDDEEJJJKKKKLLLII UBCCDDMMMNNNNNNLLLII UBOODDMMMPPPPPPQQQII UBOODDMMMRRRRRRQQQSS UBOOTTTUUUUUVVVQQQSS UBOOTTTUUUUUVVVQQQSS UBWWWXXXYYYYZZZAAASS UBWWWXXXYYYYZZZAAASS UBBBBCCCYYYYDDEEFFSS UBBBBCCCGGHHDDEEFFSS UBIIIIJJGGHHDDEEFFSS UBIIIIJJGGHHKKKLLLSS UBIIIIJJMMMMKKKLLLSS UUIIIIJJMMMMNNNNNNSS
Output
818

Test 5 Test
Input
30 YENZRGRNFKINMCAGFMMGJWVZZRVCWQ KKBAQPBNSWUXIDFHDZYNTOGTSAEKVS EGTLNXYWRHLLYTNGOYBLULNOIGVMFV WKNZBYVPCWLXZSESPZKIACDBLGNTJZ MUREWDLLJVTOGPOHWPGIRUDOLEGTRL LZKAVBAYBMNMOAAQGQKDCHGNOIBNNZ URHBKIZDYSCPSGEHRIGIFEUYAWLYLX YASRATWMWKORQIJYHKCYSWRLZIYBYX YCDYJTUOFHCWTEXEWIOJFUVVFSJLWL GUAWVRQETAUNHQLMARPFPFXCRRGVOI TGMCABQJLFBRCYDQMWEKZJBYBFMADN GZMUVJKJFZSEWAMIIZWPMWLOQRQJJH JOCNZHLCORENIIJQINMRKZDOKPYJNW MDGUSXCCKXWQGCFZRBDFGTCHHBFGSB QYAZGXUEUMZFUDCSGJZUFGHGUUBWIH NUVZDLUUYJYRGQSYHJJUKIAJGEKUQN CNBQBDXAFDXNMLSZUOCLOCGYKVOVNE PARZOFUPFZTGRITQXCMOZKXHCKBRMA IVOKPXQGEHOMLSWIEATJUXAEDBKUFJ XVLSZSAOWZOEQCZWBKOTWHNGFQNOQN ORYFEBJITOHJHJZHCLJNFZRGLHQRJA KZYENAUZGROOZIPCBKRBUNJWUPJRIG YNEPCOUEPQFEGGXSTLKWKJJJJORUZB GFNHOUWLRQVESEOFDMBQQDCACXLGYF EBNNJKZYYOGGVUIDIEROUTFNNSBBXB BHRKDBVBBLEMPYVOOKGUPUGAQNMBGT ZDOLHRCSCLHTIXRPCTZMFQXCRNNMUT SXBRAATOMKNRFGEMNEZKCSXMPKKMJV DKMJHUYLWSHBIXJHMXEOSTLMEXUPQB SZJSOCBQVELVOOWHGJCTSQOYNFTOKP
Output
2440

Validator 5 Validator
Input
30 UHSUTOVBICTUWRXAGJMMMZSWOMFMLU VIJVJZQRDCFEBEXUOESIMXGOGIXMMC MDKRXTCFPVNEJVAUMSZDYFYAEZPRUZ JCOOBFACVUUPKAKANZRZQSQBWDKSDR WCTUXOCTLXKZIMEKAUNZQDYQKWCNBJ GEWUPKOTYBTFTCKAGEVEYCOSGTXROL IKJXKDTHUOBXQBVKETABMFPOPFZVVN EEKLXQDEERRQUDTKLEUEYVRYMSXEOQ VKVAJXHESWTXKKOLTJPRKVJIAKLUPD JYNLLGKKWHUIJEDLURIYEFEHRHGPLC WQWOPOXESLBUANYVZHWPCEABHAJMYP IYWFKFSWDBKNHKBNJDELFZSBCNVQUS UJBNUJKTNJBDQGZYPJPJVMGPVRIVAO IUKAMFSQHXQCNTOBNFHBMVCXIGDAOI ZLLLNNOGVPLMTBMEJPHYSQZTDGXSGD SGXSNMTXEXISHHOIWREHTZQDYMCBJT WATWXZYRSGGMIPFAQXNNESGAQOIGDW CEPUNNESDUDOQGZRQOSVJZMKGYJZZI LDOTEKYKWMNQQWIMLOYPKDJKHWCLNL WBDNCGDXYXCUMAWEENXUPAJWIATRGI TXXRKLEMGIKFBFKQNPBONVYMHAGCZI CKSMYLKMEEDTGQWFTJFBYXKGKWTQZZ FJBLBDXSFEMEKDJMTKXXPRSWTOKXNU LWNIMFLYRRCANFUNRAUGGCJLHSRIIK EMOCCSVNNXFSDPRCWZBNFIFREJNSJB PDJSFYCCNCYCKANJKPJNLHCDEMQNJE AIQWUOIRSZXUJMEYKYBNWETORGPFLY TIRPUKCAVPAXLHLDJSYUCPCZWRBDVT FQNNPKNMXEOYGKMMWCYQHMXRSYSWKJ IURQPAXJFYYZMANZMCGKUZPOVLHDEK
Output
2397

Test 6 Test
Input
40 XZADHVCOMBACBBHTEYCCXJDNNLMYYDVRQSAOWNOI RZTKUWUMFVHBNEXKYVLQDRUFYAQKNIAIMJKBTGTA EHAOTIYXUEVIQOXLMWTXJTXHNEZIBUQDRHGWTJOV SMNHPIQCWIHIOHQBNMINYYUPKZWHSUFWKUMTENJA VLFBINPJBIIXNHREZHUCUEIXMDOBMRMYYFIGTYEA WRYSXJRQCGWOCBGQQORMTHLRYRQHACUUNRCHIRFV JZBZWXKXMCTICXQALXZKHNXMTGPXXTQMMLHPEHGL TTSURBLRCWGWSTVVELLVTCLJCRKTFSDBAOLGRHHN OQLAKHARLJNJDIYHWSJRETNNZOVXEDOGNFJBPSXT GZSTCXPBKPARDYSQGUUCKCSSPQAIKNVVFIXHWKUK KJIAHTGEOGFBMTCQMZFCZGGTALBHOIZDOAEAVUKX NABDPPDWUGXPMLOFHJBZJFNALQLXWNSPTCEOWDGD ELAECPECRDVSKPUWUECZONMBZONPMZVFJQKCYHLC XTFRWZHKFTZOCHDBVJZPPPHXYVBQEAWBOGEFXYIL JIBXPJDKZPLTINBAOBUBZIUSISQPQZKUXZEGFHVV BGVLWHNHYJNRMTQWWCLDGQVFNSHYDPRESKBWJMBN SUFTWVUHUNNBXLBLVPHFNUADPBZIYOCMMJTOGBRU VXUQTYNINPBJMLHPKFPDVCBYZCAKWASDPJEFYQPP FUOSGBXGUZSODPITUAYOUFGCTYOBQCRCPFQMXFHY JIHWAPIPQEKHFDULYPVKZVEOHWFZQJVKVIGIQRLI DPIWHKRZVKYOEINTAVFMPBXLVYMGDHCSZIQPELHM CJTVHFCMJBOGXWYWAHWXRASNTJFTAXCSJOELOYIN ARCQUIJKAJIPLKQNFTYQZFMMHADTCBPRQQUVJXOV OEUOOYJNXOUNFZWOOSOYCDISWAMEVFYZFTDCFDFG OTQRWRPTUSIKRRYKJVEYGSXQSEGNNPQPVKJJDWDU RBIIAEUNUCRKWZWNRLCBRVBFIOWWDBXLWTMBGFIW UWYVUNGLTPOAUIVZTFDNAVGPZWSVOIZGBDXNFWKF PRNRBRKQTKZPZRPXTJXZCACJFAKTGOVOWRXIQIEY ZEJHECJGTJYSAVCBXLKUCDVIGQQGRXNSCOFZSRZJ RVUJLHKDVNTYXCWGKPPSIWWTSOJXUYVAEVIFOXKH PGLLUAICYQRASURUOGTJNKHAXJLNOGOKXQHQYKRS NSVKBFGQFQHPCPUENNCPNWEEJUGUMVFUVXXFMQBA KTXYSCTFRGDRRFTKRQFDQTLFNFWRDOMVTQLRLIOX BQMCCWRYMHCAMSSRGRPCEPZTYIWAMYQCHSBCAKIM LTURGHLZQJZSTFXPPVBHZKKNAMTYPHCVEBFKBABY JGYXBZRDJEYUCGFYYZLZXBLUKFHMAJYIDKKWFKRE XLLTZANFRHDLEGTCSHWEJYNXNVGXJAJMXPJNVGSB WJQQOLKPVIYUFFEMFOJHTJCWASTILFGGHWUECWAJ HIQTTIUXRSIKZIBXVKMXEKQKBUGFUMEZGZXCBKQE DEHPKLWEXHGMYRYZTGHUAQVIHUZKRTVTARLKCVBN
Output
4832

Validator 6 Validator
Input
40 RIZCYCFHYQGFCJQOOSMMWYSIBRALAZPLDSNLXZBX IWOHWMEIJGFLRLNIVUGWHTVENNZFAUMDAGPNGXCD EZORYVUDOJKWAHXQAHWCWNJIHKSTZPHIELAYIEMZ JYVGWSSCUOMYDFPREUHSRRSDMDYBLMLEKAYTNZFW YWHNNYBMXYUGYDGXGQSUZVQYVDEGQDGERSROQRSC PKQCOAUVSMUXOFYRVVYKWFTIDQBYDLKSLDBBIGHY DPEXRHNOQPCWGQPLEVJRICROKUWECOMDFLKPFOWD CPAGHVHVXKPYIRFEAZJNKOSLEVKIXRYTTHATIERJ HENPMAQIBCIUFGHAPCXUUNBOBDWYLQZGWOVGVCFH BONQPLLAASOWZLRQOJOQCPQFZHOKTGDPTSRPDNPX APJEBLHZXFFYLSSVVTGFXABDCSPFDTYWMIVSOHPP PHOJPQOGMZXHMUFGAGANLLDJMSPPLHRCBHGANQKZ KTFRJWULWERMXWKAKNIUPTSXSBZVABJPYVVKNMWH DGDELIWGROSIXWWQXIJXBCQQOZJNUZQGDFCQZBRR SOJGIAITCYCGOCIPPAOABPHYJWGWKJAUXIZPTLEW RPUXKHPANSAZIPYVDAEYQOBDRRFKBKQLBECWMAQK SWKJKITMYKOVOWXGKIRREEWAQJTFSMPJPGJHGAWK DWCQBPTQNCBMZCYEUAIYABPIOPOSUZMEDDKIDASW KTAUKKDKZWNDHYVXZTRSWLTGJADZPLZLMCESKKMG PSZTKLLPIMIHLTUFFHZPJDSXEXFGUJGFAIJWIWPY ZOFNKEUPCSOFKJBTWXVKNONWRNIMYMKMITYJQZWX KCOWPKEOZZPFMGMSZBMREOCSTVEYBLFRNFPPUOFW XVGTPUGIIROLWJUFTQPFPVZLXVJKZDIEAGJAUJBE DFFVZGQLQXWFDLITZTNJAJRAUBRAYJZVTLAWKKUA XKQZPPKDBSRMUNLYPZUWYZFURDSPBEKKWZNPXNJD QONUHYSLVWKMSNYQGCXZVUQEZIGAXNJFBBSIIWSC YLDZEGGXXBGDQPRWQIKJNVOZUYXCWPPKHMQJFNJB AVLBJVRYHRROSVCXEATEUKLYHVPRTNKRBECUYTTA HETSISDPRCYOZONEJERYRPNGJXXJHSBOAPFVIUWN RYBIKJXRXKMEYAWJJUNUHYUDZUUYOJKFOIULYCTY JFSLJBQOMPPCVSCHMLCCYRYFTAVYNAHOBLZSYZZH DDTJWJCNZKUHKAPBRVUYZKPAMVACOBZDREROGCAJ XKNPWROISNJJHPWXZEKOBQXQNLATYGYIPHZAEZYL GWEIIUGQZGWELYVIDVLZUCBANUVPHDYATRWVZJWW XWZZNHYRWAPGTYNXARRICLSPPSDWFNYBDTMYHXKH EVEPSZMNPUFINFKQETQNXOPTCTYEPDIRKBTBPPCK OWBNLSDSXPZVXTZMEPCQJFYIZLBRGZODJRXAUEDJ FAWTFLHUUBPKMLIWIVSMRMYEKAKVLZMCLTYKSVPF JZANXCSSWYJMRJMCCSFZIIKMCRWUGGDGGCCZMMFM YOSSGXIKVLZNJNAAMMHXUYAMYFMVEVYQANJFGJOQ
Output
4809

Solution language

Solution

Stub generator input