maual input: 8 qmiqwnhwnrckeirepjgv 2 5 5 4 2 1 5 5 2 1 2 4 4 1 5 4 4 4 1 1 1 5 1 4 4 1 4 4 1 4 5 1 1 1 1 5 1 4 4 5 4 4 5 4 5 1 5 5 1 4 4 4 1 1 1 4 4 5 4 5 5 1 4 4

output: qqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjggvv 2 jjnnrrjjddmmssddmmiixxppvvrriivvkkqqttee 5 qqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjggvv 5 vqqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjggv 4 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 2 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 eettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjjee 5 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 5 qqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvvv 2 vvvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqq 1 vvvvvvvvggggggggjjjjjjjjppppppppeeeeeeeerrrrrrrriiiiiiiieeeeeeeekkkkkkkkccccccccrrrrrrrrnnnnnnnnwwwwwwwwhhhhhhhhnnnnnnnnwwwwwwwwqqqqqqqqiiiiiiiimmmmmmmmqqqqqqqq 2 qvvvvvvvvggggggggjjjjjjjjppppppppeeeeeeeerrrrrrrriiiiiiiieeeeeeeekkkkkkkkccccccccrrrrrrrrnnnnnnnnwwwwwwwwhhhhhhhhnnnnnnnnwwwwwwwwqqqqqqqqiiiiiiiimmmmmmmmqqqqqqq 4 qqvvvvvvvvggggggggjjjjjjjjppppppppeeeeeeeerrrrrrrriiiiiiiieeeeeeeekkkkkkkkccccccccrrrrrrrrnnnnnnnnwwwwwwwwhhhhhhhhnnnnnnnnwwwwwwwwqqqqqqqqiiiiiiiimmmmmmmmqqqqqq 4 qqqqqqmmmmmmmmiiiiiiiiqqqqqqqqwwwwwwwwnnnnnnnnhhhhhhhhwwwwwwwwnnnnnnnnrrrrrrrrcccccccckkkkkkkkeeeeeeeeiiiiiiiirrrrrrrreeeeeeeeppppppppjjjjjjjjggggggggvvvvvvvvqq 1 jjjjjjnnnnnnnnrrrrrrrrjjjjjjjjddddddddmmmmmmmmssssssssddddddddmmmmmmmmiiiiiiiixxxxxxxxppppppppvvvvvvvvrrrrrrrriiiiiiiivvvvvvvvkkkkkkkkqqqqqqqqtttttttteeeeeeeejj 5 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 4 vqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvv 4 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 4 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 1 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 eettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjjee 5 eejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqttttee 1 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 4 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 4 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 vvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqv 4 vvvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqq 4 qqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvvv 1 vqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvv 4 ejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttteee 5 vevjgjgjgjgnjnjnjnjrprprprpjejejejedrdrdrdrmimimimisesesesedkdkdkdkmcmcmcmciriririrxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 1 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 1 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 eettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjjee 5 eejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqttttee 1 eeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttte 4 eeeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttt 4 ziznpspstwtaaeaeswsasusubdbvwbwbhmhgdpdpzlzufjfjxbxhznznvjvuslslfyfhmwmwscsykbkbrirxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 5 vvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqv 4 vvvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqq 4 eeeettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjj 5 jeeeettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjj 4 qvvvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqq 5 qqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvvvq 1 jjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttteeeej 5 iriacfcjknkjjnjhvzvmegemtvtyzezntytolxlmwiwjuyueswsyqeqvdrdpngnvpipxcmcplvlcofokrirxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 5 vqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvv 1 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 4 vvvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggv 4 vvvvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjgggg 4 ggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvvvv 1 vvvvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjgggg 1 ggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvvvv 1 iriacfcjknkjjnjhvzvmegemtvtyzezntytolxlmwiwjuyueswsyqeqvdrdpngnvpipxcmcplvlcofokrirxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 4 null 4 null 5 null 4 null 5 null 5 null 1 null 4 null 4 qqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjggvv 2 qqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvvv 2 vqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvv 4 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 4 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 vvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqv 4 vqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvv 1 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 4 jjnnrrjjddmmssddmmiixxppvvrriivvkkqqttee 5 eettqqkkvviirrvvppxxiimmddssmmddjjrrnnjj 1 jeettqqkkvviirrvvppxxiimmddssmmddjjrrnnj 4 jnnrrjjddmmssddmmiixxppvvrriivvkkqqtteej 1 jeettqqkkvviirrvvppxxiimmddssmmddjjrrnnj 1 jjeettqqkkvviirrvvppxxiimmddssmmddjjrrnn 4 njjeettqqkkvviirrvvppxxiimmddssmmddjjrrn 4 iezuujfccwsddqyhhlrlltkvvztkkzoiizqwweierrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 5 qqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjggvv 5 qqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvvv 2 vvvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqq 1 qvvvvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqq 4 qqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvvvvq 1 jjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttteeeej 5 jjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttteeee 4 iezuujfccwsddqyhhlrlltkvvztkkzoiizqwweierrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 4 vqqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjggv 4 vvqqmmiiqqwwnnhhwwnnrrcckkeeiirreeppjjgg 4 ggjjppeerriieekkccrrnnwwhhnnwwqqiimmqqvv 1 vggjjppeerriieekkccrrnnwwhhnnwwqqiimmqqv 4 ettqqkkvviirrvvppxxiimmddssmmddjjrrnnjje 5 eettqqkkvviirrvvppxxiimmddssmmddjjrrnnjj 4 jeettqqkkvviirrvvppxxiimmddssmmddjjrrnnj 4 ridnnzvmmrnllhpccagiibshhcwcclalliznnrvnrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 5 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 2 vvvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggv 4 vggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvvv 1 vvvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggv 1 vggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvvv 1 ettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjjeee 5 eeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttte 1 vmhwwiezzeaccyglljpllevttoiuudsoolczzdhvzzkzzzhzzztzzzdzzzizzzmzzzkzzztzzzwzzzoz 5 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 1 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 1 eejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqttttee 5 eeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttte 4 eeeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttt 4 ttttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjjeeee 1 eeeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttt 1 vemehewewjijejzjznenancncryrgrlrljjjpjljldedvdtdtmomimumusdsssosodldcdzdzmdmhmvmzizikizizxzxhxzxzpzptpzpzvzvdvzvzrzrirzrzizimizizvzvkvzvzkzktkzkzqzqwqzqztztotzt 1 eettttqqqqkkkkvvvviiiirrrrvvvvppppxxxxiiiimmmmddddssssmmmmddddjjjjrrrrnnnnjjjjee 5 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 5 vvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggvv 1 eejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqttttee 5 eeejjjjnnnnrrrrjjjjddddmmmmssssddddmmmmiiiixxxxppppvvvvrrrriiiivvvvkkkkqqqqtttte 4 vvvqqqqmmmmiiiiqqqqwwwwnnnnhhhhwwwwnnnnrrrrcccckkkkeeeeiiiirrrreeeeppppjjjjggggv 5 vggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvvv 1 vemehewewjijejzjznenancncryrgrlrljjjpjljldedvdtdtmomimumusdsssosodldcdzdzmdmhmvmzizikizizxzxhxzxzpzptpzpzvzvdvzvzrzrirzrzizimizizvzvkvzvzkzktkzkzqzqwqzqztztotzt 4 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 5 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 4 vvggggjjjjppppeeeerrrriiiieeeekkkkccccrrrrnnnnwwwwhhhhnnnnwwwwqqqqiiiimmmmqqqqvv 4 vevjgjgjgjgnjnjnjnjrprprprpjejejejedrdrdrdrmimimimisesesesedkdkdkdkmcmcmcmciriririrxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 1 ziznpspstwtaaeaeswsasusubdbvwbwbhmhgdpdpzlzufjfjxbxhznznvjvuslslfyfhmwmwscsykbkbrirxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 5 iriacfcjknkjjnjhvzvmegemtvtyzezntytolxlmwiwjuyueswsyqeqvdrdpngnvpipxcmcplvlcofokrirxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 5 iriacfcjknkjjnjhvzvmegemtvtyzezntytolxlmwiwjuyueswsyqeqvdrdpngnvpipxcmcplvlcofokrirxnxnxnxnpwpwpwpwvhvhvhvhrnrnrnrniwiwiwiwvqvqvqvqkikikikiqmqmqmqmtqtqtqtqeveve 4 null 4 vemehewewjijejzjznenancncryrgrlrljjjpjljldedvdtdtmomimumusdsssosodldcdzdzmdmhmvmzizikizizxzxhxzxzpzptpzpzvzvdvzvzrzrirzrzizimizizvzvkvzvzkzktkzkzqzqwqzqztztotzt

final answer: vemehewewjijejzjznenancncryrgrlrljjjpjljldedvdtdtmomimumusdsssosodldcdzdzmdmhmvmzizikizizxzxhxzxzpzptpzpzvzvdvzvzrzrirzrzizimizizvzvkvzvzkzktkzkzqzqwqzqztztotzt