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⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢠⡶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣤⠶⣚⢟⡲⠶⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢥⡛⡜⢮⡱⣋⠖⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⢔⣂⣦⠄⢠⣔⣢⡤⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⢾⣿⡽⢶⣷⣻⡿⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⡔⢂⡤⠀⣤⠂⢠⡄⣸⠀⠀⠀⠀⠀
⠀⢀⣀⡀⠀⢧⡀⠐⠤⠤⠤⠤⠀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠚⣟⠁⣀⣩⡖⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⣄⠀⠢⠤⠤⠤⠄⢀⣠⠋⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣶⣦⣝⣶⡤⠤⠔⣒⢊⡉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⢦⣌⣛⣛⣋⣤⣴⠻⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣲⣬⣳⣦⠤⠤⢒⡒⣉⠙⡄⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⢿⠯⣇⠲⢒⣊⢉⢩⠤⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡘⣧⠈⠢⠌⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⡿⢽⡐⠖⣒⡉⡉⣥⠤⣿⡆⠀⠀⠀⠀
⠀⠀⠈⣏⡿⢿⡗⣿⢋⠬⠭⡤⣤⣶⠎⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣧⠟⣭⢛⡭⢻⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣱⠿⣿⢳⡟⣉⠭⢥⢤⣴⡶⢼⠷⡄⠀⠀⠀
⠀⠀⠀⢻⣿⠶⣽⣿⡼⣤⣤⡷⢳⠞⠋⣡⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣯⡙⢦⢫⡜⡭⢿⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠘⣟⠷⢮⣿⣧⢣⣤⣼⠞⡶⠛⠉⣴⠇⠀⠀⠀
⠀⠀⠀⠀⠉⠓⠪⣭⣧⣽⢯⣥⠶⠾⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠧⠽⡮⠵⠮⢵⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢩⣽⣬⡿⣭⡴⠶⠿⢻⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⡿⡆⠀⠀⣾⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⢀⡼⠁⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⢷⠀⠀⢰⡷⡞⠀⠀⠀⠀⠀
⣀⣀⣀⣒⣒⣒⣒⣒⣒⣓⣃⣀⣤⣠⣜⣒⣒⣂⣒⣀⣀⣀⣐⣀⣀⣂⣶⣶⣞⣘⣛⣐⣒⣒⣒⣒⣒⣊⣓⣂⣒⣀⣀⣀⣀⣐⣂⣒⣒⣒⣒⣐⣒⣚⣚⣀⣠⣀⣆⣓⣒⣒⣒⣀⣂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⣶⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠈⠉⠢⡄⠀⠀⠀⠀⠀⠀⢸⡄⢰⠷⣤⣠⡤⢾⠷⢦⣿⢹⡾⢷⡛⣏⣛⢳⢶⡯⣽⠂⠀⠀⠀⣠⠖⠋⠁⠀⠀⠉⠑⢤⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⡔⠸⣷⡟⡱⢎⢧⡛⣬⢻⣾⡙⣦⡙⢦⡙⣎⠶⣽⣿⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢀⠀⠀⢧⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠶⠅⠲⠀⠰⠶⠒⠆⢠⡇⠀⠀⠀⠀⠀⢸⡇⢠⣿⣵⣽⣿⡦⣽⣶⣿⡧⣿⣾⡿⠳⣿⣞⣿⣻⣿⠀⠀⠀⣇⠰⠆⠐⠖⠀⠿⢀⠸⠂⣼⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⢠⣤⣀⠀⠳⣄⠈⠒⠒⠒⠒⢀⣤⡋⠀⠀⠀⠀⠀⠀⢸⡧⢸⣿⠲⢽⠛⠀⠈⢋⣿⣇⠓⢛⣁⣀⣨⡽⠋⢹⣿⢤⣄⡀⠘⢦⡀⠑⠒⠒⠒⠂⣀⣴⠁⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⣿⣿⣭⣶⣬⡷⢶⡖⢺⣭⣭⠅⢳⡀⠀⠀⠀⠀⠀⢸⡇⠸⡿⣳⢄⣙⠿⠾⢟⣻⡿⡷⣦⢍⣟⣋⣥⣴⠿⠃⢸⣿⣯⡱⣶⣽⠶⠖⠒⣬⣉⡥⠉⣆⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢹⣾⣿⣯⡳⡇⣉⢭⣥⠠⡰⠒⢺⣧⠀⠀⠀⠀⠀⢸⡆⠀⢁⣼⢸⡏⠙⢍⠏⣿⣿⡇⣿⠀⠑⠌⣸⣿⣆⠀⠈⣷⡿⣿⣝⠾⣈⣋⣭⡄⢄⠖⠚⣿⡆⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠘⣧⣟⠻⣏⣷⢡⠔⠲⡄⠶⢿⣛⡟⡗⠀⠀⠀⠀⢸⣧⣰⠋⢸⢸⣓⢖⡲⣾⢿⡏⣧⡯⡹⣍⢯⢹⣷⠘⢧⡀⢻⣽⡛⢿⣻⡄⡤⠒⢶⢒⠾⡿⣹⢻⡂⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠳⣟⠳⢾⡿⡜⣲⣾⡟⠹⠛⣁⣡⡟⠀⠀⠀⠀⢸⡿⠃⠀⢸⡟⡜⡎⡵⣙⢞⣧⡟⣱⠳⣜⠪⣇⢻⡄⠀⠉⠘⢟⡚⠶⣿⣧⢳⣶⣾⠋⠟⢋⣈⣾⠁⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑⡾⠷⣷⠷⠶⠟⢛⠋⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣮⣵⣙⣶⣩⣮⡽⠿⠦⡿⠴⠯⠼⣿⠃⠀⠀⠀⠀⠈⠉⣲⠾⢶⡷⠶⠾⠛⡛⢻⠃⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢠⡏⡆⠀⠀⠿⢻⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⢀⡼⠀⠀⠀⠈⠳⣄⡼⠃⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠏⠀⢸⢱⠀⠀⠸⠟⡇⠀⠀⠀⠀⠀
⡁⠀⠀⠀⠀⠀⠀⠀⠤⠌⠤⠉⠌⠥⠡⠤⠴⠦⠌⠤⠤⠶⠤⠀⠀⠬⠬⠤⠦⠧⠍⠤⠬⠤⠧⠴⠦⠩⠤⠥⠼⠤⠤⠤⠉⠭⠴⠦⠼⠤⠁⠈⠭⠩⠭⠤⠴⠤⠦⠥⠦⠦⠤⠤⡘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣧⠀⠀⢠⣾⠀⠀⣀⣤⣄⡀⣴⣇⣠⣿⢀⣰⡷⣾⣃⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢰⡿⢀⣤⠆⢀⣠⣾⠂⠀⠀⢀⣀⡀⠀⢀⠀⣾⠃⢠⣾⢀⣀⡀⢰⣟⢀⡀⠀⣀⣄⡃
⣿⡶⢞⡻⢭⣛⠿⢿⣍⣿⣹⡿⣛⣯⢽⣿⡛⢯⡝⣹⢛⠿⣭⣻⠉⠀⠀⠀⠐⣏⢷⡾⣛⠯⣝⡛⠿⣾⣏⣽⢫⢟⡳⢶⣯⣹⢟⡶⣟⢻⡙⢯⣻⡏⣿⢟⡻⣙⠯⣿⣹⡿⢟⣫⠅
⡿⣘⢧⡙⢦⡝⣪⢇⣿⣿⡟⡴⢣⣿⣾⢣⣝⢦⡙⢦⣋⡞⣽⣿⠤⢀⠀⢀⠤⣿⡟⡴⣩⠞⡴⣩⢳⣌⣿⡿⡜⠮⣜⠣⣿⣿⣾⠹⣌⡧⣙⢦⣙⣿⡏⢮⡱⣍⠞⣽⣾⡙⢮⣜⠆
⣗⣿⣿⡟⠳⣾⢿⣿⣿⣿⢟⡺⣿⣿⡗⣷⣿⣗⠛⣷⠾⣿⣻⣿⣉⠜⠀⠡⢉⣿⢗⣿⣿⡟⠳⡷⢿⣾⣿⡿⠚⣷⠿⣿⣻⣿⣿⡿⣿⣗⠛⢷⠿⣿⢺⣿⣿⡚⠻⣿⡗⣻⢿⣿⡆
⣏⠀⣉⣀⣀⣨⡍⠉⣸⣿⣏⠀⢉⣿⣧⡁⢫⣁⣀⣠⡿⠉⢸⣿⠈⠁⠀⠀⣛⣿⣍⠈⣍⣀⣀⣬⡏⠉⣼⣇⣀⣨⡾⠉⢸⣿⣧⡁⢯⣅⣀⣠⣿⣿⣌⠈⣍⣀⣀⣽⣧⡁⠩⣧⣆
⣿⠷⡤⢭⡿⢭⣴⣾⣿⣿⣫⣷⣦⢿⣯⡟⣦⠬⡽⠭⣤⣶⣿⣿⠛⣛⣩⢭⢤⠿⢸⢳⡤⢭⠿⢭⣴⡾⣿⢭⡽⠯⣤⣶⠟⠻⠃⡟⣦⠬⡭⠯⢴⣿⣿⢳⡤⢭⠭⢿⣷⡟⣦⠼⡇
⠿⠀⣷⠀⣑⣊⣼⡿⡷⡴⢻⡇⣿⣀⣟⡇⣿⣀⣈⣊⣸⣿⣯⣃⡄⢩⣥⠔⠢⣴⢻⢸⣇⠈⢱⣂⣾⡿⣿⡀⠑⣊⣸⣿⣇⣠⠞⡇⣿⣀⣁⣊⣸⣿⣿⢺⣇⣀⣑⣡⣿⡇⣿⣀⠃
⡿⢧⡫⡝⡜⡦⢽⣿⣿⢿⣭⣷⣿⢏⡖⣧⡟⢦⠳⣜⢲⣿⣿⣿⣧⡖⠚⢳⣼⣿⣻⣾⢭⡙⢧⡚⣼⣷⡿⢯⡝⢦⢳⣯⢸⢧⣀⣷⡏⢶⡱⢪⡿⣿⣿⣼⢣⠞⣼⡏⣾⣥⡧⣛⠆
⣿⡏⡵⡹⣜⡱⣋⢿⡬⢣⣛⡯⡜⢮⡜⣯⡙⣎⠳⣌⢧⡹⡗⠿⢿⠹⣭⠿⠛⢙⣻⡏⢶⡙⢦⡹⣌⢿⠼⣩⢛⡬⢣⢻⡌⠀⠈⣯⡙⢦⡙⢧⡹⢹⣿⢣⠏⡞⣬⠳⡜⣿⢰⡹⠂
⣯⣷⣷⣷⠮⠷⠾⣾⡷⣧⣾⣷⢿⡶⢿⣷⠿⣾⠷⠾⣶⢿⡋⢹⠒⠳⣟⠛⠛⢛⣛⢻⢶⡿⢶⣷⣾⣾⣿⣶⠯⠞⠷⢿⡃⠀⠀⠓⠛⡶⠟⠶⡿⢿⡿⠷⣿⠞⠖⠳⠿⣷⠓⣿⡅
⡇⣀⡞⠉⢳⡀⣰⠏⢳⣤⠋⣨⢿⡀⣠⣟⣿⠁⢳⡄⠈⣧⠹⡞⠀⢸⢿⡀⠀⠘⠟⣹⠟⠀⣰⠋⠀⢈⣿⠉⢳⡄⠀⠀⢹⡄⠀⣀⡞⠁⣠⠞⠁⠀⢹⣦⠏⢳⡀⠀⠀⣈⣿⡉⠆
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠍⠭⠉⠍⠩⠩⠍⠭⠩⠍⠩⠍⠍⠭⠩⠍⠩⠍⠍⠩⠩⠍⠭⠩⠍⠭⠩⠍⠭⠉⠭⠩⠍⠭⠩⠍⠭⠩⠍⠭⠩⠍⠭⠉⠭⢭⠉⠉⠉⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀ ⡴⠊⠉⠀ ⠀⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀ ⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠁⠀⠀ ОПЯТЬ ⠀⠀⠈⢆ ⣇⠘⠯⠽⠂⠀⠻⠯⠵⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⢽⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀ КАКОЙ-ТО ⠀⢸⠟⠚⢦⡐⠒⠛⠛⠛⢃⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀ ИВЕНТ ⡜⠀⠀⢠⢾⠑⠒⠒⠊⠉⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣸⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢄⠀⠀ ⠀⠀⡴⠁⠀⢀⡏⢸⠀⠀⠀⠀⠀⠀⡇⣷⠀⠀⢠⣤⡤⢤⠤⣄⠀⠀⠀⠀⠀⢀⡼⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠤⣀⣀⠀⠀⠀⠀⣀⡠⠔⠋⠀⣷⣦⣸⠁⢸⣀⠀⠀⠀⠀⢈⣇⡿⠀⠀⡇⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⡟⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⢰⣟⣿⣽⣷⡼⡅⠉⠉⠉⠉⢉⡏⢷⡤⣶⣷⣶⣦⡤⣤⡼⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣽⠇⢹⠖⣶⠖⠒⡾⠟⠋⠙⡏⠉⠉⢉⣍⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⢀⡀⣀⢀⡀⣀⢀⡀⣀⣀⡀⣀⠀⢈⡿⣷⣙⣿⣆⣸⡃⢀⣀⣀⡇⢀⣀⣀⣸⣀⣀⣙⣋⣇⢀⢀⡀⣀⣀⣀⣀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢠⡶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣤⠶⣚⢟⡲⠶⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢥⡛⡜⢮⡱⣋⠖⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⢔⣂⣦⠄⢠⣔⣢⡤⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⢾⣿⡽⢶⣷⣻⡿⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⡔⢂⡤⠀⣤⠂⢠⡄⣸⠀⠀⠀⠀⠀
⠀⢀⣀⡀⠀⢧⡀⠐⠤⠤⠤⠤⠀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠚⣟⠁⣀⣩⡖⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⣄⠀⠢⠤⠤⠤⠄⢀⣠⠋⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣶⣦⣝⣶⡤⠤⠔⣒⢊⡉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⢦⣌⣛⣛⣋⣤⣴⠻⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣲⣬⣳⣦⠤⠤⢒⡒⣉⠙⡄⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⢿⠯⣇⠲⢒⣊⢉⢩⠤⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡘⣧⠈⠢⠌⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⡿⢽⡐⠖⣒⡉⡉⣥⠤⣿⡆⠀⠀⠀⠀
⠀⠀⠈⣏⡿⢿⡗⣿⢋⠬⠭⡤⣤⣶⠎⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣧⠟⣭⢛⡭⢻⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣱⠿⣿⢳⡟⣉⠭⢥⢤⣴⡶⢼⠷⡄⠀⠀⠀
⠀⠀⠀⢻⣿⠶⣽⣿⡼⣤⣤⡷⢳⠞⠋⣡⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣯⡙⢦⢫⡜⡭⢿⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠘⣟⠷⢮⣿⣧⢣⣤⣼⠞⡶⠛⠉⣴⠇⠀⠀⠀
⠀⠀⠀⠀⠉⠓⠪⣭⣧⣽⢯⣥⠶⠾⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠧⠽⡮⠵⠮⢵⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢩⣽⣬⡿⣭⡴⠶⠿⢻⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⡿⡆⠀⠀⣾⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⢀⡼⠁⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⢷⠀⠀⢰⡷⡞⠀⠀⠀⠀⠀
⣀⣀⣀⣒⣒⣒⣒⣒⣒⣓⣃⣀⣤⣠⣜⣒⣒⣂⣒⣀⣀⣀⣐⣀⣀⣂⣶⣶⣞⣘⣛⣐⣒⣒⣒⣒⣒⣊⣓⣂⣒⣀⣀⣀⣀⣐⣂⣒⣒⣒⣒⣐⣒⣚⣚⣀⣠⣀⣆⣓⣒⣒⣒⣀⣂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⣶⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠈⠉⠢⡄⠀⠀⠀⠀⠀⠀⢸⡄⢰⠷⣤⣠⡤⢾⠷⢦⣿⢹⡾⢷⡛⣏⣛⢳⢶⡯⣽⠂⠀⠀⠀⣠⠖⠋⠁⠀⠀⠉⠑⢤⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⡔⠸⣷⡟⡱⢎⢧⡛⣬⢻⣾⡙⣦⡙⢦⡙⣎⠶⣽⣿⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢀⠀⠀⢧⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠶⠅⠲⠀⠰⠶⠒⠆⢠⡇⠀⠀⠀⠀⠀⢸⡇⢠⣿⣵⣽⣿⡦⣽⣶⣿⡧⣿⣾⡿⠳⣿⣞⣿⣻⣿⠀⠀⠀⣇⠰⠆⠐⠖⠀⠿⢀⠸⠂⣼⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⢠⣤⣀⠀⠳⣄⠈⠒⠒⠒⠒⢀⣤⡋⠀⠀⠀⠀⠀⠀⢸⡧⢸⣿⠲⢽⠛⠀⠈⢋⣿⣇⠓⢛⣁⣀⣨⡽⠋⢹⣿⢤⣄⡀⠘⢦⡀⠑⠒⠒⠒⠂⣀⣴⠁⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⣿⣿⣭⣶⣬⡷⢶⡖⢺⣭⣭⠅⢳⡀⠀⠀⠀⠀⠀⢸⡇⠸⡿⣳⢄⣙⠿⠾⢟⣻⡿⡷⣦⢍⣟⣋⣥⣴⠿⠃⢸⣿⣯⡱⣶⣽⠶⠖⠒⣬⣉⡥⠉⣆⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢹⣾⣿⣯⡳⡇⣉⢭⣥⠠⡰⠒⢺⣧⠀⠀⠀⠀⠀⢸⡆⠀⢁⣼⢸⡏⠙⢍⠏⣿⣿⡇⣿⠀⠑⠌⣸⣿⣆⠀⠈⣷⡿⣿⣝⠾⣈⣋⣭⡄⢄⠖⠚⣿⡆⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠘⣧⣟⠻⣏⣷⢡⠔⠲⡄⠶⢿⣛⡟⡗⠀⠀⠀⠀⢸⣧⣰⠋⢸⢸⣓⢖⡲⣾⢿⡏⣧⡯⡹⣍⢯⢹⣷⠘⢧⡀⢻⣽⡛⢿⣻⡄⡤⠒⢶⢒⠾⡿⣹⢻⡂⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠳⣟⠳⢾⡿⡜⣲⣾⡟⠹⠛⣁⣡⡟⠀⠀⠀⠀⢸⡿⠃⠀⢸⡟⡜⡎⡵⣙⢞⣧⡟⣱⠳⣜⠪⣇⢻⡄⠀⠉⠘⢟⡚⠶⣿⣧⢳⣶⣾⠋⠟⢋⣈⣾⠁⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑⡾⠷⣷⠷⠶⠟⢛⠋⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣮⣵⣙⣶⣩⣮⡽⠿⠦⡿⠴⠯⠼⣿⠃⠀⠀⠀⠀⠈⠉⣲⠾⢶⡷⠶⠾⠛⡛⢻⠃⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢠⡏⡆⠀⠀⠿⢻⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⢀⡼⠀⠀⠀⠈⠳⣄⡼⠃⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠏⠀⢸⢱⠀⠀⠸⠟⡇⠀⠀⠀⠀⠀
⡁⠀⠀⠀⠀⠀⠀⠀⠤⠌⠤⠉⠌⠥⠡⠤⠴⠦⠌⠤⠤⠶⠤⠀⠀⠬⠬⠤⠦⠧⠍⠤⠬⠤⠧⠴⠦⠩⠤⠥⠼⠤⠤⠤⠉⠭⠴⠦⠼⠤⠁⠈⠭⠩⠭⠤⠴⠤⠦⠥⠦⠦⠤⠤⡘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣧⠀⠀⢠⣾⠀⠀⣀⣤⣄⡀⣴⣇⣠⣿⢀⣰⡷⣾⣃⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢰⡿⢀⣤⠆⢀⣠⣾⠂⠀⠀⢀⣀⡀⠀⢀⠀⣾⠃⢠⣾⢀⣀⡀⢰⣟⢀⡀⠀⣀⣄⡃
⣿⡶⢞⡻⢭⣛⠿⢿⣍⣿⣹⡿⣛⣯⢽⣿⡛⢯⡝⣹⢛⠿⣭⣻⠉⠀⠀⠀⠐⣏⢷⡾⣛⠯⣝⡛⠿⣾⣏⣽⢫⢟⡳⢶⣯⣹⢟⡶⣟⢻⡙⢯⣻⡏⣿⢟⡻⣙⠯⣿⣹⡿⢟⣫⠅
⡿⣘⢧⡙⢦⡝⣪⢇⣿⣿⡟⡴⢣⣿⣾⢣⣝⢦⡙⢦⣋⡞⣽⣿⠤⢀⠀⢀⠤⣿⡟⡴⣩⠞⡴⣩⢳⣌⣿⡿⡜⠮⣜⠣⣿⣿⣾⠹⣌⡧⣙⢦⣙⣿⡏⢮⡱⣍⠞⣽⣾⡙⢮⣜⠆
⣗⣿⣿⡟⠳⣾⢿⣿⣿⣿⢟⡺⣿⣿⡗⣷⣿⣗⠛⣷⠾⣿⣻⣿⣉⠜⠀⠡⢉⣿⢗⣿⣿⡟⠳⡷⢿⣾⣿⡿⠚⣷⠿⣿⣻⣿⣿⡿⣿⣗⠛⢷⠿⣿⢺⣿⣿⡚⠻⣿⡗⣻⢿⣿⡆
⣏⠀⣉⣀⣀⣨⡍⠉⣸⣿⣏⠀⢉⣿⣧⡁⢫⣁⣀⣠⡿⠉⢸⣿⠈⠁⠀⠀⣛⣿⣍⠈⣍⣀⣀⣬⡏⠉⣼⣇⣀⣨⡾⠉⢸⣿⣧⡁⢯⣅⣀⣠⣿⣿⣌⠈⣍⣀⣀⣽⣧⡁⠩⣧⣆
⣿⠷⡤⢭⡿⢭⣴⣾⣿⣿⣫⣷⣦⢿⣯⡟⣦⠬⡽⠭⣤⣶⣿⣿⠛⣛⣩⢭⢤⠿⢸⢳⡤⢭⠿⢭⣴⡾⣿⢭⡽⠯⣤⣶⠟⠻⠃⡟⣦⠬⡭⠯⢴⣿⣿⢳⡤⢭⠭⢿⣷⡟⣦⠼⡇
⠿⠀⣷⠀⣑⣊⣼⡿⡷⡴⢻⡇⣿⣀⣟⡇⣿⣀⣈⣊⣸⣿⣯⣃⡄⢩⣥⠔⠢⣴⢻⢸⣇⠈⢱⣂⣾⡿⣿⡀⠑⣊⣸⣿⣇⣠⠞⡇⣿⣀⣁⣊⣸⣿⣿⢺⣇⣀⣑⣡⣿⡇⣿⣀⠃
⡿⢧⡫⡝⡜⡦⢽⣿⣿⢿⣭⣷⣿⢏⡖⣧⡟⢦⠳⣜⢲⣿⣿⣿⣧⡖⠚⢳⣼⣿⣻⣾⢭⡙⢧⡚⣼⣷⡿⢯⡝⢦⢳⣯⢸⢧⣀⣷⡏⢶⡱⢪⡿⣿⣿⣼⢣⠞⣼⡏⣾⣥⡧⣛⠆
⣿⡏⡵⡹⣜⡱⣋⢿⡬⢣⣛⡯⡜⢮⡜⣯⡙⣎⠳⣌⢧⡹⡗⠿⢿⠹⣭⠿⠛⢙⣻⡏⢶⡙⢦⡹⣌⢿⠼⣩⢛⡬⢣⢻⡌⠀⠈⣯⡙⢦⡙⢧⡹⢹⣿⢣⠏⡞⣬⠳⡜⣿⢰⡹⠂
⣯⣷⣷⣷⠮⠷⠾⣾⡷⣧⣾⣷⢿⡶⢿⣷⠿⣾⠷⠾⣶⢿⡋⢹⠒⠳⣟⠛⠛⢛⣛⢻⢶⡿⢶⣷⣾⣾⣿⣶⠯⠞⠷⢿⡃⠀⠀⠓⠛⡶⠟⠶⡿⢿⡿⠷⣿⠞⠖⠳⠿⣷⠓⣿⡅
⡇⣀⡞⠉⢳⡀⣰⠏⢳⣤⠋⣨⢿⡀⣠⣟⣿⠁⢳⡄⠈⣧⠹⡞⠀⢸⢿⡀⠀⠘⠟⣹⠟⠀⣰⠋⠀⢈⣿⠉⢳⡄⠀⠀⢹⡄⠀⣀⡞⠁⣠⠞⠁⠀⢹⣦⠏⢳⡀⠀⠀⣈⣿⡉⠆
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠍⠭⠉⠍⠩⠩⠍⠭⠩⠍⠩⠍⠍⠭⠩⠍⠩⠍⠍⠩⠩⠍⠭⠩⠍⠭⠩⠍⠭⠉⠭⠩⠍⠭⠩⠍⠭⠩⠍⠭⠩⠍⠭⠉⠭⢭⠉⠉⠉⠉⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀ ⡴⠊⠉⠀ ⠀⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀ ⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠁⠀⠀ ОПЯТЬ ⠀⠀⠈⢆ ⣇⠘⠯⠽⠂⠀⠻⠯⠵⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⢽⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀ КАКОЙ-ТО ⠀⢸⠟⠚⢦⡐⠒⠛⠛⠛⢃⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀ ИВЕНТ ⡜⠀⠀⢠⢾⠑⠒⠒⠊⠉⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣸⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢄⠀⠀ ⠀⠀⡴⠁⠀⢀⡏⢸⠀⠀⠀⠀⠀⠀⡇⣷⠀⠀⢠⣤⡤⢤⠤⣄⠀⠀⠀⠀⠀⢀⡼⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠤⣀⣀⠀⠀⠀⠀⣀⡠⠔⠋⠀⣷⣦⣸⠁⢸⣀⠀⠀⠀⠀⢈⣇⡿⠀⠀⡇⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⡟⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⢰⣟⣿⣽⣷⡼⡅⠉⠉⠉⠉⢉⡏⢷⡤⣶⣷⣶⣦⡤⣤⡼⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣽⠇⢹⠖⣶⠖⠒⡾⠟⠋⠙⡏⠉⠉⢉⣍⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⢀⡀⣀⢀⡀⣀⢀⡀⣀⣀⡀⣀⠀⢈⡿⣷⣙⣿⣆⣸⡃⢀⣀⣀⡇⢀⣀⣀⣸⣀⣀⣙⣋⣇⢀⢀⡀⣀⣀⣀⣀⣀⣀⣼
пусть я ни разу в жизни ascii-подобного не писал, но некторые вещи нельзя оставлять несказанными
⠀⠀⠀⠀⠀⠀⠀|||||||||||⠀⠀⠀⠀⠀⠀||||||||||||||⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀|||||||||||||||||||||||||||||
⠀⠀⠀||||||⠀⠀⠀⠀⠀⠀⠀|||||⠀⠀⠀|||⠀⠀⠀⠀|||⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀||||||||⠀⠀⠀⠀⠀⠀⠀⠀|||||||||||||||||⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀⠀||||||||⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀||||||⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀||||||||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀⠀|||||||||||||||⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀||||
⠀⠀⠀||||||⠀⠀⠀⠀⠀⠀⠀|||||⠀⠀⠀|||⠀⠀⠀⠀|||⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀||||||||⠀⠀⠀⠀⠀⠀⠀⠀|||||||||||||||||⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀⠀||||||||⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀||||||⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀||||||||||⠀⠀⠀⠀⠀⠀|||⠀⠀⠀⠀⠀⠀⠀⠀⠀|||||||||||||||⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀||||
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀||||||||||||||
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀|||⠀⠀||⠀⠀||||||||||⠀⠀⠀||||||⠀⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀||⠀⠀⠀||.⠀⠀⠀||⠀⠀⠀||⠀⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀⠀||⠀⠀⠀⠀|||||||⠀⠀⠀||⠀⠀⠀⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀||⠀⠀⠀|||⠀⠀⠀||⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀⠀||⠀⠀||...⠀⠀⠀⠀⠀|||||||||⠀⠀⠀|||||⠀⠀⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀|||||||⠀⠀
⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀|||⠀⠀||⠀⠀||||||||||⠀⠀⠀||||||⠀⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀⠀||||⠀⠀⠀⠀⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀||⠀⠀⠀||.⠀⠀⠀||⠀⠀⠀||⠀⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀⠀||⠀⠀⠀⠀|||||||⠀⠀⠀||⠀⠀⠀⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀⠀⠀||⠀⠀⠀||⠀⠀⠀||⠀⠀⠀|||⠀⠀⠀||⠀⠀⠀||⠀⠀||⠀⠀⠀⠀⠀⠀||⠀⠀||...⠀⠀⠀⠀⠀|||||||||⠀⠀⠀|||||⠀⠀⠀⠀⠀⠀|||||||⠀⠀⠀⠀⠀|||||||⠀⠀
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣲⣒⡒⠒⠒⠲⠶⠶⠶⠶⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠶⠶⠶⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⣶⣶
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣦⣤⣤⣤⣴⣶⣤⣀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⣼⣿⣶⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣥⣶⣆⣀⠀⢀⡀⠀⠀⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣼⣹⣿⡷⢶⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠋⠙⠁⣸⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠈⠉⠙⠻⢿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣤⣿⣿⣶⣶⣄⡀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⣀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣾⣶⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠘⠏⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣶⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢻⡿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⢿⠆⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟⠛⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣾⣦⠀⠀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠹⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⢀⣿⣿⢃⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⢻⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⣾⠋⢨⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠉⢡⣀⣀⣸⣦⣀⣀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠸⣿⣄⢸⠀⠙⠃⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⡠⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⢀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢹⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⣿⣿⣿⡿⠟⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⢠⣴⠦⢴⡶⠶⠶⠢⠔⠒⠒⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⢠⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢀⣿⣷⣄⡀⠀⣀⠀⠀⣀⣀⣀⣠⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠹⡿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠈⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣦⣤⣤⣤⣴⣶⣤⣀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⣼⣿⣶⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣥⣶⣆⣀⠀⢀⡀⠀⠀⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣼⣹⣿⡷⢶⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠋⠙⠁⣸⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠈⠉⠙⠻⢿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣤⣿⣿⣶⣶⣄⡀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⣀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣾⣶⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠘⠏⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣶⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢻⡿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⢿⠆⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟⠛⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣾⣦⠀⠀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠹⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⢀⣿⣿⢃⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⢻⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⣾⠋⢨⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠉⢡⣀⣀⣸⣦⣀⣀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠸⣿⣄⢸⠀⠙⠃⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⡠⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⢀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢹⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⣿⣿⣿⡿⠟⠉⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⢠⣴⠦⢴⡶⠶⠶⠢⠔⠒⠒⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⢠⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢀⣿⣷⣄⡀⠀⣀⠀⠀⣀⣀⣀⣠⣤⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠹⡿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠈⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⡫⡪⡪⡪⡫⠻⡫⡪⡪⡨⡈⡀⡈⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡨⡫⡈⡈⡀⡈⡈⡪⡫⡀⡀⡈⡀⡈⡀⡀⡈⡈⡈⡈
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡫⡫⡪⡫⠻⠻⠻⡪⡪⡪⡨⡪⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡪⡈⡈⡈⡪⡫⡪⡀⡈⡨⡈⡀⡈⡀⡀⡀⡈
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡫⡫⡫⡫⡫⡪⡪⡪⡪⡪⡪⡨⡨⡨⡈⡈⡨⡈⡈⡈⡈⡨⡈⡈⡨⡨⡨⡨⡈⡨⡫⡪⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡫⡫⡫⡪⡪⡪⡪⡪⡪⡨⡪⡪⡨⡪⡈⡨⡈⡈⡨⡨⡨⡨⡨⡨⡨⡨⡨⡈⡈⡪⡪⡈⡈⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡫⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡨⡨⡨⡨⡪⡪⡨⡨⡨⡨⡨⡪⡪⡨⡨⡨⠻⡈⡈⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡫⠻⡪⡪⡪⡫⡪⡪⡪⡪⡪⡪⡫⠻⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡨⡪⡪⡨⡨⡪⡨⡫⡪⡨⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⠻⡪⡪⡫⠻⡫⡫⡫⡫⡫⠻⠻⡫⡪⡈⡪⡫⡫⠻⠻⡾⠻⡪⡨⡪⡪⡪⡪⡪⡪⠻⡫⡨⡈⡨⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⠻⡫⡫⠻⠻⡫⠻⠻⠻⠻⠻⡫⡫⡪⡨⠻⡪⡪⡫⠻⡫⡪⡫⡪⡫⡪⡫⡪⡪⡫⠻⡫⡨⡨⡨⡨⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡫⠻⡫⡫⠻⡪⡪⠻⠻⠻⡪⡈⡈⡈⡈⡈⡈⡈⡈⡀⡈⡀⡈⡪⡪⡪⡈⡨⡈⡨⠻⠻⡪⡨⡪⡨⡨⡈⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⠻⠻⠻⠻⡿⡪⡪⠻⡨⡨⡈⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡈⡨⡪⡨⡈⡈⡈⡈⡪⡫⡪⡨⡪⡪⡪⡀⡈⡈⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⠻⠻⠻⠻⠻⡨⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡈⡨⡨⡈⡪⡪⡫⡪⡪⡪⡪⡫⡈⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠻⠻⡾⠻⡾⡾⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡪⡀⡀⡀⡀⡨⡪⡪⡪⡪⡪⡪⡫⡨⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⠻⡾⡾⡾⡾⠻⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡈⡨⡀⡀⡀⡀⡨⡪⡪⡪⡪⡪⡪⡫⡀⡈⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⠻⡪⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⡫⡫⡫⠻⡫⠻⡪⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡨⡨⡈⡨⡀⡀⡀⡀⡈⡪⡫⡪⡫⡪⡫⡫⡈⡈⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡪⠻⡈⡈⡫⡿⣿⣿⡿⠻⡨⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⡫⡫⡫⡪⡪⡫⡈⡀⡀⡨⠻⡿⡿⡿⠻⡪⡈⡈⡈⡀⡈⡨⡀⡀⡀⡀⡈⡪⡫⡪⡫⡪⡫⡫⡈⡀⡈⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡨⡪⠻⡫⡨⡈⡀⡀⡀⡀⡪⡿⣿⣿⣿⡿⠻⡨⡈⡀⡀⡀⡈⡫⡪⡫⡫⡨⡪⡪⡀⠻⡿⣿⣿⡿⡿⡿⡿⡿⠻⡪⡈⡀⡨⡈⡀⡀⡀⡀⡈⡨⡪⡫⡈⡪⡫⡫⡈⡀⡈⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡪⡪⡪⡾⡫⡈⡈⡀⡀⡀⡀⡀⡀⡀⡪⡿⡿⡿⡿⡿⡾⠻⡪⡪⡪⡪⡫⡪⠻⡾⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡿⡿⡾⠻⡪⡪⡈⡈⡈⡀⡀⡈⡈⡈⡈⡈⡈⡨⡪⡀⡈⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡪⠻⡫⡿⡫⡨⡈⡀⡀⡀⡀⡀⡀⡀⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⠻⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⠻⠻⠻⡾⡾⡿⡿⡾⠻⠻⡈⡈⡀⡀⡀⡀⡀⡀⡀⡈⡪⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡫⠻⠻⡨⡪⡈⡀⡀⡀⡀⡀⡀⡀⡀⡾⡿⡿⡾⠻⠻⠻⡾⡿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⠻⡿⡨⡨⡨⡈⡈⡀⡀⡀⡀⡀⡀⡀⡈⡿⡿⡿⡾⠻⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⠻⠻⡾⡾⡿⡿⡿⡿⡿⡿⡿⡨⡨⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡨⡿⡪⡀⡀⡀⡨⡈⡈⡈⡀⡀⡀⡀⡀⡀⡈⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡾⡾⠻⠻⡾⡾⡾⡾⡾⡿⡿⡿⡿⡾⡪⡨⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⠻⠻⡀⡀⡀⡀⡀⡀⡨⡨⡈⡈⡀⡀⡈⡀⡀⡀⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⡾⠻⡾⡾⡾⡾⡾⡾⠻⡪⡈⠻⠻⡫⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡨⡿⡪⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡈⡀⡀⡀⡀⡈⡀⡀⡀⡪⡾⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⡾⡾⡾⡾⡾⡾⠻⡈⡈⡀⡀⡀⡈⡪⠻⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡀⡀⡀⠻⡾⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡈⡈⡀⡀⡀⡈⡀⡈⡾⡿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡾⡫⡈⡈⡈⡈⡈⡈⡈⡈⡪⡫⡫⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡀⡨⡾⡾⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡨⡈⡈⡈⡀⡈⡿⡿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡾⠻⡪⡨⡈⡈⡈⡈⡈⡈⡈⡪⡫⡨⡪⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡪⡈⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡨⡨⡨⠻⡿⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⠻⠻⠻⡾⡾⡾⡾⠻⡪⡪⡪⡨⡈⡈⡈⡀⡀⡀⡀⡀⡨⡀⡀⡪⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⡿⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡾⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⠻⠻⠻⠻⠻⠻⡾⠻⡫⡪⡨⡈⡪⡨⡈⡈⡀⡀⡈⡈⡀⡀⡀⡀⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⡿⡿⡿⡪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⠻⠻⠻⠻⠻⡾⡾⡾⡪⡪⡪⡨⡈⡈⡨⡈⡨⠻⡈⡀⡀⡀⡀⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⣿⣿⡿⡾⠻⡪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⠻⠻⠻⠻⡾⡿⡿⠻⡪⡪⡨⡨⡨⡈⡈⡀⡀⠻⡨⡀⡀⡀⡀⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⣿⡿⣿⡿⡿⠻⠻⡪⡈⡀⡀⡀⡀⡀⡀⡀⡾⣿⣿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⡾⠻⠻⡾⡿⡿⡾⡪⡪⡨⡈⡨⡨⡈⡀⡀⡀⠻⡪⡀⡀⡀⡀⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⡿⡿⣿⡿⡿⡿⠻⠻⠻⡨⡈⡀⡀⡀⡈⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡾⡿⡿⡿⠻⡪⡈⡈⡨⡪⡨⡈⡀⡈⡀⡪⠻⡀⡀⡀⡀⡨⡨⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⣿⡿⣿⡿⡿⡿⡿⡾⡪⡨⡈⡈⡈⡨⡿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠻⠻⡫⡨⡈⡨⡈⡀⡀⡀⡈⡈⡨⠻⡀⡀⡀⡀⡪⡨⡨⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡿⡿⣿⡿⡿⡿⡿⡿⡾⡫⡪⡈⡈⠻⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⡾⠻⡨⡈⡀⡀⡀⡀⡀⡀⡀⡈⠻⡨⡀⡀⡀⡪⡨⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⠻⡿⡿⡿⡿⡿⡾⡿⠻⡫⡪⡪⡪⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⡪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡪⡀⡀⡈⡪⡨⡈⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡨⠻⡿⡿⡿⡿⡾⡿⠻⡪⡪⡪⡪⠻⣿⣿⡿⡿⡿⡿⡿⡿⣿⣿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡫⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡪⡈⡈⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⠻⡿⣿⡿⡾⡿⡿⠻⡫⡪⡪⠻⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡾⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡈⡪⡈⡈⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡨⡪⠻⡿⣿⡿⡿⡿⡿⠻⡪⡪⠻⣿⡿⡿⡾⡾⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⡿⠻⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡈⡪⡈⡈⡈⡈⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡈⡨⡪⡫⠻⡿⡿⡿⡿⡿⡫⡨⡨⠻⣿⣿⡿⡿⡿⡾⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⡿⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡨⡨⡪⡾⡿⡿⡿⠻⡨⡨⡨⡫⡿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠻⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡨⡨⡫⠻⡿⡿⠻⡨⡨⡈⡈⡪⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡫⡪⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡨⡪⡪⡾⡿⠻⡪⡨⡨⡨⡈⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡪⡪⡨⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡪⠻⡿⡿⡾⡪⡨⡨⡨⡨⡨⡨⠻⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡪⡨⡨⡨⡨⡨⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡪⠻⠻⡿⡿⡿⡫⡨⡨⡨⡨⡨⡨⡨⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡪⡪⡨⡨⡨⡨⡨⡈⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡾⡾⡾⡿⡿⡪⡨⡨⡨⡪⡪⡪⡨⡨⡨⡪⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡪⡨⡨⡨⡨⡨⡨⡨⡨⡨⡨⡈⡈⡈⡈⡈⡀⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡾⡾⡿⡾⡪⡨⡨⡨⡨⡨⡨⡪⡪⡪⡨⡨⠻⡿⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡫⡪⡨⡨⡨⡨⡨⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡿⡿⡾⡪⡨⡨⡨⡈⡈⡈⡈⡈⡨⡪⡪⡪⡨⠻⡿⣿⣿⣿⣿⡿⡿⡿⡿⠻⡪⡨⡨⡨⡨⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡈⡀⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡨⡀⡀⡀⡀⡀⡀⡀⡀
⡾⡾⡪⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡨⡪⡫⡪⠻⡿⡿⡿⡿⡿⡿⡿⡿⡫⡨⡨⡪⡪⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡫⠻⡿⡿⡿⣿⡿⡿⡿⠻⡪⡪⡫⡪⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡪⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡫⡾⣿⡿⣿⡿⡿⡿⠻⠻⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡪⡨⡨⡨⡨⡈⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡪⡫⠻⡿⣿⣿⣿⡿⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡪⡪⡪⡪⡫⠻⡾⡿⡿⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡪⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡪⡪⡪⡪⡪⡪⡫⠻⡾⠻⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡈⡈⡈⡀⡀⡀⡀⡀
⡨⡨⡨⡨⡈⡈⡈⡨⡈⡨⡈⡈⡈⡨⡨⡨⡨⡪⡪⡪⡪⡪⡪⡪⡪⡪⠻⡾⡫⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡈⡪⡀⡀⡀⡀⡀⡀
⡨⡨⡨⡨⡈⡈⡈⡈⡨⡨⡈⡈⡈⡨⡨⡨⡨⡨⡪⡪⡪⡪⡪⡪⡪⡪⡫⠻⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡨⡨⡨⡨⡈⡈⡈⡈⡈⡨⡈⡈⡈⡨⡨⡨⡨⡨⡪⡪⡪⡪⡪⡨⡪⡪⡪⡫⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡫⡫⡪⡫⠻⠻⠻⡪⡪⡪⡨⡪⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡪⡈⡈⡈⡪⡫⡪⡀⡈⡨⡈⡀⡈⡀⡀⡀⡈
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡫⡫⡫⡫⡫⡪⡪⡪⡪⡪⡪⡨⡨⡨⡈⡈⡨⡈⡈⡈⡈⡨⡈⡈⡨⡨⡨⡨⡈⡨⡫⡪⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡫⡫⡫⡪⡪⡪⡪⡪⡪⡨⡪⡪⡨⡪⡈⡨⡈⡈⡨⡨⡨⡨⡨⡨⡨⡨⡨⡈⡈⡪⡪⡈⡈⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡫⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡨⡨⡨⡨⡪⡪⡨⡨⡨⡨⡨⡪⡪⡨⡨⡨⠻⡈⡈⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡫⠻⡪⡪⡪⡫⡪⡪⡪⡪⡪⡪⡫⠻⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡨⡪⡪⡨⡨⡪⡨⡫⡪⡨⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⠻⡪⡪⡫⠻⡫⡫⡫⡫⡫⠻⠻⡫⡪⡈⡪⡫⡫⠻⠻⡾⠻⡪⡨⡪⡪⡪⡪⡪⡪⠻⡫⡨⡈⡨⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⠻⡫⡫⠻⠻⡫⠻⠻⠻⠻⠻⡫⡫⡪⡨⠻⡪⡪⡫⠻⡫⡪⡫⡪⡫⡪⡫⡪⡪⡫⠻⡫⡨⡨⡨⡨⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡫⠻⡫⡫⠻⡪⡪⠻⠻⠻⡪⡈⡈⡈⡈⡈⡈⡈⡈⡀⡈⡀⡈⡪⡪⡪⡈⡨⡈⡨⠻⠻⡪⡨⡪⡨⡨⡈⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⠻⠻⠻⠻⡿⡪⡪⠻⡨⡨⡈⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡈⡨⡪⡨⡈⡈⡈⡈⡪⡫⡪⡨⡪⡪⡪⡀⡈⡈⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⠻⠻⠻⠻⠻⡨⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡈⡨⡨⡈⡪⡪⡫⡪⡪⡪⡪⡫⡈⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠻⠻⡾⠻⡾⡾⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡪⡀⡀⡀⡀⡨⡪⡪⡪⡪⡪⡪⡫⡨⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⠻⡾⡾⡾⡾⠻⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡈⡨⡀⡀⡀⡀⡨⡪⡪⡪⡪⡪⡪⡫⡀⡈⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⠻⡪⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⡫⡫⡫⠻⡫⠻⡪⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡨⡨⡈⡨⡀⡀⡀⡀⡈⡪⡫⡪⡫⡪⡫⡫⡈⡈⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡪⠻⡈⡈⡫⡿⣿⣿⡿⠻⡨⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡫⡫⡫⡫⡪⡪⡫⡈⡀⡀⡨⠻⡿⡿⡿⠻⡪⡈⡈⡈⡀⡈⡨⡀⡀⡀⡀⡈⡪⡫⡪⡫⡪⡫⡫⡈⡀⡈⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡨⡪⠻⡫⡨⡈⡀⡀⡀⡀⡪⡿⣿⣿⣿⡿⠻⡨⡈⡀⡀⡀⡈⡫⡪⡫⡫⡨⡪⡪⡀⠻⡿⣿⣿⡿⡿⡿⡿⡿⠻⡪⡈⡀⡨⡈⡀⡀⡀⡀⡈⡨⡪⡫⡈⡪⡫⡫⡈⡀⡈⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡪⡪⡪⡾⡫⡈⡈⡀⡀⡀⡀⡀⡀⡀⡪⡿⡿⡿⡿⡿⡾⠻⡪⡪⡪⡪⡫⡪⠻⡾⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡿⡿⡾⠻⡪⡪⡈⡈⡈⡀⡀⡈⡈⡈⡈⡈⡈⡨⡪⡀⡈⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡪⠻⡫⡿⡫⡨⡈⡀⡀⡀⡀⡀⡀⡀⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⠻⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⠻⠻⠻⡾⡾⡿⡿⡾⠻⠻⡈⡈⡀⡀⡀⡀⡀⡀⡀⡈⡪⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡫⠻⠻⡨⡪⡈⡀⡀⡀⡀⡀⡀⡀⡀⡾⡿⡿⡾⠻⠻⠻⡾⡿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⠻⡿⡨⡨⡨⡈⡈⡀⡀⡀⡀⡀⡀⡀⡈⡿⡿⡿⡾⠻⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⠻⠻⡾⡾⡿⡿⡿⡿⡿⡿⡿⡨⡨⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡨⡿⡪⡀⡀⡀⡨⡈⡈⡈⡀⡀⡀⡀⡀⡀⡈⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡾⡾⠻⠻⡾⡾⡾⡾⡾⡿⡿⡿⡿⡾⡪⡨⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⠻⠻⡀⡀⡀⡀⡀⡀⡨⡨⡈⡈⡀⡀⡈⡀⡀⡀⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⡾⠻⡾⡾⡾⡾⡾⡾⠻⡪⡈⠻⠻⡫⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀
⡀⡀⡀⡀⡨⡿⡪⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡈⡀⡀⡀⡀⡈⡀⡀⡀⡪⡾⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⡾⡾⡾⡾⡾⡾⠻⡈⡈⡀⡀⡀⡈⡪⠻⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡀⡀⡀⠻⡾⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡨⡈⡈⡀⡀⡀⡈⡀⡈⡾⡿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡾⡫⡈⡈⡈⡈⡈⡈⡈⡈⡪⡫⡫⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡀⡨⡾⡾⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡨⡈⡈⡈⡀⡈⡿⡿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡾⠻⡪⡨⡈⡈⡈⡈⡈⡈⡈⡪⡫⡨⡪⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀
⡪⡈⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡨⡨⡨⠻⡿⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⠻⠻⠻⡾⡾⡾⡾⠻⡪⡪⡪⡨⡈⡈⡈⡀⡀⡀⡀⡀⡨⡀⡀⡪⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⡿⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡪⡾⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⠻⠻⠻⠻⠻⠻⡾⠻⡫⡪⡨⡈⡪⡨⡈⡈⡀⡀⡈⡈⡀⡀⡀⡀⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⡿⡿⡿⡪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⠻⠻⠻⠻⠻⡾⡾⡾⡪⡪⡪⡨⡈⡈⡨⡈⡨⠻⡈⡀⡀⡀⡀⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⣿⣿⡿⡾⠻⡪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⠻⠻⠻⠻⡾⡿⡿⠻⡪⡪⡨⡨⡨⡈⡈⡀⡀⠻⡨⡀⡀⡀⡀⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⣿⡿⣿⡿⡿⠻⠻⡪⡈⡀⡀⡀⡀⡀⡀⡀⡾⣿⣿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡾⡾⠻⠻⡾⡿⡿⡾⡪⡪⡨⡈⡨⡨⡈⡀⡀⡀⠻⡪⡀⡀⡀⡀⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀
⡿⡿⣿⡿⡿⡿⠻⠻⠻⡨⡈⡀⡀⡀⡈⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡾⡾⡿⡿⡿⠻⡪⡈⡈⡨⡪⡨⡈⡀⡈⡀⡪⠻⡀⡀⡀⡀⡨⡨⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⣿⡿⣿⡿⡿⡿⡿⡾⡪⡨⡈⡈⡈⡨⡿⣿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠻⠻⡫⡨⡈⡨⡈⡀⡀⡀⡈⡈⡨⠻⡀⡀⡀⡀⡪⡨⡨⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡿⡿⣿⡿⡿⡿⡿⡿⡾⡫⡪⡈⡈⠻⣿⣿⣿⣿⣿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⡾⠻⡨⡈⡀⡀⡀⡀⡀⡀⡀⡈⠻⡨⡀⡀⡀⡪⡨⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⠻⡿⡿⡿⡿⡿⡾⡿⠻⡫⡪⡪⡪⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⡾⡪⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡪⡀⡀⡈⡪⡨⡈⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡨⠻⡿⡿⡿⡿⡾⡿⠻⡪⡪⡪⡪⠻⣿⣿⡿⡿⡿⡿⡿⡿⣿⣿⣿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡫⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡪⡈⡈⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⠻⡿⣿⡿⡾⡿⡿⠻⡫⡪⡪⠻⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡾⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡈⡪⡈⡈⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡨⡪⠻⡿⣿⡿⡿⡿⡿⠻⡪⡪⠻⣿⡿⡿⡾⡾⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⡿⠻⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡈⡪⡈⡈⡈⡈⡀⡀⡀⡈⡀⡀⡀⡀⡀⡀⡀
⡈⡨⡪⡫⠻⡿⡿⡿⡿⡿⡫⡨⡨⠻⣿⣿⡿⡿⡿⡾⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣿⣿⡿⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡨⡨⡪⡾⡿⡿⡿⠻⡨⡨⡨⡫⡿⣿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠻⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡨⡨⡫⠻⡿⡿⠻⡨⡨⡈⡈⡪⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡫⡪⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡨⡪⡪⡾⡿⠻⡪⡨⡨⡨⡈⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡪⡪⡨⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡨⡪⡪⠻⡿⡿⡾⡪⡨⡨⡨⡨⡨⡨⠻⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡪⡨⡨⡨⡨⡨⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡨⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡪⠻⠻⡿⡿⡿⡫⡨⡨⡨⡨⡨⡨⡨⡨⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡾⡪⡪⡨⡨⡨⡨⡨⡈⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡾⡾⡾⡿⡿⡪⡨⡨⡨⡪⡪⡪⡨⡨⡨⡪⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡪⡪⡨⡨⡨⡨⡨⡨⡨⡨⡨⡨⡈⡈⡈⡈⡈⡀⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡾⡾⡿⡾⡪⡨⡨⡨⡨⡨⡨⡪⡪⡪⡨⡨⠻⡿⡿⣿⣿⣿⣿⡿⡿⡿⡿⡿⡫⡪⡨⡨⡨⡨⡨⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡿⡿⡾⡪⡨⡨⡨⡈⡈⡈⡈⡈⡨⡪⡪⡪⡨⠻⡿⣿⣿⣿⣿⡿⡿⡿⡿⠻⡪⡨⡨⡨⡨⡪⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡈⡀⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡨⡀⡀⡀⡀⡀⡀⡀⡀
⡾⡾⡪⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡨⡪⡫⡪⠻⡿⡿⡿⡿⡿⡿⡿⡿⡫⡨⡨⡪⡪⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡫⠻⡿⡿⡿⣿⡿⡿⡿⠻⡪⡪⡫⡪⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡪⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡫⡾⣿⡿⣿⡿⡿⡿⠻⠻⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀⡀
⡪⡨⡨⡨⡨⡈⡈⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡪⡫⠻⡿⣿⣿⣿⡿⡪⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡪⡨⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡪⡪⡪⡪⡫⠻⡾⡿⡿⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡪⡨⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡨⡨⡪⡪⡪⡪⡪⡪⡪⡪⡫⠻⡾⠻⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡈⡈⡈⡀⡀⡀⡀⡀
⡨⡨⡨⡨⡈⡈⡈⡨⡈⡨⡈⡈⡈⡨⡨⡨⡨⡪⡪⡪⡪⡪⡪⡪⡪⡪⠻⡾⡫⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡈⡪⡀⡀⡀⡀⡀⡀
⡨⡨⡨⡨⡈⡈⡈⡈⡨⡨⡈⡈⡈⡨⡨⡨⡨⡨⡪⡪⡪⡪⡪⡪⡪⡪⡫⠻⡪⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡀⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⡨⡨⡨⡨⡈⡈⡈⡈⡈⡨⡈⡈⡈⡨⡨⡨⡨⡨⡪⡪⡪⡪⡪⡨⡪⡪⡪⡫⡪⡨⡨⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡈⡈⡈⡈⡈⡀⡀⡀⡈⡈⡀⡀⡀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⢀⡀⣰⣿⣦
⠀⢰⠉⠉⠒⠲⢄⠀⢿⣿⣿⠿⠿⣿⣿⡿⠀⡠⠖⠒⠉⢱
⠀⢸⠀⣿⣷⣦⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⣴⣾⣿⠀⡇
⠀⢸⠀⢿⡿⠋⢀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⡀⠙⣿⡿⠀⡇
⠀⠸⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢸⣇
⢠⠏⠀⠀⠀⠐⢤⣠⣤⡀⠀⠀⠀⠀⢀⣤⣄⡤⠂⠀⠀⠀⢹⡄
⠈⣧⠀⠤⣀⠀⢿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⡇⣀⠤⠀⢀⡟
⠀⠈⢳⠩⠭⠀⠀⠉⠉⠀⠀⠺⠗⠀⠀⠉⠉⠀⠭⠍⣠⠎
⠀⠀⠀⠘⠷⣄⣀⡀⠀⠀⠑⠊⠑⠊⠀⠀⢀⣀⡤⠞⠁⢾⣧⣼⡷
⠀⠀⠀⠀⠀⡔⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠉⠉⢢⠀⠀⠀⠙⠋⠀
⠀⠀⠀⠀⠀⠈⠒⠒⡏⠀⠁⠈⠁⠈⠀⠹⡒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⡰⡁⡁⡁⡁⡁⡁⡁⡁⣣
⠀⠀⠀⠀⠀⠀⠀⠧⡤⠤⢤⣤⣤⡤⠤⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡸⠁⠈⢇⣀⠎
⠀⢰⠉⠉⠒⠲⢄⠀⢿⣿⣿⠿⠿⣿⣿⡿⠀⡠⠖⠒⠉⢱
⠀⢸⠀⣿⣷⣦⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⣴⣾⣿⠀⡇
⠀⢸⠀⢿⡿⠋⢀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⡀⠙⣿⡿⠀⡇
⠀⠸⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢸⣇
⢠⠏⠀⠀⠀⠐⢤⣠⣤⡀⠀⠀⠀⠀⢀⣤⣄⡤⠂⠀⠀⠀⢹⡄
⠈⣧⠀⠤⣀⠀⢿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⡇⣀⠤⠀⢀⡟
⠀⠈⢳⠩⠭⠀⠀⠉⠉⠀⠀⠺⠗⠀⠀⠉⠉⠀⠭⠍⣠⠎
⠀⠀⠀⠘⠷⣄⣀⡀⠀⠀⠑⠊⠑⠊⠀⠀⢀⣀⡤⠞⠁⢾⣧⣼⡷
⠀⠀⠀⠀⠀⡔⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠉⠉⢢⠀⠀⠀⠙⠋⠀
⠀⠀⠀⠀⠀⠈⠒⠒⡏⠀⠁⠈⠁⠈⠀⠹⡒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⡰⡁⡁⡁⡁⡁⡁⡁⡁⣣
⠀⠀⠀⠀⠀⠀⠀⠧⡤⠤⢤⣤⣤⡤⠤⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡸⠁⠈⢇⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣿⣿⣿⣷⣿⣝⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢟⣿⣷⠿⣝⣿⣿⣿⣿⣖⣾⡛⣢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣻⠗⣾⣷⣿⣿⣾⣿⡿⠗⢛⣛⣚⣻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢵⣯⣸⣿⣾⡿⠾⣿⠾⣧⠋⠁⠀⠀⠈⢳⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢃⣿⣀⣿⣟⣾⡿⣿⣩⣿⣿⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣿⡏⠀⡟⡭⣾⣝⢷⣽⣿⣏⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠻⠀⣿⠇⠀⠳⠹⢟⣯⣽⣯⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣡⡤⠞⠛⠒⠦⣄⡀⠀⠛⢝⠳⠾⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠾⠓⡆⠀⠀⠀⢚⣏⠙⠢⣀⠈⠹⣝⣻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⠁⠀⣸⣻⡄⠀⠀⣥⣿⣷⣤⡉⢣⡀⠈⢿⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠰⣿⣽⣯⠓⠤⢽⢷⣿⣿⣿⠀⠙⣤⡀⠙⢯⣽⣆⡀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡸⠃⣱⣤⣰⣣⣻⢟⠀⢀⣀⡺⠷⠟⡷⠦⠖⠁⠉⠢⣀⠙⠛⢿⣶⣃⢧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⢹⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠁⡜⡼⠁⠀⢫⡁⠀⢸⡟⠋⢹⡆⢸⠁⠸⣇⠀⠢⡀⠈⠛⢶⠦⠤⢤⡞⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⣠⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡼⠵⠁⠀⠀⣻⣿⣷⣶⣭⣤⣗⣾⣾⢀⠀⠹⢦⠀⢙⣲⠄⠈⠳⡶⠤⢴⣦⣄⣴⣶⣶⣶⣶⣿⣿⡿⠀⠀⠀⠀⣾⡿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣁⠀⠀⠀⠀⠀⣟⣽⢿⣿⣿⣿⣿⣿⣿⠻⣧⡤⢶⣆⠀⠀⠀⠀⠀⠀⠒⠿⡿⣿⣿⣿⣟⠛⠛⠛⠟⠃⠀⠀⠀⠀⠻⠷⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢹⠁⢀⡀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣀⣾⣿⡿⢲⣶⣶⡖⢶⣶⣶⢶⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣠⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣾⣿⣿⡏⡹⠿⢿⡇⢠⣾⡿⠃⢀⢜⣁⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣩⣉⣴⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡞⠿⢯⠉⠾⣿⠁⡰⠛⢛⣽⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠋⠉⠉⠙⠋⠋⢾⣿⣧⡟⣻⣿⣿⢾⣭⣻⣆⠀⠀⠀⣿⣛⢣⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣶⣾⣿⣷⣶⣦⣤⣀⡈⡘⠁⠿⣿⣿⣿⠽⣿⣿⣷⡄⠹⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠁⠰⣾⣿⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⢿⣦⣄⠀⠀⠉⠉⠀⢀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣿⠿⡇⢈⠉⣿⣷⣼⡿⣯⣛⢿⣿⣿⠿⠷⠶⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠟⠋⠀⠀⠙⠏⠳⢿⣿⣿⣿⣦⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⣣⣿⠻⠿⣿⣷⣿⣷⣶⣒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⢾⢹⠀⠀⠀⠀⠉⠛⠻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣿⣿⣿⣷⣿⣝⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢟⣿⣷⠿⣝⣿⣿⣿⣿⣖⣾⡛⣢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣻⠗⣾⣷⣿⣿⣾⣿⡿⠗⢛⣛⣚⣻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢵⣯⣸⣿⣾⡿⠾⣿⠾⣧⠋⠁⠀⠀⠈⢳⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢃⣿⣀⣿⣟⣾⡿⣿⣩⣿⣿⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣿⡏⠀⡟⡭⣾⣝⢷⣽⣿⣏⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠻⠀⣿⠇⠀⠳⠹⢟⣯⣽⣯⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣡⡤⠞⠛⠒⠦⣄⡀⠀⠛⢝⠳⠾⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠾⠓⡆⠀⠀⠀⢚⣏⠙⠢⣀⠈⠹⣝⣻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⠁⠀⣸⣻⡄⠀⠀⣥⣿⣷⣤⡉⢣⡀⠈⢿⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠰⣿⣽⣯⠓⠤⢽⢷⣿⣿⣿⠀⠙⣤⡀⠙⢯⣽⣆⡀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡸⠃⣱⣤⣰⣣⣻⢟⠀⢀⣀⡺⠷⠟⡷⠦⠖⠁⠉⠢⣀⠙⠛⢿⣶⣃⢧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⢹⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠁⡜⡼⠁⠀⢫⡁⠀⢸⡟⠋⢹⡆⢸⠁⠸⣇⠀⠢⡀⠈⠛⢶⠦⠤⢤⡞⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⣠⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡼⠵⠁⠀⠀⣻⣿⣷⣶⣭⣤⣗⣾⣾⢀⠀⠹⢦⠀⢙⣲⠄⠈⠳⡶⠤⢴⣦⣄⣴⣶⣶⣶⣶⣿⣿⡿⠀⠀⠀⠀⣾⡿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣁⠀⠀⠀⠀⠀⣟⣽⢿⣿⣿⣿⣿⣿⣿⠻⣧⡤⢶⣆⠀⠀⠀⠀⠀⠀⠒⠿⡿⣿⣿⣿⣟⠛⠛⠛⠟⠃⠀⠀⠀⠀⠻⠷⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢹⠁⢀⡀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣀⣾⣿⡿⢲⣶⣶⡖⢶⣶⣶⢶⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣠⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣾⣿⣿⡏⡹⠿⢿⡇⢠⣾⡿⠃⢀⢜⣁⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣩⣉⣴⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡞⠿⢯⠉⠾⣿⠁⡰⠛⢛⣽⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠋⠉⠉⠙⠋⠋⢾⣿⣧⡟⣻⣿⣿⢾⣭⣻⣆⠀⠀⠀⣿⣛⢣⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣶⣾⣿⣷⣶⣦⣤⣀⡈⡘⠁⠿⣿⣿⣿⠽⣿⣿⣷⡄⠹⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠁⠰⣾⣿⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⢿⣦⣄⠀⠀⠉⠉⠀⢀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣿⠿⡇⢈⠉⣿⣷⣼⡿⣯⣛⢿⣿⣿⠿⠷⠶⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠟⠋⠀⠀⠙⠏⠳⢿⣿⣿⣿⣦⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⣣⣿⠻⠿⣿⣷⣿⣷⣶⣒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⢾⢹⠀⠀⠀⠀⠉⠛⠻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⢀⣀⡀⣀⣀⠀⢀⣀⡀⠀⠀⠀ ⣀⣀⣀⣀⠀⢀⣀⡀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣸⣧⠀⠀⠀⠀⠀⣿⡆⢀⢿⡇⠀⣿⠀⢸⡇⢠⡯⠤⠿⠆⠀⠀ ⣿⠀⢸⡇⢰⡏⠀⢹⣆⠈⢻⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⣇⠀⠀⠀⠀⡇⢻⡞⢸⡇⠀⣿⠉⢹⡇⠘⣷⣀⣠⠆⠀⠀ ⣿⠀⢸⡇⠸⣧⠀⣸⠏⢀⡜⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠁⠀⠀⠈⠉⠀⠀⠉⠉⠈⠉⠁⠉⠉⠀⠈⠉⠁⠀⠀⠀ ⠉⠀⠉⠉⠀⠈⠉⠁⠀⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⢀⣀⡀⣀⣀⠀⢀⣀⡀⠀⠀⠀ ⣀⣀⣀⣀⠀⢀⣀⡀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣸⣧⠀⠀⠀⠀⠀⣿⡆⢀⢿⡇⠀⣿⠀⢸⡇⢠⡯⠤⠿⠆⠀⠀ ⣿⠀⢸⡇⢰⡏⠀⢹⣆⠈⢻⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⣇⠀⠀⠀⠀⡇⢻⡞⢸⡇⠀⣿⠉⢹⡇⠘⣷⣀⣠⠆⠀⠀ ⣿⠀⢸⡇⠸⣧⠀⣸⠏⢀⡜⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠁⠀⠀⠈⠉⠀⠀⠉⠉⠈⠉⠁⠉⠉⠀⠈⠉⠁⠀⠀⠀ ⠉⠀⠉⠉⠀⠈⠉⠁⠀⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Praise the Sun, dudes
⠀⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢻⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠞⠀⠀
⠀⠀⠀⡷⠢⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢀⡀
⠈⠓⠲⣦⣤⣁⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⣀⣤⡶⠛⠉⠀
⠀⠀⠀⠈⠙⢿⣿⣶⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⣵⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡄⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⢟⠑⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⣴⡟⠐⡶⣦⢵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠖⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣳⢦⡀⣀⡄⠀⠀⠀⠀⢸⡏⠀⠀⠀⠄⠀⠙⡇⠀⠀⠀⠀⠀⠀⡀⣀⣴⣾⣿⣭⣶⣶⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡧⢿⠟⣿⣿⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣸⣿⡷⣗⢟⣿⣟⣻⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡯⣼⠈⣧⠹⢷⣄⠀⣴⣧⣉⣄⣐⣤⣆⣌⣁⣄⣢⡀⠀⣠⡿⠋⠀⡏⢼⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣧⡚⢦⡘⠀⠠⢿⣯⠈⠛⠿⠿⠿⠿⠿⠿⠟⣋⣁⣨⡟⠉⢀⣠⠾⢃⣸⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡶⠻⠟⠛⠋⠳⣟⣒⣦⣤⣐⣬⣿⠿⠶⠛⠉⠉⠙⠿⣷⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡷⠟⠲⠊⢻⢦⡀⠀⢀⡜⡃⠀⠀⣠⣴⠃⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠻⣼⣲⠼⠖⠱⢴⡩⣶⠁⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣠⣀⣠⣤⣿⠁⠤⠂⠠⠄⢹⣧⣠⣀⣀⣀⡀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠳⢿⣾⡀⠀⠴⢂⠀⣸⣶⡷⢯⡾⢽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⡀⣰⣿⣿⣦⣤⣥⣾⣿⢷⡀⠀⠰⣬⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡎⣴⣿⣿⡷⠛⢻⣿⣿⣟⢿⣿⣿⣦⣀⢨⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣟⣫⣜⡳⢎⣿⣿⣏⡷⣟⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⣦⣟⣦⣿⣇⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣾⣿⢿⢾⡟⣿⡿⡿⣿⣿⢿⣿⣿⣿⣦⣬⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡏⣿⣸⢾⡗⢠⣿⡅⢻⣿⢺⢿⠹⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡆⣧⢻⣿⠃⢉⡗⣧⢻⢡⣼⢸⢄⣿⢼⠇⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣾⣿⣤⣾⣿⣷⣟⣆⣇⣿⡎⣾⡎⢿⣷⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⣟⣿⢻⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢰⠃⡏⡇⣽⠋⣿⢹⢿⣿⠹⣿⢿⣿⡏⣿⡿⣽⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣾⣷⣿⣿⣦⣿⣿⣿⣿⣸⣟⣾⣶⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠩⠽⣿⣿⣿⣿⡟⠀⠀⠀⣮⢭⠿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⢼⣫⣿⣿⣿⣿⡇⠀⠀⠀⣏⣮⣽⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⢻⣯⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⣻⣿⣿⣿⣿⡇⠀⠀⠀⢸⣟⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢪⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⣇⢻⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣽⢿⣿⣿⡿⠀⠀⠀⠀⠀⣧⠫⡽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡓⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣵⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠿⣿⡁⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣐⣾⣿⠀⠀⠀⠀⠀⡿⢴⣅⡀⣉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣭⠼⢻⣿⡁⠀⠀⠀⠀⠀⣻⡿⣿⣭⡙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠴⠾⠿⠃⠀⠀⠀⠀⠀⣿⣿⣦⣜⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
У вас что были картинки?
⠋⠹⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣭⣭⣿⡏⠉⢉⣩⣭⣭⣭⣉⡉⠉⠉⢹⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⢠⣴⣤⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢺⣿⣿⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠄⠄⠄⠠⠐⢸⣿⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢙⣿⣿⣿⡿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣼⣿⣿⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣶⣦⣤⣤⣄⣿⣿⣿⣿⡀⢀⡀⠄⠄⠄⠄⠄⠄⠄⢀⡀⠄⢸⣿⣿⠁⠄⠄⠄⠄⠄⠄⣈⣛⠻⣿⣿⣿⣿⣿⠄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣼⣿⡿⠄⠄⠄⠄⠄⡀⣰⢐⣉⣻⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠄⣐⣚⣷⣶⣭⣷⣿⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠸⡹⠇⠄⠈⠉⢿⠿⠿⠃⠙⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠡⠄⠄⠄⢀⣀⣠⣄⣀⣀⣿⣏⣋⣻⣿⡟⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⣴⡆⠄⠄⠈⡟⠁⠙⣿⣿⣿⣿⣿⣿⣿⠇⠄⠄⢀⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⣿⡿⠟⣩⠄⠄⠄⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⡄⢀⣴⣶⣶⡄⢀⣤⣤⡄⠄⠄⠄⠄⠄⠄⠄⠒⠒⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣶⣦⣿⠄⠄⠄⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⣽⠿⠿⢿⣿⡿⠄⠄⣰⣶⣄⣤⣾⣿⣿⣿⣿⣿⡿⠋⣠⣿⣿⣿⠏⠄⣰⣿⣿⠏⠁⣰⣿⡿⢁⣀⣤⣴⣶⣿⣿⣿⣿⡿⠿
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⣾⡿⠉⠄⠄⠄⠇⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⡻⡏⠄⣰⣿⣿⡏⠄⢀⣾⣿⠋⠄⠄⣾⣿⣿⣿⠿⠟⠋⠉⠁⠉⠁⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣿⣿⡏⠄⠄⠄⠄⠄⠄⢂⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠿⠿⠋⠄⠄⠄⠄⠄⠄⠄⠈⠁⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢸⣿⡿⢳⣆⡄⠄⠄⠄⠄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠐⢦⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠉⠄⠈⢿⡏⢄⠄⠄⠄⢀⣀⣉⠉⠛⢿⡿⢿⠿⠟⠉⠸⠁⠄⠄⠄⠈⣷⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣀⣀⣤⣀⣤⣥⣴⣿⣿⣿⣿⠷⠄⠄⠄⠄⠄⠄⠄⠄⢀⣤⣽⣿⣧⣭⣶⣶⣦⣤⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⣤⣤⣤⣤⣤⣤⣤⣤⠄⠄⠄⠄⠒⣾⣿⣿⠿⠻⠿⠛⠏⠉⠉⠁⠄⠄⠄⠄⢠⣄⠄⠄⠄⠄⠈⠉⠉⠉⠉⠙⠛⠉⠉⠙⡗⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⣀⡀⣈⣀⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠁⢀⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⡆⡠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⠄⠉⠉⠉⠉⠉⠉⠉⠄⠄⢲⣼⡻⣿⣿⣧⡄⠄⠄⠄⣀⢀⣀⣠⠤⠄⠄⠒⠋⠄⠈⠉⠉⠛⠒⠂⠄⠤⢤⣤⣀⣀⣠⣿⣷⣿⡘⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣶⣗⣛⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣽⣿⣿⣋⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
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