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