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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⣠⣶⣶⣦⣴⣿⣹⡛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣖⣀⣾⣿⣿⣿⣿⣿⣿⡁⠘⠛⣿⣿⣯⣛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⢙⣿⣿⣿⣽⡟⢿⣿⡇⢻⣿⣤⣐⡸⡟⠏⠋⢿⣷⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣟⣸⣿⣿⣿⣿⣿⣾⣿⣷⣶⣿⣿⢻⣿⡿⠄⠂⣈⠹⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠉⣹⣿⣿⠿⣿⠀⣉⣿⡃⢀⠘⢻⣿⣿⠛⢀⢰⣶⡌⠁⠌⢘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣶⡀⣰⣿⠋⠡⢿⣿⣿⠏⠁⡀⣸⣿⠇⠉⢿⣿⣦⣦⣿⠛⣿⣧⣠⣼⣿⣯⣥⣂⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡟⠙⢿⣿⠇⡀⢂⣿⣿⣿⡅⢐⣠⣿⣿⡆⠐⠨⣿⡇⠁⠀⠀⠈⠛⢿⡟⠇⢠⣿⠿⢿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣳⡟⢸⣿⡷⢿⣿⣿⢿⣿⣿⣿⠟⠉⢻⣷⣤⣵⡿⠁⠀⠀⠀⠀⠀⠀⢿⣄⠀⠻⣷⣄⠈⠉⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣠⣿⣿⣷⡈⢂⠀⣻⣯⠿⠾⠿⢿⣿⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⢴⣄⠀⠀⠙⣷⣄⠈⠻⣷⣦⡀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⡏⢁⠈⢿⣏⠀⠰⣿⣿⣷⣎⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠙⣷⣄⣠⣬⣿⠷⣦⣭⠙⣿⣷⣦⣤⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⡟⠻⢿⣶⣾⣾⣿⠀⡁⢸⣿⡄⠉⠉⠉⠀⠀⠀⠀⠰⣤⡀⠀⠀⠹⣧⣀⣠⣴⠟⠋⠉⠀⠀⠲⣦⣽⣶⣿⣧⣌⡛⣷⡄⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣾⣿⣿⡾⠿⣿⣿⣿⣿⣦⡐⢠⣿⠇⠀⠀⠀⠀⠀⣶⡀⠀⠈⢿⣄⣀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠌⢻⣆⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣽⡯⣟⣿⣿⣿⣿⠀⣰⣤⣿⡿⠻⣿⣿⠿⠋⠀⠀⠀⡀⠀⠀⠘⣷⣀⢀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⢿⡛⠛⠁⣿⠀⠀⢻⣆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣷⣾⣿⣿⠛⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣈⡿⣿⢉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠁⢀⣴⠟⠀⠀⢸⣿⡀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⣤⣿⡿⢿⢿⣿⡿⢤⣽⣷⣿⠃⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⢿⡦⠞⠉⢳⣤⠘⣿⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⣈⣿⡇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣻⣿⣿⣿⣷⣾⣟⣽⣿⣷⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣤⣴⠶⣾⡇⠀⠀⠀⢠⠀⠀⠀⠰⣿⣧⠀⣰⠎⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣧⡉⢻⣿⣁⣾⡿⠿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠛⢷⡄⠀⠀⢠⣿⣥⣴⡿⠁⠀⠀⠀⠰⡄⠀⠀⢸⣿⣷⠀⢿⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⣼⣿⣿⣶⣿⣿⣿⣷⣷⡿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⣾⠇⠀⠙⠙⠋⠁⠀⣸⡇⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠹⣶⢇⣿⡟⢹⡆⠸⣇⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣯⣤⣴⠿⠛⣷⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢼⣆⣀⣀⣀⣀⣠⡴⠛⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⢀⣾⡿⠀⢸⡇⠀⣿⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠛⠛⣿⣿⣿⣷⣯⣰⣽⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠂⠀⠀⠀⣠⣾⠋⠀⠀⢸⡇⠀⢹⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠛⠋⠀⣺⡇⠀⠀⠀⠀⠀⢠⡀⠀⠀⣷⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠛⢶⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⢸⡇⠀⢸⡇⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣹⣇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠹⣇⠀⠀⠹⣇⠀⠀⠀⡔⠁⠀⠀⢀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⡄⠀⠀⢿⡄⠀⠀⢦⠀⠀⠀⠀⠀⠈⠀⠀⠀⡭⢀⣠⣶⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡗⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣿⡆⠀⠀⠈⣷⠀⣀⣈⣿⡀⠀⠈⠓⠀⠀⢀⣠⣀⣤⣼⣶⡿⢿⡏⠁⠘⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢹⡇⠈⠙⢻⣿⠿⠷⠾⠿⠿⠿⠛⠛⠉⠉⣷⣷⣿⡷⠶⠟⠛⠉⠈⠙⣶⣤⠀⠀⠀⠀⠹⠧⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠈⣷⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⣀⣠⡴⠞⠋⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠈⣿⡀⠀⠀⢹⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠁⠀⠀⠀⢻⡆⠀⠀⠀⣀⣰⠟⠋⠛⠳⠶⠶⠶⠶⠶⠶⠒⠀⠀⠀⣀⣴⣿⠉⠀⠉⠛⠷⣤⣀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣰⠟⠻⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠟⠋⠙⣿⠷⣦⣄⠀⠀⠀⠙⠛⢷⣄⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣴⠟⠹⣿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢹⣆⠀⠉⠻⢶⣤⣄⠀⠀⠈⠙⠻⢶⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠘⡗⠀⠀⠀⢀⣠⡾⠋⠁⠀⢀⣴⠟⠁⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⠉⠻⡷⠶⣤⣄⣀⣉⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⣤⣶⣤⣤⡶⠟⠉⠀⠀⣠⡶⠋⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠹⣿⣻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣼⡿⣶⡄⠀⠀⢀⣠⣴⢾⡏⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⢰⠀⠀⢿⡀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⣶⠟⠛⢶⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠉⣽⣿⣿⣥⣤⣴⡿⠉⠀⣸⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣿⣯⠙⣷⡿⠀⠀⢸⣿⣦⣄⣠⡄⠀⠀⣿⠄⠀⠀⠈⠉⠉⠀⣿⡿⠀⠀⢀⡿⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⡾⠋⠙⠻⠓⠀⠸⠧⠀⠀⠸⠋⠀⣿⡍⠿⡶⣸⡿⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⢸⡇⠈⣧⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣧⣄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣼⠏⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⠀⠀⣿⠀⢹⣆⠀⠈⢿⡄⠀⠀⠀⢀⣤⣄⣶⠷⣶⡾⢶⣠⣤⣤⡀⠀⠀⠀⠀⠀
⢀⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣤⣤⣶⠾⠋⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣼⠏⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⢿⡄⠀⠻⣆⠀⠈⠻⣆⡀⠰⠏⠉⠛⠁⠀⠉⠙⠿⠋⠉⢹⡿⢶⣄⡀⠀⠀
⣼⣿⣏⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⢀⡴⠂⠀⠀⢸⡇⠀⠀⠙⢷⡀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⣿⠀⠀
⢸⣿⣾⣦⠀⠀⠀⠀⠀⣾⠟⠃⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡤⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠀⠀⠀⠀⠉⠛⠻⠃⠀⠀⠀⠀⢺⣦⡀⠀⠀⠛⠿⢷⡀
⠈⢸⣿⠁⠀⠀⠀⠀⠘⡿⣦⣤⣴⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀⠐⣰⡄⢶⡶⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⢼⡧
⠀⠸⣿⠂⠀⢀⣀⠀⠀⠀⠀⠉⠀⠀⢀⣿⠋⠀⠀⣼⣿⡗⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⠿⠾⠃⠀⠀⣠⣬⣿⡇⠀⠀⢀⣵⡾⠁
⠀⠀⠙⠻⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⣠⣿⠿⡶⠾⠋⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡟⣿⠋⠀⠀⢀⣿⣿⡆⠀
⠀⠀⠀⠀⠸⣷⣀⠀⢀⣴⠀⠀⠀⠀⣠⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠋⡀⠀⢸⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣄⣀⣀⣴⣟⠀⠀⣸⣧⠀⠀⠀⣠⡾⠷⢶⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⠄⠀⠀⣰⣿⡰⢰⣽⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠷⠟⠛⠛⠷⠶⠟⠉⠀⠀⠈⠻⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡽⣷⡀⠀⠀⢸⣷⠀⠀⠀⣿⣅⣀⣀⣩⡿⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⢦⣄⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣨⣷⣌⠻⠷⠶⠶⠟⠻⠿⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠉⠙⠿⠿⠛⠙⠛⠶⠦⣤⣤⡤⠶⠚⠋⠉⠻⠿⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

new víla amálka amalka the fairy fairy amalka czech slovak magic flower crown wreath flower girl cute cartoo 1975 story czechoslovak little girl bloom slovakian czechian children kids crown

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣆⣠⣿⡟⢯⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣸⢽⣿⣿⢏⡞⣧⣿⠇⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡱⡞⣿⣿⣽⣼⣿⣏⣀⠀⢠⣿⢿⡹⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⡵⣛⠿⡿⢿⡻⣟⡿⣿⣿⣟⣎⠷⣫⣿⣆⣴⣶⣶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡿⢿⣿⣭⢳⣝⣣⢷⣭⣾⣿⣿⣿⣜⡳⡽⣿⣿⢿⣙⠮⣝⡞⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣥⢻⡜⣿⣿⢧⣻⣿⣿⣿⢿⠿⡿⣿⣿⣾⡱⣝⣫⢻⡜⣎⡻⢦⣿⣿⣁⡀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣞⣥⣻⣼⣿⣏⢶⣻⣿⡿⣜⢫⡞⣵⣭⣿⡿⣝⣳⡷⣿⣿⣾⣿⠿⣿⡿⢿⣻⣷⡄⢠⣾⡟⡯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢹⣿⡜⡶⣩⣿⠿⠿⠷⠿⢿⣿⢏⡳⣭⣿⣷⡹⢏⡿⣿⣶⣿⣟⣣⢽⣹⣿⣿⣳⡹⣓⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣷⣽⣯⡤⠦⠀⠀⣿⣏⢾⡱⢧⣿⣿⡵⣫⠞⣭⣿⣿⣷⢭⣎⢷⣿⣿⢲⠭⣯⣿⡏⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠉⠀⠀⠀⠀⠀⣿⣏⢶⣹⣻⡿⠙⢿⣧⣟⣶⣿⣯⣿⣷⣞⢮⣿⣟⢯⣾⣿⢿⡿⣷⣶⣄⢰⣿⡿⣟⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣷⠟⠁⠀⠀⠈⣽⣿⠯⣝⡺⣝⣫⢾⡵⣮⣟⡼⣙⢮⡵⢳⣫⣿⣿⣿⡵⣣⣿⣿⣷⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⣿⢧⣛⡼⣱⢧⣽⣿⡿⣭⣿⣾⣝⡶⣩⣷⣵⣿⠛⣿⡷⣱⢿⣿⡿⣝⢺⡜⣵⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣾⣷⣿⣿⢯⡳⢵⣻⡏⠛⣿⣿⡿⣿⢿⡶⣿⣿⣧⢻⣏⠷⣎⡷⣮⣿⣿⣤⡀⠀⣴⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⢧⣛⣧⣿⡇⢸⣿⢣⡝⡶⣭⣚⣽⣿⣟⢧⡺⣽⣶⣿⣻⣿⡟⢿⣷⣼⡿⢭⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣽⣽⡿⠁⠸⣿⣎⣳⣥⣯⣿⣿⠿⣹⣾⣥⢏⡿⢿⣿⣿⣓⠾⣿⣿⢣⣞⣿⣿⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⣴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠙⠛⠛⠛⢻⡿⣍⢯⣳⣿⣿⣎⢷⢫⣿⣿⣯⡹⣽⣟⢿⣿⡟⣟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⠛⠀⠀⣼⠃⠀⠀⢀⡞⠁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⡜⣮⣽⡿⠙⢿⣿⣧⣿⣿⣿⣿⡜⢯⡞⣥⢿⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⡿⠁⢀⠄⢠⡇⠀⢀⡤⠟⠀⠀⠀⢠⡏⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠸⣿⣣⣞⣵⣿⠃⠀⠀⣹⣿⢿⠻⣽⣿⣜⡳⣿⣿⡿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣰⡟⠀⠀⢸⣤⣼⣧⣤⣞⠀⠀⠙⠲⡴⡟⠀⠀⠀⢀⡟⠀⠀⠀⢀⡞⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⣾⡿⡹⣎⣿⣿⡿⣎⣳⢻⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡞⠀⠀⠀⣤⠀⠀⣼⠁⠀⠀⣰⡟⠀⠀⣠⣿⣿⣿⣿⡏⠛⢿⡄⠀⠀⠀⠈⠓⠦⠤⢟⡀⠀⠀⠀⡾⠁⠀⠀⢰⡆⠀⣤⠄⢠⠀⠀⠀⢿⣷⣽⣾⡿⠛⣿⡮⣕⣯⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⠀⢰⠇⠀⠀⣰⡟⠀⠀⢰⣿⣿⣿⣿⣿⠃⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡀⣼⠃⠀⠀⢀⡟⠀⢀⡏⠀⢸⠀⠀⠀⠈⠙⢻⡏⠀⠀⠘⠿⣾⠿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⣄⡞⠀⠀⢠⡿⠀⠀⠀⠀⢿⣿⣿⠿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣸⣇⢀⡿⠁⠀⡼⠁⢀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⣾⠃⠀⠀⠀⠀⠈⠙⠿⣦⣤⣤⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⢿⣦⠀⠘⠁⠠⠾⣡⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣹⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢰⣿⣆⠀⢸⡏⠀⣶⠒⣟⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⢹⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠉⢻⡇⠀⠀⠀⢀⣿⣀⡀⠀⢠⡞⢻⡟⠀⢻⣦⣾⠁⠰⡇⢻⡴⣉⠞⣳⡄⠀⠀⠀⠀⠀⠀⣿⠉⠙⠲⣄⠀⠀⠸⣿⣿⣿⡿⠃⠀⠀⢈⣷⠀⠀⠀⢸⡿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢳⡟⠀⠀⠀⠀⠸⣿⣍⠙⠛⢾⠇⢸⡇⠀⠀⠙⣿⣄⠸⣿⡱⣾⠥⢚⡥⣻⠀⠀⣆⠀⠀⠀⠘⠳⠦⢤⠾⠃⠀⠀⠙⢿⣍⣀⣀⣀⣴⠟⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢷⣼⡟⠀⠀⠀⢸⣿⡾⠿⣷⠀⠀⠀⠘⣧⠀⠀⢠⡟⠻⣷⣌⠳⣜⡋⠶⣽⡿⠀⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣿⠀⠀⠀⠀⠀⢈⣹⣷⠆⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠈⠛⢷⣾⡛⠛⠋⠁⠀⠀⠀⠀⠈⠛⠛⠶⠶⠞⠋⠀⣠⢾⣛⢻⡛⣟⢦⣄⠀⠀⠀⢀⡾⢫⡇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠐⠿⣿⡶⢶⣄⣀⣀⠀⠀⠀⠻⣾⡁⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡸⢿⣏⢹⣞⣮⡾⠀⣀⡴⠋⢀⡞⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⠉⠉⢷⡀⠀⠀⠈⠳⣄⡀⠀⢀⣠⠴⠶⣤⣹⡟⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⢤⠿⣻⣿⣭⡶⠞⠋⠀⠀⡼⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⡆⠀⠀⣼⠛⣦⡀⠀⠀⠈⠛⢿⣍⡀⠀⠐⠒⠯⠿⠛⠉⠁⠉⠙⠻⣷⠲⠶⠶⠶⠶⠶⠟⠛⠛⠉⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⢀⡇⠀⠈⠻⣦⡀⠀⠀⠀⠈⠙⠛⠶⢶⣶⡶⠶⢤⣀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡄⠀⠀⢸⠀⠀⠀⡿⠀⠀⢸⠃⠀⠀⠀⢿⣿⢷⣄⡀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠈⠑⢦⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠇⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣾⠀⠀⠀⠀⢸⠟⢦⣈⣙⣶⣄⣀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡟⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⣼⠀⠀⢠⡇⠀⠀⣿⠀⠀⠀⠀⢸⡇⢸⡏⠉⠉⠈⠉⠛⠶⠦⣤⣤⣤⣄⣙⣶⣄⠀⠀⣿⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣼⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣟⠀⠀⠀⠀⢸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⢦⣼⣧⠀⠀⠀⠀⢸⠃⠀⠀⢰⠃⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⡇⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⡯⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠀⠀⠀⠀⡟⠀⠀⢀⡟⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠃⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⡇⠀⠀⣸⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡞⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠀⡇⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⡇⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣼⠀⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡇⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢶⣤⠤⠦⣄⠀⠀⠀⢠⠏⠀⠀⣼⠁⠀⠀⠀⣸⠃⠀⠀⡇⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢦⣿⠀⠀⠀⣿⠀⠀⢸⡆⠀⢠⡟⠀⠀⢰⠃⠀⠀⠀⢀⡏⠀⠀⠀⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠸⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⠻⠦⠀⠀⠉⠀⠀⠘⡇⢠⡞⠁⠀⢀⡞⠀⠀⠀⠀⣸⠁⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⡶⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠤⠶⠾⣧⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡴⠋⠀⠀⢀⡞⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣾⠁⠀⠀⠀⢹⣧⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡾⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠸⣧⡞⠉⠉⠻⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠢⡾⠗⠶⣦⠀⠀⠀⠀⠀
⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠈⢿⣄⠘⠁⠀⣼⠗⠲⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⠀⠀⢿⡁⠉⣳⣤⡀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀
⠘⣦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠙⠁⢠⣤⠾⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠙⣦⠀⠀⠈⠉⠉⠙⢳⡄⠀⠀
⠀⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠋⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀
⠀⠀⣿⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⡁⠀⣠⡖⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀
⠀⠀⠈⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢧⡤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢶⡄⠀⣼⠀⠀⠀⠀⠠⣴⣤⡾⠁⠀
⠀⠀⠀⠀⠀⢿⣀⣀⣴⠀⠀⠀⢠⣶⠖⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢠⡄⠀⢀⡀⠀⠀⠀⣾⠀⠀⢀⡄⠀⠀⠀⢰⣆⣀⣰⠟⠀⠀⠀⠀⠈⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⢣⣄⣀⣸⣿⠾⠋⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠶⠖⠻⢧⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠛⠷⠖⠋⠁⠀⠀⠀⠿⣦⣤⠾⢷⣄⣀⡤⠟⠉⠉⠁⠀⠀⠀⠘⠛⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⡀⠈⠉⠁⣠⡀⠀⠀⠀⠘⣶⣤⣤⣴⠿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⣶⣄⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⣿⠁⠀⠀⠀⣿⣄⡀⠀⢀⡷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠒⠋⣿⠀⠀⠀⠀⢠⡗⠀⣠⣶⠂⠀⠀⠀⣤⡀⠀⠀⠀⢠⡆⠀⠀⠀⣿⣄⣀⣀⡿⣦⣤⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠟⠳⠦⠼⠛⠳⣤⣤⡴⠋⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠚⠋⠉⠛⢻⣁⠀⠀⠀⢰⣿⠀⠀⠀⢀⡿⠷⠤⠤⣞⣉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠓⠒⠒⠋⠁⠀⠀⠀⠈⠉⠛⠲⠶⠶⠶⠖⠒⠶⢦⣤⣀⣀⣀⣤⠶⠖⠶⠦⣤⣤⣤⠴⠞⠛⠉⠛⠛⠓⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

new víla amálka amalka the fairy fairy amalka czech slovak magic flower crown wreath flower girl cute cartoo 1975 story czechoslovak little girl bloom slovakian czechian children kids crown

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣴⣿⢏⢡⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⢿⣿⣾⣿⠹⢌⢂⣿⣿⣧⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠲⣉⣞⣿⣿⢏⠲⣈⣾⣿⣿⡟⡉⠟⣿⡄⠀⢀⣤⣾⣿⢿⣷⡀⠀⠀⠀⠀⠀⣼⣿⡟⣉⠋⣽⣿⡀⠀⠀⠀⠀⠀⣰⣿⠿⡛⡿⣿⡄⠀⢀⣤⣶⡿⣿⣷⣆⣀⣿⡟⠣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⠁⢎⠿⡋⢦⣷⣿⣏⣀⣹⣟⡨⠱⢸⣿⣶⣿⡏⢉⠌⣺⣿⡇⠀⠀⠀⠀⢸⣿⢛⠰⢂⠥⣻⣿⠃⠀⠀⠀⠀⠀⣿⣯⠑⠤⡙⣿⣷⣴⣿⣿⠉⣅⠣⣾⣿⠁⣿⡌⠱⣿⣿⣦⣴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠣⢄⠃⢯⠙⢫⠟⠿⣿⣷⣡⢊⣿⣿⡗⣐⠪⣜⣾⣿⡿⠿⣿⣷⣶⣾⣿⠢⡙⠄⢎⣽⣿⣧⣶⣾⣷⣦⡀⢻⣷⣨⢡⠘⣿⣿⣿⠏⠰⣈⠰⣡⣿⡏⢘⣿⡬⢑⣿⣿⡟⠯⡙⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢉⠥⣈⣜⣢⢌⠲⡌⣌⣿⣿⣷⣫⢿⡟⢢⣵⣿⠿⢻⣿⡐⡡⢂⠌⡹⣿⣿⣱⠌⡘⣼⣿⣿⠩⢡⠃⣍⣿⣇⠈⢿⣷⡤⢩⣿⣿⢋⠌⢳⢠⣳⣿⣿⣤⣴⣿⣇⢺⣿⣿⠥⠓⢄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⢋⢡⠰⣥⡚⠸⣿⣿⡿⢿⣿⣿⡿⠿⡛⢆⠲⢌⡜⠻⠿⢷⣾⣿⣿⣴⣬⣆⣥⡘⢩⠐⢎⡐⠿⢟⠠⢃⠂⡱⣤⣿⣿⣦⣼⣿⣷⠣⢌⠃⣌⣾⣶⣿⣿⣿⠋⢍⡉⢛⠋⠜⢋⡰⣈⣵⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠤⣉⢢⣿⣿⣗⠡⢌⠻⣿⣾⣟⢂⣑⣂⣱⣮⡄⢢⣬⡇⠔⠬⡐⢻⣿⡟⠛⠛⢿⣿⣷⢈⣚⣾⣿⣶⣌⣦⣷⣿⡿⢛⠛⢩⣙⣻⣿⠁⢎⡘⠸⣛⠿⣿⣿⣿⣾⣠⣑⣮⡜⣈⢂⠡⢻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣤⣷⣼⡿⠛⢹⣿⣇⠊⡐⣿⣿⠿⠿⣿⣿⣿⣿⠘⠌⣿⡿⠿⠶⠿⠟⠋⣠⣴⡿⠿⢋⠇⣬⡔⠩⠻⣿⣿⣿⣿⣋⠔⣩⣶⣴⣾⣿⠏⡜⠠⢼⣧⢀⠣⡰⣈⢿⣿⣿⣿⣿⠟⣠⠊⡕⡈⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⢿⣿⣶⣵⡿⠁⢀⣴⠟⠁⢸⣿⢈⠲⢽⣷⠀⠀⠀⣠⣾⠟⡱⢌⠒⣉⢾⣿⣿⣇⠲⡁⢻⣿⡿⠿⠿⠟⠋⠉⣿⡏⠜⡠⢃⣿⣿⡎⠴⢁⢢⣹⣿⡿⢋⠡⢚⣼⣷⡜⡰⢈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣴⠟⠁⠀⠀⢸⣿⣂⠑⣺⣿⠀⠀⡰⣿⣏⠐⡱⣈⢒⣾⠟⠁⠸⣿⣆⠱⢸⣿⡇⠀⠀⠀⠀⠠⣿⣍⠢⣁⢎⣿⠋⠛⢿⣶⣷⣿⣿⠣⢌⠰⣳⣾⣿⣿⣄⣣⢽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠀⢻⣷⣽⣾⠏⠀⠀⠀⠹⢿⣷⣷⠿⠛⠁⠀⠀⠀⠘⢿⣶⣽⣿⠃⠀⠀⠀⠀⠐⠻⣿⣶⣬⣿⠏⠀⠀⠀⠙⢿⣿⣿⣶⣬⣷⡿⠋⠈⠻⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⠀⠀⢤⣶⡀⠀⠀⣀⠀⠀⠀⠀⣠⡀⠀⠀⣍⠉⠁⠀⢲⡄⠀⠀⠀⠀⣀⠈⠉⠀⡀⠀⠀⠀⣀⠀⠻⣎⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⢀⣿⠇⠀⠀⠐⣿⠀⠀⠀⠀⣿⡇⠀⠀⢸⣷⠀⠀⠸⣿⡀⠀⠀⠐⣿⡄⠀⠀⢸⣆⠀⠀⠹⣷⡀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢸⡿⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⠀⠀⠀⣿⡇⠀⠀⠀⢻⣧⠀⠀⠸⣿⠀⠀⠀⢻⣧⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣿⠃⠀⠀⠀⢸⡿⠀⠀⠀⠀⣿⠇⠀⠀⠀⣹⡇⠀⠀⢹⣷⠀⠀⠀⠘⣿⡄⠀⠀⢻⡆⠀⠀⠈⣿⡄⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡇⠀⣀⣰⣿⣀⣀⠀⣀⣾⡧⡀⠀⠀⢺⣿⠀⠀⠀⠐⣿⡇⠀⠀⣾⣏⠀⠀⠀⢠⣿⡇⠀⠠⣼⣷⠀⠀⠀⢻⣇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⠁⠀⠈⠉⠁⠀⠉⠙⠉⠋⠉⠐⠛⣶⣾⣿⡦⠴⢦⣴⡿⠇⠤⣾⠿⠿⠂⠤⠤⠾⠛⠷⠤⣶⠞⠟⠐⠒⠒⠺⣿⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⣿⠀⣠⠸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⣻⣿⣂⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠾⢿⣤⣼⠃⢀⡏⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⢠⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠁⠀⠀⢀⣿⣿⣶⡾⠃⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⠀⠀⠀⢲⡟⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃⠀⢀⡿⠀⠀⢸⡇⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⣤⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⣠⣶⡾⠶⢷⣦⠀⠸⣧⣀⠀⠀⠈⢿⣿⣿⠟⠁⠀⠀⢸⡇⠀⠀⢸⣧⣀⣴⣾⣿⣿⣿⣿⢿⣟⣿⣯⣿⣟⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠳⠄⣠⡿⠁⠀⠀⠉⠛⠛⠛⠋⠉⢀⣀⠀⢀⣤⣿⠁⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣿⡁⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠶⢖⡚⢯⡱⢎⣼⣿⠃⠀⠀⠀⣸⣿⣿⣿⣟⣿⣿⡿⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⣿⣧⡀⠀⠀⢰⣾⠋⡅⢦⡘⡽⣛⢷⣤⡀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⢉⡔⡎⣝⣲⣙⣾⡿⠃⢠⡆⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣽⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⠃⠈⠿⣦⣀⠏⢮⡱⣚⢦⢳⠳⣍⠶⣌⠻⣦⡀⠀⠀⠘⢿⣦⣄⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⣐⢣⣜⡳⣭⣶⡿⢫⠀⠀⢸⡇⠀⢰⣿⣿⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣯⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠰⡟⠀⠀⠀⠈⠻⣿⣦⣳⣍⠲⣍⠳⣌⠳⡌⢣⠘⢷⡄⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣌⣳⣾⡿⠟⠉⠀⣿⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠰⣸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠾⣵⣌⣲⡑⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠛⠋⠁⠀⠀⠀⠀⣿⡄⠀⢸⡇⢀⣿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠶⢤⣤⢤⣤⣤⣤⠶⠶⠶⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣇⣸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣟⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣴⣾⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠷⠿⠧⣤⣤⣤⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠠⠖⠛⠋⠉⠉⠉⠉⠉⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢰⡿⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢠⣾⠿⠶⠶⠶⠶⢦⡄⠀⠀⠀⠀⠀⢀⣤⣿⣄⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⢛⣿⠋⢹⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⣾⣧⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⠛⠛⣿⣟⣷⣤⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣻⣿⣟⣯⣿⣿⣿⣿⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢰⡟⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠈⠉⠛⠛⠶⠶⠛⠛⠋⠁⠀⠀⠀⠀⢺⣿⣿⡏⠁⠀⣿⣿⣿⣿⢿⡿⣷⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣾⡿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣳⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣼⡇⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣧⣼⣿⠀⠀⣿⣿⣿⣾⣿⢿⣟⣿⣿⣽⣿⣿⣯⣿⡿⣷⣿⣟⣿⣟⣿⣿⣻⣿⣿⣿⣿⣽⣷⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣟⣿⣿⢿⣽⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⢠⡟⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠛⣿⣶⣶⠟⠀⠙⣦⠀⣿⣿⣿⣯⣿⡿⣿⣿⣾⣿⣽⣾⣿⣻⣿⣿⣟⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⣾⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⢀⣿⠃⠀⠀⠈⠙⠛⠒⠒⠒⠒⠛⠛⠋⠁⠀⠀⠀⠀⢻⡇⠻⣆⠀⠀⠈⢷⣾⣿⣿⣽⣷⣿⡿⣷⣿⣯⣿⢿⣾⣿⢯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⢶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣸⡟⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⡴⠻⣧⡀⠀⠀⠻⣿⣿⣿⣟⣿⣿⢿⣷⣿⣻⣿⢿⣾⣿⡿⣿⡿⣟⣿⣿⣻⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⢿⣾⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⣿⠋⠀⠀⠀⠠⠻⡁⠀⠘⣿⠓⠲⣄⠀⢀⣴⡟⠁⠀⢠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢠⡿⠀⠀⠀⠀⠀⠌⣿⡇⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠘⢷⣄⠀⠀⠈⢻⣿⣿⣿⣽⣿⣯⣿⣟⣿⡿⣷⣿⢿⣟⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣯⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣾⡿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠻⢿⣿⠛⠉⠿⢦⠀⠀⠀⠀⠀⠁⠀⢴⡏⠀⠀⢻⣦⣼⠟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⢠⣴⡿⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣈⣻⣦⡀⢀⣨⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⢿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡷⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣰⣿⠁⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠉⠉⠀⠀⠀⠈⠙⢿⣿⣿⣻⣽⣿⣿⣯⣷⣿⣟⣿⣯⣿⣟⣿⡿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⢠⡾⠋⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡿⣟⣿⣽⡿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣟⣯⣿⣿⣯⣿⣿⡿⣿⣯⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⡁⠀⠀⠀⠈⠀⠀⡀⠀⠀⣼⡟⠁⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠛⠛⠛⠳⠶⠦⣤⣀⣀⣀⣀⣀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⡿⣿⣟⣿⡿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⣠⡿⠋⠀⠀⠻⣦⣀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢤⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣾⣿⣿⣿⡿⣟⣿⣷⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⡶⠟⠃⠀⠀⠀⠀⠸⣿⣄⣀⣀⠀⠀⠈⠹⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣷⣿⣿⠻⣝⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠁⠀⠀⠀⠀⠙⠻⠛⠋⠀⠀⠀⠀⠀⣰⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠘⣦⣄⣴⠏⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⣶⣶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡏⠢⢄⢻⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⠀⣰⡶⠀⠀⢠⣄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣹⠏⠀⡀⠀⠀⣠⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠙⡤⠃⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠛⢻⡟⠀⠀⠀⠀⠀⠈⠿⣧⣤⣤⣾⣿⣀⣀⣼⠗⠀⠀⠀⠀⠀⠙⠷⢶⠶⢿⣇⣀⣀⣾⣯⣀⣠⡾⠏⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⢰⡶⠀⠙⠻⠞⠋⠀⠀⠻⣷⡿⠟⠋⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⡡⢎⢰⣱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣇⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠉⠉⠁⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿⣧⣀⣠⡾⠃⠀⠀⠀⠀⠀⣀⣀⣠⡿⢧⡀⠀⠀⠈⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣟⡏⠻⣿⡆⠀⠀⠀⠀⠀⣠⡾⣿⣿⣰⣔⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠛⠛⠛⠛⢻⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠋⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠘⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠍⡉⠐⢠⣿⡇⠀⠀⣠⡴⠛⠁⠀⠀⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⣸⡟⠀⠀⠀⣀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣴⠆⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⡆⠀⠀⢀⣦⠀⠀⠀⠀⠀⣰⡆⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⠙⠓⠶⠦⢤⣤⣤⣀⣀⣀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⢃⠠⢀⣡⣿⣿⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠾⣿⣇⠀⢀⣼⣿⣦⣤⣴⣿⣿⣄⣀⣠⣾⣿⡁⠀⠀⠀⣀⣾⣏⡀⣀⣀⣾⣯⡀⢀⣼⣷⠀⠀⠀⣠⣾⠟⠛⠳⠶⠿⠷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠾⣿⡃⢀⠂⣤⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠛⠛⠛⠋⠀⠈⠙⠛⠉⠀⠈⠉⠉⠁⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡶⠶⠛⠋⠁⠀⠀⠻⢷⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠛⠛⠓⠚⠓⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⢩⠱⡌⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⣴⣟⠻⢿⣦⣿⣇⡓⡸⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣿⣿⠀⠀⠀⠹⣿⣜⠤⢿⣿⣿⢧⣱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣤⣀⠀⠀⠈⠻⢿⣴⣎⡝⣬⠿⣿⣷⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢰⣿⠿⣿⣿⣟⠛⣻⣧⠀⠀⣠⣴⡿⠿⡙⣆⠳⢄⢣⡼⢽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠽⡛⢿⣆⠀⢀⣤⣼⣿⣾⣭⣿⣇⢣⠱⣿⣶⡿⢻⠱⣌⢡⣳⣿⡟⡻⢿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣍⣮⣿⣤⣿⣫⠙⡛⠿⣿⣿⣯⢂⡝⣿⣿⣷⣨⣓⣤⣷⠿⣿⡓⠬⣉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣷⣀⣠⣶⠿⣿⣿⣿⣿⣿⣿⣷⣭⡜⣱⢂⠿⣿⣷⢾⣿⣿⣿⣽⣯⣉⠀⠀⢿⣿⡡⢎⠜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣿⠦⣑⢻⣿⣏⣃⠳⣼⣿⢋⠭⣹⣿⡟⠻⢿⣷⣯⣾⣼⣧⢊⠔⣣⠖⣩⠛⢿⣷⠀⠈⠿⣷⣾⣼⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠿⣿⣾⣿⣆⣷⣿⣿⣿⣿⣿⣿⡗⣊⠳⣡⣿⢁⣤⣾⡟⡛⢏⣻⡿⢩⢿⣶⣣⣦⣙⣾⣿⠃⠀⠀⠈⠉⠉⠀⠀⠈⠙⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠳⣘⠻⣿⣿⡿⡍⢎⠿⣿⣶⣿⡳⠌⣣⣿⠏⣾⣯⡑⠺⣔⣮⣿⡟⢆⢫⢿⣟⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣷⣬⣑⡺⣿⣿⡑⢮⢘⡹⣿⣿⡑⢮⣵⣿⣦⣌⣛⠛⠿⠛⠛⠙⣿⡎⢆⠫⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⢼⣿⣍⠛⣿⣿⣿⣿⣿⢿⣿⣦⣣⠱⡙⢯⡙⢦⠹⣍⠹⡙⢿⣿⣦⠀⠀⠀⠙⣿⣇⣳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⢫⣿⣤⣴⣶⣌⣻⣿⡿⣃⢆⡻⣿⡆⠉⠻⣿⣧⣝⡦⡘⢆⠳⣌⡣⢍⢆⡸⣻⡇⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⢆⠀⠀⠀⠉⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣢⢹⣿⣿⡡⢎⢙⣿⣿⣷⢜⡠⢽⣿⠃⢠⣶⡿⢿⠛⢯⣽⣬⠘⡿⣿⣾⡾⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⢳⣄⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣄⠿⣷⣍⣿⣿⡔⢃⠎⣾⣿⡏⢎⣴⣿⠁⢠⣿⠏⣔⠣⡝⣾⣿⡣⡓⢬⡙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠙⣧⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⡴⢻⣧⣠⣿⣿⣿⣷⣍⡚⢾⣿⡏⢦⣿⣁⣐⣿⣿⡘⣤⣣⡿⠛⢻⣷⣉⠦⣉⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠈⢷⡄⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⡀⠀⢸⣧⢫⠔⣻⣿⣯⡙⢦⡙⠬⣏⠱⢡⠦⣡⣿⣿⠛⡟⢻⣿⣿⡛⠉⠀⠀⠀⠻⣿⣶⣌⣾⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⣦⠀⠀⠙⢿⣦⡀⠀⠀⠈⢳⣤⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠻⣦⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⡛⡹⢟⣿⣾⣷⢣⣚⣼⡟⠻⣷⣦⣹⣌⣦⣽⣶⡿⢱⣶⣢⠣⡜⢦⠹⡽⣷⡄⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⢻⣧⠀⠖⠛⠻⢿⣦⡀⠀⠀⠘⠻⣄⡀⠀⠀⠀⠀⠹⣦⠀⠀⠘⣷⡀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⢿⣷⣑⠎⡔⠛⠿⡗⢾⣿⣷⣾⢿⣿⣿⣏⠋⣹⣿⠡⡍⣿⣿⣷⡌⢆⡳⣘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠘⣿⡄⣠⡾⠿⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠉⢳⣄⠀⣴⡄⠀⠘⣷⡀⠀⠈⢿⡄⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠛⠻⣿⣿⡶⣉⠶⡘⡖⡌⡆⡜⢦⣿⢷⣿⢃⠧⡘⣽⣏⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⢻⣧⡀⠀⠀⣼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠙⢷⣼⡇⠀⠀⠈⢻⣄⠀⠀⢿⣄⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⡿⢋⠖⣔⢢⡑⣿⣾⡿⠿⠟⠁⢸⣿⣌⠲⣡⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⢹⣧⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠻⣆⠀⠀⢻⣄⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣟⡡⢋⣼⣿⣧⠰⡸⣹⣷⡄⠀⠀⠀⢿⣷⣳⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠈⢿⣧⣠⠴⠿⠛⢓⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⣸⡿⢷⡀⠀⠀⠀⠹⣦⠀⠀⢻⡆⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣴⣿⡿⠻⣿⣧⡑⢆⣻⣷⠀⠀⠀⠈⠛⠟⠋⠁⠀⠀⠀⢠⡀⠀⠀⠸⣷⡀⠀⠘⢿⣦⠀⠀⣀⣴⡾⠟⠁⢀⣴⣾⠿⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⣿⠇⠈⠻⣆⠀⠀⠀⠹⣇⠀⠀⢿⡄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠈⠳⣾⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣿⡄⠀⣈⡻⣿⡶⠋⠀⠀⠀⠀⢸⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣠⡿⠀⠀⠀⠙⣧⠀⠀⠀⠹⣧⠀⠈⣷⡀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⠀⢠⡀⢸⣷⠀⠘⣿⡀⠀⠀⠀⣙⣿⣷⣬⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢀⣤⠴⠋⢁⠠⡉⣻⣿⡇⠀⠀⠀⠀⠘⢷⡀⠀⠀⢹⡆⠀⠘⣧⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⢸⡇⠈⣿⡆⠀⠹⣿⣄⠴⠛⠁⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⣠⡟⢁⡤⢠⢌⡒⠄⣽⣿⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⡀⠀⠸⣇⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢸⣧⢸⣇⠀⢹⣿⡄⠰⠛⢿⢂⣤⣴⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⣴⣿⠟⠙⢹⡟⢡⠚⣽⣛⢧⡞⣼⣾⣿⠛⢷⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢘⣿⡜⣿⡀⠀⠛⠓⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⠟⠋⠻⠿⠶⠏⢦⡁⢏⣾⣹⢮⡽⣿⡿⠃⠀⠘⣷⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢈⢻⣇⢻⣧⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⡈⢜⢢⡙⣿⢧⢯⣻⣿⡟⠁⠀⠀⢀⡿⢿⡆⠀⠀⠀⠀⠀⢿⡄⠀⢀⡀⠀⠀⠘⣷⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⡞⣿⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⢌⡷⣻⣼⣾⣿⡟⠁⠀⠀⠀⣾⠃⢸⡇⠀⠀⠀⠀⠀⠘⣷⠀⠘⣧⠀⠀⠀⢻⡄⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⢸⣧⠹⣿⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⣾⡿⢋⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⣄⣻⢮⡱⣷⣷⣿⣿⣿⣷⣶⣶⣶⣷⣤⣼⡿⠛⠿⣦⠀⠀⠀⢹⡆⠀⠹⣆⠀⠀⠈⣿⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢻⣇⢹⣷⣿⣷⡀⠀⠀⠀⠀⠾⣶⣤⣀⣠⣴⣿⣿⣇⠀⠀⠀⠻⠿⠟⠋⠁⠀⠀⠀⣠⣾⠇⠀⠀⠀⠹⢿⣿⣿⣏⣁⣀⣾⡇⢹⣿⡟⠉⠉⠻⢷⡆⠀⢸⡇⠀⠀⠈⣿⡀⠀⢹⡆⠀⠀⢸⣇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⢻⣆⠻⣷⣿⣷⡀⠀⠀⠀⠀⠈⣿⠟⢻⣿⠁⠈⠿⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⠿⠟⠉⠀⠀⣀⣤⣶⠿⠋⠁⠉⢙⣿⢻⣷⡄⠁⠀⠀⠀⠀⢀⣿⣤⣿⠀⠀⠀⠀⢹⡇⠀⠀⢿⡀⠀⠀⢿⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠻⣦⠈⠻⣿⣷⣄⠀⠀⠀⣸⡟⣠⣼⠿⡙⠦⡐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠟⢉⣀⣀⣀⣀⣠⣾⣡⣼⠋⠀⠀⠀⠀⠀⠾⠿⠯⣽⣿⡇⠀⠀⠀⠀⠷⠀⠀⠘⣇⠀⠀⠘⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠙⣷⡀⠀⠙⢿⣷⣦⣤⣁⡸⠱⡈⠞⢡⠓⡌⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⡿⠿⠿⠶⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢹⣇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⢷⡄⠀⠀⠘⢿⡟⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠻⠛⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⢛⣩⡿⠏⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⢻⡄⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠈⢻⣦⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⣋⣡⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣤⠶⢷⣆⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠙⣷⡀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⣿⣿⣧⣤⣴⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣧⡀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠋⢡⡿⠋⠀⢀⣼⠟⠉⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠘⢷⡄⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣄⣀⣀⣀⣠⣤⣴⣶⣾⡟⠋⢻⣦⡾⠋⠀⢩⣿⡿⠁⠈⣿⠀⠈⣿⣿⣶⣶⠶⠛⠁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⢷⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣵⡿⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠈⢿⡄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⡿⠉⠉⠛⣿⣧⡀⢸⠟⠀⠀⣰⣿⣿⣄⣀⣠⣿⣷⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠈⢻⣄⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⠀⣰⠟⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠈⢿⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⡾⠟⠻⠓⠋⠀⣠⠼⠿⠿⣿⣿⠋⠙⢻⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠙⠛⠶⢤⣤⣤⣴⣿⠿⠃⠀⠀⣀⣴⠶⢿⣿⣤⣤⣤⣤⠀⠀⠀⢀⣼⣿⣤⡴⢤⣤⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⢿⡄⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣄⣿⡇⠀⢀⣠⣴⠀⠀⣼⣄⣀⣨⣭⣿⡆⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠟⣿⣄⣴⢿⣷⣴⣶⣶⡄⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠉⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⢁⣴⠟⠋⠉⢉⣩⣿⣅⣀⠀⠿⠋⠉⠀⢠⣼⠿⠛⠉⣹⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠈⣿⡀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢀⣾⡏⠀⣿⡟⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⠿⢛⣋⣷⠂⠀⠀⠀⢠⣾⠟⣿⣿⠁⠸⣿⣦⣾⣿⣿⡀⣿⠋⠀⣼⡇⠰⡄⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⠶⠦⠀⠀⠀⠀⠀⠘⠋⠁⠀⢰⠾⠟⠛⠛⠛⢻⣿⠂⠀⠀⠀⠙⠉⠀⠀⠶⠟⠏⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢹⣧⠀⠀⠀⠀⣿⡄⢠⡶⠿⢿⣿⣇⡀⢿⡿⠋⢡⣿⠉⠹⣿⣦⣶⡿⠻⢿⣷⠿⠋⠁⢀⡀⢀⣠⣿⣿⠿⠛⢻⣷⣄⣼⣿⡉⠉⠻⣧⣿⣤⣾⣿⣄⠀⢻⡄⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⡟⠁⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⢀⣾⢿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠳⣦⣤⡾⠿⠿⣦⣀⣤⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠀⠐⠸⠿⠀⠀⠀⠀⢸⡇⢸⣷⣴⣿⠁⣿⡃⠸⣿⣾⣿⣿⡀⢀⣿⡏⠁⠀⠀⠸⣿⣶⢶⣶⠟⠁⣾⠋⠉⠀⠀⠀⠀⠉⢛⢻⣿⣿⣶⣶⣿⣿⠟⡀⠈⢻⣇⠀⢿⡄⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢻⣷⠄⠀⠀⠘⠛⠛⢻⣇⠀⠀⠀⠶⠟⠛⠛⠓⢶⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠄⠀⠀⠙⠃⠀⠀⠈⠿⠁⢀⣄⡻⠆⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣿⡟⣿⣷⣾⣧⣤⣿⠋⢹⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣸⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⣼⡇⢈⣿⡄⠻⣿⡿⢿⣆⠀⢻⣆⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡶⡶⠟⠉⠀⠀⠀⠀⠀⠻⢿⣧⡀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠲⡄
⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠈⠛⠿⢶⣤⣦⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣿⣷⣿⣇⠈⠉⠻⣧⣠⣼⣿⣯⡀⠀⠀⣶⣤⣄⣀⠀⠀⢹⣿⣾⣏⣀⣤⣴⠆⠀⠀⠀⠙⣿⡧⣠⡿⣿⣷⣾⠿⢿⣾⣿⢀⣸⣿⣀⠀⠙⢷⡀⠀⠀⠀⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⣤⡿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣠⠆
⠀⠀⠀⠀⢠⣿⠿⠆⠀⠀⢀⣠⣴⣤⣾⡏⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⡀⢸⣿⠛⠻⣿⣿⣿⣿⣿⣅⡀⠈⣿⡄⠀⠀⠉⠙⠛⠿⠿⠿⠛⠛⠉⠉⠁⠀⢀⣴⣶⣦⣠⣿⣿⣿⠛⠋⣹⣿⠿⢼⣯⣩⣿⠉⠉⢻⡆⠀⠈⠻⣦⣀⠀⠀⠀⠉⠻⢷⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⣠⣤⡀⠰⣦⡀⠀⠀⠈⣻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣿⡍⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣤⣿⠿⢾⣿⡶⢰⡟⠀⣸⣿⡁⠘⢿⣷⠟⠃⠀⠀⠀⢀⣴⡿⢷⣆⠀⠀⠀⠀⠀⠀⢻⣇⠀⢹⣿⠁⢈⣿⣦⣾⣿⣯⣥⣄⠉⠉⣿⣶⣶⡿⠃⠀⠀⠀⠀⠙⢷⣄⣀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣇⣼⠟⠳⠶⣶⡶⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣠⡟⠀⠀⠀
⠀⠀⠀⣿⣤⡀⠀⠀⢀⣤⡾⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣸⡟⠀⢸⣷⣼⡿⣿⣷⣤⣠⣿⡄⣠⡶⠿⢶⣾⡏⠀⢸⣯⣤⣤⣀⣀⣴⠶⠿⠿⢷⣿⡁⠰⡿⠋⣩⣿⡿⠛⠉⣿⣧⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣄⣿⣿⣤⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⣤⠀⣰⣧⣀⠀⠀⢀⣿⠟⠉⠁⠀⠀⠀⠀
⠀⠀⢰⡿⠉⠀⠀⢀⣿⣋⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣾⣿⡄⣄⣾⣿⢿⣷⣦⣬⣿⡟⠻⣿⣿⣄⡀⠀⠘⣿⣤⣾⡟⠉⠙⣿⣿⣧⣤⣴⠟⠋⣻⡇⠀⢿⣾⣿⣿⠁⢀⣼⡿⢫⢁⣾⡟⠀⠹⣧⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠉⠉⠀⠀⢁⣀⣀⡀⠀⠀⠀⢶⣆⢀⣸⡟⠛⠉⠁⠉⠛⠲⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣷⣀⠀⠀⢀⣿⠟⠋⠁⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠐⣾⡟⠁⠀⠀⠻⠿⠿⠛⣿⣄⡀⠉⣿⡏⠀⣠⣿⣿⣿⣿⣶⣶⢿⣿⠼⣿⣶⣿⠿⢿⣏⣹⣿⣤⡶⠿⣷⣄⣸⡟⠁⣀⣼⣿⠿⣧⣾⠟⠋⠀⠀⠀⠹⣷⣄⣠⣾⠿⣋⢝⣿⡇⠀⠀⠀⣀⠀⠀⣤⡀⠀⢰⣿⣿⠀⠀⠀⢀⡄⠀⠀⣸⡿⠛⢿⣄⠀⡀⣸⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠙⠛⠛⠻⣿⣤⣠⣤⠶⠻⣯⡀⠀⣀⣠⣾⠟⠀⢀⣾⠇⠀⠀⢀⣤⠀⠀⠀⢠⣾⢿⡝⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠛⠃⣿⣿⣞⡛⠉⠉⢻⣿⡟⠀⣼⣿⣄⢸⣿⡇⠀⢸⣿⢿⠟⣿⡇⠀⠈⠛⣿⡿⠛⠋⣿⠏⠀⣿⠇⠀⠀⠀⠀⠀⠀⢙⣿⡿⡿⣁⢖⣸⣿⣿⣶⠀⢘⣿⣆⣠⠿⠿⣤⣼⣿⣇⠀⠀⢠⡾⠷⣦⣠⡟⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠻⠶⠶⢿⣇⡀⢀⣴⠿⠟⠶⠶⠾⢿⣿⣋⠜⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣾⠏⠉⠻⣿⠶⠾⠟⠻⢿⣾⣿⡿⠿⠟⠻⣷⣶⣿⣯⣤⣾⠟⠁⠀⠀⢸⣿⣀⣀⣴⣿⣤⣾⠟⠀⠀⠀⠀⠀⣀⣴⣿⡿⢋⡴⢌⣼⣿⣟⣾⠿⠷⠞⠋⠈⠁⠀⠀⠀⠀⠀⠙⠷⠶⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⢻⣇⡓⡸⢏⣿⣆⠀⠀⠀⠰⣦⡀⠘⢿⣶⡾⢿⣧⠀⠀⢻⡇⠀⠀⠀⠀⠘⢿⣦⣤⣤⣴⡿⣷⡏⠉⠉⠻⣧⠀⠀⠀⠈⠛⠛⠋⠁⠈⠉⠁⠀⠀⠀⣀⣴⣾⣟⣿⡿⣐⠣⣴⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡑⠮⡜⣿⣿⣦⣄⠀⠈⠻⢶⣄⡀⠀⠀⠙⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠉⠉⣽⠋⠀⣿⠿⣦⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠹⣿⣻⡿⡐⣣⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣥⣓⣌⡹⣿⣹⡿⠛⠶⣤⣀⠙⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡾⠏⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠈⠛⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣧⣿⣿⠿⠁⠀⠀⠀⠉⠳⠦⣄⣀⠉⠙⠛⠷⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⢉⣀⣀⣀⣀⣀⣠⣤⣤⠶⠞⠛⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⣀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⢀⣀⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⠖⠛⠋⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⢘⣿⣻⣿⢿⡿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⢿⣿⣿⣿⣿⣿⡯⢻⣷⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡐⢂⡐⠞⡿⢿⡁⠖⠻⠟⠿⡟⢯⢹⡯⣿⣟⣿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣿⣾⢽⣂⠣⠌⡛⢿⡟⣿⣾⣿⣿⣿⣿⣾⢃⢻⣿⣹⣿⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠣⣾⣷⡈⢆⣡⣿⣿⠿⠿⠻⣿⣾⣿⡿⣧⢼⣿⣿⣿⣿⢿⡿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠟⢡⢣⢭⣿⣹⣠⢌⡟⣿⣝⢦⡡⢙⣻⣿⡿⣵⢿⣿⣿⢿⡛⣤⣿⢿⣻⣿⠃⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣤⣟⣼⡿⢿⣿⣯⣻⣿⠟⢿⣷⣿⣿⣿⣿⣛⡬⠻⢅⣿⣎⣿⣿⣿⣿⣿⣿⣶⣦⣀⣴⣿⣿⣿⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⡾⠟⠋⠀⠀⠙⠋⠉⠁⠀⢀⣼⣿⡿⢃⠎⡱⣾⢁⠎⡘⣻⠿⣿⣟⡫⢉⠟⢿⣿⣿⣿⣿⠴⣦⣿⣽⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢯⡙⠄⣃⠚⣹⣿⠣⢆⡐⢡⢚⣹⣿⡷⣧⡌⢂⠻⠾⠲⡖⠢⣿⣿⡿⢻⢶⣾⣿⣿⠀⢀⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⠾⢶⡥⢾⣵⡿⣿⣿⡶⢌⣶⣡⣿⠿⢿⣾⣿⡣⢌⢁⠣⢉⠆⡩⣁⢊⣡⣚⣿⣿⡏⢀⣾⣿⡟⠻⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠃⠀⠀⠀⠀⣀⣴⠾⠛⢛⣷⡄⠀⠀⠈⡻⠿⣿⣶⠿⠛⠋⠀⠘⠿⡷⣿⣷⠿⠋⣠⣾⣿⠻⣑⢊⠤⡘⢄⠢⣅⣹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣁⠃⣿⣿⣿⣀⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⡁⠈⠀⠀⠀⣠⣾⠋⡥⣰⡾⠟⠋⠀⠀⠀⢀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢛⣋⣐⣤⣯⣿⡏⢄⠣⠄⣿⣿⣿⣩⡉⡙⢻⣿⣿⡟⠤⣉⣾⣿⣿⢿⣟⣿⣿⣿⢀⢀⣤⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢃⠀⠀⠀⢀⣠⡾⠛⠇⠢⣼⡟⠁⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣥⣭⣷⣾⣿⣌⣆⣣⢌⣧⣿⣿⣝⠶⣅⢢⡔⢠⠘⡐⢰⣾⣿⣿⣾⣿⣿⣿⣿⣥⣿⣿⡟⣿⡻⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢠⡿⠟⠀⠀⠀⠀⣿⣄⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠛⠃⠘⢿⣿⣜⣛⣻⣿⡿⠿⣿⣿⣿⣿⠀⡄⠇⡸⠸⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⡟⣸⣿⣻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⣴⠟⠁⢸⣆⠀⢠⡄⣠⣅⠀⠰⣼⡟⠀⠀⠀⠀⠂⣴⡿⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⢀⣾⣿⢇⠂⡍⡐⣦⡐⠹⠿⢿⣾⣿⣿⠿⠿⢿⢿⠿⠉⠽⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢀⣾⠏⠀⢀⣼⣿⣴⣿⣷⣶⣿⠀⠀⠘⠛⠷⢶⣜⣠⣾⠋⠀⠀⠀⠀⠀⣼⡗⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢣⡍⢢⡑⠲⣧⣿⣎⠡⢓⡭⣿⣿⣶⣡⢊⠔⡂⢂⠉⡜⡿⣍⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⣠⣹⡏⠀⡀⣼⣿⣿⣿⣿⣿⡟⢿⣇⠀⠀⠀⠀⠀⠘⠛⠻⢷⣦⣄⠀⢠⣼⡟⠀⠀⠀⠀⣸⡇⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣮⣡⣿⣿⢿⣿⣛⣾⣟⣿⠟⣻⣿⡿⢗⠂⡱⣈⠜⣼⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢠⡆⢋⣿⠀⢀⢹⣿⣿⣿⣿⣿⠏⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣯⠆⠀⠀⢸⣰⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠛⠻⠿⠟⣻⣿⠟⢫⠐⣊⣷⣿⡷⡘⣯⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⠁⢸⡇⠀⠀⠘⢿⣿⠟⠋⠁⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡁⠀⠂⠀⣾⣿⡅⠀⠀⢠⣾⡏⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡵⣠⡾⣴⣾⣿⣻⣁⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢰⡟⠀⢸⡧⠀⠀⠀⠈⠙⠳⠶⣤⣤⡴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣷⣤⢻⣇⠉⠁⠰⣾⡟⣠⠀⠀⠐⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⡶⠟⠋⠉⢻⣿⣛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣿⠃⠀⢸⣿⠀⢆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣿⣷⣾⣿⣷⣿⣷⣄⠀⡀⠀⠀⠀⠀⢠⡾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣿⠀⠀⢸⣿⣍⠐⢢⢁⢂⠀⠀⠀⠀⠀⠀⢠⣾⡶⣤⣄⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⣷⡁⠀⠀⠀⠀⢸⡟⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢸⣿⠀⠀⠈⢸⣿⡈⠆⡌⡘⠃⠀⠀⠀⠀⠀⠻⣯⣃⣘⣿⠇⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠃⣿⡇⠀⠀⠀⠀⠘⠂⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⢻⣷⡨⠴⠀⠀⠀⠀⠀⣦⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠁⢹⣿⣿⠛⠉⠀⠀⠀⠀⢤⣿⠃⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠴⠦⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠌⠻⣦⡄⠀⠀⠀⠀⠉⠻⣦⣤⣀⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠤⠰⢆⣠⣄⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠖⡹⢎⢣⠑⡆⡘⣿⡂⠀⠀⠀⠀⣀⣿⡟⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠻⢿⣭⣛⠓⠦⣤⣤⣀⣀⣀⠀⠀⠀⠌⢢⠑⠊⠄⠣⡔⢡⣈⣣⣤⣤⡶⠟⠛⣿⠃⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⢀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣾⡴⠾⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⢿⡻⠿⠶⠾⠶⠾⠶⠿⠷⠟⠛⠛⠉⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⢻⡿⣬⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢀⣀⣠⣿⡟⠋⠉⠉⠻⣄⠀⠀⠀⠀⠀⠳⠶⣤⣀⣀⡀⠀⠀⠀⠈⢻⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠛⢻⣷⣦⣤⣀⠈⡙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠗⠛⠛⠉⠉⠉⠁⠈⢻⣦⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠓⠛⠉⠻⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣧⣻⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣷⣄⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣈⣿⢻⣿⣿⡟⠛⠛⠛⠶⠶⠶⠶⠶⠶⣤⠶⡴⠶⠶⢶⡶⠟⠛⠉⠉⠀⣼⡿⠷⣤⡀⠀⠀⠀⠈⠙⠛⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢠⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡟⠁⣿⠁⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣰⡿⠀⠀⠈⠙⠛⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡶⠞⠋⠉⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡿⠀⠀⣿⠀⡇⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣻⠁⠉⠻⣦⡀⠀⠀⠀⠀⠛⠷⣦⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠹⡧⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠸⠼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⠁⠀⢈⡇⠀⢷⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡏⠀⠀⣨⡇⠀⠸⣇⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠈⠙⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡿⠀⠀⠀⣿⡃⠀⠀⢻⡆⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⢀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⡀⠀⠀⠌⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠐⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣷⣿⠋⠁⠈⠀⣻⣦⡶⠿⢷⣄⠀⠀⠀⠀
⠀⠀⣿⠇⠀⠀⠀⣿⡇⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢦⣤⣀⠀⠀⠉⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣿⠏⠿⠗⠀⠀⠀⠀⠙⠃⠘⢩⣎⣿⠀⠀⠀⠀
⠀⣴⡟⠀⠀⠀⠈⡟⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠡⣾⣷⣀⣸⣷⣶⣭⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⣤⣄⡀⠀
⢰⡿⠁⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⣿⡉⣼⣷⣄⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠙⣿⡄
⣿⡇⠀⠀⠀⢀⡠⠄⢿⡄⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣦⣀⡀⠀⠀⠀⠀⢀⣀⣤⡾⠛⢻⡏⢻⡏⠻⣿⡏⠀⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⢶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇
⠛⠛⠛⠛⠛⠾⣦⣄⠈⠻⠀⠀⠀⠀⠀⢻⣆⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⢠⡾⠀⠀⢻⡄⠈⠛⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠷⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠺⠿⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣻⣾⡳⠀⠀⠀⠀⠀⠀⠈⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠻⣄⠀⠀⠀⠉⠛⠛⠷⢶⣤⣤⣤⣤⣤⣤⣤⣴⣿⡶⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠡⠿⣷⣀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢠⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣹⡧⠀⠀⠀⠀⠀⠀⠀⢰⢿⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠙⠛⠶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⣶⣶⣶⣶⣶⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡌⢻⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢿⣶⣦⣤⡀⠀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⢿⣷⣦⣴⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠋⠁⠀⠀⠀⠈⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠙⠿⢶⡶⠾⠋⠉⠉⠁⠀⠀⠀⠀⣾⣿⣦⠤⢀⣼⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠞⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡿⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⢐⣷⡄⠀⠀⠀⢠⣿⣦⡄⣀⣿⡇⠀⠀⠀⠀⣠⣶⣦⠀⠀⣰⣶⣄⣀⣀⣸⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢠⣾⡇⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠟⠛⠙⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠈⣿⣷⠀⠀⠀⠈⣿⣿⣿⠟⠋⡆⠀⠀⠀⠀⣿⣧⣿⡳⣦⣿⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⡿⠀⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠚⠙⣿⠰⠀⢦⣄⠀⠀⠀⢨⣝⡛⠿⣶⣤⣤⣤⡴⠶⠋⠁⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣶⠟⡟⢻⠷⠾⠟⠉⠈⠀⢰⣾⣇⠀⠀⢀⣠⣽⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⣿⡐⣤⣹⡿⠦⣄⠀⣾⣿⣧⡀⠀⢀⣶⡄⠀⠀⠀⠀⢠⡘⠿⣶⡶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⠀⠀⠉⢶⣴⠂⠀⠀⠀⠸⢿⣿⣤⡴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⣤⣤⣴⠶⠶⠛⣿⠁⠀⠀⠀⠀⠀⠀⠘⠿⡿⠛⠿⢷⣬⡴⠟⠻⣿⣯⣤⣾⣿⡀⠀⠀⠀⢀⣾⡧⠄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⣿⣿⡶⠄⢀⣾⣿⡷⠆⠀⣤⣶⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣶⣴⠾⣿⡅⢀⠀⠀⠀⠀⣼⣿⡿⠂⠀⠀⣠⣿⣦⣠⠤⠀⣀⣾⠿⠛⠛⠛⠉⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣤⣤⡶⠟⠿⢶⣤⣽⠾⠛⠁⠈⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣾⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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