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

new seidnu stnaprednu sfeirb yag elcsum ralucsum yxes toh raewrednu gniraew nam tra tod tra txet tra iicsa

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⣠⠅⠒⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢁⡐⠌⢀⠉⣖⠃⠈⠉⠉⠈⠂⠐⠁⠊⠕⠦⠤⠉⠂⠒⠁⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡠⠌⠀⠜⢀⠋⠔⢣⠉⠒⠔⠤⡀⣀⠀⠤⣉⢈⠒⠤⠁⡉⡞⠼⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠐⠀⠀⠀⠀⠊⠠⠀⠁⡰⠁⡔⢀⠉⡖⠝⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠤⣠⠀⠂⠔⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠀⠅⠭⠩⠊⠒⠒⠒⠖⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠂⠒⠒⠒⠒⠐⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠀⣀⣀⠀⠀⠁⠉⠈⠒⠓⠴⡀⠀⠀⡀⠀⠂⡠⠁⡔⢀⠁⡴⠀⠀⠀⠀⠀⠐⠤⠀⡀⠀⠀⠉⠋⠖⣠⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠐⠀⠥⠩⠉⠒⠒⠄⠤⡠⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⢀⠁⠒⡠⢀⠀⠀⠀⠀⠀⠀⠀⠖⡠⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡔⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠡⢚⠤⠤⡠⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠠⢡⡈⠒⢈⠔⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⡌⠀⠀⠀⠀⠀⠀⠀⠁⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⢂⢡⡘⡍⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠁⠈⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠌⠃⡠⠕⢊⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠏⢂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠠⠀⠈⠀⠐⠀⠄⠩⠊⢒⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠂⠓⠄⠤⠠⠐⢀⠐⠀⠡⠉⢂⠒⠄⠤⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠁⠐⡠⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠒⠜⠼⡢⣄⡉⠉⢈⠒⠒⠐⠤⠤⠤⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠓⠚⠙⠉⠉⠈⠀⠊⠑⠜⠭⠦⣈⣱⢃⡩⠒⢒⠤⠤⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⡐⠒⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡈⡱⠖⣋⣴⢞⠯⠾⠶⢤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⣪⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠢⠑⠈⠀⠀⠁⠀⡁⠂⢈⡱⠮⢒⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠂⠠⢀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠒⠉⠒⠔⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡠⣀⠄⡀⣠⢐⠧⠤⠓⠒⠙⠤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡂⠔⢎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠊⠄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⣀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠬⢱⢨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡯⣙⢯⡍⠳⢌⡹⠆⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡠⣔⠀⢠⡀⣀⣀⣠⣄⣀⣤⣤⡦⠖⠱⠿⠋⠛⠒⠴⠭⠬⠤⠂⠒⠉⠀⠀⠀⠀⠀⠀⡈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⠲⠉⡀⣀⢀⠤⠂⣑⠢⠙⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⠉⠀⠤⠤⠀⠒⢍⠑⠘⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠚⠒⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡤⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠠⣀⣀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⢀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡎⣀⠄⠠⠐⠉⠠⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠐⠀⠊⠫⡱⣼⠀⠀⠀⠀⠀⡁⢜⠠⠂⢁⠌⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⡀⡸⠀⠏⢟⢣⡼⠀⠀⠀⠀⠀⠁⡴⠀⠀⠀⠀⠀⣀⠄⠠⠒⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣿⢿⣿⢠⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠄⠠⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣾⣠⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⢌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠰⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠟⡈⠀⠀⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠸⠀⠀⠀⠀⠀⠀⢘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠒⠒⠘⠽⠠⢀⡀⠱⡄⣿⠘⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢹⢀⠀⠀⠀⠀⠃⠀⣝⢾⢠⠀⠀⠀⠁⠋⠶⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡶⣤⣀⢀⠀⠀⣇⣏⢻⠀⠀⡄⠹⣧⣿⠘⠀⠀⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠃⠃⢠⠙⢹⠟⣱⠀⠻⠀⠀⠀⡼⢀⠁⠈⠙⡏⠘⠻⣟⣛⣷⣿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠋⡾⣤⢀⠀⠀⠀⠀⠀⠀⠀⢷⣿⢻⠈⠀⡄⡘⣿⣿⠈⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣼⢫⠶⣤⢠⣀⣀⣀⣤⢶⡻⢯⠙⠇⢛⠇⡏⢿⣼⣀⢀⠀⠀⠀⠀⡀⣄⣦⣷⠿⠈⠀⠀⠁⡟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⢻⠀⠀⡇⡇⣿⢸⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⣿⣿⢿⣿⣰⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠹⠁⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢱⣿⣿⢳⠀⠀⡿⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣾⢀⢀⠀⠰⢀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡏⡄⣿⣿⡸⢿⠀⣇⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⡎⣼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣯⢸⣷⣿⢸⡄⠸⡇⣯⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡆⣉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠇⢤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⣸⢸⡇⣿⢸⠀⢧⡏⣟⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⡇⢻⢹⡟⣿⢸⠀⡄⣾⣿⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⣿⣿⣻⣿⣿⢸⠀⡇⣿⣸⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠁⠰⠀⠀⠀⠀⠀⠀⠔⢀⠀⠀⡇⣿⣿⣿⣿⣿⢠⠁⡿⣾⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠢⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡸⠀⠀⠀⠀⠀⠃⡠⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⠀⡟⣿⢸⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠏⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⢇⣿⣿⣿⣿⣿⢸⡟⣿⢰⢸⠀⠀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⠀⠀⠀⠀⢏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⡛⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣬⠀⠃⢠⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⡇⡽⣿⣿⣿⣿⣟⣿⣼⠃⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢠⠀⠀⠀⠃⢠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠂⠖⡤⠃⢠⠃⢠⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠂⡇⣽⣿⣿⣿⣿⣿⣾⠀⡏⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡸⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡟⢠⠀⠁⠉⠉⠉⠒⠄⠤⡀⣄⠀⠠⠀⠀⠀⠀⠜⢀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡿⣿⣿⣿⣿⢠⠁⢸⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⡘⠀⡏⣸⡜⢍⠛⠔⡠⠁⠂⠄⠀⠀⣀⢀⠀⠀⠀⠀⠞⠈⢠⠀⠀⠀⠀⠀⠀⠀⣿⣺⣿⣿⣾⡷⣹⠀⡏⢠⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡕⣿⡄⡈⣀⡄⠘⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⢿⠀⠀⠀⠀⠀⠀⠀⣇⣿⢿⣿⣿⡌⣿⣿⠁⣼⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸⡀⣿⢼⣅⡤⠤⡖⠈⠀⠀⠀⠀⠀⠀⠀⠁⠊⡿⣞⠂⠀⡇⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣽⢦⢸⡇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠉⠀⠂⠐⠤⠠⡀⣀⠀⢸⡇⣿⢸⠁⣼⠤⠰⢒⠑⠀⠀⠀⠀⠊⡠⣇⣿⣿⠃⢜⢀⠀⠀⠀⠀⠀⠀⠅⡿⣿⣿⣿⣿⣿⠇⠀⡇⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⢿⠿⠻⠛⠙⠋⢸⣿⣿⢺⡟⣰⠠⠷⠿⠷⠾⠀⠃⡴⠥⠀⡀⢿⣯⡿⢸⠀⠀⠀⠀⠀⠀⠛⡿⣿⣿⣿⣿⣿⢸⠸⠀⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣸⣃⠂⡍⣧⣴⠀⠊⣶⣶⡷⠿⣿⡿⣿⣿⣿⠛⠉⠉⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡏⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢸⡀⠤⠚⣄⠉⠔⠀⠀⠀⠀⠀⠀⡀⣀⣤⣷⣿⣿⣿⣿⣿⣿⣿⢿⣻⣧⣿⣿⣿⣿⠇⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⣿⣿⣿⣿⣿⣿⣿⢙⣿⣷⢀⠓⣰⠀⠀⠀⠄⣷⢾⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣇⣿⣿⣿⣿⣿⣿⣧⣿⡟⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡈⣥⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⣿⣾⣿⣿⣿⣿⡷⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠉⡒⠒⠈⣄⣷⣿⣿⣻⣿⣿⣿⣿⣿⣼⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⡨⠫⡀⠢⠉⣯⣿⣿⣿⣿⣿⣷⣿⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠄⠝⢇⠙⠀⡅⣈⣿⣿⢻⠀⣿⣨⣿⣿⣿⣿⣿⡽⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣟⣿⣿⣿⣿⣾⢨⠁⠖⠤⠄⠢⠈⡄⠖⣎⠽⡟⢻⣮⢿⡙⣧⣾⣶⣶⣷⣸⢧⣏⣿⣿⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⡿⣼⣿⣿⣻⢿⢸⠸⢹⡏⣽⠻⡿⠘⠃⣼⣷⣿⣿⣿⡿⣿⠹⣇⠘⠀⠉⣯⡏⣿⣻⣿⣿⣿⣿⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⢀⣿⣿⣿⡿⢻⢹⠂⠋⣿⣿⣿⢿⣵⣔⡀⣵⣿⣿⣿⣿⣿⢻⣧⣘⠀⡆⢻⣿⣿⢾⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⡗⣿⣿⣿⣯⣝⣮⡾⣶⣶⣹⢌⢛⠀⠁⡔⣿⣯⣽⣿⣯⣿⡘⣿⠙⠀⣿⣿⣷⣿⣿⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣽⣿⡿⣿⣿⣾⢿⣷⣿⢿⠺⠉⡀⣧⡻⣿⣻⠈⡇⣻⣿⡿⣿⣽⣿⣿⣿⠃⣻⣿⣿⣿⢾⣽⣿⣿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣻⣽⣿⣿⣿⣿⣻⣷⣿⣿⣿⣿⣾⢛⣌⣿⣿⣿⠸⣷⣹⣽⣹⣦⣆⣎⣼⢻⣿⣿⣧⢽⣮⡟⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣳⣿⣿⣿⣿⣞⣻⣽⣿⣯⣿⣿⡯⣿⡿⣿⣿⣾⣯⡝⠸⡀⠰⠁⢣⢹⡆⣿⣇⡟⣳⢿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣻⣿⣯⢿⣿⣯⢷⣻⣿⣿⣿⣾⣿⣾⢿⣗⣿⡔⠱⣧⡘⠑⡇⡞⣻⣿⠏⣿⢻⣿⣷⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢾⣿⣯⣿⣟⣿⢿⣾⣿⣿⣻⡻⣺⡳⠢⡙⢦⠻⠫⣏⡿⡹⢿⣯⣳⣿⣿⢯⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢾⣿⣯⣟⣿⣻⣮⣪⣮⣿⢦⢝⠂⢌⡢⢵⣻⣯⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣻⣷⣿⣾⣿⣻⡠⠢⡉⣄⣑⣽⣿⣿⢵⣾⣟⣣⣿⡽⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⢯⣳⣯⣱⢥⠗⡙⢝⠿⡛⣯⡿⣿⣷⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⡿⣻⢾⢿⢯⡺⣿⣿⡟⢯⣳⡽⣿⣯⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⢿⣽⢿⣯⣟⣯⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣤⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀