⠀ ⠀⠀⢀⠐⠠⠐⠠⢁⠐⡠⠄⠁⠀⠀⠀⠀⠀⠀⢠⢀⠂⠤⢁⠎⡈⢅⠂⠆⠀⠀⠀⠀⠀⠈⠐⡈⠐⠀⠄⠂⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠄⡈⠄⠡⢀⠂⠈⠀⠀⡀⠀⡄⠠⠀⠂⡩⢄⠢⢉⠆⡐⢢⠑⡌⡘⠀⠘⡄⢃⡀⠀⠀⠀⠀⠀⠌⡀⠂⠄⠂⠀⠀⠀
⠀⠀⠀⠀⢈⠐⠠⠈⠁⠀⠀⠀⡀⠠⣀⠃⠀⠀⠀⠀⠀⠆⣑⠊⡔⢡⠂⢇⠀⠀⠀⠀⠀⠁⡒⢊⡔⣀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⢂⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠊⡜⠤⠀⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⣃⠆⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡰⠡⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠆⠁⠈⠀⠀⠀⠀⢀⠰⡀⠒⠈⠀⠀⢀⡀⢤⠀⣄⣀⢀⡀⣄⣀⣀⣀⢀⠀⠀⠑⠈⠐⡀⠀⠀⠑⠊⠥⣀⠀⠀⠀
⠀⠀⠀⡀⢢⠁⠀⠀⠀⠄⠀⠀⠀⠄⠑⡠⠁⠒⠊⠉⠀⠀⠀⢰⡤⣵⢲⣛⠀⠀⠀⠀⠈⠈⠐⠤⣀⠀⡰⠀⠀⠄⠀⠀⠂⡱⢀⠀
⠀⠀⠠⣁⠊⠀⠀⡀⠐⠀⢠⠐⢢⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢎⠱⣯⠎⢉⡀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠁⢒⠀⠐⡀⠀⠀⠁⢊⠄
⠠⢈⠡⠀⠀⠀⠐⡆⠀⡘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣴⢚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣂⠀⠀⠐⡀⠀⠀⠈
⠀⠂⠁⠀⠀⠀⠥⡁⠐⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢱⣿⢡⠂⠀⠀⠀⠀⠀⠀⠀ ⠈⠰⠀⠀⡱⢀⠀⠀⠀
⠀⠡⠀⠀⠀⢈⠆⠄⠰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣆⣠⡟⢱⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠢⣅⠀⠀⠀
⠀⠡⠀⠀⠀⡘⢨⠀⡈⠀⠐⠀⠀⠀⠀⠀⢀⡀⢀⡀⢀⠼⣿⣿⡇⢻⢻⣿⣿⡄⠀⠐⠠⠄⠀⠀⠀⠀⠀⠈⣀⢲⠀⠐⡬⠀⠀⠀
⠀⠀⠄⠀⢀⡞⡥⠀⡷⢴⣶⣤⢄⣀⣀⣤⣶⠗⢈⣠⣴⣾⠿⢱⡇⠀⠂⣫⠛⢿⣿⣤⡈⠲⣄⣀⣀⢴⣶⢿⣹⢮⡁⠀⢸⡁⢨⠀
⠀⠀⠀⠀⣸⡝⡇⠀⣿⣧⣿⢋⣾⣿⠿⠛⣡⣴⣿⠿⢋⡠⢔⡿⢠⣤⡞⢿⠊⠥⠼⠛⣿⣷⣬⠙⣛⢦⠸⠟⡧⣟⡄⠀⠰⢥⠀⠆
⠀⠀⠀⢠⣗⣻⢱⠀⠹⠛⢊⠚⣻⣡⣴⣿⣟⢛⣬⣥⣤⣾⣹⢡⣀⢿⢇⣈⣫⣿⣿⣿⣶⣮⣟⠿⢿⣞⣦⠱⣄⠈⠂⢀⠌⡧⠀⠱
⠀⠀⠄⢸⣽⠛⡼⠀⠂⣁⠴⠿⠶⠻⢛⣩⣷⣿⡿⣿⣻⣿⢿⡿⣫⣶⣿⣿⣿⣻⣽⣾⣟⣷⣿⡓⡇⡺⢩⡄⠉⠐⡁⢸⠠⢇⡃⢈
⠀⡐⠠⢾⠉⣰⡇⢀⡟⣡⠐⣡⠶⢚⣽⣿⣟⣷⡿⠿⠋⠉⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠙⠻⢾⣿⣷⣌⠀⠙⠀⠤⡔⠌⠃⣬⠱⠀
⠀⠄⡇⠀⣴⡿⢇⠀⡇⡇⠈⠀⢠⡿⠿⠗⠛⠉⠀⠀⠀⡀⣠⡀⠠⣄⢀⡤⠀⣀⠀⢀⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠉⠀⡅⢦⡙⡄
⠠⡌⠄⣴⡿⢣⢸⢆⠀⠐⡀⠀⠀⠀⠀⠀⣄⢠⡆⣾⣾⣿⣿⣷⣏⣿⣼⣿⢸⣿⣧⣿⡄⣄⢠⠆⠀⠀⠀⠀⠀⠀⠀⡼⣄⠦⡓⡄
⡐⠠⣼⣭⣬⡶⢱⣷⠀⠀⠰⠀⠀⠀⠀⠠⢿⠸⣃⡋⢹⡃⣿⣯⣿⣿⢸⣯⢙⣿⢹⣿⡷⣏⡼⠀⠂⠀⠄⠀⠀⠀⠀⡳⢘⡥⢓⠤
⢠⡟⣧⣟⡾⣇⣿⣿⠀⠀⠸⢀⠀⠠⡀⠂⠠⡎⢿⣷⣼⣷⣿⣯⣿⡿⣿⡿⣹⣿⣾⡇⡿⣸⡇⠂⢀⠎⠀⠀⠀⠀⠀⡇⢫⠐⢏⡄
⡞⡼⣧⠿⣽⢼⣿⠾⠀⠀⠀⠀⠀⢆⢐⢄⠀⠀⠃⠳⠛⠏⠘⠇⠻⠏⢻⡟⢿⠗⠟⢸⠇⠟⠁⣰⠏⠀⡇⠀⠀⠀⠀⠇⢊⡜⢢⠜
⣹⢳⢭⣟⡟⣼⡿⠁⠀⠀⠀⠀⠰⢘⡎⢷⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣣⠆⡜⠀⠀⠀⠀⡀⢰⣋⠼⡡⠎
⡜⣯⢞⣼⢳⣯⠅⡀⠀⠀⡀⠀⠀⢠⠻⣅⠑⣛⢿⣦⣦⣄⣀⠀⠀⢀⣀⣀⣠⣄⣠⣴⡾⢷⣿⠃⡐⢀⠀⠀⠀⠠⠀⠷⡌⢧⡑⣃
⡜⣧⣛⡞⢺⡍⠰⠀⠀⠠⢷⠀⠀⠀⠀⠻⣷⡀⣛⣌⡛⠿⢿⡿⣿⡿⣿⡟⠿⠙⢋⣀⣴⣾⣃⡔⠀⠀⠀⠀⠀⢀⠁⢸⠍⣖⠱⣂
⡜⣧⢏⡏⣿⠁⠠⠡⠀⠠⢹⡆⠀⠀⠀⠀⠹⣿⣬⣿⢿⣦⣤⣴⣴⣴⣀⢀⣠⣶⣿⢿⣻⡷⡟⠀⠀⠀⠀⠀⠀⣄⠂⠘⡞⣬⢣⣃
⢞⡵⣫⢧⣻⢀⠄⡃⢐⡄⢸⣿⠀⠀⠀⠀⠀⠘⢿⣽⡿⣯⣿⢯⣟⣯⣿⢿⣟⣿⡾⣿⡻⠉⠀⠀⣠⣼⠀⠀⠀⣯⡀⠀⢟⡴⣓⠬
⣞⡳⣟⢸⣋⠘⣀⠃⢸⡇⢸⣿⣦⠀⠀⠀⠀⠀⠈⠻⣷⣿⣻⣾⢿⣻⣟⣾⣟⣯⡷⠟⠁⠀⠀⣄⣿⡟⡀⠀⢠⣟⡇⠀⢼⡱⣋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠖⠒⠒⠒⠶⠶⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⣀⣠⣤⠶⠶⠶⠤⢤⣤⣍⡓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢬⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⠿⠿⢥⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠛⠛⠉⠠⠟⠀⠀⠀⠀⠀⠉⠛⠓⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠿⡀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⠁⠀⠀⢀⠀⠀⣾⠀⣷⠀⠀⠀⠀⠀⢱⠻⣄⠀⠀⠀⠀⢤⡄⠀⠘⣧⣀⣤⠤⠴⠶⠶⠶⠶⠶⢦⡀
⣀⣤⣤⠤⠶⠒⠒⢺⡇⠀⠀⢸⣿⠀⠀⠀⣽⠀⢀⠟⠀⠹⡆⢀⠀⠀⠀⢸⠀⠻⣄⢶⣤⡀⢸⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠁
⠸⣇⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣠⣿⢆⡾⠀⠀⠀⢇⣸⠳⢤⣀⣸⣠⠴⠛⣻⡿⠙⠻⡇⠀⠀⢸⠀⠀⣀⡠⠴⠛⠋
⠀⠈⠉⠑⢦⣀⡀⢸⠀⠀⠀⢸⣿⣠⣖⠛⣿⣿⠧⣄⣀⡀⠈⠈⠁⣠⣾⣿⣵⣶⣋⡉⠙⢲⠀⢷⠀⠀⢸⡗⠚⠉
⠀⠀⠀⠀⠀⠈⠉⣾⠀⠀⠀⢸⠻⣿⠉⠉⣹⣿⣶⣬⡉⠁⠀⠀⠀⢡⠞⢹⠉⠀⠉⠙⣆⡾⢠⣾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⢷⡸⣇⣾⠁⠀⠉⣶⠉⣶⠀⠀⠈⢻⡄⢸⠀⠀⢀⣴⠋⣠⠞⢹⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠙⢎⢿⣄⠀⠀⣿⠶⠃⠀⠀⠀⠀⠉⠛⠛⠛⢉⣤⠞⠋⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠈⠙⠲⣭⣭⣀⡀⣀⠀⠀⢀⣀⣠⣤⣴⠚⠋⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⠀⠉⠉⠳⣄⡜⠃⠀⠀⠹⣄⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⡆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⡇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢸⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠸⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇