Puny Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣚⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⠶⠦⣄⠀⠀⡇⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠘⣆⠀⡇⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠧⠒⠒⠛⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⢰⣿⣅⠞⠉⠑⡄⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⢉⣽⠶⠀⠀⢸⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠙⠛⠛⠉⢿⢄⣀⣠⣮⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣋⣁⣠⠇⠀⠀⠀⠀⠈⠁⠉⠀⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⠶⡲⡤⣫⠖⠉⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠲⠤⢌⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣋⢔⡷⢺⠣⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠂⠕⠤⣲⢖⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡼⠀⠘⠤⠞⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢻⠀⠀⠀⢀⠔⢪⠒⡗⢬⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠘⠲⠚⠀⠠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣧⣀⣀⣀⡀⠀⣠⠖⢲⡀⠐⠂⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠼⣇⠀⠀⠠⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢠⡤⠤⠤⢤⣀⣀⡏⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠖⠋⠉⠉⢫⠉⢀⣀⣈⡤⠼⢄⡈⠀⠀⠀⢀⣐⣶⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⡀⡉⡉⠉⠀⠀⠀⠀⠀⠈⠑⠢⣤⣴⣀⠀⠉⢲⡸⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠈⠉⠉⠉⠉⢓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣺⡃⠸⣋⠀⠠⢤⠀⠈⠷⣶⣼⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠭⠉⣠⠆⣼⢡⣖⡄⠀⢣⠀⢠⣀⠈⢅⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⠖⡉⠐⠋⠀⠀⠀⣰⠃⠀⠧⠘⠛⡁⠀⡜⠀⠐⠀⠀⢸⠀⣖⠁⢣⠈⠪⠹⢦⠀⢀⡀
⠀⠀⠀⠀⣰⠃⠈⠀⠀⠀⠀⠀⢰⠧⠀⠀⠀⠊⢉⣉⠙⠂⠀⠀⠀⠀⢸⠀⠈⠃⠠⠽⠖⠣⠘⡶⢁⡼⠂
⠀⠀⠀⢀⡇⠎⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠀⠀⠈⢠⣀⠀⠀⠀⠀⠀⡾⠀⠀⣧⠀⠂⠉⠁⢈⡴⠁
⠀⠀⠀⠀⢧⢠⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⠀⠀⠠⡉⣙⠃⠀⠀⣸⠁⠀⠀⠈⡇⣰⠒⠚⠋
⠀⠀⠀⠀⠈⠳⣅⡀⠤⡀⠀⠀⣀⠀⣷⠀⠀⠀⠀⠀⠳⣤⠃⠀⠀⡏⠀⠀⠀⠀⡇⡟
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠖⠊⣽⠐⠀⠀⠀⠀⠙⠶⠂⠀⠀⢳⠀⠤⣀⣠⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⣒⣾⠭⡴⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠓⠲⠼
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢭⡢⢤⣰⠇⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡳⢬⡑⠢⡌⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⢹⠂⠀⣰⠁⡀⠀⠀⠂⠀⠀⠀⠀⠁⠠⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⠼⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠖⠳⣄⠀⠄⠀⠀⠠⠀⠀⢐⣴⢟⠀⢀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⣇⢢⣀⣀⣤⠵⠛⢇⢾⢀⣝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⡉⠀⣸⣤⠂⠀⠀⠀⣼⡫⢭⣁⣩⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⣘⣭⣿⠍⢊⢠⠀⠀⠀⠹⠽⢮⣙⠋⠁⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠆⠭⠭⠵⢖⣊⡴⠃⠀⠀⠀⠀⠀⠙⠣⠬⠽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃

⠀⢀⡀⢀⠀⢀⡀⡀⢀⣀⣀⡀⠀⢀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠛⠻⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⣀⣠⣀⠀⣀⣀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣀⡀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠉⠉⠙⢷⡀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢹⡀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇⠸⠗⠒⠛⠉⠛⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⢰⣟⡃⡴⠛⠙⠢⡄⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣆⠀⠀⠈⠻⢻⣥⡄⠀⠀⢻⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢾⣷⢦⡤⠔⣿⡄⠀⠀⠀⡾⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⡞⠀⠀⠀⠀⠀⠹⠝⠦⠤⢾⣵⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣁⣤⠤⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⡽⣝⢢⡜⣡⠞⠋⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠒⠶⢤⣈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⡤⢺⠤⢜⢧⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⡇⠀⠀⠀⠀⠙⠢⡙⢄⠔⣒⣒⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡏⠀⢸⣀⣹⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠑⡒⠀⠀⣿⠀⠀⠀⠀⠀⣠⢞⠤⣼⢥⡹⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⢹⡄⠀⠀⠀⢾⡁⣸⠀⠈⡆⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢸⡇⠀⠀⠀⠀⠉⠁⠀⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡲⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⣸⣄⣀⣀⣀⡀⠀⠀⣠⠞⢻⡄⠀⠒⡎⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠳⠤⣼⣇⠀⠀⠐⠄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⡀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⠤⣤⣄⣀⣀⠀⢸⠛⢻⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣋⣠⠖⠒⠛⠳⡖⠒⠀⠈⠉⠛⠀⣸⡇⠀⠷⠴⠶⠦⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⣀⣀⣀⣤⠧⠤⠶⠖⠒⠛⠉⠉⠙⠲⠤⣀⠉⠉⢉⠟⠛⠳⢦⣉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠲⠒⠒⠂⠐⠀⠐⠒⠂⠀⠉⠒⠺⢴⣔⣂⠀⢻⡶⠃

⠀⠀⠀⠀⠂⠀⠢⡀⡀⠀⢄⠀⠀⠀⠀⢠⠀⠀⠀⠠⡀⠀⠠⠀⠀⠐⡀⠰⠀⠐⠀⡄⠀⡄⢀⠀⢀⡀⠀⠀⣀⠀⠀⢢
⠀⠀⠀⠀⠄⠀⠀⠁⠇⠀⠘⠹⠄⠀⠀⠰⠀⠱⠀⠀⠃⠸⠐⠄⠀⠀⠳⠀⠱⠀⠀⠇⠈⠇⠺⠀⠀⠁⠀⠀⠈⠀⠄⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢸⠂⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⡀⠀⡄⠲⣤⡄⠐⡾⠉⠁⠃⠀⣼⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⣀⣿⣿⡀⠀⠀⠈⢠⠀⠇⠀⠀⢀⣼⡯⣿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⡌⣷⣲⠄⠀⠠⠀⡴⢀⡐⠎⢀⣳⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢬⣽⣤⣈⣻⡄⠀⠂⡀⢠⡌⠀⢀⣴⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣄⠀⠀⣠⣠⣿⡇⣿⡉⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠀⠙⢛⠙⠋⠁⡹⠃⢸⣧⠀⠲⣄⠈⠁⠚⠒⠄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠤⠄⢀⣲⣿⣿⣿⠟⢡⣠⣾⣁⣷⠀⠐⠁⠀⠀⢹⡀⣰⣿⣿⣾⣷⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣶⣾⣿⡿⠛⢛⡏⠀⠙⠛⣿⢿⠛⢻⡄⠀⡐⠀⢰⣧⣿⣿⣿⣿⣿⣇⣴⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⣽⣥⣤⠎⠋⠀⠀⣾⢿⢈⠀⠀⢃⢠⠁⣰⠏⣿⣿⠀⣿⣿⣿⣿⣿⣇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⠟⠛⣿⣿⡄⣦⠀⢘⡏⠈⠸⢀⣀⣼⠃⠰⠁⢀⠼⠿⠦⠌⠻⣿⣿⣿⣿⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣹⡟⡟⠘⡆⠊⠁⠀⡾⠛⣇⠌⠀⠀⠀⠘⡖⠒⠀⠀⠀⠸⣿⣿⣿⣷⡡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠡⠤⠇⠀⠀⢰⠀⢠⡗⠀⠀⡏⠀⠀⠀⠀⣼⡗⠀⠀⠀⠀⠀⠙⠦⣿⣿⡟⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⢿⠀⠀⠀⣠⣴⣶⡄⢰⠀⣏⣤⣾⡇⠀⢸⡇⠀⠀⠀⠚⢉⡷⠀⠀⠀⠀⡠⠌⠸⡿⣿⣇⠞
⠀⠀⠀⠀⠀⠀⢰⢱⣷⡈⠓⠤⣾⣿⣿⣿⣿⡄⠀⠟⠉⠃⢻⣦⣾⣷⠄⠀⠀⠀⠀⣹⣿⣷⣶⡀⠀⠀⣰⣷⡈⢿⡄
⠀⠀⠀⠀⠀⠀⢸⣨⣿⣿⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠰⠀⠀⠀⠀⣴⠿⠛⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠟⣿⣿⣿⣿⣿⡄⠀⢠⡀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⡄⢸⠀⠀⠀⣤⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⢀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠀⠀⡄⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⣙⡋⣙⣋⣉⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠿⠟⢿⣿⣿⠀⠀⠀⠀⠤⠤⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⣓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢙⡓⢦⡀⠀⡇⣏⠸⡞⡇⠀⠀⠀⠀⠀⠀⠀⣰⢫⢭⡛⣆⠀⠀⢠⡞⣩⠶⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢯⠉⠳⣝⢦⣹⣽⡄⣧⣷⠀⠀⠀⠀⠀⠀⠀⢿⢸⡀⢹⡘⡇⢠⠏⡼⠁⣰⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣓⢦⣈⠳⡝⣿⣷⣹⢻⡀⠀⠀⠀⠀⠀⠀⠘⣆⢧⠈⡇⣿⢏⡾⢁⡼⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣾⠟⠛⠈⠃⠛⠈⢷⡀⠀⠀⠀⠀⠀⠀⢹⣮⠳⠟⠉⠘⠷⠋⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠈⠁⠀⠉⠀⢸⡇⠀⠀⣸⠃⠀⢀⠺⠀⠀⠐⢇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⣼⢹⡄⣀⣤⠞⠀⠀⠀⠸⣦⣀⡀⣠⣴⣄⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⡀⠐⣧⢀⣷⢹⠄⠀⠀⠀⠀⠀⣒⠸⣏⣿⠀⣿⣓⠂⠈⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⢉⠻⠿⠉⢻⡀⠀⠀⠀⠀⠀⠐⣠⠟⠈⠉⠁⠉⠁⠀⠀⡟⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣸⡗⠒⠶⣤⡽⠀⠀⠀⠀⠀⠸⠧⠶⠲⠶⢶⣋⣀⣤⠖⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⢆⠈⢄⣐⠢⠀⠀⠀⠀⣤⣖⣠⡄⣀⡀⠱⣀⣐⡄⠀⠀⠀⠀⢀⣀⣄⣀⠀⣀⣀⠀⠀⢂⣀⣀⡧⠰⠀⡀
⠀⢰⡟⠿⠀⢠⠁⠀⢸⣿⠀⢠⠿⢻⡇⠀⠀⠀⠀⣿⡆⣿⣷⣿⡇⣾⡟⠿⠧⠀⠀⠀⠀⢸⣏⣼⠟⠁⣿⣿⡆⢠⡟⠻⠿⢿⣟⣛⠃
⠀⠸⡇⢀⡄⠐⠀⠀⢸⣿⣤⠘⣧⣼⠃⠀⠀⠀⠀⢿⠇⢿⠏⢿⣿⢻⣧⣾⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⢿⣿⠸⣧⣴⡆⢸⣟⣛⡀
⠀⠀⠉⠋⠀⠈⠀⠁⠸⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠉⠘⠃⠘⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⠂⢀⠄⠀⢀⠔⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⠊⠻⣋⠀⠀⠀⢀⣐⡐⠶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠸⣧⠌⠀⡀⠀⠌⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠉⠀⠀⠈⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠖⠀⠀⠀⠀⠀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠠⠊⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠸⠄⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠚⠦⢐⠀⠀⠀⣂⣀⠤⠒⠀⠹⡄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⠒⠉⡀⠀⢠⠀⠀⠣⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠆⠀⠁⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠈⠀⠀⢆⠀⠄⠀⠀⢨⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⠄⠀⠀⢸⡆⠀⠀⢀⠈⠀⡌⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢴⠄⡀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡁⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⢀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢻⡿⣻⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄⠖⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⣹⠋⢠⡶⣾⣾⣶⡄⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⣽⣈⣿⠁⠈⠁⠉⣿⣷⡀⡇
⠀⠀⣠⣾⣟⢉⣽⣾⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢧⠀⠀⠀⠀⣹⣿⣿⡇
⠀⠀⣿⣿⣭⡘⣿⣿⣿⣯⣿⣿⢇⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠊⠑⠀⠀⢀⣀⣤⣿⣿⣿⣿⠃
⠀⢠⢿⣿⣙⣿⣾⡿⣿⣿⣿⣣⣾⣿⠀⣷⣦⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⡿⠋
⠀⠀⢼⣿⢿⣿⣿⣿⡛⣿⣿⣿⣿⠋⣠⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢩⡵⢤
⢀⡀⣀⣀⠀⢹⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣟⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⠶⡆⠈⠀⠂⠃
⠈⠡⠈⠁⠀⢹⡄⠿⢟⣩⣋⣴⣿⠟⠿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣧⢣⣼⣿⣿⣦⡰⣿⡟⢉⣿⡏⣷⣷
⠀⠂⠀⠀⠀⠀⠐⣾⣹⣫⡿⠏⣠⠒⣻⣫⣿⣿⣿⣿⣿⡿⠿⠋⢏⢫⣺⡟⡀⣉⣤⣿⣿⣿⣿⠁⣾⣿⠥⠛⣿⠟⣠⠀⠀⠈
⠀⠁⠅⠀⠀⠀⠀⠈⢿⣥⣞⡎⠉⣻⣿⣿⣿⣿⣿⡟⠙⠃⡀⣀⣦⣼⣿⡦⣼⡿⠛⠻⣿⣿⡇⣤⣽⠍⣃⢻⣿⠀⠁⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⢸⡟⢹⣧⣼⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⢻⣽⣿⣿⣋⣩⣷⣽⣿⣾⢻⣿⣷⣾⣿⠃⠁⠀⠁⠿⠠
⠀⢀⠀⡀⢀⠀⠀⠀⠸⢷⣿⣿⣿⣿⣿⣿⣿⡿⠻⡿⣿⣿⣿⣿⣿⣿⢿⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠇⠀⣶⠦
⠁⡏⠀⠁⠁⠀⠀⠀⢠⠀⢹⣿⣿⢿⡟⣿⠿⠿⠿⢿⡿⠿⠛⣁⠂⡀⠀⠀⠀⠀⣿⡟⠛⡻⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠁⠸⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠈⣿⣿⠟⠀⣇⠀⠀⠀⠀⠀⠄⠀⡘⠐⠀⠀⠀⠀⠀⣿⠙⡀⠃⠘⢿⡛⢳⣽⡀⠸⠞⢷⣄⠀⠐⠁
⠀⠄⠀⠀⠐⠀⠀⠇⡜⠀⠀⢹⡏⢰⢰⣿⠀⠀⠀⠈⠂⢀⠀⡕⠀⠀⠀⠀⠀⠀⢹⣧⣧⡀⠀⠈⢻⣾⣿⣷⡌⠀⢡⣿⢀⠄
⠀⠠⢤⣤⡀⠀⣀⡀⣧⠀⠀⠸⣯⣾⢸⣿⣄⣤⣄⢀⠀⣽⣼⣧⣤⣄⣠⣴⣦⣤⣈⣿⣼⡿⠰⠆⠀⢿⣿⣿⡇⠘⠹⠟
⠲⢆⠀⠀⢀⠄⠀⠈⠉⠉⣈⡙⣏⢻⣼⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⡿⢹⠏⠀⠀⡼⢳⣏⠸⠟⠧⠶⠗⢿⡿⣅⠀⢀⠰
⠀⠈⠐⠠⠀⢀⣺⣷⣶⣶⣶⣴⣿⣿⣿⣿⠃⠀⠀⠈⠛⠛⠿⠻⠷⢶⣶⣶⣒⠞⣣⣼⣬⣤⣤⣤⣄⠠⣼⣟⡆⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠈⠁⠿⣿⣅⢈⠉⢉⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠛⠿⠶⢶⠼⠃⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣤⣤⣤⣤⣤⣤⣴⣦⣬⣧⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣭⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠕⠀⠀⢐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡠⠒⠒⠒⠒⠚⠉⠉⣰⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠢⠀⡞⠀⠀⠄⠀⠀⠀⠀⠔⠁⠈⢣⡀⠰⣒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠇⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⣄⣻⠀⠀⠀⠀⠀⠈⠉⠀⠀⠱⠀⡀⠀⠀⠀⡀⠰⣏⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠦⠀⠀⠈⠈⠃⠀⠀⢀⢶⣠⠎⠀⠀⢈⠆⡤⠀⠀⠀⠀⠀⣄⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡤⠖⠒⠀⠓⠲⢄⡈⠁⠀⠀⣠⠃⠰⡃⠀⠀⠀⠀⠀⡌⢆⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⡰⣄⠀⢀⠱⠱⡄⠀⠀⠀⣴⠁⠣⣀⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⡠⠀⠀⠀⠀⠀⠀⠄⠄⠀⢳⠈⠓⠀⠀⠀⠙⠂⢰⠀⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠀⢀⢤⡴⠀⢰⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⢀⡀⠀⠀⠀⠀⠀⣀⠔⠁⢈⠇⠀⠀⣸⠀⠈⠀⠈⠀⠈⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠱⠤⠂⠀⠈⠀⠀⠀⠀⠈⠰⣎⠀⠑⠒⠊⠁⣀⠌⠁⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠒⠒⠒⠃⠀⠓⠀⠀⣤⠀⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠀⠘⡄⠓⠀⠊⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⠂⠊⠀⠰⠀⠀⠀⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⠀⠲⡤⠄
⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⡄⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠞⠅⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢦⠀⠀⠀⠸⡆⠀⠀⠀⠀⣸⠇⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣣⠀⠀⠀⠠⠫⠂⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⣃⡀⠀⠀⢹⡄⠀⢀⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠠⣟⠀⠀⠀⢾⣇⣀⠎⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠹⠄⢠⠆⠈⠀⣀⡀⠈⡽⠏⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡶⡄⠀⡀⠀⠀⣀⣤⣶⣽⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣽⡔⣷⡄⠀⠈⠙⠉⠁⠀⠀⠀⡀⠀⠀⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠃⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠈⢗⢀⡀⣀⡀⠀⠀⠀⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡝⣿⡄⠀⠀⠰⠀⠀⡇⠀⠈⠀⠸⢿⠛⠍⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢹⡇⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢠⣸⠁⠸⠁⠀⠀⠀⢧⠀⠀⠉⠆⠀⠀⠀⢀⠀⡖⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠜⠃⠀⢠⠔⠀⠀⠀⠀⡄⠀⠀⢦⡤⠁⠆⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⡴⠀⠋⣀⣠⠈⢵⣇⣠⡆⠠⠼⠗⠃
⣶⣶⡶⡶⢶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣦⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⠋⠈⢳⡄⠈⣧⠀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢸⠇⠀⠀⢀⡿⣂⠹⠶⢡⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠙⠛⢶⡈⠛⠀⢀⡿⠀⠀⡴⠋⠰⡟⢦⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣷⠀⠀⡞⠁⢀⠞⣁⣠⣄⢻⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠎⠀⢠⣏⣼⠃⠉⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠶⢤⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⣤⡀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⣛⣧⡠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠰⣿⣯⣴⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡿⠋⠁⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠞⠛⠉⠹⣇⣴⡦⡀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠞⠀⣤⣒⡶⠒⣼⠇
⢠⡴⠶⠶⠶⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠻⣿⡿⠃⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠈⠀⢉⣠⠞⠁
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠴⢤⣶⠀⠀⠈⠻⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣴⠖⠛⠋
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣸⠏
⠈⢳⣄⠀⠠⠖⠀⡤⠄⢠⡄⠀⠄⢀⣀⣤⡶⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠉⠛⠶⠶⣤⣤⣴⣤⠶⠶⠟⠛⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠺⣛⠶⣄⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠛⠲⣌⠳⡌⣷⠀⠀⢿⡀⣤⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢯⢼⣧⠷⠛⢢⠀⠈⣿⠉⠲⣦⣀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠸⣧⡤⠔⠋⠀⠀⠸⣇⠀⠸⣯⠷⣄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠋⠀⠀⢀⠀⡀⠀⢻⡄⠀⠘⠟⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠀⠀⠐⠈⠀⠁⣀⣀⣷⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⡓⠒⠚⣉⣉⣉⣉⣥⣤⡏⠀⠀⠀⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡇⢸⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⡇⢸⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⢶⠀⠀⠀⠀⡇⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠦⣄⣀⣀⣀⣀⡇⢸⡠⠟⠛⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⢩⠟⠈⠀⠂⠉⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠘⢦⣤⣀⣈⣉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠶⢶⣤⢤⣄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠃⠲⢶⣶⣶⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⢸⡋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣠⠴⠶⠖⠛⠛⠛⠁⠘⠳⣄⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣎⣿⣄⠀⠀⠀⠀⣀⣤⣤⠶⠶⠟⠿⠃⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡙⠷⣶⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡒⠄⠀⠀⠀⠀⠀⢀⣀⣠⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣇⣼⠖⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣤⣄⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠹⣄⠀⢸⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠘⢀⡀⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢀⣴⠄⢀⠄⠈⡀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣆⠀⠀⠘⢿⠆⢀⠀⠀⠐⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣦⣄⣀⡀⣼⠉⠀⠀⢀⡇⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢴⠇⠉⠁⠀⠀⠡⠠⢀⣠⣾⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣉⣠⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣫⢟⠢⡴⣫⠖⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠒⠲⠤⣌⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣣⢔⠗⢾⠣⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠂⠑⠤⢒⣲⡒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡸⠀⠸⣄⡼⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡠⢪⠖⢟⢤⡓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⢤⠴⠀⢸⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠲⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠐⡀⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠘⠒⠒⠒⠶⠦⢤⣞⡁⢸⡇⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⢀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⣀⠀⠀⣀⡀⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣤⠤⠤⢄⣀⡀⢀⠟⢻⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⡴⠚⠋⠉⢹⡉⠁⠀⠀⢉⣀⣸⡁⠘⠒⠒⠐⣒⢒⣀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⠤⠴⠖⠓⠒⠋⠉⠉⠀⠀⠈⠙⠲⢤⣀⢀⡌⠉⠙⠲⣦⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠘⠛⠄⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠐⠦⡀
⠀⠀⠀⡀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆
⠀⠀⠀⠀⠀⠈⠋⠠⠍⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⢄⠉⠀⡠⠀⠀⠀⠀⢀⡀⠁⠀⠀⠚⠇
⠀⠈⠣⡀⠀⠀⠈⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢁⠐⠀⠄⠀⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠀⠀⠰⠂⠁
⠀⠀⠀⠀⠑⢆⠁⠂⠀⠂⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠄⠀⢆


⠀⠀⠀⠀⢠⠖⠒⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠃⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠾⠀⠀⠀⠀⠶⡄
⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⡐⠂⠀⠀⡀⠀⠀⠀⢀⡀⠀⠰⣿⣿⡷⠰⣿⡿⠂⠀⢀⡀
⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠂⠀⠊⠀⠀⠀⠀⠈⡄⠀⠀⠈⠩⠔⠁⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠠⣤⡀
⠀⠀⠐⠺⠶⢦⣤⣀⣀⣠⣤⠶⠞⢛⠀⠀⠀⠀⢠⠐⠋⣁⠀⡎⢉⡓⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠰⠀⠀⠁⡨⠉⢌⠉⠀⠠⠂⠀⠀⠀⠀⠘⠄⠀⠁⢀⠆⠈⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡖⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠁⠀⠀⠊
⠀⠀⠀⠀⡤⣊⣀⠸⠀⡠⠄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀
⠀⠀⠀⢸⢀⠀⠸⠀⠀⠂⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠁⠀⠁⣶⢨⣤⣌⠢⠙⢢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠘⠁⢰⠁⠀⢀⡟⠈⠙⡟⠃⠀⣶⡶⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⠆⢠⠎⢙⠃⣤⣬⡅⡤⣄⢀⣀⠀⠈⢂⣀⡉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃⠠⠀⣁⣂⡈⠇⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢳⢀⣯⣅⠁⠒⠀⠱⠀⠄⠐⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠋⠀⢩⣍⣐⡃⠺⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢃⠘⠒⠂⡀⠀⠀⢈⣿⠉⠀⠀⠠⠂⠉⠋⣦⢸⠋⠉⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡀⢻⠀⠀⢤⠀⠀⢁⠄⠀⠂⠂⠀⠀⢤⣤⡄⠀⣥⢿⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣶⠛⠂⣀⣀⡀⠘⠀⠀⢀⠀⢀⡤⣤⣄⠁⣰⠛⡿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢷⣼⣿⡆⢹⠈⠋⢰⠉⠀⠀⠀⡀⠀⠈⠱⢀⢬⣇⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⢁⠀⠀⡷⠿⠀⡀⠀⠀⠀⡀⣀⡠⣤⠘⡤⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠰⡶⠀⠇⠀⠀⠁⠀⠀⠈⠁⠀⠀⠂⢸⡟⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠰⠀⠀⢀⡀⣤⢰⠒⠂⠒⠂⠘⣂⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠀⠈⠀⠀⠀⠀⠈⠀⢠⠈⠲⠄⠠⠀⠈⠟⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⠀⠀⠀⠔⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣴⡄⢠⣴⢶⡄⢸⠛⠏⠃⠹⠞⣠⣤⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⡇⣼⡟⠹⠃⡼⠟⠚⡇⢀⣀⣀⡀⠐⠟⠉⠈⠦⢰⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡄⣨⣴⣶⢀⣶⣤⣀⡃⠀⠉⠉⠁⢰⡾⠛⠻⠆⠀⢁⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣮⠀⡟⠀⠈⠸⠃⠋⠀⠁⣰⠆⠿⡇⠀⣁⣀⠀⠁⢀⠚⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢧⡈⠓⢶⣇⠀⣟⡛⠓⡃⢈⠀⢸⡇⠀⣁⣀⠀⢀⠀⠀⠤⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢹⡇⠈⢫⠠⣽⣄⢄⡁⠖⡆⠰⡆⠀⠉⠉⠀⡿⠋⠹⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⣳⠘⣏⣧⡟⠻⣼⠃⣠⡽⢬⠃⣶⣶⠀⣼⣻⡿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡅⣀⡘⣿⢳⡄⣿⡷⡏⢀⣼⠐⠋⠟⣰⢦⣍⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣍⠺⣿⣿⣷⡄⣽⣶⠀⣴⡀⠘⠃⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣛⠻⠀⣿⡏⡼⠛⠁⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠤⠘⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠠⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠔⠀⠂⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⠶⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣀⠀⠀⠀⠀⠀⠀⢻⡆⠀⡠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣼⣿⡆⠀⠀⠀⠀⠀⢸⡇⣾⣄⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣨⣿⡿⠃⠀⠀⠀⠀⠀⣼⠇⠘⠧⣼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠻⢷⣤⣄⣀⠀⠀⠀⣀⣀⣤⡾⠟⠁
⠀⢠⣾⡿⠿⣿⡟⠛⠛⠻⢦⡀⠀⠀⠈⠙⠷⣦⣤⣀⣀⣀⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠉⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠙⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣰⠏⠉⠛⠻⠷⢶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⡶⠶⠿⠛⠋⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠈⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡛⠛⠛⣿⠛⠛⠋⠙⠋⠙⠙⣿⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠿⢷⣶⣤⣤⣤⣤⣴⡶⠿⠿⠛⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢻⠿⠿⢿⠿⡹⠿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣛⣛⣛⣿⣿⣛⣛⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⣠⠶⠛⠉⠉⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⠀⠀⠀⢹⢀⠠⣤⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢗⣺⣿⠀⠀⠀⢸⠻⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠠⠶⢶⢦⡄
⠀⡴⠛⣏⠉⠃⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠀⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠳⣤⣀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣿⠀⡰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡆⠀⡠⠞⡟⣡⠋⠈⠷⡄⠈⢧⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡴⠁⠈⣧⠊⠀⠀⢯⠁⠀⠀⠀⠀⠀⢸⠃⠘⣦⠶⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣠⠏⠀⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢦⣼⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⢀⡠⠶⠒⠒⠒⠒⠦⣄⠀⠀⣇⠀⠀⠀⢀⡠⠔⠒⠢⣄⠀⠀⠀⠀⠀⠀⢸⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⡀⡆⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢽⡶⠤⠒⠁⠀⠀⠀⠀⠈⢦⡀⠀⠀⢰⠀⠈⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣀⡘⡄⠀⢣⡙⢤⡎⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢠⡀⠀⠈⠙⢲⣼⡇⠀⠀⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠙⣏⠁⠀⡱⢭⣻⡇⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣀⠀⠳⠄⠀⠀⠀⣟⡵⠀⡴⠓⣹
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠍⣲⣶⡇⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⣿⣶⣤⠀⠀⠀⡿⣊⠀⢀⣴⣃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢑⣒⡶⠋⠀⠀⠀⠀⣀⣤⣶⣿⣿⡇⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠙⢿⠇⠀⠀⡿⠁⠴⠋⢁⠎
⠀⠀⠀⠀⠀⢀⣀⣸⠄⠀⠀⠀⡸⠁⠠⠶⠾⠟⠛⠛⠛⠻⣟⠋⠁⠀⠀⠀⠀⣠⣤⣤⣤⡤⣤⡤⠤⢤⡤⠀⢰⡇⠀⡰⢠⠏
⠀⠀⠀⠀⠀⠀⠉⢢⣄⣆⠀⢀⡇⠀⠰⡗⠒⢶⣖⣲⡶⠒⢻⡟⠛⠀⠀⠀⠀⢸⡄⠀⠈⠛⠛⠁⢀⣾⠁⠀⣸⠁⡼⠓⠻⣄
⠀⠀⠀⠀⠀⠀⢰⠋⣁⢹⡄⠘⡇⠀⠀⠱⣄⣀⠉⠉⣁⣠⣾⠁⠀⠀⠀⠀⠀⠸⣯⡓⠦⣤⣤⠶⢻⠏⠀⢀⡏⢸⠃⡤⡄⢹
⠀⠀⠀⠀⠀⠀⣿⢰⠁⠀⣧⠀⢷⠀⠀⠀⠘⠛⠿⠛⢛⡽⠃⢀⣤⠤⠶⠶⣤⡀⠙⠍⠂⠀⠀⠀⠁⠀⠀⢸⠃⣾⠰⠛⡷⣸
⠀⠀⠀⠀⠀⠀⢸⣼⡩⠗⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣟⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⣰⡄⠀⢸⠀⡿⡀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢳⡝⢦⠜⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠚⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⢿⠼⣳⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣻⠁⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠴⠖⢒⣋⣡⣴⣾⡟⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠳⣶⣿⡿⠛⠛⢋⣠⠞⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠈⠛⠶⠶⢒⣋⡥⢠⣄⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⣄⡀⠀⠀⠉⢉⣡⡾⠋⠉⠁
⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⠛⠋⠁
⣿⣏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠶⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⣤⣤⣤⢤⣤⠴⡶⢺⠋⠁⣔⣄⡤⡞⠠⠝⢤⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠍⠀⠈⠦⠈⢨⠤⠴⡒⢒⣒⢲⠞⢫⠉⠁⢹⣈⣤⡤⠴⢛⠖⢂⣿
⠀⠀⠀⠀⠀⠀⠀⢠⢾⠁⣀⡥⢔⡒⠋⠹⠀⠲⠀⣄⣌⢠⠶⡬⠴⢶⡺⠋⠉⠅⠠⠀⠀⢜⡀⣱⠏
⠀⠀⠀⠀⠀⠀⢠⡟⠀⡫⠥⠊⠀⠀⠂⢠⠔⠺⡉⠁⡔⣁⣄⡡⠤⣾⣊⣤⣭⢴⣤⡜⣋⡭⠞⠁
⠀⠀⠀⠀⠀⠀⣾⠑⢫⠀⢔⡁⢤⠤⢀⣢⠶⢓⡋⠋⠀⠉⢸⡵⠊⠉⠀⠀⠈⠀⠀⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠹⡎⠀⣀⠁⡠⠆⠀⢐⠀⣀⣠⠥⢖⣒⣰⠋⠀⠀⠀⠀⣀⣠⠴⠂⠀⢸⡇⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢮⣀⠢⠀⠶⡷⠾⢏⣡⡤⠶⠛⢹⠏⠀⣀⠴⠚⠉⠁⠀⠀⠀⣠⣿⢁⡴⠒⠋⠉⠉⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠛⠉⠁⠀⠀⠀⣟⣀⠀⠀⠀⠀⠀⢀⣠⡴⢛⡵⣻⠋⠀⢀⠤⠴⠖⠒⠒⠋⠉⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣞⣻⣭⠴⠞⠋⠐⢿⣄⡀⠀⠀⠀⠀⢀⣠⠴⢚⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣛⣫⣭⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠟⢿⣯⢸⣿⣿⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⣀⣾⣿⣿⡿⠟⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣠⣿⣿⣿⣿⣷⣄⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠑⠊⠉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⡐⠁⠀⠀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⡟⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣤⣴⣿⠟⠋⠙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣥⡀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣟⠀⢀⣾⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣧⡘⠉
⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡉⢁⠄⡀⠀⣀⠉⣑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡗⠀⠠⠁⠂⠀⠀⠀⢢⠁⠈⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠓⠀⠂⢀⠀⠀⠀⠰⠀⣄⠄⠐⠄⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠉⢢⠀⠉⢉⠉⠁⢀⠄⢠⠀⠂⠐⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠁⠀⠀⠆⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⡆⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⠄⠀⠀⠀⠀⡀⠀⠀⠀⠘⠤⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠤⠄⠀⡀⡉⠀⠀⠀⠀⠀⡀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠸⠀⠁⠘⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠄⠐⠀⢀⠀⢀⠠⠀⠀⢆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠐⠢⡀⠠⠀⠠⠄⠀⡈⢄⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠐⠂⠠⠂⠸⡀⠀⠀⡠⠀⠀⠀⢸⢆⠀⠄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠈⠁⠢⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠐⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠰⠄⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡔⠒⠀⠀⡀⠀⠤⠄⠈⣀⠀⠀⡁⠉⢅⠀⠰⠒⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⠤⠀⠄⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠤⠀⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⡄⠐⠂⠀⠤⠀⠠⡀⠀⠤⢄⠀⡐⢁⠅⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣑⠐⠃⢄⠀⠄⠀⠁⠀⠜⠀⢈⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⠤⠤⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠉⠉⠉⠉⠉⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⠋⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⣼⣇⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢿⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢉⣿⣿⡄⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⣿⣿⣿⠇⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⣀⣤⡄⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋⢠⡿⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⣠⣾⣿⠛⠁⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣴⠟⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⣰⡟
⢀⡾⠋⠈⢿⣧⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠜⠁⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠛⠿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⡇⠀⠉⠉⠛⢻⡿⠿⠷⠶⠶⢶⣶⣶⣶⡶⠶⢶⡾⠿⠛⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⠶⢤⣧⣀⡀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠉⠑⠛⠓⠒⠒⠂⠀⠼⠃⠀⠒⠒⠒⠚⠓⢹⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⢀⣠⡶⠾⠛⠛⠛⠛⠛⠻⠶⣦⣴⡟⠉⠀⠀⠀⠈⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢹⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠋⠉⠉⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣀⣀⣀⠀⠀⣀⣤⣤⣀⠀⠀⢻⡾⠁⢀⣀⣀⡀⠀⣠⣤⣄⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣾⠟⢹⣿⣿⣾⣿⣿⣿⣿⣷⡀⠀⢿⣰⡟⢉⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⠉⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣼⠀⠀⠀⢀⣤⠶⢶⣶⣄
⠀⢀⣴⢿⣟⠛⠳⠄⠀⠀⠀⢷⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣰⣯⡀⠀⠀⠙⠻⠿⠛⠉⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⣼⠀⠙⠃
⠀⠈⠀⠘⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⢀⣴⠏⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⢀⣀⣤⡶⠛⠁⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀⣀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠻⠿⣿⣿⣶⣄⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠒⠢⢤⣀⠘⢿⡇⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠦⣤⡉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡁⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣇⣨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢎⢀⡀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠲⢤⣀⠀⠀⠀⣼⠃⠈⠧⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠐⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⢰⡿⠿⣿⡛⠛⠓⢦⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠴⠖⠋⠁⠀⠀⠀⠀⠈⠛⠲⠦⠤⠤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⡼⠁⠉⠉⠛⠓⠶⣶⠶⠶⠦⠤⠶⠶⠶⣶⠖⠒⠛⠁⠁⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠉⠙⡟⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠾⠧⣤⣤⣤⣤⣤⠴⠷⠞⠛⠉⠁

⠀⠀⠀⣰⠞⢩⣿⡛⢿⡷⣦
⠀⠀⢠⣏⣰⣿⣿⣿⣶⣿⡟⣷⣄
⠀⠀⢀⣟⣹⣯⡼⢻⣿⢻⣧⣿⢹
⠀⠀⢸⡟⢿⣟⣿⢿⣿⣾⣿⣷⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠈⢷⡈⠻⢭⣽⣿⡿⠿⠿⠃⠀⠀⠀⣀⡴⠞⠋⠁⢀⣀⣤⣤⠀⣀⠀⣉⡙⠳⣤
⠀⠀⠀⠀⠉⠛⠛⠹⣇⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⣶⡿⠿⠛⠉⠉⢠⢚⣼⡿⡑⠄⣤⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⡾⠁⣀⣰⣿⠟⡁⢅⠂⡥⠌⣠⣴⠿⠋⢂⢃⣼⣿⣦⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠠⢤⣾⢟⡠⡔⢁⣐⣬⣶⡿⠛⢁⠌⠒⣡⣾⡟⠀⡙⣿⣤⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣱⡿⠃⣪⣴⡾⢟⡛⢉⠑⠐⠎⣣⣬⡾⠋⠀⠻⣶⣔⠈⢿⣦⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠸⠟⣠⡿⢋⡁⢒⣠⣤⣶⠶⠶⠟⠋⠁⠀⠀⠀⠀⠈⢻⣮⠘⢿⣆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣌⢇⣾⢟⡔⣢⡷⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢲⡀⢀⡀⠀⢻⣯⠸⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⣼⡏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⢻⡇⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣹⣟⣼⠋⠀⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣤⠀⠀⠘⣿⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⣿⠁⠀⠀⢿⡀⠀⣿⠀⠀⠀⣠⠄⠀⠀⠘⣇⠀⢠⡟⠀⠀⠀⣿⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣿⠀⠀⠀⠈⠛⠛⠁⠀⠠⣾⣁⠀⠀⠀⠀⡈⠛⠋⠀⠀⠀⠀⢿⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠈⠁⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⣾⣿⣭⣙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⡇⠀⠀⢠⡾⠛⠙⠓⣦⠀⠀⠀⡗⠀⠀⠀⢠⣿⠐⡩⡻⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⡻⢷⠶⣄⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠁⠈⠛⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⠛⠛⠛⡛⣛⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⣍⠙⠛⠁⠀⠈⠋⢋⣽⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⣤⡀⠀⠀⠀⡾⠀⠊⠀⠙⠷⣦⣀⣀⣠⣾⠛⠁⠈⣠⠈⣷⠀⠀⠀⣠⡴⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣬⠿⠛⠀⠀⢹⡆⠀⢀⡇⢨⣄⠀⠀⠀⣿⠉⠉⠈⣿⠀⠀⠀⣠⡀⢹⡄⠀⢰⡃⠀⠀⠛⠻⣯⣀
⠀⠀⠀⠀⢠⡾⠋⢀⣠⣤⢶⡞⢛⢿⡄⢸⡇⢸⡏⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢿⡇⢸⡇⢠⣿⡛⢲⡶⢦⣄⡀⠙⢶⡀
⠀⠀⠀⠀⠻⠴⠞⠋⠁⠀⠀⢿⡀⠊⣿⡄⡇⢸⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⣇⣾⠣⠀⡾⠀⠀⠈⠙⠛⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠜⣿⡇⢸⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢺⡇⢸⣿⠫⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠃⠘⣷⣸⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣾⣧⣾⢃⠇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⠀⠽⠛⠿⠄⠀⠐⢿⠀⠀⠀⡿⠀⠀⠂⠿⠛⠋⠐⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠙⢿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠛⠋⠥⣤⠴⠾⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⠛⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⡄⠀⠀⠐⣤⠤⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⡿⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢠⠀⠀⠀⠀⢀⢔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠈⡽⣄⠈⠀⠀⣀⠀⣽⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢀⡄⠠⠀⠀⠀⠀⠀⢱⠐⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠛⢠⠂⠀⢤⣂⣒⣒⣀⠀⠈⠁⢠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⡀⠀⠉⠙⠲⠤⣄⡀⠉⠑⠦⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢤⢼⣈⣙⠒⠤⠤⠆⡀⠀⠈⠉⠒⠤⠤⣀⣀⡐⠀⠀⠈⢉⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⡡⠔⠀⠐⠆⠀⢤⣈⠑⠖⠤⣄⠉⠐⠂⠠⢀⠀⠄⠀⢉⠛⠓⠲⠤⣀⠀⠘⢏⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣴⠷⠒⠒⠒⠒⠦⢄⣘⠀⠉⠐⠖⠌⠉⠉⢟⢓⡲⠬⣔⡠⢅⠀⠀⠀⢀⠈⠑⣆⢸⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠉⠢⣄⠊⠀⠀⠀⠆⠀⠉⠁⢋⠐⠒⠒⠒⠢⢄⡈⠑⠠⡙⢦⡈⠑⠒⠤⠤⢄⢨⣾⣀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢧⡀⠌⠑⢦⡤⠞⠂⠉⠉⠅⠉⠈⠉⠒⠾⣄⠀⠈⣳⣄⣈⣤⣹⣄⢀⣀⣀⠤⠚⢹⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣕⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⡋⠭⠐⠒⠒⠂⠀⠉⠑⠦⡀⠂⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⢍⡳⢀⠀⣀⡀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠤⠤⠤⠿⠷⢤⣀⠀⢀⠀⣀⣀⣀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠤⠶⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠒⠒⣆⠐⡖⠒⠒⡆⠀⢐⣶⡄⠀⠀⢲⢦⡀⠐⡖⠀⣶⠂⠀⢲⠂⠴⠒⣶⠒⠆⢠⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠚⠁⠀⡏⠙⢀⡄⢀⡾⠦⢿⡄⠀⢸⠀⠙⢦⡇⠀⢻⡀⠀⣸⠀⠀⠀⣿⠀⠀⢬⡉⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠉⠁⠉⠁⠀⠈⠉⠀⠉⠁⠀⠀⠁⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⠁⠁⠉⠀⠁⠁⠀⠀⠀⠀⠉⠈⠈⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣷⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⠀⠿⠿⠿⠿⠿⠈⠿⠿⠿⠿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣶⣤⠄⠀⠀⠀⠙⠉⠉⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⣉⣙⠻⢿⠀⠀⠀⠐⠒⣶⠖⢄⠀⠀⠆⢀⠤⣶⡖⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⠠⠄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⠀⠀⠀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⣀⣀⣀⣀⠤⠊

⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⣼⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣴⣾⣿⣿⣿⣿⣿⣿⣷⠒
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⠄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣿⡇
⠈⠛⠉⠉⠉⠀⠉⠉⠉⠋⠉⠉⠙⠻⢿⣿⣿⣿⣿⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⣿⣿⣿⠟⣿⠿⠿⠟⠿⠿⠾⠏⠀⠀⠀⣿⣿⡇
⠀⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⣿⠢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠇
⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⢿⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⢸⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠈⢻⠀⠀⠀⠈⣿⠿⠋⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⢀⡴⢒⣶⠶⣶⢦⡀
⠀⠀⠀⠀⠀⣾⣠⣿⣿⣿⣼⣿⢳⣦
⠀⠀⠀⠀⠀⣿⣹⣯⣞⣿⡟⣿⣸⢻⠆
⠀⠀⠀⠀⠀⣏⢻⣯⣟⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢦⣝⣳⣾⠟⠛⠛⠁⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⢀⡴⠋⢀⣠⣴⠶⠿⠶⢶⣤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⣴⠟⠉⢀⣀⣤⣄⣀⠈⠻⣦⡈⠑⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⡀⣀⡴⠃⠀⠈⠁⣠⡾⠛⠉⠉⠉⠉⠻⣶⡘⠃⢀⣤⣤⣀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⡉⠉⠀⠀⠀⠀⣴⠟⠀⠀⣠⣶⣶⣶⣤⡈⠛⠀⠈⠉⠈⠙⣷⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⢶⣤⣤⣤⡾⠋⠀⠀⣰⠿⢦⣍⠳⡌⠻⠄⠶⠶⠶⣄⠀⢹⡇⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⣀⠈⠉⠀⠀⠀⢀⣼⠋⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠘⣧⠈⢿⡀⣧⣀⡤
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠃⢨⡟⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠞⠀⢸⣆⡈⠳⠦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⠀⠘⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡼⠛⣿⠀⠀⠈⣇⠀⣸⠁⠀⢀⡴⠀⠀⠀⠸⡀⢀⡾⠀⠀⠀⣿⠛⢷⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣤⣿⠀⠀⠀⠈⠉⢁⣀⠀⠛⠶⠀⠀⠀⣀⡉⠉⠀⠀⠀⠀⣿⣤⡼⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢿⡀⠀⠀⠀⣰⠋⠁⠀⢀⣀⣀⡀⠀⠈⠙⢷⠀⠀⠀⢀⣿⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⡄⠀⠀⠘⠀⠀⠰⠏⠁⠀⠙⠦⠀⠀⠘⠀⠀⢀⡾⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⣶⡶⢶⣶⡖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⠾⠏⠉⠉⠉⠽⠒⡶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⡞⠁⢀⠹⣧⡀⠀⠀⠀⣠⡾⠁⠆⠙⣧⠀⠀⠀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣽⠷⠂⠀⠙⣆⠀⢸⡇⣠⡥⠠⠌⠛⠛⠾⠛⠋⠐⡄⢠⡁⢹⠀⠀⣾⠁⠀⠐⠿⣯⡀
⠀⠀⠀⠀⢠⠞⠉⣀⣤⠶⣾⠛⢻⣆⢸⡇⣿⠁⢣⡄⠀⠀⠀⠀⠀⠀⢈⢸⡇⢸⡆⣰⡟⠛⡶⠶⣤⣀⠙⢦⡀
⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠘⣆⠀⢻⣼⡇⣿⡄⡆⡁⠀⠀⠀⠀⠀⠀⠈⢸⡇⢸⣷⡟⠀⣸⠃⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⢿⡇⢿⡇⢁⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⡐⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⠌⢿⢼⡇⢈⠀⣀⠀⣂⡒⠂⠀⢂⣸⣷⡟⠐⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣷⡀
⠀⠀⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀
⠀⠀⠀⢯⣀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀⣀⡝
⠀⠀⣀⠀⠈⠉⠀⠈⠁⠀⠀⢀⣤⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⡀⠀⠀⠀⠀⠈⠁⡀⠉⠁⠀⣀
⠀⠪⠤⠄⠂⢀⣀⡀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠛⠋⠙⠃⠀⠀⠀⠀⠀⡇⠀⠐⠠⠤⠅
⠀⠀⢀⣴⠾⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠚⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠙⠓⠶⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⣄⣀⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣠⠤⠖⠲⠦⢤⡖⠚⠉⠛⢦⣤⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡞⠁⠀⠀⠀⠀⠀⠉⢀⣀⣤⠾⠋⢰⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠶⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢖⠩⠭⠭⠀⠠⠀⢠⣴⣒⠯⠛⣛⣛⡓
⠀⠀⠀⡼⠀⣡⠂⡄⡀⣠⢤⢀⢄⡄⡞⠀⠀⠀⠀⠀⠀⠉⠠⢒⣐⣓⢀⣀⣀⣰⣚⡎⠊⠉⡉
⠀⠀⠀⠁⠀⠈⠈⠁⠁⠁⠈⠈⠉⠁⠁⠀⠀⠀⠀⠀⣀⠒⠷⠷⢦⣧⣷⣷⣶⡶⡚⠙⡉⣀⣁⣀⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠃⠀⠀⠀⠈⠙⠋⠉⠉⠁⠓⠒⠦⠤⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠳⢄⠀⠀⠀⠀⠀⡸⠛⠂⠀⠀⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣬⣉⣐⠦⣏⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣐⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣂⡠⣶⣖⣚⡩⠎
⠀⠀⠀⠠⠎⠀⠀⠉⠒⠀⠐⠁⠀⠈⠑⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣑
⠀⠀⠀⠀⠑⠊⠉⠉⠒⢤⠂⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⢀⡤⡤⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⣀⠀⠀⠀⠀⠠⠜⠁⠀⠀⠀⣸⢁⠂⠀⠀⠀⡀⢸⡄
⠀⠀⠀⠀⠐⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠈⠀⠐⢀⠆⠄⢀⠔⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⣀⠜⢡⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⡡⠊⢀⠄⠀⢀⣁⡴⢋⠄⠐⠃⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠇⢠⠁⢠⠃⠀⢀⢞⣾⢣⠏⠀⠀⠀⢰⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡆⠸⡀⡪⢠⣴⣭⠞⠋⣞⠀⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣤⣐⡠⠊⠉⠀⠀⠀⠙⠦⠤⠔⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠄⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⣿⣧⡆⠀⣴⣿⣿⠇⠀⠀⣀⣤⣒⣴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣒⢦⣽⣿⣿⣿⣿⣧⣾⣿⣿⣏⣤⣶⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣟⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⡿⠟⣉⣀⡠⣄⣀⣀⣠⠴⠚⠉⠉⠉⠙⠲⣤⡙⢦⡈⠉⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⡼⣫⣾⣿⠟⡠⠊⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⢆⠀⢠⡶⠛⠋⠙⠻⢶⡀
⠀⠀⠀⠀⣾⣽⢿⣿⡏⣸⠁⠀⠀⠀⠀⢀⣶⣶⠀⢹⣴⣶⡀⠀⠀⠀⠀⢸⡇⠀⠀⠳⠋⠀⣴⡟⠳⣦⡀⢻⡀
⠀⠀⠀⢰⡟⠁⣾⣿⠀⡇⠀⠀⠀⠀⠀⠈⠻⠟⠀⢸⠛⠻⠃⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠈⠀⠀⠘⡇⢸⡇
⠀⠀⠀⠀⠀⠀⡟⠹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠙⢒⣲⣶⣾⡿⠯⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠘⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡀⠀⠀⠀⠀⢀⣤⣾⠷⠒⢻⠉⠁⠀⠀⢳⠀⠀⠀⠸⠈⢳⡀⠀⠐⡖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠳⢦⣤⠴⢞⠟⢫⠀⠀⠀⢸⡀⠀⠀⠀⠈⣧⣠⣤⣾⣷⣾⣿⡄⠀⢹⡀
⠀⠀⠀⠀⢀⡴⠛⠛⠉⠀⠀⠀⠀⣴⠏⠀⠸⡀⠀⠀⢈⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣇
⠀⠀⠀⠀⡾⠀⣰⠾⠂⠀⠀⠀⢸⠁⢇⠀⠀⣱⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿
⠀⠀⠀⠀⣧⠀⢿⡀⠀⠀⠀⠀⢸⣄⢈⣷⣾⣿⣿⣿⣿⡿⢻⠟⠉⠉⠉⠛⢿⣿⣿⡿⠛⣿⡿⠀⢸⡆
⠀⠀⠀⠀⠹⣦⠈⠛⠶⠀⢀⣀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠘⠀⠀⡠⠴⢄⡏⠀⠘⣿⡀⢸⠇⠀⣾⡇
⠀⠀⠀⠀⠀⠙⠻⠶⠶⠖⠋⠘⢆⠈⢿⣿⣿⣿⣿⠿⢧⡶⠛⠙⢦⣇⠀⠈⢿⡀⠀⠸⣧⠎⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢻⣿⠟⠻⡄⠀⢣⠀⠀⠈⢿⡄⠀⠀⢷⡠⠔⣁⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⢷⣄⠙⢦⠀⠣⡀⠀⣀⡷⠤⠒⣉⡤⠞⣡⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠙⠚⠛⠊⠉⠉⠀⢀⣈⣩⣵⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠶⠶⠾⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢦⠤⠽⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠿⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠢⣀⡛⣄⠀⣀⠸⡓⠀⠀⡠⠔⠒⠃⠀⠀⠀⠀⢠⡤⠒⠋⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠾⠱⣿⡄⠀⠧⢤⣈⠀⠀⠀⠀⠐⠺⣜⣠⠤⠖⠛⠒⠛⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⡤⠔⠊⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣒⠿⠛⠉⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠠⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠈⡙⢲⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⡙⠁⠘⡆⠈⢶⢤⣀⠀⠰⡶⢄⠀⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢦⠀⢸⡀⠀⠇⠀⠘⣆⠈⠉⠐⠛⠈⢺⠥⠤⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⠀⠀⠃⠀⠈⠀⠀⠘⠆⠀⠀⠀⣰⡃⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡧⠤⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢾⣿⡀⢿⠿⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⣖⡀⠛⢁⡀⠳⡄⠰⠒⣻⠁⠀⠀⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣇⣠⣅⠀⢠⠇⠀⠀⠀⠀⠈⠒⡛⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠦⣀⠀⠀⠈⢑⣿⠉⠬⠤⠞⠢⠄⠀⠀⠀⠀⠘⢅⣠⠇

⠀⠀⢸⠁⢠⡴⠿⢶⡄⠀⣿⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣦⣤⣤
⠀⠀⢸⠀⢸⠗⠖⠾⠇⠀⣿⠀⠀⠀⢀⣶⣶⣶⣶⣤⡀⠀⣠⣴⣶⣦⣄⠀⢀⣠⣶⣶⣦⣴⣤⣤⣤⡤⣁⣤⣬⣬⣍⠉⣭⣭⣭⣭⣉⠉⠉
⠀⠀⣾⠀⠈⣀⠀⢀⡀⢀⡿⠀⠀⠀⠈⢉⣽⡉⢹⣿⣷⣾⣿⠟⠉⢻⣿⣧⣾⣿⠏⠉⠉⠉⣿⣿⠋⢹⣿⡟⠛⠻⣿⣧⣽⣿⡋⣻⣿⡆
⠀⠀⣿⠀⡠⣾⠓⠀⠉⠀⡇⠀⠀⠀⠀⣿⣿⣦⣾⣿⠟⢻⣿⣦⣤⣾⣿⠏⢻⣿⣦⣤⡄⠀⣿⣿⠀⠸⣿⣧⣄⣴⣿⡿⣿⣿⣿⣿⣟
⢀⣴⣿⠿⣿⢿⣿⢿⡿⡾⢻⣦⡀⠀⠀⣙⠛⠛⠛⠁⠀⠀⠉⠛⠛⠛⠁⠀⠀⠉⠛⠛⠁⠀⠙⠛⠀⠀⠈⠛⠿⠛⠋⠀⠛⠻⠋⠻⠟⠗
⠈⢻⣿⣿⢟⡟⠿⢻⡿⣛⠻⡏⠀⠀⠀⣿⣿⣿⡇⠀⢰⣷⠀⠀⣼⣿⣿⡏⢸⣿⣿⣗⠀⠀⢸⣿⣿⣿⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⣄
⠀⢸⣇⣄⣸⣇⣶⣸⣌⠛⣣⠇⠀⠀⠀⢸⣿⣿⣷⢠⣿⣿⣇⢠⣿⣿⣿⠁⢸⣿⣿⣧⣤⣶⣾⣿⣿⣿⠀⣴⣿⣿⣿⠟⠛⠻⢿⣿⣿⣧⡀
⠀⢀⡉⠈⠉⠻⡿⠋⠀⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⢰⣿⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⡇
⣠⣼⣿⣦⣤⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢿⣿⣿⣿⡿⢻⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⠁⠀⢸⣿⣿⣿⠘⣿⣿⣿⣄⠀⠀⠀⢀⣾⣿⣿⡇
⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠁⠀⠀⠀⢸⣿⣿⣿⠃⠈⣿⣿⣿⡇⠀⠀⢸⣿⣿⡟⠀⠀⢸⣿⣿⣿⠀⠙⣿⣿⣿⣷⣶⣶⣿⣿⣿⡟⠁
⠀⠀⢰⠳⣌⠻⠿⠿⡷⢄⡀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠙⠛⠛⠀⠀⠀⠘⠛⠛⠃⠀⠀⠘⠛⠛⠟⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠋⠀⠐
⠀⠀⠀⢳⣄⡀⡲⢶⡿⠤⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠠
⠀⠀⠀⠉⢈⣉⠔⢠⢘⣤⠁⠀⠘⡛⠃⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠤⠤⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠻⠉⠀⠀⠈⢠⣹⣷⣉⣏⡰⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠐⠮⠉⠐⢦⣈⣹⡇⠙⢾⣀⠀⣠⡀⣀⢀⡀⠀⠀⠀⠀⠀⣠⡴⠁⡧⠀⠀⠀⣈⠁⢀⠀⠂⠀⠀⠠⠒⠀⠀⠀⠉⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠰⢦⡙⠛⠁⠉⢿⡀⠘⢿⡀⡄⠀⠈⠂⠁⠀⣐⠶⠄⡺⠃⠀⡜⠁⠀⠀⡠⣴⠚⡁⠀⠀⠀⠀⠀⠚⠀⠀⠀⠴⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠯⣁⡠⠀⣷⡀⠸⡿⠽⠇⠠⠄⠀⠀⠀⠖⠀⠀⠀⠀⢣⣄⡴⠋⠆⠀⠸⠙⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡔⣧⡀⠀⠰⡀⠀⠀⠀⢀⠀⠀⠀⣈⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡞⣻⣄⠀⢡⣄⠀⠲⠶⠦⠀⣸⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⡀⠤⠴⢶⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⡏⣻⡿⣁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠰⠀⠀⠀⣀⡸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣾⡿⣿⣆⠈⢳⣤⡔⠀⣿⣿⣦⣀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⢀⡀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣽⣿⣿⣿⣿⢤⠿⡉⠙⣾⣿⡉⠻⣭⡙⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⡿⣿⣯⣸⣿⡆⡀⠃⢰⣼⣿⣀⡶⢿⣿⣿⠄⢀⠀⠀⠀⠀⠀⠀⠂⡠⠃⢠⠛⡀
⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⣿⣿⠙⢿⣎⠹⣿⣿⣿⠿⣶⣨⣿⡿⠋⠀⠀⢻⣿⢗⡁⠄⠀⠀⠀⠀⠢⠀⣠⠄⠀⢠⠇
⠀⠀⠀⠀⠀⣰⠟⢛⣿⣿⣧⠙⢷⡈⢻⣿⣿⣿⠿⣿⣶⣿⠋⠀⠀⣀⣀⣜⡿⢸⣇⡀⢆⡉⠔⠀⠀⠈⣁⠀⣡
⠀⠀⠀⠀⢰⡟⠺⠟⣡⣴⡿⠳⣀⠀⠀⠻⢿⣿⣿⣿⣿⡧⠀⠀⣾⣿⣿⣧⣧⠾⠇⠉⠁⠀⠀⠀⠠⠚⡁⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⢸⣿⣶⠼⣿⣿⠀⡂⢩⠀⠀⠀⣀⣉⣉⣍⣉⣥⣠⣄⡼⠿⢿⣿⣿⠀⡿⠈⢁⠀⢀⡄⡔⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠂⢉⣿⣗⣠⣾⣿⣿⡿⣋⣾⡯⡙⢷⣇⠀⣼⣿⠇⢠⡇⠀⠀⠀⠈⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣮⠶⣿⡟⢹⡏⢀⡿⢙⣿⡀⠀⢢⠙⢷⣽⣿⣶⢼⡏⠀⠀⢠⠀⣃⢠⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⠃⣠⠚⠁⣾⣿⠃⠀⠀⢳⡄⠙⢿⠛⠘⡇⠀⠀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⢀⣞⡁⢀⣸⣿⣿⡀⠘⠀⠈⡿⣄⠀⢳⣤⠻⠂⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣶⣶⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⣴⡿⠉⢈⣯⣉⣽⣿⣿⡀⢈⡧⢸⣤⣦⡈⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⠃
⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠉⠉⣠⠈⠁⠈⠁⠀⠀⠉⠀⠀⡀⠀⠀⠱⣻⡟⠦⡀⠀⠾⡅⠀⣀⡠⠄⢚
⢸⣿⣿⣿⣿⣿⡇⠀⠀⠠⠀⡄⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⣿⡇⠀⠈⢺⣦⠛⢾⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⡖
⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⡇⠈⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢼⣿⣿⣿⣿⣿⡇⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛
⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠋⣽⠉⡄⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣧⡀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⡏⠀⠹⡄⠀⠀⠀⠘⡇⠀⢹⠀⠀⣄⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃
⢻⣿⣿⣿⣿⣿⡟⠃⠀⣿⠀⠀⠀⠀⠀⠀⡀⠁⠀⢸⠄⠀⠀⠹⠀⠀⠀⠀⠡⠀⠈⠃⢠⠉⠉⠀⠀⠀⠀⢰⠲⡆⠐⡶⠀⠀⠀⠰
⠘⠛⠛⠋⠛⠛⠃⠀⠀⠋⠀⠀⠀⠀⠀⣰⢷⡶⣶⠶⠶⠤⢒⣶⢧⠀⠀⠀⠀⠀⠠⡄⠈⠀⡀⠀⠀⠀⠀⠘⡇⠻⣴⠃

⠀⠀⠀⠀⠒⠀⠢⡀⡀⠀⢄⠀⠀⠀⠀⠀⡄⠀⠀⠀⢄⠀⠀⠄⠀⠀⢰⠀⢤⠀⠐⠀⡄⠀⡄⢀⠀⠀⡀⠀⠀⣂⠂⡀⠰⡀
⠀⠀⠀⠀⢀⠀⠠⠃⢇⠀⠸⠘⢄⠀⠀⠀⡇⠐⢆⠀⠸⠀⠀⠂⠀⠀⠈⡧⠀⢷⠀⠀⡇⠈⡇⠺⠀⠀⠃⠀⠀⠈⠇⢃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠥⢌⡑⠀⠠⠑⠄⠀⠄⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠃⠀⣀⠦⠅⠀⠀⠤⠋⠹⣄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢶⣦⡐⠁⣰⡏⠀⠀⠀⠐⠀⠀⢀⣴⣇⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡠⠋⠀⠀⠙⢁⠀⠀⠀⠀⠀⢠⢲⡀⢈⣧⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢠⠁⠀⠀⣠⠶⢦⣄⠓⠤⠔⡡⠈⠀⠴⢛⠉⠐⣤⠆⠀⠀⠀⠀⣀⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⡀⠸⡄⠀⠀⠷⡾⠀⠂⠈⠀⠈⠀⢀⠀⢄⡼⠃⠀⠀⣾⡀⠀⢻⣄⣋⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣿⠂⠘⠦⣄⢀⡠⠂⠤⣄⠀⢀⣴⣍⠑⠈⢷⠀⠀⠀⠛⣵⠀⠀⢨⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠻⣧⡤⠀⠀⢾⡇⠠⠐⢿⡇⠘⣦⣅⠈⠀⣨⢠⡼⠁⢰⠇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠄⠀⠀⠀⠚⣿⡀⠈⠙⠁⠀⠈⢈⡆⠀⢸⡏⠀⢀⡝⠒⠓⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⠀⠀⠠⣿⡅⠀⠙⢳⣄⢠⡟⠠⠀⠈⣧⠀⠜⠁⠀⡆⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⣠⠿⡇⠀⠈⠉⠉⠁⠀⠀⠀⠀⢘⡉⣀⡠⢀⠼⠒⠋⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠬⠤⢴⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣁⠀⣄⢠⠤⠀⠂⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣾⡿⠿⢿⣿⣿⡷⢾⣆⣀⣀⣀⣤⣴⣇⢹⠋⠀⢸⠋⡖⠂⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⢠⡇⢸⣿⢿⣅⣤⣴⣿⣏⣿⣤⣼⠏⣄⢳⡄⠸⢧⣿⣁⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⢀⣀⢸⡇⠈⢣⡞⠉⣼⡿⢹⣿⣿⠉⢻⡈⢕⣸⢇⣤⡤⠀⢀⣠⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⢠⣾⡇⢸⡇⡄⠘⢧⠴⡿⠁⣿⣿⠙⣧⣬⣿⡾⡁⣾⡟⢃⣀⣀⡦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⣿⡇⢸⡇⣧⠀⠀⣼⣇⣰⠏⠉⣦⢹⣿⣿⡽⣧⠸⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⣿⡇⢸⡇⣿⡄⠘⠛⠻⡟⠀⣀⣿⣧⣿⣿⡇⡉⠀⠀⣿⣿⠁⠀⠐⢤⠂⠤⠴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⠀⣷⢸⣧⠀⠀⠠⡆⠺⡅⠈⣿⣿⣿⡸⣇⠀⢰⡟⣿⡄⠀⠀⠒⠒⠒⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⣿⣿⣿⡇⢠⢻⡌⣿⡆⢦⣠⣿⡄⠙⣦⣿⣿⣿⡆⠻⢧⣀⣴⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣧⢻⣿⣿⣿⠈⣾⣷⢹⣿⡼⣿⣿⣿⡀⠘⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣆⢻⣿⣿⣿⣿⣿⣆⢿⣷⣹⣿⣿⣿⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⢻⣿⣿⣿⣿⣿⡌⢿⣧⢻⣿⣿⣿⣌⢦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡙⣿⣿⣿⣿⣿⣌⢻⣧⡹⣿⣿⣿⣦⠳⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠛⢿⡿⣿⣿⣦⠙⢷⡝⢿⣿⣿⣷⣝⢦⡙⢿⣿⣿⣿⡟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⡄⠙⠈⠻⣿⣿⣿⣷⣿⣮⠻⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⠩⠿⣁⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣎⠒⠶⢤⠘⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡨⢠⠈⢀⡰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⠁⠀⠈⠑⠢⢤⣠⡏⠀⠀⠁⠃⠀⠨⠓⢄
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢴⡾⡋⠢⠤⠄⠀⠀⢀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⢀⣠⠖⠋⠁⣀⠐⢱⠀⠀⠴⠆⠑⠂⢄⡀⠀⠈⡌⠀⠀⠀⠀⠀⠀⠜⢀⡀⠀⠑⡀
⠀⠈⢻⣄⠀⠘⠄⠸⠃⠈⠢⡀⡀⢀⠤⡪⠀⣈⡴⢻⠁⠀⠀⠀⠀⠀⠘⠀⠀⠑⠀⠀⠈⠠⡀
⠀⠀⢸⠈⠓⢤⡀⠀⡀⠈⢆⣀⠍⠓⣨⠴⠚⠓⠂⠣⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢄⡠⠣⡀
⠀⠀⢸⠀⠀⠀⠙⠢⡉⠀⢀⣠⠖⠋⠁⠀⢀⠴⠋⠀⠀⠉⠓⠂⢀⡴⡀⠀⠀⠀⠀⠀⠀⢑⡢⡈⡆
⠀⠀⢸⠀⠀⠀⠀⠀⢹⠚⠉⡇⠀⠀⢺⠚⠁⠀⠀⠀⢀⣠⠔⠚⢁⣀⡜⠀⠀⠀⠀⠀⠀⠐⠠⠬⡀
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⢖⠈⣿⠀⠉⠉⣏⢸⡇⠀⠀⠀⠀⠀⠈⠒⠤⠥⠃
⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⡜⢆⠀⠀⠈⡄⣿⠀⠀⠀⡿⠈⡇⠀⠀⠀⢠⣶⣻⣛⡏⣻⢙⣓⡄
⠀⠀⠈⠳⡄⠀⠀⠀⢸⠀⠀⣿⠀⠀⡇⠈⢆⠀⠀⠸⡇⠀⠀⠀⡇⠀⣷⠀⠀⠀⠈⣿⣟⣏⣹⣉⣯⣿
⠀⠀⠀⠀⠙⢦⠀⠀⢸⠤⠒⠋⠉⢹⠀⠀⠈⢧⠀⠀⢣⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡀⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⣄⢸⠖⠒⠋⠉⠁⠀⠀⠀⠈⢧⣀⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣾⣆⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣰⣷⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠾⠇⠙⠃⠙⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠋⠘⠋⠸⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠀⠈⠳⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠞⠁⠀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠅⠀⢀⣀⣀⠈⠀⢀⣴⠶⠞⠳⠶⣦⡀⠀⠁⣀⣀⡀⠀⠨⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠉⠀⣴⠏⠀⠀⠀⠀⠀⠀⠹⣦⠀⠉⠻⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠆⢸⡇⠀⣀⣀⡀⢀⣀⣀⠀⢸⡇⠰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢻⡾⠋⠉⢻⡟⠉⠙⢷⡟⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣴⠟⠁⠀⢀⣼⣧⡀⠀⠈⠻⣦⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠁⠀⠀⣠⡞⠁⠈⢳⣄⠀⠀⠈⢷⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠼⠋⠀⠀⢀⡾⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠙⠧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣧⣤⣤⣤⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣼⣧⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠠⠠⠀⠀⠤⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⠻⠓⢉⠀⠰⣄⠀⠀⣠⣾⢷⣘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢹⣿⢆⠀⠰⠁⠀⠀⠀⡙⠈⢩⣴⣿⢟⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣟⡹⣀⠰⠇⠀⠀⣴⠛⠀⣫⣶⡂⠈⢉⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠶⡟⠟⢛⣈⠁⡞⣭⣀⠀⡄⡄⠁⠐⣱⠈⢠⣶⣗⣀⣩⢿⡟
⠀⠀⠀⠀⠀⠀⢀⠀⢐⣿⣇⡰⠜⠃⣚⣀⢰⡶⣖⠿⣴⡦⣰⣿⢤⣀⢀⠁⣄⢰⣾⣿⣎⣿⣿⣿⣷⡔⠁⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⡠⠂⢱⠷⢚⡘⢵⡖⠉⠀⠛⢘⣃⢠⡵⣦⠻⢄⣣⡙⠁⣴⣷⡼⢟⣯⣿⣿⣿⣿⣿⠿⠋⢀⠤⠒⠉⣁⡀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⣰⠊⡷⠀⠀⣦⣀⠐⠀⢙⣭⢰⡄⠻⠉⡧⠁⡼⢧⠿⣙⣧⡘⣿⣿⡟⠹⠿⠛⠛⠉⠉⠀⢠⡔⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣜⢆
⠀⣼⣿⡁⢴⣂⠄⠀⣤⠂⠉⠊⢣⡀⢿⣂⠠⣶⣧⠁⣨⡄⢿⢉⣥⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠲⢷⡔⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⢸⣈⣷⣿⣆⣶⠀⠀⠈⠀⠂⣈⡀⢸⣟⣫⠇⢉⣴⡖⣹⣟⡰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⣓⠉⣓⢐⠀⢤⣈⣁⣀⣐⡶⡶⣞⣿
⣿⣿⣟⣷⣽⡛⣉⣄⠒⠘⣹⣉⣱⠈⢙⣥⣶⡆⠓⣦⣴⣿⡧⠄⠁⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠛⠃⠬⣹⣳⣾⣾⣿⡿⣿⠿⠟⠁
⢿⣿⣷⣽⣿⣽⡿⣿⣿⣿⣦⣤⣴⣟⡙⠿⠿⠿⠾⢻⣟⡋⠀⠀⣴⠞⣋⣤⣴⡷⠤⠦⠄⠀⠀⠀⠀⠉⠀⠠⡀⠀⠀⠀⠀⠈⠉⠉⠉
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢚⣉⣀⡄⢀⠀⡀⠀⠀⠀⠈⠑⠚⢴⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠈⠻⠿⣿⣹⣿⣿⣟⣵⠏⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠄
⠀⠀⠀⠀⠀⠀⠉⠉⢻⣅⣠⡀⣀⠀⠀⡀⡀⠀⢀⢀⠀⠀⡠⠀⠐⠁⡐⠁⠀⡀⠀⠀⠀⡊⣀⣀⣤⣮⡥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣵⡟⠀⠨⣚⠐⢿⡭⣣⠊⠴⠖⠐⠾⣿⠲⣿⡷⠺⣿⠿⠿⠊⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣟⡛⣿⣿⢶⡿⠿⠓⠚⠋





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠈⠈⢶⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠠⢾⠏⠀⠀⠀⠀⠀⡾⠀⠀⠀⠠⠄⠀⠈⡄
⠀⠀⢀⠀⡰⢁⡎⠀⠀⠀⠀⠀⢠⡧⣤⣀⠀⢰⠇⠁⠀⠀⠄
⠀⠠⠃⡴⠁⢺⠀⢰⠀⠀⠀⢀⡎⠀⠀⠈⠙⢦⡠⠂⠀⢀⠀⠀⣄⣤⠤⠤⣄⣀⡀
⠀⠀⠈⠀⠀⢹⠀⠸⠀⠀⠀⠘⠀⠀⠀⠀⠀⢈⢳⡀⠴⠁⠀⠐⠂⠈⠀⠀⠀⠀⠉⠑⠲⢄⡀
⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠀⠀⢠⣤⣤⣈⡉⠉⠀⣯⠀⠐⡠⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⡤⠀⢸⡇⠀⠀⠀⠀⠀⣼⠁⣴⡟⠻⣷⣄⢸⠂⢀⡴⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠸⠁⠄⢸⡇⠀⠀⠀⠀⠀⡏⢀⣿⣀⣴⣿⡟⢸⠃⠁⠀⠀⠀⣠⠞⠁⠈⠉⠀⢀⢀⡀⠀⠀⠀⢀⠑⠂
⠀⠀⠀⠀⠀⣎⡇⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⠟⠀⠘⡇⠀⠀⠀⣰⠃⠀⣠⣴⠶⠶⢬⡀⣁⡀⠀⡴⠋⠀⠀⡇
⠀⠀⠀⠀⢸⠁⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⣳⣤⣤⠏⢠⣾⢿⡿⢿⡆⠀⣿⡀⠀⠍⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠐⡀⣽⡀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⡟⠀⠀⠀⢿⣿⣿⠠⣾⠃⣠⡿⠁⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠻⣄⠒⠀⠄⠛⠉⠀⠻⣄⠀⠀⠈⠫⠥⠪⠅⠊⠀⠁⠀⠀⠀⠀⢀⡼⠃
⠖⠛⠓⠒⠲⠤⣀⣷⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠙⢒⠶⠀⠀⠀⠀⢠⠋⣠⠎⣰⠁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⠇⢰⠃⠀⠀⠙⣖⠂⠀⢆
⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣼⠀⡎⠀⠀⠀⠒⠛⣆⠀⢨
⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠚⢸⡇⠀⠀⠀⠀⡄⢸⠀⡎
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⠏⠀⠀⠀⠀⠘⣇⢀⡀⠀⠀⠀⠀⢰⠀⠁⠀⠀⣠⠀⠀⣸⠠⡇
⠀⠀⣀⣠⣴⡋⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠈⠂⠐⣄⠀⠀⢀⣴⣿⠀⠀⠷⢦⡇⡀
⠀⡜⠉⠁⠈⠙⠓⠒⠶⡶⢶⡟⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣄⠀⠘⣦⠾⠟⠁⢻⡀⠀⠀⠈⢿⠴
⢰⠀⠀⠀⠀⠀⠀⠀⡸⠁⢸⡃⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠈⢧⣀⠇⠀⠀⠀⢸⡅⠀⠀⠀⠘⣧
⡄⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⢱⡀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⠀⢸⡇⠀⠀⠀⠀⢸⡆
⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢳⠀⡾⠀⢷⡄⠀⠀⠀⠀⢀⡟⠀⠀⡦⠀⣿⡇⠀⠀⠀⠀⠀⣧
⠰⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠻⢦⣀⣀⣤⠞⠀⠀⠀⠃⠀⣸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣇⣠⣀⣀⣀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⣀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠹⠿⠶⠶⠒⠖⠂⠀⠤⠦⠼⠦⠔⠲⠖⠒⠳⠒⠒⠒⠒⠉⠁⠿⣤⣤⣤⣤⣤⣤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⣠⣤⣾⣿⣿⠟⠋⠉⠉⠉⠉⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠉⠉⠙⠛⠿⠿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦
⠀⠀⠀⣠⣾⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷
⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣦⣀⠀⠀⠀⢀⣤⣾⣿⠿⣿⣿⣷⣤⣀⡀⣀⣀⣠⣤⣶⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠉⠛⠿⣿⣿⣿⡿⠿⠿⠛⠉⠉⠉⠻⣿⣿⣶⣄⣀⣤⣄⠀⢾⣿⣏
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⠀⠈⢿⣿⣷⡄
⠀⠀⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠙⣿⣿
⠀⠀⢹⣿⡇⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⢻⣿
⠀⠀⣸⣿⡿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⢸⣿
⠀⣼⣿⡿⠁⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⣼⣿
⠰⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⣀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⣿⣿⡄⠀⠀⣴⣿⡿
⠀⢿⣿⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⡄⠀⢿⣿⣧⣤⣾⣿⠟⠁
⠀⠘⣿⣿⣄⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠈⠛⠿⠿⣿⣿⣆
⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⢰⣿⣿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠁
⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋
⠀⠀⠘⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠈⠻⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠀⠀⠀⠀⠉⠉⣻⣿⣿⡟⠛⠉⠉⠁⠀⠀⠀⠈⣻⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⡿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠉⠙⠻⢿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠿⠛⠋⠁⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⢀⣿⣿⠛⣿⣿⣄⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣷⣄⡀
⠀⠀⠀⣠⣶⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⡀⠀⣼⣿⡟⠀⠙⢿⣿⣦⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣄
⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣷⣤⣤⣾⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⡶⠀⠀⣀⣠⡤⠶⠖⠚⠛⠛⠛⢛⣛⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⢁⣴⣫⡴⠞⠋⠉⠀⠀⠀⠀⣀⣤⣖⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢛⡽⢖⣠⡤⣤⣄⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢯⣥⠀⠀⠈⡼⠋⠀⠀⠀⠀⠙⠳⣄⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀⠀⠀⢴⠚⠉⠀⠀⢀⠞⠛⠀⠀⠸⡇⠀⢀⣤⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠙⢦⡀⠀⡤⠤⢬⡀⠀⢌⠉
⠀⠀⠀⠀⢰⢋⣽⠀⠀⠀⠀⠰⣶⠓⠀⠀⠀⠏⠀⠀⣤⠖⠛⠛⠲⣥⣿⡿⠀⠀⠀⠀⣸⠃⠀⢀⣀⣀⡀⠙⣎⠣⣤⡞⠉⠙⣦⡤⣄
⠀⠀⠀⠀⠸⢣⡏⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⡆⠀⠀⠀⣀⡴⠋⠀⠐⠉⠀⠠⡟⠉⠻⣦⠏⠉⠉⠜⢁⣀⣸⠃⡴
⠀⠀⠀⠀⠀⢸⡇⣴⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⣧⡀⠀⠀⠈⣹⡟⠒⠚⠛⠉⠀⠀⠀⠀⠀⢀⣠⠟⠙⢲⡈⠀⠀⣠⠞⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠻⠙⣆⠀⠀⠀⣀⣀⡀⢹⠀⠀⠀⠀⠈⠙⠒⠒⢊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡡⠤⠀⣸⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠋⢉⣉⣉⣉⠉⠃⠀⠚⢯⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⡉⠲⢤⡴⢣⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠛⠷⠶⠋⢁⣴⣄⠀⠀⠈⠙⠒⠦⠤⣤⣤⣤⡤⠴⠖⠛⠉⠙⣆⠀⠈⠣⡀⠙⢧⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⠴⠞⠋⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⢩⣷⡀⠀⠀⠀⢀⣧⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢻⡋⠀⠀⠀⠀⠀⢠⠖⠀⠀⠈⠉⠙⠓⠒⠒⢚⡿⠯⠭⢤⣤⣀⣸⠶⠿⠦⠤⠶⠋
⠀⠀⠀⠀⠀⢀⣰⡟⢻⡀⣠⣿⣶⣄⣀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢯⡀⠙⠜⠛⠁⣨⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⣾⡋⠑⢂⣠⠼⠉⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠁
⠀⠀⠀⠀⡼⠁⠉⠉⠉⠀⠀⠀⠀⢀⡴⢋⡴⠋⠉⠉⢀⡤⠞⠁
⢀⣠⠤⠾⣧⡀⠀⠀⠀⠀⠤⠤⣴⣏⣴⣏⡀⠀⣠⡴⠋
⣟⠀⢠⠞⠧⠽⠛⠲⢤⣤⣄⣴⣋⣤⡤⠴⣶⣫⢿⠉⢳⡄
⢿⣓⣛⣓⣚⣛⣛⣭⠭⠵⠚⠯⢽⣓⣒⠒⠾⠶⠛⣒⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⡀⠀⡀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡸⠯⠧⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠹⠟⠪⠽⠋⠛⠤⠏⠃⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡸⢾⠔⠚⠃⠁⠒⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠙⠦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⢠⣤⠞⡛⠁⠁⠀⠀⠀⣀⢀⠇
⠀⠀⠀⠀⠀⠀⠲⠤⠛⠉⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠴⠖⠉⠁⠀⢀⡀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠢⣀⡀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠁⠀⠀⠀⠈⠙⠉⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⠲⠤⣄⣀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠳⠶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠂⠀⠀⠀⠀⠈⠩⠀⠁⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠘⢦⡁⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠈⠛⢷⣂⠔⡦⠠⣀⣠⣀⣄⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠈⡀⠀⠤⣤⣀⡤⠜⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠳⣤⡠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⡂⢀⡝⠀⠀⠀⠐⠂⠀⠀⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠰⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠬⠴⠃⠀⠀⠀⠀⠀⠤⠀⠦⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠙⠀⠀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠂⡸⢀⠊⠉⠆⠀⡗⠢⠘⠂⠪⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡎⠀⢀⠁⠀⠀⠀⠐⢄⠈⠀⠈⡀⡄⠀⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣉⡁⠀⠢⣀⣀⣀⠘⠀⠓⠒⠀⠉⢉⡀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡌⠀⠈⡆⠀⠀⠤⠤⠀⠀⠖⠀⡆⠘⠁⠈⠄⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠀⡆⠀⠀⢰⠀⠁⠀⠃⠠⠀⢁⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠢⠀⠁⢃⠀⠀⡀⢠⡀⡐⠀⠣⠤⠊⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡀⢄⠀⠀⢈⡉⠁⠀⠀⠀⠀⠀⡀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠁⠀⠉⠑⠀⠊⢀⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣈⠀⠀⠈⠒⠀⠒⠀⠂⠀⠈⠃⠂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠑⠀⠉⠀⠉⠑⠀⠂⠈⠆⠄⢢⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠃⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣈⠁⠒⠊⠀⢣⡀⢀⡀⠴⠀⡀⠀⢀⡝⠤⠐⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠂⠀⠈⠐⡄⠀⡤⠤⠤⢄⡀⠀⡀⠀⠀⠀⠔⠀⠀⢀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠦⠀⢀⣀⡀⠀⡁⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⢀⠀⠀⡀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡤⠤⠀⢀⡀⠀⢈⣐⠀⠒⠀⠁⠈⠒⠒⢒⠊⠀⢠⠤⠄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⡆⠀⠈⠁⠀⢱⠀⡄⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⣠⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠁⠀⠈⠀⠑⠀⠀⠠⠤⠆⠀⠄⠠⠄⠂⢀⠭⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠒⡉⠉⢢⠐⠂⠁⠐⠄⡠⠂⠒⡄⠀⣂⠠⢂⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣑⠊⠐⠤⠤⠔⠀⠤⠀⠔⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠲⠶⠶⠦⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠻⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢿⣍⣉⣉⣉⣽⡟⠁⠀⠀⠀⠀⠀⠻⣯⣉⣉⣉⣩⣿⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣾⣯⣤⡶⠶⠿⠿⠶⢶⣦⣽⣷⡀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣦⣤⣤⣤⣤⣴⡶⠾⠟⠛⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣤⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⢁⠀⠀⠀⠀⠐⠶⠛⠉⠀⢀⠀⠛⠳⠆
⠀⠀⠀⠀⠀⠀⡤⠈⠤⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠐⠰
⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⠴⣄
⠀⠀⠀⠀⠒⠲⣄⠀⠰⢤⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢀⣠⡀⢀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠓⡺⠚⠟⠉⢀⠀⠀⠀⠀⠀⠀⣘⣷⣭⢀⢘⣿⡆
⠀⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠄
⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠈⠦⠀⡀
⠀⠀⠀⠢⣀⠀⡀⠈⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠈⢄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠠⠴⢤⣄⣀⣀⣀⣠⡤⠶⠖⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠖⠒
⠀⠀⠠⠀⠉⠉⠉⠉⠉⠀⠀⠁⠀⠀⡀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠠⠀⠀⠈⠄⠀⠉⠀⠐⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⡤⠒⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⡤⡤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠤⠤⠄⠀⠀⠀⠀⢤⢤⣤⣤⣤⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣇⠀⠘⢻⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡿⠻⢿⠀⠀⣻⣻⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⡛⠿⠿⠛⢿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣟⢻⣿⡇⢧⣀⢀⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣯⣥⠄⣿⣿⣿⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣏⢛⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⡿⠟⠛⣮⢿⣿⣿⣿⣧⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣾⣧⣨⢻⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⡟⣉⣵⣿⣿⣿⣏⢹⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡟⣳⠿⡙⣿⣿⣿⣿⣿⣿⡿⣿⣦⡈⣿⣿⣷⣸⣿⣿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣻⣶⣼⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠤⠠⠄⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⡔⢤⣄⢀⠐⠒⠄⠠⣤⠀⠀⠀⠀⠀⣠⠔⠚⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣇⠈⠁⠈⠐⠂⠒⠠⠚⠂⠈⠉⠉⠀⠀⠀⢴⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠳⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢈⣏⣉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠋⠁⢀⣰⣀⠈⠶⠁⠀⢻⣻
⠀⠀⣠⠤⡄⠀⠀⣠⠞⠁⠀⠀⠀⠸⣇⣷⢂⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⣀⠀⠀⢠⣴⣷⠆⠀⠀⠀⠀⠀⠀⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉
⢠⠚⢛⠛⢻⡑⠂⡿⠊⠀⠀⠀⢀⠂⣋⣿⡤⠂⠀⠀⠀⠀⠀⠀⠐⣿⣃⡀⡆⢰⣿⣾⠀⢰⠆
⠈⢧⣨⠛⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⢇⢳⠆⠀⠀⠀⠀⠀⠀⠀⣙⡖⠀⠀⠈⠣⠈⠀⠸
⠀⠀⢣⠈⢧⠀⠀⢴⢿⡆⠀⡌⢀⠀⠸⢸⠀⠁⠀⠀⠀⠀⠀⡰⡀⠉⢱⠀⢀⡆⠀⣴⣀⠀⠀⠀⡠⠴⣶⡄
⠀⠀⠘⣶⠀⠀⠈⢻⢶⡇⢸⡀⡸⠀⠀⡜⡆⠀⠀⡀⠀⠀⢠⠃⡓⠀⡟⣤⡁⠁⠀⡍⠀⠀⠀⢈⡿⣰⣿
⠀⠀⠀⢻⡦⠀⠞⠢⠈⠃⠀⢹⣧⣀⠀⠇⠙⠁⠀⠀⠀⠀⠀⢸⠭⡯⢹⠃⠀⠀⠀⣸⠳⠈⠻⣟⢀⢸⣧⡄
⠀⠀⠀⠘⠃⢠⠸⡀⠀⠀⢀⣎⡤⠀⠉⣟⢴⠂⠀⠀⠀⠀⠀⠫⣿⡧⠟⠙⣤⣤⣀⡟⠃⠘⢠⢟⠈⠀⠉
⠀⠀⠀⡇⠀⢈⡄⠁⢨⣀⠘⠋⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⢿⡟⠃⠀⠛⠒⢾⣤⢤⣀⡘⠛⣇⣀
⠀⠀⠐⠓⠂⠀⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠋⠁⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠲
⠀⠀⠀⠀⠀⡤⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃
⠀⠤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠠⠀⡀⠀⡀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠈⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠊
⠀⠀⠀⠑⢤⠀⠀⠐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⡀

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠋⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢀⠋⠁⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠙⠂
⠀⠠⠀⠀⠉⠁⠀⠀⠈⠉⠀⡀⠀⠀⠀⢠⠁⠀⠀⠤⢫⠀⠀⠐⠀⠀⠀⠀⠀⠈⣴⣤⣦⢢⣤⣦
⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠛⠁⠂⠉⠁⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠁

⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⣀⡴⠆⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠀⠘⠳
⠀⠀⠈⠉⠙⠛⠒⠶⠺⠏⠉⠘⠀⠀⠀⠀⠋⠀⠔⠀⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⢴⠀⢨⠀⡈⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀
⠀⠀⠀⢇⠀⠨⠄⠀⠃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠀⠒⠒⠦⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠁⠀⢀⠤⠐⠒⠊⠁⠀⠀⠀⠀⡔⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠒⠁⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⠎⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡄⠀⠀⠜⠀⠀⠀⠀⠈⠀⢀⠖⠉⢁⠀⠈⢀⠎⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠛⠤⠀⠀⠁⣠⠊⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣠⠤⠐⠒⠊⠀⠀⠀⡀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⡠⠒⠈⠁⡀⠀⢀⡼⠀⠀⠀⠀⠐⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢈⡤⠀⠠⡄⠀⠀⡠⠄⠀⠈⠀⠀⠠⠀⠈⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⣀⠤⠒⠁⢀⠀⠀⠀⣀⠜⡀⠀⠀⠦⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⠁⠀⢀⡰⠃⠀⡠⠀⣠⠁⠀⠀⡔⠁⢀⡀⠀⠈⠁⠐⢊⠑⠄⠈⢀⣀⡠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠱⡀
⠀⠀⡆⠀⠰⠁⠀⡠⠎⡰⠋⠀⡠⠶⡊⠀⠀⠀⡠⠄⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⢃⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠃
⠀⢠⠁⢀⠆⠀⠘⠀⢀⡀⠤⠊⠀⠀⠀⡠⠔⠊⠀⠂⡰⠀⢡⠃⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁
⠀⠸⡀⡜⠀⠀⠁⠀⡏⡀⠀⠐⠀⢀⢎⡀⠈⠂⡠⠊⠉⢠⠂⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⢤⣀⡀⠑⣄⠀⡀⠠⠄⢒⡡⠊
⠀⠀⢣⡱⡀⠀⡔⠋⠀⠈⠂⠀⣀⠜⠀⢀⣠⠎⠑⢀⡴⠁⡜⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡆⠀⠐⠈⠁
⠀⠀⠀⠱⣁⠘⠀⢀⣀⡀⣠⠎⠀⣀⠴⠁⢀⡠⠖⠁⢀⡞⠀⢀⡀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠈⠓⠦⠥⢀⣈⣀⣒⡊⠤⠤⠒⠉⠀⠀⠀⣎⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⠈⠛⠋⣉⣁⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠰⠗⠂⠀⠀⠀⢾⠿⠿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⠟⢡⣶⠸⠂
⠀⢠⣈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠙⠇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠿⠟⠃⣸⣿⣿⣿⣼⣿⡿⠇⠐⢎⠛
⠀⢤⡙⢷⣌⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⠀⠀⢀⣠⡴⣶⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⡄⠁⠈⠛⢷⡿⢿⠉⠁⠀⠀⠈⠁
⠀⣮⡻⢷⣌⠻⣦⣙⠃⠀⠀⠀⠀⢀⣀⡤⠖⠚⠀⠀⢀⣀⣴⣶⡟⣿⣿⣶⠛⣯⠀⠸⣿⣿⣿⣿⡟⢻⣿⠁⢀⡴⠞⠁⠁⠀⠀⠀⠁
⠀⠘⢿⣦⡙⢷⣬⡙⢷⡀⢠⠴⠚⠋⠁⠀⣀⣤⣶⡿⣿⣿⣿⣿⠿⠋⠉⠁⡄⢿⠀⠀⢈⣿⡟⠈⠉⠉⠁⠀⠀⠉
⠀⠀⠀⢻⣿⣦⡙⢷⡄⢀⡀⢀⣤⣴⣾⣿⣻⣿⣽⠛⢿⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⠰⠆⢱⣶⣦⣤⡀
⠀⠀⠀⠀⣿⣿⣿⡎⢷⠘⣿⣿⣿⣿⡿⠟⠛⠁⠈⠂⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣄⣘⣿⡉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠘⣿⣿⣿⣾⣧⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠀⠂⠀⠘⠋⢽⣿⣿⡿⠟⠀⠀⠀⣩⡔⠓
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⢰⠟⠁⠀⠞⠋⠀⠀⠀⠀⠀⣿⣍⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣀⠀⠀⠀⢴⡄⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠘⠋⠀⠀⠀⠈⠁⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠁⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⢀⡴⠃⢠⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣶⣾⣧⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⡴⣸⣿⠳⡖⠀⠐⠛⠁⠀⠸⣦⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣴⠖⠻⡟⢡⡛⠙⢷⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢈⠙⠛⠿⠿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣤⠔⠀⠉⢡⡾⠁⠀⠀⠀⣸⠁⡆⠀⢁⠀⠀⠀⠀⠀⣶⢸⡿⠀⠀⠀⠘⢧⡀⠀⠀⠀⠉⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⣸⢻⡀⠀⠀⢿⣤⣴⠆⠀⠀⣿⠀⣧⣾⠛⣷⣄⣤⠆⢀⡍⢸⡇⠀⠘⠗⠰⣾⡇⠀⠀⢠⡆⠸⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆⠀⠀⠾⠈⢳⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡏⠰⡎⠉⠉⠀⢨⠁⢸⡁⠄⠀⠀⠀⠈⠁⣄⠀⢸⠇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⢢⠀⠘⡇⠀⠀⠀⠀⠀⠀⠸⠇⠀⢸⣿⠀⢸⠀⠀⢀⡌⠀⠈⣧⠀⠀⠀⠀⠀⠀⠸⣧⠈⡀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠹⣿⣧⠀⢈⠀⢄⡇⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⢿⡀⢻⡅⠀⠈⠇⠀⠀⣿⠀⠀⠀⠀⠀⢠⣤⣿⠀⣿⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⢻⡿⣀⠀⠘⣿⡏⠁⠀⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣸⣿⣿⠀⣿⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⣾⠁⠙⢆⠀⢹⠇⠀⠀⠟⠀⢀⣼⣿⣇⠀⠀⠀⠀⡟⣿⣿⠀⣿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣴⣿⣿⡇⡆⠀⣧⠀⣄⠀⠀⠀⠀⣿⠀⠀⠈⠳⡌⠀⠀⢰⠀⢀⠾⠉⢹⣿⠀⠀⠀⠀⠇⣹⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣠⣶⣿⣦⣿⣿⣿⣿⡇⢻⣄⣿⠀⣿⠀⠀⠀⢠⣿⠠⣀⠀⠀⠹⣦⣠⠌⢠⡎⠀⠀⢸⣿⡄⠀⠀⠀⠀⣿⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⡀⢻⡇⠀⠀⣾⣿⣷⣌⠷⣄⣰⣿⣿⢀⣾⣤⠖⣀⠾⢿⡇⠀⠀⠀⠀⢸⣧⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⢸⡇⠀⠀⣿⠇⠀⠀⠀⠈⠛⢷⣦⣿⣟⡡⠀⠀⠀⢿⣷⠀⠀⢀⠀⠀⢿⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⠘⡇⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⣹⣉⡿⠃⠀⠀⠀⠈⣿⡄⠀⢸⡆⠀⢸⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡾⠿⣿⣦⠃⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⢄⣩⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⡀⢸⣿⡟⠉⠠⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡉⠉⠠⠒⣫⣿⣤⠀⣸⣿⢻⣆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣾⣿⣷⡌⣿⣷⣸⣿⣟⠻⣦⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣤⡀⠀⠛⠛⢻⠀⠒⠶⠞⣁⣿⣿⠀⣿⣿⠇⠉⠻⠶⢶⠆⠀⠰⢮⣿⠿⠛⠀⠂⠀⠉⣹⣿⣿⡿⣿⣿⣿⣿⣿⠎⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡉⠉⢿⣿⣿⣿⣷⡦⠀⢸⡇⠀⠀⠘⠋⠻⣷⢸⣿⠙⠳⢀⠀⠀⠀⠀⠀⢰⡄⢻⡆⠀⠀⠀⠀⠀⣿⠿⠟⢿⡎⣿⣿⣄⠀⠰⠦⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⣿⣿⣿⣿⣷⡄⢸⡇⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡌⠻⣆⠀⠀⠀⢧⠀⠀⠀⢿⣷⣿⣿⣿⠇⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⠜⠋⣹⡿⢽⠟⠁⠙⣧⠀⠀⡇⠀⠀⠀⠀⠀⢹⣿⣣⠈⠳⣤⡀⠘⢷⣠⣤⣶⣿⣿⡿⠿⡿⠆⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⡉⢀⡄⠀⠀⠀⠈⠳⣦⣁⠀⠀⠀⠀⢠⣿⣿⣯⠳⣄⠈⠀⠖⠛⠋⠁⠘⠋⢹⡄⠀⠀⠑⠄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⢈⡇⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⣼⣿⣿⣿⣷⣜⢧⡀⠀⠀⠀⠀⠃⠀⠀⢰⠆⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⠏⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣿⣿⣿⣿⣿⣟⢦⡝⠦⠀⠀⠀⠀⠀⠀⠈⣷⣄⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣄⠐⠀⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠹⣶⣤⣀⠀⠀⠀⠀⢀⡿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣈⣹⣿⣿⡄⠹⣿⣿⠿⠂⣠⡤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⡇⠈⠻⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠟⠉⠀⣹⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣠⠆⣻⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⡇⠀⠀⢸⣿⣀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠜⠁⠀⣿⡇⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⢶⠚⠉⡅⣄⣀⡴⢃⡐⢂⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⠋⠙⠛⡄⠂⢉⣉⡡⠬⠥⠤⢥⠼⢒⠒⠉⠛⡄⢉⣀⣠⠼⡯⠄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢐⣀⠤⠴⠒⡆⠠⠬⠂⠀⡂⢉⣡⣑⣠⡬⠤⠶⠚⢛⢩⠁⠀⡈⠇⠙⣽⠁
⠀⠀⠀⠀⠀⠀⠀⣼⢁⠷⢚⡩⠂⠉⠀⠄⣁⡠⡴⠒⠋⡩⠃⡠⠁⣀⣸⠽⠄⣐⣡⣄⣀⡦⢖⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢰⡟⠼⠈⢀⡴⠀⠈⡀⠠⣁⣴⠥⢤⠖⠒⠊⢙⣫⠴⠚⠋⠉⠙⠋⠉⠓⢾⡋⠁
⠀⠀⠀⠀⠀⠀⢸⡥⠒⠇⠔⠉⣈⠉⠄⡂⠉⠀⢸⣊⣀⠤⢬⠞⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠻⣌⠒⢂⠈⢁⣴⣠⣴⠔⠚⢋⣡⡴⢶⡏⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⣰⡇⠀⣀⡤⠴⠒⠒⠒⠲⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⣬⣭⣥⠧⠶⠛⠉⠀⠀⡞⠀⠀⠚⠁⠀⠀⠀⠀⢀⣤⢞⣽⡵⠋⠁⠀⢀⣀⣀⣀⡠⠤⠂⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣤⣤⣀⣠⣤⠴⢞⣫⡴⠋⣼⠁⠀⠐⠊⠉⠁⠀⠀⠀⣀⡤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠛⠉⠁⠀⠀⠉⠻⣦⣤⣄⣤⣤⠤⠖⣛⣭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠦⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠙⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⠉⠉⠛⠲⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢠⡞⣡⠲⣦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏⠸⣇⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢻⣷⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣲⣿⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⣠⣶⠶⠿⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣼⠁
⠀⢀⡞⠉⢿⡄⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠈⠙⠲⠤⠤⠤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠈⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠛⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠙⠛⠛⠿⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠉⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠒⠦⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⢲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⡼⠷⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣠⠾⠛⠉⠉⠉⠉⠉⠛⠛⠶⣏⠁⠀⠀⠀⠀⠉⠳⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠙⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢒⠿⠛⠋⣉⣉⣭⣉⢓⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣁⣤⠶⣶⠁⠀⡴⠋⠁⠀⠈⠫⡝⠻⣷⢶⣤⣈⠑⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠊⣠⠖⠻⡜⠉⠁⠉⠟⣻⠀⠈⠀⠀⠀⠀⠁⠊⠀⠁⠉⢯⡛⠢⣌⠓⢦⡀
⠀⠀⠀⠀⢀⡴⠋⣤⠊⢀⣴⡦⠀⠀⠀⠀⠀⠀⡄⢻⠀⠐⠖⢡⠁⠀⠀⠀⠀⠀⢱⣦⡀⠑⣄⠙⢦⡀
⠀⠀⠀⣠⠎⢠⠎⢀⡕⠉⣴⡟⣀⠀⠀⠰⡤⠾⣄⡁⠀⠀⠀⠂⠩⡁⠀⠄⠀⡠⢛⣦⢙⢮⡀⠱⣄⠱⡄
⠀⠀⣰⠃⣰⡁⣠⠏⠀⠀⢙⣸⢈⣁⡀⠶⣿⣤⡷⠄⣈⡀⡀⢀⠆⡉⠀⠀⢉⡀⢿⡯⠀⠀⠙⣄⢈⣦⠙⣆
⠀⢰⠃⡴⠁⡸⠛⣄⠀⠀⡸⢷⣏⠁⠀⠀⡸⠁⠀⠀⢀⣨⡽⠗⣉⣤⠀⠀⠀⠀⣬⡇⠀⠀⣠⠘⢇⠈⢦⠙⡆
⢀⡇⢰⠁⢰⠃⠀⡮⠑⣨⢯⡲⢝⠳⣤⣀⣇⣠⡴⠞⣋⡥⠖⣋⡥⠖⡇⠀⠀⠀⡼⠙⣄⠋⠁⢰⠘⡆⠘⡄⢹
⢸⠁⡏⠉⡟⡀⠀⠃⢤⠇⠀⡝⠦⣑⢮⣙⣫⠵⠖⣋⡥⠖⠋⠁⣀⣤⢧⢀⣀⠜⠁⠀⠸⡄⠀⠂⣀⢻⠉⢱⠘
⡟⠀⡇⢸⡣⡈⠁⠪⣸⠀⠀⢸⢲⣌⠳⣿⡠⠔⠋⢁⣠⢴⠺⠑⢻⢸⢸⠟⠋⠀⠀⠀⠀⣇⠐⠉⢑⢘⡆⢸
⣇⢀⡗⢺⡀⢀⠀⡀⣿⠀⠀⠀⢎⠻⣷⣿⡿⠔⠚⡁⢼⣨⠐⠚⠋⠸⡌⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⢠⡗⢺⡄
⣿⠰⡇⠸⡗⠺⠆⠊⢹⠀⠀⠀⠸⣃⣘⠻⣷⠀⢈⡤⠖⠉⡇⢀⡀⠄⡇⠅⠀⠀⠀⠀⠀⡇⢑⠸⢗⢺⠃⢸
⢸⡀⢣⡠⣷⠀⢁⡂⠨⣇⠀⠀⠀⢧⠙⡆⣻⡄⠂⠀⠀⠠⠆⠀⠀⣀⡇⠀⠀⠀⠀⠀⣸⠁⠀⣰⠀⣾⢀⡼⢰
⠀⣧⠸⡄⠘⡆⠘⣣⠜⠘⣆⠀⠀⢘⡅⢷⠈⣧⠠⠀⠀⠈⠰⡄⠀⠀⢹⢠⠀⠀⠀⣰⠁⠢⣨⠃⢼⠃⢰⠁⡼
⠀⠘⣆⠸⡄⣹⣄⠁⠄⠠⠈⠣⡀⢯⡛⣺⡌⢻⡄⡀⠖⠈⠀⠛⠛⢈⡼⢚⡰⢆⠜⠁⠄⠰⠈⣠⡇⢠⠏⣰⠃
⠀⠀⠘⣦⠘⣄⠘⢦⡑⣈⠴⠂⠈⠲⣵⣌⠻⡻⣇⢡⢠⣴⡾⠖⣊⡥⢚⣩⠖⠉⠐⠆⣉⢁⡴⠃⣠⠇⣴⠃
⠀⠀⠀⠈⢧⡈⢦⡀⡱⢄⡀⢃⠀⠀⡠⣈⠳⣌⠻⡼⢋⣡⠴⠿⠗⠊⡥⢜⠀⠀⡀⢈⡠⢎⢀⠔⢁⡼⠁
⠀⠀⠀⠀⠀⠙⢤⡙⢢⣀⠙⠶⣞⡚⠁⢸⢀⣮⢳⠚⡉⣁⠈⡆⣤⡠⡇⠨⠓⣳⠶⠋⣀⠔⢉⡴⠋⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠑⠶⣁⠉⠚⠶⣧⣚⣉⣺⣁⣉⣗⣈⣓⡼⠶⠓⠉⣈⠶⠊⣁⡴⠋⠀⠀⠀⢀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⣉⠒⠒⠧⣤⣀⣀⣈⣁⣀⣀⠤⠼⠖⠚⣉⣡⠶⠛⠁⠀⠀⠀⢀⠀⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⣤⠤⠤⠤⠴⠖⠓⠋⠉⠀⠀⠀⠀⠀⠈⠀⠁

⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢂⠄⠀⠀⢀⠤⠒⠚⠒⠠⠅⣀⣠⣄⡀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣅⡂⠠⠂⡀
⠀⠀⢀⠠⢀⠀⠀⢀⣌⡀⠄⠉⠀⠀⠀⠈⠓⢤⣤⠤⣴⣶⡞⣽⣥⠁⠈⢶⠀⠐⠂⠀⠀⠀⠀⠀⠀⠙⠁⠀⠻⠏⠀⢀⣠⡀
⠀⠀⠥⠁⠈⡴⣦⠜⠋⠁⠠⠃⠀⠀⠀⠀⠀⠘⠇⠀⠀⠛⠁⠘⠋⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⡠⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉

⠀⠀⠀⢀⠤⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠠⡀
⠀⠀⠐⠁⠀⠀⠀⠈⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀
⠀⠀⠀⠀⠀⠁⣤⡆⢠⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣨⡅⢀⢘⡧⠠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⢩⠁
⠀⠀⠀⠀⠀⡀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⢀⠀⢰⠶⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⡨
⠀⠒⠀⠀⠀⢡⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢱⠇⠀⠉⠋⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠐⣊⠂⠀⠀⠀⠖⠀⠀⠀⣀⠀⠀⠀⠀⠒⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠄⢤⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠉⢅⣄⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⡈⠂
⠀⠀⠀⢀⢦⠀⡄⠈⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⣦⠐⢿⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢱
⠀⠀⠀⠁⠀⠀⠓⠄⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢐⠓
⠀⠄⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠤⠐⠁
⣀⣀⣀⣀⣀⣀

⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠊⠙⢿⠉⠁⠀⠐⠒⠃
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣾⣶⣶⣾⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⣛⣛⣿⣭⣭⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣽⣭⡽⢿⡾⡳⠛⢿⣻⣿⠉⣹⣞⣩⣿⣿⣿⡿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣏⣝⣇⣻⣼⣧⣿⣿⣷⣷⣾⣿⣿⣿⣭⣿⣿⣷⣾⣿⣿⡿⢘⣿⣿⣿⣷⣤⣸⡍⢻⣿⣷⡀
⠀⠀⠀⠀⣈⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣟⣛⣉⣉⣭⠿⣿⣿⣯⡇⠀⣿⣿⣿⣿⣿⣿⣿⣾⣧⣘⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠥⠤⠒⠚⠛⠉⠉⢸⠀⡏⠉⠈⠀⠀⠀⠀⠘⠉⡋⠀⠀⣿⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣻⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠠⠀⠀⠀⠀⢀⠀⠙⠀⠀⣿⢰⢸⡇⣿⣿⢻⠻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⠻⢾⣿⣿⣿⣸⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⣼⠿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠀⣼⣿⣿⣿⠙⠲⢸⣿⣿
⠀⠀⠀⠀⠀⠘⠃⠀⡇⠀⣀⠀⣀⣀⡀⠀⢈⠀⢃⣀⣠⡤⠤⠦⠤⠆⢸⡇⠀⠀⣿⣾⣾⣿⣿⣿⠀⢈⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⡀⡀⠉⢛⣉⣀⣀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠁⠀⡏⠛⠛⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣀⡃⠀⡇⠀⠀⠀⠀⠀⣈⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡈⡇⠀⡇⠀⠀⠀⠀⠀⡟⠀⢸⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡏⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣧⠀⣷⣦⡠⠀⠀⠀⠀⠀⠀⢐⠧⠀⠒⠀⠀⠀⠀⠂⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣇⠀⣧⣦⢤⠤⠤⠤⠤⠀⠀⠀⡥⠤⠤⠄⠀⠒⠶⠖⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣽⣿⣿⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣧⣏⡀⠀⠀⠀⠀⠀⠀⢀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⠀⣯⠀⠀⠀⢀⠀⠀⠀⢀⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⡆⠀⢸⢈⣿⠀⠠⠄⠈⠀⢀⣲⢸⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠀⢸⣟⡿⢶⠖⠲⠶⠶⠺⢿⣿⣿⣰⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸⡏⣷⣾⣶⡶⠶⢶⢶⣶⢸⣿⣏⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⣿⣿⠋⣰⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⢾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⡄⣀
⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠳⡀
⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠠⢤⣀⣀⡀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠑⠒⠤⠄⣀⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⡠⠤⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠙⡆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢀⠎
⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁
⠀⠀⡰⠁⠀⠀⠀⠂⠀⡰⠋⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠤⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑
⠀⢠⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⢄⠘⢄
⠀⠈⢦⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢘⠀⠀⠉⠒⠠⠔⠊
⠀⠀⠀⠙⠢⠤⠤⠋⠀⢀⠔⠒⠂⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⢄⡀⠀⠀⡄⠀⠀⠀⠀⣠⠎⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠳⠄⠤⠒⠊⢠⠔⠉⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠘⢄⡀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣴⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣆
⠀⠀⣼⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡀
⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠋⠁⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⣠⣽⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣠⣴⣦⠀⠀⠀⠀⢰⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⣾⡿⠛⢻⣿⡇⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠿⠿⠀⠀⠀⠀⣿⣿⣷⣿⣶
⠻⣿⣶⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⣀⣀⡀⠀⠀⠀⠹⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⠁⢀⣽
⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠿⠛
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠻⠛⠉⠙⢿⣷⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣦⣤⣤⣤⣤⣶⣶⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠾⠟⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⣴⠦⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⣀⣀⣴⣇⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢄⠀⠀⠐⡀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠦⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠰⠂⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⣈⠘⠁⠀⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠒⠂
⠀⠀⠈⠂⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠠⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠅⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠷⠀⠀⠀⢠⣄
⠀⠀⠀⠤⢤⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⡀⠉
⠀⠀⡀⠀⠀⠈⡁⠀⠀⠙⡀⠀⠀⠀⠀⠛⠛⢶⣦⣤⣤⣤⡶⠚⠛⠋⠀⠀⠀⠀⠀⠀⢾⣟⡶⠈⠰⣿⣟⠑
⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⡀⠀⠀⠠⡄⠈⠀⠀⠀⠔⠉⠢⠀⠀⠔⠁⠀⠀⠀⠤⠀⠐⠛⠿⢋⠔⠜⠛⠋
⠐⡆⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠈⠂⠄⠀⡀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠨⡁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠈⠇⢲⠀⠀⠐⠂⠀⠁
⠀⠀⠘⢤⠄⠠⠀⠠⠀⢂⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠘⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢼⡄⣀
⠀⠀⠀⠀⠁⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠠⠴⢤⣤⣀⡀⡀⣀⣠⡴⠶⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠶⠲
⠀⠠⡀⠈⠉⡙⠛⡉⠃⠀⡠⠁⠀⠀⠀⠀⠀⠀⢀⡄⠈⢠⠀⠀⠀⢀⡀⠀⠀⠣⠀⠈⠋⠀⠶⠀⠉⠁⠀⠈
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠠⠀⠄
⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠶⠶⠒⠒⠒⠒⠲⠦⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣓⡲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠯⣍⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣤⣤⣀⣀⠀⠀⠀⢀⡀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⣀⠀⠀⠰⠖⠒⠒⠒⠒⠚⠓⠀⠀⠀⡠⠉⠈⠉⠁⠒⠚⠏⠁⠒⠲
⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠱⢄⡈⢳⡀⠀⣄⢰⡓⠀⠀⢀⡤⠒⠛⠉⠉⠉⠉⠁⠚⣤⠴⠚⠉⠉⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠦⢿⠳⡽⡄⠀⠻⣄⣀⣉⡀⢀⣀⣀⠠⠴⣇⣂⣀⣠⠴⠾⠖⠒⠛⠋⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢋⣩⣭⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠋⠉⠁⣈⡠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠒⠛⠛⣻⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠖⠒⠋⠁⠀⠀⠉⠒⠤⠀⡀⠀⠀⠀⠀⠀⠘⢉⡵⠚⢁⣀⣠⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢉⠀⠸⠉⢙⣐⠒⠒⠒⠒⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠑⠰⣄⣸⠉⣁⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠢⣄⠀⡉⢳⡇⢈⡑⠒⠀⠄⠐⠒⡖⠂⠀⠀⣀⠀⢠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⠈⡙⠁⠘⢦⠀⢳⡦⣄⡀⠀⠐⣷⢦⠘⢻⠁⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⣄⠀⢳⠀⠀⢸⠀⠀⢳⡀⠉⠙⠒⠛⠀⠓⣏⣀⠤⠼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠁⠀⡇⠀⠀⣇⠀⠈⠀⠀⠀⢣⡀⠀⠀⠀⠀⡈⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⠀⣈⠄⠀⠀⠀⠀⠀⢳⠀⠀⣠⣾⣿⣿⣿⣿⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢜⣩⣌⡽⠍⠀⣴⠀⠀⣀⣠⣴⠃⠀⠘⢿⠿⠛⠉⠁⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠛⠚⠒⠒⠒⠒⢺⠉⡛⠉⠁⢠⡇⠀⠀⠀⠀⠑⣄⣀⡴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠤⢶⡴⣷⣦⠀⣾⠀⠀⠀⠀⠀⠀⠈⣡⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡑⠦⢤⣀⣀⣀⡭⠽⡄⠴⠒⠒⠉⣲⠄⠀⠀⠀⠀⠀⠙⢤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠞⠉⠀⠀⠀⠀⠀⠉⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠢⠐⠄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠐⠐⠀⠀⠂⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⡿⠿⢿⣿⢻⡿⢿⣿⠛⣻⣿⡟⠛⠛⠃⠀⠀⠀⠀⣤⡄⢀⣴⡀⣶⡶⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢰⣿⠃⠀⢸⣿⠸⡇⢸⣷⣄⠈⢻⣿⡂⣿⡇⠀⠀⠀⠀⢿⠿⠿⢿⠇⣿⣿⣄⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣦⣤⣾⣿⣶⣶⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣷⡆⢰⣾⣿⣿⣿⡏⠹⡟⠉⣿⣿⣿⣥⡀⣠⣿⠈⠟⢸⡟⠀⣸⡇⠀⠀⠀⢰⡿⢷⣰⡿⢻⣶⣿⠛⠘⢿⡟⢾⠟⣷⣿⣿⡇
⣿⣿⣿⣿⣟⣃⣘⣻⣿⣿⣿⣧⣤⣤⣄⣼⣿⣿⣿⣧⣼⣿⣠⣶⣸⣧⣀⣹⡇⠀⠀⠀⠸⢷⠟⠙⢷⡾⠟⠿⠦⠀⢾⠃⠹⢷⠟⠟⠻⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠻⠿⠛⠿⡿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣴⣦⣤⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠿⣿⣿⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣆⠈⠛⢋⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣤⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢷⡀
⣿⡏⠙⠛⠿⠟⠛⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⣿⡀
⣿⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢹⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣴⣆⣀⣠⡄⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠛⠦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣷⠿⠉⠉⣿⢸⠟⠀⠀⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣿⡄⠀⠀⣉⢸⡆⠀⠀⠀⢡⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣴⣏⣼⣿⠀⠀⠀⣋⡂⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢹⣿⡟⠁⠈⢻⣿⣿⠁⠀⠀⠀⣿⡅⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣼⣿⣧⡀⢀⣼⣿⣿⡀⠀⠀⠀⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠿⣿⣿⣿⣿⠃⠀⠀⢰⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⡏⠀⠀⢹⣷⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣰⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢿⣿⣷⡄⠀⠼⠋⠿⠇⠀⠀⠀⠘⠛⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⡶⠛⠉⠉⠉⠉⠉⠉⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠦⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠂⠠⢄⡀⠙⠒⠶⢤⣤⣤⡀⢀⣀⠀⠉⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⠀⠀⠄⠀⣀⠀⠈⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠐⠒⠒⠢⠬⡉⠐⠋⠉⠒⠒⠄⠀⠀⠀⠄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠽⠿⣶⣷⣖⣶⣀⣤⡤⢤⣤⣀⠀⠀⠀⠦⢀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⢀⡾⠋⠀⠈⠀⠀⠀⠀⠀⠀⠙⠳⣄⡲⠄⣀⠉⠂⠀⠀⠀⠀⠀⡀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢆⠁⠀⠀⠀⣲⣾⣿⣅⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣬⣀⣀⠀⠀⠀⣠⣀⣤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣤⠖⠒⠒⠛⠉⠉⠉⠁⠀⠀⠀⠀⠙⢷⣄⣀⣤⠄⠠⠞⠋⠉⣠⠿⠋⠉⠙⠉⣉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⢁⣠⠤⠤⠖⣫⠕⠒⠒⠀⠈⠉⠉⠀⠀⠈⠁⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡡⠚⠁⠀⠀⢀⡴⠃⠀⣀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠉⠛⡛⠓⢤⣀⣀⢀⡀⣠⠴⠺⠏⡠⠊⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣀⣀⣈⡉⠉⠉⠀⣀⠴⠊⠁⡠⠐⠐⠒⠒⠀⠠⣀⠈⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠉⠁⠀⢀⡞⠄⠀⠀⠀⠀⠀⠀⠀⠙⠢⢌⠙⠒⠶⠤⠤⠤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⢀⣀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⢸⠘⢹⠁⡇⡞⢸⢠⡇⡎⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣽⠟⠉⠉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠻⢯⣍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡾⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠹⣦⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⠀⠀⠀⠀⢀⣠⡶⣻⡟⣿⠀⣿⢿⡿⣦⣀⡀⠀⠀⠀⣀⣤⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢯⣍⠛⠛⢿⣿⡏⠁⣴⠟⠀⣿⠀⣿⠘⢷⡀⢩⣿⡟⠛⠛⣩⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠙⠷⣦⣬⣭⡴⠞⠁⠀⢀⡿⠀⢻⡀⠈⠻⢦⣭⣥⡴⠟⠉⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠹⣦⡀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠴⠶⠛⠁⣀⣀⣀⣀⣀⣈⠛⠷⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⢯⠀⠀⠀⠀⢹⠋⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⠀⠀⠀⠘⡄⠀⠀⠀⡞⠀⠀⠀⣠⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣶⣷⣴⣴⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⢿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢠⣍⠿⠿⢿⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⣠⣶⣿⣿⠟⠉⠙
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢀⣼⢟⣽⣿⠁⢀
⠀⠀⠀⢠⠀⠂⠀⣼⡧⣄⠀⠀⠐⠀⠀⠀⠀⠀⣀⡾⠃⣴⣀⡄⣠⡿⢫⣾⣿⣏⠀⢸⣇⠀⠀⠀⠀⢄⠀⠀⢀⡀⠠⠄
⠀⣄⠻⠇⠀⠀⠐⢧⣥⠀⠙⢳⡆⢀⠀⠀⢠⣼⡟⣠⡄⣿⣿⡟⢋⣴⣿⣿⣿⣿⡆⢸⣿⣷⠦⠤⠐⠛⠉⠁
⠀⣿⣧⡀⠀⠀⠀⠀⢠⣼⡷⠀⠘⢦⡑⣴⣿⣏⣾⣿⣷⡾⠿⣵⣿⣿⠿⠿⢛⠛⠉⠈
⠀⣿⣿⣷⡄⠀⠀⠀⣤⠸⠥⣄⠠⣤⣸⣮⡉⣉⡸⠋⠁⠀⠀⣨⠁⢀⠀⢰⣭⣷⣦⡀
⠀⣿⣿⣿⣿⣤⣴⣾⣿⢰⡇⠟⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡿⠁⠀⠀⠙⡆
⠀⣿⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⢺⡇⢀⠄⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⢠⡿⢸⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⢀⣠⠾⠃⢀⣿⣷⢤⣀⢀⢠⣧⡰⣤⡄⠰⢀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⣾⠁⣿⣰⢄⠀⠈⠛⠷⣝⡷⣐⠈⡀⠀⠙⠃
⠀⠀⠀⠀⠀⡆⠀⠀⢈⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠈⣼⣿⣿⡇⠀⠀⠀⠘⣱⡏⠉⢻⣄
⠀⠀⠀⠀⣠⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣨⡭⣾⠁⢀⡀⠀⡀⠉⣄⠀⢸⣿⣷⣄
⠀⠀⠀⠀⢹⣿⣷⣾⣿⠀⠐⠂⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢅⣶⣶⣿⣄⣠⡟⠀⠀⠁⣈⠀⠀⠉⠛⢿⣶⣄
⠀⠀⠀⠈⢦⣿⣿⣿⣿⢀⡶⠟⠋⠙⣧⠀⠀⠈⢦⡐⠀⡄⠀⠀⣿⣄⠀⠀⠙⣿⣦⣈⡽⣄⠀⠀⠀⣹⣷⣸⡀⠀⠀⠈⠛
⠀⠀⡖⠒⠚⠛⠛⠛⠓⠒⠒⠒⠒⠒⠛⠒⠒⠒⠚⠓⠓⠓⠒⠒⠛⠚⠓⠒⠲⠛⠓⠚⠓⠛⠒⠚⠚⠛⠛⠛⠓⠒
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢸⣷⣯⡆⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⢀⣠⡤⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⣽⡿⡆⠀⠀⣀⠀⠀⠀⠀⠀⢠⣦⣶⣾⣾⣧⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣄⠀⠀⠀⢰⡿⠛⠺⠚⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠏⠈⣿
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠚⠒⠒⠂⠚⠒⠒⠚⠃⠀⠀⠛⠒⠒⠐⠒⠒⠀⠐⠂⠘⠚⠓⠐⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣒⣈⣉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⣓⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠷⠶⢶⣤⣤⣬⣉⣉⣓⠒⠒⠢⢵⣴⣾⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⠶⠶⣶⣤⣤⣌⣉⣉⠙⠛⠛⠿⠾⣿⣿⣿⣿⣿⣿⢿⣛⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣿⣭⣭⣛⣛⡿⠿⢶⣶⣿⡿⢟⣫⣽⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⡟⠻⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⠋⢁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⡧⢤⢀⡀⣿⣿⡏⠈⠉⠛⢻⣿⣿⣿⡟⠋⠡⢸⡧⠖⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⢀⠀⠀⣿⣿⣷⠰⠠⢄⢸⣿⣿⣿⣧⠴⠊⣽⣇⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡿⣿⣶⣾⣿⣿⣀⠀⠀⢸⣿⣿⣿⡇⣀⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⣳⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣉⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢍⡛⠻⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠬⣉⠛⠿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣽⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣉⣉⡉⠀⠒⠈⠉⠉⠁⠀⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣚⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠤⠾⣖⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠒⠒⠂⠀⢴⠒⠒⠒⢜⣋⣡⠦⠤⠒⢴⠀⠀⠀⠀⠀⠉⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡩⡟⠀⠀⢀⠞⢀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄⠀⠀⠀⠈⢳⣌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⢄⣠⡊⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⣈⢆⠀⡀⠠⠼⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⡁⠀⠓⠚⠀⠀⠀⠀⠀⠀⠐⡒⠋⠀⡱⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠰⠁⣬⣑⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠔⣩⠌⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⡠⣄⡤⢀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⣶⣶⡖⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢒⢘⣉⡉⠏⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⢊⣩⠀⠈⠉⠉⠉⠉⠀⢠⠀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢈⣽⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⠉⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠺⠁⠌⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⢋⠑⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢲⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⠉⠁⠈⠉⠉⠙⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠶⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠆