Holidays Emojis & Symbols

⠀⠀⢀⡀⠤⠠⠄⠀⣀⠀⢀⠀⣆⢠⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⡠⢄⠀⢰⣶⡆⣠⣄⠀⠀⠀⠀⢠⢤⣠⡤⡴
⠀⠀⠰⣴⣴⣼⣧⢙⣾⠘⢢⣶⣟⣩⠏⠀⠀⠀⠈⠙⠫⠁⠐⢲⡀⠈⠣⣤⣭⡄⠛⠛⢀⡀⡔⠒⠋⠀⢀⠀⣇
⠀⠀⠐⠷⠶⠮⡻⢿⣿⣟⠲⢿⣿⣷⣾⠏⣰⠟⣡⣶⣶⣄⡀⡀⠉⠢⠀⠀⡟⢁⡏⠈⠉⢿⡁⠀⠀⡸⠃⠀⡈⠂
⠀⠀⠀⠀⠐⠛⠈⣛⣓⠟⣴⠀⣿⣿⡟⣰⢃⣾⡿⢋⡥⠶⠛⠪⣀⠃⡅⠀⠵⠚⢀⠂⠀⢰⠁⠜⠋⠁⢀⣸⡅
⠀⠀⠀⠀⣷⠉⣤⠊⠙⣇⠸⣇⢻⣿⣧⠿⡞⠛⢵⣫⣴⣾⣿⣿⣿⡇⠀⢸⠆⢄⡦⠀⢀⠼⠂⣠⠤⢔⣅⣴⣤⣤⣆
⠐⠿⠿⠶⠙⡃⢻⡆⢸⣿⣧⣘⠷⡽⢡⠁⠑⠄⡀⠙⣛⣩⣭⣉⡉⠳⠰⠛⠀⠸⠁⢠⠃⠀⠉⠲⠶⣿⣿⢿⡟⠓
⠀⠀⠠⠾⠿⣋⣐⢅⢨⠛⢿⣿⣷⡇⠒⠓⡀⠀⢣⠀⢱⣶⣶⣬⣍⡓⠸⣿⡷⠥⣴⣮⣤⣀⠀⠒⢤⠈⠛⠲⠛⠊⠓
⠀⠀⣤⠀⠚⢛⣩⣴⠜⠻⢦⣌⣙⠃⠱⡀⢘⢀⡇⣀⢀⠙⠻⠿⠟⠡⣾⣿⠀⣸⣿⡿⠋⠁⢀⣂⣤⡀⣀⠀⡆
⠀⠀⠀⠈⠀⠐⠈⠅⢐⡷⣦⣌⣉⣹⠤⠓⠈⠀⠀⠀⠀⠀⠈⡂⣰⠀⠘⢿⡀⢿⡿⢀⣶⣿⣿⣿⣿⡍⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣈⠑⠜⢷⣯⣥⣀⡀⠀⠉⢿⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⣖⡛⠿⡖⠀⠀⠀⠀⢀⠀⠀⠀⡛⠛⠛⠛⢋⣵⡞⣧⠉⠻⣿⣷⣄⢸⠟⠴⠟⠃
⠀⠀⠐⠀⠀⠀⠀⢀⠋⠀⠀⣸⣶⣭⣛⢧⠀⠀⠐⠶⡀⠬⠛⡀⠐⣦⣶⣾⣿⠏⢰⣿⡇⠀⢹⣿⣿⡇⢿⣦⠙⠿⣶
⠀⠀⠀⠠⠒⠂⠀⠎⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠈⠻⣿⣥⣔⣺⡿⠋⢀⣴⣿⣿⡇⠀⡸⠛⠉⠃⠈⠙⠃
⠀⡊⠈⣓⣀⠀⡀⠀⠀⠀⢰⣼⣄⣉⠛⠻⣿⡐⠀⠀⠀⠀⠘⢷⣶⣚⣻⣶⡈⠉⠉⠉⠁
⠀⠀⠀⢇⣀⡽⠀⠀⠀⠀⣽⣷⣯⣉⠙⠲⢤⣇⠈⠄⠀⠀⠀⠀⠻⣿⢟⠿⢅⡒
⠀⠀⠀⠤⠤⠆⢀⠄⢄⠀⢿⣿⣿⣿⣿⣷⣦⣉⡀⠈⢂⠀⠀⠀⠀⠙⠞⠐⠤⠉
⢀⣠⠔⠁⢀⡔⠁⢀⠼⣷⡾⠛⢷⡛⠛⠿⢿⣿⣧⠀⠀⠀⠀⢀⠀⠀⢂
⢀⡄⣀⣀⠁⣀⢤⣯⡀⢿⣠⡾⠟⠛⣟⠲⠦⣬⡙⠆⠀⠰⠀⠎⠀⠀⠰
⠘⣉⣁⣸⣿⣷⣾⡙⠛⢲⡿⡙⠲⣶⠎⣷⣶⣤⣉⠻⠀⠀⠃
⠀⠠⠬⠿⢛⠟⣫⠗⣶⣟⢀⣿⣤⠋⠀⢙⠛⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠘⢱⡿⣿⢫⢻⣏⠳⠀⢀⣼⡟⠶⣤⣉⠻⡄
⠀⠀⠀⠀⠀⠀⣋⣼⣿⡀⣿⠑⠂⠀⢉⣡⣸⣷⣶⣍⣻⠇
⠀⠀⠀⠀⠀⠘⢩⣿⠿⡟⠀⠀⠀⠰⠟⠋⠆⢿⣿⠛⠋
⠀⠀⠀⠀⠀⠈⡱⢹⠀⠁⠀⠀⠀⢀⣶⣿⠹⣶⡍⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⣿⡆⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠐⠛⠷⠶⣦⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠌⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠐⠀⠀⠀⠉⠛⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠙⠀⠀⠲⠅⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠠⣀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣉⠿⠀⡔⠂⠀⠀⣹⣦⠊⠀⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠘⠈⠀⠀⠀⠀⠉⠢⢠⡄⢠⠺⣄⡀⠐⠋⢀⡀⠀⠀⢀⣀⣠⠐⠛⠀⠀⠘⠁⠀⠰⡂⠶⠀⢀⡤⢛⡽⠂
⠀⠀⠀⠀⠀⢀⠃⠃⠀⠀⠀⠐⠀⠈⣡⡶⠚⠓⢦⠂⠈⠻⠅⠀⠀⠛⠁⠷⠊⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢋⡀⠂⠌⣞⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣰⠛⠀⢀⡀⠀⢇⠀⠀⠀⠠⠀⠈⠀⠢⠀⠀⠀⠈⠤⣁⠠⠀⠂⠀⠀⠀⡄⠁⠤⠀⢁⠴⠆⠔⠛
⠀⠀⠀⠀⠠⠘⠻⠆⠀⠠⠄⠊⣉⢉⣀⠀⠺⢏⣳⠋⠀⠀⠀⠀⠈⠐⠀⠀⢁⠀⠆⡁⠤⠀⠠⠐⠀⡔⠀⠂⠀⠀⣀⡰⠂⠀⡀
⠀⡐⠷⠒⠲⠖⠄⠀⠀⠴⢲⠴⠋⠀⣠⡆⢀⣤⡮⡡⠀⠀⠀⠀⠀⠀⠘⠰⠁⠀⠐⠚⠀⠁⠀⠀⠀⠐⠈⠈⠀⠂⠈
⠀⠀⢂⠀⢀⡀⢦⢂⠀⠂⠀⣂⡀⠀⠉⠀⠀⠁⠊⠀⠀⠀⠤⠤⠤⠖⠂⠀⠀⠀⠀⠀⠙⠂⢤⠠⡀⢀⡳⠀⠈⠠⢀⡀⠀⠀⡌
⠈⠀⠰⠠⠤⠐⡀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣶⠁⣾⣷⣿⣮⡵⠟⡆
⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢲⡂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠉⠈⣀⣤⡀⠀⠀⠀⠀⠘⢻⣷⠒⠚⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⢒⡲⠶⠶⠇⠀⠀⠀⠉⠀⠉⠑⣇⣀⣀⢠⠀⠀⠔⠈⢶⣀⡀⠒⠁⠙⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠬⢆⣀⣒⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⣛⠛⠗⡓⢠⡑⡀⠀⠈⠁⠀⣈⢁⠥⣀⢈⡁⢄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠆⠃⡀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢨⠄⢈⡐⠆⡸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠦⠐⠀⠀⠸⠇⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣴⣶⣤⣤⣈⣿⣿⣇⣠⣄⠀⣶⣶⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢠⡄⢠⣄⣹⠀⠀⣹⣿⣏⠛⢿⣿⣿⡿⣿⣿⡇⣸⣿⣟⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣷⠀⠈⠁⣤⣼⣿⡤⣔⣸⣿⣿⣿⣿⠿⣿⣶⣦⡾⠱⠟⢾⠉⢍⣀⣦⠴⠞⢓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣋⣀⠀⠀⠼⢿⣷⣔⡙⠛⣩⣿⡏⠀⠈⠻⣿⣦⣄⡀⠀⠓⢌⠛⢇⡠⢂⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣽⡿⢟⣿⢿⣦⣴⡄⠉⠛⡇⠘⢿⣿⠁⠀⠀⠀⠘⣿⢿⡟⠛⠶⠀⡄⠀⣡⣾⠯⣁⠀⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣄⠉⢠⣶⢾⠟⣿⣿⣧⡊⠀⠉⠀⠈⠛⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⣽⢷⣿⣿⣶⣍⡀⠈⢡⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢉⣿⠀⠙⢀⣿⣄⣝⣽⡏⢫⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢄⠻⠻⢿⡄⢹⣿⣿⣿⣬⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣆⡀⣬⠀⠒⣿⡟⣿⣀⣴⠏⠁⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠼⣧⣰⣾⣧⠈⣹⣿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⣠⡜⠉⠉⠻⠁⠈⣙⣿⣷⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢾⣿⣼⣿⡷⠸⠅⣀
⠀⠀⠀⠀⠀⠀⣩⠀⢠⡴⣤⣄⠀⠠⢻⣁⣀⣈⣇⡀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠹⡿⣿⠃⠐⠀⠈⣈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠫⢿⣄⣄⣽⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣼⡤⢄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡇⠈⠻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⢿⠁⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⣷⡆⠀⢰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠻⠃⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⡨⢿⠙⣿⡿⠈⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠾⠲⣆⠄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣤⣾⣤⣴⣶⣶⣿⠿⠆⠸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢿⢀⣤⡿⢶⣿⡅⠀⢠⣶⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡅⠹⠛⠷⣯⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢱⠾⡿⠁⠀⢶⣻⣄⠛⠋⠶⠄⠀⠀⠀⠀⠀⠀⠒⠃⢾⡉⠹⢿⠀⠀⠤⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠛⠃⡄⠀⣶⣏⡃⠙⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⡀⠀⠉⣷⠊⠛⠿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠇⠉⠀⠀⠀⠀⠀⠀⢲⣿⠛⢿⣿⡏⠀⣴⣿⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⢀⣾⠃⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⢀⣿⡇⣴⢏⣴⣦⡄⣴⢀⡤⣦⡶⢀⢤⣄⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⠤⠐⠒⣾⠏⢠⢏⡟⢱⣟⣼⡣⣋⣼⡿⠰⣡⡞⣿⢡⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠳⠐⢁⣤⡄⣰⠏⠀⠘⠈⠁⠈⢹⡟⠀⠉⣸⠏⠀⠁⢀⢜⡿⠁⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⢀⣰⣾⡿⠞⣱⡇⠀⠀⠀⣴⡇⣈⠀⠀⠀⢁⣾⠃⠀⠥⠋⠈⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠖⠉⣾⡟⣀⣼⣟⣴⡦⣄⣸⡟⣠⡛⢀⣤⣤⣾⠋⣤⣶⣤⡄⣤⡄⢀⣤⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⡠⠤⣾⡿⠉⢰⢟⣿⠿⢲⢻⡟⣸⡟⣰⡿⠋⣾⠃⣾⠟⣵⠟⣸⡟⢁⣾⠇⣿⠟⣡⠴⠒⠂⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⣰⡿⠁⠀⡟⠈⠧⠔⠁⠾⠈⠻⠊⠻⠔⠁⠿⠚⠗⠂⠿⠊⠻⠄⣿⠏⣸⡟⠋⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣰⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠏⡔⣽⢣⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣰⠏⠀⠛⠁⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡼⠋


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⢶⡶⠶⣶⡶⣶⣶⢶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⢀⡤⠖⠁⠀⠀⣹⡆⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣽⡗⣰⠟⠀⠀⠀⢀⣨⣭⣄⠻⢦⣄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠇⣴⡿⠁⣼⠏⠠⡄⠀⠀⢾⣏⠀⠀⣷⡄⠀⠀⠀⠀⢸⣿⠄
⠀⠀⠀⠀⠀⠀⣞⠀⡠⠋⣸⣿⠃⣼⡏⣠⠾⠃⠀⢠⣶⡙⡛⠋⣻⣇⠠⣤⡀⢴⣯⢉⣶⡄
⠀⠀⠀⠀⠀⢀⣈⡅⠀⢠⣿⡟⢰⣿⢉⣴⠶⢠⣾⢺⣿⠃⢸⡇⣿⡇⠀⣼⡇⣾⡏⢸⡿⠀⢳⡄
⠀⠀⠀⢀⣼⠋⣿⣀⡄⣾⣿⠁⣿⡇⣾⡏⠀⣾⡏⢸⣿⢀⣿⠃⣿⡇⣰⠟⠁⠿⠇⢸⡇⣠⠟⠁
⠀⠀⠀⢸⡏⠀⠈⠛⣹⣿⠇⠀⣿⣧⠹⠷⠄⠻⠃⣿⡇⠉⠁⢸⣿⠇⣠⠔⠂⠀⢀⡿⠉⠁
⠀⠀⠀⠈⠻⠄⣀⣴⠿⠃⠀⣠⡭⠁⠀⠀⣰⡿⠁⣿⡗⠀⠀⣬⡯⠀⢿⣦⣄⠠⠊
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⣼⡟⠀⠀⠀⢠⣿⠇⢤⠉⠀⣀⢠⣿⠇⣀⣀⣤⡄⣤⡄⣴⣦⣾⠟
⠀⠀⠀⠀⠀⠀⢠⣿⡇⢰⣿⠁⣰⠖⡀⢸⣿⢀⣾⡆⣾⠋⢸⣿⢰⡿⢸⣿⠁⣿⠃⣿⡏⢿⡆
⠀⠀⠀⠀⢰⡎⢠⣿⡇⣼⡿⢸⡟⠀⠀⣾⡏⢸⣿⠸⣿⠀⢸⣿⢸⡇⢸⣟⢸⣿⢀⣿⡇⠀⢻⡄
⠀⠀⠀⠀⢀⣩⣽⣿⠀⣿⡇⠸⣧⣀⠀⢹⣷⠘⠿⠄⠻⠷⢺⣿⡈⠛⠈⠉⢀⣉⢹⡿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠠⠞⠉⢧⠸⣿⠀⠈⣵⠂⠀⠀⢀⡴⠀⠀⠀⠘⢛⡥⠀⠀⠀⠘⢿⣾⣇⣀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠳⠸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⡸⣦⡀⠀⠀⠀⠈⠛⠷⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠆⠀⠀⠀⠀⠀⠀⠂⠄⠀⡀⠀⠀⠀⢿⣦⣤⡴⢿⠃⠀⠀⢀⠀⢄⠀⠀⠲⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⡀⠀⠀⠘⣷⣤⣤⡴⡿⠀⠀⠀⢀⠀⣄
⠀⢰⡟⠋⠁⠰⠀⠀⣀⣥⣝⠂⡤⠀⠈⠙⠙⠛⠁⠀⠀⢰⡀⢠⣦⠟⢠⠀⠀⢴⡟⠉⠈⠢⠀⠀⣀⣬⣛⢀⡆⡀⠈⠉⠙⠋⠀⠀⠀⣴⠀⣰⡴⠛⡀
⠀⠘⡃⠀⠀⠀⠃⢠⠞⢡⠈⠏⡀⠀⠀⠀⠐⠂⣠⡄⠠⢮⣭⢿⠿⣄⠁⠀⠀⠸⠀⠀⠀⠐⠀⡠⠏⣄⠉⢋⠀⠀⠀⠀⠘⢀⣤⡀⠠⣯⡭⣿⢯⡈⠃
⠀⠀⡈⠐⢦⣁⠀⠃⡄⠀⠀⠀⠀⠆⠀⡄⠀⠊⢉⡡⠐⠛⠣⠿⠰⠋⠀⠀⠀⠀⡁⠐⢦⡇⠀⠃⡀⠀⠁⠀⠠⠀⠀⠄⠐⠉⣉⡅⠒⠛⠲⠟⠸⠉
⠀⠈⠛⠀⠀⠁⢀⡀⠀⠂⡀⠀⠀⠼⠃⠀⠀⡴⠛⠁⣰⣾⠿⠲⠀⣀⠀⣤⠀⠘⠋⠀⠀⠀⣀⡄⠀⠂⠀⠀⠀⠜⠁⠀⠀⠜⠛⠀⣴⡾⠿⠦⠀⡀⢀
⡶⠒⠀⠀⠀⠀⠺⠣⠀⠀⠀⠂⠁⢀⠀⠀⣀⢠⠀⠀⠹⡛⠛⠛⢃⣼⣿⣿⠖⠂⠀⠀⠀⠀⠻⠃⠀⠀⠐⠀⠀⣀⠀⠠⡀⠀⠀⠀⠿⡛⠛⠛⢀⣽⣿
⠛⠀⠀⠀⢀⠀⠀⢀⡀⠀⣀⠀⠀⠙⠁⠠⠈⡐⢄⠀⠀⠻⠃⠀⡀⡀⠿⠉⠓⠀⠀⠀⢀⠀⠀⢀⠀⢀⡀⠀⠀⠛⠀⠠⠡⡂⣌⠀⠀⠿⠀⢀⢀⡀⠟
⠀⠰⠄⢈⡘⠀⠤⠊⠀⠈⠚⠃⠀⠀⠀⠀⠀⠃⠀⠀⣀⣀⠀⠠⢿⣿⠂⠀⠀⠠⠤⣀⢈⡈⠄⠂⠀⠈⠻⠂⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠸⣿⣷
⠠⠄⠀⡂⠄⣈⠒⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⣦⣤⣤⡁⠀⠀⠈⠀⠀⠀⠠⠄⠐⠠⠈⡏⠒⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⣤⣤⣬
⠀⠀⠐⠁⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⡴⠁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⡞⠀⢢⡄
⣱⣄⡠⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⢀⣠⣥⡄⠸⣿⣷⣤⡄⠁⠀⠀⠀⠀⢊⣴⣀⡄⠀⡀⠀⠀⠀⣴⡀⠀⠀⠀⢀⣠⣡⡄⢸⣾⣶⣤
⢀⠀⠀⠀⢻⣦⠀⠀⠘⣿⣴⡾⠿⠟⠋⠀⠀⠀⠈⠉⠁⠀⣠⣶⣶⣦⡀⠀⢀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣶⡾⠿⠟⠁⠀⠀⠀⠉⠉⠁⠀⣴⣶⣶⣦
⠸⣄⢠⢀⣼⡟⠀⠀⠀⠿⠋⠀⣀⠀⠀⢀⣀⣴⣾⠃⠀⣀⠹⠟⠛⣽⡗⠀⠸⡀⢠⣀⣿⠏⠀⠀⠸⠟⠁⠀⣀⠀⠀⣀⣀⣴⡿⠀⢀⡈⠹⠛⠩⣿⡇
⠀⠈⠛⠛⠁⠀⠠⠀⠠⠀⠀⠀⠛⠀⡞⠉⠀⠀⠙⠄⠀⠁⠀⠀⠀⠚⠁⠀⠀⠉⠛⠋⠁⠀⠀⠘⠀⠀⠀⠈⠋⢀⡎⠉⠀⠈⠳⠀⠈⠃⠀⠀⠐⠋
⠆⠀⢀⢀⠀⠀⠀⠊⠀⡀⡀⠀⠀⠀⢿⣦⣤⡴⢿⠃⠀⠀⢀⠀⢤⢀⠀⠻⠂⠀⠀⣀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠘⣿⣤⣤⡴⡿⠀⠀⠀⣀⠀⢄⡀
⠀⢰⡞⠉⠉⠑⠀⠀⣀⡥⣍⢀⡔⢀⠀⠉⠉⠉⠀⠀⠀⢰⣀⣠⣦⠛⣡⠀⠀⢰⡞⠉⠀⠲⠀⠀⣠⡤⣏⢠⡆⡀⠈⠉⠉⠉⠀⠀⠀⣦⣀⣰⣶⠋⡀
⠀⠘⡁⠀⠀⠀⠁⡠⠚⠡⠀⢋⡀⠀⠀⠀⠘⢃⣠⡄⠠⢮⡤⣿⠻⣄⠁⠀⠀⢘⠀⠀⠀⡀⠀⡄⠏⠤⠈⢃⠀⠀⠂⠀⠘⢀⣤⡀⠰⣧⡤⣿⢣⣈⠁
⠀⠀⣀⠀⢦⡥⠀⠃⡄⠀⠀⠄⠀⠆⠀⠀⠐⠉⣁⡥⠐⠋⠒⠟⠰⠋⠀⠀⠀⢀⡁⠐⢦⡅⠀⠃⡀⠀⠁⠀⠐⢀⠀⠄⠐⠉⣈⠄⠐⠛⠒⠟⠐⠁
⠀⠈⠛⠀⠀⠀⢀⡄⠀⠂⡀⠀⠀⠼⠃⠀⠀⠼⠋⠁⣰⣿⠟⠓⠀⣀⡀⣶⠀⠘⠋⠀⠀⠀⣀⡄⠀⠂⠀⠀⠀⠞⠁⠀⠀⠎⠉⠀⣴⡿⠛⢂⠀⣄⢀
⡗⠋⠀⠀⠀⠀⠹⠓⠀⠀⠀⠃⠁⣀⠀⠀⣄⠠⠀⠀⠹⣏⠙⠙⢁⣼⣿⣿⡓⠃⠀⠀⠀⠀⠛⠃⠀⠀⠈⠂⠀⣀⠀⠠⡀⠀⠀⠀⠻⡋⠛⠙⢠⣽⣿
⠙⠂⠀⠀⢀⠀⠀⠀⡀⠀⣀⠀⠀⠉⠁⠠⠈⡐⢌⠀⠀⠻⠃⠀⡀⡀⠿⠉⠓⠀⠀⠀⢀⢀⠀⢀⠀⢀⠀⠀⠀⠉⠀⠠⠀⡂⠌⠀⠀⠛⠁⢀⢀⡄⠟
⠀⠐⠠⢈⡐⡀⠤⠁⠀⠈⠚⠃⠀⠀⢀⠀⠀⠁⠀⠀⣄⡀⠀⠀⢿⠿⠁⠀⠀⠐⠠⣠⣐⡀⠄⠀⠀⠈⠚⠂⠀⠀⡀⠀⠀⠀⠀⠀⣄⡀⠀⠰⢿⢟
⠀⠄⠀⡐⠆⠊⠑⠒⠠⠀⠀⠀⠀⠀⠘⠀⠀⢰⢦⣴⡤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡰⠀⡏⠓⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⢰⢦⣴⡤⡀
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠆⠀⡴⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⡖⠀⢠⡄
⡵⣄⡤⠀⣀⠀⠀⠀⣰⡆⠀⠀⠀⣀⣠⣤⡄⠸⣿⣿⣤⠄⠀⠀⠀⠀⠀⢪⣵⣤⠄⠀⡀⠀⠀⠀⣼⡀⠀⠀⠀⣀⣤⣤⠄⠸⣿⣷⣤
⢠⠀⠀⠀⢻⣧⠀⠀⠘⣿⣶⡾⠟⠛⠁⠀⠀⠀⠀⠉⠁⠀⣴⣾⣿⣶⡄⠀⢀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣶⠿⠟⠛⠁⠀⠀⠀⠈⠉⠀⢀⣴⣾⣷⣦⡀
⠘⣆⢰⢀⣼⠟⠀⠀⠀⠟⠉⠀⣀⠀⠀⢀⡠⢴⣿⠃⠀⣀⠙⠛⠁⢿⡇⠀⠸⡀⡠⣀⣿⠏⠀⠀⠘⠟⠁⠀⣀⠀⠀⣀⠤⣴⣿⠀⢀⡌⠛⠋⠙⣿⠇
⠀⠈⠙⠛⠁⠀⠀⠀⠠⠀⠀⠀⠉⠀⠞⠉⠀⠀⠙⠂⠀⠉⠀⠀⠀⠋⠀⠀⠀⠈⠙⠋⠀⠀⠀⠐⠀⠀⠀⠈⠉⠠⠎⠁⠀⠀⠱⠀⠈⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠁⠁⠀⠈⠈⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢀⡤⠞⡖⠒⠒⣁⡤⠴⠒⠒⠒⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⣸⠁⠀⠀⡏⠀⢀⠃⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠖⠁⢠⡧⠈⢑⡄⠈⠉⠀⠀⠀⢄⠈⠱⠀⠀⡔⠈⠳⡄⢀⡼
⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⡿⠀⠀⣼⣀⡴⠋⠀⣄⠀⠀⣧⢀⡀⢤⠀⣤⠀⠈⠂⠤⡿⠋
⠀⠀⠀⠀⠀⢠⠎⢀⠤⢤⡀⡇⢀⣴⡟⢉⠄⣴⠀⣿⢈⡇⣿⢀⡇⢾⣠⡏⢠⠎⠉⡼⠉⢦⠀⣀⡤⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠘⡀⠸⠀⠠⢃⡿⠋⢰⡇⠸⡄⠿⠄⡏⠚⠃⣿⠉⠁⠀⢸⣇⡸⢶⣊⠜⣀⣼⣴⣇⠀⡴⠲⡄⠀⡇
⠀⠀⠀⠀⠀⠀⣈⠀⠀⢠⢿⡇⠀⠘⡇⠀⠰⣄⠀⡇⠀⠀⠿⣠⣔⡈⣹⠀⠀⠀⢀⡞⡱⠃⢠⣈⡇⢇⡈⠀⡠⠃
⠀⠀⠀⠀⣴⠋⠁⢉⡆⠋⣼⠁⠀⠀⠳⣀⡠⠋⠀⡡⠔⠈⠸⣇⢀⣠⠋⠙⢦⡀⢸⠋⠀⠀⠀⣀⠤⠤⡀⠉
⠀⠀⠀⠀⢧⡀⠀⠉⢀⡴⠃⠀⡴⢳⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠉⠁⣠⠊⠀⢷⠘⣄⠀⡠⠊⡄⠀⠀⡨⢷⠤⣄
⠀⠀⠀⠀⣀⠉⣛⡋⠉⠀⠀⣸⠵⠋⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠟⠀⠈⢳⠗⠚⠁⠀⠀⠓⣋⡀⠈⣷
⠀⠀⠀⢎⠀⠀⠀⢙⣦⠒⠉⣿⠀⠀⢀⡟⢰⡔⡄⢀⠞⠁⠀⢱⡄⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠌⠁⠿⢀⡟
⠀⠀⠀⠀⠁⢀⠔⠁⡈⡇⠀⣿⠀⠀⣼⠁⠀⡰⠃⣾⠀⠴⣠⠞⠀⡇⠀⠀⠀⢀⡀⣄⢠⠳⠶⠀⠀⠀⠈⠓⠚⠉
⠀⠀⠀⠀⢠⡏⠀⠿⠭⠓⠀⣿⠀⢠⣇⣤⠞⠁⢠⡧⠖⡋⠁⡠⠠⡇⣴⠙⡇⢸⡇⣿⠠⢭⠆⣠⠔⠂⠀⠒⣄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⣠⠀⣿⡤⢾⡏⠀⡴⠐⣤⡇⠀⡇⠀⣇⡠⢧⠙⠒⠛⠀⠉⣿⠀⢀⠞⠁⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠛⠒⢚⠵⠋⣿⠀⢸⡇⠀⠣⠴⠃⠓⣂⣭⠥⠶⠶⠶⠶⠖⠦⠤⢴⠷⣴⠯⠤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⣿⠀⢸⡇⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣠⠏⠗⠀⣷⠀⠀⠀⠀⠙⠦⢤⣀⣀⣤⠤⢔⣚⡥⢤⡾⠥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢤⠀⡠⠞⠋⢀⡴⠋⡴⠂⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⡸⠁⠧⠴⠚⠁⠀⠀⠣⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣷⣠⠶⣆⠀⢀⡤⡄⠀⠀⣠⠀⠀⡀⠀⢀⡄⣠⠤⡄⢀⡶⠀⠀⣀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠘⠃⢸⡇⠀⣏⢀⣽⠀⠀⣿⢠⠋⢹⡦⢼⡗⠁⣠⡿⢹⡇⠀⣰⡏⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠊⠉⠁⢿⣀⠐⣿⠏⣐⣻⠃⢸⠁⠸⡵⠃⠀⠑⣈⣸⣇⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢙⡆⠀⠀⠀⠀⠀⣠⡄⠀⠀⣿⠀⠉⠁⠀⠸⠀⠀⠀⡴⠚⠉⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣟⡠⠔⠋⠀⠀⠀⠀⠀⣼⢁⠇⠀⠀⠉⠀⢀⡴⠀⠀⠀⠀⢸⡅⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⣠⢼⡇⠀⠀⠀⣴⠛⠳⡄⣸⠗⠁⢀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⡤⢤⡀⠀⣤
⠀⠀⠀⠀⠀⢰⡇⠸⣇⠞⣷⠀⢸⡗⠒⡏⣿⠀⠀⣌⠀⢠⠞⢻⡏⠀⣰⠋⢹⠄⢀⡾⠁⠀⣤⢸⣇⠘⣁⡤⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠟⠀⡿⠀⣼⣄⡰⠁⢿⣀⢴⡇⠀⣿⣤⢾⠀⠀⣿⠄⣿⠀⡸⣇⣀⣼⢃⠔⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠘⠦⠔⠁⠀⠈⠉⠀⢀⡼⠁⢿⣄⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣼⣕⠒⠉⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⣀⣀⣠⠤⠴⠒⠉⡜⢉⡉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠼⠁




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

⠀⠀⠀⣠⡄⠀⠀⣀⡀⠀⠀⣀⣠⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠘⡻⡧⠤⠞⠟⠋⠀⡌⠈⣿⡿⣦⢬⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣶⣄⣀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠄⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠂⡈⠨⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡉⡉⣱⠀⠉⠉⠁⡑⠦⠀⡀⠄⠁
⠀⠀⠀⠀⡠⠀⠠⠄⠀⠀⠀⠄⠁⠀⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢜⡾⠀⠀⠀⠀⠎⠀⠀⠑
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠁⠄⣸⠀⠀⠈⠑⠢⢄⣆⠀⠀⢀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠐⣆⠀⠀⡰⠃⠀⠀⠀⠀⡇⠀⢠⣇⠀⡆⠀⠂⢀⠀⡏⢉⢉⣀⠀⣀⣀⠀⡀⠈⠁⠀⠀⠀⠲⢴⣤⣿⣶⣤⠶
⠀⣀⠎⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠃⠀⠀⡏⠆⠉⡆⠇⢣⠐⠇⠸⠸⠹⠰⠇⠃⠈⣤⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛
⠀⠀⠀⠀⠊⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⢈⠒⠦⣄⣐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣤⡦⠄
⠀⠀⠔⠁⠀⡠⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠄⢼⢀⢀⠄⡏⢩⠍⡇⠀⡀⡀⠀⠀⡔⠀⠀⠀⠀⠀⠶⠀⠀⡮⠏⣑⠚⣦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠸⠘⠀⠇⠃⠃⠀⠀⣕⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠂⠶⢠⡏
⠀⢀⠀⠐⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠎
⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠉⠀⠶⠀⠀⠀⠘⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢰
⠀⠀⢱⠀⠀⠴⠀⠀⠀⠀⠭⠄⠀⠀⠀⠀⠀⠀⢠⠀⣄⠀⠀⠀⠀⠀⠀⣢⣤⠖⠛⠃⠰⠀⡠⠔⠐⠂⠉⠀⠀⠀⡄
⠀⠂⠈⢸⠀⠂⠀⠀⠀⣾⠭⢭⣷⣶⠀⠀⠠⣻⢿⣿⡗⢶⣄⠤⠀⠚⡋⠉⠀⠂⠀⠀⡐⠀⠣⠤⠤⠀⣀⣀⣀⣠⠃
⠀⠀⠀⠀⠱⡄⠀⠀⠀⠦⠀⠀⠀⠻⠀⠀⠀⠀⠈⠰⠉⠀⠀⠀⠀⠐⠒⠂⣤⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⢤⡀⠀⢀⠔
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⠠⠀⠀⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠀⠀⠀⠀⠀⠀⢄⠠⡜⢣⡜⣤⠀⢠⡄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠐⠆⠰⠀⠀⠀⠀⠀⠀⠰⠄⠄⣤⠢⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣄⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⣀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠁⠒⠀⡠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠛⡄
⠀⠀⠀⠀⢀⠔⣁⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢠⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠢
⠀⠀⠀⠠⡁⠐⠉⠀⡀⠀⠀⠀⠈⢀⠄⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⢀⡀⢤
⠀⠀⠀⢀⠐⢀⣤⠐⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠠⡃⠀⠂⠀⠁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢈⠶⠀⣄⠈⠫⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⢀⠠⠈
⠀⠀⠀⠁⠀⠈⡅⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠣⣸⣎⠐
⠀⠀⠑⠰⠀⢀⣀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠊⢀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⠀⠀⠆⠀⠀⠀⠀⢐⣀⣠⡊⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠙⠉⠀⠁⠘
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠄⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣶⣿⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠘⠠⠄⢀⣀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⠁⠠⣀⠁⠀⠀⣀⣦⡀⠀⠀⠀⠀⠘⠤⠃⠀⡄⢀
⠀⠀⠀⠈⡄⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢀⠆⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠔⠁⡃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠻⠩⠦⢀⣀
⠀⠀⠀⠀⠘⠉⠉⠁⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⠗⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⣀⣀⠃
⠀⠀⠀⠀⠀⠢⣤⠀⠀⢀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠶⠖⠲⢦⣶⠋⢧⡀⣀⣤⡀
⠀⠀⠀⠀⠀⣼⠋⠉⢹⣧⠀⠀⠻⢤⠀⣴⠒⠒⢦⣰⡏⠉⣩⡉⠻⡇⠀⠘⠃⠀⡿⢦⠀⠉⢁⣠⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠛⠀⠀⠀⠸⡆⡇⠀⡄⠈⢿⡇⠀⠈⠀⣠⢿⠀⠀⣶⠚⠁⣼⠀⡾⠉
⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣠⠀⠀⠘⣷⠇⢀⡤⡄⠘⣇⣀⣸⣏⡁⠘⠶⢖⣋⣀⡀⢙⡶⣇⠀⠀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⣟⣇⠀⣀⣸⠓⠚⢁⣹⣾⠭⠿⡟⠉⢉⠙⢦⣾⠁⠁⠙⣿⣄⠈⠳⠚⠉⣹⠏⠀⠀⣉⡇⠀⠀⠀⢀⡶⠛⠳⣆
⠀⠀⠀⠀⢀⣀⡀⠳⣤⠤⣏⣈⠉⡟⠛⢳⡄⠸⣥⡀⠀⡴⣇⠀⢸⣷⠈⡇⠀⠒⠀⠹⡜⣧⠀⣴⠚⣽⠗⠦⠄⠉⢳⠀⣀⣀⣸⠁⠀⠀⢻
⣠⡤⠤⣴⡋⠉⢻⣄⣰⠋⠉⡉⠳⣷⠀⠀⣇⣀⣨⡇⠀⣧⣿⠀⠈⢁⣼⣇⣀⡟⣧⣀⣿⢿⣠⡏⠀⠹⣄⣀⣀⣠⠞⣸⠋⠉⠻⡆⠀⠀⣸⠟⠙⢳⡀
⢿⠀⠀⠸⠗⠀⠀⠘⣏⠀⠐⣿⡆⢸⡀⠀⠉⠈⣧⣤⡤⠼⠛⠛⠋⠉⣠⣭⡉⠀⠈⠉⣠⣤⡀⠀⠀⠀⠀⠉⣉⣁⣀⣹⣄⣀⡀⠡⠠⠤⠥⣀⣠⣾⣥⣤⣤
⠘⣧⠀⠀⢀⡀⠀⠀⢿⣆⡀⠈⢀⡾⠳⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢦⢤⡞⠁⠀⢻⠀⠀⠀⠀⣿⠉⠉⠉⠁⠀⡀⡃⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸
⠀⠸⡆⠀⠸⣿⣀⣀⣨⡇⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠾⠲⠶⠶⠃⠂⠳⠖⠒⠺⠷⠶⣶⠀⣿⡀⠂⠀⡠⠈⠀⡃⠀⠀⠀⠀⠋⠀⠀⢀⠔⢸
⠀⠀⠻⣤⡤⠏⠉⠉⠁⡴⢶⣴⠛⣇⡴⢶⡄⠀⠀⠀⠀⢸⡇⢀⠀⠄⠄⠀⠠⠀⡀⠀⠄⠀⠠⠴⠂⢻⡄⢻⠁⠀⠌⠀⠀⠈⠐⠀⠀⠀⠀⡀⠀⠐⠁⠀⣸
⠀⠀⠀⠀⠀⠀⢸⠛⠻⣇⠈⡟⢠⡿⠁⣼⣥⡀⠀⠀⠀⢸⣗⠒⠒⠒⠒⠒⡒⠀⣇⠀⢋⡉⠉⠉⠉⢽⠆⢸⡆⠁⠀⠐⠁⠀⢠⠀⠀⠀⠀⠂⠀⠀⡠⠊⢸
⠀⠀⠀⠀⠀⠀⣾⢧⡀⠙⣄⡏⢸⣃⣞⣡⣾⣥⣤⡤⢤⡄⣿⠀⠀⠀⠀⠀⡳⠀⠀⢠⣸⠦⠀⠀⠀⢸⠀⢸⡇⡠⠀⠀⠀⠂⠰⠄⠀⠀⠀⠀⡠⠊⠀⠀⢸
⠀⠀⠀⢠⣤⡤⠼⠷⠾⠓⠛⠉⠉⠈⠉⠉⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⠀⢀⠀⠂⠀⠀⠐⠊⠀⢀⠄⠀⢸
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣧⠀⠀⢀⠄⠀⠀⠀⠀⠀⠨⢇⠔⠁⠀⢀⢼
⠀⠀⠀⠈⣗⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⣿⠀⠔⠁⠀⠀⠀⢒⠀⠀⠐⠁⠀⢀⠄⠀⢸
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠐⠀⠀⡠⢺
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠠⠊⠀⢸
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣖⠒⠁⠑⢀⡰⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡠⠤⣡⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⠀⠀⠀⠀⠀⠈⣧⠀⠆⠠⠠⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣡⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣦⠀⠀⠀⢀⣄⣀⣄⣀⣀⣠⠞⠁⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⡀⣤⠀⣷⣼⡟⣸⡇⣸⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⣸⢃⠟⣀⡀⠀⣸⣷⣿⢸⡿⠙⢷⠟⠛⢿⠇⠀⠀⢀⡴⠁⢀⡰⠂⠤⠤⠴⠒⠋⠁⠒⠁
⠀⠀⠀⢀⣤⠶⠟⠋⡇⠀⣿⠋⢸⡟⣿⠆⣿⠏⠧⢾⡇⠀⢠⠀⢀⡿⠀⠀⠖⣺⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂
⠀⢠⠶⠋⠀⠀⠀⢸⠔⠈⣿⠀⣿⣇⣿⠼⡿⠀⠀⠸⠀⠀⠀⠉⠋⠁⠀⠀⠈⠁
⡰⠃⠀⠀⠀⠀⢰⡿⠀⠀⢻⣴⠋⠛⠁⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀⣶⣄⠀⠀⠀⠀⠀⣤⣀⠀⠀⢰⡆⣼⣿⡄⢀⣴⣶⣶
⢇⡀⠀⠀⠀⣄⣼⠃⢰⣷⠀⠀⣰⡆⢠⣶⣦⡀⠀⢸⡿⠀⠀⠈⢙⡿⠛⢸⣿⠛⢦⠀⠀⠀⣿⣿⠀⠀⢸⢀⣿⣿⠀⣸⣿⡟⢹
⠀⠀⠀⠀⠀⠛⠁⠀⢸⣿⣀⣀⣿⡇⣿⡟⠈⣿⡀⢸⡇⠀⠀⠀⢸⣿⠀⢸⡇⠀⠈⣧⠀⠀⣿⣿⡄⠀⠸⠾⣿⣿⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⣿⠁⣿⡇⢀⣿⡇⢸⣧⠀⠀⠀⢸⣿⠀⢸⣇⠀⢀⣿⠀⣰⣿⣿⣿⠛⠂⠀⣿⡇⣀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⡄⢻⣷⣾⣿⡇⢾⣿⣶⣶⡄⣾⣿⡀⠸⣿⣤⡾⠃⠀⣸⡟⠀⢿⡀⠀⢰⣿⡇⠻⣧⣸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠻⠇⠀⠙⠻⠟⠀⠈⠙⠁⠀⠀⠈⠛⠃⠀⠈⠁⠀⠀⠸⣿⣇⠀⠈⠳⠀⠈⠛⠇⠀⠈⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢢⣦⡄⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠊⠡⠜⠀⠀⠀⠀⢀⠀⠄⠥⡂⠐⠀⠀⠪⡄⠃⠰⢤⡄⢙⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⠉⣹⠀⠀⠈⠢⠄⠠⠌⠀⠀⠀⠀⠠⢀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠙⠀⠀⢹⡄⠀⣇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⡄⣀⠀⠀⢀⣀⠀⠀⢳⠀⢹⠀⠘⠀⠀⠀⠀⠀⣰⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣸⣿⠀⣀⣤⣤⣜⠀⣠⣤⣥⣤⡀⢠⣥⣤⣤⡀⢠⣄⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⢻⣿⠐⣹⣥⠾⣿⠀⣿⡏⠀⢻⡇⢸⣿⠁⢸⣿⠈⣿⣄⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡘⠿⠀⠀⠸⠿⠀⠻⠷⠾⠿⠆⣿⡿⠶⠿⠃⢸⣿⠶⠾⠏⠈⠘⣿⡏⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠘⠟⠠⠤⠒⠰⠿⠛⠀⠀⠤⠴⠆⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣨⣉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣱⣿⠏⠀⣼⣧⢸⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⢱⣿⠏⢀⣐⠸⠷⠸⠟⠿⠀⠀⠀⠀⠂⠀⠀⠀⢠⣐⠢⠤⣄⣈⠉⠉⠛⠒
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⢠⣿⡟⣀⢸⣿⠀⠀⢀⠀⣶⡆⢰⡆⠀⠀⣶⡄⣴⡆⠈⠱⣶⡀⢉⣶⠆
⠀⠀⠀⠀⠰⠿⠀⠀⠀⢠⣿⣿⣬⣥⣼⣿⣤⠰⠃⠀⣿⡇⢸⡇⢰⠀⣿⡇⣿⡇⡀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡭⠉⢻⣿⠋⠸⣷⣤⣿⠃⠸⣿⣤⣴⡿⠃⣿⣧⣭⣤⡄⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⡖⠈⠉⠁⠀⠀⢨⠉⢭⠀⢢⠈⠉⠉⠉⠀⠈⠁⠙⠂⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⣿⠀⢸⠄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠦⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠑⠄⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡂⠀⠡⠂⠀⠄⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⠄⠞⠂⡑⢄⠀⠀⠀⠀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠈⡀⢀⠀⠀⠀⠀⠘⢄⠁⠀⠀⠀⠈⠢⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⠄⠈⠕⠀⠀⠀⠀⠀⣬⡤⠴⠓⠀⡐⠀⠀⠠⠑⠀⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡑⢄⠂⠀⠀⢈⠢⡀⠢⡑⣌⠢⣀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣦⠀⠊⠁⢈⣣⡚⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠁⠁⢀⠀⠋⠜⠂⠈⠑⠶⠈⢢⡄⠀⡀⠤⣖⡱⠐⠀⠀⢀⠀⠰⡣⠀⠀⠨⠓⠁⠀⢀⢘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⢌⠢⢃⠂⢄⠈⠀⠀⠒⠲⠦⣤⣤⠖⠋⠁⠰⠂⠁⠘⠛⠛⠃⠁⠀⠀⠁⠘⠁⡤⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢡⣌⠓⡀⠄⠐⣊⣤⠗⠋⡙⠦⢰⢤⠂⡿⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡆⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠜⢋⡡⠶⡛⠁⠀⠀⣚⣅⢀⡉⡆⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⢻⠀⢸⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠡⠂⠀⠀⠀⠢⡙⢯⠀⠈⠁⠀⠀⠀⢠⣘⣇⠀⠀⣠⣤⡀⠀⠀⠀⠌⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠄⠀⠀⠀⠰⡏⠀⠀⣹⣿⠁⠀⢙⣷⣤⣤⣤⣤⡞⢠⠍⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠁⠈⠑⠒⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠅⠀⠅⠨⠀⠅⠀⠄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡂⢀⡔⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⠆⠴⠀⢶⢰⢆⠴⢤⠶⢰⠆⠰⠄⠖⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠈⠉⠁⠉⠈⠉⠉⠈⠁⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣆⣀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑⠒⠀⠠⠤⠤⠀⠤⠤⠤⠒⠚⠂⠉⠁⠀⠀⢀⠠⠀⡄⠢⠀⢰⡄⢰⡀⠀⠐⠀⠀⡄⡀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢨⠀⠀⡗⠎⠀⠈⠇⢸⠠⡄⠀⠀⠀⡆⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⡰⠀⠀⠆⠰⢸⡀⠀⠀⠀⡇⠀⠀⠚⡆⠀⠀⠀⠀⠀⠇⠘⠀⠃⠐⠘⠀⠃⠐⠄⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠋⠀⠄⢰⡆⢨⠀⠀⠀⠀⡃⠀⠀⠀⠐⠀⠀⢀⣀⠠⠄⠒⠒⠒⢀⠊⠀⠐⠒⠢⠤⣀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⢀⡀⠀⠀⠈⠃⠀⠀⢀⣉⠀⠤⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠉⠢⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⠶⠖⠶⠲⠶⠲⠶⠒⠖⠲⠒⠲⠒⠶⠒⠶⠒⠶⠒⠶⠲⠶⠲⠖⠒⠖⠲⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠂⠀⠀⠀⠂⠐⠀⠐⠀⠐⠀⠂⠀⠂⠀⠂⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⡀⠈⠀⠘⠀⠈⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠈⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠂⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠸⠀⠀⠐⠒⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⣿⠿⠿⠿⡿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⡸⢣⢇⢔⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢱⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⠀⠈⠀⢀⠴⠙⢻⣶⠖⠀⠀⠀⠀⠐⠀⢀⠀⠀⢉⢶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠀⠀⠀⠀⢠⢡⣛⠻⠿⣧⠀⠀⠀⠀⠸⠋⠘⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢀⠐⠿⣳⡆⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣢⠇⢰⡄⠀⠀⢩⠶⣝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠌⠀⠀⠀⣠⠀⡌⠣⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡴⣰⢰⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⡀⠀⠀⠀⠈⠀⠠⢦⣄⠉⠀⠂⠀⠁⣊⢞⢔⣭⣠⠄
⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠒⠲⢿⡢⠀⠀⠀⠜⠁⠄⡽⠷⠭⠤⠀⠄
⠀⠀⠰⠄⠀⠈⡹⢦⠀⠀⠀⢀⠀⠄⠀⠋⠸⣄⡄⠂⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠨⠙⢒⣨⣍⡙⠃
⠀⠀⠀⣤⢀⠀⢨⠷⠠⠀⠀⠐⠻⠀⠀⠀⠁⡤⢿⣥⠀⠀⠀⠨⠀⠀⠠⠄⢀⠀⢀⠀⠀⠲⡤⡙⢾⣛⠅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠶⡶⠀⠄⠀⠀⠠⠂⢴⡧⡎⠀⠸⠀⠁⠀⢘⡛⠓⠭⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠓⠁⠃⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⣶⠀⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⠖⣶⠃⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣦⣄⣥⣾⣽⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠈⠉⠉⠱⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⢀
⠀⠀⢠⣄⣨⣗⣦⣾⠂⣾⣶⠶⡾⢷⠀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠄
⠀⠀⠈⢙⣿⣿⣯⣥⠀⠋⠰⡶⠀⠛⠿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢠
⠀⣻⣲⡶⠟⠁⢀⠀⠀⡎⠁⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡻
⠈⠉⠉⠀⡄⠀⠀⠀⣼⡀⢦⡀⠘⢇⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠀⠐⡆⢉⡇⢮⣵⡀⡾⠴⠀⠀⠀⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⣴
⠀⠀⠀⠀⠀⠀⣶⣴⡟⠉⠃⢈⡟⠀⠀⠈⠁⠠⢿⣦⠀⢃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⠐⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣤⠴⠋⠀⠈⣹⣶⣟⠁⢠⣄⠀⠀⣠⣤⣿⡆⠀⢇⠀⠀⠀⠄⠀⣞⠀⠀⠀⠀⠀⠀⠀⢲⡇⠀⠘⠣⠶⣗⣀⢸⠿⠂⠀⠀⠘⠒
⠀⠀⠀⠀⠀⢤⠼⠷⣶⠉⣿⢻⣷⣿⡻⢷⠟⠁⠀⢻⣿⠀⢀⣁⠀⠂⢀⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠷⠀⠀⠈⣵⡒⠒
⠀⠀⠀⠀⠀⣤⠄⠈⠙⣤⣨⣼⣿⣇⠀⠀⠀⠀⠈⠩⢹⣷⢾⣇⢀⣠⠟⠛⠒⠂⠀⠀⣀⠀⠈⠑⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣭⡥⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠛⣿⡝⢫⡔⠀⠀⢠⡀⠀⠛⠀⠂⣿⡿⠁⢶⢃⣀⠀⠈⠉⢻⢠⡇⣰⠖⠛⠉⠁⣡⠄⢺⡇⠀⠀⠀⠀⠻⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⣿⣿⣷⣆⠀⠀⠀⠀⠁⠀⠀⠀⢸⠿⣶⢦⡞⠻⠿⣿⠷⣤⣴⣾⣿⠣⠀⠀⠁⣾⣿⠀⢿⡆⠁⢀⣴⠂⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣉⠛⡄⠀⠠⠦⠼⠀⠀⠀⠉⣰⣧⣀⠥⠤⢄⣠⡼⠉⠛⣿⡌⠷⠁⣠⡚⠁⢀⡀⠀⣀⣀⠀⠋⠐⠶⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⡀⠀⠀⢠⡇⠀⠀⠀⠀⣿⡏⡄⠐⠐⣎⠹⣿⣷⣄⡀⢐⣘⣁⠉⠈⠛⠃⠀⢸⢇⡈⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄⣠⣤⣦⢻⣶⣶⣄⠐⠙⠳⠄⠢⡄⠙⢢⣿⣾⠁⡀⠀⠘⢏⢢⣶⣦⣠⡀⠘⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠋⠻⣿⢎⣿⣿⡏⠃⣀⠴⣷⡦⢀⢶⠟⣙⠁⠛⠁⠀⢠⢤⣾⣟⣂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠘⠛⣠⠀⠀⠈⠻⡀⠈⠃⢠⠆⠀⠀⡨⢟⣿⠛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠉⠉⠒⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠆⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣀⠱⡀⠂⠁⢀⠁⠂⠀⣰⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⠤⢤⠄⠀⢀⣀⣀⠀⠐⠐⢄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⠐⠦⠷⠶⠶⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠀⠀⠀⠀⡀⠀⠀⠄⠁⠀⠀⠀⠀⢀⠌⠀⠀⠀⣓⡠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⢀⠀⠀⠀⡠⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠤⠾⣁⠼⠀⠈⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠰⠂⢠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠁⡠⠀⡊⠈⠂⠀⠀⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠠⠁⡀⠀⠀⠉⠒⠀⠠⠤⠀⢀⣀⣀⡠⠊⠀⠄⠅⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠘⠀⠂⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⡜⠀⠀⠀⠀⠒⠠⠤⠤⠀⠀⣀⠊⠀⡔⠀⢀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⣀⠀⠀⠀⡔⠁⢀⠎⠀⠀⠀⠀⠀⠀⣀⡀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠒⠐⠃⠀⠀⠀⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑⠀⣠⠀⠀⠀⣩⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠀⠀⠄⢠⠒
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠂⠒⣤⠘⢇⠉⠉⠁⠀⠐⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⣆⠀⠀⣄⣀⣤⣰⣀⣰⣠⢄⡠⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠃⢁⠀⠄⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⡀⠀⢀⡀⠳⢤⠔⢊⠴⠚⠀⠀⠉⠓⣮⡗⡶⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⢧⡀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠈⠇⡇⠀⡸
⠀⠀⠀⠁⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠤⠤⠤⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣨
⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⣧⢸⣸⡸⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⣀⣈⣤⠀⢀⠀⠀⠀⢬⣓⣬⣾⣿⣿⣟⣥⣐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡆
⠀⠐⠀⠀⠁⢡⣙⠃⠒⠤⠀⠀⠀⡦⠶⣿⣿⣿⣿⣿⣿⡭⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠠⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠐⢛⡩⢻⢿⢿⢟⢮⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠀⠀⠀⠈⠐⠻⠸⠸⠘⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠐⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⡈⣐⡚⣼⣄⣤⠁⠀⠠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠄⠪
⠀⠀⠀⠀⠀⠀⠀⠂⡩⠙⣿⣿⡁⠖⠀⠠⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⡡⠢⢓⠉⠀⠂⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣤⣴⣦⣤⡄⠀⠀⢐⠒⠒⠂⣀⡀⠀⠀⠀⢀⣰⣾⣾⡆⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⣠⣾⣧⣠⠂
⠀⠘⠿⠿⠿⠿⠇⠀⠀⠘⠀⠀⠣⠀⠀⠀⠀⠻⡿⠛⠻⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠄⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾
⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠀⠀⠀⠚⠁⠟⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣾⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠠⢨⡂⠀⠀⠀⠀⢸⡇⣶⣿⣿⠀⠀⠀⠀⠀⣠⡺⠟⠁
⠀⠀⢹⣿⣾⡿⠀⠀⠀⠀⢠⢏⠷⡄⠀⠀⠀⠈⣇⣻⣿⡟⠀⠀⠀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⡦
⠀⠀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⡇⢥⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⢐⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠤⢀⡀⡄⠀⢠⡄⠴⠦⠶
⠀⠀⠀⡀⢰⠀⠠⠐⠂⢽⡞⠁⠀⡀⠀⠀⠑⠈⠑⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⢈⣿⣆⠤⠤⡖⣠⢀⣤⡀⠀⢢
⠀⠁⢠⣿⡟⠁⠀⠀⣴⣯⣿⠻⣏⢻⠀⠅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱⣧⡿⠿⡼⡿⣷⣠⠴⠀⠉⠀⠁⠄⢂
⠀⠀⣸⠼⠀⠠⢌⠂⠈⠁⢹⡦⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢈⣠⣤⡞⠁⢷⡽⢴⡦⠀⡂⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⣈⠀⠀⠰⣽⣇⣠⡤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠄⠀⠀⢻⡭⢸⠖
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⢀⡀⠀⠠⠅⠀⠀⠯⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠓⠚⠉⠙⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠃⠀⠂⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣼⣁⢉⣉⣉⣉⣈⣘⡛⠛⠳⣟⣻⣋⣗⣀⡀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⠿⠤⠸⠷⠥⠀⠀⠀⠀⠀⠒⠚⠦⣝⠰⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⡀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⡙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠁⠉⠀⠀⠀⠀⠂⠶⡦⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠂⠀⠐⠂⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠱⠶⠒⠀⠀⠑⠒⠒⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠐⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡀⠔⠲⠻⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠁⠀⠀⠀⢀⠀⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⢯⣱⡉⣿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢆⠠⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠚⠸⣿⣼⡀⠛⠀⠀⠀⠀⠆⠀⢀⡄⠀⠀⠀⠀⠀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠐⠀⠀⠪⠀⠀⠠⡀⡔⡰⢠⠃⣨⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠠⢄⣀⢊⡪⠴⣡⠞⠐⠁
⠀⠀⠀⠀⠀⢀⠀⠀⣀⠧⢀⡀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠲⠋⡛⠴⡚⠷⣃
⠀⠀⠀⠀⠀⠐⠀⠀⠳⠄⠚⠃⠤⠟⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣠⣆⡜⠠⢀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⢀⣠⡴⠀⢤⣟⠷⠞⠛⠒⢦⣈⠲⢄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠕⠒⠤⠐⠽⣭⣙⢯⡯⡓⡄⠙⡀⠀⠀⡛⠑⢄⠑⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⣁⠀⠀⠀⠀⠀⢀⠤⠺⡕⣧⠔⠀⡃⢀⠴⠛⠀⠀⠱⡈⢆⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠀⠆⠀⠀⠀⠀⠈⠲⡤⠂⠙⢣⠀⠈⠁⠀⠀⠀⢀⡀⣷⡈⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠯⠙⠂⠀⠀⠀⠀⠀⠘⣷⠚⣃⢰⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠚⠠⡀⠀⠈⢆⡀⠀⠀⡠⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠶⠯⢽⠀⠀⢠
⠀⠀⠀⠀⢀⣀⣄⣰⣉⣉⣉⣹⣆⣀⢀⡀⠈⠛⢄⣈⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢸⢀⠀⠘
⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⡀⠀⠀⠀⠉⠳⡤⠒⠂⠀⡀⠀⠀⠀⠀⠀⠈⠂⠐⢲⡆⠘⠀⡀
⠀⠀⠀⠐⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⢁⣒⣄⣀⣀⣀⣀⣀⣸⣠⣇⣰⠥⢴⣶⠴⠶⡖⠶⠶⠶⠶⠶⠖⠂
⠀⠀⠀⡄⠀⢃⢰⡆⠀⠀⠀⠀⣰⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢀⠈⠉⠉⠉⠉⠉⠉⢩⠀⠀⠀⢠⢂⡶⢛⢷⣎⢢⠀⠀⠀⠀⠘⢠
⠀⠀⠀⠃⠀⠀⠸⠏⠀⠀⠀⠀⠹⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢰⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠐⣧⣊⣸⡟⢠⠀⠀⠀⠀⠀⠎⡀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠢⠄⣀⠀⠀⠀⢀⠃⠀⢀⡏⡓⠠⠀⠀⠀⣀⠀⣇⠠⠔⠊⢣⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠃
⠀⠒⠚⠀⢠⠊⠉⠉⠉⠉⠉⠉⠉⠉⠱⠀⠀⠟⠓⠦⠤⠈⠁⢀⠉⠈⠉⠠⠖⠡⠒⠀⠘⠃⠀⠒⠂⠀⠀⠀⠀⠣⡀⠀⢀⠃⠀⠀⠀⢀⡀⠴⢀
⣖⡂⡄⠀⠸⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⡆⠀⠁⢐⡲⠂⠤⢤⠀⠀⠀⠤⠀⠺⢀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢀⠵⡄⢸⠉⠉⠉⠉⠀⠀⠀⡞
⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠆⠦⠀⡐⠑⠶⣾⣧⣇
⠣⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣀⠜⠀⠒⠚⠒⠒⠒⠒⠒⠄⠠⠃⠀⠀⠀⠀⠀⠀⢀⠠⠊⠈⠁⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠈⢆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢰⢰⣲⣤⣤⣖⣀⣈⣹⣀⣠⠤⠤⠶⠶⠖⠚⠒⠒⠒⠒⠒⠒⠚
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⣨⠞⠛⢵⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣛⡓⣨⠐⠿⣾⠦⡀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⡿⠛⢃⡘⠟⠀⢩⣦⡀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⣿⣿⣿⣿⣷⣄⣼⣿⣶⡀⠀⠉⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠁⢀⣀⡀⡘⣿⣿⣿⡿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢀⣤⣾⣿⣿⠦⡀
⠀⠀⠀⠀⠀⢠⣖⣟⣟⣗⣦⠀⢸⠀⠀⠀⠙⢢⣴⣶⣦⣄⠀⢠⡞⠁⠆⠀⠈⠛⠉⡟⠀⠉⠦⡀
⠀⠀⠀⠀⠀⡧⢼⠤⡧⢸⠤⡇⢸⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠳⡼⡄⡧⡼⡤⠃⢸⠇⣠⡀⠀⠀⠈⢻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣬⣭⣭⣭⣀⣄⢸⣍⠀⠀⠀⠀⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢸⣿⡄⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠞⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠈⠹⣆⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠃⠀⠀⢦⠈⢿⣤⣤⣇⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⠇⠀⠀⠘⣺⣷⣾⠁⠀⢨⡗⠋⣉⡁⠀⠀⠸⣆⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢈⡇⠀⠀⠀⠘⣁⣴⣇⡀⠀⡾⢿⡿⠭⠀⠀⢠⡾⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⠶⠶⠒⠛⣩⠏⡏⠉⢻⣷⡀⠃⠀⠀⢀⣼⠋⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⢀⡇⠀⠸⡏⢳⡄⠀⠀⢨⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⣻⣗⣀⡴⠋⢻⡀⢀⣹⡄⠙⠳⠶⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⠳⣾⡏⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠦⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠀⠈⢃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄
⠀⢰⢀⠀⠀⣠⠀⠑⡄⠀⡠⠒⠁⠀⠀⠀⠀⠄⢀⣇⠐⣹⠀⠔⡡⠂⠢⡑⢄⠀⠀⠀⠀⠀⡴⠃⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠨⢀⠱⡊⠀⣠⠂⢁⡜⠀⡠⠤⠭⣄⠀⠀⠰⠁⠈⢁⠔⡡⠊⠠⠀⠀⠈⠂⡑⢄⠀⢠⠞⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠉⠉⠣⡈⡔⠈⢀⡳⠺⣠⠊⠉⠉⠉⠙⢂⠀⠋⢉⠝⡁⠊⠀⠂⠀⠀⠀⠀⠀⠈⠢⡙⢇⡀⠀⠀⣠⡏⠉⠉⠉⠉⠉⠉⠉⠉⣙⠌⠉⠉⠉
⠀⠀⠀⠙⠮⡐⠉⠠⠇⠁⠀⠀⠀⠀⠀⠀⠂⠜⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠄⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⢌⠊
⠀⢀⠀⠀⠀⠈⢲⠐⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣥⡅⠀⠀⠀⠀⠀⢀⡢⠁⠀⠀⡀
⠀⢈⡃⣀⠀⠀⢘⡀⠈⣄⠀⠀⣀⡠⢊⠔⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢌⠹⣦⡀⣀⣀⡠⣑⢁⣀⣀⠚⡈⠂⢄
⠀⠀⢫⡹⡀⠀⠈⢱⠀⢻⠀⡠⢉⠔⠁⠀⠃⠈⠀⠃⠈⠓⠀⠀⡏⠦⢄⠀⡜⠠⠠⡀⠈⠋⠳⠃⠀⠑⢌⠻⣈⠛⣵⡅⠀⡨⢃⠌⠀⢀
⠀⠀⠀⢻⢷⡀⠀⠘⡅⡠⠋⠔⠀⠀⠀⠀⠈⠅⠀⠀⠀⠭⠀⠀⡇⠐⠈⠈⠃⠐⠊⠁⠁⠀⠀⠀⠀⠀⠀⠐⠈⠻⡇⠀⡐⢠⠂⢠⡶⠂
⠀⠀⠀⠀⢳⢱⡀⡠⠋⠄⠀⠀⠀⠀⠀⠊⠃⠀⠅⠿⠄⠉⠢⠴⠄⠄⠀⠀⠠⠠⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠐⢈⠪⡐⠁⠀⡐
⠀⠀⠀⠀⠘⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠠⢈⠀⠀⠀⠦⠠⠀⠀⡍⠤⢠⠑⠀⠀⠀⠹⠗⠈⠂⠈⠁⡠⠤⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⢰⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠀⠀⠀⢠⢆⠀⠀⠁⠘⡃⠘⢄⠈⠀⠐⠀⣃⠀⣷⠀⠒⠂⢁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐
⠀⠀⠀⠑⢌⠢⡀⠀⠀⠀⠀⠀⢘⠀⠘⠒⢂⡄⢈⣈⠀⢂⢰⠸⠀⠼⠀⠑⡄⠈⠒⠁⠀⢋⠀⠰⢄⠈⡄⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠑⢌⠢⡀⠀⠀⠀⠀⠀⠈⠀⠘⠑⠁⠀⠙⠊⠈⠁⠀⠓⠋⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠐⠋⠀⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠈⢠⠈⠈⠈⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠼⠉⠁⠐⠢⡀⠀⡾⡀⠀⠀⠢⡀⢆⠒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠉⠁⠉⠀⠉⠉
⠀⢠⠀⠈⠃⠀⠀⠀⠀⢠⡈⠂⠀⠀⠀⠀⠀⠀⢠⠀⠇⠐⡀⣱⠠⠀⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠋⠢⢀⢀⠌⢤⣌⡑⠄
⠀⠀⠉⢀⣠⠤⣀⣀⠔⠁⡨⠢⡀⠀⠀⠀⠀⠀⢸⠀⠒⠊⠀⡜⠀⠰⠼⠀⢆⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠈⠂⠤⡌⠰⢤⣁⠁⠂
⠀⠠⠖⠉⢄⠢⡀⠀⠠⠚⠀⠀⠘⠢⡑⢄⠀⠀⠘⠀⠈⠀⠉⠀⠃⠊⠁⠑⠘⠚⠀⠃⠀⠠⠄⢀⠔⡠⠚⠙⠒⢦⠄⠀⠠⠁⠄⠀⠀⠸⠒
⠐⠀⠀⠤⠀⠢⡈⠀⡈⡄⠀⢀⠔⠉⠈⠢⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⡊⠀⠀⠀⠀⠀⠙⣀⡂⠆⠀⠀⠀⠆
⠀⠈⠢⡄⠘⠂⠈⢓⠎⠀⣰⢄⡘⠃⡈⠐⢄⢂⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠡⠘⢄⠙⡆⠀⠀⠀⠀⠀⠈⠩⠄⠂⡄⡜
⠀⠐⠀⣌⠢⠀⠘⠡⢐⠠⡐⠀⠀⠑⢄⡀⠒⠀⣉⢤⠑⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⣁⠀⠀⠀⠈⠆⢹⠀⠀⠀⠀⠀⢠⠒⠠⠀⡔⠁
⠐⠙⠑⡋⠖⣂⠤⠊⠑⠀⠀⠀⢀⣀⠤⣄⠬⠼⠃⠂⠛⢄⠑⠀⠀⠀⠀⠀⠀⢀⠶⢅⠑⠒⠢⢀⠘⣀⣗⡀⠀⠀⠀⣇⠀⠀⠼⠃
⠀⠔⡠⠀⠈⠀⠀⠀⢀⠀⣀⠬⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠒⠀⠤⡁⢀⣈⣦⡀⠀⠣⣀⠴⠃
⠃⠁⠀⠀⢀⡠⠤⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⡉⡑⢿⡄⣸⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢣⠀⢠⠀⢠⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠂⢸⠀⠂⢀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⢉⣀⡀⠀⠀⠐⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣼⡿⠛⣷⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⡀⡼⣿⣦⣤⣝⠂⠐⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠔⠈⡀⠐⠁⡉⠀⠑⢀⠁⠈⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠄⠀⠀⠁⠠⠀⠡⠀⠀⠀⠑⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⢠⠀⠀⠀⠈⠀⠀⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠠⠀⢠⠃⠀⠀⠂⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠄⠂⠠⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢧⣄
⠀⠀⠀⠀⢠⡞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡭⣭⣭⣭⣽⡇
⠀⠀⠀⠀⢿⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡼⠀⠀⠀⡠⠓⠀⠀⠀⠀⠀⠀⠀⢀⡼⡡⠀⠀⠀⡀⢀⠳⣄
⠀⠀⠀⠀⢀⡭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣛⡓⠛⠖⠲⡄⣀⣳⣞⣀⡀⠀⠀⠀⠀⠀⠈⢳⡑⠀⠀⠀⠃⠌⡴⠋
⢠⡶⠶⠚⠋⠀⠀⠙⠓⠶⢶⡄⠀⠀⠀⠀⠘⣏⠙⠒⠲⠶⠶⠶⠾⠛⢺⡷⠄⠀⠀⠀⠘⡏⣿⣤⠏⢻⠛⣯⢯⢩⠷⡟⠀⠀⠀⠀⠀⠀⠀⣿⣓⣚⣚⣛⣻⡇
⠈⢷⣐⡒⠰⠆⠲⠂⣒⣢⡞⠁⠀⠀⠀⠀⠀⠹⣆⡻⠒⠗⠐⠆⠲⢂⡿⠁⠀⠀⠀⠀⢰⡇⡇⠀⠀⢸⠀⡗⠈⠉⢠⡇⠀⠀⠀⠀⠀⠀⠀⠏⠉⡹⢩⡙⠹
⠀⠀⠉⠛⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠚⠀⠛⠲⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠂⠆⣁⣎⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠺⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⣰⣳⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠋⠙⠑⣦⡀
⠀⣠⠞⠓⢦⣈⣁⡴⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠗⢤⡴⠾⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣿⣭⣭⣽⣋⣿⠀⠀⠀⠀⠀⠀⠀⠤⠈⡟⡏⠉⠉⢹⢻⠃⠤
⣞⠡⠈⡴⠋⠁⠉⠳⣄⠡⢜⡆⠀⠀⠀⠀⠀⡤⣿⢤⣠⢼⠧⣄⡤⡷⢄⠀⠀⠀⠀⠀⠀⠀⠻⠂⠈⢳⡷⠁⠐⠾⠁⠀⠀⠀⠀⠀⠤⠤⠀⡇⠀⡜⢣⠀⢸⠆⠠
⠈⢩⠟⠁⠀⠀⢀⡀⠈⢳⡉⠀⠀⠀⠀⠀⢸⣅⣀⣠⣧⣀⣀⣼⣀⣀⣠⡃⠀⠀⠀⠀⠀⠀⣰⣛⡀⠈⡇⢀⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡔⠻⣄⢸⡀⠦
⠀⢯⡀⠀⠀⠀⠨⠅⠛⣀⡗⠀⠀⠀⠀⠀⠘⠯⣭⢭⣭⡭⠍⠉⢭⣭⠽⠃⠀⠀⠀⠀⢀⡽⢭⣭⣽⣧⢧⣯⣭⣭⢿⡀⠀⠀⠀⠀⠀⠀⠘⢿⡉⡀⡉⢋⡽⠃
⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠗⠀⠘⠚⠀⠀⠙⠂⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠿⠭⠭⠥⠭⠽⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠧⢸⡇⠸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⡑⠘⠁⣋⠴⢆⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣄⣄⡤⢄⣀⡀
⠀⠀⣏⠀⣠⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠙⢦⠘⠃⡰⠛⠡⠦⠀⠀⠀⠀⠀⠀⠉⡥⠶⠌⠀⠀⠡⢒⠲⠆⠀⠀⠀⠀⠀⠀⣯⡧⠄⢒⣿⢾⡗⠲⠶⣭
⠀⠀⠈⠓⠿⠿⠀⡏⠉⠉⢣⠀⠀⠀⠀⠀⠀⠲⠶⠶⠀⢮⡵⠀⠶⠶⠶⠀⠀⠀⠀⠀⠘⠃⣰⠊⣱⣄⠀⣠⣈⠙⠈⠃⠀⠀⠀⠀⠀⡷⣗⣋⣩⣿⣻⣏⣙⣛⠶
⠀⣠⠤⠴⢶⡄⢰⣶⡮⢀⣠⠃⠀⠀⠀⠀⠀⠘⢋⣴⠎⢠⡄⠙⣦⡘⠒⠀⠀⠀⠀⠀⠙⠀⢹⠟⣛⡏⢺⠧⣼⡇⠙⡁⠀⠀⠀⠀⠀⣏⡯⠤⠴⣿⣽⡷⠤⢭⣛
⠠⠋⠀⢀⣀⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⢘⡃⠰⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⢴⡇⢸⣓⣺⡇⠀⠁⠀⠀⠀⠀⠀⠧⠗⠒⠪⠉⠏⠙⠒⠲⠾
⠘⠦⣄⣘⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢹⠀⠈⡛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠡⠂⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⢺⣏⡽⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⢀⢀
⠀⡔⠲⢅⣿⣅⣸⡷⡬⠒⢢⠀⠀⠀⠀⠀⠀⠀⢰⢤⠈⡵⢶⡄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡦⡴⠠⠀⠓⡤⢢⡔⠀⠀⠀⠀⠀⠀⠀⢀⣲⣡⠖⣧⣬⠳⣄⣗⡀
⠀⢇⢈⡏⡀⢠⠄⣁⢻⠀⡘⠀⠀⠀⠀⠀⢰⠲⢎⢹⣲⢰⢁⢤⢉⡃⡄⠀⠀⠀⠀⠀⠈⠒⠰⢤⡴⠁⠈⠣⡤⠥⡐⠁⠀⠀⠀⠀⠀⡭⣧⣾⠚⠧⠸⠓⢻⣤⠯
⠀⠘⠀⠇⠈⢈⡀⠁⡸⢠⠁⠀⠀⠀⠀⠀⠀⣙⡙⢶⣿⢸⠫⢭⣴⠉⣗⢺⠀⠀⠀⠀⠘⠹⢃⡠⣃⠀⠀⢀⢇⣈⠃⠃⠀⠀⠀⠀⠀⣄⡷⣼⠋⣀⢠⡈⣻⡼⣁
⠀⠀⠷⢚⣿⠀⠀⣿⡓⠜⠀⠀⠀⠀⠀⠀⠑⢬⠿⢢⡻⣌⠓⠄⣱⣚⠍⠁⠀⠀⠀⠀⠘⠉⡈⣄⢠⠃⠐⣇⢠⣄⠈⠃⠀⠀⠀⠀⠀⠐⠣⠾⣍⣳⣴⣋⡽⠴⡗
⠀⠀⠀⠀⠘⢆⠀⠛⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠄⢢⡋⠠⡥⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠳⠞⠣⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢀⡔⣂⠀⠀⠀⠀⣶⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠙⠟⠀⠀⠀⣠⠛⠦⠀⠀⠀⠀⠉⠻⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⢀⠼⠑⠆⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠛⠙⠂⠀⠀⠀⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠁⠀⠀⠀⠀⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⣦⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⢚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣤⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠗⡀⠀⠁⠀⡀⠀⠀⡠⠀⢓⠴⠊⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠈⣠⠀⠈⠑⢤⢠⣩⠚⠋⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⡖⠰⠿⠁⠛⠁
⠀⠀⠀⠀⠀⢠⣿⠋⠀⢀⣾⣿⣷⡤⠀⠶⠚⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠏⠀⠉
⠀⠀⠀⠀⢀⣾⠃⢀⣴⣿⣿⠿⠋⠀⠈⣠⣄⡈
⠀⠀⠀⠀⣼⠃⣠⣾⡿⠛⠁⣀⣤⣶⣿⠿⠛⠋⠁
⠀⠀⠀⣸⢃⣾⠿⢋⣠⣴⠾⠟⠋⠁
⠀⠀⢰⣷⣿⠵⠞⠋⠉
⠀⠀⠛⠉

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢠⢰⣖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣤⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⡀⠀⠀⠀⢽⣦⠄⠀⠘⢉⣿⣖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢢⣌⠈⠀⢁⠝⠳⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠂⣸⢰⣾⢏⡞⣼⣷⠀⡠⠀⠖⠀⠀⠀⠀⢉⢿⣭⡅⠀⡀⠀⡀⢠⢠⢠⡆⡀⠀⢀⣉⠋⠁⠀⠀⠐⠿⣝⠿⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡙⢦⠡⣔⠈⡏⡾⠐⡿⣫⠞⣠⠾⡃⣷⡟⠰⠀⠈⢷⠿⠷⢤⡈⠃⠳⠈⠋⣘⢿⢔⣅⣤⡄⢆⣠⠀⡀⠀⢦⣛⢿⡃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⠌⢀⠁⠘⠀⠃⠀⣠⠖⡡⠎⣲⡿⢷⣛⡯⠀⢰⠁⠎⠀⠒⠾⢿⠎⠀⠀⠐⢁⠤⠿⠿⢾⢵⠟⠇⠌⠃⣀⠘⢏⠛
⠀⠀⠀⠀⠀⠐⠛⠛⢺⣿⡢⠶⠁⠀⠀⠀⠔⠁⠀⢴⣩⣵⣾⣯⣶⣤⣤⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠐⠉⢹⣥⣭⣉⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⣂⣀⠀⠈⠉⢀⠀⠉⠀⠀⠀⢐⣚⣢⣬⣤⠤⠶⠶⠶⠶⠤⠀⠀⠀⠀⡀⢚⣤⡆⢠⡀⠀⠙⢦⣍⢾⣕
⠀⠀⠀⠀⢀⣩⠴⠒⠂⢀⡠⠄⠀⠀⠈⠀⠀⠀⢈⠄⠀⠤⣽⡿⢶⣦⣤⡀⠀⠀⠀⠈⠐⡿⡻⣠⠈⠇⢀⠀⠸⣌⠛⠂
⠀⠀⠀⠀⠀⠔⠪⠀⠀⠜⡴⡀⣢⡄⠄⣀⠀⠀⠀⠑⢧⣤⡉⢙⣯⣓⠶⠄⠀⠀⠀⢠⠀⡇⣥⡟⣦⣶⣿⢿⡷⠈⡀
⠀⠀⠀⠀⠀⠠⢒⡥⢆⣴⡾⣣⣾⠃⠀⢿⡄⠘⠀⠀⢀⢰⡾⣷⢭⡛⠗⠀⠙⢦⣄⠲⡙⡆⢸⠛⣽⢃⣿⡿⣠⠞⢁⣤
⠀⠀⠀⠃⠀⠀⢉⠔⠹⣿⡟⣹⠏⢠⠀⠉⡇⠀⡐⠀⠀⢳⣧⡀⠑⢽⣲⢦⣐⠢⠙⠧⠙⡆⢸⠀⠁⠐⢋⡼⣫⢖⣫⣤⣀⣠⠤
⠀⠀⠀⠀⠠⠀⠀⠀⠔⠙⠰⡝⠰⢀⠇⠀⠅⠠⣧⠂⢈⣆⠉⢳⣀⣤⣄⣙⣶⡕⠠⠦⡀⠀⠈⠀⢀⠼⠋⠜⣉⠵⢚⣫⡭⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠆⠄⠀⡆⡆⣴⣿⣄⠘⡜⠃⠀⠉⠰⠾⠻⠿⣍⠺⠃⢀⡀⠀⠐⠋⠀⢀⠚⣶⠾⠿⠿⠿⠿⠶⠶
⠀⠀⠠⡀⡀⠶⢲⣧⡀⠀⡀⠈⠳⣅⢘⠏⡏⠏⣽⣣⢊⡤⠀⢀⣀⡩⠤⠀⠀⠀⠀⠤⠀⠀⠐⠈⠀⠨⣍⡽⠶⠶⣖⣚⠛⠛⠛⠻⠆⠀⢠
⠠⠭⣧⡄⠀⠀⠚⣉⣿⣞⣛⢳⡄⢈⠀⠃⠁⢠⠖⠕⡹⢾⡶⢯⡤⠖⡛⠋⢉⡠⠄⠀⠀⠀⠁⠀⠀⠀⢀⠠⡀⠰⢶⣽⠻⠷⣶⣤⡄
⠀⠴⠀⠀⠀⠀⠈⠛⢪⣭⣛⠛⠿⠃⠠⠀⠀⠁⢠⣓⡚⣛⣛⣳⣖⠩⢒⠀⡴⡠⠂⢘⣔⠠⠂⡆⠀⠀⠀⠙⢮⣦⣄⠩⣻⢭⣓⢶⣄⢀
⠀⡀⣺⣴⠂⡆⠀⠙⣾⣿⡿⠂⢀⠀⠀⠀⠀⠀⠙⠈⠩⣵⢶⣤⣩⢖⣥⠖⣠⣶⢏⣼⡿⠀⠀⣷⠀⠘⠆⠀⢀⠨⣪⣷⣮⣝⠿⡿⠋⡛⢦⣆⡀
⠀⠀⠋⠃⠀⠀⣰⠠⡙⠊⠃⠰⢶⡀⣦⠀⣄⠀⡀⠙⢶⣌⡹⣿⡓⠙⡡⢊⣿⣵⢏⡿⠁⠀⠀⢻⡇⠀⠀⡀⠀⠱⣽⡈⠛⢿⡳⠆⠈⢠⣞⡿⣷
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠊⢴⣿⢺⠃⠀⢻⠀⠀⠀⢸⣏⠻⡪⠁⠈⠀⡠⠫⢃⢮⢃⠆⢣⠀⠈⡇⠀⣇⠇⠀⣦⠙⠻⣏⡀⢀⠀⠀⠀⣄⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠎⠂⡇⠀⠀⣿⠀⣦⠙⢆⠀⠀⡀⠀⠁⠀⠈⢎⢊⢀⠊⢠⠀⠁⣰⣿⠀⠈⡞⡧⠐⠻⣿⡟⠐⡇⠀⠨⡟⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⡘⠀⢸⢸⠀⠹⠁⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠇⠸⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡟⣦⣀⢿⢄⡀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⡞⢻⠛⣶⣞⠁⠀⠀⢀⣴⣿⣿⣿⡟⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢾⣦⡇⣿⡏⢼⣿⡷⢊⣟⡄⢀⡄⠀⠀⠀⠀⠀⣤⣼⣧⣬⡞⣾⣥⣿⣤⡄⠀⢸⠿⢿⣧⢿⣿⣿⢀⣀
⠀⠀⠀⠀⠺⠰⠧⠚⠸⢣⠻⣈⡿⠛⠋⠉⠉⠛⠾⣿⠟⢚⠟⡀⠀⠀⠀⠀⠀⠀⠘⣷⣞⢹⢙⣶⡟⠀⠀⠀⠘⣷⣾⣻⢸⡻⣻⠙⠿
⠀⠀⠀⢀⣤⣄⢀⡄⠃⡌⠛⣭⠀⢀⣄⠀⢠⡄⠀⢨⡘⢋⣭⣤⠀⣤⣤⡀⠀⠀⠘⠉⠙⢻⠛⠉⠙⠂⠀⠀⠀⠘⠻⠿⠷⠓⠙
⠀⠀⠀⠘⢧⣄⢸⡇⠀⡇⢠⡿⣇⣸⢿⡀⣼⢿⣀⡿⣧⢸⡷⠶⠀⣿⣼⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠰⢦⠟⡈⠷⠴⢇⠸⠇⠹⠏⠸⠇⠿⠈⠿⠁⠿⠘⠷⠴⠀⠿⠹⠆⠀⠀⠘⣦⣤⣸⡜⠀⠀⠀⠀⠀⠀⠻⣿⢟⡻⣻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠉⠐⢺⠋⣰⣷⢦⣀⡀⠀⠀⣠⣠⢬⡈⢉⠩⡁⣄⢠⡄⡄⠀⠀⠐⣺⣿⣿⢺⡧⠀⠀⠀⠀⠀⠀⠐⠨⣵⣿⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠷⠺⠟⡇⣸⡿⢻⣿⡇⢠⣬⡈⡌⠄⠉⠀⠉⠀⠀⠉⠀⠀⠀⠴⣹⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠝⠻⢏⣊⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⢇⣺⠻⠙⣼⠛⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠘⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠊
⠀⠀⢰⢛⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⣧
⠀⠀⠈⠉⣹⣶⢯⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡸⣯⢿⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⣷⢦⡀⠀⣠⢾⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡆
⠀⠀⠀⠛⠁⠈⣿⡀⠀⣀⣹⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⠀⠁⣶⢶⡶⠀⠀⠀⠀⠀⠙⣯⡻⣾⣣⡟⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣇⡙⣶⡡⢹⡦⣀⠀⠀⠀⠀⠸⠄⢠⠇⠀⠐⡏⠋⢹⠀⠀⠀⠀⣀⣴⠾⣻⣿⣿⣿⣿⣿⠶⠀⠀⠀⢠⣿⡇⣸⣿⢻⣿⡆
⠀⠀⠀⠀⢠⣀⣌⣙⣋⣠⡾⣠⠞⢁⣄⠀⠀⢀⠀⡐⠀⠀⠀⢷⠀⢸⡇⠀⠀⠾⠿⠚⠛⢹⣧⣿⠁⠀⠀⠀⠀⠀⠀⢾⣿⣧⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠙⠋⠉⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⡃⠈⢁⠀⠀⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠈⠐⠶⢶⣦⣥⣬⣭⣥⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠑⠀⠂⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢀⣽⣄⣤⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣤⡀⡀⠀⠀⠀⠀⢀⠠⢀⣰⣥⡀⠰⠀⠀⠀⠀⠀⠀⠸⣻⣿⣞⣛⣟⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣾⣿⣿⣿⣿⡹⢻⡟⠉⡡⠆⠀⠀⠀⠀⢤⡨⠌⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⣠⣤⡀⠁
⠀⠀⠀⠹⠛⠊⠀⠸⢃⡾⠀⠁⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⣇⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢀⢀⡄⢿⣽⣤⠃⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⢃⣀
⠀⠀⠀⠀⠀⠘⠦⠾⠴⠗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⢀⠀⢄⠀⠠⠀⠂⢀
⠀⠀⠀⠀⠂⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠈⠀⠈⠀⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⡒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠢⠀⡀⠁⠈⢈⠀⠀⠀⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠄⢀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠄⡃⠰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⠄⢳⡀⡿⠣⢀⣗⠅⡀
⠀⠀⠀⠀⠂⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢒⡙⠦⠤⠅⠀⠐⡡⠴⠃⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢋⠛⠇⠀⢀⢩⣐⢒⡖⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡟⣤⠊⡠⢸⣀⣈⣳⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢁⡜⢣⢘⠁⣯⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⢠⠷⠀⠀⠀⠀⢨⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢺⡗⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⢀⣀⡠⠀⠀⠀⣡⣿⡍⠀⠀⠀⠀⢠⡀⠀⠀⠀⢽⠅⠀⠠⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠠⣼⣷⠄
⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠘⣡⣿⣌⠢⠀⠀⢠⣿⣷⡀⠀⠀⢺⡒⠀⢠⣿⣿⡄⠀⠀⢠⣆⠀⠀⠀⠴⣿⣿⠶⠆
⠀⠀⠀⠀⠀⠖⠒⠂⠀⠀⠔⣩⣿⡝⠢⠀⢀⣿⣿⣿⣧⠀⢐⠱⣝⠀⢠⣾⣿⣄⠀⠀⣾⣹⡀⠀⠀⠾⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣱⣿⡝⠢⠀⣼⣿⣿⣿⣿⣇⢁⡼⣌⠁⠉⣽⣯⠉⠀⣸⣷⢺⣇⠠⠴⠾⣿⣿⣟⣉⣀
⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠚⠁⢺⠈⠂⠸⠿⠿⢿⠿⠿⠿⠀⢸⠀⠀⣾⣿⡿⠷⢠⣿⣷⣼⣿⡄⣠⡾⢿⡿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠘⠃

⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⡇⠀⠀⣠⣤⣤⠀⠀⠀⣤⣤⠀⠀⠀⢀⡄⠀⠀⠀⣶⣶⣶⣦⡄⠀⢰⣶⣶⣶⣄⠠⣤⣄⠀⠀⢠⣶⡆
⡇⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⢀⣾⣿⡄⠀⠀⣿⣿⠀⣹⣿⠀⢸⣿⡇⢸⣿⠆⠙⢿⣧⢠⣿⠟
⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⡿⢹⣿⡄⠀⣿⣿⠿⠿⠟⠀⢸⣿⡿⠿⠋⠀⠀⠈⢻⣿⡏⠀⡀
⡇⠀⠀⣿⣿⡏⠉⠉⢹⣿⣿⠀⣸⣿⣷⣾⣿⣷⡀⣿⣿⠀⣾⢳⡄⠈⣿⡇⠀⢀⢰⡀⠀⢸⣿⡇⠰⣿⠂
⡇⠀⠀⣿⣿⡇⠀⠀⠸⣿⣿⢰⣿⡟⠀⠀⢻⣿⣧⢹⣿⠀⠘⠋⠀⠀⣿⡇⠀⢸⣿⢟⠂⢸⣿⡇⢘⣿⠃
⡇⠀⢠⣴⣆⣴⣦⣆⣤⣦⣠⣠⣀⣠⣠⣠⣠⣠⡀⠘⠋⠀⠀⠸⡷⠀⠉⠁⠀⠀⠈⠀⠀⠀⠉⠁⠚⣿⠃
⡇⠀⠈⠙⠻⠙⠻⠋⠻⠙⠻⡟⠋⠉⠝⠛⠙⠛⢡⣄⢸⣿⣧⠀⠀⠀⣿⠀⢶⣦⢠⣶⠆⣠⣤⣤⣄⠉
⡇⠀⠀⣿⡇⢸⣿⠀⠘⠏⣓⣟⡹⠃⠀⣿⡇⠀⢨⣭⠀⣙⣟⡊⠀⢠⣿⡇⠈⢿⣿⠏⢰⣿⠏⠙⣿⡇
⡇⠀⠀⣿⣷⣼⣿⢠⣾⣿⣿⣿⣿⣷⠀⣿⣇⠀⢸⣿⠀⣿⡟⣿⡄⢸⣿⣷⠀⠀⣿⠀⠈⣿⣇⡀⠙⠃
⡇⠀⠀⣿⡏⢹⣿⠸⣿⣿⣿⣿⣿⣿⠆⣿⣿⠀⢸⣿⠀⣿⡇⣿⡇⣿⣿⣿⡆⠀⣿⠀⣀⠈⠛⢿⣷⡄
⡇⠀⠀⣿⡇⢸⣿⠀⠙⠻⢿⡿⠿⠋⠀⣿⣿⣤⣤⠀⠀⣿⣇⣿⠇⣿⣿⣿⣷⠀⣿⠀⣿⣇⠀⣠⣿⡇
⡇⠀⠀⠿⠇⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠘⠛⠋⠀⠀⠻⠇⠀⠀⠛⠀⠈⠛⠛⠛⠋
⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠁⢒⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⢠⣎⣀⠀⠀⠀⠀⢀⠔⠉⠀⢛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⢝⠂⠀⠀⠈⠙⢲⡀⢠⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡉⠉⠋⠀⠀⠀⠀⠀⠀⢱⣇⣀⡀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⡰⣖⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⣸⠋⠑⢄⠀⡇⢀⠀⡾⠀⠀⠀⠀⠀⠀⠠⣀⡳⠜⠀⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⢀⡀⠀⠀⠀⣰⠃⠀⠀⠈⠷⠋⡠⠈⠴⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤⠠⠒⣓⡄⢠⢀⠤⢡⠒⠢⢴⠃⠀⡠⠀⢀⡠⠊⡱⠷⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠈⠖⢥⠀⠀⢠⠃⠀⠀⠀⠑⡏⣀⠴⢋⠔⠙⠦⠤⠊⢀⡀⠀⠀⠀⢀⠔⢲⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢽⡖⠨⡷⠔⠂⠄⠀⠀⡾⠀⠀⠀⢀⣠⢼⡥⢚⡁⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡠⠎⢳⣀⣠⠗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠠⡀⠔⠀⠐⢦⣀⣇⠀⡠⠞⠉⠀⢀⡟⡉⢁⡀⠀⠀⠒⠀⠀⠀⠢⡀
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡿⠀⠄⠉⠋⠀⠑⠀⡇⠀⣏⠀⠀⠀⠀⣼⠁⡀⠄⠩⡒⠀⠒⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠒
⠀⢀⡗⡁⠀⠀⠀⣀⣂⣀⣃⣤⣼⢥⣿⣿⣱⠁⣠⣨⣁⡖⡀⣉⣞⣀⣑⣤⡠⠾⠷⠏⠘⠚⣢⠈⠂⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣳⡜⢻⡄
⠀⡌⠁⠁⢠⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠙⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠉⠂
⠀⡃⠀⠘⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇
⠀⠿⠲⢶⠃⠀⠀⣠⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏
⡴⠛⠈⠚⠲⡀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣠⣇⣀
⡇⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡆⡴⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⢈⠀⠀⠃
⠘⠠⠄⣀⠴⣧⠃⠀⠘⢀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡠⠀⢁⢧⠀⠀⠀⡰⠃⠰⠄⠉⢹⡂⠘⠆⠁⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⡤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠈⡏⠍⠉⣉⢱⠀⡔⠀⠀⠠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⠢
⠀⠀⠀⠀⣰⣀⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⠦⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡃⢐⡃⢘⡀⣓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠈⣠⠤⢀
⠀⠀⠀⠐⠀⠀⠀⠚⠘⠁⡇⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣠⡜⠀⠀⠀⠀⠀⠀⠀⠎⠁⣈⠄⠁⠄⠈
⠀⠀⠀⢸⢠⡥⢹⠀⣀⠖⠆⠀⠀⠀⠀⠀⠀⠀⠁⠰⠟⢀⠂⠀⠀⠀⠀⠀⠀⠀⡧⠶⠶⠶⠀⢠⢤⣾⠀⠀⠀⠀⠀⠀⠀⢀⣾⠡
⠀⠀⠀⢸⡀⠀⡘⠠⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠓⠚⠚⠓⠁⠉⠈⠃⠀⠀⠀⠀⠀⠒⠁⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠐⠆⠻⠉

⠀⠀⠀⠀⠀⠀⡁⢁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠁⠀⠁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠖⢤⠔⠂⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠂⢤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠚⢁⠱⠦⠰⠏⠈⠁⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠄⠀⡆⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠺⡏⠶⠒⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠃⠀⣤⣄⡀
⠀⠀⠀⠐⡨⠁⢀⡀⠈⠭⠀⠀⠀⠀⠀⢀⢠⠄⠊⠀⠀⠈⠣⢆⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠚⢠⠤⡔⠤⣌⣈⢭⡈⠆
⠀⠀⠀⠘⢀⡠⠃⠘⠄⠀⠁⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠂⠒⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⢄
⠀⠀⠀⠀⢀⠂⠡⠄⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢎⠃⠀⠈⠆
⠀⠀⠀⠀⠤⠄⠤⢠⠠⡤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠓⣆⠃⠀⠀⠀⠀⠀⠐⢀⢰⠂⠐⠆⠒⠓⡀⡂⠀⠀⠀⠀⠀⠀⠆⡈⡁⠯⠘⠡⠄
⠀⠀⠀⠀⠠⠄⢀⡰⠠⠇⠀⠀⠀⠀⠀⢀⣠⣄⣀⣄⣀⣄⣡⣄⠀⠀⠀⠀⠀⠀⠘⢈⠘⠁⣆⠨⢳⡟⠁⠀⠀⠀⠀⡀⡡⠊

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⠈⢰⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡣⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡐⠛⠘⠂⢁⠒
⠀⠀⠀⠉⠘⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠰⡁⠀⢼⡱⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠘⢁⠐⠃⡚
⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠓⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠄⠁⠄⠌

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡠⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠂
⠀⡤⢊⠄⠀⠀⠀⡀⠠⠀⠀⠀⡡
⠀⠄⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠀⡆⠄
⠀⠠⠀⠀⠀⠀⠀⠈⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⣿⣿⣿⣿⣿⡇⡄⠀⢀⣶⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣷⠁⠀⠀⢿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡾⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠟⠃⠢⡤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠗
⠀⠀⠘⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡟⠙⡆⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⣼⠿⡄
⠀⠀⢠⠿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠟⠀⠐⠀⠀⠀⠀⠀⠀⠃⣰⡏⣰⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⡾
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠙⢿⣿⡆
⠀⠀⠀⠀⠀⣿⡇⠘⣿⡇⠀⠀⠀⠀⠀⠙⠛⠿⠿⠆⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻
⠀⠀⠀⠀⠀⣿⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡏⠀⠰⠟
⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠾⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠆⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠋⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠄⠀⠀⣐⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⣻⡀⠀⣀⠀⠀⠘⢧⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⠀⠀⠀⠈⡾⡄⠈⠐⠀⠀⣄⠀⠀⢠⠦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢨⠖⠛⢁⣀⣀⡀⠀⠀⢐⠿⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⢳⡐⠀⠀⠀⢀⡀⠠⠤⢈⣀⣿⣀⢃⠈⠶⣤⠂⠀⠰⣾⠄⣠⠀⠶⠘⠇⠀⠀⠁⠀⠀⠀⠀⠈⣶⠈⡄⠀⢞⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠀⠀⠀⡴⠏⠁⠀⠈⢧⠀⠀⠉⠂⠀⠀⠠⠀⠉⠀⠀⠀⠀⠄⢠⠀⠁⠀⡀⠀⠐⡀⠂⠠⠈⠸⢀⠀⢀⠀⢀⣔
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⣠⢼⠁⠀⡤⣤⣄⣚⡄⠀⠀⠀⠁⢀⠀⠀⠈⠂⠀⠀⢀⡀⠓⠔⠋⠀⠀⠀⠀⠀⠝⠀⠘⠃⡀⠒⢛⠃
⠀⠀⠀⠀⠐⢆⠉⠛⠀⠀⠐⠈⠁⣤⢠⠤⠀⠈⠛⠬⢇⠀⠀⠀⠀⠀⠀⠈⢀⠀⡨⠄⠉⠄⡐⢒⠀⠂⠉⠀⠆⢀⢁⠀⠀⠠⡶⠋⠀⠀⠄
⠀⠀⠛⠛⠉⠒⠥⠀⠀⡀⠞⠹⠚⠁⠀⣴⡷⠀⣴⣶⠢⠅⠀⠀⠀⠀⠀⠀⠈⠌⠂⠁⠀⠉⢩⡀⠀⠀⠀⠀⠈⠐⠀⠀⠈
⠀⠀⢅⡀⠀⣀⡨⠖⢄⠈⠐⠀⡢⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⣐⣶⠴⠖⠒⠁⠀⠀⠀⠀⠀⠀⠉⠠⠤⠠⡀⢀⡽⠀⠠⠠⢂⣀⠀⠀⢠
⠈⠀⠐⠒⠠⢆⢃⠀⠀⠀⠀⠊⠀⠀⣀⡒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢐⠑⡶⠧⡄⠰⠈⡀
⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠘⠉⠛⠒⡖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠤⢤⡴⡆⠀⠀⠀⠉⠁⠈⠙⢲⣀⠀⠐⢄⠀⠀⡠⠈⢰⣄⠀⠠⠖⠒⠛⠀⠀⡄⠀⠀⠀⠀⠀⠈⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣛⠈⠄⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠯⠷⠀⡲⠄⠀⠉⠛⠁⠀⠐⠐⢇⠀⠈⠂⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠁⠀⠳⣌⠰⠀⠀⠀⠈⠉⠰⠊⠁⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠀⠒⢀⡈⢠⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⡉⡀⠘⠄⢱⡎⠁⢳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⢸⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠹⣷⡀⠈⡇⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢻⣧⠀⠀⢰⠃⠀⠈⠀⠀⠀⠀⢀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⣄⡀⠀⠐⠲⢤⣀⠀⠈⢻⣷⡀⠀⣿⠀⠀⠏⠀⠀⠀⠀⠀⣠⣶⡿⠋⢁⣠⣤⠤⠄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠈⠳⣄⠀⠹⣷⠀⢹⡇⠈⠀⢀⡖⠀⢠⣾⠟⢁⡴⠚⠋⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠒⠢⠄⡀⠀⠙⠻⣦⡀⠀⠈⢳⡄⢹⣇⢸⡇⠀⣠⠟⠀⣴⠟⢁⠞⠁⠀⠀⣀⣤⣶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢢⠹⡄⣿⠀⠁⣰⠏⢀⡾⠋⠀⠁⠀⣠⣴⠿⠛⠉⠀⢀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⠿⢷⣶⣦⣤⣀⡀⠀⠂⠈⢷⡀⠀⠱⢸⡇⢠⠏⢠⡞⠁⠀⣀⣴⠟⠋⠁⠀⠄⠒⠉⠉
⠀⠀⠀⠀⢀⠀⠀⠀⢀⣁⣀⣀⣀⣀⠀⠀⠉⠙⠛⠷⣦⣀⠀⠻⡄⠀⠋⡇⡜⢀⠟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢶⣤⣄⡀⠒⠉⠳⢦⡙⡄⠀⢰⢀⠎⢀⡜⠉⠠⠀⠀⣀⣠⣴⠶⠟⠛⠉⠉⠁⠤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⠶⠶⠶⠶⠶⠤⠤⠉⡙⠳⠦⣄⠀⠑⠄⠀⠀⠈⠠⠋⢀⣠⠴⠚⣛⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠈⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠡⠒⠛⢉⣉⡉⠉⠉⠙⠛⠛⠛⠿⠶⠄
⠀⠀⠀⠀⠁⣀⡴⠖⠋⠉⠀⠀⠀⢀⣀⣤⣤⠴⠶⠖⠒⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡉⠉⠉⠙⠛⠻⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⣠⣴⠾⠛⠉⣡⠄⠂⠀⠀⢀⡠⠀⠁⡠⠀⢀⠀⠀⠀⠀⠐⠢⣌⠙⠷⣦⣄⡀⠀⠀⢀⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠂⢀⣴⡿⠟⠁⠀⣰⠞⠁⠀⠀⢀⡴⠋⠀⣠⠞⠀⢀⠎⠀⠀⡌⠀⠰⡀⢈⠙⢶⣄⠙⠻⣶⣤⡀⠉⠓⢦⣄⠈⠁⠀⠄
⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⢀⠞⠁⠀⠀⠁⣠⠏⠀⠀⣼⠃⠈⢀⡞⠀⠀⠀⠸⡀⠀⠹⣆⠀⠀⠈⠻⣦⡀⠙⠻⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⣾⠁⠀⠀⣼⠃⠀⠀⠀⠀⣧⠀⠀⠘⣧⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣾⠇⠀⠀⢸⡟⠀⠀⢀⠀⠀⢸⡆⠀⠀⠘⣷⡀⠀⠀⠀⠹⣿⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠁⠀⠀⣸⡏⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⠘⡇⠀⡄⠀⠘⣷⡄⠀⠘⢆⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⣿⠁⠀⠂⠀⣿⡇⠀⠀⢹⠀⠀⠀⠃⠀⢷⠀⠀⢹⣷⡀⠀⠘⣧⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢻⡇⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⠀⠀⠀⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⢀⣦⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠀⠀⠀⢀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⡄⢀⠀⣶⡧⠀⠀⢀⣿⣿⠟⢳⣄
⠀⠀⠀⠀⠀⠀⠐⡾⢁⠀⠀⠀⠀⠀⠀⢰⢋⠉⠀⠀⠀⢰⡀⡀⠀⠀⣤⠏⠓⡂⠀⠀⠀⠠⣗⢚⡄⢉⠃⡀⠐⢩⣿⣷⡖⠁⠛⢃
⠀⠀⠀⠀⠀⠀⢀⡷⢻⠀⠀⠀⠀⠀⣰⠿⠟⠀⠀⠀⠀⠤⠓⠃⡀⠀⢠⡄⠘⠟⢀⡄⠀⠀⣻⢼⡃⠀⠰⠀⡘⣿⡟⠉⠀⣀⡴⣿⡀⢀⡄
⠀⠀⠀⢀⢀⣰⣿⣃⣀⠁⢠⡄⠀⢀⣁⡄⠀⠀⠐⢶⠀⢼⠃⣿⠁⣶⠈⠁⢀⣀⠀⢳⡴⠞⠓⠐⠛⠦⣄⠀⠈⠛⣡⡶⠛⠁⠠⠸⠃⢀⡧⡀
⠀⠀⡰⠀⢼⣿⡿⢅⣠⡀⡨⢦⡀⠸⡿⠃⣀⡀⣿⡿⠀⣾⠶⣿⠀⠉⠠⣦⣾⡟⢲⣿⣤⣤⣤⡤⠤⠶⠞⣛⡀⢞⠙⡾⠀⣠⠶⠁⢀⣼⠄⢷⡀
⠀⠀⢧⠸⣿⣀⢶⡎⠀⢈⠃⠄⡇⡆⠈⠐⠿⠷⠈⠁⠸⠁⠀⠸⣧⠀⠠⠃⠘⠃⣾⣤⣤⣠⣤⣀⣤⢠⡶⣿⡧⠈⢢⡿⠋⢀⠄⠀⢀⣅⠀⢠⣅
⠀⠀⠘⡇⣾⣽⣔⢑⣄⣡⢈⣤⡠⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢻⣄⠀⠀⠀⠀⠹⣿⣼⡷⣦⡿⠴⠌⠿⣾⠃⠀⠀⠁⢴⠉⠀⠀⣸⣄⣀⣀⣸⣆
⠀⠀⠀⠈⠻⢿⣿⠿⠤⠀⠉⠞⠁⠀⠀⢀⣼⣤⣀⣀⡄⠀⠀⠀⢸⡟⢀⠀⠀⢀⠄⠙⠳⣶⠶⠶⠖⣲⡞⠋⠀⠀⠀⠀⠀⠀⣀⣼⣯⣥⣤⣤⣤⣽⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠉⢡⡀⠀⠀⣼⠁⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠟⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠋⠙⠒⠀⢿⡀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⢐⠃⠀⢀⠠⡀⠄⡀⡀⠀⢠⠀⠀⡄⡄⡀⢀⠀⡄⠠⢀⣠⣀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠰⠸⠁⠘⠀⠃⠘⢘⠁⠀⠠⠀⠀⠁⠀⠁⠈⠀⠅⠆⠘⠈⠀⠐⠸⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣄⠀⠀⠈⢧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⡀⠀⠘⣆⢰⠀⠈⠉⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠱⡀⠀⠘⡄⡷⠖⠚⠉⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠤⣄⠀⠀⢹⠀⣄⠀⠱⡄⠀⡿⠃⠉⠉⠉⠉⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢄⡀⠀⠐⡄⠀⠙⢦⠈⣇⠘⢆⠀⢹⡾⠔⠒⠒⠒⠒⠂⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⡀⠙⢦⡀⢹⡀⠀⡈⢳⣹⡀⠈⢧⣞⡤⠤⠖⠂⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⢦⠀⠳⡀⢧⠀⡇⢀⠹⣧⠀⠌⢀⣠⢴⣒⣯⠥⠴⠶⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠳⣤⠴⡶⠗⡺⢾⡧⠀⠀⠚⠛⠋⢉⣠⠴⠒⠋⣀⣀⣀⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⢀⡜⠁⡞⠀⡜⢡⠏⣴⢟⡆⠈⢲⠶⣉⡀⠤⠒⠉⠁⢀⣀⡀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡠⠊⠀⡼⠀⡜⠀⢠⠞⡽⡼⡇⠀⢸⠀⢸⠓⢦⡔⠒⢋⣩⠤⠄⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠀⠀⠊⠀⠀⣠⠴⠋⢰⣿⠃⢻⠀⣼⠀⢸⠀⢸⠀⠀⢠⡤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠤⠤⠴⠖⠋⠁⠀⢀⣿⠃⠀⠈⢧⠹⠀⣾⠀⢸⠀⡆⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠈⢦⠀⢻⠀⠸⡀⠳⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡀⠠⠖⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠱⠀⠐⠁⠠⠴⠒⠶⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⠉⠀⡀⢀⠴⠛⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠈⠀⡇⡌⡀⠠⠂
⠀⠀⣠⠆⠀⣀⠘⠉⠁⣤⣀⠈⠁⡤⠀⢀⣉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠐⠤⡁⢠⢀⡜⠐⠕⡊⠀⠠
⠀⠀⠀⣠⠞⠁⣠⠴⠂⢀⠀⠠⠄⠀⡀⠈⠉⠀⠘⢦⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠠⠄⣉⣁⢈⣛⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠀⠃⠆⠴
⠀⠀⠀⠋⡠⠀⡀⠀⠐⠋⠀⡀⠀⣀⠈⠃⠀⠀⠐⡄⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠄⢀⢄⠼⡟⡿⠁⡝⢅⠁⡀⠈⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠘⠁⣰⠁⡀⠀⡀⠘⠁⠀⠙⠀⢠⠀⠘⡄⠸⠄⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠈⡁⢈⢊⠄⢋⠈⠈⠂⠁⠀⠁⠀⠀⠀⠀⢒⡀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠋⣸⠁⠸⠁⢀⠀⡄⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠦⠑
⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡞⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣤⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠛⢉⣀⡀⢆⠈⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠣⠀⢿⠀⠀⠈⠀⣴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡤⠬⣻⡾⠷⠆⠈⠉⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⢄⠀⢸⠀⠘⠀⡼⠁⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡔⢡⠎⡿⡙⠂⠲⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⡀⢀⡠⠀⠀⠂⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠈⠀⠘⢀⡇⠃⢠⠀⠁⠀⠀⠀⠀⠀⠈⠛⠛⢋⡁⠀⠠⢍⡾⢄⡒⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠈⠘⠆⠁⠀⠂⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠈⠉⢀⣠⠖⠁⠀⠁⡀⠀⢠⡀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠐⢃⡀⠐⠂⠀⠈⠁⠀⣴⠃⠀⣿⠀⠀⠓⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠐⠀⠈⠀⠀⠤⠈⠓⠀⠀⠀⠀⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠀⠊⡀⠀⠀⠀⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠡⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢈⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠃

⠀⠀⠀⠀⡀⠀⠀⡀⠀⣀⠀⠀⡀
⠀⠀⢀⡾⠙⣄⢿⣿⣷⣶⣶⡤⠠⠥
⠀⣠⠎⠀⠀⠈⢿⣿⣿⣿⣿⣇⢀⡤⡄
⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⡀
⠀⠀⠀⢀⠀⠀⠀⢈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⡀⠈⠋⠉⠀⠀⠄⠂⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⡟⢺⡟⠀⠌
⠀⠠⡀⠀⠀⠀⢸⠀⠀⠀⢤⡀⠀⢨⡄⢠⡄⠼⠀⠀⠂⢀⠆⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣠⣄⡼⢀⣿⣿⣦⡄
⢠⠦⠁⠀⠀⢀⣹⠀⠀⢐⡋⠀⢀⣿⡷⢃⣀⠐⠀⠀⠈⠁⠀⠀⣺⣟⠁⠀⠀⠀⠀⠀⠈⠛⠛⣧⣾⣻⣿⡟⠄
⠀⠀⣀⡤⠔⠊⠻⢦⠀⠀⢹⡆⢠⢬⡅⠀⢈⡇⠀⣶⠀⠀⠀⢪⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⣿⠒
⠀⣈⠍⠀⠀⠀⠀⠀⠀⠂⣼⡇⢰⣌⣿⠀⢘⠓⠀⢨⡅⠀⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⢠⡽⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⣞⢻⠁⠀⠸⠀⠈⢛⡅⣀⢹⣿⢛⣷⣿⣏⠀⠀⠀⠀⠀⢀⡀⡠⠀⠀⠀⡹
⠸⠀⠸⣷⣞⡿⠆⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⢘⣼⡇⢡⠀⡀⡀⠈⣿⣿⡄⠄⠠⠀⢀⠘⠤⠷⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⢰⣾⣿⣷⠀⢀⠀⠀⠈⢫⣵⣾⣦⣷⣷⣟⣿⣿⣷⠄⠀⠠⠿⢿⠂⠀⠀⠀⠀⠀⢠
⠰⣶⣷⣄⣀⠀⠀⠀⠇⡀⠈⣿⡿⠙⠀⠈⠷⣾⣠⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣻⠀⠀⣴⣿⣿⣦⣀⡀⠀⠀⠈
⢰⣶⣤⣭⣿⡏⣵⣤⣀⣥⣀⣙⣄⣀⡠⠤⠤⠀⢻⣿⠛⢻⣿⣿⡿⣿⣿⡿⣿⣿⡀⣴⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠉⠉⠛⠿⠿⠶⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠛⠋⠀⢀⢝⠂⢾⣇⣀⠈⠉⠉⠿⠿⠿⠿⠿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣭⣻⣿⣾⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡀⠛⢩⣿⣿⣿⣿⣅⣀⣶⣤⢶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡼⣿⢿⣿⠿⣾⣯⣿⠿⣷⣾⢟⣉⣯⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠫⣼⣛⠈⣭⣽⣷⣴⣿⣿⢛⡭⣡⡴⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⢘⠀⠰⣷⢏⣀⡴⡿⣦⣽⣿⣿⣿⣹⣿⣿⣿⣿⣟⣩⣭⠝⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠲⣿⠀⣰⣷⠉⣩⡄⠉⡇⣿⣿⣿⣿⣿⣿⣯⣟⡻⠟⢹⡏⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⠀⠀⢰⣿⣄⣿⡟⠉⠉⠿⣤⣷⣿⣿⣿⣿⣟⡙⠿⠋⠁⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣴⣤⣶⣾⣿⣿⡿⠃⢻⣏⣹⡿⠁⣽⣿⣿⢿⣿⣿⣶⢶⣾⣧⣴⣾⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣻⢹⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣄⣬⣁⣀⡶⢹⠉⣺⣿⣿⣿⣿⣟⣾⣵⢞⣛⠛⠛⠲⡷
⠀⠀⣀⣴⣦⡀⠀⠀⠁⠘⠊⣿⣿⣿⣿⣿⡇⠀⣰⣿⣄⠚⠹⠙⢷⣾⣴⣿⣿⣿⣿⣿⣯⣤⣶⣴⣶⣦⣤⣤⣤
⠀⣺⣿⣿⣿⣿⣦⣠⣤⠀⠀⠘⣿⣿⣿⣿⣷⠀⢥⣴⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⠿⢿⣉⠉⠀⠉
⠀⠹⣿⣿⣿⣿⣿⡉⢻⣄⣾⠿⣸⣿⣿⣿⣿⣯⣹⠤⣭⣅⠻⠇⠛⣻⣿⢿⣿⣿⣿⣀⢸⡀⢀⣓⠀⣴⣿⣿⣿⣦⢀⣴⣶⣤⣄⣀
⠀⠀⠈⠙⢻⣿⣿⣷⣾⣿⣿⢠⣿⣿⣿⣿⣿⠫⡔⠘⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⡄⣀⡴⣾⢿⣷⣼⣿⣿⡟⠁⢸⠉⠉⢻⣿⣿⣟⡥⠌⠿⠿⠿⣿⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣏⣨⣵⣿⣯⣾⣻⣿⣧⣤⣼⣤⣤⣾⣿⢿⡷⣚⢫⠄⠀⣠⣤⣤⣶⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⢃⡻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠭⣽⠓⠒⠀⠚⢀⡈⢈⣭⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⡏⢙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣽⠀⠀⢂⠁⠚⠛⠛⢉⡉⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⢿⠛⣿⠻⣤⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣼⣷⣆⣸⣿⣯⣤⣴⡿⣷⠀⠀⢰⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⣿⣿⠻⣿⣿⢠⠰⢾⣾⣿⠿⢟⡿⠛⢛⣿⣿⢿⠿⢿⣯⣿⣿⣿⡿⠛⠉⢩⠟⠛⠙⠀⢭⢤⠀⢸⣿⣿⢿⣿⣇
⠀⠀⠀⠀⠀⣿⡟⣿⣿⠀⠀⣿⡏⠀⢻⣧⣼⡞⢉⠊⠀⠀⣯⠀⠀⢨⠟⠇⠸⢀⡜⠉⠙⣟⡿⠇⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⢸⣿⣷⢸⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣇⣿⡇⠀⠺⣿⣇⠀⢿⣿⡈⠁⢠⠀⠀⠀⣿⠐⠂⢹⠖⠒⠂⢸⡄⠀⠀⠸⠇⠀⠀⠀⣸⠀⠀⢀⠄⠉⠀⠀⠚⣿⡟⠘⠿⣿⡗
⠀⠀⠀⠀⠀⠛⠛⣿⢿⣦⠀⠹⠷⠀⠀⠹⠧⠀⠀⠀⠀⠀⠛⠀⠀⢸⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠃⢠⣾⡿⠟
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⢸⡅⠀⢠⣄⣤⡄⣤⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠏⡌⢻⣤⣀⡀
⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡑⠶⣴⣿⡤⠖⣩⡟
⠀⠀⠀⢸⠀⠀⠀⢲⠀⢻⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠞⠛⢧⢸⡏
⠀⠀⠀⢸⠀⠀⠀⢸⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⢾⣿⠶⢼⠇
⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣼⣛
⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⢀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣷⡆⢻⣦⡙⠻
⠀⠀⠀⠈⠙⠿⣿⣶⣶⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⢠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣠⣿⣧⣿⣿⣷⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠀⠈⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣾⣿⢡⣶⣮⢻⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⡤⠀⠀⣤⠶⠂
⠀⠀⠀⠀⠀⢻⣿⣮⣛⣫⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠛⢉⣏⠈⠃⢤⣄
⠀⠀⠀⠀⠀⢠⣤⣄⣰⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠙⠉⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⡿⠿⢿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⠀⠀⠈⠃⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠫⡐⠄⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⠤⣤⣴⣶⣶⠦
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣤⣶⠀⠉⠒⠁⠀⠰⠚⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠸⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⢸⡆⠀⠀⢀⠁⠀⠀⠀⠀⡆⡆⣰⢰⠰⡆⠐⢰⠀⡆⠀⠀⡀⠁⢠⠀⠑⠂⠀⠀⠀⣤⠀⠀⣠⣶
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⠏⠸⠁⠃⠨⠀⠃⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣆⠰⠀⡇⡖⣖⣰⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠃⠃⠇⠛⠏⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠀⠀⢀⣤⣁⣶⡀⠀⣰⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⢀⠤⢠⠀⢀⠠⠄
⠀⠀⠠⠀⠀⠀⢾⣿⡗⠀⠀⠀⠀⡀⠘⠿⢿⠟⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⡄⠄
⠀⠀⢿⠓⠀⠀⠀⠉⠀⠀⠀⠀⢴⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⡏⡉⠀⠀⢠⠂
⠀⢸⣼⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠄⠀⠀⢀⢀⠀⢠⣷⠁⠀⠀⠸⡀⣀⡤⣤
⠀⠘⠷⠿⠀⠀⠞⠃⠀⡀⠈⠂⠀⠀⠄⠀⠀⠀⠀⢰⣿⠂⠘⠇⠀⢄⠀⠰⣭⣾⣹⡿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⢠⢾⡟⠀⠀⠀⡶⢶⠀⠀⠈⠛⠉⢠⠀⢢⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⢀⣟⡿⠁⠀⠀⠀⣿⡜⡆⠀⠀⠀⠀⡇⠀⡉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠀⠐⠂⣖⡡⠀⠀⠒⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠈⠱⡀⢄⡁⠀⠇⢳⣧⣴⣦⣖⣲⡄⢰⡄⠀⣁⠉⠄⠶⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⡑⠔⣌⣄⣀⣵⡴⠿⠟⠛⠛⠋⠉⠉⠙⠛⠛⠻⠷⢾⣼⣞⣰⡕⠡⠃⢀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠈⠂⢢⣑⣮⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣅⣠⡂⢢⠔⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠑⢦⣽⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡡⣮⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠜⠫⢴⣴⠟⠁⠀⠀⢀⡤⠶⠒⠲⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠈⠻⣿⣠⡎⡠⢃⡄
⠀⠀⠀⠀⠀⠀⠀⢍⡁⠢⢤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠃⠀⣠⣀⣀⠀⢀⣿⡄⣴⠃⠀⣘⣿⣅⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡟⠁⠉⠉⠑⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠉⠀⠀⠀⠀⠀⠈⠙⢷⣤⣿⣿⣿⣶⣿⣿⠋⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣠⣿⣿⣿⣿⣿⣟⣿⣿⣦⣈⣉⣉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢩⣿⡏⢹⣿⠈⢳⡍⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠛⢁⡬⠋⡀⠀⢳⡄⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⣆⣿⣴⣿⣃⣀⠀⣿⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣯⣅⠀⢸⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠰⠿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⢿⣿⣿⣿⡿⠯⠉⠀⢸⣇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⡏⠈⠿⠈⢦⡀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⣀⣀⣀⣀⣀⣀⡀⠀⠉⢛⠛⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠷⠶⠾⠟⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢠⣠⢤⢠⢀⡤⡄⠆⡴⠀⡦⠀⣠⢦⣤⢠⢀⣤⢰⠃⡴⢠⡄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠐⠂⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠔⠉⣀⡤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠐⠒⠒
⠀⠀⡇⠀⠊⡇⠀⣰⠴⢺⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡰⠀⠀⠉⠉⢉
⠀⠀⢴⠀⢀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⡀⢀⣠⡠⠆⣰⠁⠈⠀⠀⠀⠀⡼⠂⢤⠇⡀⢀⢀⡴⠁⠠⠄⠀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡰⡆⣳⡟⠸⠱⡤⠃⠀⠘⠂⠀⠀⠠⠁⠀⡞⠰⠀⢈⡏⣠⠞⡤⠒⣠⠊⠈⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⠤⢤⡄⢠⠀⡆⢸⠇⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠀⢞⡥⠂⡠⢆
⠀⠀⠀⠀⢰⣇⣀⣀⣀⠸⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠠⠉⠙⡖⢁⡤⠊⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠛⠋⠤
⠀⠀⠀⠀⣤⠂⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢀⡐⠈⠏⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⡰⠁⠀⠀⠀⢀⠘⢝⣂⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⠂⠍⠀⣵⣀⠀⠀⠀⠈⠿⠁⠀⠂⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠚⢀⣼⣿⣿⣿⣦⣄⣠⠂⠣⡈⡴⠑⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⠀⡀⢄⠔⠥⠂⠰⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠑⠢⡀⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⢠⠀⠀⠂⠀⠀⠹⠤⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠺⠟⣿⡀⠘⡟⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣐⠀⠈⠶⢤⠢⡀⠀⠆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢸⠇⠤⡉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠉⠓⢁⣀⣘⡆⠀⠘⢀⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠀⠀⠉⠚⠠⠟⠀⠀⠟⠛⠉⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⠎⠉⢹⣿⡖⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢂⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⢁⠀⠀⠆⠀⢠⣤⠀⠀⡻⢃⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠁⠀⠀⠀⠈⠀⠀⢢⠀⡇⠀⣠⠀⠀⢀⠠⡀⠈⡄⠀⢦⠀⠀⠐⠶⠔⠁⠸⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⢊⠠⠀⠀⠂⢠⠀⠀⠀⠀⠀⢈⢢⠁⠞⠁⠀⢀⠌⠀⢳⡀⠀⠀⠀⠇⠀⡌⢀⠐⠀⢀⡄⠀⢠⣃⣠
⠀⠀⣀⣤⣤⣤⠃⠀⢠⣼⣀⠇⠀⠀⠀⢀⠀⣮⡜⠀⠀⠀⠀⡌⠀⠀⠀⠱⡄⢀⡀⣀⠐⠀⣰⠀⠀⢀⢙⣈⢉⣴⠟
⠀⠘⠻⠿⠿⣧⣤⣶⣿⣿⣿⠀⠒⣻⣿⠁⢀⣿⡇⠀⠀⠀⣼⣿⣷⣦⡀⠀⣈⠃⡈⠀⡤⠊⠑⢄⣀⣤⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢠⣿⣷⠀⢾⣿⡇⠀⠀⢰⣿⣿⣿⣟⡁⠀⠀⠀⠀⠂⠋⡆⢠⠞⠛⢿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠻⢷⣾⠛⠇⠀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠴⠃⠘⠀⣠⠂⠈⡁⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠢⣄⠒⣾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠁⢀⠀⠈⠲⢤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡁⠰⠃⡡⠄⠀⠀⠀⠀⠑⣄⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣱⠀⠤⠄⠁⠀⠀⠀⠀⠀⠏⠠⠃

⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⢸⣿⣶⠶⠦⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠤⣤⡍⠀⢻⠀⠀⠀⣠⣄⡀
⠈⠛⠁⠀⠀⠀⠀⢠⣴⣿⠀⠀⠀⠀⠐⠞⢆⠀⠀⠀⠘⠀⠀⠀⠲⢶⡏⠉⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠠⠀⢤⠄⠀⢰⣘⣦⠀⠀⠀⠀⠀⠀⣤⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢐⣀
⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣠⣴⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠂⠀⠀⠉⣤⠆⠀⠀⠀⠀⠐⠩
⢸⣿⠀⠀⠐⠾⣿⣷⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄
⢠⣤⣠⡄⠀⠀⠻⠿⣦⣤⡄⠀⠀⠸⠏⠀⠀⢀⣀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢠⣌⠙⠃⡀⠀⠀⠀⠀⠀⠻⠠⣤⢀⣀⡀⠀⠘⠛⣷⣤⣦⠀⠀⠘⠛⠂⠀⠀⠀⠀⢀⠀⢠⡋⠇⠀⣴⡆⠀⠀⠀⠀⠀⣦
⠈⠛⣷⣶⡷⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⢀⡀⠀⣼⠏⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠿⠊⠗⠀⠱⠂⠀⣹⣇
⠀⠀⠉⠰⠿⠦⣀⣠⣄⣈⠛⡶⠀⡀⠀⡏⠉⠳⡽⣤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠁⢠⣤⣤⣥⡀⠀⠀⠀⠀⠀⢠
⢀⣄⣀⠀⠉⠛⠋⠀⠉⢻⣷⠤⠀⠃⠀⠓⠿⢷⡅⠀⣤⠀⠀⠀⢴⣶⡔⢿⡃⠙⠆⠈⣿⣦⠀⠛⠿⠟⢷⡄⠀⠀⠀⠀⠈
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡄⢀⡀⠀⠀⠀⠈⠇⠀⠉⡄⠀⠀⠀⠀⢻⣀⣷⣶⠀⠀⠁⢨⣷⢺⡀⠀⠠⠅
⢸⣿⣿⠀⠀⠶⡄⠀⢀⣾⣿⣧⣾⣳⣷⣄⡠⡤⠀⠀⢀⣵⠀⠀⣼⣿⣭⣿⣿⣷⣴⡗⢠⡄⠃⠘⢳⡆⠐⢶⡀⠀⠀⠀⢀
⢸⣿⣿⡀⠀⢰⣿⡿⠛⠛⢍⠛⠿⣿⠛⠻⠿⠇⠀⠀⠼⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠻⠿⢤⡟⠃⠀⠀⣴⡟
⠘⠛⠋⠁⠀⠀⠈⠃⠀⠀⢘⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⠿⠋⠀⠀⠈⠛⠛⢿⡄⢠⡀⠀⠙⢧⡀⠀⢀⠈⣿⣷
⢰⣶⣶⣶⣤⡄⠀⠲⣄⣀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣀⣤⠑⠀⢀⡀⠸⢃⣿⣷⡄⠀⢸⣇⠀⠿⠀⠻⢿
⢸⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠈⠰⡾⢭⣽⢷⡄⠀⠂⠀⣼⣿⣿⣿⣶⣌⢿⠀⠀⠀⠀⠈
⠘⢿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⡜⠁⣠⣍⡈⠙⠟⢡⡄⣨⣿⣿⣶⡶⡀⠀⣀
⠀⠀⠈⠉⠉⣿⣿⡟⠀⠀⠹⠷⠶⠶⠈⣽⣿⣿⣿⡟⣹⠟⠋⠹⠀⠀⠀⠀⠀⠛⠏⠉⠙⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⢈
⠀⡤⢠⡤⠀⠙⠋⠁⠀⢀⣀⠀⢀⠀⠠⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⣀⣤⡉⢛⠿⣿⣿⣿⣇
⢰⣇⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⣷⣶⡿⠛⠓⠒⠀⠀⢁⢀⣤⡀⣀⡀⠐⠀⠀⠀⠀⠀⠿⠟⢡⣿⣄⠠⣤⣠⣾⣿⣶⠶
⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⢿⠃⠀⠀⢠⡏⠙⢿⠟⣴⣿⠋⠙⠞⠀⣀⣤⣤⡀⠀⠀⢺⣟⣿⠀⢿⠿⣿⣿⢀⣠
⢀⡌⠙⢿⡄⠀⠀⠀⠀⠀⠸⢿⣧⠀⠸⠇⠀⠀⠘⠃⠀⠘⠀⠉⡈⠁⣀⣴⣶⣿⡿⠀⣧⢀⣴⣿⣿⢿⣄⣴⣾⣿⣿⣿⣿
⢠⣶⣶⣿⣧⠀⢀⣀⠀⠀⠀⣿⡟⠀⢀⣀⣰⠶⢿⣶⣄⣤⣶⠀⢿⣿⠟⢃⣿⣿⣷⣾⣿⠁⣸⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿
⢸⣿⣿⢿⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠄⠨⢿⣿⣿⣧⣾⡿⣤⠈⠻⣿⣿⠶⣤⡄⠘⢦⠤⡼⠤⠿⠿⠿⡿⠻⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⣸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣆⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢳⣹⡀⠀⠀⢲⣷⣗⠀⠀⢸⢡⡇⠀⠀⣴⡆⠀⠀⠀⢀⡴⢺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠏⠀⠀⠀⠀⠀⠀⢳⣷⠀⠀⠈⠉⠀⠀⠀⣾⣸⠀⠀⢰⠟⠁⠀⢀⡴⣫⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡢⣄⠀⠀⠀⠀⢻⣧⠀⠀⣤⡀⠀⠀⣯⠇⠀⠀⠀⠀⠀⣠⣮⠞⠁⠀⠀⠀⠀⣠⣖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢷⡄⠀⠀⠀⠻⣆⠀⢧⢳⠀⢰⡿⠀⣠⡆⠀⢠⡾⠋⠁⠀⣠⣄⠀⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠹⣆⠘⣾⡀⢸⠇⢰⡷⠃⠴⠋⠀⠀⠀⠐⢿⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠮⢭⣓⣲⠤⣄⣀⡀⠘⠦⣙⣦⡉⠀⠘⠃⠈⠀⠚⠁⠀⢀⣤⣾⠟⠀⠀⣀⣀⡤⠤⢶⣒⣛⣛⡭⠷
⠀⠀⠀⠀⠀⣤⣴⣒⣦⡤⠀⠀⠀⢠⡤⢭⣉⡙⠛⠻⠷⢶⣤⣍⡓⠀⠀⠀⠀⠀⠀⠀⠚⠋⣭⠴⠶⠿⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢒⣺⠽⠟⠛⠉⠀⢀⣤⠆⠀⠀⠀⠀⢀⡀⠀⣤⡀⠉⠑⠒⠋⠀⢰⣿⣗⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⣉⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⣖⡽⠁⣠⠆⠀⢠⠀⠈⣷⡀⠈⠻⡷⣄⠀⠀⠀⠀⠉⠀⠀⠉⠻⠭⣓⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣴⣴⠄⠀⠉⢠⣾⠃⠀⠀⢸⡆⠀⠻⡇⠀⠀⠙⢮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡷⠀⠀⠀⠀⠟⠋⠁⢀⣴⡿⠁⢀⣿⠀⠈⣷⠀⠀⣴⣶⡄⠀⠀⠙⢦⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣴⡾⠃⠀⠀⣠⢯⠞⠀⠀⡼⡟⠀⠀⣿⡆⠀⠙⠛⠁⠀⠀⠀⠀⠙⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠞⠀⠀⠀⣰⡷⠃⠀⠀⢀⣧⠇⠀⠀⢻⣧⠀⠀⠀⢰⡄⠀⠀⠀⠀⠈⠳⢤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣿⡄⠀⠀⠈⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠘⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⢀⠀⠄⠦⣄⣀⢀⣀
⠀⠀⠀⠀⠀⢀⠜⠉⠁⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⡀⠈⠢⠀⠉⠑⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠞⠁⢀⠐⠀⠀⠀⢀⠁⠀⠀⢱⡀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⡀⢀⠔⠈⠀⠂⠀⠐⠁⠀⠀⠀⠰⠃⠀⠀⠀⠀⢡⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠷⠀⠀⠀⠀⠀⠀⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶⠀⠁⡂⠈⠄⠀⠀⠀⠀⢠⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠈⢀⠠⠀⠀⠈⢀⠀⠀⠀⠀⠁⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⠀⠀⠀⠀⠑⢄⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⣠⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠢⡆⠀⠀⠀⠀⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⣤⠠⠐⠀⠹⢍⠈⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣦⡀⣄⠀⠀⠡⡀⠙⢆⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠱⠈⠣⡠⠀⠘⣤⡄⠀⣄⠰⣅⠀⠀⠀⢀⣀⢀⣀⣀⠀⠀⠀⠀⢠⣥⣤⣀⣠⣀⣄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠈⠂⡀⠋⠀⠑⠐⢌⠪⡠⢀⠚⠴⢬⣑⣘⠂⣀⣠⠽⣈⣠⡤⣤⠤⢤⠀⢈⣿⢏⠔⠉⠋⠻⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠈⢁⠀⠀⠀⠀⡔⣰⠣⣀⠤⢀⣨⠴⠛⡉⣄⠀⠆⠀⣀⣀⠀⠀⠀⣸⡟⠁⠊⣄⠀⣄⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠁⠀⡆⠀⠀⣀⡴⠘⡋⠄⢞⠉⡠⡐⠅⠊⠁⠀⡤⣼⠉⠈⣳⠀⢀⣿⡆⢀⡨⠬⠛⡩⣄⣴⡏
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠠⡔⠁⠀⠎⠁⠀⠀⠀⠀⠢⡙⢀⠀⢠⠀⠀⠀⠠⠞⠓⠘⠛⢠⣷⡟⢻⡁⠀⠄⣀⣤⢴⣿⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠈⠊⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡂⢑⢠⡶⠇⠉⠀⣸⡟⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡛⣛⠧⢤⣤⣄⣈⣿⠁⠀⠠⠄⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠁⠀⠀⠀⠀⠔⠉⠀⠐⢄⠉⠀⠐⠒⠒⠂⠀⠈⢀⠠⠁⠀⠁⡺⢀⠈⠉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⢀⡤⢠⡄⢰⣦⠄⣄⢰⣧⠄⡄⣤⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⡇⢸⣇⣾⡇⣸⣏⢀⠏⢸⡇⠴⠃⠻⠷⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⠁⠁⠘⠛⠀⣿⠀⠀⢸⡇⠀⠀⢀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠈⢁⡀⠀⠦⠰⠃
⠀⠀⠀⠀⠀⠀⣠⢾⡏⠉⣳⡄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⠀⢠⡷⠁⢀⡀⠀⠐⠋⠉⠓⣲⠗⠀⢐⠒⠂
⠀⠀⠀⠀⠀⠀⠁⢸⣿⣠⠟⠸⠯⣴⠄⣴⠏⠗⣾⠁⢀⣿⠀⣠⠖⣿⠀⣴⠏⠜⢰⢀⠞⣽⠀⣿⠀⢰⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠼⣿⡅⠀⠀⠀⢿⡠⢿⣄⡰⠉⣷⡄⢿⡴⢿⠔⣿⡴⠿⣀⠔⢻⡏⢰⡏⣰⡟⢠⠎⢳⣔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠈⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠙⠁⢠⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢦⠀⡠⣠⡀⢠⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⡸⢸⠁⣿⡇⢸⣧⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠈⠉⠘⠃⠀⢠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣍⠂⢀⡴⠁⣀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡘⡆⠰⢋⡤⠶⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⡠⠤⠀⠈⢐⣂⣀⠀⠀⠀⢠⣤⣄⣛⠳⣄⠳⠀⠐⣫⠶⢂⣀⣤⣤⣀
⠀⠀⠀⠠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⠆⣿⠀⠀⠉⠖⡁⠀⠀⠠⡉⣀⠀⠀⠖⠒⠀⢀⣉⣑⠂⠳⠀⠞⣁⣤⡴⠆⠀⠀⠁
⠀⠀⠀⢀⣭⣭⣶⣤⣄⣀⣠⠆⠀⢠⢿⣡⣾⣷⣾⠏⠀⠀⠀⠘⡀⠇⠆⠃⠉⠈⠀⣠⠔⣂⣠⡬⠭⠭⠉⠀⠀⠈⢁⣐⣒⠶⢤⣬⡑⠦
⠀⠀⠀⣿⣻⣿⣿⣧⠞⠋⠁⠀⠀⠀⠀⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠘⡋⠁⣠⠴⢋⡥⠀⠀⠀⠠⣀⠉⡙⠓⠈⠉
⠀⠀⢰⣿⣿⣥⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢇⠀⢠⠎⠀⢘⠁⣠⠏⠀⡆⢸⡈⣆⠈⢳⡌⠳⣤⡀
⠀⠀⠀⠛⠿⢻⣿⠉⣿⣇⠀⠀⠀⠀⠀⣾⡟⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⠀⠀⠀⣰⠃⣴⠏⡰⢰⡇⢸⡇⢸⡆⢠⠛⠀⠈⠃
⠀⠀⠀⠀⣴⣿⠋⠀⣾⡟⠀⠀⠀⠀⠀⣿⣇⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠉⢀⡇⠘⠃⢸⡇⠈⠃⡀⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠂⢷⡀
⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣾⣿⡀⠀⠀⣠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢸⡇⢾⣿⡇⠀⠀⠀⠀⣤⣦⡀⠀⣀⡀⠀⠀⠀⠙⢷⣄⠀⢿⣿⠇⣠⡴⠋⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠈⢷⣶⣿⣦⣰⠇⠀⡀⠛⠟⣱⣾⣏⢻⡆⠀⠀⠀⠀⠉⢻⣾⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⢸⣿⣿⡏⠁⠀⠀⠻⠶⠞⠻⣿⣿⣧⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⣿⠀⣄
⠀⠀⠀⠀⢸⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢹⠀⣿
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣼⡟⠁⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠐⠢⢄⠀⠁⠸⠀⠀⠀⠀⢀⣭⠇⠀⠀⠀⢸⡄⣿
⠀⠀⠀⢠⣿⠇⢸⣿⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣄⡉⠂⠀⠆⠀⠀⠀⠲⠄⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠈⢑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⠃⣿
⠀⠀⣤⡀⠀⠀⣠⣄⠀⣀⣤⠀⠀⠀⠀⠀⣀⣀⠸⡆⠀⠀⠀⠀⣀⡀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⣀⠀⠀⠀⠀⢸⠀⡏
⠀⠀⠈⠙⢶⡜⢿⡿⠃⣨⡟⠀⠀⠀⠀⠘⢿⡿⢠⡇⠀⠀⠀⠸⣿⡿⠙⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⢺⣿⡗⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⢹⣿⣿⡟⠉⠀⠀⠀⠀⢀⡴⣾⣿⣿⠀⠀⠀⠀⠀⣴⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⣿⣦⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠠⡟⢰⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣇⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠁⡏
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡧⠀⠀⠀⠀⠈⠻⣿⡋⠉⠙⠿⠂⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣿⠹⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⡆⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣰⣄⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣟⠡⡨⣻⣦⣀
⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣾⠁⣄⢹⢊⠂⡏⣰⣉⣷⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⢿⣿⡿⣛⡶⠲⠶⣶⣶⠶⡛⡟⠋⣽⡵⣎⢿⣧⡈⢓⡄⢠⠚⢁⣼⡿⣱⢮⣯⠙⢛⣛⠶⣶⣶⠶⠖⢶⣛⣿⣿⡿
⠀⠀⠀⠀⠈⢿⣷⢳⣷⠄⣈⠃⠹⠀⢸⣥⡾⢹⣇⣸⢄⣉⡻⢶⣄⣠⡶⢟⣉⢰⣇⣸⡏⢷⣤⠇⠀⠇⠼⣁⠠⣾⡞⣾⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⠟⣿⣷⣿⣕⢄⠙⠾⣄⣬⠷⠁⣿⣿⡗⠀⠹⠯⠀⢺⣿⣿⡈⢾⣅⣠⠓⠏⠠⣪⣷⣾⣿⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣾⣯⢏⠹⣿⡆⠄⣉⠂⠀⠀⣀⠻⣿⡇⣀⢀⡀⣀⢸⣿⠟⢀⠀⠈⠀⣍⠰⢰⡿⠏⡹⣽⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠀⣹⣽⠈⠛⣰⣿⢀⡤⢴⢏⠳⣽⢏⡹⣯⠞⡹⡦⢤⡀⣿⣆⠛⠀⣽⣇⠀⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⢽⠀⠀⢱⠁⡈⠒⠁⣾⢰⠿⠆⠰⠿⡆⣷⠈⠒⢁⠈⡏⠀⠀⡏⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠈⢸⠣⣤⣼⣿⣾⠀⠀⠀⠀⡧⣿⣧⣤⠼⡆⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢼⣿⣙⡏⢉⣿⣧⡀⢀⣼⣿⡉⢹⣋⣿⡧⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠳⠿⠿⠟⠓⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠚⢻⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣞⠁⡠⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠔⣾⣿⡿⠟⠁⠶⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡼⠋⠉⣠⣤⣵⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣴⣶⣿⢹⣭⢀⣴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣻⣿⣁⣴⣿⣈⣠⠔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠁⡴⠋⠈⣿⣿⣿⠛⢁⣴⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠷⠦⠺⠞⠋⠉⣉⣥⡟⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⡴⢶⡶⠁⢸⣟⠛⣏⡀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠟⠀⠘⠳⠆⠀⠿⠂⠀⠙⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠘⠁⠀⠀⣠⡄⠀⠀⢰⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠀⠀⣴⡶⠈⠀⢀⠀⢸⡀⠀⠀⠀⠀⠀⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⣠⣼⡿⠁⠀⠀⢸⡄⣸⠅⠈⣀⣠⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣶⠂⠓⠈⠉⠛⠃⠠⢼⡶⠿⠋⠀⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⠀⣵⣿⣡⣦⣤⣤⡤⠀⢠⣟⡹⢂⡤⣴⡶⢤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣻⠏⢡⣿⡿⠁⠀⠠⠋⠉⠀⠀⠀⠉⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⢠⡄⠉⠉⠛⠁⠠⣿⠟⠀⣀⠀⠱⠆⠀⠀⠀⠈⠒⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠈⠓⠀⠀⠀⠀⣾⢧⡴⠑⠈⠓⠂⠀⠀⠈⠀⠀⠀⠀⠠⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⣤⣃⠉⡀⠈⠀⢉⠘⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣦⠀⠀⠆⢰⡇⠀⠿⣽⠷⣄⠰⠀⠹⢋⠐⣤⠠⠐⢁⡠⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⣀⠠⠀⢀⠜⠁⡀⠀⠀⢰⣧⡠⢈⡀⠘⠒⢉⣀⠐⠋⠀⠀⠀⠄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠐⠄⠀⠘⠲⣧⠤⠶⠟⠂⠰⠓⠆⠷⠺⠿⠟⠋⠁⣠⡴⠎⠃⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠸⠖⠂⠤⠠⡤⠠⠰⠄⢀⠀⣤⣤⠤⠄⠂⠖⣹⣧⣌⠾⠃⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣿⠰⣿⣿⠃⠀⠀⠀⣀⣀⠁⠉⠠⠀⠀⠙⢠⡎⠀⢀⠰⠄⠛⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠄⠀⠀⠀⡀⣸⠿⠶⣶⡊⠈⠀⢛⡿⠃⠀⠀⢠⠄⠹⢧⠀⠀⠑⢲⡀⠀⠀⠀⠒⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠷⠀⣴⡾⠋⠀⠀⠀⡞⣴⣲⢠⣁⡷⠀⠀⠀⢠⠀⠀⠀⠳⣀⠀⡄⠀⠀⡀⣈⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠠⠄⢁⢿⣿⣿⣿⠇⠠⠤⡄⠡⠀⠄⡀⠀⠩⡄⠀⠀⠀⠑⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⡘⠀⠀⠀⠐⠠⠂⠀⢹⣿⢻⣿⠀⠰⠆⠛⠀⠀⠘⠇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣷⣿⣿⣷⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⢰⣿⣇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⢰⣏⣽⢆⠀⣿⣿⡆⢸⢀⡇⢀⣀⡾⠁⠀⠀⢢⠀⠀⣼⣿⣿⣿⣿⣀⣤⠤⠀⠀⠸⣿⡿⠀⠔⣈⣀⡪⣄⢀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⠐⠆⠀⠚⠊⠁⢀⠈⠻⠇⠈⢼⠃⠘⠉⠀⠀⠀⠀⠚⠂⠀⠈⠙⠛⠿⠿⠿⠀⠀⠀⠄⠀⠀⠁⠈⢸⣝⣷⠿⢾⡆⠆
⠀⠀⠀⠀⠀⠀⠸⣾⣿⡇⠀⣰⡦⠸⠿⠿⠯⠿⣤⣄⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠄⠀⢷⣄⣀⣠⠄⠐⠜⢿⣶⠗⠾⢃⠂
⠀⠀⠀⠀⠀⠀⡈⠙⠛⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡠⠁⡀⡀⠀⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠰⣤⣦⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⡄⠘⢤⣄⣄⡤⢀⠐⠆⢤⡀⢀⠀⡙⠟⠁⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠒⣿
⠀⠀⠀⠀⣛⣿⣿⡿⠁⠠⠆⠀⠀⠀⠙⢖⠀⠁⠀⠁⢄⠀⠠⢤⡈⠛⠀⢠⠉⣉⢳⣈⠱⣄⡀⣀⠀⠹⠋⠀⠀⠀⣀⠐⣆⠐⡄⠐⡄⢤⡀⠀⠋
⠀⠀⠀⠈⠉⠙⠋⢀⡀⠐⠀⢠⣴⡀⠀⠈⠀⣰⣃⠀⠸⠀⠀⡄⠉⠋⠓⠀⠃⠘⢃⣻⠘⣅⠂⣜⢂⠀⠀⠄⢒⢀⡉⠀⠱⠀⠰⠆⠰⠆⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠠⠛⡟⣦⣤⣴⠏⢙⣁⡀⠀⠀⠀⠛⡜⣧⠷⣦⡼⠿⠿⢒⠋⠁⠀⢸⠀⠀⠈⠽⠆⢰⡀⠀⠂⠐⣲⠀⠲⠈⢟⡅⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣷⡀⠰⣾⡧⠖⠽⠻⣗⠤⠻⠟⠀⠀⠀⠀⠙⠋⠞⠀⠶⠀⢤⠀⢦⠉⠀⠀⢀⠤⠀⠀⠻⣶⣭⣯⣤⣻⣄⣝⣧⣶⡶⠋⣀⢾⣸⡅
⠀⠀⠀⠀⠀⠀⠸⠛⠛⠇⠀⢈⣀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢉⣁⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⠦⠦⠀⠀⢀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠰⣎⣙⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢰⣿⣿⣿⠀⠴⠖⠀⢤⣾⠀⢠⣤⡄⠁⠀⠆⠘⠇⠙⠂⠉⠀⠉⠈⠉⢀⠀⠀⠂⡈⠀⠉⠐⠂⠠⠂⡀⠀⠀⢶⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠾⡿⠂⢸⣿⣿⣿⠀⠀⠀⠀⠋⠛⠆⠀⠈⠑⠀⠀⢠⣴⣶⠄⠀⣠⣤⣶⣶⣦⡈⠀⠀⠀⠆⠀⠁⠈⠀⠆⢠⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⠈⠻⡿⢛⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣠⡄⢾⣿⣿⣿⡿⠟⠁⡀⠐⠠⠀⠀⠀⡅⠀⠀⠰⠀⠸⡧⢯⣍⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⢀⠉⠀⠀⢎⣱⠀⠀⡀⠀⠀⠈⠐⠣⣠⠇⠀⠀⠘⠗
⠀⠀⠀⠀⠠⠀⠊⠀⠃⠃⠀⠀⠀⠁⡄⡄⠀⠀⠀⠘⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠈⠀⠠⠀⠂⠀⠀⣀
⠀⠀⠀⠀⠠⣲⠀⠀⠀⠀⠀⠁⠂⢄⠀⠑⠀⠀⠀⠠⠠⠀⠀⠐⠈⠀⢠⠀⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠰⠔⠹⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⢀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠂⠈⠀⠀⠀⠟⠀⢀⠀⢠⢢⠀⠓⠲⠁
⠀⠀⠀⢒⠊⠢⠀⠁⠂⡀⠠⠀⠐⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⡈⠉⠀⠒⠀⠄
⠀⠀⠀⠘⠈⠃⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⢔⠆⠀⠀⢁⠢⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠣⠃⡀⠁⠀⠀⠀⠐⠰⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠰⠍⠆⠀⠀⢹⡤⠼⠁
⠀⠀⠀⠀⠀⢀⠁⡠⠀⠀⠔⢁⠐⠁⠀⠀⠀⠀⠐⠟⠀⢠⠀⠰⠭⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠮⠆⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⣩⢈⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠂⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢼⣥⡤⠀⠄⠀⠀⠀⠀⠀⠀⡀⣀⣠⡴⣄⣄⣄⣀
⠀⠀⠀⠀⠀⠀⢠⠞⢻⢱⣿⡟⢻⡄⠀⠀⣀⣴⣴⣶⣾⣿⣿⣿⡟⣿⣿⣿⣿⣷⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠇⠀⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡷⠄
⣀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⡇⣿⣿⣿⢿⢿⣿⠷⠙⠉⠉
⣼⡿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈
⠹⠀⠘⡆⠃⠀⠀⠀⠁⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⣀⠀⠀⢰⡀⠀⠀⠀⠰⣆⡀⠁⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡿⢻⣶⡆
⠀⠀⣃⠀⣔⠋⠉⡶⢀⡄⣴⡰⠉⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⣀⠀⠀⠀⠘⠀⠟⠃⠃
⠿⠂⠉⣀⠈⠛⢀⣱⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠃
⠀⠀⠉⠉⠀⠀⠈⠉⡐⠂⢀⣠⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠶⢶⣶⣶⣶⣶
⠀⠀⠀⠀⢰⣦⡀⠀⠟⠀⠀⠈⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠿
⠀⠀⠀⠀⢸⣿⡠⢻
⠀⠀⠀⠀⠀⠁⠙⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠸⣷⣄⢀⡀⠈⠙⠒⠶⠄⣀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣀⡀⠀⠀⠀⠉⠛⠳⠶⢶⣄⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢤⣀⠀⠀⠀⠈⢱⡤