Therapist Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⠖⠛⠉⠉⠉⠉⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⣉⣩⣭⣉⡉⠛⠲⣄
⠀⠀⢀⡾⠁⠀⢴⣛⣿⢿⣥⣤⣤⣠⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣰⡿⠛⠉⠉⠉⠻⣷⡀⠈⢷⡀
⠀⠀⡾⠀⠠⣚⣿⢿⣿⣾⣧⣭⡁⢙⣿⡄⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢷
⠀⢰⡇⠀⢆⣹⣿⣿⣹⣿⣿⣿⣿⣿⣟⡕⠀⠸⠃⢀⡀⠤⠄⠀⠐⠒⠀⠠⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡆
⠀⢸⡇⠀⠀⠢⠛⣷⣿⣿⣿⣫⡟⣸⣿⣀⠠⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠤⠀⠀⢀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⣀⣴⠏⠀⠀⢸⡇
⠀⠈⡇⠀⠀⠐⠺⢣⡄⣤⣁⣈⡿⠛⠁⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠁⠒⠀⠀⠙⠿⠿⠿⠿⠛⠁⠀⠀⠀⢸⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠘⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠁⠀⠀⢷⠀⢀⠀⣠⢟⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢀⣾⠋⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣄⣧⢀⣏⠀⣯⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣿⡇⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠙⡟⢛⡦⠛⣆⢀⡔⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣀⣀⡀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢰⠀⠀⠀⠀⠃⢸⣧⠎⠙⠆⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⢈⠆⠀⠀⠀⢻⡄⠀⢀⡜⠁⠀⠀⢀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢳⡀⡼⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⠌⠳⢤⡄⠈⠀⠀⠀⠀⢷⡀⠀⠀⡇⢀⢄⠀⠀⠰⡂⠀⠒⠈⠀⣸⠃⠀⠀⢀⡾⠀⠀⠀⠀⢀⣀⣀⣹⣇⡀⠀⠀⡜⣾
⠀⠀⠀⠀⠀⠀⣠⠛⠛⠲⠦⣤⣔⣀⡀⠀⠈⠁⠐⢤⡖⠛⠒⣮⢠⠗⠋⠉⠐⡟⠛⠋⠋⠉⠉⠈⠀⠀⠀⣼⠁⠀⠀⠀⠡⢀⣀⣄⣀⣀⣀⢉⣶⢱⣿
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠢⣀⣤⡿⠋⠀⠀⠘⡇⠡⠀⠴⠚⣇⣀⣠⡤⠤⠤⠤⠤⠤⠼⠛⢲⡄⠀⠀⠀⠀⢹⢀⠀⣼⡇⠀⡟⡞
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠂⠀⠈⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⠉⢘⡇⢸⡀⡇⡇
⠀⠀⠀⠀⠀⠘⡇⠀⠀⡀⣿⣭⢭⠤⠭⠭⠽⡿⡟⢻⡀⠀⠀⢀⠁⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠙⣲⣤⣼⠀⢸⡇⣆⢷⣇⠹⡀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⢳⣷⣿⢸⠦⠤⠤⠾⡿⣷⣦⣷⣰⠀⢸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠀⢈⣿⡏⠙⠒⠚⠋⠉⠉⠉⠉⠉⢹⠁⡝⠉⠉⠛⣿⠶⠃
⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠯⢿⢸⠥⠬⠭⠬⡭⠅⠒⠚⡇⠀⠸⡄⠀⠀⠀⢠⠇⠀⠀⠀⠀⣼⠃⢻⠀⠒⠒⠒⢲⣖⡒⢲⣖⡿⢀⡷⠦⠤⣴⣯⢀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡄⢸⣸⠀⠀⠀⠀⡇⡇⠀⠀⣇⠀⣀⣇⠀⠀⠀⡼⠀⠀⠀⠀⢠⡟⠀⠀⢃⠀⠀⠀⢸⣒⡇⢩⣟⣟⠉⠑⠋⠉⠉⠓⠼⠂
⠀⠀⠀⠀⠀⠀⠈⠹⡏⠙⡇⠈⣿⠀⠀⠀⠀⢻⠇⠀⠀⢸⠇⣸⠁⠀⠀⢀⡇⠀⠀⠀⠀⢸⡷⠖⠂⠉⡀⠀⠀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠛⠠⢷⠀⡇⠀⠀⠀⠀⠘⠂⠀⠀⠘⠒⢻⡀⠀⠀⡼⠀⠀⠀⠀⠀⣿⠀⢶⣟⣋⣩⣤⣤⣤⣤⣤⠛⣤⡼⠒⣤⡤⢤⣀⣀⣀⣄
⠀⠀⠀⠀⢠⡔⠒⠁⣀⣀⣸⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠓⢦⡀⠈⣒⠤⣤⣀⣀⡇⠀⠐⢿⣹⠆⠀⣠⠞⣩⠴⠿⠥⠬⠶⣦⣍⡋⢍⡉⠹⣽⣢
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⡝⠛⠂⠉⠁⣀⣀⣈⣉⡇⠀⠀⠀⠀⠀⢸⢧⣞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⣮⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠿⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢏⡵

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠓⠀⣿⠛⣿⡆⢠⡾⠛⢻⣦⢰⣿⠀⢸⣷⠠⣿⠛⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⢻⣷⠀⣿⠻⣿⡀⢸⣧⡀⣸⡿⠸⣿⡀⣸⡏⢸⣿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠀⠈⠉⠀⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⡀⠀⣀⠀⢀⣀⣀⡀⢀⣀⣀⣀⠀⠀⢀⣀⠀⠀⣀⣀⣀⡀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠁⣿⣧⣤⣿⡇⢸⣯⣭⡅⢸⣿⣉⣿⠂⢀⣿⢻⡆⠀⣿⣏⣹⡷⠈⢿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⣿⠇⢸⣧⣤⡄⢸⡿⠙⢷⡄⣾⠟⠛⢿⡄⣿⠏⠉⠀⠀⠸⣿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣴⠞⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⠀⣀⡴⠏⠀⠀⢀⡿⣷⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⣿⠛⣯⡀⠀⠀⢀⡾⠁⣿⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⢀⣀⣿⣤⣼⡟⠛⠛⣻⣤⣴⣏⣀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠀⢀⡾⠋⠉⠁⠀⠀⢹⡛⢻⠏⠀⠀⠈⠉⠙⢦⡀⠀⠀⠀⠀⠈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⠀⠀⠀⡀⢸⡇⣿⠀⠀⠀⠀⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⣤⠼⣷⢸⡇⣿⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡿⠀⠷⣤⠟⢸⡇⢿⠀⠀⠀⠀⠀⣷⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⣴⠋⠙⣧⠰⠋⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣉⣉⣉⣉⣉⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠷⠄⠀⢀⣹⣤⣤⣟⡀⠀⠀⠾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠉⢉⣉⠉⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣾⠋⠁⠀⠀⠀⠉⢳⡀⠰⠏
⡀⣀⠀⠀⠀⠀⢠⡞⠁⠀⣴⣾⠉⡷⢶⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣷⠂⠀⠀⡇⢰⠀⠀⠀⠀⣶⢸⡇⠀⠐⣶⡟⠋
⠉⠙⡿⠛⣧⣴⠾⠗⣶⠾⡇⢸⠀⡇⢸⡇⠉⠙⢦⡀⣀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⡇⢸⠀⠀⠀⠀⣿⢸⡇⠀⠛⠉⠁
⠀⠀⡇⠀⡇⠀⠀⠀⣿⠘⡇⢸⠀⣿⢸⡇⢀⣀⠀⠙⣿⠈⡗⠀⠀⠀⠀⠀⠀⠀⣠⣴⢀⡄⠀⣇⣸⠀⠀⠀⠀⣿⣸⡇⢠⣀⢰⣄⡀
⠀⠀⡇⠀⡇⠀⠀⠀⣿⠐⠇⠈⠀⠁⢸⡇⣾⢹⡇⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠛⠉⠟⠋⠁⠀⠉⢻⡆⢸⡇⠀⡟⠉⠀⠀⠉⠻⠉⠙
⣀⣀⣧⣤⡿⣦⡀⠀⣿⠀⠀⠀⠀⠀⠘⠿⠋⣼⣃⣠⣿⠀⡷⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢸⡇⢸⡇⢰⡇
⠉⠉⠁⠀⠀⠈⠻⢦⣿⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠉⠛⠛⠷⠶⠆⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣧⠸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣀⣀⣀⣀⣠⡟⠁⠀⠀⠀⠀⠀⠐⢷⡀⠀⣠⡞⠁⠀⠀⣴⠶⣦⠀⠀⠀⢠⡶⢶⡄⠀⠀⠀⣠⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⣉⣉⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠋⠀⠀⠀⢘⣧⣀⣼⠀⠀⠀⢸⣄⣠⣟⠀⠀⠀⣿⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠉⠛⢶⠞⠋⠉⠉⠉⠻⣶⠛⠉⠉⠉⠙⠳
⣶⣶⣶⡶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾
⣿⣿⣟⣀⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠈⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢁⠀⠄⢠⠲⡀⣀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣆⠔⢺⠀⠆⠀⠀⠀⠉⡱⢀⠇
⠀⠀⢠⠊⡙⠁⠈⢆⠠⠂⠀⢀⠔⠀⢈⣵⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠐⠚⢋⠀⠀⠊⠘⠭⠍⣇⡤⠊⠀⡜
⠀⠀⠹⢀⢑⡢⣀⠈⢶⠉⠀⣺⣤⡎⢁⡎⠠⠐⠈⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡇⠉⠉⠀⠀⢰⠁
⠀⡠⠚⢅⠋⠀⠈⣳⠈⢦⣊⡽⠏⠚⠥⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠂⠓⠉⠀⢠⠖⢄⠀⠀⠀⠀⠀⠀⢀⠇
⡌⠀⡄⠀⠡⡰⡃⠒⡠⡄⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⠀⠀⠀⠀⠀⠀⠀⠦⣀⠜⠀⠀⣀⠀⠀⠀⡜
⠣⡀⠀⣀⡀⠑⠈⠀⠀⢡⠀⠀⠀⠀⣀⠠⡀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠠⠤⠥⡤⡐⢲⢀⡀⢀⠀⠀⠈⠢⠀⠘⠰⠊⠀⡸
⠀⠀⠀⠀⠙⡄⠘⢧⡖⠠⡄⠀⣠⡪⠷⠋⠁⡤⠀⠀⢸⠁⠀⠀⣱⣀⠀⠀⠠⠅⡎⠀⠀⠀⠈⢠⠧⢞⡰⠀⣄⢁⡀⢤⡴⠂⠈⠇⠀⢠⠃
⠀⠀⠀⠀⠀⠈⢆⠀⠀⣆⠤⣄⣉⠉⠘⠒⠋⠠⠤⢀⢷⠚⠀⢉⠝⠁⠀⠀⠀⢰⡄⠀⠀⠀⠀⢏⠀⢀⠇⣼⢭⣝⣑⠇⠀⡤⢀⡃⢀⠇
⠀⠀⠀⠀⠀⠀⠈⢣⠘⣧⡄⠀⠉⠊⡄⠐⠠⠤⠃⠀⠓⠀⠀⠀⠄⠰⡄⢀⢀⠀⣡⠆⠒⠠⠦⡀⢹⡔⣠⠷⢠⡤⢭⡴⠏⠄⠴⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢾⣦⡀⠀⠳⡀⠀⠀⠀⠀⡀⠄⠐⠀⣀⡤⣼⠉⢹⠀⠘⡄⠠⢤⣄⣈⠙⠧⡀⡰⠁⠄⠀⢣⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠂⠍⠓⠦⣤⣓⠂⠀⠉⢐⢄⠀⠀⠀⠀⢻⠀⠈⡆⠀⡇⠒⠺⢤⡌⢝⠓⠙⠃⠀⣀⠠⠇⠀⠀⢠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠲⠂⠤⢅⣉⠉⠟⡘⠋⠄⢀⠀⠀⠀⠈⡗⠒⣫⣄⠇⠀⠀⣴⣃⢈⡇⠀⡤⡸⠀⠠⠀⠀⠄⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠒⠠⠭⢐⡂⠄⠅⢐⠛⠒⠀⠀⢀⠔⠙⠊⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠠⢀⡠⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⠑⡀⢀⡴⠊⠉⠀⠀⠉⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⡔⠊⠉⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡠⢦⠀⠀⠀⠀⠀⢸⠖⠐⠤⡀⠀⠀⠀⢀⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⠄⠊⠀⠈⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⡹⠁⠀⡜
⠀⠀⠀⠀⠀⢸⢸⠀⢀⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⢨⠑⠆⠀⠀⠀⠀⠈⢆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠣⡔⡶
⠀⠀⠀⠀⠀⢸⠈⠶⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⢸⠀⠀⠀⠀⠀⠀⢑⣦⢠⢋⠀⠀⠀⠀⠀⠀⢀⠴⠜
⠀⠀⠀⠀⠀⠸⠀⡷⠀⠀⠀⡇⠀⢠⠎⠉⠉⠉⠹⠉⠉⢦⣆⠀⠀⠀⠀⡠⣞⠈⠏⠉⠉⢢⠀⠀⢀⠴⡁
⠀⠀⠀⠀⠀⡆⠀⠛⠀⠀⠀⠀⠐⠚⡄⠀⠀⠀⠸⡀⠀⠀⠛⠢⢄⣤⡾⠕⠁⠀⠀⠀⠀⠈⡗⢂⠏⠀⢸⠂⠤⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⢉⠛⢅⠀⠀⠀⠀⠈⠑⠒⠚⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢃⡀⠀⠈⠆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠃⠀⣼⠀⠀⠀⢸⢍⡓⢞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⢸⠀⠀⠟⠀⠀⠀⢸⠂⠽⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⣠⠔⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⣠⠔⠉
⠀⠀⠀⠀⠚⠀⢸⢸⠀⠀⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡄⠀⠀⠀⠀⡔⢣⠀⠀⠡⠀⠀⠀⢀⠴⠊⠁⡠⠔⠉
⠀⠀⠀⠀⡇⠀⡎⠀⡀⠀⠀⠀⡇⡘⠀⡇⠀⡠⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠀⠀⠀⡇⠀⠀⠀⢸⡃⠘⡀⠀⠀⢣⡠⠒⢁⡠⠔⠉
⠀⠀⠀⢀⠁⢠⠁⠀⡇⠀⠀⠀⣇⣇⡠⡇⠀⢁⢡⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⣠⡞⢈⠙⢆⡣⠂⠀⠙⡦⠔⢁⡤⠒⠁
⠀⠀⠀⢸⠀⡌⠀⠀⠃⠀⠀⠀⢉⢇⠀⡇⠀⠸⡀⣆⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠈⡄⠇⠘⢄⡯⠥⠀⢸⣖⣠⠖⢊⠤⠊⠉⢣
⠀⠀⠀⡆⢠⠁⠀⠀⢰⠀⠀⠀⢹⡞⢀⠃⠀⠀⢣⠘⡄⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⢡⠘⢄⣀⣙⣬⣥⠞⢋⡥⢾⡁⠀⠀⠀⠈
⠀⠀⢠⠁⡬⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⠀⠀⠀⠈⡆⠘⢄⠀⠀⠀⠀⠉⠐⠢⡄⠀⠸⠀⠀⠀⠀⠀⡦⠚⠁⠀⠀⠑⢄⡀⠀⡸
⠀⠀⡘⢀⠃⠀⠀⠀⠸⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠘⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⡆
⢀⠀⠀⠀⠀⠀⠐⣸⡟⠁⣐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠸⡄⠀⠀⠀⢰⣿⣿⣿⣀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⠐⠟⠀⠀⠀⠀⠈⠀⠀⠒⠤
⠀⠇⠀⠀⠀⣼⠻⠛⠟⡇⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢸⡀⠀⠀⣿⣶⣶⡶⠷⢘⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢘⠁⠀⠐⢿⣿⣿⣷⡷⠈⠉⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠺⣉⡑⠀⣀⠀⠄⠀⠀⠘⡀⣀⠀⠤⢄⣀
⠀⠈⡹⣿⣦⣠⣋⣛⣋⠁⠀⢠⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡏⠀⠐⣀⣀⢀⠸⠁⠄⠀⠠⠐⠂⠁
⠀⠀⠁⠸⣿⡗⠋⠙⢿⣇⢠⣿⠃⠀⠀⠀⠀⠘⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⡀⠀⠘⣧⠀⠀⡏⠁⠀⠀⣤⠠⠀⠂
⠀⠀⣷⠤⣹⡃⠀⠀⢀⣉⣉⡻⠿⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⠀⠀⠀⠀⢀⡀⡀⠀⣀⠀⠀⠀⠀⠀⢏⡒⠀⠠⠟⠠⠀⠐⠀⠉
⠀⠀⠉⠈⠉⠟⠛⠋⠙⠉⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠⢀⣀⠤⠄⠲⠖⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠖⠤⠆⠀⠀⠀⠖⠴⠤⠂⠰⠠⠄⠤⠤⠄⠂⠀⠰⠠⠤⠤⠤⠀⠤⠤⠀⠤⠄⠄⠰⠒⠀⠆⠤⠠⠤⠤
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠁⠀⠀⠉⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣦⡀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡇⠀⠀⢹⣿⣠⣶⣤⣤⣤⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣿
⠀⠀⠀⠀⣀⠀⠙⢷⣦⣴⡿⠃⠀⠀⠸⡿⠋⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣴⡾⠋⠀⣀
⠀⠀⢰⡿⠛⣿⣤⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⣿⠛⢿⡆
⠀⠀⢸⡇⠀⣿⡟⠁⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠈⢻⣿⠀⢸⡇
⠀⠀⢸⡇⠀⣿⡇⠀⣀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢸⣿⠀⠀⣀⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⣿⡇⠈⣿⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢸⣿⠀⢀⣿⠁⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⠹⠷⠶⠶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠶⠶⠶⠾⠏⠀⢸⣿⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⣿⡇⠀⠸⣷⣤⣤⣤⣤⣤⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣤⣤⣤⣤⣤⣾⠇⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⢿⣇⠀⠀⠈⠉⠉⠉⠉⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠉⠉⠉⠁⠀⠀⣸⡿⠀⢸⡇
⠀⠀⢸⣇⠀⠈⠻⠷⠶⠶⠶⠶⣶⡄⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢠⣶⠶⠶⠶⠶⠾⠟⠁⠀⣸⡇
⠀⠀⠈⢿⣦⣤⣤⣤⣤⣤⣤⣤⣽⣧⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣼⣯⣤⣤⣤⣤⣤⣤⣤⣴⡿⠁
⠀⠀⠀⠀⠈⠉⠉⣿⡏⠉⢹⡏⠉⣿⡄⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⣿⠉⢹⡏⠉⢹⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⡇⠀⢹⣧⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣼⡏⠀⢸⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣿⡇⠀⠀⣿⡄⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢠⣿⠀⠀⢸⣿⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⡃⠀⠀⢸⣷⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣾⡇⠀⠀⢘⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢰⠀⢼⣿⣾⣶
⠀⠀⠀⠀⠠⣶⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣴⣿⡇⠾⢃⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⠏⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠺⡿⡇⢀⣾⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣈⣡⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠙⠛⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣶⣿⣷⡄
⠀⠀⠀⢸⣿⣿⣿⡧
⠀⣀⣀⣀⣿⣿⣿⣅
⢾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠂⠀⠀⢰⣴⣿⣦⠎
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⣠⣿⣾⡇
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠙⣿⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⠠⡄⠀⠀⠀⠀⠁⠀⠀⠠⠀⠁⡀⠐⠂⠈⠀⠀⠀⠀⠀⢀⠀⠰⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠊⠐⠀⠓⠀⢀⠀⠔⠄⠎⠈⠑⠠⠀⠀⠀⠁⡀⠀⠐⠀⡀⠀⠀⠈⣻⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⠀⠀⠀⠀⡀⢀⢀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠃⠀⠈⠂⠀⠀⠀⠀⠠⠄⠀⠗⠀⠀⠀⠀⠀⣀⠄⠀⡖⠐⠀⠈⠉⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⣀⡀⠘⠀⠂⠀⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⡀⠀⠲⢂⡄⠄⠐⠀⠀⠎⠁⢄⠀⠀⡒⠀⠂⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠡⠄⡀⠀⠂⠀⡂⠀⠀⣤⣽⣷⡄⠀⠀⣄⠘⠁⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣀⡴⠈⠰⢀⠐⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠈⠉⢀⠀⠌⡀⠀⡙⠛⠛⠰⠠⠊⠀⠄⠁⢈⡀⠀⠀⡀
⠀⠀⠀⠠⠀⠁⠐⡃⠂⠡⠄⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠈⠂⠈⠀⠁⠀⠀⠅⠀⠀⠀⢀⠀⠎⠁⠀⠀⠁⠠⠂⠄
⠀⠨⣠⠀⠀⠀⠀⠠⠘⠀⠆⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠔⡀⠠⠄⠠⠀⠀⠀⡀⠀⠄⠉
⠀⠀⠈⠀⠀⠀⠁⠈⠀⠠⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠚⡀⠠⠀⢁⠀⠀⡁⠡⠀⠐⢠⠀⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢀
⠀⠠⠀⠠⠤⢈⡁⠤⣀⠀⠎⢀⠂⠁⠈⠃⠁⠄⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠈
⠀⠠⡀⠀⠂⠀⠀⠠⠀⡠⠀⠃⠠⡁⠐⠀⠀⠂⠀⠁⠊⡓⠰⠄⠐⠒⠁⢀⠀⡆⠀⠀⢰⠀⠀⠀⢰⡀⠐⠀⡀⠘⠀⢀
⠀⠂⠐⠀⠀⠀⠠⠀⠠⠀⡀⠉⠀⠳⡄⠀⠀⠰⠐⠀⢚⡁⠀⠀⠀⠀⠒⠂⠀⠇⠄⠀⢘⠀⠀⣀⠀⠠⠄⢨⠅⡄⠀⠘⢰⡀⢒
⠀⠒⠀⠢⠐⢀⠐⠁⠁⠄⠀⡀⠐⠦⠁⡀⠀⠀⠐⢀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠂⢰⠒⢂⠈⠀⠀⠁⠁⠀⡘⠁⠩
⠀⢀⠈⠀⠠⠀⠰⠀⠀⠠⠀⡀⢀⡀⠀⠀⢐⠀⠀⠤⠀⠄⠀⠉⠐⠀⢤⡐⠐⠀⠀⠀⠀⠀⠀⡀⢉⠃
⠀⠀⠈⡠⠀⢀⠀⠀⠁⠂⠈⠀⢀⠀⠐⡠⠉⠐⠀⠀⠀⠀⠀⠊⢢⠀⢸⡀⠀⠀⠈⠂⠒⠒⠶⠁⠛⠦⠄⠄⠀⠀⠀⡀⠀⠀⢤
⠀⢀⠁⣈⠀⠀⡀⠈⡀⢀⠀⠐⡀⡁⠈⡉⠄⠠⠀⠆⠀⠀⠻⠀⢈⡖⢢⠠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁
⠀⠀⠀⡠⢙⡈⠡⠠⠄⠀⡂⠀⠑⠂⠔⠈⠐⠀⡀⣀⢈⣄⡃⠘⠄⠂⣠⠀⠈⠙⠒⠈⡂⠨⠠⣄
⠀⠙⠠⠀⠈⠀⠀⠀⠁⠀⠀⠉⠨⣄⠑⢀⣁⡀⢄⢀⡀⠡⠁⠐⡀⠈⠄⡆⠁⠀⠀⠀⠀⠄⡀⠘⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠁⠙⠇⠹⠌⠄⠋⠀⢘⠀⢂⠠⣿⣁⠀⢀⣦⠀⠚⠠⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⠁⠀⠉⠹⠈⠁⠈⢠⡆⠉⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠁⠀⠀⠐⠀⠀⠀⠂⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⢀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⡀⠀⣈⡠⠁⠀⢀⠀⠂⠚⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⡀⢀⠀⠁⣰⢶⡀⠀⠀⡙⢦⡉⢣⠀⠀⠈⠓⠤⢾⠇⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠈⢀⠀⠀⠀⠄⢀⠀⢘⠦⡀⢧⡐⠀⠀⠺⠓⢂⣂⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠄⠒⠀⢀⠂⠀⠀⠀⠈⢐⠘⢃⠀⠀⠀⠀⢀⠔⠁⠀⠷⠦⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠒⠒⠊⠁⠀⠳⣤⠛⠒⢏⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡗⠦⣀⠀⠆⡈⠀⠀⠴⣄⠞⠛⡀⠉⠀⠈⠀⠃⠂⢠⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢤⠀⣷⠘⢆⡢⠀⢈⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⣶⣷⡄⢸⣧⠀⠑⢄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠛⡀⢀⢻⣷⠄⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠰⢧⠀⢀⡁⣂⡀⠹⠷⢗⢂⠠⠀⠀⠀⠀⠀⠄⢀⠔⣄⠀⠀⠀⠀⠀⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡾⠛⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⡀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠢⡀⢤⡒⠃⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⣤⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠂⠁⠀⠀⠀⠀⡨⡮⠠⠁⠀⢁⠀⠉⠀⠐⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠐⠀⠀⠀⣀⡀⠀⠀⠀⠁⢀⡸⠐⠀⠠⠄⡀⡊⠰⣤⠂⠃⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⢀⠂⠀⠀⠸⠤⠇⠀⠀⠀⠀⣀⠜⠀⢀⣈⠄⠀⡄⠠⠀⡈⠐⢁⡎⠀⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠂⠄⠀⠠⠀⠂⢱⠄⠀⠱⠀⠀⠂⢁⠒⠄⠣⠄⠐⠂⣀⠐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠂⠀⢀⡄⡀⠠⢎⡁⡀⢡⠄⡉⣁⠐⠀⠼⡋⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⡀⠀⢐⠁⠀⡀⢁⣀⠀⠊⠆⠓⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⠀⠀⠀⠀⠄⠀⠈⠀⠀⢨⢀⡈⠀⠀⢠⠈⠀⠒⠆⠀⡤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠲⢀⡠⢀⡠⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠒⠠⠄⠸⡄⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠉⠁⠒⠲⢄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣄⠀⠻⣄⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠈⡳⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠉⠓⠤⡴⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢂⠀⢀⣀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⡠⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢿⡎⠔⣵⢶⡇⡀⠀⠀⠀⠀⠈⠢⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠘⠠⣄⠀⠁⠂⠤⣀⠀⢀⡤⠊⠀⠒⠊⠰⡀⠛⡻⢁⡅⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⣸
⠀⠂⠒⠒⠒⠠⢀⠀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠉⢀⠎⣵⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⠀⠀⠀⠀⠀⡏
⠀⠀⡔⠀⠀⠀⠀⠚⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠞⣁⠔⠁⠀⠉⠐⠒⠣⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠙⠦⣤⣀⣀⣠⠎⠀⠀⠀⠀⣀⡤⠚⣩⣌⡉⣹⠶⠦⢤⣀⡀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠀⠘⣆⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠉⠂⠠⠄⠔⠂⡹⠁⢠⠂⠀⠣⢄⣀⣠⠔⠊⠁⠉⠓⠲⢤⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⡤⡾⠉⠀⠀⣸⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⢀⠔⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠳⣆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⡼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⣄⣀⣢⠀⠀⠀⠀⢸⠀⠀⠔⠉⠉⠁⠀⢲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠴⠃⠀⠀⡜⠁⠈⠙⡇⠀⠀⠀⢸⠀⠀⠙⠧⠤⠼⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇
⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⣀⣀⡤⠤⠤⠷⠶⠦⠤⠿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠃⠀⠀⢸
⠀⠀⠀⠀⠈⠒⠧⠴⣅⡴⣒⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣠⠀⢀⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣀⣠⠂⠀⢰⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⣠⠖⠚⢻⡤⢸⠗⢷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡆⠄⢀⡞⡿⠒⠋⠄⠀⠈⢆⡞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣚⡋⠁⢻⣤⠋⠀⡧⠑⣼⠀⠀⠀⢸⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠉⠳⣾⡷⢿⢤⣧⣀⠘⡄⠀⠀⠀⣿⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⠳⣤⣲⡿⣮⣿⠃⠀⠹⢷⣲⢶⡒⣷⠿⠚⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠈⠑⠈⠻⣿⢄⣽⣷⣦⣤⡀⢈⣷⡟⠁⢁⣠⡴⢦⣀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢻⣦⡂⠀⠀⠈⢳⣤⣿⡝⠻⣿⣿⣿⣽⠶⠋⠁⠀⠀⠙⢦⣀⣀⠔⠁
⠀⠀⠀⠀⠀⢸⣿⡗⠒⢺⡛⢻⣿⠷⢶⣤⣤⣽⣼⣧⣴⣿⣯⢷⣴⢺⠀⢀⣀⣀⡀⠀⠀⠹⡁
⠀⠀⠀⠀⠀⠈⠙⢷⠀⠀⠉⠉⠹⣿⡄⢰⣏⢉⠻⢿⣿⡍⢿⣀⣻⣴⣾⡿⠛⢹⡷⢦⣀⠀⠳⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠤⣿⣿⣼⣯⣽⣄⣠⣽⣿⣿⣿⣿⣛⣯⣴⣞⣋⠀⠀⠙⢳⡖⠚⠑⠄⠀⠰⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⣾⢿⣿⣍⡙⠛⠙⠛⢿⡟⢻⣛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣦⣬⣂⡿⠀⠀⠀⡀⠀⠀⠀⠸⡇⢀⡠
⠀⠀⠀⠀⠀⠀⠈⡸⠀⠀⠙⠻⢷⣶⣤⣈⣿⣿⣿⣿⣿⡿⡿⠋⠉⠀⠀⣠⣄⣸⣿⡶⡋⠱⣤⣀⠴⡤⠤⠤⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠊⠁⢀⣤⣄⣀⣉⣿⣿⣿⣿⡟⠋⠉⠁⠲⠤⠤⠌⠀⢸⠊⠻⣷⣤⡵⠄⢸⠀⠈⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠛⠛⠛⣻⣿⣿⣿⡟⣿⣷⣦⠀⠀⠀⡘⠛⠄⠀⣏⠀⠀⣻⣽⠿⣄⠘⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⣿⣿⣿⣷⣿⣾⣿⣿⣿⣷⣶⣴⣄⣀⡤⢽⡛⠉⠉⠀⠀⠉⠙⠛⠵⣄⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠿⣿⣷⣷⣶⡧⢤⣄⢀⡀⠀⠰⢆⠀⠀⠉⢉⠪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠔⣿⣿⣿⣿⣷⣦⣾⣭⠁⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠛⡿⠿⠆⠀⠈⠛⣿⣷⡉⣿⣿⣧⣤⣮⣥⡾⠿⣟⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠿⡛⠻⠭⣽⣏⡄⠀⠙⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⣾⡇⠀⡰⠈⠓⠄⠈⠻⠟⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢌⣦⠬⣿⣄⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠉⠀⠈⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⡆⠀⠀⠀⣸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡀⠀⠀⠀⢠⠇⠐⠂⠀⡇⠀⠀⠀⠀⠀⠷⠀⠀⠀⡸⢃⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠣⠀⠹⢆⠱⡀⠀⠀⠈⠀⠀⠤⠐⠁⠀⠂⠐⠃⠈⠀⠀⠀⠠⣹⢪⠁⣰⠃⢀⠖
⠀⠀⠀⠀⠳⣅⡀⠱⡀⢂⠂⠑⠂⠀⠀⠠⠀⠀⠀⠤⠂⢀⠀⠄⠲⠀⣄⣀⠀⠁⠂⠜⠁⠀⠀⢀⠄⠁⠠
⡀⢦⡈⠢⡀⠘⠝⠆⠈⠀⡀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠉⠀⠀⡆⠈⠯⡈⢿⣦⣤⡀⠀⠁⠠⠃⡠⠊⠀⠠⡆
⠈⠳⠱⣔⠌⠐⠀⢀⠄⠀⠀⠀⠀⠤⡀⠀⠛⡀⠀⠀⠄⠀⠀⡀⠒⠀⠀⢷⠀⠀⠙⣽⠷⣤⡀⠈⢀⢐⠟⠁⡠
⠀⠀⠀⠊⠀⣠⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⢴⠀⠀⠀⠀⢐⠀⠀⠈⣃⡿⠺⣧⠀⠘⢿⣄⠀⠡⠶⠊
⠀⠀⠀⠀⣨⠁⠀⠐⠀⠀⠀⠀⢠⠆⠀⠀⡀⠀⣀⣀⡀⣀⡠⠀⠈⠀⠀⠰⣿⣇⠀⢸⣧⡄⢸⣿⣆
⠀⠀⠀⢰⡙⠀⣠⠆⠀⠀⠀⠀⣾⡄⠄⠈⠉⡁⠀⠀⠀⠀⠀⠐⠒⠄⣤⣤⠦⠙⣈⣿⠁⢠⣿⣍⣿⣆
⠀⠀⠀⢸⠃⠀⠈⠀⠀⠀⠀⠀⠋⢀⠀⠠⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠈⣀⡴⠟⠋⢡⣠⣼⠟⣻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⡆⠀⠈⠈⠁⠀⠀⠀⠠⠀⣀⡐⣡⣦⣤⣄⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠠⣝⡻⠗⣲⡽⠇⠀⠐⠀⠀⢳⣤⣄⣴⣿⣿⣻⣯⡝⠃⠀⢄⡉⠉⠉⠹⢿⣿⣇⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣛⣁⣴⠏⠻⢿⣿⣿⠿⣶⣄⠀⢠⠌⠻⣶⣶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠀⠉⡙⢷⣶⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⠀⢠⠀⠀⠀⠀⢠⠅⠀⠀⠀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠂⠀⠀⠀⠄⠀⠀⢈⠕⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠘⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠋⠀⠰⠊⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⠀⠀⢙⠂⠀⠀⠀⠂⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠈⠀⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⠀⠈⡀⠀⠁⠆⠙⠦⠀⠀⡁⠀⠂⠈⢀
⠀⠀⠀⠀⠀⢭⣓⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠿⣇⠀⠀⢸⡆⠀⠀⣀⡤⣤⠀⠀⠄⠒⠃⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡇⢀⣬⠡⠔⢈⣷⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⡶⠂⠀⠀⡰⠛⠀⠀⡠⠚⢻⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⢆⡀⠀⠀⠀⠀⢈⣿⠃⠀⠀⢀⣤⠖⠋⠀⡴⢋⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢣⣀⣠⠏⠀⠙⠒⠲⢿⣿⠀⠰⠊⡡⢄⣠⡤⠞⢀⡈⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠐⠈⠀⠤⠾⣿⠀⠀⣀⠄⣠⠀⠀⣀⡸⠁⣩⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢄⠀⠁⠀⠀⠀⢺⡟⠀⢁⣤⣯⡴⠾⣏⠠⠎⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠓⠤⠀⢀⣰⡄⠀⠀⣾⢁⠠⠊⠁⣠⠔⠋⠐⠒⢢⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⢀⠋⠠⠚⠋⠐⡮⢁⣀⡴⠋⢛⡀⢋⣽⣩⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⢈⣩⢷⠞⣩⠗⠀⡆⠙⠉⠀⣁⡴⠋⣀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣈⣷⣈⣤⣴⣿⢀⠀⠀⢭⡀⢉⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠃⠈⢃⣲⣾⡿⠛⠉
⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁
⡁⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠄⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠄⠂⠐⠀⠀⢠⠀⠀⠁⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠠⠄⠄⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠐
⠁⠀⠀⠀⢰⠈⠠⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⣀⣤⢂⠶⠜⠖⠄⠄⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡤⢸⡅⠆⠉⠠⠀⠃⢆⠄⠑⡄⠀⠐⠀⠀⠀⢀⠃⠐⠀⠂
⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡔⠂⠡⡀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠓⡠⡇⠄⣤⠄⠐⠠⢀⢀⠠
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠢⠀⠀⠀⠀⠀⠀⠀⡐⢋⠀⡘⠘⡋⢅⡄⠈⣤⡄⠘⠒⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡀⣀⠧⠁⠘⠀⠨⢅⠀⠌⡀⠀⢀⡫⡈
⠂⠀⠀⠀⠀⠀⢠⠋⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⢀⠽⠀⠀⠈⠠⠈⠸⠨⠁⠐⠀⠔
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠲⠭⠟⠋⣉⡷⠛⠃⠀⠀⠀⠀⣀⠀⠐⠀⠀⠀⠐⠊⠂
⠀⣀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁

⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠻⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⡇⠀⠀⠀⢘⡔⠚⠛⢃⠸⠓⣟⠟⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⠀⠀⠀⠘⠙⠛⠛⠛⠛⠂⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠀⠈⠣⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣌⣁⣴⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠉⠚⢱⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⣀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⣴⣀⣄⣄⠀⠀⠀⢿⢿⠁⠀⠀⠀⠻⠿⠃
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣧⠘⠛⠀⠀⠀⢰⣶⣾⣶⣶⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⠂⠀⠐⠂
⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣿⣿⣿⡿⠿⡫⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣶⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠹⠍⠋⡃
⠀⠀⠀⠀⠻⣿⣇⢻⡀⣷⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⣟⣿⢿⣏⣻⠛⠛⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣀⡔⠁
⠀⠀⠀⠀⠀⣽⠿⠿⠿⠛⠻⣿⣿⣿⣿⣿⡃⠘⣿⢯⣯⠿⣅⠿⣿⣮⣯⣯⣳⠒⠈⠘⠿⠟⠛⣹⣿⡋⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠸⣷⣶⣶⣷⣶⣿⣿⣿⣿⣽⡉⠲⠈⠁⠙⠃⡀⡉⢘⠃⠒⠎⢳⣾⣿⣶⣾⣾⣿⣿⣿⣿⣿⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⢶⠆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠂⠀⠀⠠⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠰⣀⠄⠉⢉⠜⠉⢀⠤⠀⠀⡠⠀⠀⠀⠀⠀⠒⠀⠤⡉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⡌⠄⠐⠉⠛⠐⣠⠏⢀⠔⠁⠀⡰⠋⠀⢀⡴⠁⠀⠑⠢⠤⠤⠞⠳⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠈⠂⠘⠦⠤⠴⢻⠀⡜⠀⠀⣰⠁⠒⠚⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⢀⠠⡄⠀⡀⠢⢾⡀⢇⠀⡤⣏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢆⢎⠂⠐⡤⣥⠖⠀⢧⠘⢆⠉⠹⡀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠒⠄⠀⠝⠺⠀⠀⠈⠳⣌⠓⢤⡑⢄⠀⠙⢦⣀⠀⠀⠀⣀⠴⢁⡰⠋⡼⠀⠈⠙⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣈⢄⡀⡀⢘⠀⢀⠈⢻⠀⣠⠈⢧⠀⠈⠢⡉⠒⠤⢄⣉⣉⣩⠤⠖⠋⡀⣰⠁⢠⠖⠒⢦⠀⠈⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠁⠀⠙⠶⢝⢦⠸⠄⠋⣄⠑⠶⠊⠺⣁⣀⠇⡜⢇⣄⠀⠀⢀⠶⠐⠋⡡⠃⠀⠈⢧⡀⠀⠀⢠⠏⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡣⠑⠞⠃⠀⠀⠀⠀⠈⠁⠸⡁⠘⠤⢯⣩⢷⠊⡀⢸⡗⠀⣄⠀⠀⢹⠀⢀⠎⠀⠠⣮⡖⠛⠾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⠉⠉⠀⡔⠈⠓⠲⠤⠴⠒⡋⠁⠐⢄⣀⠈⠓⠚⠁⢀⠎⠀⠀⠘⡇⠁⢉⠀⡽⠅
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣭⠷⡀⠀⠀⠀⠀⠀⢘⠠⣤⡤⡄⠀⠐⠒⠸⠤⣀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⠉⠲⠤⠄⠈⠀⠀⠐⠭⣮⠒⡒⠚⡤⠫⣀⣀
⠀⠀⠀⠀⠤⠤⢄⠀⠀⠀⢸⠠⡑⢄⠀⠀⠀⠀⡘⠀⠀⠀⡔⠁⠀⠤⢍⣐⠂⠁⢀⠀⠂⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠐⠂⠈⢕⠓⢤⣀⠔⢓⡄⠢
⠀⠠⠆⣤⠍⠩⣤⡥⠴⠀⢸⣀⣈⠢⢍⠲⠆⠊⠀⠀⢠⠊⣠⢾⣿⣷⠀⢀⠁⠀⡜⠀⠀⠠⠸⠀⠠⠀⢸⠀⠀⠀⢠⠐⣄⠀⠈⠎⠁⠀⣀⠠⠄⠐⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⠀⠀⠈⠉⠐⣧⠀⠀⣔⣁⣀⣉⣉⣁⠁⠈⠒⠀⢰⠁⠀⠀⠀⠀⠈⠅⠀⢸⠐⣀⡄⠀⠑⢄⠑⢄⠀⠈⢉⡀⠀⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢒⠂⢤⢤⣤⠽⠀⠈⠛⠝⠂⠂⠀⠀⠈⠀⠀⢀⡈⠀⢔⣒⣊⣙⡛⠓⠲⠶⠀⠀⠇⠀⡠⠀⢵⠋⠀⠐⢋⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢀⠂⢜⠛⠨⠲⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⣀⠸⠴⢁⡈⣁⣈⣀⣠⣄⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢸⢰⡄⢒⠒⣇⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢒⢐⠁⢎⡅⠀⠭⢍⢰⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠁⠛⠃⣿⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⡶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠶⣤⡀
⠀⠀⠀⢠⣾⣿⢹⣾⣿⣯⢻⣿⣷⡀⠀⠀⠀⣴⣟⢾⠿⣿⣿⣿⡝⣿⣧⠀⠀⠀⢀⡾⣟⠟⠁⢁⣒⣤⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⠿⠿⠀⠀⠀⢰⣿⣿⣿⣿⣔⣿⣿⣿⠿⠟⠀⠀⠀⢸⣿⣥⠂⣞⣷⣿⣿⡿⠿⡇
⠀⠀⠀⣿⣿⣿⠿⢿⠏⠀⢀⡀⠘⡀⠀⠀⠘⣿⣿⡿⠿⣿⠃⠀⢀⡀⢠⠀⠀⠀⢸⣿⣷⡿⠿⡿⠁⠀⣀⠀⠇
⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠁⢠⠇⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠈⠀⡠⠂⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠁⠀⠜
⠀⠀⠀⠀⠈⠟⠃⠀⢀⣀⠀⢀⠇⠀⠀⠀⠀⠀⠙⡟⠁⠀⢀⡀⠀⣨⠃⠀⠀⠀⠀⠀⢹⠛⠀⠀⣀⠀⠀⡸
⠀⠀⠀⠀⢀⡇⠀⠀⢸⡀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣇⠀⠉⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⠈⠁
⠀⠀⢰⣾⣿⣿⣿⣾⣿⣿⣶⠄⠀⠀⠀⠀⣴⣿⣿⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣶⠶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠉⠹⣧⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿
⣿⣿⣅⠀⠀⠀⠉⠀⠀⠀⠀⠀⣴⣿⣿⣶⣦⣴⣶⣦⠈⠀⠀⠐⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠁⠀⠀⣽⣿⣿
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣴⣯⠀⠀⠈⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣆⡀⠀⣰⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠋⠀⠀⠀⠀⠀⠀⢠⡘⠎⢃⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡟⠀⠀⣀⢀⠀⡀⡄⢇⠡⠘⡀⢂⢡⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣿⣿⣿⣿⢆⠱⠘⡈⢂⠡⡘⡄⠦⠱⠰⠌⠂⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠛⠙⠁⠙⠛⢿⣿⣿⡆⠂⠡⠐⡀⠤⠁
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⠛⢩⣾⣦⠆⠃⠉
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢤⠄⠚⠉⣀⣤⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠈⢿⠇⠀⢀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣰⣶⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⡆⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⢿⣟⣻⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠁⠢⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠀⡐⠈⠑⠈⠈⡂⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣽⣿⡾⣿⣵⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⡂⠀⠰⡀⢊⣁⠆⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣵⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⠀⠀⠘⡄⠠⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣼⣏⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢣⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡜⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⢀⠔⠂⠈⠉⠐⠢⢄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠐⣠⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠂⢀⠤⠒⠤⠔⠒⡌⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢆⡠⠀⢢
⠀⠀⠀⠀⡠⠀⠘⡀⠀⠄⢤⡠⢃⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡔⠀⠀⠡⠀⠀⢀⡠⠊
⠀⠀⠀⠀⢑⠀⠀⠈⢆⠐⠊⡠⠂⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠆⠀⢠⡄⢃⡜⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⢲⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣧⣄
⠀⠀⠀⢠⣤⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣤⣄⢀⣾⣿⣿
⠀⠀⠀⠸⢿⣿⣿⣷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣈⣻⣿⣿⢿⣿⣿⡆⠀⣴
⠀⠀⣶⣿⣷⣿⣿⣯⣿⣿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣿⠉⠉⠉⠉⠉⠉⠁⢿⣿⣿⣦⢻
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣀⡀⠀⠀⠀⢸⠀⣿⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣸⡆
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⢸⠀⣿⠀⠀⠀⠸⣿⣿⣽⡏⠉⠉⠁⠀⢻
⠀⠀⠀⠀⠀⠀⢹⡟⠉⠉⠉⠉⠉⢉⣹⣿⣿⡿⠁⠀⠀⢸⠀⣿⠀⠀⠀⠀⠘⣿⣿⣿⢶⣤⣄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠟⠉⣿⣟⠁⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⣀⣬⣿⡇⠀⠹⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠛⠀⠀⠛⠛⠛⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠶⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⡀⠻⣦⠀⠀⠀⠀⠀⠀⣴⠟⢀⡀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⠈⢻⡄⢸⣇⠀⠀⠀⠀⣸⠇⢠⡟⠁⣤⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣸⠇⢸⡇⢀⣿⠀⠀⠀⠀⣿⠀⢸⡇⠸⣇⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢀⣨⠿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠉⢠⡿⠁⣸⠇⠀⠀⠀⠀⠸⣇⠈⢷⡄⠉⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣄⡀
⠀⠀⠀⢀⣴⠟⠁⠀⠉⠻⠶⣤⣤⣤⡴⠶⣟⠁⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠈⣻⠶⢦⣤⣤⣤⠶⠛⠁⠀⠈⠻⣦⡀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣿⠀⠀⠀⣦⡀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣴⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠘⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠃⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠸⣧⣤⣤⣿⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣿⣤⣤⣼⠏⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠁⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡟⠙⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢦⣤⡀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠙⢦⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢦⣀⡀⠀⠀⠀⣀⠴⠋
⠀⠀⢀⣀⠀⠀⠀⣠⣤⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠉⠉⠉⠛⠷⠄⠀⣴⣶⣶⡄
⠀⠀⠻⣿⣧⡀⢼⣿⣿⣿⠀⠀⠴⠟⠓⠲⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠰⠦⣤⣤⣀
⠀⠀⠀⠙⢿⣿⣎⠛⠛⣫⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄⢠⡟
⠀⠀⠀⠀⠈⠻⣿⣷⣄⢿⣿⣿⣷⣤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⠋⢉⣿⣿⣿⠇⡾
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣹⣷⣿⣤⣟⣻⣯⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣬⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⡀⠀⠸⣿⠿⢿⣿⣿⠿⢿⣿⡟⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠟⠃⠀⠀⠐⣿⣻⣿⣧⢺⣿⣿⣿⣂⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠉⣿⣿⡈⠙⣿⠉⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠏⠀⠻⠿⠃⠀⠿⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢆⠀⠰⣦⣄⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣤⠞⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠁⠀⢠⡀⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡆⡎⠙⠀⠀⠈⠉⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡟⡇⠐⡀⠀⢠⣦⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢸⣿⣶⣴⣿⣷⣧⣄⠱⡀⡇⢻⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⡇⠈⣿⣿⣿⣿⣿⣸⣿⡇⢻⠁⣾⢿⣷
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⠀⢨⣿⣿⣿⣿⣿⣿⡟⠺⢾⡿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢻⡄⠀⣿⣿⣿⣿⣯⠿⠀⠀⣸⣼⣿⣿⠀⠠⢠⡀
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣿⣿⣿⣿⠆⠀⢀⡟⣽⣿⣿⡄⠀⠀⢀⡀⣠⣄⣠⣤⣀⣀
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠈⢙⣿⣿⣿⣤⣤⣾⣾⣿⣿⡿⠛⠁⠀⢀⣶⣿⣿⣿⠿⠋⠁
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣦⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣇⣀⣠⣶⣿⣿⣿⠿⠃
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠘⣾⣯⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢘⣽⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣫⣿⣿⣿⡄
⠀⠀⠀⠀⢸⡄⠀⠀⠘⢦⡀⠈⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⢛⣝⣡⣿⣿⣿⣿⣿⣧⢳
⠀⠀⠀⠀⠀⣇⠀⠀⠀⢻⣿⣷⣤⣉⣛⣻⣿⣿⣿⠿⠟⠋⠀⣀⣤⣶⣿⣿⣿⣿⠿⡋⡙⣿⡎⣇
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⢧⡉⠛⠛⠛⠛⠛⠉⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣡⣾⣷⡇⢸⣷⢸⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣇⢷
⠀⠀⠀⠀⠀⠀⡇⢰⠖⠲⠶⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢿⣿⣿⣿⣿⡇⠀⣿⣿⡜⣇
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠉⠭⠙⢦⡀⠀⠠⠂⠉⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠸⣿⣷⡹⣆
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣷⠀⠀⢿⡿⠞⠉
⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⡀⢂⠘⣷⣤⣀⣠⣄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⣿⣿⣿⣇⢸⡀⣿⠛⠛⠛⠩
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⠀⣇⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣀⣽⣴⠟
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣭⣵⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⣿⠁⠪⣿⣦⣤⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡴⣂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠈⠈⠸⡷⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⣀⣤⣤⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢰⡿⠀⢀⣾⡿⠋⠁⠀⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠑⠧⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢠⣿⠃⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠘⠐⠲⠞⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠆⠁⠀⠀⠀⠀⠀⢠⣾⠏⠀⢀⣾⠇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⣾⠏⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⣾⠏⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣠⣿⠃⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣅⠀⣴⡿⠁⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣨⣿⠟⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⣿⡇⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⡿⠛⠁⠀⠀⣠⣶⡿⠋⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣨⡷⠀⢀⣴⣾⠟⠉⠀⠀⢀⣿⠟⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣴⠟⠁⢀⣾⡟⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡿⢷⡄⠀⠀⠀⣸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⣿⣿⣿⣿⠀⠀⣴⣾⣶⣤⠀⠀⠘⢿⣿⣿⠏⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠙⠋⠁⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠨⢄⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⣤⣤⣤⣤⣴⣶⡾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⠖⠒⠢⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠈⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠠⠂⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠊⠉⠉⠉⠉⠒⢄⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠉⠳⢤⡁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⠀⠀⠈⠀⠀⠀⢀⠋⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢠⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠚⠤⡀⢠⠁⢀⠟⠒⠲⠤⠤⣀⣀⡣⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢞⠓⠀⠀⠰⡄⠀⠉⠰⢏⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⣰⠁⠀⢙⡆⠀⠀⠀⠀⠠⢲⡆⢨⡴⠊⠘⡄⠃⠀⠀⠀⠀⢣⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢀⡸⠄⠀⠘⠄⣀⠀⢀⠀⠓⠈⠐⡙⢾⠅⢰⠀⡆⠀⠀⠀⠀⠀⠧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡃⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢏⠀⢀⣄⡀⠀⢀⠜⠁⠀⠀⠀⠀⠘⠦⠔⠃⡸⠑⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡇⠀⠀⠀⠀⠀⡞
⠀⢠⠀⠈⠉⠁⠒⠰⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⡇⠀⠀⠀⠀⠀⡇
⠀⡆⠸⠂⠀⠀⢀⡀⠀⡗⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠈⠐⠢⠄⣀⠀⠀⣠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣧⠀⠀⠀⠀⠀⡇
⠀⠣⡎⠀⠀⢀⠋⠂⠀⡇⠀⠀⠀⠀⠀⠀⡠⠊⠴⢦⣤⣀⡀⠀⠀⠉⠘⠃⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠂⠀⠀⠸⡄⠀⠀⠀⠀⢻⡀
⠀⠀⠈⠑⠲⠼⣦⣤⡴⠁⠀⠀⢀⣠⡴⠊⠀⢠⠐⠂⠁⠀⠈⠁⢲⠀⠀⠀⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢸⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠛⢩⠁⠀⠀⠀⠁⠉⠉⢸⠀⠀⠀⢸⡀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⣣⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢣⠀⠀⡘⠀⣄⠀⠀⠙⠒⠚⠁⠀⠀⢸⣠⠞⠉⠀⠀⢀⡤⠊⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡠⠎⠀⢠⠇⠀⠈⣱⠒⠦⢴⡀⠀⠀⠀⢸⠁⠀⢀⠊⡉⠉⡀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡠⠤⠠⠤⠤⠤⠄⠀⠀⠤⢤⠤⠖⠋⠀⠀⢰⠃⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠘⠒⢦⠤⢇⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠦⠾⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠎⢠⠀⡀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠀⠒⠒⠚⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⢺⣀⡃⢠⡇⠀⡷⡶⢋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠾⣀⣠⣇⠀⢀⡝
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠹⣴⠋⠀⡞⠀⠀⠸⡏⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠦⠤⠤⠾⠃
⣿⣷⣶⣶⣶⣾⢷⣾⣷⣷⣿⣶⣶⣿⣶⣶⣶⣿⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣾⢷⠾⠷⠿⠷⢾⣿⠿⠿⠿⠿⠿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⢉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠴⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠊⠀⢆⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣂
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⠀⡀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠤⠀⢀⡌⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢈⠰⠀⢣⠬⠑⠏⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣀⢵⠒⠒⠁⢇⢄⠀⢘
⠀⠀⠀⠀⠀⠀⠔⠩⡀⠡⠀⢢⢔⡐⢦⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡰⡀⣥⢇⢀⡠⢤⠎⠀⠉⠙⢄⠉⠉⢦
⠀⠀⠀⠀⠀⠰⠀⠀⠘⠀⡁⠸⣇⡟⠊⡸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡙⢽⠄⡰⢑⠋⡏⠈⠉⡰⠃⢲⡚⠀⠀⢸⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡑⢄⠠⢁⠎⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣜⣉⣀⣁⠘⠀⡇⣠⠎⣀⠔⠛⠂⠀⠀⢸⠀⠀⡌
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢂⡀⠈⠈⢙⠁⠀⠃⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠉⠉⠑⣄⠁⠊⠀⠀⠀⠐⠀⠀⢸⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⠐⠠⡉⠀⣀⣢⢢⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠵⡀⠀⠠⣴⣸⠦⡀⢀⠀⠄⠃⠀⠀⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠈⡖⠄⣀⠀⠀⠀⠰⠀⠀⠀⢸⠀⡷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣄⠀⢯⠭⡀⠈⠀⠆⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠐⠂⠈⠀⠠⠤⢜⡒⠁⢀⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⠀⠀⠈⠓⠒⠂⠒⠉⠁⠐⠐⠐⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠣⠤⡤⠐⠂⠁⠀⠉⠒⢄⠀⠱⡀⠀⢳⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠒⠤⠬⠭⠔⠒⠲⡄⠀⢸⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠊⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⠤⡇⠀⠀⡀⠀⠇⠀⠈⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢇⠀⠀⠀⠀⠀⠸⠄⠀⢀⠤⠤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠇⣀⡀⣀⣀⣀⡀⢀⢁⡄⠃⠀⠀⠀⠀⠀⠀⠀⡅⠀⠆⠦⠘⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠣⠀⠀⢢⠒⠠⠤⡤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡗⠒⠒⠇⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠡⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⡁⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠐⣠⠒⠒⠀⠀⠇⣀⣀⣶⢗⣤⠴⢵⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠤⣖⡽⢁⡠⢊⣼⠀⠒⠀⡀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠤⠀⠐⠂⠀⠓⠒⠀⠉⠉⠍⠃⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠉⠹⠭⠵⠊⠁⠀⠒⠀⠀⠠⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡛⠗⠘⢻⣿⠛⢰⣿⠛⢿⡆⢻⡟⢛⠃⣴⣟⠻⠂⣴⣟⡛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣿⠆⢸⣿⠀⢸⣿⠻⣿⠁⣿⣟⣛⡃⣈⣛⣻⡷⣨⣛⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠀⠈⠉⠀⠈⠉⠀⠉⠁⠈⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⢠⣤⠀⢠⣤⢠⣤⣤⡤⢠⣤⣤⣤⡀⠀⣤⣤⠀⠀⣤⣤⣤⡀⣤⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠶⢾⣿⢸⣿⠶⠶⢸⣿⣤⣿⠃⣰⣟⣹⣧⠀⣿⣦⣾⠇⠈⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠸⠟⠀⠘⠟⠸⠿⠶⠶⠸⠟⠈⠿⠠⠿⠋⠛⠿⠆⠿⠀⠀⠀⠀⠸⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣦⡀⠀⠀⠀⠀⣀⠀⠀⠶⠀⠀⢀⡀⠀⠀⠀⠀⣠⡾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡇⠘⢿⣦⠀⠀⠈⣿⡄⠀⣴⡄⠀⣾⠇⠀⠀⣠⣾⠏⠀⣿⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⡀⢰⣶⠿⠷⠀⠀⠸⣷⠀⣿⠇⢸⡟⠀⠀⠰⠿⢷⡶⠀⣩⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣸⣧⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⣤⡾⠟⠛⠛⠛⠛⠿⣶⣄⠀⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣠⣬⡿⠛⣱⡆⠀⠀⠀⠀⠀⣠⣶⣦⣀⣀⡀⠘⣷⡘⠿⣿⣄⣠⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣾⠿⠿⠛⠛⠉⠁⠀⢀⣿⠁⢰⣷⣶⣶⠾⠛⠁⠈⠙⢻⣷⠀⢹⣧⠀⠀⠉⠙⠛⠻⠿⢿⣤⣴⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣄
⠀⠀⠀⠀⠀⢠⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢻⣆⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣀⣹⣷⣤⣀⣠⣴⣿⣁⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠆
⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠛⠛⠙⣿⡉⠉⠉⣽⡏⠛⠛⠛⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠈⢡⡄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠈⠻⣶⠾⠋⠀⠀⠀⠀⠀⠈⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉
⠀⠀⠀⠀⠀⠶⠎⡱⠶⠆⠀⠀⣴⠟⠋⠙⢿⣆⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃
⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⠀⠀⠰⠷⣀⡰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⣀⣠⣤⣀⡀⠀⢀⣠⣤⣄⣀⣰⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣰⡿⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠙⠛⠉⠉⢙⣿⠿⠛⠉⠉⠉⠛⠛⢻⣆
⣀⡘⠿⣀⡀⠀⠀⠀⢀⣴⡶⠿⠾⠿⠿⠿⠿⠿⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠘⢻⣷⣤⣶⠟⠀⠀⠀⠀⠀⠻⣧
⠉⢡⣦⠙⠁⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢠⣶⢿⣿⠉⣿⠿⣷⣄⣀⠀⠀⠀⠹⣷⡀
⠀⠀⠁⠀⠀⠀⠀⣾⠇⠀⣼⡆⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣷⡀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⢾⡏⢹⡇⠀⠀⢠⣿⣷⡶
⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⢸⡇⢸⣿⠀⣿⠀⢾⡇⢸⣇⣠⣴⠟⠁
⠀⠀⠀⠀⠀⣠⣾⠃⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟⢿⡇⢸⣿⠀⠿⠀⢾⡇⢸⡿⠋⠁
⠀⠀⠀⣠⡾⠛⠀⣠⡾⠋⢹⡇⠀⠀⠀⠀⠀⠀⢾⡏⠻⣷⣄⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⢠⣾⠋⠀⣠⣾⠋⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣸⣇⠀⢈⢻⣷⣄⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⠿⣶⡾⠟⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⣷⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠈⠻⢶⡄⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⣿⠁⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠉⠀⠀⣾⡷⠶⠶⠶⠶⠶⠶⠾⢿⡆
⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⢃⣄⣀⣀⣀⣀⣤⣾⠟⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣉⣉⣙⣿⣋⣉⣉⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⢀⣀⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⡿⠋⠀⠀⠀⠀⠀⠀⢻⠑⢄⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠚⢦⡀⠀⠀⠀⠀⠀⢠⡃⣀⣀⡀⠀⠀⠀⠀⢠⠀⢀⡽⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠰⡇⠀⠀⠑⢄⣀⣀⣠⡔⠉⠉⠉⠀⠈⠙⣆⠀⣠⠏⠀⠸⡀⠀⠀⢠⠞⠉⠓⢛⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⢈⡟⠉⠀⠀⠀⠀⠀⢀⣀⡼⠞⠁⠀⠀⠀⠈⠒⠚⢧⠀⠀⢀⣎⠔⠋⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣖⠒⠶⠖⠚⢦⡀⠀⠀⠀⠀⠳⣄⡤⣤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⡰⠋⢏⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠉⠓⡄⠀⠀⢹⠀⠀⠀⠀⠀⡏⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⠤⠒⠉⠀⠀⠈⢳⡀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⡠⠃⠀⠀⠈⢧⡀⠀⢀⡴⠃⠀⡞⠀⠉⠉⠓⠲⣄⠀⡰⠉⠀⠈⠑⢦⡀⠀⠀⠀⠀⢀⡸⢇⡀⠀⠀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠤⠚⠋⠙⢇⠀⠀⠀⠀⠀⢀⡬⠟⠉⠀⠀⠀⢧⡀⠀⠀⠀⠀⢈⡶⠃⠀⠀⠀⠀⠀⠈⢳⡤⠒⠚⠉⠀⠀⠈⠉⠉⢁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠒⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢀⣾⣀⣤⣤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣠⠶⠊⠉⢟⣉⣀⡠⢞⡝⠀⠀⢀⣠⢞⣡⠤⠒⠚⠒⠲⠄⠸⡇⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⣄⡀⢀⣀⣾⣡⡤⠴⠟⠛⠛⠉⠉⠉⠛⠚⠋⠉⠀⠀⠀⠀⢀⣠⠴⠖⠛⢤⡀⢰⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⣠⣴⡋⠀⠀⠀⠀⠀⠉⠃⠳⣀⢀⠀⠀⠀⠀⠀⠀⢠⠞⢀⡴⠉⠀⡹
⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡿⠿⠿⠿⠶⠶⠦⢤⣄⣀⡀⠈⠉⣽⠀⠀⠀⣀⠴⢋⡴⠋⠀⢀⡼⠁
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠖⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠟⠛⠛⠓⠚⠛⠉⠉⠉⢀⡴⠋
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠤⠤⣤⣠⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⠴⠞⠉
⠀⠄⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠶⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡰⠉⡀⠀⢄⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢠⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢊⡁⡲⢩⣉⠖⠳⢶⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⠤⠚⠉⠶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠤⠀⢀⠴⠞⢠⠃
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠙⡆⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡽⡶⠽⠗⡶⣥⠎
⠀⠀⠀⠀⠀⠀⢹⠀⠐⡄⢰⣇⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠳⡀⠀⠀⠀⡜⢨⣻⡇⡌⢐⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠓⣾⠉⠲⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⠤⣤⠋⠲⡏⠉⠉⠉⢹⠿⠖⠋⠀⠀⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⡄⠀⢳⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣱⠀⠀⠀⠘⡀⠀⠀⡆⠀⢹⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⡄⠀⢣⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢰⡂⠉⠑⡆⠉⠀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠹⡄⠀⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠒⠚⠛⠀⠊⠛⠋⢻⠁⣾
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⢆⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⠛⠳⠬⠽⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣠⠤⠖⠊⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡉⠉⠛⠛⠓⢲⣄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⢹⠒⡲⠒⢲⠿⠴⠶⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⢹⠉⠉⠉⢻⠋⢹⣫⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠃⢠⠏⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⢸⠀⢸⢸⣄⡤⢤⠀⠀⢀⡠⢔⡳⠾⢤⡞⠀⠀⣀⠼⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣊⡈⣢⠀⠀⣼⣦⣬⣋⣈⡧⠴⠃⠀⠻⠾⠭⠤⠤⠴⠃⠀⠘⠓⠒⠒⠒⠛

⣿⠟⠋
⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢢⣴⣾⣿⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠁⠀⢀⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⡜⡡⠂⢀⠀⠀⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠘⠃⢠⠆⢀⠰⠈⠇⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⢧⡄⠀⢀⠘⠀⠀⠀⢄⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⢸⡇⠐⠀⠀⠀⠧⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣧⠀⡄⠀⠐⠀⠣⡀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢃⠀⠂⠀⠀⠀⣠⣾⣤⢴⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠤⣾⠶⣿⠿⠉⢿⡄⠙⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠘⢦⡀⠀⢁⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠤⣦⣤⡴⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣶⡟
⣓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣁⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠁⢀⡀⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⡟⠻⣿⣷⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡀⠈⣀⣬⣙⣿⣿⡿⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡈⠀⠠⠀⠀⠀⠀⠀⠀⠛⠻⠿⣶⠀⠈⠉⣸⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⣻⣿⣷⣦⣀⠀⠂⠀⣄⣀⣁⣤⣄⣨⡻⠀⠀⠈⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⣿⣿⣿⣿⣷⣤⣷⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⣿⣫⡄
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠈⠉⠟⠉⡉⢻⣿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⡀⠀⣀⣤⣠⡆⢀⣽⣿⠋⠀⠀⠀⠀⢀⠙⠛⠛⠋⣱⣏⠈⢻⣿⣿⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢀⣈⣤⣿⣷⡖⠉⠉⠁⠀⠀⠀⠀⠀⠁⢄⡄⣀⠀⢠⡄⠀⣸⣿⣿⣿⣿⣿⣾⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠸⠋⠛⢁⡴⠃⡄⠀⠀⠀⠀⠴⠶⠀⠚⣧⣿⣶⠃⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣴⣷⣤⡶⠛⢋⣠⣾⠇⠀⣀⣀⣀⣀⣄⣀⡀⣿⣿⣿⣶⡟⢿⣿⣿⣻⣿⣿⣿⣿⠏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠷⣦⣿⠟⢿⡿⣤⠀⠭⠟⠃⣴⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣧⠐⣤⡏⢀⠀⡀⢀⡀⠻⡟⠻⢻⣿⣟⣽⣿⣿⣿⣿⣿⣦⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠿⣿⠛⣿⣡⣶⠈⠲⠁⠀⠈⢻⣿⣿⣟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣧⣄⠀⠀⣿⣿⣿⠁⢐⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠄⣈⣤⢾⣿⣿⣿⣿⣿⣿⣧⡈⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⣈⠈⠙⠻⣦⡉⢿⣿⡿⠿⠛⢊⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢁⢀⡀⡀⠉⠙⡿⠁⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡜⠃⣴⠂⠁⠀⠂⠀⠁⠄⢀⣴⣶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢢⣽⣿⣿⣷⣾⣤⡆⠠⠀⠀⢀⠀⣾⣿⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠫⢩⣿⣿⣿⣿⣴⣋⠶⠞⣶⣼⡃⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡤⢀⣡⣿⣽⣿⣿⣿⣄⣿⡽⠛⠃⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠉⠛⠛⠋⢩⣿⡇⠐⢦⢹⣿⠇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣠⠟⠉⠋⢠⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠠⠄⠀⣿⣿⣿⣿⣿⣃⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣦⣄⢶⣤⣀⡀⢸⡿⢿⣿⣿⡏⢉⣿⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣆⠙⢻⠿⣈⡀⠀⣝⣿⠁⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣾⣿⣿⣷⣭⡛⠈⢻⡿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣭⠷⠒⠲⢦⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠂⠀⠀⠀⢻⠀⠀⣴⠞⠉⠉⠈⠉⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⢀⡤⠀⣼⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⣸⠏⠀⠀⣰⠟⠀⠀⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⡼⠃⠀⢀⡾⠁⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⢠⡞⠛⠛⠒⠒⠲⠞⠁⠀⣴⠏⠀⠀⠀⠀⢸⡇⣸⠀⠀⠀⠀⠀⠀⢠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠉⠛⠳⢶⣤⣤⣤⣄⣀⣠⡞⠁⠀⠀⠀⠀⠀⢸⠇⣿⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⣀⣤⣤⡤⠤⠽⠿⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⣼⢀⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣥⣾⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⠷⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢠⡟⠀⠀⢈⡟⠉⠉⣽⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⡉⠉⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡴⠞⠀⠀⠀⣸⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃


⡿⢿⢿⢿⢿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠛⠉⠙⠛⠓⠶⣴⡶⠒⠓⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠉⠛⠦⠀⡄⠀⠀⠀⠙⠆⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⡤⠴⠦⣤⡀⠀⢧⠀⠀⠀⠀⢠⡆⠀⠀⠀⣤⠴⠿⠶⣤⡀
⠀⠀⠀⠀⠀⣠⠞⠛⠙⠃⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⢶⡶⠚⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⢳⡀
⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡀⢰⡇⠀⣠⠴⠦⠤⠴⠋⠀⠀⡷⠀⠀⠀⠙⠲⠶⠞⠋⠉⠻⠆⢘⡇
⠀⠀⠀⠀⠸⡇⠀⣀⣠⡞⠀⢸⡁⢸⠃⠀⠀⠀⠀⢀⡆⠀⠀⣀⡴⠶⠒⠶⢤⡀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠙⣆⠉⠁⠀⠀⠘⣧⠀⠀⠈⠛⠶⠶⠛⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢶⣠⠏
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣘⣧⣀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡀⠀⠀⠀⢠⡏⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠓⠶⠶⠶⣞⣁⣠⡴⠋⠀⠀⠀⠀⣿⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠿⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣀⣄⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠁⠀⢹⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡼⠀⠀⠘⠷⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣦⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⣿⡿⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠇⣰⣿⣿⣧⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢡⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣏⣶⣿⣿⣿⣿⡷⠃
⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⣋⣭⣥⣴⣦⣬⣕⠾⣾⣿⣿⣿⠟⠁
⠀⣾⣿⣷⣮⣭⣭⣁⡒⠤⢀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⠞⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣀⣀⡠⠠⠀⣄⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡰⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠶⣾⣿⣿⡿⠿⠟⠿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡜⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠈⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢿⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣶⣿⠟⠀⢰⣿⣿⣿⣾⣿⣿⣇⢿⡿⡗⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣧⠀⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣭⡆⠀⠘⣿⢿⣏⡽⣿⣿⣿⣯⣁⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⠇⢿⣿⣿⣿⢿⣿⠘⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠖⠋⠀⠀⠀⠙⣦⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠇⡼⠀⡞⣿⣿⣿⠈⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠋⠹⠿⠛⠀⢀⣀⣀⡀⠀⠘⠛⠉⠙⣿⣿⣯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢠⠃⠀⠸⡿⠙⣿⡀⠀⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⢀⠆⢰⣿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⠎⠀⠀⠀⠹⡄⠈⠃⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠙⢛⡛⠛⢀⡠⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡴⠋⠀⠀⠀⠀⠀⠈⠲⢤⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⠻⡉⠻⠝⡇⠠⣾⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⢟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢳⡀⣀⠜⣶⡘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⢋⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣸⣿⣿⢟⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⢴⣶⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣇⡩⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠀⢣
⠀⠀⠀⡄⠀⠀⠀⠂⠀⠀⠀⠐⢟⣻⣿⠿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⣄⣀⣰⣤⡼⠃
⠀⠀⢨⡁⠀⠀⠀⢀⡠⠄⢒⠨⠀⠈⠀⠀⠀⠈⠀⠛⠋⣉⣁⣋⣙⠋⠵⠃
⠀⠀⠀⠈⠀⠒⠐⠋⠀⣆⠀⠀⠀⠀⠀⡠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠧⣤⣦⡰⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣿⣥⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣶⣾⣿⣯⣿⣷⣾⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠶⠀⠀⠀⠀⠀⣀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠘⢦⡐⠲⡇⠀⠀⢐⣀⣀⣴⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠉⠉⠀⠀⠀⠂⠱⣂⠘⡄⠠⠀⠀⢭⡍⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⢠⠀⠂⡀⠀⠀⠐⠠⢀⠰⡄⠘⠀⠀⠀⢀⡀⠂⢠⣨⡁⠀⠀⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡂⠀⠀⠠⢤⡤⠀⠐⣄⠀⡤⣠⡎⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡵⣀⠀⠀⡄⠀⠀⠀⢬⣁⡴⠒⢼⠤⢄⠀⣀⠀⠀⣀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⣧⠰⠍⢡⠌⠓⠀⢀⣬⠀⡍⠲⠀⡦⢚⠓⠆⠀⡄⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⣤⣾⡀⢸⣧⠈⠪⡀⠈⠃⣅⠸⠦⠀⡄⠠⡀⢈⣁⠛⠏⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⢻⣦⡀⠘⡁⢸⣇⡑⠂⠀⢆⠠⠌⠠⡄⠑⣿⠮⣍⠒⢶⣖⠺⡗⠤⡍⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠶⢠⣦⠀⠀⠁⢈⡤⠿⣦⣤⠜⣶⣿⡁⣋⡠⡆⣠⠈⠖⠸⠞⠡⠳⣄⢃⣈⢿⠻⣙⢦⣄⠑⠌⠻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⢻⡏⠠⠋⣽⠁⡜⢱⡇⠈⠉⡤⠴⢅⢸⡗⣻⣤⣄⠀⠀⠈⠑⠀⣇⠙⡄⢿⡛⣶⡶⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠰⠞⢇⠘⠧⠐⠙⠙⣄⠔⠉⠀⠀⠀⠸⠀⡜⢹⢻⠄⠇⢹⠃⠀⠀⡄⠀⠈⢢⡀⡔⠁⠘⣍⠲⢌⡙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡤⣿⠇⢈⡁⢐⠉⠉⡄⠐⠲⡀⠀⡨⠄⠀⠀⡁⠸⢠⣆⠉⢸⠀⠀⠀⠈⠀⠀⠈⠈⠁⠀⠀⠈⠓⠤⣈⣐⣀⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣴⠉⡤⠈⠓⠊⢀⡙⢏⣩⠰⡙⠳⡀⠠⣳⠤⠪⢿⢯⡉⠲⡄⠀⡀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⢀⡔⢊⡭⢶⠛⣡⢻⡟⠠⡇⠚⣀⠓⢌⡁⡝⠀⠐⠌⠒⠤⠞⢹⠀⣦⠘⢆⠹⣂⣙⣄
⠀⠀⠀⠀⠀⠸⡀⢋⠴⢇⠘⢣⠾⠀⠀⠈⡏⠉⣢⢿⣥⢻⡱⣤⠀⠀⠀⠀⠀⢧⠘⠧⣌⡁⣘⣏⡒⠤⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠒⠁⠀⠀⠀⠀⠁⢰⠃⡞⢸⠀⡇⡉⠁⠀⠈⠇⠀⠀⠕⠦⠁⠉⠉⠦⡉⠒⠤⡉⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠁⢾⡷⠤⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠒⠂⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡎⣏⠢⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠢⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠄

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠈⠻⣆⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢟⣫⣾⣦⣝⠿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡟⡵⢮⠻⠟⡵⢦⢳⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣝⣫⣾⣷⣝⣫⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣛⣛⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⡄⠈⣛⣛⠁⢠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢫⣾⣧⢿⡿⣼⣷⡝⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠻⣿⡸⢇⣿⢟⣼⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢫⣿⣿⠿⢷⣿⣇⣸⣿⡾⠿⣿⣿⡝⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢏⡾⣫⣶⣿⣷⣮⡹⢏⣵⣾⣿⣶⣝⢷⡹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⣼⡇⡿⢿⣿⣿⣿⡇⣾⣿⣿⣿⡿⢿⢸⣧⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡆⣶⣿⣷⣎⢻⣿⡸⣿⣿⡟⣱⣾⣷⣶⢰⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠇⣿⣿⣿⡿⣸⣿⣿⣮⢻⣇⢿⣿⣿⣿⠸⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠻⣿⠇⠟⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⢸⡿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢸⠇⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢸⡇⠉⠀⠀⣠⣶⣾⣿⣶⣶⣄⡀⠀⢀⡀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠉⠛⢿⣦⣼⣧⣠⠄⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢀⡀⠀⠀⣠⡉⠛⠛⠋⠀⠀⠀⠀⠀⣿⠇⣠⣶⣦⢰⡿⠁⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢰⣿⣿⢀⣾⣿⡟⣰⡟⡆⣼⢀⣾⡇⣸⡟⣼⢋⣾⢃⣿⠇⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣿⣿⡟⡼⢱⣿⢿⣿⠞⢡⣿⡿⣿⣰⣿⣴⠿⠋⠛⠋⢿⣾⠟⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⣿⣿⣿⠃⣾⣿⡾⣿⣤⠟⠟⠀⠙⠁⠉⠁⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⢸⣿⡏⠀⢿⣿⠁⠀⠀⠀⠐⠀⠀⣤⠀⣰⣆⣀⣶⣦⣤⡾⠟⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡇⠈⠛⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⣼⠹⢺⡟⢉⣿⠏⣩⣤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⣿⠁⠀⣿⡄⠀⠁⠀⡀⠀⣠⣶⡆⣸⡷⢡⣿⢁⣼⢏⠜⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⢰⣿⠁⢀⢀⡾⣻⣰⡏⣼⢃⡟⠁⣺⣧⠂⣿⠃⣼⣿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢰⡟⢸⡷⢃⣿⡼⣇⠸⡧⠁⠘⠃⠀⠀⢰⣿⠇⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢰⣿⡁⢸⣇⠾⡴⠏⠉⠀⣀⢀⡄⠀⠀⠀⠀⢀⣿⡿⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⡿⠀⠘⠋⠀⠀⠀⠀⣰⡏⣸⡇⢰⡆⠀⠀⢸⣿⡇⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢠⣿⠃⠀⠀⠀⠀⠘⣿⣇⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠾⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁





⣿⢿⠿⠿⡿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣟⣻⣿⣿⣟⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠠⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⠄⠒⠒⠒⠢⣄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢋⠑⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠊⡀⠑⠄⠀⠀⠀⠘⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠁⠢⡞
⠀⠀⠀⠀⠀⠀⠠⠊⠱⡀⠀⠢⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⢔⠋⠉⠉⠉⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⢄⠁⠀⠀⠀⠀⠀⠘⠓⠠⡄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⢦⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢀⠄
⠀⠎⠀⠀⠐⠀⠀⠀⠀⠀⠛⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠄
⠀⢆⣣⣀⠴⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠁
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⠎⢠⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠈⠢⠤⣀⡠⠤⠴⡊⢁⠔⠻⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠔⠀⡠⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢸⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡸⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡰⢡⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⣀⡴⢋⠔⠁⠀⠰⢁⡜⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠱⡖⠊⠁⢮⣀⡄⢀⣠⠗⠈⠀⠀⢀⠎
⠀⢀⠆⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠤⠒⠓⠀⠀⠀⠀⢱⠀⠀⠀⠀⠉⠡⡅⡀⠀⠀⢀⡜
⠀⠈⠮⣀⣀⣀⣀⡀⠀⠤⠤⠐⠒⠒⠒⠒⡲⠛⠉⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⣀⠀⣠⣀⡤⠒⠊⠉

⠀⠀⠀⣾⡿⠳⡄
⠀⠀⠀⠻⣦⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⣤⣤⡶⣶⣾⣞⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣩⣽⡇
⠸⣿⣷⣄⠘⣿⣷⣄⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⣦⠿⣏⣀
⠀⢹⣿⣿⣄⠙⠿⣿⣧⢻⣿⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⡤⣴⣶⣿⣿⣿⢡⠃⢰⣿⡿⣦⡶⢶⣶⠤⣤
⠀⠀⢿⣿⢻⣿⣷⣦⣌⣹⣽⣵⣦⣽⣶⣿⠿⠓⠀⠀⠀⠀⠀⠀⠻⡍⠻⢹⡿⠿⢾⡿⠛⢹⣿⡇⣼⠀⣿⣿⣷⣿⡇⠀⣿⠀⣾
⠀⠀⠈⣿⣷⡻⣿⣿⡿⣿⡿⠿⠿⠟⠿⠍⣽⡖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⣸⣿⣇⣿⣀⠿⣫⣿⣿⠁⠀⣿⣤⣟
⠀⠀⠀⠸⣿⣿⣷⣶⣶⣶⣤⣬⣬⣘⡈⢠⣿⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣛⣤⣻⠟⢻⡿⢿⢡⣾⣿⣾⡇⣠⣚⣡⣴⢸
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⠸⣧⠸⡀⠀⠀⠀⠀⠀⢰⣿⠻⢧⡿⣽⠏⢰⣾⡶⠟⣹⣿⣿⣿⡟⠈⠉⣿⣵⢾
⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠉⠙⠛⠛⠛⠛⠹⣦⠹⣇⢳⠀⠀⠀⠀⠀⢸⡇⠀⢸⣇⣿⡀⢸⣿⠇⠈⣿⣿⣿⣿⠁⠀⢠⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠈⢧⡹⣾⣿⠶⠖⠀⠀⠸⡇⠀⢸⣿⣿⠭⢼⣿⢐⣯⣿⣿⣿⡟⠀⠀⢸⣟⢲⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠱⡹⣄⠀⠀⠀⠀⠀⣇⣀⣸⣿⣿⢩⣿⣿⣾⣿⣿⣿⣿⣇⣀⣀⣸⣯⣦⣾
⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⢷⣿⣷⡦⠀⠀⠀⠀⠈⢽⡿⠟⢛⣿⣿⣿⡟
⣿⣿⢟⠿⢛⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⣤⣤⡀⠀⢀⣤⣤⣤⣤⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⠀⠛⠛⠁⠀⠈⠻⠛⠛⠛⠃⠀⠀⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣦⡀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣄⠀⠈⠻⣿⣿⣆⠀⠀⠘⣿⣿⣦⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧⡀⠀⠘⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⠀⠀⠻⣿⣿⡄⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣿⣿
⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠙⢿⣿⣧⡀⠀⠹⣿⣿⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀
⠀⢀⣼⣿⡿⠛⠛⠛⢿⣿⣷⡀⠀⠀⢿⣿⣧⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣰⣿⣿⠟⠛⠛⠻⣿⣿⣄
⠀⣼⣿⡿⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⢸⣿⣿⠀⠀⣿⣿⣷⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⡄
⠀⢿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣼⣿⡿⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠘⣿⣿⣦⡀⠀⢀⣠⣿⣿⠇⠀⢸⣿⡿⠁⠀⢰⣿⣿⠃⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣄⠀⠀⣠⣾⣿⡟
⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠀⠀⢠⣿⣿⠏⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⡀
⢀⣾⣿⡿⠛⠉⠉⠉⠙⢿⣿⣷⡄⠀⠀⠀⠀⠘⠛⠃⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠉⠉⠉⠙⠻⣿⣿⣆
⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠻⢿⣿⣷⣄⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⡆⠀⠀⠀⠀⣾⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣧⣤⣤⣤⣤⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠟⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣻⣿⣃⣀⣀⣀⣀⣀⣀⣀⣈⣻⣟⣀⣀⣘⣿⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣟⣀⣀⣘⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠖⠒⠲⠤⢤⣀
⠀⠀⠀⠀⠀⣼⠧⣼⡿⢳⣤⠤⠶⠖⣶⢶⠶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⣠⠀⠀⣠⠄⠀⠀⠈⡳⣄
⠀⠀⠀⠀⠀⣏⠙⢺⠟⠉⠀⢀⡠⠞⣡⠋⢰⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⣚⣉⠥⠒⢩⡯⠔⢧⡞⢆⠳⡈⢳⡀
⠀⠀⠀⠀⠀⠈⢹⠧⠤⠖⠋⠁⣠⠞⠁⣠⠋⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠑⢦⣀⣧
⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠴⠊⠁⣠⣼⠁⠀⠀⠐⠆⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⣰⠒⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⠸⣆⠴⡶⠀⠀⣀⣀⠤⣄⠀⠀⠀⠈⠛⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠈⢏⣉⣩⠽⠶⠂⠀⠀⠀⠀⠀⠀⠦⣄⣠⠏⠀⠀⠀⠀⠀⠀⡔⠒⢲⠉⢆⠙⢦⣀⠀⠀⢷⣀⣀⠜⠀⠀⠀⣀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢧⣑⠈⠂⢸⣄⠀⠈⠙⢲⡶⢶⢦⡶⢶⡒⣿⡿⡑⢍⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠛⠋⠉⠉⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡍⠈⢦⠀⣰⠛⣧⢸⣸⠁⢰⡁⢸⠙⠮⣹⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⠁⠀⠳⡄⠋⠀⠖⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠴⠛⠀⠀⠀⠀⢢⠘⡇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡄⠀⠘⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⣀⠔⠁⢠⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠤⠤⠤⠽⠶⠦⢄⡀⠉⡷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢠⣞⠁⢀⠔⠋⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⢄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢼⡅⠈⢹⠁⣀⣠⠤⠞⠉⠉⠓⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡊⠉⠀⠈⠳⠤⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠛⠛⠉⢸⠗⠒⠒⠒⠒⣚⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠘⢏⣓⠒⠒⠒⠒⠒⣒⣈⡡⢾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠒⡶⠶⢦⠤⡶⠚⠉⢹⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠉⠁⠀⠀⠈⡟⠙⡏⠉⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⢸⠀⢹⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⠀⠀⠀⡧⠀⣇⡀⠧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⠿⡀⢸⣠⠋⢧⣀⡠⣇⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣀⣧⣄⡀⠀⠀⢿⣀⣐⣉⢙⠧⠜⠃⠀⠀⠀⠀⠀⠀⢰⡋⣉⠴⠶⢳⠛⢁⠟⠻⠥⣤⢤⣤⣤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠤⠤⠤⠤⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⣶⣶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⠢⣐⠀⢭⣺⣿⣿⣿⣀⣔⠠⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⠔⢄⠀⠀⡇⢹⢹⠀⡀⠀⠈⡦⣷⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣟⠿⢯⡢⢠⠆⠀⠘⠃⠈⠛⠀⠀⡺⣰⢿⣿⡿⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠎⠀⠑⠮⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡁⡠⠓⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣬⠒⠒⢤⠀⠀⢀⣀⢀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⡀⣸⡘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⣉⠀⠀⠈⠚⠉⠁⠓⠉⠚⠉⠁⠀⠀⠰⠽⣥⣶⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⡹⢯⠥⠞⠊⠀⠀⠇⠖⠿⠃⠿⠧⠧⠾⠃⠎⠀⠰⡂⠈⢻⢿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡀⢀⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⡱⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢉⣧⣤⣪⢔⠆⠀⠀⠀⠀⠀⠀⠀⣠⢀⢵⣉⡢⡔⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣯⡜⠁⠀⠜⢳⢠⡟⡄⠀⠡⡀⣹⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡯⠥⢑⠠⡠⢤⣼⣾⣦⢧⡀⠠⢌⠈⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣸⣿⣿⣿⣱⠆⠈⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⣶⣿⣿⣿⣿⣷⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⢯⣟⣛⡻⢿⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡧⠞⡛⠃⠉⠁⠀⠁⢻⢿⡿⢽⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⢱⠿⠁⠀⠀⢂⣤⠀⠂⠀⠀⠻⣿⠘⣿⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠉⠉⠙⠻⣿⣦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⣷⠌⠐⠀⢀⡏⢘⣵⣾⠆⠋⠀⢰⠜⣦⣿⡻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⢠⣄⠀⠠⠌⠬⡙⠧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣹⡅⠂⠀⢠⡆⢨⠋⠙⠀⠀⢠⡖⠀⣸⢏⣷⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠈⠁⠐⡟⣓⠀⠀⠈⢀⠙⠿⠿⣿⣿⣿⣿⣿⣕⢦⡀⠸⣦⡄⢉⠀⠈⢀⣄⣡⢀⡿⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡅⠒⠐⠟⠈⠁⠐⣨⡽⠋⣻⠶⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣶⣶⢶⣤⣤⣤⣤⣶⣾⣵⣾⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠛⠛⠻⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡿⠂⠉⠛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠄⠛⠛⠛⠉⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⢠⣭⣶⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⢿⣿⣿⠟⠁⠀⣰⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠉⢻⣿⡿⠟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀
⣤⣤⡄⠀⠀⠀⠙⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⢛⣿⣷⠀⢠⣤⣤
⣿⣿⡇⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣿⣿⣿⠋⢀⣾⣿⣿⠀⢸⣿⣿
⢸⣿⣧⠀⠀⠀⣿⡟⢿⣿⣧⣠⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⣿⣿⣿⠀⣾⣿⡇
⢸⣿⣿⠀⠀⠀⣿⡇⢸⣿⣿⡿⠿⠛⠛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠘⣿⣿⠀⠀⠀⣿⣧⣈⣡⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⠁
⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿
⠀⠛⠛⠃⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠘⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢪⠁⠀⠪⠉⢱⠉⢩⡽⠷⠁⠀⢩⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⡏⠂⣤⠎⠒⠅⠀⠀⠏⣺⠦⢄⠂⢈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠐⠤⠊⠙⢖⠚⡆⠤⠆⠀⠘⠦⢺⣀⡠⠁⠀⢑⣌⣷⠔⢄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠑⠀⡐⠠⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⣂⠊⠉⠈⡆
⠀⠀⠀⠀⠀⠀⢰⣱⣄⠠⣾⣤⡤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠞⠉⡃⠤⠲⡽
⠀⠀⠀⠀⠀⠀⠀⢹⠙⠴⠶⠁⠼⠀⠀⠀⣔⣠⣤⡔⣤⣠⣤⠄⠀⠀⠈⠓⠂⠈⢢⢴
⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⢀⠀⠀⠀⣀⣀⣀⡀⣀⡀⡀⣀⣀⡀⠀⢀⡤⠠⣄⣴⠈⡄
⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⣣⠀⣸⡃⠀⠀⠈⠉⠃⠉⠉⠉⠉⠀⠁⠀⡤⠷⢶⡮⠀⢿⢻
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡈⠛⣇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡌⢇⢀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢦⣿⡗⠼⠁⠀⢀⠔⠳⡀⢤⠀⠀⢠⠤⣘⣉⣂⠀⢀⢇⡠⠪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠜⠂⢁⠢⣤⡗⢤⠀⠀⢀⡀⡬⠗⢈⣝⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠇⠀⢈⣄⠽⠄⠰⡊⠀⡀⠀⠈⣙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠭⠼⠋⠁⠉⠉⠘⠓⠒⠋⠁

⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⡦
⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣧⡶⠶⠶⢿⡗
⠀⠀⠀⢸⣿⡇⠀⠉⠹⣿⠀⠹⣷⣄⣤⣤⣤⣤⣤⡆⠀⠀⠀⠀⠀⠀⢀⣾⢿⡏⠘⢿⡄⠀⢸⡇
⠀⠀⠀⢸⣿⢿⣆⠀⠀⣿⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⣾⡇⠀⣨⡿⠂⣾⠇
⠀⠀⠀⢸⣿⠀⠻⡧⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⣿⣠⡾⠋⠀⠀⣿
⠀⠀⠀⠀⣿⡀⠀⠀⠀⢹⣇⢀⣀⣠⣤⣤⣴⣶⠀⠀⢤⣴⣿⣷⣶⣶⣤⣼⣿⠋⠀⡀⠀⣸⡏
⠀⠀⠀⠀⢻⣷⡾⠃⠀⠘⠿⠿⣿⣿⣭⣤⣤⣿⣀⣀⠘⣿⡄⠀⢀⣴⣿⣟⣁⣀⣘⣿⣦⣿⠁
⠀⠀⠀⠀⣼⡟⠛⠿⠿⠷⠶⠶⢾⡟⠁⠀⢹⣿⡿⠋⠀⢘⣿⣾⠟⠉⠉⠉⠉⠉⠛⠛⢿⡇
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣼⣿⠁⠀⠀⠸⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⡿⠋⣿⡀⠀⠀⠀⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⢿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠸⡄⠀⠀⠀⣄⡞⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠹⡄⠀⢀⡿⠁⠀⠀⠀⢠⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢿⡀⢸⠁⠀⠀⠀⢠⠞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣧⡇⠀⠀⠀⣠⢏⠀⠀⢀⡇
⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⢀⠐⠤⡀⠀⠀⠀⡀⠀⠀⠠⠈⠳⣀⢸⡇⡀⠀⡴⠃⠈⠂⢠⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⣀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠘⢈⢣⡀⠀⠀⠈⢦⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠙⠼⠃⢀⡼⢡⠀⠶⡀⡀⠁⠔⠂⠀⠀⠀⠈⣀⠔⠁⠀⡴⠁⠀⠀⢀⡜⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⣇⠀⠠⠳⠄⠠⠀⠀⠂⢀⠀⢀⠀⠀⢚⡁⢀⠀⠀⠀⠀⠀⠄⠂⠐⠀⠀⢠⠏⠀⠀⣸⠁⠀⠀⢀⡟
⠀⠀⠀⠐⠤⢀⣀⡀⠀⠹⣄⠀⠀⠸⡇⠐⠀⠀⠀⠀⠐⡄⠀⢀⠀⠄⠀⢀⡴⠋⠀⠀⠶⠀⣌⣤⠀⡀⡠⠀⠉⠀⠀⢸⠇⠀⠀⣠⠏⠀⢀⣀⡀⠠⠂
⠀⠀⠀⠀⠈⠣⣄⠉⠙⠒⠮⢧⣄⠀⢱⡐⠀⠀⠤⠀⠀⢠⠀⠈⡀⠀⠊⠉⡀⠀⠂⡠⠐⠘⣋⠛⡁⠁⠀⠤⠈⠀⢀⠎⠀⣠⡴⠵⠖⠋⠉⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠬⠳⣄⢀⡀⠀⠲⢀⠼⠤⢿⢿⢠⡁⠐⠦⠔⠚⠁⣀⠠⠎⣁⠀⠀⠀⠀⠀⠀⢈⠎⣠⠞⠥⠤⠤⠔⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠙⠀⠀⠈⠈⠁⠀⠘⠃⠀⠀⠂⠈⠀⠲⠈⠁⠂⣅⠀⠸⡄⠠⠀⣀⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠐⠀⠀⢚⠀⠠⠀⢀⠀⠀⡀⠁⠘⠢⠀⠀⠈⡵⠃⢩⠀⠀⣨⠆⠘⠅⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⣉⠁⠀⠺⠃⢀⠀⠀⠈⢄⡈⠀⠀⡀⠀⡀⠀⠐⡢⠴⠡⠄⠚⠒⠚⠛⠛⠉⠉⢉⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣦⣤⣬⣅⣤⠀⠀⠑⠂⠀⠱⣰⡞⠉⠐⠃⠀⠠⣄⣤⣤⣤⢤⣴⡖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠋⠁⠀⠀⠀⠀⢄⡾⠃⠀⢒⢀⠌⠀⠀⠐⠐⠀⠻⣆⢀⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⣀⣀⠤⠒⣡⠎⠀⠀⢰⠀⠠⠄⠀⠄⠀⣶⠀⠀⠈⢧⡑⠢⢄⣀⡀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣀⠤⠒⠚⠉⠁⠀⣠⠞⠁⠀⠀⠀⡸⢃⠤⠀⠀⠘⢄⠹⠀⠀⠀⠀⠙⢦⡀⠀⠉⠙⠒⠦⢄⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⡠⢾⠃⢸⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢰⠀⢻⠦⡀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠊⢠⡏⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⣧⠈⠲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⡾⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡄⠀⠀⠈⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠊⠀⠀⠀⠀⠠⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡱⠀⠀⠀⠀⠘⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠉⠉⠉⠓⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠛⠓⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⠴⠒⢎⢫⠙⡄⠲⣄⡀⠀⠀⠀⠀⠱⡄
⠀⠀⣠⠞⠁⠀⠀⡠⠠⠄⠀⢈⡇⠀⠙⡀⠈⠀⠢⢀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⢞⢱⠀⣣⠎⢂⠡⠈⡄⠱⢸⢆⠀⠀⠀⠀⠹⡀
⠀⡴⠁⠀⠀⢀⡀⠀⡶⠀⣀⣀⡍⠀⡤⠙⢔⠀⢀⡔⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡾⠘⡌⡔⢁⠎⢀⡆⢣⢸⠀⡙⡘⡇⠀⠀⠀⠀⡇
⣸⠁⠀⡐⠀⠀⠈⠂⡘⢀⡤⢠⠤⠴⢖⡑⠞⠓⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⡘⢀⠃⢠⠃⢰⠸⢈⠔⡡⠁⠛⠀⠀⠀⠀⢸
⡏⠀⠀⠡⡀⠨⢀⠋⠱⢦⡰⠺⠐⢐⣍⢁⡃⠶⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢒⢅⣘⠀⠃⣀⠄⠒⣁⣼⠔⣂⡇⠀⠀⠀⠀⠘⡄
⣇⠀⠀⠐⠀⡴⠦⢤⡘⠮⣛⣳⠂⣭⠾⢋⠳⠀⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢖⡂⠤⠬⠭⠙⣉⠥⠐⠅⣨⠎⠀⠀⠀⠀⠀⠀⠸⡄
⢹⡀⠀⠂⢴⠖⢟⡭⠝⢢⡘⡟⠠⡌⢀⣻⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠑⢍⣂⠥⣁⡝⣠⣪⠮⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⢧⠀⠀⠸⠤⠘⠉⢫⡳⢝⡦⠌⠀⠀⠉⠤⡀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⡆⠀⠀⠀⠐⠂⠀⠀⠔⠁⠁⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠈⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠈⠉⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠊
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠈⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⣿⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⣄⣀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⠃
⠀⠀⠀⠀⠀⢨⠀⠈⠛⠻⠿⠿⠿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⠀⣠⣿⡟⢹⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠃
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⢹⣿⣿⡇⠀⢹⣿⠿⣿⠿⠟⠁⠀⢀⣴⣿⡏⠀⣸⣿⠃⢰⠀⠉⠙⠋⢹⠀⡟⠁⠀⠀⢹
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠐⠾⡿⠛⠿⠁⠀⣿⡟⠀⢸⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠈⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠿⢿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠏⠩⠁⠀⠀⠀⠀⠀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢾⣿⣆⠀⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠙⢻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠔⠛⠓⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢇⠀⠀⠀⢀⠲⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠂⠀⠱⡀
⠀⠀⠀⠀⠀⡆⠀⠰⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠤⠒⠃⡼⠀⠀⠀⠀⠉⢡⠀⢠⠀⠀⠀⠀⢠⠊⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣀⣀⡠⠈
⠀⠀⠀⠀⠀⢸⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⡀⡼⠀⡄⠀⠀⢸⡇⠈⣓⠇⠀⠀⠀⠀⠀⡀⠟⠀⠼⠇⠀⠘
⠀⠀⠀⠀⠀⢸⣀⠈⠀⠀⠀⠀⠀⠤⠤⠄⣀⣀⡉⠁⣿⣤⠀⠻⡀⠀⠀⡀⠂⠀⢠⠈⠀⠀⠀⠀⣀⢀⢁⣠⡀⠀⣆
⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣱⡒⣀⣤⡶⠛⠂⢀⣄⣤⣤⣦⡁⡔⠉⠈⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⡆⢸⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠢⠀⠀⠂⠐⠀⠀⣒⣣⣄⣀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣄⣀⠀⠒⠂⠂⠀⡏⠁⠉⠈⠉⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠀⠀⢀⠔⠂⠀⠹⠜⠀⠀⠀⠓⡄⢷⠐⠆⠀⠒⠒⠚⠒⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⡀⢀⡠⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠂⠊⢀⢼⠎⠁⡄⠂⠀⠀⠂⠂⠁
⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀⠀⠀⠀⠀⠀⠀⠰⡤⠄⠀⠀⠀⠀⠂⠀⢹⡆⠀⠨⠁
⠀⠀⠀⠀⠀⡆⠀⡜⠀⠀⠀⠀⠀⠀⠠⠠⠇⣔⠸⡄⠀⠀⠀⠀⠀⠀⠐⠦⠆⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠃⠀⠇⠀⠀⠀⠀⠀⠀⠶⠶⠶⠤⠤⠶⠴⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡀⠤⠤⢤⡎⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣸⢦⡤⢤⣴⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⣀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⢸⠘⣯⡼⣬⣿⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⡸⡏⠐⠒⠋⠳⣧⣀⣀⣀⠠⣖⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠣⢼⠊⢹⠻⠭⡾⣿⠤⠄⣀⠀⠀⠀⠈⡆⠀⠀⢇⠐⡀⠀⠀⠀⠉⠢⠤⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⠀⣂⠈⠉⠚⣁⣹⡷⣦⣄⣉⣳⠄⠀⢸⣔⠀⠈⠣⣌⠢⢀⠀⠀⠀⢀⣠⠭⠛⠉⠉⠙⠛⠒⠤⣤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⣍⠉⠑⠳⠝⡛⠠⢄⣈⠪⣧⠉⢹⠀⠀⠀⠿⠝⠁⠂⠤⣉⡓⠯⠿⠈⠉⠁⠈⠉⠒⢄⡀⠀⢀⢀⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠒⠤⠤⠼⠁⠀⠈⢢⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⡀⠀⠀⠀⠀⣉⠭⠛⠻⢒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⢸⠀⠀⣠⣉⢿⢤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⢳⠂⠉⠀⢠⠤⣀⣑⠚⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠨⠊⠉⠧⣀⠈⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⢠⢤⡀⡃⠐⠆⠀⠀⡄⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⢠⣠⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠈⠀⢑⡆⠀⠰⠔⠀⠀⠀⠀⠠⠀⠀⠄⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠀⠚⠀⠀⠀⠀⢂⣥⣀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⢄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠃⠀⠀⡙⠀⠀⠀⠀⠀⠀⠘⠀⢈⠎⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠆⠡⠁⢁⠈⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⢆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠠⢬⠀⠘⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⢄⢀⡀⡀⠀⡈⠁
⠀⠀⠀⠀⠁⠀⠁⠘⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣛⠀⠀⠄⠀⠡
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠌⠀⢰⣅⠉⠤⠀⠠⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠈⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠈⠁⠀⠀⠀⠀⠐⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⠀⠉⠄⠀⠀⠁⠄⠀⢀⠀⠀⠀⠀⣠⠔⠒⠀⠀⠀⠂⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⡄⣈⣠⡄⢃⠀⠈⡄⠀⠄⠀⠂⠀⠀⢁⠄⠀⠀⠀⠀⠀⠀⠈⡀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠄⠀⠠⠊⠀⠀⠈⠠⡕⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠄⠠⠀⡄⠁⠀⠀⠀⠴⠘⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⡀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⢀⡾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠺⡖⡀⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠸⡇⣨⠀⠨⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⢻⡈⠁⠀⠘⢁⡄⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠇⠀⠃⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠃⠀⠀⠠⠐⠄⠀⠀⠀⠀⠀⡀⠈⠉⠀⢀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠤⠀⠀⢠⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈
⠀⠀⣈⠁⠴⣂⠀⣤⠐⠁⠀⠈⠓⠂⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⢂⡠⡄⠶⣀⣀⣐⢀⡃⠈⠴⠂⠄⠀⠌⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠠⠆⠲⠀⠙⢃⡀⠀⠐⠋⠀⠀⢀⠔⠂⠈⠀⡀⢀⠈⠒⠀⠒⡀⠐⠀⠀⠙⠙⠣⡀⠀⢴⠐⠀⠐⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⢠⣰⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⡀⠀⠃⠀⠀⡀⠈⠣⡀⠈⠂⠀⠀⠂⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠠⠋⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠄⠂⠀⠀⢀⡤⠠⣀⠀⡀⠀⢄⠀⠄⠀⢀⠀⢀⠀⠈⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠁⠐⠒⠀⠱⡀⢀⠐⡦⣀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⡠⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢂⠐⠀⠀⠀⠀⢀⠇⢸⠀⡀⢣⠐⠀⠀⠀⠀⠀⠈⠀⠀⠊
⠀⠀⠀⠀⠐⠂⠀⠰⡄⠀⠀⠁⠀⢀⠐⠀⡆⠨⠀⢴⠀⡄⠀⠡⠆⠀⠀⠀⠀⠀⠀⠀⠠⠊⣠⠆⣀⡤⠂⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠒⣀⠄⠉⠀⠄⠀⠀⠰⢀⠀⠆⠠⠊⢀⠁⠔⠀⠉⠉⠉⠉⠀⠀⠐⠲⠂⠞⠁⠈⠉⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠄⠉⠒⠀⠸⠤⠘⠄⠀⠀⠈⠀⠄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⣤⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⢀⠁⠑⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠤⣈⠀⠐⡍⢀⠀⢀⡠⠄⠓⣦⡀⠀⠐⠀⠀⠀⣠⠤⡖⠒⠒⢲⠤⣀⠑⠄⠀⠀⠀⠀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠊⠁⠰⡄⠀⢸⠃⠈⠀⡆⠀⡔⢩⠀⡆⠀⠀⢸⠀⠈⠣⠈⠆⠀⠂⠀⠀⠀⠁⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠁⠀⠈⡄⠀⠀⠀⠀⠊⢰⡄⠠⢸⠀⢸⠀⢀⠀⡄⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡇⢠⢸⡀⢻⡆⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡅⠁⢈⠙⠃⢸⡇⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠿⣀⠀⢀⠀⠀⠀⠀⠈⡄⠄⠈⡇⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠃⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠆⠀⠲⣦⡄⠠⠄⠆⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢱⣂⡄⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠈⡀⠲⠠⠄⠉⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣟⣥⢬⣟⡛⠛⣛⡛⣛⠛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠉⠉⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠤⠖⠒⠒⠤⣄⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣄⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠈⢀⡎⢸⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠤⣀⠀⡜⠀⢠
⠀⠀⠀⠁⣀⠤⠤⠒⠲⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢧⠀⠀⠀⢣⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠙⢧⡴⠋
⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢀⡈⠂⠀⠁⠀⠀⠈⠳⣄⣀⣠⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠊⠈⡆⠋⠈⢳⡀⠀⢣⠀⠀⠀⠀⠉⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠇⢰⣦⠉⢷⡆⠀⣇⠀⠀⢂⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠦⠤⠊⠀⠳⣄⣠⠇⠀⠈⢦⠳⢄⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣰⠋⠀⠀⠉⠉⠀⠀⠙⡆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⢑⠀⠀⢰⠟⠀⣠⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠓⠲⠤⠧⠖⠓⠚⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⢧⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣄⣀⠀⠀⣸⢦⣀⠀⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡏⠈⣧⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠙⢥⣤⣭⠟⠻⡁⠱⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⡇⠀⠈⢣⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⢋⠇⢀⡔⠁⠀⢠⠏⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⡘⢤⣠⠞⠀⠀⠀⠀⠀⣠⠴⠋⢉⠁⢠⡏⠀⠀⢀⡏⠀⢠⠏
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⡗⠦⠤⠤⠘⠦⣀⠀⠀⠀⢲⡖⠉⠣⢧⢤⣇⡤⢞⠔⠒⠒⠚⠀⢀⡞
⢠⠊⠁⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣀⣨⠷⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢯⣰⠀⠀⡆⠀⢻
⣇⣰⠃⢠⠀⠀⡀⠀⢀⣀⣀⡤⠖⢛⡭⠖⠒⠒⠚⠛⠉⠁⠀⠀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠘⠓⠒⠓⠶⠚
⠈⠉⠳⠾⣤⣤⠿⠉⠉⠉⠀⠀⠀⡟⢰⠂⢠⠆⠀⢠⡶⠒⠛⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣻⣶⣾⣦⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠁⠒⠦⣄
⠀⣀⡀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠲⣄⠀⠀⠀⠀⡠⠊⡠⠔⠒⠒⠒⠒⠤⣀⠀⠀⢈⡇
⡞⠁⠀⠀⠀⠀⠉⠲⢄⣀⠠⠤⠒⠒⠒⠤⣠⠋⠀⠀⠀⠀⠀⠈⠣⡀⠔⣋⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉
⠑⠲⠴⠤⠤⣄⣀⠠⠤⠄⠒⠒⠉⠀⠑⢢⠀⠀⠀⠠⠀⠀⠓⠀⠀⠀⠺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠃⠀⠛⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⣀⣤⠤⠤⠤⠤⢤⣀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⠀⢈⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡀⠀⠳⡀⠰⣄⣀⣤⣴⠫⠔⠉⠀⠀⠀⡼
⠀⢀⣀⣴⠛⢳⡤⣄⠀⠀⠀⠀⡜⢠⠃⢣⠀⠀⠀⠉⠉⠉⢻⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢻⡀⠙⠀⠘⠀⢈⠇⠀⠀⠀⢇⠘⠂⣐⢧⡀⠀⠀⠀⠀⡘⠈⠲⠤⣤⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢴⠉⢀⠀⠉⠢⡀
⠀⠀⠙⡄⢀⣀⢢⡏⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠢⠤⠤⠚⡅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠻⣆⣠⣀⡹
⠀⠀⠀⠹⡄⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠏
⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡉⠓⠶⠤⣤⣀⣀⣀⣀⣀⡜⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⣀⡤⠞⠋⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⣤⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣉⣉⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣿⣤⠶⠶⠛⠛⠛⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠦⣄⡹⣄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠞⢁⡾
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠈⠐⠤⣀⡀⣀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠖⠛⠳⠤⠤⠤⠄⠒⠉⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⣀⣀⠀⠤⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⢶⡒⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣈⣹⠏⠛⠛⠛⠛⠉⠙⠧⠤⠤⠶⠶⠶⠶⠶⠦⡄⠀⢀⠀⢀⢹
⠀⠀⠀⠀⠧⣴⣠⡀⢰⠆⠒⠒⠚⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠼⠥⠞⠋

⠀⢰⣻⣳⡄⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡂⣐⢀
⢀⣈⣛⣋⣀⠀⠀⠀⠀⠀⠀⢸⠻⠂⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠛⠡
⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠢⠬⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⣀⠅
⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⢀⡀⡏⠒⣱⠀⠀⠀⠀⠀⠀⢨⡿⠿⢿⣳⠀⠀⠀⠀⠀⠀⠀⣤⣬⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⡆
⢘⠄⠀⡔⠼⠂⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⡭⠿⡛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠈⠉⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⠄⠀⣀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⠤⣎
⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⠁⠀⡆⠀⠀⠀⠀⠀⠀⣀⣀⢩⣷⡄⠀⠀⠀⠀⠀⠀⣌⣀⢀⣀⣑
⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⠖⠁⠉⠉⠀⠀⠀⠀⠀⠀⠻⡿⠟⠀⠛⠋⠀⠀⠀⠀⠀⠀⢷⠤⠶⠿⣴


⢀⡖⢰⡏⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⢸⣧⣬⣥⡾⠁⠀⠀⠀⠀⠀⣾⣿⣯⣿⣷⡀⠀⠀⠀⠀⠀⣴⠡⠴⠬⢅⣢⠀⠀⠀⠀⠀⠘⠻⠿⡶⠃
⠈⠛⣿⡿⠇⠀⠀⠀⠀⠀⠀⠻⢿⣧⣿⠿⠃⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣈⠀⠀⠀⠀⠀⠀⢠⢒⠀⠀⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢏⠹⠇⠀⠀⠀⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠉⠉⠃⠀⠀⣿⠟⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠁⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠂⠒⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠀⠊⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠠⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠀⢀
⠀⠀⠀⣠⠄⣰⢆⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡇⢤⢀⡄
⠀⠀⠈⣏⠝⠞⢸⠁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡕⣸⠁
⠀⠀⠀⢹⡌⡵⢸⡀⠀⠀⠒⠠⠀⠀⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢢⡏
⠀⠀⠀⠀⢧⢀⠊⢧⠀⠀⠀⠀⠊⠀⠀⠤⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠰⢦⣠⠈⠀⡀⠀⠀⠄⠂⠀⠀⢠⡇⣾
⠀⠀⠀⠀⠸⡆⠰⢒⣿⣶⣤⣶⣾⣿⣶⣶⣾⣿⣤⡝⠀⠀⠀⠀⠀⠀⠀⢗⡊⢀⣠⡁⠀⠀⠀⠀⠀⢀⡞⢡⡇
⠀⠀⠀⠀⠀⣷⠨⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣶⣶⣾⣿⣤⣸
⠀⠀⠀⠀⠀⢹⠿⠿⠿⡟⠛⠻⢛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⠿⣛⡛⠛⡛⣹
⠀⠀⠀⠀⠀⠸⣏⣍⠸⠨⠤⠐⠄⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠫⠮⠉⠑⡢⠢⢆⣂⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠙⠉⠉⠉⠉⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣀⠂⠀⠀⠠⠐⢀⠠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠓⠛⠓⠒⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⢀⣀⠴⢏⣹⣿⣿⣿⡏⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠀⢙⠤⠔⠒⢾⠽⣿⣿⡿⠧⠄⠣⢍⠒⠴⠴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⠚⢄⠀⠀⢸⠦⢽⢸⠀⢀⠀⠀⠀⡹⣒⣷⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠲⡟⡿⣿⡓⢄⣀⡇⠀⠀⠙⠋⠀⠙⠃⠀⠀⠾⣁⡾⣿⣿⣿⡟⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠜⠉⠲⣤⣋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⡔⠁⢉⠧⢄⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠓⢎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠁⠀⠈⡄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣮⡉⠉⢱⠆⠀⠀⢠⢒⣠⣖⢤⠖⣤⡄⡆⣶⠄⠀⠀⠀⢀⢤⡤⠴⠧⡜⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⢭⢤⡀⠀⠀⠀⠉⠁⠁⠁⠉⠁⠉⠁⠁⠀⠀⠀⠀⠛⠼⠶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠿⣭⠤⠾⠜⠁⠀⠈⡇⠗⠶⣟⡁⠿⣇⠾⡄⠟⠋⡞⠀⠀⣴⠈⠁⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣀⣀⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠜⠤⡔⠁⢀⠇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙⢀⡀⣀⡞⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣶⣿⣷⣧⡞⢢⡍⠀⠀⣀⠀⠀⣀⠀⠀⠀⡖⠂⢌⣧⣤⣮⣯⢤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣢⠋⠀⠀⠘⠉⢱⢸⠭⣵⠀⠀⠑⢄⣰⣿⣿⣿⣷⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⢧⢌⡑⠠⡀⠤⣤⣾⣾⣧⢼⣄⣀⠠⢜⠀⠙⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢇⠀⣿⣿⣿⣿⠛⣤⠔⠒⠈⠑⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠃