Flora Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠰⣤⠤⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣖⠼⠒⠼⣧⣄⢛⣤⣄⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣴⣿⡿⠞⠙⠳⣾⣯⠿⢿⡁⢀⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠻⡏⠀⠀⠀⡠⢨⣁⢀⣄⡇⡫⢾⣟⠅⠃⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣄⣤⣾⣴⣿⣿⣿⣿⣿⣷⠟⣡⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠄⠀⠚⠾⢭⣭⣿⣦⣶⡶⠶⠟⠛⠋⣡⢞⣁⠀⠀⠀⠀⢀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢶⠶⠶⠞⠛⣹⡿⣳⡙⠲⠦⠤⠄⠷⡟⠁⠀⠀⢼⠿⠋⠞⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠰⡏⠀⠉⠉⠳⣶⣄⡀⠀⣀⡶⠖⠒⠀⡀⣀⣀⣀⣠⠴⠖⠂
⠀⠀⠀⠀⠀⣠⣤⣥⣶⠶⠞⢓⠒⠒⠚⠛⠒⠢⢄⣷⡀⠀⠀⠀⢹⣿⣷⠞⠁⢀⣀⠴⠛⠋⠁⠀⠋⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠛⠋⠀⠀⠀⠀⢀⡀⠀⣈⣻⣦⣤⣤⡿⠿⠑⠲⠾⢗⡀⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⠿⣻⠏⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣸⠵⠛⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠖⠋⠁⠀⠀⠀⠀⠀⠀⡜⣀⣠⣤⣶⣴⡾⢥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⣨⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢀⠀⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⡆⠀⠀⠀⠀⡀⠀⠀⠄⠘⠁⠀⠀⠀⠛⢭⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣀⠀⡄
⠀⠘⠇⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⠀⢄⣀⣀⣀⣤⣀⣀⠑⠀⠀⠀⠀⢁⠀⠀⠀⠀⢠⠄⠈⠐⠂
⡀⠀⠃⠀⠰⠀⢨⡀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠿⡿⠛⠛⠉⠙⢻⣷⠀⠀⠀⠁
⡧⠬⣁⠀⠀⠀⢐⠁⠠⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠐⠳⠂⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⢿⠀⠈⠀⠂⠀⢸⡀⢀⠀⠀⠀⠀⠀⠘⣧⣴⡔⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠈⢀⠀⠀⠤⠂⠃
⣀⡧⢄⠈⠀⠀⠸⡆⢀⠤⠀⠀⠀⠀⠀⠈⣿⠃⡠⣶⠀⠀⠙⠀⢀⠠⠀⠠⣰⠧⠀⠀⠀⠠⡀⠒⡠⠄⠁
⠁⢠⣄⠃⠘⡀⢸⡦⣾⠀⠀⠀⠀⠀⠐⢢⠈⠆⣐⡅⢨⠄⡀⢠⡋⡄⢉⠀⣯⠆⠀⠀⠀⠀⠉⠲⣀⠀⠘
⠀⠋⠀⣧⠀⣁⣺⠀⡿⣧⠒⠀⠀⢀⢰⡆⣰⠀⠀⠀⠺⠄⠟⠒⠀⢦⠘⢜⠿⠀⠘⢄⡠⠀⠀⠀⠀⠀⡄
⡠⠀⠐⠬⠺⠅⢹⠠⠑⢫⡷⡄⢀⠈⡼⠁⠘⠦⡀⡈⢈⠀⠀⠈⠁⣮⣷⣄⡀⠀⢀⡨⢬⡤⠨⠀⠑
⠀⣦⠦⠤⣴⡟⢻⠖⠁⠸⡇⠰⠀⠶⣶⠂⡀⠪⠜⠏⢺⠉⠁⡰⠀⢐⣿⣄⠆⠀⣬⡀⣼⠎⠉⡀⠀⠐⢆
⣁⢰⣶⡄⠹⠧⣿⣧⠈⠐⡄⣄⣉⣿⣅⣐⠉⠁⠀⠀⣯⢄⡎⣸⡻⢸⠈⡎⠼⠠⠉⠀⠁⠈⠱⠎⢤⢶⣂
⡨⢶⢿⣾⠟⢷⠜⠃⠀⣀⢁⣟⣿⣿⣿⣻⠋⢄⡀⠩⡷⡿⠅⢿⢾⣾⠶⢀⠥⠛⠂⡄⣸⡶⣎⣠⣿⣄⠈
⠁⢼⣇⣤⡈⣉⡴⣷⣶⢭⣜⣏⠉⣴⡞⣿⣀⣴⠂⣴⣟⡆⢁⡘⠲⡗⠀⠘⡀⠶⡆⠺⠽⢣⣻⣽⢷⡻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡶⠎⢻⡄⠀⠀⠀⠀⠀⠀⢠⣾⠛⠙⠋⠿⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡙⠚⢻⣿⡄⢀⣠⣞⠟⠛⠛⠟⠀⢀⣀⣤⣤⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣧⣿⠙⠈⠀⢀⣰⣶⣾⣿⣿⢟⣿⣿⠃⢰⡖⣲⡤⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣿⠇⠀⡞⢡⣿⣿⡼⢂⣼⣿⣻⠿⢶⣼⣿⣿⣷⡿⢉⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⡿⣿⠿⣿⣿⣿⡿⢋⣀⣉⠈⣿⣿⣿⣿⣿⣿⣏⠀⢄⠀⠘⠛⣿⣷⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢤⣤⣶⣿⣿⣿⣷⣿⣿⣿⣷⣤⣽⣿⣿⣯⣟⣹⡄⠀⣆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠛⢛⡿⠋⠉⠻⢿⣿⡿⠿⣿⣾⣿⣿⡟⠁⠀⡁⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠚⢃⣁⣄⡀⠀⢀⣀⠀⠶⠶⢾⣿⣶⣿⣷⣄⠀⡁⠈⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠈⠚⠹⡶⢿⠿⠿⣶⣄⢀⣿⣿⣿⣿⣟⡁⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠙⠂⠀⠀⠀⠠⠀⢠⣀⣈⣿⣿⡏⠸⠟⢿⡉⠑⠶⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⢤⣀⡀⠃⠀⠀⣠⣿⠿⣿⣿⣿⠄⠀⠀⠈⠙⠀⠀⠀⠀⣠⠴⢚⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠄⠉⠓⠄⢸⣿⣯⢰⡿⣿⣿⡄⠀⠀⣀⠀⢀⣤⡴⠟⢁⣼⠋⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⢠⡖⠁⢸⣿⣿⡟⣇⣿⣿⣷⡶⠿⠏⠀⣼⣿⠓⠀⣨⢁⡄⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⡅⢠⣾⣿⣷⣾⣯⣿⣿⣿⣤⡀⠀⠀⣿⣿⠂⢠⣇⡾⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢿⡦⢄⡸⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡄⠀⣿⣯⠕⣸⣏⠒⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣍⠁⢸⣿⣵⣦⣪⣿⣷⣿⣿⣿⣿⠋⣿⠈⠓⠘⣿⣆⠹⣿⡄⣿⣯⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣽⣿⣿⣿⣿⣶⣾⣿⠛⠛⠛⠁⠀⠋⠀⡤⠀⣬⣿⡄⠘⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⣩⣿⣿⡷⢹⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⣴⣖⠒⠶⣦⣀⠈⢛⣿⣿⣿⣷⣈⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⠉⠻⣶⣤⡀⢹⡟⢿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⡌⠻⣦⡀⠀⠈⣿⡄⠀⠀⠙⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣂⠘⣻⣆⠀⠀⢷⠀⠀⠀⠀⢿⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⡸⣿⣷⠀⠘⡄⠀⠀⠀⢸⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣀⢻⣷⣄⣷⡀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣾⣿⣿⣿⣦⡀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠙⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠠⢄⣀⢀
⠀⠀⠀⠀⠀⠀⢠⡖⠦⡀⠀⠀⠀⠀⠀⢰⠏⢀⣴⢱⡿⢛⡎⣑⢒⣳⣶⣾⣦⣴⢯⡠⡄
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⢶⡀⠀⠀⠀⠰⢬⢣⡄⠈⠹⢮⠑⣮⣿⣿⣿⣿⣿⣿⣦⡷⣿⠄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣾⣇⠀⠀⠀⢠⣡⢻⠙⢉⢳⣼⣀⠸⠉⠉⣿⣿⡟⠉⠻⢧⢿⣆⡴⣠⡄
⠀⠀⠀⠀⠀⠀⠠⣳⣶⣛⣿⠃⠀⠀⣀⡏⠙⠳⣄⣹⡆⠧⠬⣉⠙⠲⠣⢽⣿⣵⣶⡛⠛⣿⠃⣸⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠶⡄⠠⠀⠃⠈⣟⠻⠉⠛⣧⣰⠂⠈⠓⠀⠀⠀⠛⡻⠭⣤⣤⣿⣝⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣓⡛⣆⠉⢽⣿⣿⣧⣼⣏⣛⡉⡉⠈⠙⡷⣾⣻⣯⣽⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⡀⢱⠀⠋⢿⡡⢩⡗⠂⠤⠄⠤⠋⢹⣿⣏⠛⢙⣿⣿⣿⢯⣠⠾⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⣦⣶⡵⣿⡾⡫⠊⠐⠀⡤⠰⠒⠺⠛⠪⡟⡛⢿⣮⣍⣙⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⢌⣻⣵⣿⡭⠴⠂⢀⣶⠆⠀⠀⡆⠀⠀⢠⠤⠶⠯⢁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣷⡖⣦⣈⣿⠁⢀⠆⢰⣿⡔⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣆⡝⠀⠘⢁⣠⣴⡎⣩⠂⠀⠀⢢⠀⡀⠀⠀⢠⡞⣹⣋⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢁⣀⣀⢹⣄⡇⣾⠿⠿⠛⢻⣀⣠⠘⣦⡰⠀⡠⣰⣿⣟⣫⠏⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠚⠻⠿⣗⠷⢦⣧⣀⢀⠀⠀⠘⢧⡅⠀⠀⠀⣿⣏⣇⠀⣼⡇⢰⠟⠋⢰⡍⢀⣰⣢⣤⣴⣾⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢶⣿⢷⣌⣄⠀⠀⠣⡀⠀⠀⡆⢿⡟⠀⣹⠠⠞⣶⣯⣾⣾⣫⠭⠥⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡭⠷⠿⢿⣾⣴⣤⣈⡐⢤⡇⠘⡇⠔⠁⣠⣞⠋⣙⣻⣉⣴⣟⢂⣄⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⡤⠟⠊⠉⠉⠉⠉⠙⠻⢷⣛⣿⣛⠻⠛⠷⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣁⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠠⢀⣀⠔⣁⣠⠔⣀⠀⠀⣘⣻⣕⣤⣤⣄⡘⠄⠀⣃⣀⠀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠈⢦⡘⠂⡉⠻⢧⠀⠈⠳⡈⠈⠷⡀⠙⠓⠢⠄⠀⠀⠈⠂⣞⡁⠀⠀⠀⠨⠓⠨⠀⠀⠀⠘⠃⠀⢸
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠒⠂⠁⠐⠀⠓⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣥⣀
⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠂⠂⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠴⠀⡂⠄⠲⢀⡄⠈⠆⣰⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⡀⠐⣄⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠛⠒⠙⠚⠛⠛⠛⠉⠙⠛⠁⠀⢸⢿⠷⠀⢀⠘⠋⠀⠀⢋⠴⢙⠖⠀⠀⠈⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣿⣦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⡠⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠰⠀⠀⢀⠀⠁⠀⠐⠃⠸⠀⠙⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⢀⣾⣿⡦⠄⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡞⠀⠁⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⣤⠂⠀⠀⡴⠻⢷⡟⠀⣠⠀⠀⠀⠚⠉
⠀⠀⠀⠀⢀⡀⢀⠀⢀⢼⣿⠛⠁⠀⠀⢸⣦⣤⠈⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠋⢢⣴⠀⢀⡏⠁⠀⡐⠛⠹⠀⠀⠀⠀⣄⣴⣄⡀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡞⠀⠀⡼⠀⠀⡌⠀⠀⣤⣾⣿⡏⠉⢳⡄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⢰⣿⠋⠉⠀⡀⠀⠋⠀⠀⠐⠱⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡀⠰⠆⠀⢁⡠⣀⡀⠁⠀⠀⠀⠆⠘⠋⠀⠀⠀⡀⢀⣾⡄⠀⣳⡄
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡁⠚⠃⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣤⠾⡟⠂
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠰⠀⢻⠂⠀⢸⣷⢠⡄⠀⢀⠈⢀⠀⠀⠀⠀⠀⠁⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢰⠈⠙⠂⡀⢋⠀⠈⣇⢲⡿⠷⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢠⠉⢾⡀⠀⣏⡼⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠂⠀⣷⡄⡟⢀⣶⣧⠀⠀⠀⠐⠂⣤⣁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⣄⡄⣧⠉⡄⠸⣿⠋⡀⢀⣃⠀⠀⠛⠛⠋⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢳⣿⡅⢹⡀⠁⠀⠉⠀⠷⠏⣿⠏⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢻⠁⢸⡁⠀⠀⣀⣼⣶⣶⠠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠸⡇⣸⣵⣦⣾⠿⢋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠛⠓⠀⠀⣧⡟⣟⣉⣥⣶⣼⢿⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⢹⠇⣿⢀⢙⣿⣿⣿⣷⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠛⢦⣀⠀⠀⣿⡠⣿⠏⠿⠿⣿⣹⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠻⣦⠀⣿⣷⡇⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⢀⣧⣤⡄⠒⠒⠂⠐⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣦⣴⠟⠉⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢤⣀⡀⠀⢆⠀⠀⠠⠼⠛⠉⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠈⡩⠋⠙⣦⠞⠛⠲⠆⣤⣤⣴⣖⣋⣁⡀
⢀⣥⣤⣤⣶⣾⠀⠀⢀⠏⠀⣠⡤⠶⠻⣿⣿⣿⣿⡿⠟⠓⣀⣀⡀
⠐⢟⠋⠹⡏⣿⠀⠀⣮⢠⣾⡋⡠⡠⠑⠀⠀⠀⠀⣠⠴⠊⠀⠀⠠
⠀⠀⠑⣆⠁⡁⠀⠀⣧⣿⡿⣳⡞⠁⠀⠀⠀⢀⡞⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠸⣾⣿⣆⠀⡟⣻⣹⣟⡀⠀⠀⣀⡴⠋⢀⠄⠀⣸⡏⢀
⠀⠀⠀⠜⠻⢿⡟⠛⢻⣧⠟⠛⠛⠛⠛⠋⠀⠀⠀⢀⡀⢹⡇⠀⡓
⠀⠰⠀⠀⢀⡞⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⣰⣮⠀⠀⢣⠀⡇⠀⠀⢄
⠀⠀⣠⣾⠛⠻⠦⢀⡀⠀⠙⢷⡀⠀⠀⠀⠀⠀⣿⡃⠀⠀⢀⡀⢱⠀⠀⢸⣷⡀
⠀⠘⢿⠙⠛⠓⠂⢀⡠⠤⠤⠀⠙⢦⡀⡀⠀⠀⣾⣧⠀⢀⣼⠃⢨⣧⡀⣸⣿⣷⡀
⠀⠀⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⢧⡤⣄⣿⣿⡿⠊⠀⠀⢀⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢹⠇⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠀⠀⠀⣀⠈⠻⣿⢤⡀⠀⠀⠄⢧⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⠋⠁⠀⠀⠀⠀⠚⣿⡄⣀⢠⡝⢧⣂⣄⠉⠛⢹⠁⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⣀⡐⠀⠠⠄⠀⢨⣿⣿⣇⠈⠀⠉⠳⢆⣤⣼⠀⠀⠀⠀⠈⠃⠀⠰⣴⡔⠀⠀⠁⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠴⠂⠙⠷⠀⠈⠀⠉⠙⠳⢾⣿⠋⣍⢹⣿⣶⣀⠀⠀⠈⠙⢿⣶⡀⠀⠀⠀⣠⡞⠳⣾⣧⠀⠀⠀⠸⣿⡏⠹
⠀⠀⠀⠀⠀⠀⠀⠤⠖⠚⠿⣶⣶⣤⣦⣾⣛⣿⣿⣾⠋⠈⠉⠙⠳⢦⣄⡀⠙⢿⢦⣀⠈⠉⠀⠀⠙⠋⠅⡀⠀⠀⢀⠹⣷
⠀⠀⠀⠀⠀⠀⠲⠗⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢀⡀⢈⠛⢦⣄⠳⡸⡆⠀⠀⡄⠀⠀⢀⣷⣀⠀⠈⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠉⠉⠉⠛⠿⣇⡻⣿⣄⠀⢸⣲⡴⣾⣿⣾⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⣻⠿⠿⠿⠿⠿⢿⣏⣽⡿⠀⠀⠀⠀⠀⠀⠈⠱⡝⠻⣆⡬⡛⣦⣼⣿⠛⣧⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣶⡾⠿⠶⢤⣀⠀⠀⠀⠀⠀⠀⣀⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢻⡄⠘⣽⡛⠿⣀⢩⣽⠞⠙
⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠈⠑⠐⠂⢀⣐⣂⣉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⡆⣷⠀⠈⢻⣷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⡿⡿⣿⣿⣿⡵⡶⠉⠁⠀⠀⢀⠄⠛⠋⢶⣦⣔⢸⡄⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠟⠉⠀⢠⣤⣤⡤⣴⡁⠀⠀⠀⠀⠈⢏⢸⡇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠋⠁⠀⠀⢠⣿⣿⣿⣽⠟⢳⡄⠀⠀⠀⠀⠘⣼⠁⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡏⠀⠀⡟⠀⠀⠀⠀⢳⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠛⠓⠶⠶⠶⠂⢺⣿⣿⣿⣿⠟⠀⠀⡰⠁⠀⠀⠀⢰⠿⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢿⣯⡤⠖⠋⠀⠀⠀⠀⠀⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠉⠀⠀⠀⠀⠼⠛⠓⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⢀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢈⣿⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣷⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠸⣿⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢐⡬⠃⠰⠀⠀⠀⠀⠀⠀⠀⠰⠆⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠳⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣾⣀⣿⡀⠀⠀⠀⠀⠀⣠⠆⠀⡼⢃⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣤⣽⣯⡻⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⢠⣾⣿⣶⣿⣿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠛⠛⠿⠿⠿⣿⢿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠰⠿⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⣴⠀⠀⠀⠀⣀⠀⣈⡨⠿⣿⣿⠿⠿⠌⠛⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠹⣿⣿⣿⣿⡦⠶⠿⠿⢿⠛⠙⢷⣄⠈⠛⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢴⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣤⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⣶⣶⠟⠀⠀⠀⠀⠀⢀⡾⠛⠋⠁⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣾⣷⣴⣶⣄⡀⠀⣠⣶⣾⣿⣋⣀⣀⣀⣼⠇⠀⠀⠀⠀⠀⢀⠐⣤⣻⣗⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⢸⡗⣯⣩⣿⡿⠀⠀⠀⠀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠟⢹⡿⢻⡟⠀⠉⠻⣿⡿⠻⣿⡿⠛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠛⠧⠾⠋⠁⠀⠀⢻⣿⣿⡄⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⢁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣿⣿⡶⠋⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⠶⠟⠻⠿⠿⠷⠀⠀⠿⣿⣦⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠆⢠⡟⠀⣿⣿⡇⣠⣾⠃
⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⡀⢉⡀⢀⣀⣀⡀⠺⢦⣠⣴⣿⡏⢀⣾⠏⠀⣰⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠉⢙⣿⠟⠛⠁⠀⠀⠀⠈⠛⠻⣇⢸⡏⠀⢰⣷⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⣄⡀⠀⠀⠀⠀⠀⠈⠀⢠⣾⠏⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠐⠁⠀⣸⣿⣿⣿⡷⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠚⢶⡾⠿⢿⡿⠆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠾⠞⠛⠃⠀⠀⠀⠀⠀⣠⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⢋⣉
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⠿⠷⡄⠀⠀⣀⣴⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⠀⣼⡿⠿⠛⣿⣿⣿⣿⡄⠀⠀⣰⣿⠃⣼⠏⠀⠀⠀⠀⠀⠀⠀⣤⠂⣲⣈⡶⢆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣤⣘⣋⠁⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢹⣂⣽⡋⠂⠌⠀⠀⠀⠀⠀⠀⠀⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⣿⣿⣿⡿⣿⣿⠻⢿⣿⡍⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠚⠿⠛⢋⣡⣾⡿⠋⠋⠀⡟⢹⣇⢀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⠛⠁⠀⠀⠀⠀⢻⡈⣿⡈⠉⠉⣡⣾⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠸⣷⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣿⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣧⠀⠀⠀⠀⠈⠙⢛⣻⣶⣦⡄⣀⠀⠀⣀⣀⣠⠞⠁⠀⣰⡿⠃⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣆⠀⠀⠀⠰⠾⢿⣿⣿⠟⠰⠿⠿⠟⠛⣩⣵⣦⣀⠊⠉⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⢀⣠⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⡟⢹⡆⠀⠀⠀⠀⠀⣸⠏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠁⠈⠀⠀⠀⠀⠀⢠⠏⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⢷⡄⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⡟⣿⠳⠈⢻⢿⡆⠀⣠⢚⣿⠟⡷⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⡖⣷⠘⡂⠀⠈⣼⢨⣤⢋⡯⠋⡸⢱⣇⢠⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣿⣿⣤⠀⢣⠀⠀⢹⣼⣿⣞⢁⡶⣡⣿⣿⠟⠖⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⣿⠄⠀⢳⣦⠈⣾⣿⣿⢛⣵⣿⣿⣵⠂⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣽⣿⣿⣿⣾⣷⣿⣿⣿⣿⣯⣾⣿⣿⣝⣦⣤⣾⣿⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⠻⠿⣿⡿⠟⣋⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣦⣀⢀⠀⣰⠆⠈⢿⡟⠀⠀⠀⠀⡀⠀⠀⣶⣿⢻⢻⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡒⢄⣙⣿⣯⠀⠻⣇⡀⠀⠻⣤⡀⢰⣿⠏⠀⠰⣿⣿⣬⣼⣾⣿⠟⠀⠀⢀⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣫⣭⣷⣿⣿⡿⠛⠛⠛⠛⠛⠓⠺⢿⣿⣇⡀⠈⠁⠈⢹⣿⡟⠙⢁⡴⢃⠁⡸⢁⣰⠤⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡀⠀⠀⡾⠁⠁⣰⣿⡁⠀⡰⠀⠋⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⡲⠤⠤⠀⠠⣄⡀⠙⣇⠀⢰⠀⠀⣰⣿⡯⣷⣾⣁⣀⠀⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⣶⣶⣶⣶⣷⣄⠀⠀⢰⣿⠁⠀⢻⣦⣸⡇⠀⢿⠹⣿⣇⣠⢅⣤⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡞⠛⣸⣿⣻⢻⡿⠄⠀⣼⣿⠀⠀⠈⣯⣿⠇⣴⣣⣿⣶⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⣾⡇⢠⠟⣿⣟⣿⢿⣆⣼⣿⠋⠀⠀⠀⣿⠋⣼⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⢶⣿⣿⣿⣯⣾⣿⡋⠀⠀⠀⠀⠀⢿⣿⠃⠀⣠⢶⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣴⣒⣾⣿⣿⡟⢉⣥⡟⣼⠧⣤⠀⠀⠀⢸⣿⢠⣴⡟⣄⠃⠰⣽⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠟⠉⠀⠀⠙⣇⢸⣿⣶⣯⣌⣽⠀⠀⠀⢸⡇⠨⣿⣧⣿⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⣿⠛⠟⠋⠀⠀⠀⣸⠁⠀⠀⣽⡿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⣦⠀⠸⣆⢻⡀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⡄⡟⣆⠀⠈⢩⣷⠀⣰⣫⠄⢰⣏⣠⠞⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠶⣻⣇⣻⣷⣤⣄⣹⣧⡟⠁⠀⡞⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣤⣼⣿⣿⡿⠋⠙⠻⣷⣀⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡴⢶⡽⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠄⢀⡀⠀⠀⠀⢀⣠⣠⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⢀⣼⢇⡄
⠀⠀⠀⠀⠨⠵⢞⣳⡟⠻⠂⠀⠀⠀⣠⣀⣤⡀⠀⠀⠀⠈⢢⣄⣠⡄⠃⠀⠀⠀⣿⣿⡟⠁⠀⣀⣾⣿⢋⠈⠀⠀⠀⠀⠀⠀⠐⣯⠁⡄
⠀⠀⠀⠀⠀⠀⠁⢻⠀⠀⠀⠀⠀⠰⣿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠠⠔
⠀⠀⠀⠀⠀⠀⠀⡎⠰⠃⠀⠀⠀⠈⢾⣿⣽⡞⡗⠀⠀⠀⠀⢲⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢀⠀⠀⠀⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠉⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⣤⠀⢘⣦⠾⠁⠀⠠⠐⣦⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢠⣤⢞⠀⠀⢀⠈⡄⢠⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠔⠋⠀⠊⠀⠀⠀⠀⠀⠀⠅⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠋⠉⠁⠀⠀⠈⠀⢑⡺⡍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡇⠀⠀⠀⠀⠀⠈⠰⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⢀⡄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣨⠁⣉⠀⠀⠀⣶⡶⠀⠀⠀⡇⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⡀⢉⠀⠀⠀⠀⠆
⠀⠄⠀⠀⠀⠀⣀⠀⡦⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡃⡿⣃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠀⠀⠀⠾⡷⠄
⠀⠂⠀⠀⠀⠀⠈⢰⡖⠚⠀⠀⠸⠿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠉⠳⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣾⠆⠄
⠀⠂⠀⠀⠀⠀⠀⠘⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉
⠀⡂
⠀⠁
⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠂⢠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠈⠁⠀⢀⠠⠀⠀⠴⠆⠈⠐⠀⢀⠘⠀⠀⠀⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠠⠧⠀⠁⠀⠀⣐⡄⠀⢠⠄⢈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⡌⡀⠀⠀⢀⠀⠀⣂⡀
⠀⠀⠀⠀⠑⠀⠆⠀⠠⠀⡄⠚⠀⠀⠧⡀⠄⠁⠀⢀⠀⠂⠀⠀⠀⢀⡀⢀⠀⠌⠀⠀⠬⡆⠠⠀⢐⠀⠃⠀⠄⠆
⠀⠀⠀⠀⢉⠀⠬⠀⠐⠒⠒⢢⠀⠄⠉⠂⠀⣠⡁⠀⠤⠐⠈⢐⠀⠠⢄⡀⠁⣀⣆⠠⠀⠀⠀⠉⠙⠁⠁⠀⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⢀⠤⢰⡀⠈⠀⠄⠀⢀⠬⠯⠠⠀⢢⠀⠈⠁⡋⠈⠁⣂⣀⠀⠀⠘⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠅⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠈⠀⠀⠄⠠⠤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⡕⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⠀⠉⡀⠀⠈⢲⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⠃⢠⡈⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠠⠤⢄
⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⢧⠀⠀⠠⠈⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⠖⠒⠢⠄⣤⡁⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠓⠐⣆⠀⠀⢀⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠶⠀⠀⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠃⠀⡀
⠀⠐⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡴⠀⠐⠂⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢄⠊⠄⠚⡑⠀⠀⢤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢸⡄⢠⡀⢀⣐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⡒⠑⠤⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣃⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⢸⡟⡼⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣽⢿⣟⠐⠂⢴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡎⣿⠁⠷⣟⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡶⠚⠙⠻⢇⣴⣛⣯⣭⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⣰⣿⡿⣿⠇⡄⠀⢡⡌⠉⠛⠻⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠄⢠⣿⣯⡗⠀⣹⣄⣓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⡟⠀⢀⠟⠋⣴⣶⡿⡷⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⠀⠀⣶⣆⡾⠶⠷⠄⠛⠋⣐⣘⣉⣀⠈⠉⠹⣿⣿⣶⣯⡻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣹⣷⠆⣿⣟⡈⣚⠀⡈⠁⡀⠙⣿⣿⣭⣛⣷⣄⠀⠙⠻⠿⢿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⡀⣶⠿⠋⠤⢀⣹⡷⠋⠉⢀⣀⡘⣇⢯⣀⢀⣰⡅⠀⠈⠻⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣛⠛⢆⡀⠂⠀⣧⠀⢻⣿⣦⣿⣦⣟⣿⣯⠝⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠿⠿⠸⢎⣷⣴⢖⠏⠀⠀⠈⠉⠈⠻⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣭⠻⢏⡤⠶⣚⣿⣯⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣻⣿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣶⣶⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢍⡱⠋⠉⠀⠀⠉⠒⢰⠆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⠻⠿⠓⢟⣀⠬⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⣳⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢿⣠⣤⡀⢼⣇⠀⢀⣞⠀⢲⣾⣿⣶⠛⠃⠀⣤⡙⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣿⣷⣾⣿⣿⣿⣧⣶⡿⠊⣡⣤⣤⡐⢀⣀⡤⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣏⢹⠉⠁⣞⣵⣷⣤⡎⣿⣿⣿⣿⣿⠯⠃⠉
⠀⠀⠀⠠⠤⠤⡄⢸⠀⠀⣆⡖⠀⠁⠃⣸⠘⣿⢻⡋⣰⡏⠻⠛⡌⣽⣿⣿⣿⡅⠎
⠀⠀⠀⠀⠈⠂⠀⢸⣇⠀⣡⠁⠀⠀⠂⠘⠆⢻⣆⣿⣿⣧⢀⣰⢧⣻⣿⠯⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠛⠗⠀⠀⠀⠀⠐⠂⠹⣦⣽⣿⣮⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠓⠀⡤⠊⠁⠀⠀⠀⠀⣄⣾⣿⣿⣿⠒⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢿⡧⠄⠀⠤⠀⠀⠀⠀⠀⠘⢛⣿⠛⣿⣽⣿⡿⠘⢹⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣤⣠⣼⠷⠶⠓⠒⠀⠀⠀⠀⠀⢀⡟⠙⢯⣜⣥⣿⢥⣞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠂⠈⠉⠙⠙⠆
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠐⢀⠸⡇⠈⠑⢄⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠳⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⡈⠃⠀⠀⠤⠀⠀⠈⠀⢀⠀⠱⡀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡄
⠀⠀⠀⢀⠐⠂⠐⠂⡃⢸⠀⠀⠈⠀⠀⢀⢀⡀⡀⠀⠀⠙⠢⣽⣀⡌⠀⣀⠶⡤⢤⣀⠀⠀⠀⣶⢰⠟
⠀⠀⠀⠀⡠⠐⠀⠀⠁⢨⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣣⠏⠀⡄⠀⠀⠀⠀⠤⣴⣯⣀⢀⡀⠀⢀⠶⡃
⠀⠀⠀⠀⠀⣠⠖⣃⠀⠀⢀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣯⣭⣭⠛⠀⠁
⠀⠀⠀⠀⠀⠨⠁⠙⡂⠀⠈⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠛⢿⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠂⠀⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠢⣀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⡀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠸⡀⠀⡌⠁⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⢣⠀⢀⡔⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢘⢦⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⢿⣿⣷⡀⢄⠀⠀⠈⢓⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠂⠐⠓⠒⠲⠿⢀⠀⡛⢋⡁⣀⠀⠀⠀⠄⠀⠀⠀⠁⠀⢁⠀⠀⠀⠈⠀⠀⠀⢢⠀⠀⠈⢉⡙⠒⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠏⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠗⠲⠘⠄⠀⠀⠈⠀⠒⠀⢄
⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⡉⢇⠈⠀⠀⢀⣦⣴⠀⠀⡁⠂⠀⠀⢀⣴⣾⣶⣦⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠰⢀⡄⢴⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠠⠀⠀⢠⣿⣿⠟⠀⠀⣀⡀⠀⠀⠈⢻⣿⣿⡿⠅⠀⠀⠀⠐⠀⠠⣶⣾⣷⠀⠀⠀⠄⠀⢿⣿⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠙⠛⠋⡀⠁⠀⠁⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠛⠻⢿⠀⠀⠠⠀⣀⠙⠟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⣅⠀⠀⠐⠃⠀⠤⢤⣀⣀⡀⠀⠀⠀⠈⢰⡖⠀⠊⠉⠀⢀⡀⡀⠀⠀⠀⠀⠀⠆⠈⠈⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠦⠀⢩⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡏⠁⠀⠀⠸⠁⠀⡄⣠⣀⣠⡤⠅⠀⠀⢹⡿⠦⠴⠀⠘⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠄⠀⠀⠐⠒⠲⠤⠶⢰⠀⠀⠣⠀⠀⠀⠔⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀⠀⠀⠀⠀⣀⠀⠸⡃⠀⠘⠀⠀⠀⠀⢀⠐⠁⠀⠙⠶⣄⠀⠀⠀⠀⠀⠞⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⡃⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠦⡀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠉⢠⣄⣀⠀⠀⠀⠀⢱⣼⣷⣾⠄⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣤⡀⢤⣚⣿⢿⡟⠀⠀⠀⠈⠀⠀⠀⠑⠄⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠑⠤⣄⡀⠀⠀⠀⠀⠀⢈⡄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣿⣿⣻⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⡠⡀⠀⠀⠂⠄⠐⠰⢄⣀⢀⡠⠀⠠⠉⠀⠐⠀⠀⢹⢿⣿⡿⠄
⠀⠀⠀⠀⠀⠸⠅⠀⠀⢀⠄⠉⠀⠀⢰⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠏⠃⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠀⠀⠸⡺⣄⠀⡀⠀⠀⢃⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠤⠄⣀⠈⠻⢿⣾⣷⡤⠂⠁⠀⠀⠸⠁⠀⣤⣀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⡠⢮⡿⠁⡀⠀⠠⠬⠿⢻⣿⣿⢷⡦⠤⠖⠚⠁⠙⢷⡏⠿⠛⠀⠀⡁⠀⠐
⠀⠀⠀⠾⠁⠉⠀⠀⠈⠁⠀⠀⡄⢀⣨⠶⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠜⠃⢨⠀⣠⠀⠀⠂⠀⠀⠀⠀⠀⠀⣰⠌⠀⢀⡏⢓⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠠⣿⡃⠀⠀⠑⠒⠀⠒⠂⠁⠀⠀⠀⠩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠢
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠶⢦⡴⢶⣖⣛⠛⠉⠙⠛⠛⠳⢦⣄⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡆⠀⠀⠀⠀⠀⠉⢷⡀⢠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣩⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⢣⠠⢤⣤⣤⣄⡀⢻⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⡟⣹⠞⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣄⡀⢿⠀⠀⠙⠾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣾⣥⠟⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠙⣻⣇⣀⡀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⠏⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⣤⡾⠋⣀⣠⣤⠖⠲⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⠉⠉⠉⠀⠀⠀⠈⠙⢦⡙⢦⡀⠀⣠⠄⠀⠀⠠⡄⢀⡼⣡⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠻⣦⠱⣴⠃⠀⠀⠀⠀⢹⠏⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢴⠤⣤⣤⣀⡀⠀⠀⠀⠀⠈⢳⡉⡄⠀⠀⠀⠀⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⠀⠀⢻⡜⡄⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⡀⠀⢿⣰⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⡇
⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⣀⣀⠀⠀⠈⠀⠀⠀⠀⠈⢣⡀⠀⢇⢇⡀⠻⠒⠂⠀⠀⠀⠀⠀⠀⣠⡶⠊⠉⠀⠀⣿
⠀⠀⠀⠚⢏⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⢀⠀⠛⠒⢤⣀⠀⠈⢷⡀⠸⡘⢻⠆⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠉⠓⢿⣍⡉⠙⠳⣤⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠓⢦⠘⣧⠀⠇⢸⡄⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⣠⡄⠀⠀⢠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⡄⢸⠈⡃⠀⠀⣤⠎⠁⠀⠀⢀⢀⠞⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⠐⣦⣀⣀⠀⣤⣀⣰⡶⠛⠛⠉⠀⠙⠷⣄⡀⢳⠀⢰⡇⠀⠀⡀⠀⣸⠋⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡀⣿⠀⠀⠀⠹⣮⠃⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉⠉⠙⠿⣄⣀⣀⣠⣉⡀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠙⠳⣄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠙⢦⣸⢦⣷⣤⠶⠞⠛⠛⠙⠛⠶⣄⠀⢀⣀⣀⣀⣀⠈⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠛⠉⠉⠉⠉⠉⠉⠛⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠞⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠁⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⣰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴⠤⣝⣋⠩⣙⣻⠇⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡇⠀⠀⠀⣴⠒⢦⣄⠀⠀⣰⣿⠀⣿⡀⠿⠃⢀⣼⢿⣔⢇⡦⠞⠁⠀⠀⠀⠀⠛⠷⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠻⣄⣀⣴⡟⠀⠀⠈⣳⡾⠃⠹⣧⣌⠙⠳⣤⡏⠁⠀⠹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⢷⣄⠟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⠠⠤⠤⣀⣾⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⡴⠶⠤⠶⢤⡀⠀⠀⢀⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⡇⠀⢀⣴⠏⠀⣠⡴⢶⠉⠉⠀⢀⡿⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣠⡤⠤⠤⠚⠋⠁⢀⡼⠋⠀⠘⠳⢄⣀⡼⠃⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠷⢦⣄⣀⣀⣴⠞⠉⢩⠟⠁⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⣠⡶⣿⠖⠴⠶⠛⠛⡉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠋⠉⡜⠁⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠷⣤⣀⣀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠉⠉⠉⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣀⣀⣠⡶⠏⠥⠤⠤⢤⣬⡽⢶⣤⣀⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠎⠀⠴⠀⣀⣠⠄⠀⠀⠄⠀⠐⠀⠆⠀⠈⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠈⠔⠀⢀⡀⠀⠀⠀⠠⠀⠀⠀⠋⠁⠀⠁⠐⠄⠀⠠⠀⠋
⠀⠀⠀⠐⡄⢀⠀⠀⠀⠀⣨⠉⠁⡄⠄⠠⠘⠀⠀⠃⠐⠀⠀⠄⠀⠀⠀⠄⠀⠀⡄⠓⠀⢀⢀⡄⠀⠨⠒⠂
⠀⠀⠀⠀⠤⢈⠀⠈⣀⣁⡀⠀⠨⠵⡀⠀⠄⠐⠀⢁⠄⢀⠁⢐⠂⠒⠈⢀⠀⠉⠁⠈⠤⠴⠤⠀⡘⠈
⠀⠀⠀⠀⠉⠀⠀⠀⠀⢦⠈⠀⣀⣄⠠⠒⢋⠉⠉⢀⣦⠐⠠⡄⠓⠒⠲⠛⠋⠀⠀⠀⠀⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢠⠊⠄⠊⠀⠀⠈⠀⠀⠁⠘⠀⠀⢨⠆⠀⠀⠀⠀⠪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠃⠖⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠈⡉⠐⠀⡔⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡑⡀⠁⠀⠀⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⡄⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠁⢠⠀⡀⢠⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠠⠃⠈⠑⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡶⠀⠀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡻⠻⠆⠀⠀⠀⠀⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⠀⠀⢀⣠⣆⣠⠀⠀⠃⠀⢀⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⡿⠁⠀⢠⡋⠉⠹⢃⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠶⠆⠂⠀⠺⢿⢇⡀⡀⠀⡸⠿⠛⢀⡿⢶⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⢻⡃⢠⠇⠀⢠⠂⠀⠠⠀⠀⠀⣴⣿⠟⠲⣄⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢠⠏⠀⠀⡇⠀⢠⣿⠟⠻⠀⠀⢹⠆⠀⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢠⣄⠀⠘⢀⡄⠀⠃⠀⠉⠉⠀⡴⠞⠀⠀⠀⠀⢠⡆⠈⢢⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠈⠀⠀⠀⠞⢷⡛⠱⠄⠀⠀⡴⠀⠀⠀⠀⠀⠀⠐⠿⠃⣀⣸⡟⠦
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡄⢲⡆⠀⢠⣷⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⢸⡋⠁
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡎⠑⠇⠀⢘⠉⠘⡇⢢⣿⡶⠊⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠃⠀⠠⡘⢾⡄⠀⣏⡼⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⣷⡄⡟⢀⣶⣇⠀⠀⠀⠲⢀⣄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀⢠⡄⢱⠙⡄⢸⣿⢋⡀⣘⣀⠀⠘⠛⠛⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠱⣾⡇⢸⡄⠁⠀⡇⢈⠷⠛⡟⢃⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⣤⣾⣶⡷⠴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠈⡇⣸⣷⣷⡿⠟⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⢳⡏⣿⠥⣶⣶⣽⣿⡴⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠠⣄⡀⠀⠀⠀⣸⠇⣿⣠⣨⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⠙⢦⡀⠀⣿⡔⡿⠃⠛⠛⢿⣼⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢿⡆⢿⡿⡇⠀⢀⣀⡀⠋⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣿⠾⠃⠀⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠀⠀⠈⠡⠀⢷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣤⣦⣤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠢⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢏⡜⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠈⠙⡆⠈⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡼⣄⣀⡂⠀⠀⠀⣇⠀⠀⠠⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣡⠤⠶⠚⣟⠁⠀⠀⢠⠝⠀⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠾⠵⠒⠶⣅⣀⢸⡆⡀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠁⠈⢣⡀⠀⢰⠀⠈⠉⠑⢢⡤⠂⠀⠀⠀⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⡤⠀⠀⢀⠀⡀⠈⠳⡀⠀⠀⢸⡆⠀⠀⢁⢀⠀⠀⠇⠀⠀⠀⡔⡠⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣠⠀⠀⠀⠀⣀⣀⡀⠐⠄⠀⠀⠙⠀⠐⢌⡴⢂⠀⠀⠀⠀⣐⣎⠋⠀⠉⠂⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠈⠢⠀⠀⠸⡄⠀⠐⠀⠀⠈⢢⠹⢦⣾⠠⠂⠀⠀⠠⠀⠐⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠁⢀⡊⠀⠀⡄⠤⠆⠀⣤⡀⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠀⢠⡀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠠⠶⠂⠒⡻⢆⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠂⣷⡋⠂
⠀⠀⠀⠀⠀⠀⠰⠀⠀⡇⠐⠚⠞⠁⠀⣈⣀⠤⠤⠬⢶⡀⠀⠀⠀⠀⣤⢤⡀⠀⠀⠀⠀⠆⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⣀⡤⠂⠉⠁⠀⡀⠠⠀⠐⠳⠆⣀⠀⠀⡇⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠈⢀⠄⡜⠱⠶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢄⡄⠤⣠⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠖⠉⢶⠞⠁⠀⠀⠀⠀⠀⠀⠡⡀⠀⠙⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢨⠦⣴⡟⠠⠄
⠀⠀⠀⠀⢀⠀⠂⢚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠆⠀⠀⠁⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⡈⣤⠀⣤⣄⡂⠀⠀⠀⠀⠀⢀⢤⠔⠳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠊⠀⢴⣾⣿⣿⠀⠘⠈⠙⠓⠀⠀⠒⠀⠀⠀⠐⠁⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⡿⠀⡀
⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⠀⠀⠀⠄⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠄⠀⠀⠀⠀⠀⠀⠀⠋⡟⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾
⢀⠔⠈⠁⠈⠁⣀⠀⠀⠀⠀⢠⣖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢀⣾⣏
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤⠀⡴⠊⠉⠉⠐⢄⠀⠀⠀⠁⢄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣀⡀⢀⣤⣿⣿⣟⡡
⠁⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠦⣄⡠⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⡀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠑⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡻⣿⣿⣷
⠙⠂⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠴⠊⠁⠀⠀⢀⣿⡟⠃⠀⠃⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀
⠀⠀⠀⠈⢱⣄⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠈⢆⠀⠉⠁⠀⢄⠵⠶⣦⠀⠀⠀⠀⠀⢀⠀⠀⢽⣿⣿⡇⠀⣾⠇⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢀⣀⢀⡀⠉⠉⢻⣿⣿⣧⢠⣿⣷⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠻⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠳⡀⠀⣰⠁⠀⠠⡄
⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⡀⠐⠃⠀⠁⠈
⠀⠐⢄⢿⡄⡀⠀⠀⠀⠀⠕⠀⠄⠀⠀⠀⠀⠀⠀⠒⢂⣩⡴⠋⡉⠀⠙⢷⡀⠈⠀⠀⠐⠒⠒⠄⠠⠄⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆
⠀⠀⠀⠀⠙⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠅⡔⠁⠀⠋⠀⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣴⣶⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠖⠀⠀⠀⠀⠀⠀⠁⠰⣀⠀⢀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⠀⠀⠀⠈⠙⠙⠓⠚⠠⢄⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠉⠉⠒⠆⠒⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣦⢠⠀⢀⣴⣿
⠀⠀⠀⠀⠇⠑⠂⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢺⣧⣠⣿⣿⣿⣿⠏
⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠸⠁⠀⠀⢀⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢀⣀⠀⠀⠀⠈⢻⣿⣷⣀⢠⠀⠀⣤⣿⣿⠋⢀⠀⠠⠠⠀⠠⠄⠀⡸⠉⠐⠙⠧⣐⠀⠤⠤
⠲⢀⠈⠁⠀⠁⠀⠀⠠⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠈⠻⣿⣿⠛⠃⢸⣿⣿⡡⠊⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⠒⠒
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣷⣶⣦⣉⡀⠃⢌⣿⣟⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠐⠚⠉⠉⠉⠻⠛⠛⠛⢻⡿⢿⠁⣠⡆⢫⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰
⠀⠀⠀⠀⢠⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠉⠅⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⣾⡇⡴⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠤⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡀⠀⠰⢴⡿⠟⢁⠍⠆⠀⠀⠀⠅⢀⠀⢀⢠⣮⣣⡄⠒⠀⣿⠟
⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⣰⡟⡃⠑⠟⡁⢂⡉⢤⠀⠀⠾⠃⠀⠀⠀⢠⡆⡜⠀⠀⣠⡧⠄⠄⢺⣷⡅
⠀⠀⠀⠀⠀⠀⢀⡬⢷⡐⠈⠄⢀⢨⠹⠃⠌⢉⢻⠄⠰⠀⠀⠀⣀⠀⠈⠀⠀⢀⠀⠙⠁⣠⢀⣿⣴⠶
⠀⠀⠀⠀⠀⢀⡈⢱⡟⠁⠰⣾⣿⡂⠀⢀⠀⠀⠈⠀⠀⠀⠠⠈⢀⣀⣦⣄⣤⣤⡧⡀⠙⢁⠎⣈⣛⣾⣗
⠀⠀⠝⠻⡇⠉⢀⣼⡱⣦⣐⣿⠏⠁⠀⡆⠘⢆⠀⠀⠀⠀⠦⢀⣿⣧⣿⣿⣿⣄⠸⠛⢢⠊⢠⡍⢹⡿⣿
⢀⡀⠀⠀⠁⣴⠟⢸⠀⠼⣻⠏⠀⠐⢸⠅⠀⢘⠆⣴⢀⡀⠠⠀⣴⣿⣿⡧⢿⣿⣧⢀⣾⡷⠉⡀⠀⣇⡌
⠀⢀⣥⠀⠘⢻⡄⢅⡀⢠⣴⣶⣴⣞⣿⠆⠀⠛⣧⣩⢻⡇⠠⢾⡟⢿⡿⢧⣾⠙⢘⡿⣿⢆⣴⣤⣾⠟⣧
⠀⠈⠓⠘⠐⣿⠇⣾⡇⢠⡿⠀⠉⢛⢻⠀⠀⠀⢋⠥⠚⢿⠆⠈⠉⠈⠀⠸⠃⠀⣫⠿⣿⣿⣿⣿⣿⣽⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠈⠰⢧⡤⢣⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣋⠝⢃⠂⡀⠀⣀⣀⢴⡠⠀⠠
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠤⠤⠀⠁⠀⠈⣴⢤⡀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⡠⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠱⡛⠣⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣉⣤⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠊⠁
⠀⠀⠀⠀⢀⠈⠉⠀⣬⠧⠀⠀⢤⡄⠀⠀⣠⡄⠀⢀⡀⠀⡀⠀⢤⡄⡄
⠀⠀⠀⠀⠀⠀⠔⠂⠉⢷⡀⠢⠾⠷⠫⠞⠿⠅⣤⢛⠉⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⣄⣠⠴⠈⡈⠀⠄⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⣾⣷⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠛⠍⢙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡀⣰⢀⠁⠁⠘⢧⠴⢦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⠟⣄⠠⠁⢠⠀⣠⠃⠀⠙⣴⣯⣾⣷⣡⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣽⠷⠾⠓⠠⠼⣋⣁⣁⠠⠔⠉⠹⢿⠛⠭⡛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠄⣀⡀⠀⣻⣗⣀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⡐⠋⠉⠠⠆⠉⠿⢿⣃⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢿⣀⠀⠈⣁⣠⡶⣶⣶⣏⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡽⠿⠋⠻⣽⣟⣽⣠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠲⣤⣶⠘⠟⣧⣷⣚⠁⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⣭⣀⡀⠀⠀⠈⢻⡄⠆⢹⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⣈⡁⠒⢦⣆⣻⠈⠀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠛⣷⣰⣿⣷⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⣽⣿⡽⠐⡏⠉⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡻⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠢⡀⠀⠀⠀⠀⡔⢨⡁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠈⢣⠈⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠆⠀⠀⢲⠆⠐⠊⢀⣀⡀⠀⠀⠉⠂⠀⠰⠀⠠
⠀⠀⠀⠀⠀⠀⢡⡄⠉⡀⠀⠀⠙⢦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣨⠐⠠⣄⡀⣂⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢤⠁⠐⠓⠨⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢅⡏⢀⡽⠾⡭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠖⠀⠘⢳⡤⠒⣦⣤⣤⡈⠓⡂⠒⠛⢋⡽⠃⢄⠀⠰⣈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⠀⠀⠀⠀⢴⠀⠀⣾⣿⡿⠀⠉⠠⡀⠀⠀⢉⡆⠈⠀⠀⠀⠁⠇
⠀⠀⠀⠀⠀⢠⠐⠀⠀⡼⠀⠀⠀⠀⠸⣆⠘⠉⠹⠀⠀⠀⠀⠈⢃⠈⠁
⠀⠀⠀⠀⠐⠁⠀⠀⢀⡰⠲⠆⣀⡤⠀⠁⠀⠀⢰⡀⠀⠀⠀⠀⡆
⠀⠀⠀⠐⠀⠀⠰⠒⠊⣀⣀⡴⠋⡋⠀⠀⠀⠀⢘⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠊⣽⡝⢀⠈⢡⠀⢠⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠔⡢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡄⠈⠆⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠣⡀⠀⠀⢦⠀⢠⠁⠀⠀⢠⡀⠀⢃⡜⠠⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠚⠡⡐⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⢀⡀⠀⠀⠉⢵⣟⣷⣧⣀⣀⠠⠐⠀⠒⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠨⠐⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡈⠀⠆⠘⠅⣀⠀⡠⠛⢻⡿⢍⠉⠁⠦⠀⣠⠆⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⡤⠂⢀⠄⢀⢐⠀⠀⡘⢠⠉⠁⠂⠢⡾⠟⢈⠈⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⡐⠀⠰⠈⢃⠈⡀⠘⠧⡀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠱⡄⠀⡃⠀⠴⠐⠀⢀⠟⠀⢠⡼⣿⣹⠶⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠑⠢⣄⣼⡾⠳⣆⢀⡠⠔⡃⠀⣀⠀⠀⠈⢿⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣄⠙⢆⣀⣤⠈⠁⠀⣘⣿⣄⣱⣿⡅⠀⠀⠀⠐⡙⠠⡄⠁⠀⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠠⠴⠄⠲⣺⠋⠉⠀⠀⠋⡟⠟⠉⠳⡄⠠⡀⠀⠇⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠃⠈⣂⣴⠇⢀⠘⡀⠀⡆⢀⠉⠒⡤⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠮⠬⠑⠒⠉⣽⠈⠊⠁⠐⠧⠠⠂⠈⠀⠀⠀⠒⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠋⠀⠀⠘⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⡠⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠤⣀⣶⣾⣾⡅⡲⠇⢀⣀⡴⠀⡠⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⡹⢿⣿⠿⠋⠐⠀⠀⠙⠀⡜⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣀⡴⠉⢧⡖⠘⠂⠀⠀⠔⠀⢳⣀⣤⡤⠂
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣀⠀⡎⠀⠀⠀⠀⠘⢄⣀⠀⠀⠃⢀⡜⠁⠀⠀⠀⢀⡀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠐⢄⠎⠈⠑⢌⠀⠀⣀⣀⠀⠘⠘⣆⢀⠔⠋⠀⠠⣎⠀⠀⠀⠀⠨⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠓⠒
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⢰⢇⠀⠣⢀⡴⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋⠙⠄⡑⢺⠁⢠⡀⠀⡴⠀⢠⠎⠁⠀⠀⠀⠀⠀⠊⠡
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠢⣄⡨⠓⠠⢀⡉⠁⠀⣰⠋⠀⠠⢄⠀⠀⠀⠀⠠⠀⠐⡠⠒⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠁⢋⡏⠀⠔⠠⢪⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠈⠦⣠⠄⠼⡤⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⡀⠀⠀⠐⠀⠀⠀⢳⡀⠐⠤⣸⡴⢀⠀⠒⠛⠴⡒⠓⠆⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣠⠞⣡⠐⠀⠀⠂⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠁⠀⠀⠀⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣀⡀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⢉⡴⠋⠸⠉⠣⣾⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣤⣀⠄⠀⢠⡎⠀⠀⠀⠀⠀⠸⠆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢆⠀⠤⢄⢠⡏⢀⠈⣻⠛⠁⠀⠀⡆⠀⠀⠠⠦⠤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⢄⠀⠀⠀⠈⠁⠀⢳⡷⠀⠀⠀⠀⠀⠀⢊⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠂⠀⠀⢠⠀⠀⡐⠀⠀⠀⢠⡎⢧⣀⠀⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠰⣸⣂⣾⣁⠀⠀⠀⠀⠃⡌⢳⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠽⢏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠐⢾⡿⠟⠃⠀⠀⢤⣰⡴⠁⠘⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣢⣿⣿⠏⠀⠀⠀⠹⣄⠀⠀⠀⠘⣿⡇⣀⠄⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⡀⠀⠀⢀⡈⣳⣤⣄⡀⠘⢓⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠈⢓⡄⠘⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⠜⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⠚⠉⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠞⠁⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣤⠀⠂⢰⡆⠀⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢄⢠⠁⠀⠐⠘⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠑⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠠⠋⠀⠘⠲⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣠⠀⡠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⣿⣿⡿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠃⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⠟⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠙⣿⡟⠁⠈⢂⠰⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠞⠀⠀⠀⠀⢀⡼⠋⠻⠀⠀⠹⠓⢄⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃

⡟⢿⣷⠀⠀⠀⣾⣿⣿⣿⡗⠀⠛⠛⢿⢿⣟⣿⣿⣿⣿⣁⣀⠀⠈⣿⣿⣯⣹⣷⡀⠀⠀⠀⠀⠀⠀⡿⡟⢻⣿⣿⢽⣧⣼⣣⣄⣀⣆⠀⢀⣀⡀⠀⠀⢀⡀⠁
⠀⠀⠈⠣⣄⣾⣿⠟⠋⡉⠙⠃⠀⠀⠀⠈⢿⣿⣿⣿⡿⢯⠈⢹⣴⣽⣿⣷⡾⣿⣇⠀⠀⠀⠀⢀⣼⣷⢿⣿⣿⣉⢼⣻⣿⣿⣿⣿⣿⣿⠿⣿⣤⣤⡤⣾⢁⠤⠤
⠀⠀⠀⠀⠸⡿⣯⣘⠂⠤⠘⠠⡴⠲⡤⢄⡀⢹⣿⣿⣾⣦⣵⣾⡿⣿⣿⣟⠻⣿⡇⠘⠀⠠⠻⢾⣿⣇⣴⣿⣿⣻⣿⣟⠻⣿⣿⡿⠳⢈⢁⠻⢿⣿⠰⠀⠛⢷⣿
⡷⣦⣤⡄⡤⢀⣯⣭⣿⡶⠖⠉⠠⠐⠠⣐⢴⣿⣿⣿⣿⠻⣿⡿⠀⠉⠃⠈⢶⡽⣧⡄⢀⢀⡀⠀⢬⣿⣿⣯⣿⡿⠳⠈⢡⣨⠈⣇⡠⣙⢻⢻⡿⢿⠟⢈⠁⣘⣿
⣿⣿⣽⣿⣵⣾⣿⣿⣿⣿⣷⣿⣷⣌⣠⡿⢏⢉⣣⠔⣿⠀⢸⡇⠀⠀⠀⠀⠘⣱⡯⠀⢿⣯⠀⢴⡛⠛⢿⡟⠠⡤⠆⠀⢺⠃⠀⠛⠃⠘⠂⣼⠞⠲⡀⠞⢣⣅⣿
⠛⠛⠋⠙⣾⣿⣿⣿⡿⢿⣿⣮⣙⣿⠻⢿⣾⣯⠉⣴⣿⣄⣼⣷⡄⠀⠀⠀⡸⠋⢁⠐⢪⣨⡔⠆⠻⠀⠀⢈⣀⢀⣠⡀⠘⡄⠀⢆⠀⠀⠑⢇⡘⠓⠷⣢⡏⢥⣿
⠀⠀⢀⠙⣿⠃⠻⡌⢻⣸⣿⣿⣦⢽⣯⢸⡟⠛⠻⢨⣄⣿⠿⡏⢿⡀⣠⣾⠁⠀⠈⠡⠜⣯⡉⣀⡿⠶⢚⣿⣿⣷⣾⡛⢦⡙⢰⡘⣆⠀⣾⢀⢡⡜⠒⠋⣴⣁⣸
⣄⠀⠸⢤⣿⣄⠀⠱⡄⢣⠌⠟⠻⡼⢛⠃⢦⣴⡀⣼⣯⣉⢴⡿⣦⢠⣌⣈⣤⣠⣜⠛⠋⣨⡉⠩⠛⢀⠀⢛⡀⠰⣬⣽⣷⣽⣿⡿⡾⣿⣝⣿⣿⠗⣯⠂⠉⠻⣿
⠻⠁⢿⣆⠛⣻⣖⠋⠳⣝⢛⣂⡉⣼⠠⠞⠈⠩⠀⢨⠎⢻⠄⣶⣯⣴⠁⢹⡿⣿⣿⣦⠾⠂⣠⡸⠆⢠⡀⠀⠀⢠⠔⠋⠉⠉⠙⠻⢾⣟⢓⣾⠇⠈⠀⠀⠀⠀⠈
⣄⣀⣀⡿⠓⠿⠿⣾⡷⠛⠛⢙⣓⢾⣷⣦⠋⢣⡄⢺⣷⢔⡀⠿⠿⠛⠲⡉⠻⢿⣿⣿⣀⠀⠉⢹⣷⣾⣥⣄⣚⠓⠂⠠⢀⣴⡀⣀⣠⣾⣿⣿⠀⠀⠀⠀⢠⣤⣄
⠻⠗⠉⠁⠀⠀⠀⠛⠀⠀⠀⠞⠈⠛⢻⣇⠉⠻⣴⠶⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡀⣁⣼⣿⣿⣿⣿⣿⡋⢀⣑⡦⣽⣿⣿⢻⣯⠻⣿⠀⠀⠀⢲⡜⠋⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣾⣦⣽⣴⡁⠀⠀⢠⠂⢀⠆⠀⠀⡀⠀⠀⣿⣿⡿⠿⠿⢿⣿⣿⣿⣤⡤⢴⢾⣿⣿⣿⣶⣿⢮⣿⡧⡀⠰⣮⠁⠀⣤
⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⣠⡷⠖⠟⠻⢿⣇⠓⠀⠀⠀⠀⠀⠀⢸⣷⣬⠾⠛⠛⠊⠀⣀⠀⡈⠉⢫⣴⣾⣿⠛⠁⠻⡿⠈⠙⠓⠟⠀⠀⢻⠀⠀⣸⣷
⠀⠙⠳⣤⣀⠀⡀⢠⣇⣀⠇⢰⡉⠻⣏⡱⠶⠄⠒⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⡀⠀⢀⣀⣤⠁⠈⠄⠀⢀⣿⡟⠃⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢟⠘
⠀⠀⠀⠈⠻⣿⣦⣾⣿⣿⡴⠻⠁⠀⠸⠀⠀⢀⣀⢼⣿⠀⠀⠀⠀⠀⠀⠀⢐⠏⢠⣶⠛⠉⠁⠈⠁⠀⠴⠶⠿⠿⣧⡀⣀⠀⠀⡸⢢⣸⣧⠀⠀⠀⠀⢀⣔⠁
⢀⡤⠂⠀⠀⣻⣿⣟⣵⡿⠀⠀⠀⠀⣰⡧⠀⠘⠉⠀⠈⢳⡄⠀⠀⠀⢀⣾⢳⣾⡿⠃⠀⡀⠀⠀⠸⠷⣦⣄⠀⢀⣀⠽⣿⡶⠋⢀⠼⠋⠙⠇⡀⠀⠀⢘⡿⡧⡀
⡿⠄⠀⠐⠚⠛⠉⠉⢸⠇⠀⠀⢀⣠⣿⡇⠀⠀⠐⠢⠶⢶⡿⣦⣨⠤⢨⡝⢜⣛⢶⡶⠋⠀⠀⠈⠀⠀⠀⠌⠀⠉⠉⢀⣈⣀⣠⣴⣾⡀⠀⠀⠈⣽⢾⠟⣅⠀⠉
⠢⠀⠀⢈⡁⠀⠀⢀⡜⠒⣠⠚⠋⠉⠙⠳⣀⠈⠳⡄⠀⠀⠓⠁⠣⢍⢕⡪⣝⠪⠷⢥⠄⠒⠀⠀⠀⢀⠴⠄⢀⡧⠀⠈⣩⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⡄
⣆⣀⣀⣀⣬⡾⠷⣷⣿⣆⠀⠀⠀⠀⠀⠀⣈⣿⡿⠛⠦⣀⣀⠀⠀⠀⠶⣙⣏⣟⠆⠚⠒⠂⠀⠐⣮⣗⠀⠀⠂⠀⠀⠠⣿⣿⣧⣄⠀⠀⢀⣴⣦⣤⡄⠀⠀⠃⣤
⣴⣾⠿⣧⣤⣶⣃⣿⡿⢿⣷⣶⣄⢀⡴⠚⠁⠈⠁⠀⠀⠉⠿⠷⠂⠤⡀⠖⠤⢠⠤⢤⣴⡶⠲⢾⣷⣦⣴⣾⣁⣠⣴⣾⣾⠏⣀⠁⠰⣷⣿⣿⣿⣿⣷⡀⠀⠆⢀
⣾⡿⠉⣿⠟⢯⡽⠁⠈⠀⠙⣿⣿⣿⠁⠀⠈⢀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠄⡀⠀⠀⠀⠀⠁⠀⠀⠤⠈⠉⠻⣟⢩⠟⡩⢉⡱⣿⠀⠀⣿⣿⠏⠉⡛⢿⣹⣶⠂⣤
⢛⠃⢠⠤⡌⠋⢷⠄⢀⠀⠀⣿⣋⡁⠀⠀⠀⠉⠁⠀⠠⢀⣾⡟⠋⠁⠀⠀⠈⠳⢦⣄⣀⠀⣠⣞⠃⠀⠀⠀⠉⣤⣳⣬⣦⣱⣾⣧⣰⣿⠛⡀⢀⣈⢁⢛⣿⣪⣅
⠈⠁⢸⠆⣤⣰⠮⣤⡘⣆⠈⠁⢹⡁⣴⠇⢀⡀⠀⠶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢈⡿⠁⠉⠀⠀⠀⠀⠀⠀⣾⡟⢻⠛⠟⠿⣿⣿⣿⡄⠀⠀⢋⡸⣯⡀⢨⡙
⣄⢈⠻⣜⡦⠍⠦⠈⢳⣾⡏⠀⣊⡀⠀⠀⣈⠀⢀⠿⢍⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣷⠄⢀⠉⠹⠿⠁⢱⣤⡽⠁⠈⠙⡎⠁
⠰⣦⡏⡐⠄⣰⡈⢛⣶⣯⡰⢙⠋⢀⣤⡈⠁⠐⠄⣴⣿⣽⡿⠆⠀⠀⠀⠀⠀⠀⠀⣚⣏⡄⠀⠀⠀⠀⠀⠀⣠⠞⢹⣿⣇⣂⣨⡂⣄⠀⠀⢤⢿⡇⠠⣣⠄⠁
⠦⢈⣙⣷⣴⠿⠋⣨⣿⡦⢚⠛⠋⠀⠀⠈⠻⠂⢀⣼⣿⡿⠤⢀⠀⢀⣀⣀⣀⣠⠨⣿⣿⠀⠀⠀⠀⠖⠻⡛⠈⢀⡿⡋⣿⣏⣉⣙⣦⣄⣀⣀⣾⣿⣻⣗⡢⢠⡖
⠚⠉⠉⠻⢷⠴⣾⢡⠍⠁⢉⣠⠛⠒⠀⠠⣤⣴⠋⢻⣿⡧⣄⣀⠀⣼⣿⡿⠋⠀⠀⠀⣸⡂⠀⠀⢀⠀⢂⣀⠐⠚⠃⠁⠙⠛⡛⠿⣿⣿⠟⠋⠉⠙⠋⠀⡙⢾
⠂⠠⠴⡾⠃⠈⢋⠈⠠⡖⠉⠉⠀⠀⠀⡀⠙⠃⠄⠸⣿⣿⣿⣿⣿⣿⣿⣁⣤⠀⣀⣀⠙⣷⣰⣶⣯⡄⠻⠋⠀⠀⠀⠀⠀⠸⣛⢿⣿⡏⠀⡀⠀⡃⠀⠀⠘⠄⠃
⠀⠀⠀⠀⢀⡴⢰⡀⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⢿⣷⢿⡉⠀⣷⣿⣯⣄⠈⣷⣷⣤⡀⠀⠀⠀⢰⠘⢿⣾⣿⠃⢀⣵⡄⠀⠀⠀⠀⠈⠃
⠀⢀⣴⠁⠈⢁⣼⡇⠀⠀⠀⢰⡈⠢⡀⢀⣀⣄⣰⠿⠿⠿⠿⠻⠛⠿⢢⣄⠓⣼⣧⣞⣁⣦⣤⣠⣽⡛⢛⡉⠁⢰⠀⠀⠀⣻⡾⣌⡿⠗⠋⠙⠓⠀⡀⠀⣤⣄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠚⠯⠁⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⡀⠀⠠⠀⣟⠀⢠⢠⡄⣤⣼⣀⣄⡂⠉⠹⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⠐⠭⢿⣞⣢⣿⣷⡱⢶⣿⠶⢿⣶⢛⣄⡴⠂⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⢢⡿⠌⡟⡿⣮⠷⡜⣏⡷⡫⢿⡾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠌⢳⠀⢿⡛⢢⡟⢳⠛⣿⠹⣄⣲⢯⣯⣵⡟⠌⠙⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢳⡛⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⣟⢸⣷⢠⣦⡠⠧⣛⢑⢺⣍⢿⣧⡄⠀⠀⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠥⢤⡬⠞⣉⢓⣲⢤⡀⠀⠀⠀⠈⠀⠰⢾⣥⠝⣯⣄⠶⠺⣥⣍⠤⣈⣿⡅⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⢠⠚⡿⠩⠀⢠⠦⢄⠔⠒⣾⣿⣍⣛⣶⠀⠸⠀⠀⠠⠻⢫⣤⣄⣻⡿⠶⣶⡆⠚⣭⠮⣿⠀⠄⠠⠎
⠀⠀⠀⠀⠀⢠⠀⠰⢈⠀⠀⠎⢨⡋⠀⠀⠈⢻⣻⡁⠉⠁⠳⣀⡰⠃⠀⠈⢁⣿⠋⠷⠚⠾⠍⠉⠐⢦⡍⠁
⠀⠀⠀⠀⠀⢸⠀⣦⠿⠀⠀⠠⢈⠯⠷⠾⠉⠀⠙⠁⠀⠀⠀⠀⠸⢀⡤⢶⣛⠕⠀⠈⢆⠀⠀⠀⣀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠡⠁⠀⠃⠀⠀⠀⠠⠤⠥⠄⠀⠀⢤⡤⠤⠴⠂⠀⢍⠫⣸⡅⠀⠀⠀⠀⠉⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⡄⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡐⣀⡀⠀⠈⡦⣾⢻⠀⠀⠀⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠉⢤⡳⢮⣰⣦⢀⣠⣤⠾⠛⠉⠉⠉⠉⡉⠉⠁⣩⠷⢽⣮⢸⡀⠘⢱⡏⠀⠀⠀⠀⢀⡐⠲⣈⣧
⠀⠀⣠⡤⢐⣦⣴⣽⡟⣻⣿⣿⣿⣿⣶⣷⡦⣀⠀⠀⢀⠐⢀⡪⠭⠿⢴⣭⣇⢷⠠⣸⡇⠀⠀⡠⢶⠷⣑⠀⠀⠙
⠀⠀⠑⢌⡐⣉⠠⠔⠾⣿⡿⣿⣿⣿⣅⠚⡙⠉⠀⣀⠁⢀⠁⣀⡂⣤⢀⢐⣛⢪⣆⠈⠧⠀⠀⢀⠀⢀⠋⢠⠀⠀⠖
⠀⠀⠀⠸⢎⠙⠀⠠⠀⣸⠁⠘⠈⠧⠈⢂⠈⡀⠀⠨⠀⡤⠈⠀⠀⢀⠀⠄⠐⠦⣽⣧⠜⢧⡀⢀⠁⠐⠾⢾⡀⠂
⠀⠀⠀⠀⢠⠃⠀⠀⢀⡟⡀⠀⠀⠀⣦⡀⠙⣈⠂⠀⠰⠄⠀⠀⠈⠂⠀⠲⢃⡁⡛⠻⢷⣄⣙⢂⢀⣀⠀⢤⠇⠊⡀
⠀⠀⠀⠀⢤⡀⠤⠒⣀⢒⣁⠀⠀⠠⣃⣳⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⡃⠔⡁⠆⠐⠀⠉⠈⠉⠁⠀⢊⠿⠂⠓⠒⠙⠂⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⣤⣠⣠⠍⡁⠠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠵

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⡄⠘⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠒
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠼⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⡄⠀⣎⠀⠀⠀⠀⠀⠀⠑⠦⣀⢠⠆⠀⠀⠀⣼⣿⣷⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠂⠀⠈⢦⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⠈⠉⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠁⠉⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⠀⠀⠀⢀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⠎⠀⠀⠀⠀⠻⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠦⠠⠄⠀⠀⢹⠄⡄
⠀⠀⠀⠀⠈⠓⠶⢄⡀⢆⡔⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⡴⠀⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠰⠈⠀⠙⠀⠉
⠀⠀⠀⠀⠀⠢⠤⣤⡀⠀⡤⠊⠀⠀⠀⠀⠄⢤⣘⣤⡈⡐⣶⠆⡘⠀⣸⣧⠀⠀⠰
⠀⠀⠀⠀⠀⠂⠀⠀⠁⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡶⠡⠊⡇⢰⡿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⢀⠄⠴⠏⠀⠀⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⣀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠙⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁