Pharmacy Emojis & Symbols

⠀⠀⢠⡄⠀⠀⠀⢤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⢤⡤⠤⠤⠤⠤⠤⢤⡤⠤⠤⢤⣤⣤⡄
⠀⠀⢸⡇⠠⣶⣦⢾⣶⡶⣶⡶⣶⡶⣶⡶⢶⣶⢶⣶⣶⣾⣷⣶⡆⠀⠀⠀⠘⡃⠀⠀⠀⠀⢀⡇
⠀⠀⠸⠁⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⡆⠀⠀⠀⠀⢀⣦⠀⡒⣦⠉⣀⢲⡀⣲⣐⣖⣦⣾⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⡇⠂⠀⠀⠉⠉⠉⢉⣡⣍⣈⡉⠉⠉⠉⠉⠁⠀⢿⠀⠀⠀⣀⣤⣤⣘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣷⣒⣇⣀⣒⡀⣴⣿⡿⠉⠙⣷⣀⣧⣭⣤⣴⣢⣿⡀⠀⢀⠿⣿⣿⣿⣷⠀⠀⠀⠀⢸
⠀⠀⠀⡟⠉⠉⠉⠉⢱⣿⣿⠛⠂⡛⢹⡇⠀⢀⢀⢀⡈⢻⠁⠀⢻⠋⠹⣿⣿⣿⠠⠄⠀⢹⢸
⠀⠀⠀⣇⣟⣇⣄⡰⢈⡿⣿⠠⣤⣤⣞⣁⢿⠼⠴⠤⣧⣼⠀⠀⠈⢣⣠⡤⢖⣛⣄⠀⠀⠀⢸
⠀⠀⠀⡏⠉⠉⢲⠟⠁⠀⡌⣶⣶⠰⠀⢙⣃⠀⢠⢄⠈⢹⠀⠀⠀⡠⠼⠋⠉⠀⠀⠉⢧⠀⢸
⠀⠀⢰⡧⠾⠕⡟⠀⢰⠀⠙⢿⡇⠰⠿⠿⠈⣤⠼⠚⠒⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸
⠀⠀⢸⣧⣤⣤⣧⣤⣾⡅⠀⢸⠃⢀⡤⠼⠿⢬⣆⠀⠀⢸⠀⠀⡏⠀⠀⡄⠀⠤⠤⠦⠄⠛⢸
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣴⣼⡄⢠⡀⣙⠾⠿⠀⢀⣀⣘⣀⣼⠁⠀⡟⠀⠀⠀⠀⠀⠀⣦⣼
⠀⠀⢸⠿⠿⠻⠿⢿⣿⣿⡟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠔⠽⣯⣴⣂⡼⠁⠀⠀⠀⢀⣠⡄⣸⠋⠙⢛⡀
⠀⠀⢸⡤⣀⣀⣀⣀⣉⡭⠭⠤⠤⠶⠒⠒⢒⣒⣚⣋⣉⠉⠩⠭⢩⣄⣀⣀⣴⣿⣯⣾⡼⡏⠉⠉
⠀⠀⠘⠳⠼⠧⠤⠤⠴⠖⠒⠒⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢲⠓⣆⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠚⠛⠛⠻⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⡀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠈⣧⠀⠀⠈⠁⠈⠀⠀⠉⠉⠉⠭⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠁⠁⠉⠀⢆⠀⠀⠀⢀⠾⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⡭⠭⠭⠭⠭⠭⠭⠐⠋⠉⠉⠉⠉⠉⠉⢭⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣃⣂⣀⠀⠘⢂⣘⡀⣈⣀⠘⠀⠀⠀⣁⣸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⡔⠂⠂⠒⠒⠒⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⢨
⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⡀⠀⠀⠀⠈⡄⠰⠤⠤⠄⠀⠀⠠⡿⠀⠰⠀⠀⠀⠀⠀⠠⡇⢸
⠀⠀⠀⠀⠀⢸⠈⠋⠋⠉⠉⠊⠙⠙⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠒⠒⠀⠀⡇⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⣴⣒⣒⣒⣒⣒⣠⣿⠀⣶⣶⢶⣶⣶⣖⣖⣧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠭⠥⠤⠤⠤⠄⠠⠤⠯⠥⠬⠤⠬⠄⠬⠤⠭⠤⠥⠤⠤⠬⠤⠤⠤⠤⠤⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⢀⠂
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠈⠃⡒⠃⠘⢒⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠃
⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠃⠘⢀⡴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⢡⠤⠤⠤⠤⠤⠤⢤⠀⢤⠤⠤⠤⠤⠤⠤⡤⠀⡤⠤⠤⠤⠤⠤⠤⣜
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⢸⠀⢸⠀⠀⠀⢀⠀⠀⡗⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢄⠀⠀⢸⠀⢸⠀⠀⡠⡂⠀⠀⠇⠀⡇⠀⢀⠔⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⡡⠡⠊⠀⢸⠀⢸⠀⢈⠄⠔⠁⠀⡇⠀⡇⠀⡠⠠⠊⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠊⠐⠀⠀⠀⢸⠀⢸⠀⠁⠂⠀⠀⠀⡇⠀⡇⠈⠐⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⡘⠦⠤⠤⠤⠤⠤⠾⠀⠸⠤⠄⠀⠀⠤⠤⠇⠀⠷⠤⠤⠤⠤⠤⠴⢗
⠀⠀⠀⠀⠀⠐⠃⢀⢄⠐⠀⢠⣀⢀⢀⠀⡄⢠⣀⢀⣀⡄⢠⠐⡠⠀⣀⠀⠀⠀⠀⡀⢄⠘⠂
⠀⠀⠀⠀⠀⠠⠀⠙⠊⠀⠀⠘⠀⠈⠉⠈⠉⠈⠉⠀⠉⠃⠉⠁⠑⠀⠈⠀⠀⠀⠀⠑⠊⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⠤⠤⠤⠤⠤⡄⡤⠤⠤⠤⠤⡄⢠⠤⠤⠤⠤⠤⠤⠤⠤⡜
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡗⠛⠀⠀⡆⠀⠀⡇⡇⢀⡔⢢⡀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠬⠤⠄⡇⠀⠀⡇⡇⠀⠄⠀⢄⡿⢸⠀⠀⢀⠔⡠⢀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠒⠒⠂⡇⠀⠀⡇⣇⠀⠀⠀⢈⡧⢸⠀⠀⠁⠊⠐⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠀⠀⠀⠇⠀⠀⡇⡟⠉⠉⠉⠉⣧⢸⠀⠔⠡⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡿⠶⠶⠶⠶⠶⠶⠶⠶⡇⣇⠀⠀⠀⠀⡏⠸⠶⠶⠶⠶⠶⠶⠶⠶⣷
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠉⠉⠉⠉⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠛
⠀⠀⣿⡆⠀⠀⠀⢀⣤⣤⠀⣤⠀⡄⠀⣤⡄⠀⣤⣤⡀⣠⡄⣤⡄⠀⣤⡄⠀⣠⣤⡄⣤⣠⡄⠀⠀⠀⠀⣿
⠀⠀⣿⡇⠀⠀⠀⢸⡿⠛⠀⣿⠛⡇⢰⡿⢿⡀⣿⢿⡁⣿⢿⡿⡇⢸⠿⣷⠀⣿⣤⡄⠈⡿⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⢠⡿⠛⠛⣛⠛⠛⠛⣛⠛⠛⠛⢛⡛⠛⠛⠛⣛⠛⠛⠛⢛⡛⠛⠛⠛⣛⠛⠛⠛⢛⡛⠛⠛⠛⣛⠛⠛⢿⡆
⢠⡿⠁⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⡆⠀⠀⢸⣷⠀⠀⠀⢿⡆⠀⠈⢿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠛
⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⡇⢸⣿⠛⠛⠛⠛⠛⢻⣿⠟⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⣿⠛⠛⠛⠛⠛⣻⡿⠟⣿⡇⠀⣿
⠀⠀⣿⡇⢸⣟⣠⡾⠃⢀⣶⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡶⠟⢀⣴⠿⠋⠀⠀⣿⡇⠀⣿
⠀⠀⣿⡇⢸⣿⠋⠀⣴⠟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡾⣿⡇⠀⣿⠀⠸⠟⠁⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠋⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠸⠋⠀⠀⠀⣿⡇⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⣿
⠀⠀⣼⡀⢸⣿⠀⠀⠀⠀⣠⡾⠋⠀⢸⡇⠀⠀⠀⠀⢠⣾⠟⠀⣿⡇⠀⣿⠉⣀⠀⠀⠉⠉⠉⠉⣿⡇⠀⣿
⠀⠀⣿⡇⢸⣿⠀⠀⣠⡾⠋⠀⠀⠀⢸⡇⠀⠀⢀⣴⠟⠁⠀⠀⣿⡇⠀⣿⠀⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⣿⡇⠸⣿⣤⣾⣿⣶⣶⣶⣶⣶⣾⣷⣴⣶⣿⣷⣶⣶⣶⣶⣿⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣿
⣶⣶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡀⡀⣀⠀⡀⢀⣀⠀⣀⣀⠀⣀⠀⣀⡀⣀⣀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠟⠁⠟⠿⠸⠻⠸⠿⠵⠿⠿⠤⠟⠇⠻⠤⠸⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⢀⣞⣀⣀⣇⣀⣸⣇⣀⣸⣇⣀⣐⣇⣀⣀⣇⣀⣀⣇⣀⣀⣧⣀⣀⣷⣀⣘⣆
⠀⠀⠀⠀⠀⠈⠉⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢰⡟⢛⠛⠛⣻⠟⢿⠛⠛⠛⠛⠛⠛⡇⢰⡟⡛⠛⢛⣿⠟⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⠋⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⣠⡇⢸⡟⢩⠶⠋⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠁⠀⠀⠀⢻⠀⠀⠀⣠⠞⠁⡇⢸⡇⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣠⠀⣼⠀⠀⠈⠁⣠⠀⡇⢸⡷⠶⠶⠶⠶⠶⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣠⠞⠁⠀⣽⠀⠀⣠⠞⠁⠀⡇⢸⡇⠙⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠘⠓⠚⠓⠒⠒⠒⠛⠒⠚⠓⠒⠒⠒⠃⢸⡇⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣇⣀⣀⣀⣀⣀⣿⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⡤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠀⠀⠁⠈⠁⠀⠀⠙⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣰⠋⠙⠓⠒⠛⠉⢷⡀⠀⢠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠶⡏⠀⠀⠀⠀⠀⠀⠘⡷⢤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡇⠀⠀⠀⠀⠀⠀⢀⡧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠶⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⢿⡀⠀⣸⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⢧⠀⠀⠀⣀⣤⡀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠈⢧⣀⠀⠚⠟⠃⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣇⣀⣁⣀⣀⣀⣀⣀⡀⢩⣟⣒⣒⣒⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠐⠸⠊⠀⠛⠉⠰⠗⠀⠀⠑⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠌⠠⠀⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢀⠀⢀⠀⣀⠘⠀⣀⣀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠀⠁⠀⡀⠀⠀⠠⠋
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠂⠄⠀⠀⠈⠁⠀⠀⠀⠄
⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⢨⠀⢠⠀⡀⠀⡄⠀⡄⢠⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣⡠⢄⡰⢀⠠⢀⠄⡀⠄⡀⢄⠠⣀⠆⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢠⠀⢸
⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠠⠄⠔⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⢸⠀⠀⠀⠀⠸⠀⢸⠀⢀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠸⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⢤⡸⢀⠘
⠀⠀⠀⠀⠤⠤⠠⠴⠤⠤⠄⠀⠀⠠⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠥⠴⠄⠀⠀⠤⠀⠠⠆⠤⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⣒⠒⢒⠒⢒⠒⠒⡒⠒⠒⣒⣒⠒⠒⡒⠒⢒⠒⠒⢒⠒⠒⢒⣒⠒⡒⠒⢒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣹⠇⢸⣤⣼⠀⢰⠻⡆⠀⣯⣩⡗⢸⣿⣄⢿⡇⢠⡟⣇⢠⡏⠉⠃⠙⣦⠏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⠀⠸⠀⠟⠉⠻⠀⠇⠘⠇⠸⠃⠛⠸⠇⠞⠉⠻⠀⠳⠴⠃⠀⠻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⢰⠆⠐⠐⠂⠐⠂⠂⠐⠐⠀⠐⠀⠒⠐⠂⠐⠀⠒⠀⠀⠶⠐⠀⠂⠀⠒⠃
⠀⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠩⠭⠭⠭⢵
⠀⠀⠀⠧⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠬⢭⡍⠽
⠀⠀⠀⠀⠀⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠴
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠒⠍⠉⠩⢖⡦⡀⠀⣗⣀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⣠⣔⠦⠍⠉⠵⢖⣤⡀⠀⠀⢸⣀⣀⢀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⣤⠖⠀⠀⠀⠀⠀⠀⠈⢫⣦⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⢺⠀⢀⢞⠏⠀⠀⠀⠀⠀⠀⠙⢟⡄⠀⢸⠀⠀⢰⠀⠀⢀⡀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⢀⠀⠔⠀⢱⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡎⠀⠀⠀⠀⠀⢀⠀⠒⠈⣼⠀⢸⠀⠀⢸⠀⡤⠴⠀⠸⠤⡄⢸
⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⣀⠤⠒⣁⠤⠒⠀⢸⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⣠⠴⠊⣁⠤⠒⠀⡟⠀⢸⠀⠀⢸⠀⠧⢤⠀⢠⠤⠇⢸
⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠉⡠⠔⠊⣁⠔⠂⠀⢸⠀⠀⡇⠀⠀⠞⠑⣦⡀⠀⡄⢸⠀⠀⡇⠐⢉⡠⠔⠉⡠⠔⠂⠀⣷⠀⢸⠀⠀⢸⠀⠀⠐⠒⠒⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⢸⡇⠐⢉⠀⠐⠉⠀⠀⠀⠀⢸⠀⠀⡇⠠⡞⠊⠉⠀⠸⡀⡄⢸⠀⠀⡇⠘⢁⠀⠒⠉⠀⠀⠀⠀⣿⠀⢸⠀⠀⠘⠒⠒⠒⠒⠒⠒⠂⠚
⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢡⡀⠤⠖⠚⠁⠇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠨⣇⣀⣀⣀⣀⣀⣀⡀⢀⣀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⠀⠀⠋⠀⠘
⠀⠀⠀⠀⠀⠀⡇⡞⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣓⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡂⢠
⠀⠀⠀⠀⠀⣀⣇⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣓⣀⣀⣀⣀⣀⣀⣀⣠⢺⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣸⣀
⠀⠀⠀⠀⠀⣗⣒⣒⡒⠂⠐⠀⠀⠀⠀⠀⠀⣀⣍⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸





⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢗⣏⣱⡺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⢹⣦
⠀⠀⠀⠀⠀⢀⣴⢟⣵⠟⠁⠈⠻⣮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿
⠀⠀⠀⢀⣴⢟⣵⠟⠋⠛⠈⠋⠋⣋⣻⢮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢘⣿⢀
⠀⠀⣴⡟⣵⡟⢡⢤⡄⡄⣲⡾⢩⣡⣽⡼⢻⣮⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⢠⠶⠶⠾
⠀⠀⠈⠻⣮⡻⣦⣉⣫⠿⠟⠓⠋⠉⢀⣴⢟⣵⡿⠋⠀⠀⠀⠀⠀⠢⣾⣠⢸⠉⢀⣀⡬⣽⡶⠖⡟
⠀⠀⠀⠀⠈⠻⣮⡻⣦⠶⠤⠄⠶⣴⢟⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⣤⣴⣟⣻⣹⣟⣶⣷⣿⠴⠒⠛
⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⣦⢴⢟⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠛⢩⢍⡀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠞⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣙⣛⣺⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠉⠧⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡟⣰⠀⠀⠀⢢⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠈⠰⠤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣧⠿⢈⣉⡀⠩⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢰⠑⢄⠀⠀⠙⢂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣤⣤⠴⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠻⠶⠾⣀⣀⣁⢀⣀⡈⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠐⣴⠶⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⢷⠿⢵⣥⢾⠿⢹⣮⣼⣽⣦⠕
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡖⣒⠒⡖⣲⡉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⡈⠉⠙⢿⣭⣽⠉⠩⣯⣭⣎⠟⠇
⠀⠀⠀⠀⠀⠀⢸⣿⠿⣅⣈⣁⣃⣉⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠑⢼⣤⣤⣇⠞⢁⠖
⠀⠀⠀⠀⠀⠀⠘⣿⣄⣿⣶⣿⢷⣦⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⠄⠹⠾⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⣶⠶⠿⠀⠀⠿⠶⣶⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⣿⠁⠀⢿⡇⠀⠀⣿⣀⣀⠀⠀⣀⣀⣿⠀⠀⢸⡿⠀⠈⣿⡀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠸⣧⠀⠀⠉⠉⣿⣀⣀⣿⠉⠉⠀⠀⣼⠇⠀⠀⢸⣇⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢹⣧⡀⠀⠀⠙⠙⠛⠋⠀⠀⢀⣼⡏⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸⡏⠛⠷⣤⣄⣀⣀⣠⣤⠾⠛⢹⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣼⣇⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣉⣹⣏⣉⣀⣀⣀⣘⣿⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣀⣸⣧
⠀⠀⠀⠀⠀⢿⡛⠛⠛⠛⠛⣻⣟⠛⠛⠛⠛⢛⣿⡛⠛⠛⠛⠛⣻⣟⠛⠛⠛⠛⢛⣿⡛⠛⠛⠛⠛⣻⣟⠛⠛⠛⠛⢛⣿
⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⡾⠋⠙⢷⣤⣤⣴⠟⠉⠻⣦⣤⣤⡾⠋⠙⢷⣤⣤⣴⠟⠉⠻⣦⣤⣤⡾⠋⠙⢷⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢰⡶⠶⠶⠶⣶⡆⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⢰⡶⠶⠶⣦⠀⢰⡶⠶⠶⣶⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⣤⣼⣧⣤⣤⣿⣤⣼⣧⣤⣤⣿⣤⣼⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠸⣷⣶⣶⣶⣾⠇⠀⣿⠀⠀⣿⠀⢸⣿⠛⢻⡇⠀⢰⣿⠛⢻⡇⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⣿⣀⣸⣿⣀⣸⣇⣀⣸⣿⣀⣸⣇⣀⣸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣄⠀⠀⠀⠀⠀⣴⢒⣲⣲⣒⣖⣖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠉⢻⣤⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⡟⠁⠀⠀⠀⡤⠇⣏⣀⣠⠤⣄⣈⡇⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀⠀⢰⡇⠀⠀⠀⠈⡻⣆⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠢⡀⢳⡇⠀⠀⠀⢀⡇⠀⠀⠀⢁⣀⠈⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠉⢀⡿⠙⠲⢤⣀⠀⡇⢹⠀⠀⠀⣾⠛⠋⠀⢀⠀⡱⣴⡾⠋⠀⠀⠀⠀⠀⡇⠀⠀⣤⡿⠙⣧⣄⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⣸⡁⠀⠀⠀⢈⡽⢃⡞⠀⠀⢠⣬⠷⢄⠀⣄⣱⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⡄⠚⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠛⠤⡤⠴⠋⠙⠲⢤⣬⡥⠴⠋⠀⠀⠀⠀⠱⣤⡞⠳⣬⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⢒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠠⣰⠂⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠑⠕⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣚⣒⣒⣀⣐⣒⣚⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⡼⠃⢠⡞⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠍⠉⠉⢍⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⡞⠀⣠⠏⠀⠀⠀⠀⠀⣼⣧⠞⠀⠀⠀⠀⢀⡔⣡⣯⠖⢢⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⡙⢫⡎
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠂⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⠫⡑⢄⣀⡠⢔⠵⣜⣻⠅⠀⣊⣱⠤⢤⠀⠀⠀⡇⠀⠰⡥⠉⠁⠰
⠀⠀⠀⠀⠀⠀⠀⡸⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠁⠀⠈⠧⠠⠊⠀⢧⣀⣀⠇⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠸⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠉⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣴⠒⢲⣶⠒⢲⡄⡿⠀⠀⠀⠀⠀⣴⠋⡠⠤⠤⠤⠤⣜⡣⠀⠀⠀⠀⠀⠻⠉⠙⣾⠀⠀⠀⢀⠎⡙⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣙⡛⠋⡎⠛⣛⣹⠇⠀⠀⠀⠀⢰⡿⠾⠷⠶⠶⠒⠒⠛⠓⢲⠀⠀⠀⠀⢸⠀⡀⣿⠀⠀⢀⡞⣰⡿⠁⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡉⠹⣇⣀⡾⠉⢹⡄⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⢀⣀⣠⠴⡏⠀⠀⠀⠀⢸⠀⡀⣿⠀⢰⠛⢶⡉⢧⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣆⡀⠉⠳⣦⠶⣿⠀⠀⠀⠀⠀⣀⡤⠤⠼⠧⠼⠥⠟⢠⡇⠀⠀⠀⠀⢸⠀⣁⣿⢠⡏⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠁⢠⡿⠳⣦⠀⢤⡞⠀⠀⠀⠀⠠⣇⣴⣶⣶⣶⣶⣶⣶⠋⠀⠀⠀⠀⠀⠸⣎⣉⡿⡞⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠙⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠉⠀⠀⠙⠛⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠁⠀⣶⠀⠀⣶⣄⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣄⠀⠙⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⡀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠛⠻⢿⠀⠀⠿⠀⢀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣄⣀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢐⡆⠰⢆⢲⣖⠊⠴⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠐⠀⢨⡏⠂⠀⠐⠀⢹⣨⡷⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡀⠐⢀⠀⢁⠀⡈⠀⢀⡱⠓⠁⠁⠪⢆
⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⠄⣘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡐⣥⣼⣷⢨⢬⡣⠸⣇⠀⠂⠀⢀⡕⢣
⠀⠀⠀⢠⠊⡠⠂⠉⡀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢏⠌⠸⠺⡼⠶⠚⢸⣦⡇⡠⡪⠊⠉⠈
⠀⠀⠀⡆⠐⠀⠀⢏⣈⠂⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠟⠛⠚⠛⠚⠢⣮⢏⢴⠎
⠀⠀⠀⢃⠘⡀⠀⠢⡤⠃⢀⠄⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠁⡠⠊⠉⠉⠉⠢⡈⢻⠁
⠀⠀⠀⠈⠢⡈⠒⠄⠀⠔⢉⢠⠁⠉⠉⠉⡩⠭⠭⠭⠭⡉⠉⢉⢟⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⢄
⠀⠀⢰⠉⠅⠭⠩⠩⠉⠉⠉⠉⠉⢢⠤⠤⠭⠬⠭⠬⠭⠥⠤⡎⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠊⠛⠻⠛⠛⠋⠉⠉⠉⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢆
⠀⠀⢱⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠂⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⠛⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣽⣉⣉⣋⡦⢰⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠋⠑⠛⠀⢸⣀⡠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⡠⠄⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡇⠀⠠⠔⠁⠀⠰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣐⣀⣀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠚⢧⠀⢀⠗⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂⠈⠓⡴⠡⠤⠀⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠠⠀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⠀⠀⣄⢋⣰⠈⢢⠠⠤⠤⠤⠼⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠨⠈⠂⠀⠀⡀⡀⠀⠈⠁⠆⡈⢸⣀⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⠂⠀⠀⠀⠀⠈⠧⡟⢱⠒⡦⢄⡡⠂⠀⠀⠉⠉⠁⠐⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣧⡠⠊⠀⠀⢀
⠀⠀⠀⠀⠀⢀⢤⠖⡫⠉⠉⡐⠠⢍⡁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⡠⠊
⠀⠀⠀⡠⠚⡱⠃⠀⠀⠀⡠⠃⢠⢄⡌⢝⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⢀⣠⠴⡁⠑⡄⢀⡠⠖⠉
⠀⠀⡜⠀⠘⠂⠤⢀⣠⠌⠀⣐⠣⠆⣠⠋⠲⡑⢨⠃⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⢇⠀⠘⣄⠜⠉
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠉⠒⠠⢉⡒⠦⢌⠔⢀⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡆⠀⠀⠀⠑⢄⡇⠀⠀⠃
⠀⠙⠒⠠⠤⠤⠤⠀⠀⠀⣀⣀⡀⠈⠑⠢⣤⠎⠀⠀⠰⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠢⠄⣀⢤⣀⠀⡀⠀⢀⡁⠤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠤⠤⠤⠄⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡤⠤⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠴⠶⠖⠒⠛⠛⠉⠉⠉⠉⠀⠀⠈⢧⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠉⢹⡏⠁⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠉⠓⠚⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣠⠟⠀⠀⠀⠀⠀⣰⠏⠀⢀⣼⣷⣤⠀⠈⢳⡄⠀⠀⣠⣤⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠁⠀⢀⣀⠀⠀⠀⡏⠀⠀⢿⣯⣤⣀⠀⠀⠀⣷⠀⠐⣇⣀⡽⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡇⠀⠠⡏⠉⣳⠀⠀⣧⠀⠀⠀⠉⠙⣿⡷⠀⠀⣿⠀⠀⠈⠉⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠀⠀⣇⠀⠀⠙⢛⡥⠖⠒⢻⣆⠀⠘⠛⢿⡟⠁⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢿⠤⣤⠞⠉⠀⠀⠀⣸⠋⠛⠦⣤⣤⣤⠴⠚⠁⠀⠀⠀⠀⢀⣸⣇⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⣀⣠⡼⠞⠁⠀⠀⢀⣠⠞⢁⣀⣀⣀⣤⡤⠤⠴⠶⠖⠒⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⢀⡴⠛⠋⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣤⢾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⣩⣴⡏
⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠘⢧⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢸⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⢠⡜⢛⠛⠀⠀⠀⠀⠀⢸⡗⣿⢺⡇⠀⠀⠀⠀⠀⠀⢀⡞⠉⢻
⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣟⠀⠀⠀⠀⠀⠀⢀⣿⡧⠄⠀⠀⠀⠀⠀⠀⢘⡋⣿⣙⠃⠀⠀⠀⠀⠀⢀⣿⡗⠓⢺
⠀⠀⠀⣨⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⠀⠀⠀⠀⠀⠈⠱⣿⣿⡇⠀⠀⠀⠀⠀⣨⣿⣷⡶⠚
⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠄⠀⠀⠀⠀⠀⠙⠻⠟

⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠿⠿⣿⣯⣽⠿⠿⠃⠀⠀⠿⠿⣿⣿⣽⠿⠿⠃⠀⠀⠿⣿⣿⣿⣿⣿⠿⠃⠀⠘⠿⠟⡍⣉⡩⠻⠿⠃⠀⠀⠿⠟⠍⣉⡩⠻⠿⠃
⠀⠀⠀⠀⣿⣿⣿⠀⡶⠀⠀⠀⠀⠀⣿⣿⣿⠀⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣏⠉⢱⠀⡶⠀⠀⠀⠀⠀⣊⠉⢱⢀⣆
⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢄
⠀⠀⠀⠀⢸⣿⡇⢜⢦⠀⠀⠀⢀⠞⠛⢷⣦⣄⠀⠀⠀⠀⠀⢸⣶⣶⣶⡇⠀⠀⠀⠀⠀⢸⠛⠛⠛⡏⠀⠀⠀⠀⠀⠀⣤⣴⣦⣾⣧
⠀⠀⠀⠰⢁⣀⠀⣇⠀⠀⠀⠀⡜⠠⠸⡋⠉⠈⡄⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠘⢤⣀⡠⠃⠀⠀⠀⠰⢶⣤⣠⢣⠀⠀⠸⡀⠀⠀⠀⠘⢻⣿⡿⠃⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⣶⣿⣿⣿⣯⣤⣤⡀
⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠷⠶⠛⠃⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠸⠶⠿⠷⠇⠀⠀⠀⠀⠿⠛⠛⠛⠻⠿⠿

⠀⠀⠀⠀⣤⣿⣤⣀⣤⡀⠀⠀⠀⠀⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⣤⣿⣤⡀⠀⠀⠀⠀⠀⠀⣤⣿⣤⣀⡀⠀⠀⠀⠀⠀⣤⣿⣤⣠⡀
⠀⠀⠀⠀⣇⣀⣸⠉⠄⢣⠀⠀⠀⠀⣇⣀⣸⣿⣿⡇⠀⠀⠀⠀⣇⣀⣨⣿⣷⠄⠀⠀⠀⠀⣇⣀⡰⠛⡑⢄⠀⠀⠀⠀⣇⣀⣹⣿⣷⡀
⠀⠀⠀⠀⣿⣿⣿⢗⢂⣀⡆⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠍⠉⠀⠀⠀⠀⠀⣿⣿⣿⠆⣤⡄⠀⠀⠀⠀⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠻⠿⠟⠈⠋⠉⠀⠀⠀⠀⠻⠿⠟⠈⠉⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠈⠁⠀⠀⠀⠀⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⣀⣀⣀⣀⡀⢀⣀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢷⣤⣤⣖⠊⠁⠀⠀⠈⠛⣔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠋⠀⠀⢄⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡤⠒⠊⠉⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠑⠄⠀⡀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠈⠢⣀⡠⠒⠁⠀⣡⣀⠙⢿⣿⣷⣄⠀⢀⣴⣦⡈⠳⣄⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡠⠖⠁⠀⣣⣀⠙⢿⣿⣷⣌⠻⡿⠋⠀⠈⢳⠊
⠀⠀⠀⠀⠀⠀⠀⢆⠀⡠⠊⠀⠀⡠⠊⠀⠀⡧⢄⠙⢿⣿⣷⣄⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡠⠊⠀⢀⡤⠋⠀⢀⠇⠀⠙⢿⣿⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⣀⡴⠋⠀⢀⠔⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠔⠉⠢⣀⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⣤⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠶⠶⠶⠆⠠⠶⠶⠄⠀⠀⠀⠀⠀⢀⡴⠖⠛⡛⠳⢦⣄⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣈⣁⡄⠀⠙⣧⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠴⠤⠦⠤⠤⠴⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠦⠤⣤⠀⠀⢹⠆⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡄⠀⣤⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢷⠹⣄⠀⠐⠒⡒⠋⠀⢀⡿⠀⠀⠀⢸⡇⠛
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣌⠳⣝⠶⣤⣈⣁⣤⠴⢋⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⣙⣛⣛⣋⣉⣉⣉⣉⣉⣙⣙⣛⣋⣸⡇⠀⠀⣤⣤⡄⠀⠀⠈⠳⣬⣛⡲⠶⠶⠶⠚⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡴⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⢷⡘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣡⠟⣀⣀⣈⠉⠉⣁⣀⡈⠉⠉⣁⣀⡉⠉⠉⣀⣀⡉⠉⢉⣀⣀⡉⠉⢉⣀⣀⠉⠉⢉⣀⣀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⢁⣀⣈⣉⣉⣁⣀⣈⠉⠉⠁⠀⠈⠉⠉⠀⠀⠈⠉⠉⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣏⣉⣉⣉⣉⣉⣉⣙⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠖⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠐⠛⠛





⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠔⠒⠊⠉⠀⢀⣀⡨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠒⠒⠉⠁⠀⣀⣀⠤⠔⠒⠂⠉⠁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⣀⡠⠤⠒⠒⠊⠉⠀⠀⠀⠀⠀⢀⠤⠤⠒⠒⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒⠉⢡⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠰⠠⠀⠆⠀⠀⠀⠰⠀⠀⠀⠀⠰⠰⠰⠰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠂⠀⠀⠀⢒⠤⢹⡶⡖⠒⠒⠒⠀⠂⠀⠀⠐⠒⢒⡊⢳
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡦⡸⢹⡄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠇⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠄⠀⠉⠁⠀⠘⣡⣿⡞⠃⠀⠀⠀⠀⠀⠈⠀⠈⢉⡀⠀⠀⠇⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⣽⡏⢡⡀⠀⠀⠀⠀⠀⡤⠀⠀⠻⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀⠀⡈⠀⠀⠻⢣⣸⡇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣯⠘⠋⠁⠀⠀⠀⢀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢘⡫⠀⠀⠀⠀⠐⠂⠎⠸⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣯⠀⡀⠈⢉⣭⣿⣶⠆⡖⠰⣦⠴⠆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣯⣿⣟⢚⠸⡱⠿⢿⣻⣖⠀⠀⠀⠀⡀⠀⠀⠐⠛⠆⣳⣾⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣯⣭⣭⣟⣻⣿⠏⠁⣀⡀⠙⠛⠳⠶⠶⣤⣤⣄⣀⣀⠚⠛⠉⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠤⠤⣈⣀⣐⠶⠯⢥⡀⠉⢟⣛⠿⢿⣶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠛⠛⠙⠒⠚⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣄⣀⣄⣀⢀⣀⣀⣀⣠⡀⣼⠀⡓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢸⠀⡇⠀⡉⢉⠉⢉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣀⠀⠁⠀⠀⠀⢸⠀⠱⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠈⠑⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⠚⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⢤⡀⠀⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡷⠀⠄⠘⠦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⢒⡒⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⠒⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢒⠒⠒⣒⠒⣐⢒⠒⡒⡒⠒⡒⠒⢲⠀⠀⠀⡠⠶⠉⠋⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠋⠀⠀⢠⠟⣡⠌⠻⡄⠀⠀⠙⡆⢸⠀⠀⣜⠃⠀⢰⠛⠄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⢸⡀⢈⡦⢀⡇⠀⠀⠀⡇⢸⠀⠀⢏⡀⠀⢀⣙⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⠤⠤⠤⠷⠦⠴⠾⠤⠤⠤⠖⠁⢸⠀⠀⠈⠣⣤⠀⡁⢀⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢸⣿⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⢸⣿⣷⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣯⣭⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣿⡇⠀⠀⠀⢸⣿⣟⣛⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⣉⣉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠀⠀⢸⡇⠀⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣷⢰⡶⠀⠒⠀⢀⣶⡤⠤⠤⠀⣿
⠀⠀⠀⠀⢸⣇⣀⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠛⣿⣿⣿⠯⠭⠉⣿
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠛⠉⠛⠤⠤⠠⣿
⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡿⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⢸⡟⢉⣉⡉⣉⠉⡉⠉⠉⢉⣩⠿⣷
⠀⠀⠀⠀⢸⡇⢠⣿⡦⠀⠀⡁⡀⠀⡀⡀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠐⠒⠀⠒⠒⢂⡤⠖⣉⣤⣾⣿
⠀⠀⠀⠀⢸⡇⢀⣀⣀⠀⣀⣀⣀⡀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⡴⠚⣡⣴⣾⠛⠛⣿⣿
⠀⠀⠀⠀⢸⣇⠐⠀⠂⠐⠀⠀⠂⠂⠘⠟⠀⣿⠀⠀⠀⠀⠀⠀⢸⣧⣴⣋⣡⣶⣿⣿⣿⣿⣤⣤⣿⣿
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠑⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⠁⠀⠉⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⣦⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠠⠁⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⣧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡗⢀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣼⢃⣼⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡀⠙⣆⠀⠀⠀⠈⠢⣀⠙⠦⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠞⡥⠋⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⣼⠃⠀⠈⠓⢦⡀⠀⠀⠈⠉⠐⠛⠛⠷⠒⢶⣶⡾⠟⠋⠉⠁⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⠀⠐⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⡴⢖⣿⡿⠟⠛⠛⠉⠉⢙⣽⠟⠛⠉⠛⠛⠒⠶⣥⣀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣠⠞⠉⣠⠞⠋⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠂⠈⠣⣀⣠⠞⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⡡⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢸⠇⠲⣤⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇
⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⣉⢻⣿⡏⢸⡏⢠⡈⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣧⠹⡟⢡⡌⢻⡟⢡⡎⢻⡏⢡⡌⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⡿⠛⢻⣇⢸⡇⠸⠁⣿⠀⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⠘⠋⣰⡇⣿⡇⣸⣇⠸⣷⣾⡇⢸⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣏⢸⣿⡇⢸⡇⢸⡇⠀⢾⣿⡄⣿⣿⣿⣿⡏⠀⠀⠀⠈⢻⣿⣿⢰⣦⢸⡇⢻⠇⣼⠿⣦⠹⣿⠿⡄⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠛⣀⣸⣇⣸⣇⣹⡌⢻⡁⠙⢻⣿⡿⠀⠀⠀⠀⠀⠈⢿⣿⣈⣁⣼⣷⣤⣤⣿⣆⣉⣠⣿⣄⣉⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⢛⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠿⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⣶⣿⣷⣾⣽⣷⣬⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⣹⣿⣿⣟⡛⢿⣷⡿⠃⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⣤⣤⣤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠤⠤⠤⠀⠀⠐⠂⠀⠀⣀⣀⡀⣀
⣿⣛⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣛⣻⣿
⣿⣿⣿⣿⣿⣶⣾⣡⡖⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⢨⣿⣿⣿⣿
⣿⣿⣿⣿⣼⣿⣿⣿⣼⢃⣄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⠀⠀⣀⢃⣸⣷⣴⣿⣿⣿⣿
⣿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠛⢁⠄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣠⣀⣿⣿⠛⣿⣿⣿⣿⡟⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠈⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣧⣾⣿⣿⣧⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿
⣿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢀⣉⣍⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠨⢉⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢘⠆⠀⠀⠆⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠀⣀⠒⠈⢌⡐⠂⠤⢀⣀⠠⣤⠼⠉⠠⠶⠏⣤⣀⡀⢐⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠉⠅⢘⡂⠸⠁⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣤⣠⠀⠐⢊⠓⠟⠇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠂⠀⠐⠢⠖⠚⡇⠀⠀⠀⠀⠀⠀⢀⠂⣅⡉⠉⢙⠃⠀⠀⠐⠛⠛⠉⠲⠦⠤⠀⡠⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠖⠒⠒⠠⠴⠀⡄⠸⠂⠀⠀⠀⠰⠤⠜⢃⣀⡀⠄⠤⣄⢰⢒⣋⡕⣒⠷⠶⣣⣅⣒⡦⠤⡁⠀⠉⠓⢈⡉⢄⠔⢒⠉⠉⡅
⠀⠀⠀⠀⠀⠃⠤⠀⠠⠼⠁⡅⠰⠦⣀⣀⣀⣀⣀⡠⢞⠈⠉⢈⠢⣿⠸⠀⠒⠨⠍⠛⠁⠀⠬⣁⡈⠉⠀⠍⠐⠽⢒⠉⢉⠩⢀⠀⠀⡇⡀⣠⢀
⠀⠀⠀⠀⠐⠣⠤⢤⡗⠟⠋⠭⣝⠄⠀⠀⠀⠀⠀⢀⡼⢄⠀⠀⡥⣴⠶⢄⠤⣠⣤⣀⣤⣄⣤⣄⡀⠀⠀⢀⣤⠤⠶⠎⣒⣩⡅⠖⠓⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣐⣀⣠⣆⣀⠀⠀⠀⣙⣰⠞⠓⠲⠒⢚⢭⢆⢲⠂⠀⠀⠀⠀⠈⠙⠙⠻⠽⠀⡠⠤⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⢪⡁⠒⠀⠐⡒⠂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠐⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠛⠛⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⢠⡞⠛⠉⠉⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣷⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⣿⠀⠀⢐⣁⣸⠆⠀⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠀⢸⠄⢼⠤⠤⠭⠭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⠀⠑⠚⠒⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⠆⠰⠀⠆⠰⠀⠀⠢⠘⠄⠐⠐⠂⠀⠐⠆⠶⠐⠀⠆⠀⠰⠀⠶⠐⠔⠒⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠣⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠉⠉⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⡆⠀⠀⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣧⡀⠀⠀⠀⠀⠉⠻⢷⣤⠀⣀⠔⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣾⡃
⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣧⡀⠀⠀⠀⠀⠀⠀⢙⠶⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠊
⣾⠃⠀⠀⠱⡄⠀⢀⣀⡀⠀⠀⠀⠸⡆⠙⠿⡄⠀⠀⢀⡤⠊⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠃⠀⠀⠀⠈
⢷⡀⠂⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⢦⣀⣀⣤⣄⣤⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠂
⠈⢷⡀⢠⡀⠀⣱⡀⠀⠀⠀⠀⠀⠀⡖⣤⠀⠀⠀⢀⣠⣀⠀⠀⢀⡀⠀⠀⠀⢘⡜⠛⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠋⠀⠀⠀⠀⠀⢠
⠀⠈⢷⣴⣿⠉⣿⣿⡄⠀⠀⠀⠀⣸⡿⣾⢀⡴⠢⠎⠝⢭⢗⣶⣴⢾⣥⣶⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠟⢋⣩⡄⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠘⣿⣿⣧⠈⢿⣿⡄⠠⠤⠴⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠛⠻⠻⣛⣤⠀⠀⠀⠀⠀⠀⠀⣏⢉⣁⣤⣾⣿⣿⣧⣤⡴⠖⠋⠉
⠀⠀⠀⠘⣿⣾⣧⠘⣿⣿⠀⠀⠈⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢠⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠘⢿⣿⣿⡁⠋⢠⠆⠄⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢠⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠑⣼⣿⣷⣄⠀⠀⠐⠒⠒⠒⠛⠋⠁⠀⠀⢀⢴⣿⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢄⡈⠛⢶⣤⣿⡏⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠻⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢷⣤⣤⣀⣀⡀⠠⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢄⠉⠻⣿⣷⣆⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⡄⠀⠈⠛⢿⣿⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠸⠷⢤⣀⣠⢀⡀⣠⠔⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢧⣽⣿⣷⣴⣼⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣵⣿⣿⣿⣿⢿⣾⣙⣻⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣽⣿⣿⣿⢿⣵⣿⣿⣾⣿⣿⣿⣭⣭⣝⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠈⠿⠋⠈⠋⠁⠉⠉⠛⠛⠋⠉⠉⠉⠛⠛⠻⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⠀⠀⣀⣠⣤⣶⠿⠛⣉⣠⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣶⡿⠟⢋⣁⣤⣴⡶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣶⡿⠿⠛⠋⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣏⣿⣿⣿⣿⣿⣏⣀⣤⣤⣶⡶⠶⠂
⠀⠀⠀⠀⠨⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⢻⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁







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

⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⢀⣠⣄⣤⣠⡄⣠⠄⠀⠀⠀⢠⣤⣤⠀⠀⢠⣤⡄⠀⠀⣤⣤
⠀⠀⠀⢀⣴⣟⣽⣿⣿⣿⣿⣿⣿⣿⣷⣯⡻⣦⡀⣰⠟⠁⢉⣹⡟⣱⣿⣾⣇⠀⢠⠰⣿⡇⠀⠀⡘⢿⡂⠀⡀⣻⢻⣀
⠀⠀⢠⣟⣽⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣮⣻⡿⣦⣰⣿⠟⠁⠉⠉⠿⣿⡇⢸⣯⠭⢍⣷⣿⡥⠤⢽⡂⢻⠥⠤⣽⡅
⠀⢠⡟⣾⣿⡇⠀⠀⢰⣦⠀⠀⠀⣿⣿⡿⠟⣿⣿⠀⠀⠁⠉⠀⠀⠠⣆⠀⢹⣧⣼⠓⠒⠀⣻⢹⠛⠒⠈⡇⢸⠛⠒⢻⡇
⢠⣼⣷⣿⣿⡇⠀⠀⠈⠁⠀⠀⢾⡿⠋⠀⢀⣸⣿⡆⠀⠀⠀⠀⠀⣬⣴⡶⢀⡱⣿⣦⣶⣦⣿⣾⣤⣤⣤⣧⣾⣤⣤⣼⣧⣀⣀
⠈⢹⡏⣿⣿⡇⠀⠀⢰⣿⣦⠀⠀⠀⠀⣴⣿⣿⣿⣟⠚⠛⢲⣤⣴⢾⣯⣇⡌⢴⣿⢠⣿⣭⠀⠀⢸⣿⣏⠀⠀⣹⣿⠁⣰⡄
⠀⠀⢿⡹⣿⣧⣤⣤⣼⠟⠋⠀⢀⡀⠀⠈⣻⣿⢫⡿⣄⡻⠟⠀⠀⣎⣉⡉⠀⣾⣠⡖⠚⠳⢦⣴⠖⠃⠓⠲⡦⠼⠯⢴⣿⡇
⠀⠀⠀⠻⣌⠻⣿⣿⣅⠀⢀⣴⣿⣿⣦⣾⢟⣵⠟⠁⠘⣧⠰⠚⣿⣁⡤⠅⢀⣿⡏⠻⣤⣤⣛⣿⣊⣈⣁⠂⣷⡚⣛⣺⣿⣿
⠀⣀⣀⣀⣈⣛⣮⣽⣛⣷⠿⢿⣿⣛⣯⣷⣛⣁⣀⣀⣠⡼⢧⡈⠀⠻⠅⢀⡾⣹⠃⠀⠹⡌⠉⠉⠙⠛⠛⠚⠓⠛⡉⢸⠿⠟
⠀⠛⠛⠛⣛⣛⠛⠛⠛⣻⣟⠛⠛⠛⠛⣛⣿⣿⡿⠟⣿⠀⠸⡏⠓⢶⣾⠟⠀⡿⢦⣀⣠⣤⠄⠀⠀⠀⠘⣧⠀⡄⠻⣩⣿⣧⣤
⠀⠀⠀⣠⣸⢿⢠⣀⡬⠿⢧⣄⣠⣶⣿⡿⠟⠉⠀⢰⡇⠀⢀⣿⢠⡿⣿⠷⣼⡇⠀⠛⠿⠧⣄⡀⠀⠀⠀⢿⢀⣿⠀⢻⣌⣿⡄
⠀⠀⠀⣿⠀⠈⠀⣿⡇⠀⠀⣿⡟⠉⡁⠀⠀⠀⠀⠘⢷⣦⡎⢸⡏⢸⣿⡄⣿⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⢸⣾⡇⠀⠀⠻⣿⡁
⢀⣀⣀⣻⣀⣀⣀⣿⡇⠀⠀⣿⠇⠀⣧⠀⠀⠀⠀⢟⠉⠀⠀⠀⢷⣸⣿⣷⠇⠀⠀⣠⣿⠏⠀⣠⣦⠀⠀⠀⣿⠁⠀⠀⠀⣹⡇
⠨⠿⠿⠿⠿⠿⠿⠟⠟⠋⢉⣿⠀⢠⢻⡄⠀⠀⢀⠸⣷⡀⠀⠀⠘⣿⣿⡟⠀⠀⣴⣿⠋⣤⣤⠿⠿⡴⠀⢸⡇⠀⠀⡰⢺⠇
⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⡏⣆⢸⡄⣷⠀⠀⠘⣧⡘⢿⣄⠀⠀⢹⡟⠀⢀⣾⠟⠁⠀⠀⠀⠀⠠⡇⠀⠀⣧⠀⠞⢡⠏⠀⢈
⢀⡠⢥⣥⣤⠤⣤⠀⠀⠀⢾⢁⢻⢸⡇⢹⡆⠀⢢⠀⠱⡌⠻⣦⣀⣼⣠⠶⠯⣤⣄⣀⣠⡔⢢⠴⣄⣀⠀⠀⣿⣧⡀⡯⠔⠋⠁
⠀⢳⣰⣼⣵⣶⠃⠀⠀⢠⡜⢸⡎⣯⣇⠀⢳⡄⢠⠱⣆⠈⣾⡟⠛⣿⡏⠀⠀⢰⠒⠾⢁⡴⢁⡐⢩⠌⡁⢀⣿⠟⠓⠺⠿⠛⠃
⢠⣤⣧⣬⣶⣯⣤⣤⣠⣏⢻⡄⢿⠘⣿⢀⣶⣿⣆⢳⡈⢠⡟⠛⢳⣿⣄⣀⣀⡇⠘⣀⠏⢁⣎⣠⣇⠎⡴⢸⢻⣷⡄⠛⠻⢿⡀
⠈⠉⠻⢿⣿⣿⣿⣿⡿⠀⠀⠻⣾⡇⠈⣼⣿⣿⣿⣇⠹⣼⠇⠀⠘⣿⣙⡛⢻⣥⣤⣭⣀⣺⡟⠋⠋⠰⠇⡏⠀⠉⢻⡀
⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠤⠤⠼⠷⣀⣿⣿⣿⣿⣿⣦⣹⣄⠀⠀⣿⣾⡈⠉⠉⠛⠛⠿⠿⠿⣆⣀⣨⠴⢻⣿⣶⡈⣃⣀⣠
⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⣠⡸⣿⣿⣿⠻⣵⣀⢹⡏⠀⠀⢸⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢸⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⢀⣾⠟⢓⣛⣛⢢⣼⣿⣿⣺⠀⠀⠀⠀⢿⡿⠁⢀⣴⢶⠀⠀⠀⠀⢰⡿⠀⢸⣿⣿⣯⢶⣶⡆
⠀⠒⠒⠒⠛⠛⣿⢷⣄⡀⠀⢸⡇⠒⣲⣶⠶⠼⠟⢙⡟⣸⠤⠶⠶⠶⠾⠷⠖⠘⠛⢿⣶⠒⠒⠒⠚⠒⠒⠚⠛⡛⠛⢓⣚⡃
⠀⠀⣷⠀⠀⠀⡿⢹⠸⢹⢶⢬⣑⢶⣶⣿⠿⣥⣶⠆⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⡴⢮⣽⣭⣽⠿⢿⠭⣿⣤⣴⡏⢠⡎⠉⠁
⠀⠀⣿⠀⠀⠀⡇⢸⠀⢸⢸⠀⡅⣻⣷⣿⠀⠘⣿⣦⣼⠃⠀⠛⠛⠛⠛⠛⠻⠟⢷⢠⣴⣘⣎⠢⣙⣳⡟⠀⠀⡿⢾⣗⡒⠂
⠀⠀⡇⠀⠀⠀⡇⢸⠀⢸⠈⠀⠁⢻⣿⣿⣤⣶⣋⣿⣟⣶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠣⣽⠉⠈⢀⡸⠋⠀⠀⠀⡇⢸⡇⢰
⠀⠀⠧⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢸⣿⣿⠛⡿⠛⢿⡟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⡶⡼⠻⣿⠀⠀⠀⡇⢸⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠸⢿⣿⠀⠃⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠇⠀⣧⠀⠀⠀⢇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀⠀⠀⠸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇⠀⠀⡏⠀⠀⠀⢈⡗⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣥⣤⣌⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠍
⠀⠀⠀⠀⢴⣶⣶⣾⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣧
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣵⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⡻⠟⠷⣞⣧
⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣬⣭⣤⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣿⣿⣿⣶⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⢉⡿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⡿
⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢠⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣅⡀⠀⢀⡾⠁
⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠸⣧⠀⣰⡟⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡟
⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠃


⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⠞⠁⠉⢓⡴⠟⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⡀⠀⢠⣄⠈⡆
⠀⠀⠀⢸⡁⠀⢀⣴⠏⡱⣆⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣉⡁⠀⢈⣉⠀⡇
⠀⠀⠀⠀⢙⡴⣏⠡⠀⡅⢨⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢉⣉⣉⡉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠃⠀⠘⠋⠀⡇
⠀⠀⠀⣰⠏⠁⠈⠳⣄⠂⣠⠞⠁⠘⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠤⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠃⠀⠘⠟⠀⡇
⠀⠀⠀⠘⢦⡀⠀⠀⣨⢟⡁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣤⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠾⠆⠀⠰⠷⠀⡇
⠀⠀⠀⠀⠀⠙⠳⠞⠁⠀⠙⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⡀⠀⢀⠀⡀⢀⠀⠀⢀
⣿⣯⢽⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⠴⠳⠤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠙⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⡿⠒⢿⣮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⣿⣋⣀⣀⣀⣙⣿⢮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣴⡿⢋⣴⡿⠛⠋⠛⠀⠛⠛⠛⠛⣘⣿⢎⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⢸⣿
⠀⠀⢀⣴⡿⢋⣴⡿⠋⡀⠀⣀⣀⠤⢤⣶⣺⢍⡟⣂⡹⢿⣮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⣿⡆⣡⢤⣤⡤⡆
⠀⠀⠘⢿⣦⡻⣿⣄⡈⣍⠟⢢⣣⡼⢇⣁⣿⠾⠿⠙⢁⣴⡿⢃⣼⡿⠃⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⣷⠧⠀⠀⢀⠸⢻⠐⣋⣉⣭⠉⠁
⠀⠀⠀⠀⠙⢿⣮⡻⢳⣥⠬⠞⠛⠉⠉⠀⠀⠀⢀⣴⡿⢋⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣓⠖⣶⡆⢏⣀⣠⡤⢴⠒⣾⢽⠛⠁⣆
⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣷⡴⣶⣴⣤⣲⢶⣰⡿⢋⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢶⢲⠋⣏⢻⡅⣷⣜⣶⣯⠦⠟⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣷⣄⢀⣴⡿⢋⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣭⠾⠾⢛⠛⠉⠁⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡮⣏⢈⡯⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢄⢻⡴⣲⣢⣝⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣢⣤⣔⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⢡⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠒⠖⢚⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡫⠊⠁⠀⠀⠨⡉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠁⣞⠀⠀⡀⠀⢱⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠢⡀⠀⠀⠘⠓⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣯⣀⣀⣁⣀⣉⡠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠀⠐⡌⠢⡀⠀⠀⠀⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⡀⠀⣀⠀⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⡀⠸⣧⣤⣴⡇⠀⢈⠢⡀⠀⠀⠨⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⣀⠛⠞⢟⡉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⡈⣏⣹⣦⣚⡟⢲⣲⣶⣖⣲⠖⡲⡖⣒⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⡘⠻⠝⠚⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠻⡴⣳⡛⠸⠷⠶⠛⠇⠚⠺⠷⠿⠷⣧⡷⡺
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠓⢒⠒⢲⡖⣲⣋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣀⠉⠉⠉⠻⣿⣭⣽⡏⠉⠹⣯⣭⣵⡩⠞⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠘⠒⠸⠏⠹⢉⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠈⠣⣀⣇⠀⢀⡇⣠⠟⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠈⣿⣁⣚⣿⣈⡉⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⡠⡀⠀⠈⢻⣟⣿⠟⡁⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣿⣿⣭⣏⣻⠷⠧⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠐⠚⠉⠓⠉⠈

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

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠗⢀⡀⠀⠀⢸⣿⣿⢰⣿⣷⡀⣰⣿⣷⠀⠀⡿⠻⡆
⠀⠀⠀⠀⡐⠉⠗⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⢠⣿⣷⡷⠀⠈⣿⣿⠀⠙⢿⣿⣿⡟⠁⠀⠀⡇⠀⡇
⠀⠀⠀⣰⣧⠎⠀⠀⠀⢀⡠⣤⠋⠀⠀⣠⡄⠀⠀⠀⣾⣿⣷⣬⠙⠁⠀⠀⣿⣿⠀⣰⣿⣿⣿⣷⡄⠀⠀⣇⢀⡇
⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⡸⠀⠘⠉⠀⠀⠀⠀⠀⠈⠹⣷⣿⡧⠀⠀⠀⣿⣿⠘⠿⠟⠁⠙⠿⠟⠀⠀⢿⣿⠃
⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⢀⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠿⠒⠒⠀⠣⠝⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢚⠡⠼⢃⠀⡇
⠀⠀⠸⠋⠹⠿⠀⠀⢀⣀⣀⣀⡀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠈⢁⡄⠑⠋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⡉⠉⠂⠘⠃⣠⠖⡄⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠂⠖⢀⢡⣔⢸⠗⢂
⠀⠀⢸⠉⠒⠃⢸⠀⠀⠀⢸⠽⠁⠀⠀⠀⠋⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠸⠌⢓⡐⠟
⠀⢨⢸⠀⠀⠀⢸⠀⢀⠀⢘⠒⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⡿⠀⡐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⣠⡀⠘⢄
⠀⠈⠚⠒⠖⠒⠋⠀⠈⠛⠛⠂⠀⠀⠀⠀⠙⠿⣿⣿⠿⠟⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠻⡀⠈⡄
⠀⡀⠀⠀⡀⢠⠀⠀⠀⠀⠠⢅⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠇⢀⠁⠖
⠀⠻⣦⣬⣁⣠⡗⠀⠈⠙⠖⢯⡀⠐⠚⠀⠀⠀⠀⠀⠀⠢⡄⠀⢶⣆⣶⣆⠔⠁⠀⠀⢀⡀⠉⠋⠁⠀⡠⠊⠸⢠
⠀⢠⣄⣀⡍⠁⠀⠀⠀⠀⠘⠦⠀⣀⣠⠀⠀⠀⠶⠆⢰⡶⠸⠀⠠⢛⣽⣿⣿⠄⠀⠁⢀⣀⣤⣠⣤⠀⠀⠀⠈⣸
⠀⠀⠈⠉⠀⠘⠷⠶⢃⠀⢠⣿⡦⠀⠀⠀⠀⠿⣧⠄⠙⠃⠀⠀⠀⠁⠹⠋⠁⠀⠰⣷⣾⠛⢿⣿⡿⠀⠀⠀⣓⡟
⠀⢀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠑⢄⠀⠀⠀⠀⠀⠀⢀⣤⣾⡶⠀⠀⠀⢠⣤⡄⠠⣼⣿⡷⠿⢿⣇⣤⡀⢸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⣠⠹⣦⡀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁⠀⡆⠀⠙⠛⠃⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠈⠛⠄⢸⠉⠀⡀⢘⡔⠃⡤⢠⡤⠤⠤⡄⠀⠀⢰⣷⠀⠀⠀⢀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡵⣅⢦⡅⠀⠀⠀⠈⠤⣃⡴⠩⡍⣠⡀⢸⡇⠀⠀⡇⠀⡰⢫⣿⣦⠀⠀⠀⣿⠃
⠀⣆⠀⠀⡸⣄⣀⣀⣠⠀⢸⡷⠿⢼⡇⠀⠀⠀⠙⣒⠧⠙⠓⡺⠄⠈⢹⣧⣄⣠⡇⠀⢻⣿⣿⡿⠀⠀⢠⡇
⠀⠀⠉⠁⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠉⠀⠚⠀⠙⠛⠋⠁⠀⠀⠈⠉⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠶⠾⠛⠋⠉⠉⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠛⠛⠉⠉⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⡀⢠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⡀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠉⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⡇⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⣤⢤⡀⣤⠤⢠⡤⣄⢠⡄⣤⡤⠀⢀⡤⡄⢠⣄⢀⡤⣤⢠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡄⣿⢺⡁⣿⣃⢸⣧⡿⢸⡇⢸⡇⠀⠸⣄⣄⡿⢿⡬⡟⢿⢸⣧⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠃⠀⠒⠒⠒⠂⢬⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠔⣠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⡠⠒⠒⠂⠉⠁⠀⠀⣠⣾⣿⡿⠋⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠐⠤⣀⣴⣁⣀⣀⣀⣀⠀⣠⣾⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠒⣩⣾⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠉⠀⠀⠈⠺⣿⡿⠋⡠⠎
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠊
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠑⢄⠀⠀⡠⠊
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠑⢎
⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠐⠋





⣏⠉⣹⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣛⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⡏⣬⡍⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⡏⣭⣥⣿⣧⣭⣍⢹⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣧⣭⡍⣿⡏⣩⣥⣼⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣇⣙⣁⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡴⠟⠛⠛⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠉⠉⠉⠉⠉⠋⠙⠉⠉⠉⠉⠉⢁⣤⣶⠛⠉⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⡀⣀⣀⣀⣀⣀⣀⣾⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠛⠷⢶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⢤⢤⠤⠤⣄⢀⡤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠚⠚⠚⠒⠒⣿⢸⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣄⠀⠀⣿⢸⢐⠶⡶⡶⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠘⠧⣌⠠⠄⣹⠘⠒⠖⠒⠶⢒⣲⣒⠲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠶⠟⠀⠀⣿⠀⠀⠀⢀⡼⠋⣭⡙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣠⣀⣄⣿⠀⠀⠀⠸⣇⠀⣽⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠿⠧⠤⠤⠟⠀⠀⠀⠀⠙⠳⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡿⠿⣿⣿⣿⡿⠿⢿⣛⡇⠀⣰⠞⣛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣏⢺⡇⡷⠀⠀⣿⡇⢸⡇⠀⣻⡅⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣶⣶⣾⣿⣿⣷⣶⣾⣉⡇⠀⠻⣦⣭⣥⠾⠁





⠀⠀⠀⠀⠀⠀⠀⢰⣖⡆⣴⡄⢦⡴⢰⣄⣶⢰⣒⢰⣆⣴⢲⡖⠀⣦⣠⡆⣶⡒⢲⡖⢰⣀⣆⡔⢲⣰⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⠙⠘⠁⠘⠉⠘⠘⠒⠘⠈⠋⠈⠁⠀⠃⠁⠃⠛⠒⠈⠃⠘⠀⠃⠑⠚⠘⠓⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣼⣿⠇


⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⢀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣤⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣝⣛⣛⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠈⠉⣿⣿⣿⣿⣿⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⢤⣤⡀⣀⣷⠀⠀⢾⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⣤⣤⣤⣬⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣄⣬⣉⣟⣛⣛⣋⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠁⠈⣿⣿⣿⣿⣿⡿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⢻⣿⠋⠀⢀⣹⣿⣿⣿⣿⡆⠘⢿⣿⣷⣆⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠿⠛⠛⠛⠛⠋⠀⠀⠙⣿⣿⣿⢿⣏⠙⢧⡀⠉⠻⠎⠁⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⣼⠉⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡶⢿⣿⣶⣿⣿⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⣣⣞⢻⣾⣿⣿⣿⣿⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⡛⠿⢛⣿⣋⣽⣿⣿⣷⠆⠀⠀⠀⠀⠀⢠⣦⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⣽⣿⣄⢋⣽⣿⢟⣶⢿⣿⣿⡧⠀⠀⠀⠀⢸⣍⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡉⣿⣿⣯⢉⣽⣿⣩⣾⢿⣿⡿⠀⠀⠀⠀⠀⠹⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠰⣞⣿⣷⡈⣽⣿⣟⢁⣼⣿⣷⣾⣿⣿⡆⠀⠀⠀⠀⢐⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣄⣼⣿⣿⣯⣿⣯⣴⣿⣿⡇⠀⠀⠀⠀⠈⢹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣦⣤⣀⣶⣦⣆⣹⣿⣧⣾⢿⣷⡿⣿⣷⣿⣿⣿⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⣿⣿⣿⣼⣿⣽⣿⣿⣿⣿⣧⡻⢿⣶⣿⣵⣿⣿⣿⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡗⢿⣷⠞⣻⣿⣿⡟⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠾⠟⢿⣿⣿⣿⠃⠀⣿⣹⣿⣿⣿⣼⣿⣾⣿⣶⣷⣿⣿⣧⣤⣤⣤⣤⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⣼⣿⣿⡿⣾⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⣿⣿⣿⣇⣿⣷⡎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡛⢻⡋⠈⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡷⣾⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣁⣼⣿⣿⣿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⢸⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠛⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢸⣿⣟⣿⣯⣝⣿⣦⣤⣋⣁⣀⠛⣩⣿⣿⣿⣿⣿⣿⣹⣷⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣇⣀⣠⣤⡄⢀⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠓⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣻⣿⢿⣭⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⠛⡁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⡀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢉⣠⣾⣿⣯⣿⣿⠟⠛⡟⢿⠿⢿⡿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠶⢦⣤⣤⣤⣤⣉⠉⠙⠛⠛⠉⢈⣩⣉⣭⣤⣬⣤⣴⣶⣾⣿⣿⣿⣿⠟⠛⠁⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠉⠛⠋⠉⠈⠛⠛⢻⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠉⠉⠋⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡰⠫⠍⡒⠤⣀
⠀⠀⠀⠀⡰⠑⠀⢠⣀⠁⠀⠉⠒⠤⣀
⠀⠀⠀⡰⠁⠀⢠⡏⠻⠿⣶⣤⣀⠀⠀⠉⠒⠤⣀
⠀⠀⡰⠑⠀⢠⣿⡃⠀⠀⠈⠉⢿⣓⡄⠀⠀⠁⠂⠍⡒⠤⣀
⠀⠠⠀⠀⢠⡿⠷⠹⠦⣄⡀⠀⣼⡟⠃⠀⠀⠀⢀⣤⣀⠀⠀⠁⠀⠄
⠰⠀⠀⢀⡻⣏⠀⠀⠀⠈⠐⠂⠚⠃⠀⠀⣀⣄⢻⢿⣿⡇⠀⠀⠀⠁⠂⠅⡢⢄⡀
⠡⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⡿⠛⠁⢸⣿⡇⠀⠀⠀⠀⠀⣄⣀⠁⠀⠕⡢⢄⡀
⠀⠀⠁⠒⠤⡀⠀⠀⠀⠀⠀⢀⣴⣶⡍⠿⢳⣦⣀⣨⣿⡇⠀⠀⠀⠀⣼⡿⠏⠀⠀⣤⣀⠁⠊⠕⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⢻⣿⡇⠀⠀⠀⢸⣾⠏⠀⠀⠰⣿⡿⢿⣶⣤⡀⠁⠊⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠤⣄⠉⠀⠀⠐⣿⡟⠀⠀⠈⠙⣿⣷⡀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢐⣄⡟⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠂⠀⠀⠈⠀⠀⢀⠂⣌⡀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠳⢗⣦⣠⣶⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠛⠲⠤⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠣⢤⣄⠀⣀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡿⢏⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⠑⢚⣀⣉⣀⣬⣸⠥⠆⠀⠀⠀⠀⠸⡆⠘⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣧⠴⠀⠺⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠈⠈⡏⠀⠀⣼⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⡝⢲⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢒⠀⠠⠀⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡔⠈⢉⠧⡀⠀⠀⠀⠀⠀⠤⢄⢀⠕⠂⢄
⠀⠀⠀⠀⠀⣀⠴⠁⠁⠠⢀⣫⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣓⠀⠊⠀⠀⠈⠢⡀⠀⠀⠀⣰⡽⠁⠀⢀⠄⠳⡄
⠀⠀⠀⣠⢞⠁⠀⠀⢠⠀⢄⢽⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠰⠁⡆⠀⣰⠁⠀⠀⠉⠢⡀
⠀⠀⢰⡇⠀⠉⢆⠀⠀⠢⡈⢺⣇⣁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠸⣄⢋⠂⡗⠠⠇⢳⠀⠀⠀⠀⠘⢦
⠀⠀⠘⡇⠀⠀⠈⡆⠀⠀⠈⠢⢹⣇⠸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠱⡀⠀⢸⠀⠀⠀⠀⣿⠉⠰⢠⠀⠸⡌⣇⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⣇⠠⠶⠂⣐⠀⠀⠀⠀⠘⡟⠀⡎⢢⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠰⣣⠀⡛⠀⠀⠀⠀⣏⢷⣶⠀⢣⣀⠱⠘⢆⣴⢾⠇⠀⡀⡏
⠀⠀⠀⢹⠀⢀⠤⣺⣇⠀⠀⠀⣀⣃⠤⢃⣠⡳⡤⠄⠀⠄⠀⠀⢰⠁⠀⠀⠀⣏⡏⣰⠃⠀⠀⠀⢸⣧⣤⠹⡇⠄⠈⢣⠁⣠⠗⠤⠔⠋⡸
⠀⠀⣀⣘⣇⣁⣰⣊⣟⣙⣉⣁⡘⣅⠀⢰⣥⡾⠱⠙⣄⠁⠀⠀⠞⢂⠀⠀⢰⢿⠱⠁⠀⠀⠀⠀⣸⣄⣀⣸⢩⣷⣶⢩⡿⡃⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠊⡉⠋⢅⢣⠀⢸⠃⠉⢩⠁⢳⡈⠆⠀⣼⠋⠀⠀⠀⠀⠀⠀⡿⠈⡵⢇⡀⠀⠀⢹⡏⢹⡖⢠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠑⢍⠉⣇⣲⣌⡻⡜⣅⢀⡴⠃⠀⠀⠀⠀⠀⠀⢰⠃⠸⠁⠨⡅⠀⠀⣸⣄⠈⠇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠈⠉⠺⡄⠉⠉⢹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⢀⡇⠀⠘⢹⠈⠉⠳⠀⣟
⠀⠀⠥⠤⠤⠤⠤⠭⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠶⠶⠒⠒⠒⠒⠺⣁⠐⣲⠀⠀⠀⠀⠀⠀⠀⠸⡆⣇⠰⠺⣅⠀⡆⣾⠀⠀⠀⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⣴⠁⠀⠧⢧⣤⣀⣀⡇⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⣧⣰⣿⢠⣇⣀⠀⠀⠀⢠⡞⢱⡜⣧⡉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠖⢓⡞⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢘⡃⠀⠀⠜⠉⠀⠀⠀⠀⢉⡿⡽⣮⢯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠀⠻⠶⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠃⠘⡎⣇⠀⠚⠉⠀⠀⠀⠀⠀⠠⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣓⣊⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣘⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢸⣿⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠧⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠸⢻⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⡷⠒⠲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⣸⠀⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⢸⠀⢠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⡀⠘⠆⢀⢔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⠀⠀⢸⠘⢻⠛⢸⢰⢋⣌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡰⢣⡈⠊⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠁⠀⠀⠀⠀⠀⢸⣀⠀⢀⣸⠘⠦⠥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⢃⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠊⠀⠘⠲⡄⠀⠀⠀⠀⠀⠀⡸⠀⢞⠁⠀⢣⡀⠀⠀⠀⠀⡀⠘⠀⢰⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢸⡀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢀⠞⠀⠀⠈⠣⠀⠀⠑⠄⠀⠀⣌⠀⠀⣀⣤⠵⣤⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠟⠀⠴⠾⠋⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⡆⠀⠐⣦⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⢻⠏⠀⠙⢯⠀⠀⠻⠀⠀⠀⠀⠀⠐⣦⡤⠄⣀⠇⠀⠀⠀⠀⠀⠐⠰⠀⠐⠰⠒⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢠⡄⢶⢼⠀⠀⠀⡄⠀⠀⠀⠀⣰⠀⠀⠀⠀⣶⠀⠀⠀⢀⡤⢶⠰⢖⢀⢀⣐⢶⢐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢰⣦⣶⢸⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⡀⣀⡀⠿⡀⠀⠀⣿⢸⡁⠀⠈⠀⠀⠀⠠⡀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠖⢿⣀⣀⣀⣸⠗⠲⠚⠁⠀⠀⠀⢰⠃⠉⠗⠘⡏⠈⠇⠀⠀⠈⠒⠦⠴⠉⠉⠉⠙⠠⠭⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣷⣶⣾⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠟⠛⠉⠉⠉⠙⠛⠿⢷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠛⠛⠉⠉⠉⠛⠻⢿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣿⣟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣶⣦⣤⣤⣶⠞⠛⠋⠉
⠀⠀⠀⣠⣶⣾⣿⣿⣽⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠋⠉⠁⠈⠉⠛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠖
⠀⣠⣾⠿⣥⣄⣠⣽⣿⡇⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠽⠟⠳⠶⣾⣉⡁
⠠⣿⠋⢀⠟⠿⠷⠾⠟⣽⢿⣷⠆⢀⣠⣤⠀⠀⠀⠀⠀⠉⠉⠋⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣖⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⣤⣤
⠀⠻⠆⠁⠀⠀⣴⠀⠜⢱⣿⠃⢰⡿⡿⠋⢀⡴⣶⡟⢀⣤⣶⣄⢠⣤⣀⠀⡶⠆⠀⠀⢉⣽⠟⠛⠛⠻⠿⠿⠿⢿⣿⣶⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⣶⡀⠀⠙⠓⠚⠻⠷⠐⢿⣆⢿⠶⣿⡅⠘⣻⢿⡿⢋⣾⢃⡾⢷⡖⣾⢷⡟⢁⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠿⠷⢶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⠓⠺⢧⣾⠗⠚⢿⣇⣞⣡⡏⣿⢸⢋⡗⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿
⠱⡞⠀⠀⠀⠛⠉⢻⡻⢶⠄⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠉⠈⠁⠀⠁⠘⠁⠦⠓
⣤⣄⣠⣦⣀⣩⣯⣿⣧⣤⡄⣼⣦⣦⣤⡋⠀⢱⣷⣶⣶⣶⣶⡄⣶⣦
⠁⠀⠉⠙⠛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⣌⣀⣀⣀⣀⠐⠒⠲⠂⠠⢤⠤⠄⢀⡀⠀⡀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣾⣿⣿⡄
⠁⠀⠀⠀⠀⣿⣷⣽⣿⣤⣧⣼⣿⣿⣯⣻⣿⣿⣿⣟⣛⣻⣿⣿⠏⢻⣿⠿⢿⣿⣿⣿⣿⣿⡶⣶⢶⣶⣶⣶⣶⣤⣤⣭⣤⣁⣀⣙⣫⣤⣄⡀⠀⢹⣿⣿⠟⣾⠿
⠂⠀⠀⠀⠀⢛⣟⢻⣿⢏⣟⠻⣿⣿⣿⠙⠟⠻⡿⢻⡿⢿⣿⣶⠶⣦⣴⣿⣤⣽⣭⣭⣤⣼⣦⣯⣬⣭⣥⣯⣤⣼⣿⣤⣩⣭⠙⠋⠹⣿⣋⣹⡿⡋⠀⠀⠐⠻⠿
⢀⡄⠀⢐⣢⣻⠿⣿⣿⢿⢿⡛⠿⠿⠿⠿⢿⡏⠉⠈⠉⠻⣿⠓⠛⢩⣗⢩⡉⢾⠉⠉⣹⣿⣅⣈⣙⣏⣩⣉⣛⣆⣿⣬⣭⣯⠀⠐⣗⣿⣻⣹⣋⣿⡆⠀⠀⠀⠛
⣾⣁⣠⣿⣷⣧⣶⣶⣿⣶⣶⣷⣶⣶⣶⣶⣾⡇⠦⠀⣌⣠⣿⢿⠿⠿⣿⢿⣿⣿⡿⢿⣿⣿⣛⣏⣉⣋⣿⣭⣹⣿⣿⣽⣿⣿⣷⣶⣿⣶⣾⣿⣿⣿⣿⣢⡄⣰⣯
⠛⠛⠛⠛⠛⠣⣟⣿⣿⣿⣿⣿⣿⣿⣯⡹⠟⠃⠀⠀⠉⠁⣻⣆⣀⣀⣀⣨⣿⣇⣤⣤⣧⣿⣿⣿⣽⣭⣬⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣍⡽⠋⠛⠛⠛⠃⣿⢻
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⠐⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⡿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣶⣤⣽⣾
⣿⣿⣶⣶⣶⣶⣦⡄⠛⠃⠀⠀⠈⠉⢩⣥⣥⣶⣤⣩⣭⣯⠯⠶⣿⡟⠛⠐⠃⠈⠀⠐⠉⠛⠛⠛⠃⠛⠛⠛⠋⢋⣻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠒⠒⠘⣃⣉⣈⣉⣉⣀⣤⣤⣿⣧⣠⣤⣴⣴⣶⣧⣶⣾⣾⡦⣵⣥⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣏⢚⣉⣉⣁⣈⢹⡅⠈⠉⠉⠉⢉⣉⡇⣉⣉⣉⡈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣅⣵⣼⡇⠈⢈⣛⣛⣯⣭⣭⣿⣷⣿⣿⡿⣿⡿⠻⠿⠿⠟⠛⣛⣛⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⣀⡀⠀⣿⣿⣿⣿⣿⠗⠛⢻⡇⠿⢿⠟⣿⣿⢍⣿⣿⣿⠁⠉⠹⠟⢛⡐⢾⣿⠻⠿⡿⡿⣿⣿⣿⣷⣤⡶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⣀⠠⠤⠻⠛⢛⣛⣉⣥⣤⣤⣾⠐⠚⢒⣉⣉⣭⣤⣤⣶⣶⣾⣿⣿⣿⡇⢸⣷⣤⣾⣿⣧⣿⣿⣿⣿⣽⡿⠿⠿⣿⣿⣯⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢛⢺⣿⣿⣿⣿⣿⣿⣿⢯⣽⣿⣿⣿⣿⣷⠸⡿⠋⠩⠟⠋⢉⣉⣩⣥⣴⣶⣾⣿⣿⣿⣟⣿⣿⣿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣛⡡⢄⠊⠀⢿⣛⣿⣿⣿⣿⣿⣧⣈⢸⣿⣿⣿⢻⠿⠟⣷⣻⣿⠿⠿⠛⢛⣉⣠⣤⣶⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⠄⡀⠀⣀⡄⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣿⠿⠿⠚⢋⣉⣩⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⢠⡴⠖⢋⡁⣿⣿⣿⡿⠿⠟⢛⣉⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⣿⣿⣧⣦⣤⣤⣴⣬⢸⡷⡾⠟⠇⣩⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⢿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄
⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠛⠋⠉⠙⠛⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣧⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢛⣛⣛⡛⠋⠉⠉⠁⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣀⣠⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠉⠉⢹⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣤⣤⣬⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣿⣿⠻⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⣛⢸⢘⡇⣟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠈⠁⠉⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢠⠌⠀⢀⠀⠀⠀⢀⠴⣀⢤⢀⠀⠀⠀⠀⠀⠀⠘⠀⢄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠶⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠉⠀⠀⠀⡀⠃⠀⠰⢶⠀⢰⠆⠀⠀⠀⠰⠚⠂
⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢀
⠀⠈⠁⣶⠀⠀⠀⠀⠀⠈⠐⠯⠅⠀⣠⠏⠀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂
⠀⢠⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠉⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠤⣤⣤⣤⠤⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⣾⠉⠳⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣿⠤⠴⠃⣧⢤⡀⠀⣀⣀⠀⣀⣀⢠⣀⣀⡀⠀⢀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⡐⠲⡗⢂⠀⣀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⣿⠀⠀⠀⡇⠀⡇⣞⠁⣸⣀⣿⠉⢸⣿⡏⣷⢸⢉⣇⡀⡏⢀⡸⡗⠚⡁⣇⢀⣇⡀⡇⢾⢸⡉⣀⣴⢉⣏⠀⡇
⠀⠀⠀⠉⠀⠀⠀⠁⠀⠁⠈⠉⠁⠁⠉⠀⠈⠈⠁⠉⠈⠉⠈⠁⠉⠉⠀⠉⠉⠁⠈⠉⠀⠀⠁⠈⠀⠉⠁⠈⠉⠈⠀⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠿⣿⠃⢠⣴⣿⣿⣤⠀⠈⠂⡀⠀⠀⡶⠏⣦⡀⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⠛⠀⠀⠀⠀⠁⠈⢑⡶⡎⠀⠀⡀
⠀⠀⠀⠀⡀⠰⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠃⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⣰⣧⠄⠈⡹⠟⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⡆⠀⠀⠀⠀⠀⢸⣿⢉⡉⢻⣷
⠀⠀⠀⠀⠀⠈⠁⠚⠿⠟⠂⠀⠀⠀⠀⠀⠘⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠛⠻⠋⠁⠀⠀⠀⠀⠀⠸⠿⠤⠥⠼⠿


⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡴⢯⣽⢟⣳⠆⠀⠀⠀⠀⠀⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡷
⠀⠀⠀⠀⠀⠻⣼⠿⣹⠞⠁⠀⠀⠀⠀⠀⠀⡿⣹⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣾⣣
⠀⠀⠀⠀⠀⠀⣠⠿⠿⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⣴⣿⣾⡻⠎⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠙⠋


⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠃⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠂⠀⠀⠀⠀⠀⠀⢀⡴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡿⠃⠀⠀⠀⠀⠀⢀⣴⣏⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢶⡶⠀⠀⠀⠀⠀⠀⠐⢿⡷⠋⠀⠀⠀⠀⠀⠀⠀⢐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⣶⣶⠎⠁⠀⠀⠀⠀⠀⠀⢀⡄⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤
⠀⠀⠀⠀⠀⠰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣤⣈⣉⣉⣉⣉⣉⣉⣉⣏⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠻⡿⣿⢻⣿⣛⠿⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣛⣛⣿⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣉⡭⠷⡄⠀⠀⠀⠀⢠⡏⠗⡦⣄⣀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣉⡡⠴⢚⡉⠀⠀⠀⢹⠀⠀⠀⠀⡼⠛⠲⢤⣈⠈⠟⢲⢤⣀⡀⠈⠙⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⡤⠖⢋⡥⠖⣚⣨⠵⠚⠛⣆⢸⠀⠀⠀⢠⠇⢀⠀⠀⠈⠙⠓⠦⣌⡁⠿⢳⠦⣄⣀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⡞⢀⡜⠁⢀⣠⠤⠒⠋⠁⠀⠀⠀⠀⣿⢸⠀⠀⠀⢾⡀⠈⠁⠲⠄⣀⠀⠀⠀⠉⠛⠲⢤⣁⠛⠹⠖⢾
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠉⠓⠦⢄⣀⠈⠁⠲⠄⣀⠀⠀⠀⠈⠉⠓⠦⣼
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⡇⠀⠀⣠⠖⢋⣉⣉⠙⠲⠄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣨⠀⡀⢠⠞⣡⠚⣉⣤⣍⠙⠂⠀⢺⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⡏⡼⠁⡴⠁⡠⠄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡋
⠀⠀⠀⠀⠀⠀⠀⣧⣽⠘⡇⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⣚⣩⠷⠒⣿⡉⣿
⠀⠀⠀⠀⠀⠀⠀⡿⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣀⣠⠤⠖⠚⣉⣡⠤⠖⠋⠁⠀⢀⣀⣻⡧⠿⢤
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⢀⣠⠴⢺⡇⢸⢸⠀⠀⣴⣋⣁⣠⣤⣖⣋⣭⡤⠤⠴⠖⠚⠋⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⡇⠀⢀⣠⢴⢚⣭⠰⣼⠀⡇⢸⢸⠀⠀⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⢚⣹
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⣿⣾⢉⣿⣯⡇⢹⢸⡇⢸⢸⠀⠀⡗⠶⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢹
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⣿⣿⠉⠸⠇⢃⣨⠼⠃⢸⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⢺
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⡏⠋⣀⠴⠚⠉⠀⠀⠀⣼⢸⠀⠀⡷⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⢾
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⠛⠉⠁⠀⠀⠀⠀⣠⠞⠁⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡃⡇⠀⠀⠀⢀⣠⠤⠖⠋⠀⢀⡴⠋⠀⠀⣟⠒⠒⠚⠉⠉⠀⠀⠀⠀⣀⣀⣠⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠙⠒⠚⠋⠉⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠙⠶⠶⠒⠒⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠾⣇⡀⣀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡴⠊⠉⠉⠙⠓⠒⠂⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠒⢤⡀
⡇⠀⠀⠀⠤⢄⠄⠒⠄⡠⠄⡄⠤⢄⡠⠤⢤⠀⠀⢄⠀⠀⠤⡀⣀⣀⠀⢀⡀⡀⢀⠀⠀⢱
⡇⠀⠀⡇⠀⢏⠀⡁⠆⡁⠸⡅⠀⠀⡭⠀⢇⠁⠀⠊⠀⠀⠰⣁⢐⠂⢄⢈⣼⡀⠆⡁⠀⢸
⡇⠀⠀⠈⠐⠊⠑⠋⠊⠙⠒⠂⠒⠈⠑⠒⠂⠀⠊⠀⠀⠈⠐⠉⠀⠈⠉⠉⠈⠁⠉⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⣶⠀⠉⠟⠃⡆⠀⠀⠀⠄⡄⠀⠠⡄⢠⡀⡀⠀⡄⠀⡀⠀⢄⢀⡀⢀⠀⠀⠀⠀⢸
⡇⠀⠀⣧⠀⠀⡀⠀⡇⠀⠀⠀⠁⠁⠀⠈⠁⠀⠁⠈⠀⠀⠈⠓⠀⠃⠘⠃⠉⠃⠀⠀⠀⠸⣄⡀
⡇⠀⠀⠋⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⢀⠒⠀⠠⠀⢄⠄⢄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⡀⠀⠉⠒⠤⣄⡀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⣅⣈⠁⣀⡁⠅⢸⠸⠈⣄⠑⠁⡔⣔⣢⣒⡄⠀⠈⠚⠧⣨⠒⠂⠀⠀⠀⠈⠑
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠓⠀⠐⠓⠀⠚⠀⠂⠀⠈⠀⠉⠉⠁⠉⠁⡀⠀⠀⠀⠀⠉⠚⠌⠘⠀⠀⢀
⠀⠓⠦⠤⠤⠤⠤⠤⠤⠤⠤⡄⠠⠤⢤⠤⠤⠤⠤⢠⠀⡤⠤⡤⠀⠤⠤⠤⠤⠄⠠⠀⠊⢐⡐⠠⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣀⠈⠉⠙⠃⠢⡘⡐⠐⢂⡄⠀⠀⠔⠢⡀⠀⠀⠀⠀⠀⠀⠓⠐⡟⢠⠄⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⡀⠈⠉⠁⠀⠀⡄⠘⢀⠴⢈⡵⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣄⡀⠈⠉⠀⢄⣛⠀⡀⢠⢀⠂⠠⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⡀⠀⠙⠒⠂⢀⠁⠤⠈⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠈⠉⠀⠀⢠⠎

⠀⠀⠀⠀⠀⠀⠰⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣦⡀⣄⣠⠀⣴⡀⢠⣦⠀⣤⣠⡄⢠⣦⠀⡴⠦⢠⣤⠄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠋⠐⠏⠹⠰⠛⠓⠸⠻⠘⠛⠟⠇⠚⠛⠂⠳⠖⠀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣼⠀⠀⢸⡇⠀⢀⣟⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠘⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣤⣤⣤⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣠⡶⠀⣠⠞⠁⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⣤⠆⢀⡴⠟⠁⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠋⠠⠞⠁⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⣿⠀⢸⠁⠘⠋⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠋⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⢀⣴⠆⢸⡇⠀⠀⠈⢀⣴⠄⣿⠀⢸⠗⠓⠒⠒⠒⠒⢻⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢀⣴⠟⠁⠀⢸⡇⠀⢀⣴⠟⠁⠀⣿⠀⢸⠄⠋⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠿⠶⠿⠷⠶⠶⠶⠾⠷⠶⠿⠷⠶⠶⠶⠿⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⢰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢹⡅⠈⠁⠀⠀⠰⡄⠀⠀⠀⠀⠀⡄⠀⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠨⠋⢸⣷⠇⠀⠀⠀⠀⠘⠀⠀⢠⠀⠰⠀⠀⠈⢹⣿⣿⡿⢻⣷⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠦⠘⠏⢁⣈⢻⢟⡂⠻⣿⣿⠉⣿⣿⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⢦⠘⠀⠀⢸⠆⠛⠖⠰⠄⠀⠀⣿⡥⣤⡍⡀⠀⠘⣟⣁⣘⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠄⠀⣀⡀⠀⠀⠐⠀⢠⣴⣶⡄⠀⠀⢀⣟⣻⡻⡤⣅⠸⠆⣿⣛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⠠⠟⣻⣿⡷⠈⢡⡞⠁⠈⢷⠀⡀⠸⠹⣧⢿⡃⣶⢠⡄⣀⠀⢀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⠀⠀⠀⠀⠠⠄⠀⠀⠘⠁⠁⠀⠀⠁⠀⠀⠀⡘⠉⠀⠀⣼⡀⠁⠀⠀⠉⠀⠀⠃⠸⠘⠛⠻⠛⣏⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢆⡀⠀⠀⠃⠀⠀⠈⢀⢁⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠚⠘⠰⠀⢰⠀⠀⠀⡏⠃⠀⠀⠀⠀⠀⠀⠀⠰⠖⠈⠀⠉⠁⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠀⠇⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠁⠢⠄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠦⠀⠀⠀⠄⠄⠀⠀⢰⠤⠀⠀⠀⠀⠀⣀⣀⢀⡀
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⢀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠞⠛⠉⠁⠀⠀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⣀⣠⣼⣇
⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠁⠀⠀⣀⣠⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⢻⡄
⠀⠀⠀⣴⠟⠋⠉⠀⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢻⣄⣤⡴⠖⠛⠉⠁⠀⠀⠀⠀⢀⣀⣤⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠸⣧⡤⠶⠚⠋⠉⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡴⠚⢛⣷⠞⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⣾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣿⠀⠀⠀⢳⣄⠀⠹⣆⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣀⣿⠀⠀⠀⠀⠉⠛⠛⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠋



⠀⡁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠖⠶⠲⠖⠲⠖⠶⠲⠖⠶⠒⠶⠲⠖⠶⠲⠖⠲⠖⠶⠲⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠤⠥⠤⠤⠬⠤⠥⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠲⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⣢⢴⠀⣦⡆⠐⢰⠀⡦⠐⢐⢀⡄⢴⠰⣴⠀⠂⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣧⣀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡗⡀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠛⠛⠛⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠛⠛⠛⠲⢶⣤⣉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡙⠷⣄
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠹⣦
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠒⠒⠒⠒⠂⠀⢀⡗
⠀⠀⠀⠀⣿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠸⣧⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣀⣤⡴⢦⣤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣠⡞⠉⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢰⡟⠀⠀⠰⣄⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⣄⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠁⠀⠀⠀⠀⠀⣠⣞⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠙⠳⣦⣀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣴⠶⠋⠁
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⡏⠙⠳⠶⢦⣤⣤⣤⣤⣤⠶⠞⠛⠁⢿⡀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠴⣤⡀
⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⢸⡇⢀⣤⠶⢻⡏⠁⠀⠈⣿⠗⢶⣄⡀⢸⡇⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢸⡷⠋⠁⠀⠀⡿⠛⠛⠛⣿⠀⠀⠈⠻⢾⠇⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⢀⣼⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢷⡀
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠸⣇⠀⣀⣀⣼⣇⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣸⠇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢿⠀⠈⠉⢹⡏⠉⠀⣤⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠲⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣶⣶⣶⣶⣶⣶⣻⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣇⣀⣀⣀⣀⣙⣳⣶⣶⣶⣦⣦⣤⣤⣴⣶⣶⣶⣶⣾⣋
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣉⣭⣝⠛⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠛⠉⠁⠀⠀⣾⠏⠛⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⣀⡀⠀⠀⣼⠏⠀⠀⠀⠀⠈⢿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠙⠻⠷⣾⣿⣀⠀⠀⠀⠀⠀⣼⡏⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣴⠾⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⣰⡟⠀⠀⣄⠀⠀⢀⡄⠀⠀⣠⡀⠀⠀⣄⠀⠀⢀⡀⠀⠀⣠⠀⠀⢀⣄⠀⠀⢠⡀⠀⠀⣄⠀⠀⢻⡆
⠀⠀⠘⢷⣤⣴⠿⣦⣤⡾⢿⣦⣴⡿⣷⣤⣾⠿⣦⣤⡾⢷⣤⣴⠿⣷⣤⣾⢿⣦⣴⡿⢷⣤⣴⠿⣦⣤⡾⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⣶⠶⠶⣦⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠛⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾⣿⠀⠀⠀⣿⡇
⠀⠀⢀⣀⣸⣿⣀⣀⣿⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣿⣇⣀⡀
⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣀⣀⣀⣀⡐⠂
⠀⠀⠀⠀⡠⣤⡤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣬⣈⠬⠄⠁⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠉⠉⠉⠉⠈⡇
⠀⠀⠀⠀⡇⣿⡇⠀⣠⣄⡋⠀⢂⠀⠀⠀⠀⠀⠀⠀⢰⣀⣂⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⢨⢐⢒⢒⢒⢒⢊⠠⠀⠀⠀⠀⢀⣈⣀⡠⠀⠀⠀⣠⠀⠀⠇
⠀⠀⠀⠀⡇⣿⣿⡈⠷⠊⠑⠄⠀⠣⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠂⠐⠲⢰⡆⠀⠀⠀⠀⢸⠨⢎⡨⢌⡨⢌⠀⠀⠀⠀⠀⡆⠀⢾⣵⠔⣁⣈⡀⠇
⠀⠀⠀⠀⡇⣿⣿⡇⡄⢑⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⢸⢨⣣⢠⡣⢘⡣⢐⠀⠀⠀⢀⣥⣤⣤⣶⣾⣿⣿⣶⣧⣤⡀
⠀⠀⠀⠀⡇⣿⣿⠇⠃⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐⠆⣂⠆⢆⡒⢸⡇⠀⠀⠀⠀⢸⠐⡱⠔⡁⠄⠡⠈⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠤⠒⡠⡃⠢⠔⢸⠇⠀⠀⠀⠀⠘⢴⢲⣶⠒⠒⡦⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠊⡒⠉⠒⠉⠑⡀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠭⠤⠂⠀⠀⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣷
⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⢁⣀⣸⣀⡀
⠀⠀⠀⠀⠀⣾⣒⣛⠃⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠓⠠⣤⠄⠃
⠀⠀⠀⠀⢨⣝⠩⣫⢡⡢⢙⣥⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣄⣰⣖⣲⢰⡦⣑⡀⠀⠀⠀⠀⠀⠀⠠⡏⠉⠉⡹⠋⣹⡂
⠀⠀⠀⠀⠀⣆⣀⣀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠄⠀⢽⢹⣿⡆⠉⠀⣯⠀⠠⠀⠀⠀⠁⠀⢀⣠⡀⡠⢊⣼⡶⠀⠀⠀⠀⠀⠀⣇⠠⠊⡠⠊⢸⡁
⠀⠀⠀⠀⠀⠥⠤⠤⠤⠥⠤⠄⡠⣪⣾⠗⢄⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡹⢊⣴⣿⠋⠀⠀⠠⠀⠀⠀⠀⡇⡠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡴⠀⡠⣪⣾⣿⠁⠀⡠⠃⠀⠀⠀⠀⢸⣿⠿⠇⠀⡇⠀⠀⠀⠀⠀⠖⠖⣪⣴⡿⣫⠇⠀⢀⠔⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠰⢀⣀⣀⣁⣀⣘⠿⡻⠁⡠⠊⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠐⠀⠛⢌⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠇⠀⢀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠃⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠁⠠⠈⡊⠀⠀⠈⠓⠂
⠀⠀⠀⠀⠀⣉⣉⡀⠂⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⡠⠶⠤⡀⡀⠀⠀⠉⠉⠙⠀⠀⠀⠌⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢴⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢀
⠀⠀⠀⠀⣦⣀⢀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠂⠀⠀⠣⡀⠠⠑⠀⠀⠐⠣⠀⠀⠀⠐⠀⠂⠀⠈
⠀⠀⠒⠀⠀⠀⠊⠉⠹⠀⠀⠀⠘⠄⣀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⠀⠀⠀⠉⠀⠅⠀⠀⠀⠀⠤⠀⠆
⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡠⠀⠠⡀⠀⠀⡠⠠⢀⠀⠀⠀⠀⠀⠀⡑⠉⠀⠀⠀⡜⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢠⢁⡀
⠀⠀⡀⠀⠀⠈⡢⠊⠀⠀⠀⡀⠀⠀⠀⠰⡄⣀⠀⣰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠠⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠈⢂⡠⠊⠀⠀⠀⣠⠊⠀⠀⠀⠂⠀⠀⠘⠁⠀⠀⠀⠀⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢢⣀⢀⡀⢠⠇
⠀⠀⡠⠊⠀⠃⠠⡢⠚⠉⠢⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠁⠁⠀⠐⠆
⠀⠀⠀⠀⠀⡠⠚⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠐
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢲⠀⠀⡆⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠁⠀⠀⠀⢀⡌⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⣐⢫⡕⢀⠀⠀⠀⠀⠀⠐⠂⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢶⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠂⠀⠀⠀⠀⠈⠈⠂⠀⠀⠀⠘⢭⡅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡀⠋⠰⠉⠇⣰⠀⠀⠀⠈⠀⠁
⠀⠀⠀⣤⡀⢀⢀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡉⠈⠛⠰⠃⠀⠀⣂⠈⠉⡁⡠
⠀⠀⢠⠀⠉⠹⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠚⠃⠁⠁⠀⠄
⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⠐⡢⠒⠠⠀⠀⠀⡀⣀⢀⠀⠀⡀⠀⠀⠀⢀⣀⢀⠀⠈⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠄⠵⠁⠔⠀⠀⠀⠉⠊⠘⠀⠁⠁⠀⠀⠉⠋⠉⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠰⠀⠆⠆⠠⠰⠀⠂⠆⠰⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠵⠞⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⡷⣿⡷⣿⣿⣿⣹⡭⣯⣿⣻⣽⣿⣿⣋⢋⣉⣿⣿⣿⡇⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠉⠉⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⡿⣿⣿⢿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢛⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣠⣾⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠙⠽⣹⣿⣿⣿⣿⣉⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠦⡀⢀⣀⣤⣤⣴⣶⣿⣿⣷⠟⠁⠀⣠⣿⣿⣿⣿⣿⣿⠏⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣾⣿⣿⣿⣿⣿⣿⠏⠀⠁⠀⣄⣀⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄⣑⣾⣾⣿⡿⠋⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡂⡀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⠀⣀⣀⡖⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢖⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⢀⣀⣠⣤⣶⣿⡿⣟⢏⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡦⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠴⠶⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡙⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡴⢂⡀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⣿⣿⣿⢙⣛⢛⢻⢛⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣀⠀⢀⡀⠀⠴⠄⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣭⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠫⠍⠛⠛⠽⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⣤⣤⣶⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⢉⣀⣬⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣭⣵⣶⠿⠛⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⣁⣠⣤⣶⣿⣿⡿⠟⢛⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣛⣫⣭⣶⠾⠟⠛⠉⠁⠀⢀⣤⣤⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⡉⣀⣴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆⠀⠀⠀⠀⣿⣿⣿⡏⣶⠿⠋⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⢿⠿⢿⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⡄⣀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣷⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣼⠀⠈⠉⠉⠀⠉⠉⠀⠉⠉⠀⠉⠉⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠇⣿⣷⣶⣾⣿⣶⣶⣿⣶⣶⣿⣷⣶⣿⣿⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠟⠉⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠃
⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢷⡟⢻⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣬⡛⠋⠛⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠶⠮⢷⢶⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠉⠀⢀⣽⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣼⠇
⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢠⣾⠃⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⢀⣼⠋
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⡿⠁⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣶⡾⠁
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣟⠁⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⠙⢳⣶⣶⣶⣶⣶⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠉⠳⢀⡴⠋⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⣀⠀⠀⢀⣀⠈⢳
⠀⠀⠀⢠⡞⠁⠀⠀⢀⡴⠻⣤⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣭⣭⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⠀⠀⠘⠛⠀⢸
⠀⠀⠀⠀⠙⠦⢀⡴⢋⠀⢛⠈⠻⣦⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡿⠀⠀⠸⡿⠀⢸
⠀⠀⠀⠀⢀⡴⠋⠳⣌⠁⢉⠀⠋⣠⠟⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠒⠒⠒⠒⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣦⠀⠀⢠⣦⠀⢸
⠀⠀⠀⠠⣏⠀⠀⠀⠈⠳⣌⣠⠞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠚⠛⠛⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⣉⠀⠀⢈⣉⠀⢸
⠀⠀⠀⠀⠙⢳⣄⠀⠀⣠⠞⣥⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠟⠀⠀⠘⠟⠀⣸
⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⠀⠀⠙⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠤⢍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣤⡴⠶⣧⠀⠀⠀⠀⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠠⣌⣙⡛⠲⢦⠀⠀⠦⣤⢶⡾⢋⠙⠳⠤⠀⢂⠀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⡄⢿⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⠀⢸⡏⣷⠚⠁⠀⠀⠉⠀⢤⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⠀⠀⠀⠀⠐⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠉⣿⠁⢯⡀⠀⠀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠟⠀⠀⠀⠀⠀⢀⡵⡋⠤⢤⣤⣤⡀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⡟⠀⠀⣤⡀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢤⣤⠶⢋⠆⠀⠄⠈⠋⠉⠄⠀⡄⠀⢀⣾⢁⠀⠠⠶⠟⠁⠀⠀⡠⠈⠃⢀⠆⠠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠘⠲⠟⠱⠇⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡾⠋⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣶⡂⠀⠀⠀⢈⡓⡀⠀⠠⠄⠠⠀⠀⠄⣈⣳⣥⡄⢠⣴⡎⠻⣄⡀⠀⠀⠀⠀⠐⢀⡠⠁
⠀⠀⠀⠀⠁⠀⠂⠀⠀⣸⡇⠀⠀⠀⠀⠀⢰⣁⡠⠘⠛⠸⣟⠲⣦⣤⣤⠆⣹⣇⠀⢠⠀⠀⠀⠀⠀⡿⠛⠙⠏⠉⠀⢰⡞⠛⠦⠀⢧⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞⠀⠀⠀⠀⠀⠀⢸⡟⠇⠀⠀⠀⠹⣇⣠⣽⠃⠀⠀⠙⢦⠀⣿⣿⣤⣀⢠⣆⡀⠀⡀⣐⣤⣟⣧⠉⠒
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡈⢢⣤⣴⡟⠻⠟⠀⠀⠀⠀⡈⢿⡿⠛⠛⣛⣺⠿⠿⠿⣟⠁⠁⠘⡆⠑⠤⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠉⠉⠉⠙⠉⠀⠀⠀⠄⠐⠂⠁⠀⠘⢧⣤⣥⣴⣾⣾⣿⣿⣿⠃⣀⠀⠸⣄⡴⠋⠀⠀⠤
⠀⠠⠄⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠢⠀⣀⣠⠐⠀⠀⠀⢀⣶⣄⣹⣧⣀⠀⠌⠛⠛⢻⣏⠀⠀⠀⠈⠑⠂⠀⠀⢀⡅
⠀⠀⠀⠠⠤⢦⠼⠉⠀⠀⠀⠀⢀⡠⠘⢃⣠⡀⠀⠀⠄⠀⠀⠀⠈⠳⡀⠀⠀⢲⡞⢿⣣⣰⣧⣽⡿⡄⡀⠀⠀⠈⣧⠀⠀⠠⣄⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠹⡇⠈⠙⠓⠠⠤⢤⣤⠆⠈⠛⠒⠋⠠⠋⠀⠈⠀⠹⣤⣆⣔⣷⡶⠞⠁⠙⠒⠀⠉⠓⠂⢈⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡜⡠⠀⢠⡄⠀⠀⠀⠆⠀⠔⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣀⠦⠀⠒⠂⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⠏⠀⢰⠏⡇⠀⠀⠀⠀⡐⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠈⣦⠎⠉⠀⠀⠀⡀⠐
⠀⠀⠀⠀⢀⠵⠂⠀⠀⠀⠀⠹⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⡆⠀⠉⡀⠁⠀⠀⠀⠀⢀⣄⡼⠀⠀⠀⠀⠴⠒⠚⠂⠀⠀⠀⠀⠰⠋⠀⠀⠰⣄⠐⠊
⠀⠠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠋⠀⠀⠀⠀⡀⢀⡿⠋⡤⠖⠀⠈⠂⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡘⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣸⠦⡄⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠟⢻⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣷⣶⠿⠟⠋⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠋⠁⠀⠀⠀⠀⣿⠘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢛⣿⡛⠛⠛⠛⠛⠛⢳⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣵⡶⠒⢶⣶⣶⣶⣶⣶⡝⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⢀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣋⣴⡿⢸⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⣠⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢟⣩⣾⣿⢟⣀⣀⣀⣀⣀⣀⣀⡀⣿⣿
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣸⠥⣤⠤⣤⠤⠤⠤⠤⠞⠀⠀⢸⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⢇⣛⢛⣛⠛⣛⣛⣛⣛⣣⣿⣿
⠀⠀⠀⠀⢀⡞⠀⠀⠀⣠⠗⠾⣥⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣱⣿⣿⣿⠟⣨⣑⡛⢡⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣴⣿⣷⣄⠀⠰⠚⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠙⠿⢿⣯⣥⣾⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⣿⣿⣷⣄⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠘⠿⡿⢛⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀
⢠⣾⢟⣩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡂⠀⠀⠀⠀⣀
⠿⠣⠯⡞⣣⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠛⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠑⠋⡶⠶⠶⠂⠀⠹⡆
⠀⠀⠀⠀⣿⠀⣀⣒⣶⣾⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣶⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣻⡜⣷⡄
⠀⠀⠀⠀⣿⠀⣿⣾⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠾⡚⢹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣗⣖⣖⣖⣇⢹⣿⣿⣿⣷
⠀⠀⠀⠀⣿⠀⠈⠉⠉⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⡀⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣷⣿⡆⢿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣏⣹⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋




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

⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠠⣶⠆
⠀⠀⠈⠁⠘⠀⠀⠀⠀⢰⣿⠿⠉⠉⠁⠀⠀⠸⠿⠿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄


⠀⠀⢰⣋⡍⡣⠀⠀⠀⠀⢺⠿⠿⠂⠀⠀⠀⠀⢸⡿⠿⠇⠀⠀⠀⠀⢸⡿⠿⠇⠀⠀⠀⠀⠐⡿⠿⠗
⠀⠀⢿⣍⡙⠟⠀⠀⠀⠀⠸⠿⣇⣤⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠸⠿⠿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢀⣀⠀⠀⠀⠀⡀⢺⣿⠟⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⣠⣤⡴⠂
⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠰⣿⡟⠛⠁⠀⠀⠀⠀⠀⠻⢀⠀⠀⠀⠐⠁⠐⠗⠐⠀⠀⠀⠈⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠠⢦⡔⠂⠀⠀⠀⠠⠖⠻⡷⠀⠀⠀⠀⢠⣼⣯⡝
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠲⠿⡶⠆⠀⠀⠀⠰⣷⡦⠟⠹⠂⠀⠀⠰⡿⠿⢳⡷⠄

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⣀⣀⢸⣷⠄⠀⠀⠀⣸⣟⡛⣗⠀⠀⠀⠀⡀⢂⡐⢀⠀⠀⠀⠀⢾⣿⣿⠆
⠀⠀⠸⠛⠓⡆⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⢿⣿⠇⠋⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⠀⠠⡶⣦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠛⠉⠁⠀⣀⠀⢀⣀⣤⣤⣶⡾⣤⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠉⠉⡀⡀⣀⣀⣤⢶⡼⣿⡿⢷⢻⡹⣞⣧⣿⡟⠁⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠚⠋⠉⠀⣰⣶⣷⢋⣿⣝⡟⢷⢿⣽⡰⣇⢹⣹⣼⣾⢋⡝⠙⠉⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⢠⢟⠛⣵⣍⢯⢱⣜⣤⢬⡟⠛⠵⠋⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⡐⡀⠀⠀⠀⠀⠀⢎⣆⣒⡽⠼⢞⢟⠃⠁⠈⠁⠀⢀⠠⢠⠂⡰⡡⡡⡓⡀⠀⠈⠀⠀⠀⠀⠘⣇
⣠⠚⠉⡸⡠⢂⢌⢔⠀⠀⠀⠀⠀⡔⣐⣧⡀⠀⠀⠀⠀⠈⠋⠙⠈⠀⠀⡀⠀⠀⠀⠀⠀⠐⠡⠁⡔⡔⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠃⢀⠜⠔⡡⡣⡣⢂⠄⠀⠀⠀⠘⠀⠈⠈⠑⠀⠀⠀⠀⠀⡀⢠⢀⠆⠜⡔⡡⠠⠠⠄⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠈⢊⢜⢔⠔⢵⡅⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡜⡠⢡⢃⢎⠜⡰⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢞⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠪⠪⠊⠃⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠎⡔⡠⠁⠆⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠠⠘⠐⠀⠀⠀⠰⠂⠀⣠⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠣⠀⠒⡀⠀⠀⠠⠃⠘⠀⠀⠀⠀⠀⠀⠀⡄⡄⡶⠄⠠⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠲⠀⠀⢹
⠀⠀⠐⠀⠀⠀⠀⠀⠆⠀⠡⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠁⠀⠀⠂⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠄⠁⠀⢀⠄⠁⠠⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠆⠀⢃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠐⡁⠀⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⡀⣨⠅⠀⠀⠀⠀⠀⣀⠀⠄⠈⠁
⠀⠀⠀⠀⠀⢀⡐⢶⢤⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠆⡘⢌⢶⠱⠑⠈⠊⠠⠀⠐
⠀⠀⠀⠀⠀⠀⢺⢃⡦⢣⢊⠌⡐⣤⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠋⠄⠜⡜⠌⠘⠈⠈
⠀⠀⠀⠀⠀⠀⠀⣾⢡⢃⢎⠌⡔⡡⠈⠢⡀⠀⠀⠀⢲⠏⢼⠃⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠰⢂⢎⢂⠌⠜⡐⡑⡠⡀⠀⠀⢀⠈⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢡⢂⠆⡌⡜⣐⡰⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢄⠀⡀
⠀⠀⠀⠀⠀⢀⠄⠔⠂⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢁⡀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠠⣀⣄⣀⣀⣀⣈⣈⣂⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⢀⢤⢌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠋⠤⠏⠡⠄⠉⠉⢩⢩⢩⠉⡍⢩⢩⢩⡉⡍⢩⠉⡍⠩⡉⠉⢹
⠀⠀⠀⠀⠉⠉⠈⠀⠈⠀⠀⠀⢸⠀⠀⢆⠁⣆⡐⢉⡄⠀⠁⠘⠘⠐⠘⠘⠑⠀⠉⠂⠊⠃⠃⠀⠃⠀⢸
⠀⠀⠀⣀⡀⢀⡴⠂⠄⠀⣀⡀⠀⠙⠥⠈⠁⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠍⠀⠀⠀⠀⣠⠰⠂⠀⠒⠠⡀
⠀⠀⢘⠁⢈⠘⢄⡠⠂⠞⠁⢈⠀⠀⢠⣄⣀⣀⣀⣀⣀⣠⡤⠄⠀⠀⠀⠀⠤⣄⡀⣀⣀⣀⣀⣒⡜⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠹⣁⣀⣀⣇⣀⣈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡂⠕⡂⢸⠀⠀⠄⡂⠅⡂⠀⠀⠀⠠⢒⠅⡂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠁⠀⢸⠀⠐⠁⠂⠁⠀⡀⠀⠐⠈⠐⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⠀⢄⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢠⢱⠆⠠⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡍⠀⠈⠀⠀⠀⠡⠭⠭⠭⠬⠭⠭⠬⠭⠽⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⠀⠀⠀⠒⠒⠒⠂⢠⡍⠉⢠⣉⣉⣝⣍⣭⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠠⠤⠶⠖⠀⣒⠒⠒⠀⠒⠒⠀⣹⣿⣉⣈⡋⡆⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢡⠰⠀⠓⠀⠀⠈⠓⠀⠉⠉⠁⢸⠆⠂⠑⠍⠁⢧⠸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⡘⠄⡐⠀⢠⠃⠈⣷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢃⢠⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⣼⣰⢡⢡⢃⠂⢠⢿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⢀⠔⠊⣁⡤⢤⣤⣉⠙⢦⡾⡞⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⡄⠀⠀⠀⢠⣁⠔⡺⢱⡏⡱⠀⢪⣳⠂⠀⣟⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⢠⠀⠀⣠⠤⠬⣤⠳⢸⢰⠡⢡⢣⢉⣏⣿⡝⢰⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡄⠀⠐⠀⡀⠛⠧⣧⣣⣆⣞⡧⠖⠉⢀⢱⡣⢊⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢠⠀⠀⠃⢨⢓⣤⣄⣈⣉⣀⣀⣤⠶⡻⡳⡡⣦⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣃⣭⡧⠤⠤⠭⠽⠟⠒⠛⠛⠓⠓⣧⢩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⡀⠀⣾⠋⡥⢠⡀⡔⢰⣴⣾⣇⠲⢼⠹⠀⣽⡆⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢁⢠⢼⡀⠁⠈⠁⠀⣀⣀⣠⣤⡤⢤⢒⠎⠘⡅⢺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⡏⢈⢏⠍⡝⡙⡙⢩⣳⢃⣿⢣⢪⢊⠎⢐⠄⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣥⣰⣾⣷⣲⠾⢖⠲⠖⠷⠂⠥⣷⡾⠧⠀⣼⣻⢟⡿⡗⣿⢿⠿⣶⣶⡤⠀⢤⣀⣀
⠀⠀⠀⠀⠠⣶⠢⢀⠀⢐⣶⡶⢖⡛⠟⡻⢛⠟⠹⣏⣉⣉⠙⣷⢶⣤⣀⡀⠀⠀⠀⠉⠒⠲⢾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⣿⢙⣶⣌⣜⣋⠙⠳⠥⣚⠛⣷⠦⡿⣾⣟⣿⣰⣷⣿⣿⣿⣷⠀⡖⡀⡀⣀⣱⢸⣿⣭⣏⣽⣿⣧⣷⡿⡿⣶⣿⣾⣿⡅
⠀⠀⠀⠀⠀⣿⣖⢤⣭⣉⣛⠯⣒⠲⠦⢐⣻⣿⣽⣿⣽⣿⣿⣿⣿⣿⡿⠿⣋⣀⠙⠛⠛⢻⡟⣿⣿⣱⣷⣿⣷⣿⣟⣿⣿⣿⣿⣿⣧⣤⡀⢀
⠀⠀⠀⠀⠀⣿⣧⣬⠍⢛⡛⠻⣿⣛⠶⠀⣞⣿⣿⣶⣿⣿⡿⣿⣿⣿⣧⣀⡀⠀⢈⣹⢙⣏⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠉⢀⠋
⠀⠀⠀⠀⠀⠙⠲⢭⣝⡓⠦⢽⣟⣳⠿⣞⣻⣽⣿⡯⠝⣠⣄⠀⠀⠈⠈⣻⣱⣄⡉⠹⢉⡏⣍⣼⢏⡳⣞⣲⠊⠉⠘⠛⠒⢻⣻⣐⠤⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠮⢷⣽⠺⣻⣿⣿⡿⣀⣀⠀⢈⣙⢸⣉⣘⣼⡏⠑⢺⠛⢛⡋⣽⢃⠘⣇⠀⠈⠉⠋⠩⠉⠋⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠑⠘⣧⡀⠀⠀⠀⠉⠙⢹⠉⣿⡿⠷⠚⡛⠻⣯⠟⠒⠀⠈⠉⠓⠒⠛⠚⠛⠋⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠄⠰⠂⠐⠶⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠉⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⡍⠉⠉⠉⠹⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⠀⣴⣦⠀⡁⢠⣶⡄⠀⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢬⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣹⠀⠈⠁⠀⠃⠀⠉⠁⠀⡇⠀⠀⢀⣥⣀
⠀⠀⠀⠀⠀⠀⠳⠤⠏⠀⠀⣈⣿⣉⣉⣉⣉⣻⣉⠀⢾⡷⠀⠇⠰⣿⠆⠀⡇⠀⠀⠸⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠦⠀⢠⡞⠉⠉⠉⠉⠉⠉⠉⠉⠹⡆⠀⠀⡆⠀⣀⠀⠀⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢰⡀⢸⡇⠲⠶⠶⠶⠶⢶⠀⠀⠀⡇⠀⠀⡄⠘⠿⠃⠀⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡇⠀⠀⠀⠀⠀⢸⠀⢀⡤⢧⡀⠀⠁⠀⠀⠀⣠⠇⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⣷⠈⠉⠉⣉⠉⠁⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠛⠛⠛⠛⠛⠀⣿⠉⠉⣿⢀⡾⣏⠉⠙⢦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠹⣤⡤⠏⢸⡅⠈⠳⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠙⠶⠤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣮⣛⡎⠉⠉⠉⠉⣽⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢶⣝⣯⡽⠃⠀⠀⢀⣴⠛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⢿⡅⢰⡆⣨⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⢠⣿⠀⠀⠁⢿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣀⣸⣿⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠛⠛⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣴⡾⣳⣿⣿⡿⣿⣿⣶⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⢐⣿⣿⣿⣿⣿⣿⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣿⣿⣿⡄⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⡿⠟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣻⣏⢿⣿⣿⣿⣿⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡟⠋⢀⣤⣤⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⡿⣾⣿⣿⣿⠀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠹⢷⣷⣿⣿⣿⣾⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢿⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠙⠛⠛⠋⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠋⠉⡍⠂⣠⢆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠖⠛⠒⠶⢤⡀⠀⢀⣼⣶⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠒⠦⠤⣀⣀⠀⠀⠀⠉⣻⣿⣿⣿⠇⢤
⠀⠀⠀⠀⠀⠀⠀⢀⠦⡄⠁⠀⠀⠐⠄⣤⠠⠍⣟⣷⠠⢠⣿⡿⠏⣸⣾⣿⡆
⠀⠀⠀⠀⣾⠤⣚⣡⠀⡐⠀⠀⣀⣀⢀⣠⣴⣿⣿⣿⢀⣿⠟⠒⠺⣿⡿⡗⠁
⠀⠀⠀⠀⡇⠙⠶⢬⣝⢶⣵⣡⢞⣥⣮⣿⣿⣿⣿⠟⢋⡁⢀⣠⠢⣿⡾⢄⠓⠦⠠⢀⡀
⠀⠀⠀⠀⠑⠂⠠⢒⡪⠅⣉⠛⡛⣿⣿⣿⡟⠁⠡⠄⢒⣿⡟⡗⣹⠟⠚⠉⠆⢦⣈⣵⣿⡀
⠀⠀⠀⠀⠀⠀⡠⢴⠏⠙⠂⠭⠴⠟⠋⠐⠀⠀⢀⣤⣿⣿⣏⡼⠁⡠⠀⠀⠀⠈⠌⠙⡟⠃⠄⣀
⠀⠀⠀⠀⢰⡇⠀⠀⡈⠂⠠⠵⢄⣀⠀⢂⠔⣠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠡⠀⠀⣄⣀⠥⡺⣇
⠀⠀⠀⠀⠈⣧⣀⠤⠐⠀⡀⠀⣀⡤⠄⣬⣀⣿⣿⣿⣧⣄⠠⣤⢀⡀⠀⠀⠀⣀⢂⣑⣥⣶⣿⢾⠃
⠀⠀⠀⠀⠀⢹⡆⡲⡺⠥⠤⠤⠴⠶⠾⠴⠮⠽⣟⢅⠀⠙⢳⣢⡭⣬⡵⣶⣿⣿⡿⠟⢛⠩⣐⠼
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠑⠠⢤⡀⠠⢀⣀⣈⣤⣼⣿⣄⡀⠀⠀⢰⣿⡿⣛⣭⣕⠲⠒⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡗⠮⢭⣴⣿⣿⣿⠿⠋⠁⠐⠀⠼⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈⠂⢸⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠞⠛⠉⠁⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⠉⠀⠀⠀⢠⠖⡐⡴⡋⢉⠑⣄⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠉⠀⠀⠀⢀⠤⢆⣞⠉⠻⡄⢈⡓⡴⣌⡠⠏⠀⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠀⠀⢀⣠⠤⢤⠀⠀⢸⠀⠮⢾⣰⠖⠛⠚⠉⣁⣠⠤⠤⣀⠠⠖⢋⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⣤⢄⣏⣤⠰⡏⠀⠀⠀⠑⠒⠚⠁⠀⣠⠔⠊⠁⣀⠀⠀⠘⢶⠊⣉⠤⠚⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⢀⣤⡄⢾⠁⡐⢶⡌⢣⠈⠦⠜⠀⠀⠀⠀⣀⡠⠤⢾⡄⠀⠀⡏⠉⠳⡀⠀⠈⡏⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⣴⠞⠛⠉⠀⠀⣀⣠⠖⡒⣾⠈⢹⣎⢧⣤⠞⠈⠉⠀⠀⢀⡠⠄⠒⠉⠠⠔⠂⣉⠽⢶⡩⠖⠦⠔⢁⡤⠖⠃⠀⠀⣀⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⠋⢀⡟⠇⢀⣁⣳⠤⠜⠁⠀⠀⠀⢀⡤⠒⡡⠐⠊⠀⡀⠤⠒⠉⠀⠀⠈⠳⡤⠴⠊⠁⠀⠀⡠⣄⠀⠩⣇⡠⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢦⡈⠓⣻⠞⠉⠁⠀⠀⠀⠀⠀⠀⢨⠀⢨⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠀⠀⣜⡤⠀⠉⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⢿⡑⡀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⣨⠆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢆⠀⠑⠟⠊⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⢉⠤⠒⠈⠀⣠⠞⠀⠀⠀⢠⠔⢦⠀⢳⡀⠀⠓⠈⠀⠀⠀⠀⠀⠀⡀⣄⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡜⡄⠀⢀⡠⠴⠒⠈⣁⠀⠀⢈⣠⠤⠖⠚⠉⢠⠤⣄⡎⠉⣆⠢⠞⠀⠀⠁⠀⠀⠀⠀⢀⠠⢐⣨⣵⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⡞⢁⡠⠤⠒⡉⠠⠐⠊⠁⢀⡄⠠⡄⠀⠘⣄⡼⠙⠚⠁⠀⠀⠀⠀⠀⡀⠤⢐⣨⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣏⡤⠒⠁⢀⡠⠀⢠⠀⠘⠒⡖⠙⠻⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⣡⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⡆⠀⠀⠈⠟⢉⡎⠚⠯⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣆⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡠⢔⣪⣥⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⠢⣀⠀⢀⢀⣠⠤⠒⣩⣴⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣍⣉⣁⣤⣴⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠉⠉⠉⢩⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣶⣶⣶⡶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠁⠀⠀⠀⠈⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⣾⣿⣿⣿⣿⣶⣦⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⠀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⣿⣿⣿⡿⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡉⠠⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠷⣿⠃⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣿⡆⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⡿⡟⠀⠀⠛⠃⠹⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠟⠀⠆⠈⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡷⡷⢠⡤⡤⣤⣾⢿⣿⣦⣤⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⠶⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿