Fellow Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠈⠋⠢
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡌⠁⠠⠐⠑⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⢐⠐⣄⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠐⠀⢈⡐⢱⠉⡀⠀⠀⠀⠂⠂⠀⢀⠀⠱⠂⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⡛⠃⠀⠀⣀⢀⠀⠀⠀⡆⡄⣠⢠⠀⠀⠦⡀
⠀⠀⢀⠀⡮⠃⠀⠀⠀⠁⠀⠀⠀⠈⠪⣆⠖⠢⠄⡀⠀⠀⠘⠀⠀⣀⢆⡆⣸⠀⠀⠀⢠⠀⠀⠈⠀⠱⡀⠀⠀⠀⠘⠈⠉⠛⠢⡀⠀⡅
⠀⠀⠀⠐⠀⣀⢄⣠⢀⠀⠀⠀⠀⠀⠓⠳⠀⠀⠀⠀⠑⠀⠆⠠⠂⠁⠂⠀⢧⠀⠀⠀⠀⠂⣤⠜⠴⣊⡀⠀⠀⠀⠐⡀⡀⠀⡀⠔⠊
⠀⠀⠀⠀⠠⠙⠛⠋⠡⠠⢄⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⣆⣀⣤⢀⣤⡤⠔⠀⠀⡄⠢⠑⡈⠂⠈⡄⡉⡀⠀⠀⠠⠂⠳⠀⠳⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⢬⠄⡦⣤⠴⡲⡀⡀⠀⢂⠀⡈⠀⠃⢹⣦⠌⠁⠲⡀⠀⠀⠀⠃⠀⠀⠈⠁⠀⢁⠀⠀⠀⠀⠼⠀⠀⠀⠈⠆
⠀⠀⢀⠀⠀⠂⠀⡀⣤⠀⠼⣗⡜⠒⣑⣍⡃⠀⠀⠈⠰⠀⠐⠑⡌⠻⠂⠀⠄⡇⠀⡀⠀⠀⠀⠀⢀⡀⠾⢉⢴⣅⣇⣀⠀⠀⡀⠀⢀⠃
⠀⠀⠀⢄⠀⠈⠃⠀⢈⠇⠑⠘⠊⠉⠡⠭⠁⠐⠂⠀⢲⠀⠀⠀⡷⢷⢬⡪⣣⢰⠀⢡⠀⠈⠐⠢⠎⣰⣤⣆⣬⠔⣈⡄⣀⠉⠀⠀⠈
⠀⠀⠀⠘⠢⠀⠄⠂⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⢄⡠⠪⠘⣐⢭⠉⢬⡿⠀⢨⠕⠂⢄⡀⣠⠈⠢⣜⠔⠀⠅⡀⠀⠀⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⢰⠀⠀⠀⢀⡸⠀⡀⠀⠀⠀⢸⡀⣀⠅⠀⠀⠀⠀⠀⠀⠠⠝⠶⠋⠀⠘⡤⠢⡀⡀⠀⠐⡊
⠀⠀⠀⠀⠑⡤⠴⠤⠤⠚⠁⠀⠐⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄

⠀⠀⠀⢀⣀⣄⡴⠖⠃⢐⠀⢐⢒⡄
⠀⠀⡞⠛⠄⡤⣠⣶⢿⣷⡾⣯⠌⣧
⢀⡾⠿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⢫⣤
⠀⡏⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢹
⠀⢹⡮⡟⠀⠀⢴⠟⠁⠀⠀⠀⠀⣅⡈⡀
⠀⠀⣿⠶⡆⠀⠀⢠⡄⠈⠂⠈⢄⠁⠀⠸⡄
⠀⠀⠸⡞⠄⠀⠀⠈⠁⠀⠠⠄⠼⠀⣤⠀⡇
⠀⠀⠀⠘⠦⡄⠀⠀⢠⣤⡠⠤⠒⣺⠏⠀⡇
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠛⢛⣋⠄⢰⠇
⠀⠀⠀⠀⠀⠀⢸⣄⠰⣄⡀⠀⠀⠀⣀⡼⡛⠲⡶⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣸⢧⡉⠂⠭⣛⠛⠋⢡⠃⠘⢆⠙⢦⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⣰⡇⠀⠳⡄⠀⠀⠉⠓⣿⣶⣄⡈⢦⠀⠳⣄⠀⠀⠹⡄
⠀⠀⠀⢀⡼⠃⠸⡄⠀⠙⣦⠀⠀⡰⠙⠻⣇⡙⠲⢧⠀⠈⢢⡀⠀⢻⡀
⠀⠀⢠⡞⠁⠀⠀⠹⡄⠀⠈⠳⣤⠃⠀⠀⢻⣿⣦⡈⢧⠀⠀⠙⢆⠈⣧
⠀⣰⠋⠀⠀⠀⠀⠀⠙⣄⠀⠀⠈⠳⣄⠀⠘⣿⣿⣷⡌⢧⠀⠀⠈⡷⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⣀
⣼⣡⠄⠊⠉⠉⠓⢦⡀⠘⢆⠀⠀⠀⠈⠳⣄⠹⣿⣿⣿⣎⣆⠀⠾⣅⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⢤⢨⣉⡓⠢⢄
⢿⠁⠀⠀⠀⠀⠀⠀⠉⠂⠈⢳⡀⠀⠀⠀⠈⠑⢿⣿⣿⣿⣿⡄⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠢⡟⠀⠈⠉
⠘⣄⠀⠀⠀⠀⠀⠀⢀⡀⠳⡀⠙⠒⠒⢲⠆⠀⠀⠉⠻⣿⣿⣷⠀⠀⢸⠀⢻⡀⠀⢀⣠⡔⠁⠀⠀⠀⠀⠀⣀⡳⡅
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠉⠳⢬⣆⠀⢀⡟⠀⠀⠀⠀⠀⠀⠙⠿⣧⠀⣸⣀⣼⠷⠚⠻⡍⢃⠀⣀⣀⣤⠔⢬⠥⠴⠃
⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⠉⠓⠒⠦⢄⣀⣀⡤⠴⠚⠛⠉⠁⠀⠀⠀⠀⢹⡈⡟⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣈⠀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⢿⣿⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡿⣟⡛⠯⣉⡉⠥⡤⠴⠒⣚⡙⠛⢛⣛⡿⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⠿⣛⣫⣭⣶⣻⣭⡵⢶⣿⣿⣿⣿⡿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⣡⣤⣤⣼⠶⠏⠉⣻⣿⣿⣿⣿⣶⣍⠀⠀⢉⣡⠴⣞⣿⣿⡿⠞⠁⡠⠘⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠖⣋⣭⣴⣶⡶⠀⠛⢿⣿⣿⣿⣿⣿⣦⡔⠛⣁⣾⠿⠋⠁⠀⣠⡾⠃⠀⠙⢿⡿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⣼⣿⣿⣿⡷⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⣠⣾⠟⣠⢆⣰⣷⣶⣶⡈⢿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣇⢀⡔⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠟⢿⣿⣿⣿⣿⣿⣿⣠⡼⣋⣵⣿⣿⣿⣿⣿⣿⣿⢟⡈⢿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢿⡿⠛⠛⠙⠿⠛⠁⠀⠉⠉⠩⠿⠟⣡⠞⠁⣼⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⠀⠀⣿⣿⡷⢞⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷
⠀⠀⠀⠀⣿⣿⣾⠿⠟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣠⡤⠴⣿⣿⣥⣴⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⢰⠋⢠⡄⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣾⢰⠏⠙⣆⢸⣿⣿⠇⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⣿⠘⠀⢀⣼⡆⣿⣿⠀⠀⠀⢀⣾⠿⠟⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁
⣿⠀⢠⣿⡿⠃⠘⠛⠀⠀⠀⠈⠁⠀⢀⣀⣀⣈⣉⡙⠻⢿⣇⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣷⣶⣤⡀⠀⠀⠀⢸⣿⡇
⢹⡄⢸⠏⣴⠆⠀⠀⠀⠀⠀⠀⠀⠐⠋⠹⢿⣿⡿⠛⢦⠀⣿⣦⠀⠀⠀⢠⣶⠟⠛⠛⠛⠛⠻⠿⠿⣿⡄⠀⠀⣸⣿⣉⣿
⠈⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠈⠋⠀⠀⠀⠛⠁⠴⠛⣟⣷⣶⣤⡀⠀⠀⠀⠀⠀⣿⡿⠋⡙
⠀⠸⡇⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠛⠛⠁⠉⠀⠀⠀⠀⢠⡟⠀⢠⠃
⠀⠀⢿⣀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⣸⡗⠀⡞
⠀⠀⠀⠉⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡾
⠀⠀⠀⠀⠀⣿⡇⠀⢠⣶⠀⠀⠀⣀⣴⣾⡿⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⠃
⠀⠀⠀⠀⠀⣿⡇⠀⢸⡿⠀⠀⣼⣿⠟⠉⠀⠀⠀⢳⣦⡀⠀⠀⠀⠀⠀⢀⡴⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⠋⣼⠃
⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⢹⠃⠀⠀⠀⠀⠀⠘⠻⣿⣶⣤⡤⠖⠋⠁⠀⠸⣿⣷⡄⠀⠀⠀⠀⣰⡿⠛⠃
⠀⠀⠀⠀⠀⢻⣇⠀⠀⣇⠀⠀⠀⠀⠰⣦⣤⠤⠤⢄⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠸⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠉⠉⠉⠛⠉⠁⢁⣴⠶⠀⣸⡟⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⠶⠖⠛⠉⠀⠀⠀⠃⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⣠⠞⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣤⣤⣤⡴⠾⠛⠁
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣠⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡏⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣷⣷⣶⣤⣴⣶⣶⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢻⣿⣿⠿⠟⠿⠉⠁⠀⠀⠈⠿⣿⣿⣷⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣳⣶⣦⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⣴⣾⣿⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⢠⣾⡿⠿⣿⠿⢿⠟⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠉⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡖⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⣠⣴⣾⣿⣿⣿⣿⣷⡄⠀⠀⠘⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⣤⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣶⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣤⣄⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⢹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠠⣿⣿⣿⠀⢻⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠉⠻⠃⠀⠹⠿⠟⠀⠈⠉⠁⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠈⢿⡿⠃
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⠉⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⢺⣿⣿⣿⣿⣯⡄
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠗⠀⠀⠀⠈⠙⢿⣿⣿⡿⠀⠀⠤⠖⠊⠉
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⠀⠀⠁⠀⠀⠀⢸⣏⣀⠀⠀⢀⠴⠶⠄⠉⠉⠁
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠙⠛⠐⠃⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠈⠁⠂⠉⠀⢀⣠⣤⣤⣤⣭⣿⣿⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⠁⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣾⡿⣿⣿⣦⣿⣟⢿⣿⣿⣿⣯⣼⡿⠃⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢢⣶⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠛⠿⣿⣿⣿⣬⣟⣿⣿⣿⣿⠿⣿⢱⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⣿⡏⠛⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠈⢻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠙⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⡃⣇⡀⣇⢰⣉⠞⡶⢧⠃⣿⢸⠶⣶⢸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣧⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⠉⠉⠉⠉⠉⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣦⣄⣀⠀⠀⠀⠀⣠⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⠀⠈⠉⠙⠛⠛⠛⢹⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠠⠆⠀⠀⠴⠄⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⡖⠈⠻⢦⣤⣤⡴⠟⠁⢲⡶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠻⣆⠀⣴⠄⠠⣦⠀⣴⠟⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠿⠋⠰⠆⠙⠟⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣐⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⣆⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⠖⠒⢠⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠍⡤⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻⠋⢿⢥⣤⢀⡜⡻⣿⡏⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠝⠀⣠⣴⣶⠛⠀⠉⠠⠉⠀⠋⣽⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⣾⡶⠞⠀⣿⡿⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⣹⡟⣷⣶⡤⠰⡶⠿⣯⡿⣙⣤⣿⠈⢿⣶⡄
⠀⠀⠀⠀⠀⠘⠨⠍⢉⣠⣶⠏⠀⠀⠀⠀⠐⠄⠀⠀⢐⡷⠶⠤⠔⠋⠉⠀⠀⠏⠀⠈⢃⣼⠻⣤⡀⣈⣻⣿⣆
⠀⠀⠀⠀⠀⢀⠀⡴⣤⣿⣿⠤⣦⡤⣤⣤⣤⣄⠑⠊⠉⠀⠀⠀⠀⠀⠀⡀⠾⠀⠀⠉⠁⣨⠁⢈⣷⠈⠙⢿⣹⡆
⠀⠀⠀⡀⠌⠢⣼⣵⣿⣿⣥⣶⣿⠟⠋⠁⠘⠁⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠂⢂⠋
⠀⠀⠀⢹⣈⣦⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠃⠐⠦
⠀⠀⠀⣸⠂⠛⠋⠉⠉⠀⠀⠀⠀⠀⢀⣤⣴⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⡃⠀⠀⡐⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣀⠆⠀⠀⡍⢶⣄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣶⣾⣿⣾⠋⠁⠀⠀⠀⠗⠸⡿⣦⣤⣆
⠀⠀⠀⠀⢀⠀⢀⡀⠰⣄⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢄⠀⠀⠸⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢀⠙⢦⡌⠓⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⣿⠛⠛⠓⠓⠐⣨⣤⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠸⣕⡠⣈⣈⠿⢦⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⢰⣿⠷⢦⠤⠤⠄⢋⣤⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣥⣶⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠏⣿⣷⡄⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣏⣭⣴⢿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⠿⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠡⢀⡷⠀⠀⠠⠀⠀⠀⢠⣿⣿⣟⣿⣽⠟⠉⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠈⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡾⠛⢿⣿⣿⠠⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢠⣼⡟⠀⠀⠈⣻⣷⡈⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡼⠀⢀⠰⣄⠠⡄
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⣧⣆⣼⡅⠒⠀⠛⠛⣻⡇⠀⢳⣇⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣈⠙⠂⠀⠀⠈⠷⠞⠻⠆⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣾⣿⣿⣷⡀⠀⣤⣦⠀⣷⠿⠦⠉⡿⠦⠤⡤⠀⠠⡴⠖⠈⠿⠛⠓⠂⠷⠀⢠⡶⡏⢀⠀⠸⡀⠁
⠀⠀⢠⣴⣾⣿⣿⣶⣄⠈⢺⣏⣿⡎⢈⣷⡄⠀⣴⣟⣁⠀⠀⣐⣶⣶⡄⣻⣎⢢⣴⠃⣀⡤⣤⣀⠀⠀⠀⠀⡇⢁⠸⠸⠘⠃
⠀⠀⠛⠛⠛⠛⢿⣿⣧⣴⡺⣿⣿⣿⣌⡿⠟⣬⠤⠘⠯⣿⣶⣏⣿⣿⣷⣾⣿⢾⣿⣴⣏⠐⢿⠟⢷⣤⣤⢔⡇⣸⠀⠀⣄⠰⣆⡀
⠀⠀⣤⡄⠠⠤⠀⣿⣿⣿⡿⣡⠼⠿⠋⠴⠁⢨⣤⠘⣿⣇⣿⣿⠿⣿⣿⣿⣿⣦⣄⣽⣿⣦⣼⠂⢺⣷⠙⠘⠀⠀⣠⠀⣿⡆⣿⣧
⠀⠀⣧⠀⠀⠀⠀⠀⣿⢷⡙⣡⠀⠀⠉⠀⠀⢸⠛⣿⡿⣿⡶⢦⠀⠷⣶⡾⠿⣿⡝⣹⣿⣿⣧⠐⡳⠎⠠⡇⠀⡆⠹⠀⠁⣤⣿⣿⠈
⠀⠀⣿⣿⣁⣠⠀⠀⠈⠀⠻⣃⠀⠀⠀⠀⠀⣠⣷⣿⣧⡈⠁⠀⠀⠀⠈⠀⣰⣿⣿⣻⣿⣿⡿⠃⠀⡝⠒⢟⡆⠀⠀⠘⢿⡿⡓⣿⠀⠀⢠
⠏⢀⡘⠿⣯⣛⠀⠀⢸⠀⠘⢿⣿⡄⠀⠀⠀⢀⣿⣾⣿⣁⠀⠸⣶⡂⠀⢀⣾⣻⣿⢀⢿⡿⠃⠀⠀⠀⠀⠘⠗⢀⠘⠀⠀⠙⠀⠉⢻⡷⠋
⠀⠉⢙⣦⡙⠻⠷⣄⠘⠀⠚⠈⣮⡉⠀⣀⠀⠸⣿⣿⢿⣿⣖⠀⠒⠂⢀⣿⣿⣿⣿⠟⠞⠇⠀⠀⠀⠀⣠⣴⡶⠩⡇⣾⣷⣆⡾⢿⢿
⠀⠸⡛⣉⠁⠀⠀⣤⡅⣀⡄⣸⠇⢹⣿⣍⡍⢾⣿⣏⡁⠉⠻⢷⣾⣿⠟⢻⣿⣿⣇⣲⣤⠀⠈⠀⠀⠀⣿⠋⠀⠀⠃⡿⢉⠀⢀⢸⠈
⠀⠀⢛⣷⣤⠀⠠⡿⠘⠛⡅⠋⡔⢀⣽⣿⣧⣈⠹⣿⣷⣤⣌⣑⠲⠾⢿⣟⠈⠛⠛⣿⣿⠓⣀⠀⠀⡀⣟⠀⠉⠀⡀⠿⠏⠀⢺⠈
⠀⠀⣽⠹⡟⠄⠑⠁⠀⠀⠇⠸⣠⣿⣿⣿⣿⣿⣿⣷⣿⡟⠿⢿⣿⠿⣦⡈⠙⠶⣦⣤⣉⠛⠷⣄⢸⣁⠈⠀⠀⢸⡿
⠀⠸⠏⣐⣇⠲⣄⡁⠀⠀⠐⢲⠟⣹⠟⢁⣿⢿⡿⠛⠁⢤⡄⠶⣶⢀⣀⠀⠀⠀⠈⠙⠿⣷⣦⠉⠈⠿⣻⣷⡀⢰⡊⢁⣾⣶⣤⡄
⠀⠤⣉⡛⠀⠡⢈⣅⠀⢀⡟⡀⡼⢫⠦⠋⠁⠁⣠⣾⡇⠈⠳⠀⠈⠘⣿⠿⠀⠀⠀⠀⠀⡉⢿⡅⠀⢰⡿⢻⡟⡟⢠⣌⢩⠙⣿⣇
⠀⠀⣨⡿⠷⠆⠀⣿⠠⡾⢡⡟⢠⡟⠀⠈⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⣄⠀⠹⣆⢹⠀⠀⠀⠀⠁⠁⠘⣧⠦⢼⣥⠼⢃
⠀⢠⡿⠁⠀⠀⠀⢹⠀⠘⠈⣴⡟⣴⠆⣠⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠂⠀⠀⠀⠀⠀⣀⡄⢙⣣⣄⣩⣠⡈
⠀⠈⠁⠀⠀⣄⠀⠈⠀⠀⣸⣿⡞⠁⠰⠋⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⢁⣽⠟⣫⡔⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠐⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡀⣴⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠦⠈⠘⠃⠀⠀⣠⠙⠿⣿⢛⣷⣡⠴⠃⢘⠿⡿⢆⣀⣠⠀⣤⣤⠀⠀⠀⣤⡄⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠠⣹⣧⣿⣿⡶⣿⡤⣸⣿⣷⣍⢉⣿⠙⣿⠀⠀⠀⣄⠻⣶⡗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⣛⢋⣿⣧⢉⠁⣤⠘⠿⠛⠫⣄⡘⠧⠈⢳⣶⡍⠃⠹⠃⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠻⠁⠘⠂⠋⡠⠀⢠⡀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢠⡶⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣧⠀⢸⠃⠀⠀⠀⢀⣀⣀⡰⠛⠉⠙⠇⠐⢲⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⡀⢀⡴⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⡈⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠀⠀⠀⠀⣄⢠⡄⠀⣀⡸⠃⠐⠣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠛⠁⠙⠒⠚⠃⠙⠲⠶⠞⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠶⣦⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⡳⢸⠂⠀⢀⣴⢦⡄⠀⠀⠀⠀⠁⠀⠀⠈⢳⡀⠀⠈⣷⠀⠀⠀⠀⠰⠶⠒⠛⠛⠋⠉⠁
⠀⣤⣤⣀⠀⠀⠀⠻⣦⣀⠀⠁⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠈⠉⠙⠃⠀⠀⠘⡷⠂⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠛⣠⠄⢻⡄
⠀⣴⣶⣶⣶⠶⠆⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⢀⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠃⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⢈⡧⠀⠀⠀⠀⠀⠘⡇⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⠀⢈⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠁⠀⢦⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣿⠉⠛⠒⠶⠦⢾⣤⣤⣤⣤⣤⣤⠴⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⢷⣄⠀⠀⠀⠀⢀⡿⠇⢉⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣤⣀⡀⣸⢸⡃⢀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡏⡾⢹⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠋⠉⣉⡉⠓⢤⠏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠉⠛⢦⣸⣅⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠇⠀⠲⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣻⠁⠀⠀⠀⠀⠓⠦⣌⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣈⠧⠤⡤⠠⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢁⣇⣀⡀⠀⠀⠐⠲⢤⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⡀⠀⠰⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣖⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⣀⣤⣶⣾⣷⣾⣦⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣠⣤⣤⣄⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠈⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⠛
⢀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⢻⡀⠀⠀⠀⡼⠛⠛⠛⠛⢛⡿⠿⠛⠛⠻⣿⡏
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⠋⠁⠀⠀⠀⠈⠉⠀⢠⣖⣉⡿⠉⠁⣸⣓⡒⠲⣤⣀⣀⣀⠤⣔⣒⣲⣬⣷⠒⠚⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠴⠂⠒⠒⠒⠢⣀⣊⠏⠉⠀⠀⠀⢯⡀⠀⠻⣍⢒⡒⠒⠉⠁⠀⠀⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠭⠤⠤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠋⠙⠲⠦⠤⠤⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⣿⣿⣿⠹⣿⣤⡀⢀⣴⣿⠟⣿⣿⣿⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠸⣿⣿⡿⠀⠀⠙⢿⡿⠋⠀⠀⣿⣿⣿⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⢀⣤⣤⣤⡀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⣤⣤⣤
⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿
⠙⠿⣿⠿⠃⠘⠛⢿⣿⡛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣻⣿⠟⠃⠘⠿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢠⣶⣶⣶⠀⠀⣠⣶⣦⡀⠀⠀⣶⣶⣶⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣐⣿⣿⣿⣠⣾⠟⠁⠙⢿⣦⡀⣿⣿⣿⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁








⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⢰⡖⢰⡄⢰⠀⢰⠒⡆⢆⣶⣰⠰⣖⢰⣤⡆⡆⣶⡦
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣾⣷⣾⣿⣾⣿⣷⣾⣶⣷⣾⣿⣾⣶⣷⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⡤⠤⡤⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⣸⠀⠀⣳⠀⠀⠀⠀⣰⢋⣴⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⢨⡷⡇⡤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀⡾⠁
⠀⠀⠀⢹⠁⢐⡷⠀⠀⠀⠀⠘⢿⡟⣾⢂⣶⢐⣶⢰⣆⠀⠀⠀⠀⠈⠀⠈⡯⡇⠀⠁⠀⠀⠀⠀⠀⠨⠉⠉⠁⡾⣆
⠀⠀⠀⢩⡣⠊⠀⠀⠀⠀⠀⠀⠀⢬⡯⢨⣯⠨⣿⠬⣿⡄⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⠄
⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢙⣿⠉⠋⠉⠁⠀⠀⢀⣀⣀⣤⣋⣼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠐⠠
⢤⡀⢀⣴⣦⣾⣷⣤⣄⠀⠀⠀⠀⠀⢀⡀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢳⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠿⠉⠀⠹⠇⠀⠀⠀⠈⡿⠿⣿⢸⣿⣿⡏
⠀⠘⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣹⣏⣿⣻⣻⡇⠀⠀⠀⠀⣁⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⢰⡉⡎⣹⢸⣿⣿⣷
⠀⠀⠉⠾⠎⠛⠱⠿⠊⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠠⠿⠀⠾⠀⠧⠀⠠⠄⠀⠀⠀⠾⠿⠿⠿⠯⠿⠿⠿⠆
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠳⢴⠀⠀⠀⠀⠀⠀⢰⣷⠖⣲⠒⡶⢲⢲⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠘⠇⣸⠒⠀⠀⠀⠀⠀⣼⠏⠀⠁⠈⠀⡿⣼⡇⠀⠀⠀⢀⣀⣰⣺⣲⣀⣀
⠀⠀⠀⢀⣻⣟⡅⠀⠀⠀⠀⠀⠀⢀⡀⣋⢙⡋⣙⣀⡀⠀⠀⠀⢀⣿⢀⡀⠠⠀⢸⣇⣿⡇⠀⠀⠀⢈⣿⣉⢹⠉⣹⣏
⠀⠀⠀⠚⠓⠓⠓⠂⠀⠀⠀⠀⠀⠐⠂⠒⠐⠂⠒⠐⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠙⠛⠃⠀⠀⠀⠐⠂⠒⠐⠒⠂⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⡎⣭⣭⡝⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡀⡴⠋
⠀⠀⢰⣿⠀⠀⢰⡇⠀⠀⠀⠀⣀⣤⣄⢴⠟⠻⣇⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⢮⠀⣼⣿⡀⠀⠀⠀⢀⣴⣿⣿⣦⡀⢀⡴
⠀⠀⠘⣿⠀⢠⣿⡇⠀⠀⠀⠀⢿⣿⣿⣦⣄⢀⣭⣦⣄⠀⠀⠀⠀⠀⣏⣛⣛⣉⠀⠛⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠻⡄⣾⡿⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⢺⣿⣿⣿⡇⠀⠀⠀⠀⡧⠷⠿⢼⠀⠀⠁⠀⠀⠀⢀⣼⣿⠿⠻⠿⠟⠁

⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠈⠉⣤⣶⣦⡉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣷⣿⣷⡆
⠀⢰⣶⣶⣶⣷⣿⣿⣿⣿⡇⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⢻⣿⣿⣻⣿⣻⣿⡁⢤⠈⠁⠀⠀⠀⠀⠀⠀⠐⢤⠤⣿⡧⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠻⠿⠇

⠀⣀⣠⣴⣦⣤⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⡀⠠
⠀⠛⢛⣉⣉⣉⢩⣭⠡⣤⡄⣶⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⣇⣿⣇⡀⠀⠀⠀⠀⢸⡇⠀⠀⡀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢰⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠠⣾⣿⣿⡆⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠁⠀⠀⣿⣻⣿⣿⣛⣿⣻⡿⢿⣛⢿⣿⡟⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠶⠿⠿⠿⠷⠾⠿⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣄
⠀⠀⠀⢀⡒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠛⠓⠂
⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⣤⣀⣀⡀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙
⠀⠀⢰⣿⢻⡖⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢀⣀⣀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⢀⣸⣿⣼⣧⣿⣼⣇⣴⣿⣦⣤⣀⠀⠀⠀⣀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣙⣀⡀⠀⠀⠀⠒⣁⡐⠀⠀⠀⠀⠀⠀⠼⠾⠆
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠶⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣠⠏⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣸⠆⠀⠀⠀⣠⠴⠶⢦⣄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠿⠛⠓⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠀⠀⣼⠁⠀⠀⠀⠈⢧⣀⣀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⡏⠀⣹⡂⠀⣠⠖⠋⠉⠉⠉⠙⠲⣄⣀⣤⡾⠟⠋⠛⠶⠦⠶⠋⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠙⠊⠉⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢰⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠁⠀⠀⠀⠀⠉⠙⠛⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⡁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣦⣀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡴⠋⠀⠉⠻⣗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣶⠛⠉⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣤⣤⡾⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠹⣄⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⢦⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⠤⠞⠁⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠓⠦⠤⠤⠤⠤⠤⠤⠤⠖⠚⠉⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⢱⣤⡶⠶⢷⡀⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠋⠀⠀⠀⠀⠙⠲⠦⠤⠖⠋⠀⠙⠿⣦⡤⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡰⠃

⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠝⠁
⠀⠀⠀⢰⣷⠄⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠀⢀⡀⠀⠀⠠⠆⠀⠈⠛⠋⠀⠀⠿⠇⠀⠀⠀⠀⠀⠈⠛⠁⠀⢰⣶⠄
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠻⠿⠋

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠋⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠈⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⣠⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣴⠀⠀⠀⠰⢀⠀⠀⠀⢈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⣒⠀⠀⢰⣘⢗⣀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠂
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⡀⠀⣾⣤⣼⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠞⠛⢠⣿⣻⠆⠰⠄⠘⣻⣶⣶⠠⠂⠀⠴⡂⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⣤⣾⣧⣾⣭⣯⣥⣦⣬⣽⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠖⠒⢛⣛⣛⡋⣉⠉⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡏⣡⢶⣤⣶⡄⢾⣽⠃⢹⡇⠸⢷⣿⠀⣾⠋⠉⠉⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⢸⡇⣿⠟⠹⠟⣿⠘⠛⠦⠈⠁⠲⠾⠋⠀⣿⡀⣀⣀⡀⠛⢭⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠿⢶⡄⠀⠈⣷⢈⣁⣀⣤⣤⠴⠶⠚⠛⠛⠛⠛⠛⠙⠛⠉⠉⠉⠉⠉⠛⠛⠂⠀⣀⡴⠂⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⡄⢼⠀⣃⠀⢠⣟⣠⠶⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⢰⣦⣤⡤⢤⣤⣤⢴⣾⣋⢿⠀⠀⠀⣷⡂
⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⡇⠀⠘⠋⠁⠀⣄⣀⣀⣀⣀⣠⢤⣤⣶⠋⢻⡐⣷⠀⠀⠀⢸⠟⠁⢿⡾⠁⠻⡾⠀⠙⠿⠀⣼⠄⣿⡇⢀⣀⡀
⠀⠀⣠⠤⠔⠒⠒⠿⠿⠖⠷⠤⢤⡀⠀⠀⣾⢼⠃⣿⣀⡿⢸⣿⣼⡇⠈⠿⠉⠁⠀⠀⠀⠀⣶⠈⢁⡄⡀⠀⢀⣤⡄⠀⣼⡎⣿⠇⠘⠿⠃
⠀⠀⣿⠀⠁⠒⣒⠒⠒⠂⠈⣁⡀⠹⡆⠀⠋⠛⠀⠛⠉⠃⠈⠃⠀⠡⣄⠀⣶⠀⣴⠀⠀⡾⢿⠀⠀⣿⡇⠀⠈⡿⢧⡀⢸⡷⠀⢠⡄⠀⠀⣶⡆
⠀⠀⣿⣼⢻⣾⡏⡷⣼⢻⣷⡟⣷⢰⡇⠀⠀⠀⢠⣄⣴⣆⣀⠀⠀⠀⢻⠛⣬⠋⣸⠀⡼⣒⢽⡆⢸⡧⢹⡄⢠⣟⣛⣷⡀⠀⣄⣻⣿⣽⠁
⠀⠀⢸⣧⠈⠉⠛⣷⡿⠚⠋⣀⠿⣾⣁⠀⣀⣠⡤⣿⣿⠗⠯⢤⡀⢀⣬⡀⢈⣭⡄⠀⠉⠉⠉⠀⠻⠷⡴⠷⠈⠛⠋⠉⠀⠀⠀⠯⠟⠊
⠀⢰⢚⡛⠦⠿⠤⠤⠾⠦⠤⠿⠚⠉⠈⢳⠹⣤⠤⢾⣿⠶⠒⢾⠃⠀⣇⣿⣾⣬⣆⠀⠰⡎⣕⠢⢲⣒⢠⡄⢀⡤⢤⣄⢠⡖⠓⢢⠀⠀⣿⡶
⠀⢸⣀⣀⡀⣠⢦⢈⡿⣆⢀⣤⡄⢠⣤⢸⡇⣷⠀⢸⣿⡀⠀⡟⠀⢻⡿⠿⡿⠿⣿⠀⠀⠑⠞⠓⠲⠿⠛⠀⢸⡁⠀⠙⠏⠀⠀⣸⢁⣄⠈
⠀⠈⣿⠉⣷⡟⢸⣿⡇⣿⣼⠃⢧⣿⠈⣿⠃⢹⡀⢸⣿⣇⣰⠇⠀⢸⡷⢀⢀⡻⡇⠀⠃⠀⢀⣴⠖⠲⣤⠀⠈⠳⢤⡀⠀⠀⣰⠏⠘⣿⣿⠋
⠀⠀⣷⣀⡌⡑⠌⠻⢀⢊⣑⣠⢬⡗⢖⣿⠀⠀⡡⠐⣄⠀⣀⣀⠀⠀⠳⠶⠿⠶⠃⠀⢀⣀⣸⠇⠀⠀⢹⣇⡤⢤⡀⠈⠻⣿⠃⠀⠀⠉⣁⡀
⠀⠀⠙⠮⣟⣙⣋⣛⣋⣛⣭⠥⠖⠚⠋⠁⠀⠀⠣⣴⣿⣾⣥⡼⠃⢀⣄⠀⡀⠀⠀⢠⣟⠁⢿⠀⠀⠀⢸⡏⠀⢨⣷⠀⠰⣇⠀⠀⡴⠋⠁⠀⠙
⢀⡼⢦⣄⠀⠀⢀⣁⣀⣤⡄⠀⠀⠀⢗⣳⠀⣾⠙⢹⡏⢹⡏⠁⣳⣺⣿⣿⠿⢢⡾⠉⠈⢳⡼⣆⠀⢠⣿⡶⠛⠙⢷⡄⠀⠈⣷⢸⠃
⢉⣦⣌⣧⠸⣛⠿⠿⠟⠚⠃⢺⡳⢂⣞⣷⡀⢸⡂⢸⡇⢸⡃⠀⣽⢸⣿⢻⡇⢼⠁⠀⠀⢸⣿⠟⠻⣯⣿⠃⠀⠀⢸⡿⠀⢠⡏⠘⢇⡀⠀⣀⡴
⢈⡁⣀⠀⠀⠁⢀⣠⢦⡀⠠⣏⣷⠈⠙⡋⠀⠸⢧⣤⣧⣼⠥⠬⠗⠼⠿⠼⠃⠘⢦⣀⣠⣿⡏⠀⠀⣿⣿⡀⠀⢀⡼⠃⠈⠉⠀⢀⡞⠋⢉⡉⣀
⣸⣋⡻⠄⣀⡴⣉⣹⠛⠃⣀⡤⣤⣾⠁⣣⠀⡀⠀⠀⠀⠀⠀⣀⠴⣤⠀⠀⠀⠀⠀⠛⠃⢸⣇⠀⢰⡟⠀⠹⠟⢋⡤⠄⠠⢄⠀⢸⠀⢠⣸⣿⣿
⢀⡉⠀⠀⠱⢽⠋⠁⠶⣅⣻⠷⠜⠉⠀⢉⡾⢷⡀⠀⠀⡴⢏⣙⣴⣯⣷⢄⠀⠀⠀⠀⠂⢰⠈⣶⠏⢀⠀⡰⢰⠋⠀⠀⠀⠀⢧⠈⢧⠀⠘⠚⠁
⠈⠁⣴⡶⠶⠤⠤⠤⡤⣈⠁⠀⠀⠀⣔⡛⢒⣒⣛⣦⠈⣷⢦⣭⣤⢴⣶⡞⠀⢮⠀⠀⠈⠤⡂⠸⢀⠎⡐⠁⢹⡀⠀⠀⠀⢀⡾⠀⢸⢂⣰⣶⡀
⠀⠀⣿⡀⠟⠂⣀⣤⡾⢻⣧⣀⠀⡸⠇⢌⡡⠶⢤⠾⡄⢻⣻⣿⣸⣸⣿⠁⠀⣾⣗⠀⠀⠀⠙⣆⢂⠜⠀⠀⠈⣳⣤⣤⠴⠟⠁⠠⠋⠀⠙⠉
⠀⠀⠸⣧⣴⡟⠏⢉⣤⠾⣣⠏⠀⢹⡶⡶⢲⢲⣺⢹⠇⠀⠉⠉⠉⠉⢀⠎⠁⠁⠈⠉⠢⢄⠀⢸⡃⠀⠀⠀⡴⠋⠁⡀⠀⢰⣷⠀⠀⣿⡶⠂
⠀⠀⠀⠀⣻⠶⠶⣋⡵⠚⠁⣦⣤⠀⠳⠯⠿⠿⠷⠞⢀⡄⣴⣿⣄⡀⠹⣄⣀⣀⡀⣀⣠⡞⠀⣾⠇⠀⠀⠀⢇⠀⢾⡿⡇⢠⣠⢶⡀⠈⠁
⠀⠀⠀⠀⠷⠖⠋⠁⠀⠀⠒⣟⠯⠂⠀⠀⠀⠀⠀⠀⠀⣼⣻⣟⡞⠁⠀⠈⡇⣏⣯⣇⣿⡇⠀⠃⠐⠀⠀⠀⣸⠂⠈⠀⠀⣼⣦⣸⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣷⣿⣟⣛⣉⣁⣀⣀⣀⣀⣀⣞⣁⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀
⣿⣿⡛⣻⢛⡉⡛⣻⠛⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠁⠀⣤⠀⠀⠀⠁
⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡌⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⢰⠀⠃⡆⠀⢠⣤⣤⡀⠆⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠑⠂⠀⠴⣤⣄⠀⠀⢀⣴⣶⣶⣦⠀⠀⣤⡀⠒⠀⠀⠀⠀⠐⠓⠂⠀⠐⠀⠛⠛⠀⢰⡆⣿⡉⢸⣿⣿⣡⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠙⢯⣽⣽⣿⣛⣁⣀⣉⠋⠐⢲⣶⣶⡀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠉⣩⠄⣾⣿⣿⡦⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⠀⠒⠀⠀⠺⠿⠿⠿⠿⠿⠶⠶⠶⠛⠛⠙⠉⠉⠉⠁⠀⠀⠀⠀⠁⠒⠲⠬⢴⣿⣏⣹⣷⣠⣶⣿
⠀⠀⠀⢠⠀⢠⠀⠀⠇⠀⠉⣀⣌⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣏⣩⣉⢀⡒⠂⣰⠄⠐⠢⠀⠠⠤⠄⢀⢩⣙⡛⠿⣿⣿
⠀⠀⠀⠈⠠⣤⡰⣶⡎⠿⣷⢹⣿⡜⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢐⠒⠂⡮⠤⢴⣀⣠⡂⡀⣼⠃⠉⡸⠁⠑⡒⠚⠀⡤⠆⠀⣀⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠙⡇⠀⢱⠀⠸⣆⠈⢷⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⢀⠌⠀⢠⠃⠀⣰⠏⠈⠉⠋⠑⠓⡖⠐⠥⡤⢰⣀⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⠀⠘⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠤⢤⣆⣀⣠⠁⠀⣰⡟⠀⠀⡌⠀⠀⡌⠀⠀⢰⠁⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⣶⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣶⠛⠠⠤⠼⣀⣀⠰⠁⠀⢀⡇⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡖⣾⠖⠤⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠸⠿⠧⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠄⢠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣴⣶⣶⣄⠀⠀⠀⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠶⣀⢢⡈⠀⢀⢀⣀⣀⡈⢡⣼⢧⣀⡹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈
⠀⣹⣿⣿⣿⠇⣤⣶⣿⣗⢻⣿⠀⠴⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣤⣴⣶⣷⡄⠀⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣡⣄⠀⠀⠆
⠀⣿⣿⢿⡟⠀⣙⣣⣿⣿⡆⠃⠀⠀⠀⠀⢰⣿⣿⡟⣌⣥⠀⠀⠀⠀⢿⣿⣿⣿⣟⡁⡆⣼⠀⣤⠈⠛⠿⠃⢰⣧⡹⢿⣿⣇
⢾⣯⣿⣾⣧⣼⣿⣿⣽⡟⠁⣀⣿⠄⠀⠀⠀⠸⠟⠃⣿⣿⠀⢸⣷⡄⢼⠻⠛⢿⣿⢿⡆⠀⠀⠉⠀⠀⠀⠀⠀⡿⠟⠈⢻⣿⡇⢸⡿⣷⣦
⢰⣯⢁⠙⣿⣿⣿⠋⠀⠀⠀⠉⠉⢀⡴⠟⠀⠛⠂⠀⠈⣿⠀⠀⠉⠀⠀⠀⠀⢸⠁⠸⠇⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣀⡤⠀⠀⠷
⣼⠟⢘⣧⠈⠁⠁⠀⢀⡘⡀⠀⠀⢠⡇⢾⠆⢀⡄⠀⢾⣿⡇⠈⠀⠀⠀⠀⠀⠈⠀⢀⣀⠀⡤⠀⠀⠀⠀⠀⠈⠀⠀⣿⣆⠙⣧⠀⢠⣤⣴
⠀⠀⠛⠛⡀⠀⢠⣾⣿⣿⣧⣴⠇⣾⠀⠸⠇⢠⣿⠃⣾⡟⢡⠀⠀⠀⠀⠀⢀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⠆⠀⡔⣿⣿⣿
⢀⣀⠀⢘⣻⣷⣾⡿⠛⠛⠀⠆⣀⠋⡤⠀⠀⠻⠋⠀⠟⢐⡂⠀⠀⠐⣉⣁⡈⢀⠀⢺⣙⠁⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⣿⣿⣿
⠘⠻⠏⠀⢿⢿⣿⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⢿⣇⡀⣴⣿⣿⣷⣄⣿⣿⣿⣿⡮⠀⠀⠁⠀⠀⠀⠀⠠⢶⡀⠀⠀⠀⠻⢿⣔⠺⣾⣇⠈⠻
⣰⣶⠗⠀⠀⠊⠉⠀⠀⠀⠚⠿⣿⣿⠇⠀⠀⠈⣿⡀⠟⢿⣿⣿⣯⣿⣿⡿⠛⠁⠀⠀⠀⠀⣀⡀⠀⠀⠈⣷⡄⢠⣶⡶⠀⠈⠓⠻⣿⡆
⠈⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⠛⠀⠰⢄⣴⡻⢿⣆⢨⡿⠿⠿⣿⣯⡄⢠⣶⠾⠀⢰⠛⠿⢟⣀⣀⣠⣼⠿⠮⠁⡀⣠⣠⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠉⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣸⡟⠺⠃⠀⠀⠉⠋⠠⣀⡅⠲⠀⢠⣶⠃⢺⣿⠏⠈⣥⠀⠀⠀⠈⠛⠋⢀⡀⠀⠀⠐
⠀⢴⣶⡇⠀⠀⢠⠽⢃⡀⠀⠀⠀⠀⠁⠀⣠⣶⣦⡈⠁⣤⠀⠀⠀⠀⣀⡀⠛⠤⠀⠀⠸⠫⠀⣈⠉⠀⢀⡉⠀⢶⣦⠀⠀⣰⠿⠏⠽⠈⣗
⢰⣾⣿⡿⠀⠀⣶⠀⠈⣡⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣄⢰⡦⠀⠀⠀⡿⠓⠀⠀⠐⢁⠔⠀⠀⢙⣀⠀⣿⡄⠀⠀⠛⠀⠀⠉⠀⠀⠀⠐⠛
⠈⠉⠀⠀⣀⠀⢸⣶⡿⠃⠀⠀⠀⠀⠰⣤⣝⡛⠁⡈⢧⢸⡇⠀⠀⠀⣴⣾⠀⠀⠀⡖⠀⡀⢸⣿⣯⠁⠙⠿⠲⡷⠀⠀⠀⠀⢳⣤⠀⠀⢠
⠀⠀⠀⢸⣇⠀⢸⡿⠁⢀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⡦⢠⠤⢸⡏⠀⠀⠐⠉⠘⠻⡿⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀
⠀⢀⣤⣤⣤⡐⠛⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠋⡹⠀⠀⠀⠀⠀⠀⢀⣬⢉⣇⠒⠀⠀⠀⠀⠀⣩⠃⣸⣇⠀⢺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣻⣿⣿⣿⡏⠀⢰⣶⣧⣶⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠻⣥⣌⣬⣥⣦⡀⣿⠛⠂⠀⠸⣟⣹⣿⣷⣿⣿⢃⡀
⠀⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⢠⣾⣿⣷⡄⣠⠀⠀⡀⢰⣿⣿⣿⣿⣿⣷⣤⣤⣴⠆⠀⠉⠉⠉⠉⠀⢹⣿⣿⡇
⣼⡿⠿⠿⠁⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣷⠸⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⢿⣄⡀⠀⠀⢀⣸⣿⣿⣿⣷⣶⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣿⣿⣯⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣯⠈⠛⠿⣧⡙⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣇⡈⣻⡠⣤⠠⠾⠿⢷⠘⢥⣶⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠲⣄⠀⠐⠸⣇⡤⣶⠘⠃⢻
⠀⠀⠀⠀⠀⠉⠉⠉⠉⢛⣽⣿⣿⣧⠀⢀⣠⡀⢻⣴⣤⠛⣶⣄⣀⣀⠀⢀⣤⠄⢲⡶⠶⠄⣦⠀⢀⣤⡆⠀⠀⡆⠘
⠀⠀⢀⣤⣶⣶⣶⣄⠀⠢⡟⣿⡝⢹⣦⠈⢉⣽⠟⠁⠀⠀⣤⣤⡈⣷⡔⣬⡴⠀⣀⣀⡀⠀⠀⠀⠈⡇⠁⠿⡆⠾
⠀⠰⠿⠟⠛⠻⣿⣿⣄⡶⣿⣿⣷⣸⡿⠗⣀⠁⠿⢳⣶⣟⣿⣿⣷⣿⡷⣿⣇⣼⡋⢾⡿⢷⣄⣤⢴⡇⣤⠀⢠⡀⣴⣀
⠀⠀⣤⠀⠤⠄⢹⣿⣿⣿⣉⠭⠿⡋⠴⠀⣧⣄⢲⣿⣽⣿⡿⣿⣿⣿⣿⣮⣨⣿⣦⣬⠃⢸⣿⠙⠘⠀⠁⡄⢸⣷⢸⣿⡄
⠀⠀⣦⠀⠀⠀⠀⢺⡿⣜⣥⠀⠀⠁⠀⠀⠟⢻⣿⢿⣷⢶⠀⠷⢶⡿⢻⣿⣍⣿⣿⣿⡔⡛⡎⠰⣇⠀⡄⠇⠈⢠⣼⣿⠇
⢀⠀⣿⣯⣤⡄⠀⠀⡀⠙⣃⣀⠀⠀⠀⠀⢼⣿⣿⣄⠀⠀⠀⠀⠀⠀⣼⣿⡯⢽⣿⣿⠃⠀⠍⠋⢫⡆⠀⠀⠙⢿⣛⣺⡆⡀⣠
⠃⣠⣘⢻⣮⣅⠀⠰⡇⢈⠛⢿⡆⠀⠀⠀⣼⣿⣿⣧⡀⠈⠿⠅⠀⣠⣏⣽⣇⡜⣿⠋⠀⠀⠀⠀⠈⢋⣀⡁⣀⠀⠁⡀⣹⡟⠉
⠀⢀⣼⣷⠉⠙⠻⠄⠁⠈⢁⡷⢤⣀⣤⡀⣻⣿⣟⢿⣿⣄⣉⣁⣴⣿⣿⣿⠟⠙⠉⠀⠀⠀⠀⣴⡿⠛⠸⡁⣿⠿⠾⢛⡟⠆
⠀⠘⣥⡆⠀⠀⢸⠇⣴⡆⡼⠃⠘⢿⣶⡎⠿⣿⣦⠀⠈⢙⣿⣻⣉⣼⢯⣿⣶⣿⣆⠀⠀⠀⠀⣿⠀⠄⠀⢹⣧⠄⢀⡼⠇
⠀⠀⣼⢿⡇⠠⡹⠀⠀⡷⢠⠋⣴⣿⣿⣷⣶⣽⣻⣿⣷⣶⣬⣭⡛⠳⣤⣀⠘⠻⢥⣴⡂⢠⠆⠹⠀⠀⢰⡎⠉⠀⠈⠃
⠀⢰⠟⢸⡌⡀⠠⠀⠀⢠⣌⡾⢿⡿⠛⣿⣿⣿⠿⢛⡈⣩⣟⠉⠙⠃⠀⠙⠻⢷⣦⣌⠻⠈⣷⣶⣄⠀⢘⠡⢀⣦⡀⡀
⠀⣉⠰⠾⠑⠈⢲⠀⠀⣰⠘⣡⢟⣁⠞⠩⠋⣡⡔⠉⢿⠈⠹⠹⣷⣦⠀⠀⠀⠀⠙⢿⡃⠀⢉⣾⢿⡶⡿⢀⡸⠻⢿⣏
⠀⠀⣹⡷⣤⠀⢹⣇⣴⢇⡵⢃⡾⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠋⠀⠀⠀⢄⡀⠘⣆⢻⡀⠀⠁⠈⠋⠃⢸⣡⣁⣞⣩⡶
⠀⢰⡟⠀⠀⠀⠸⡇⠈⠘⣡⡿⣡⠆⣀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠈⠂⠁⠀⠀⠀⠀⣀⠀⢓⣀⢙⡁⡘⠁
⠀⠈⠁⠀⠀⡀⠀⠁⠀⢰⣿⡿⠁⠰⠃⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠆⠀⠀⠀⠀⠀⠀⠉⢘⡿⠟⣯⠛⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡀⣠⣀⣦⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⠆⠈⠃⠀⠀⡤⠙⠿⣯⢻⣧⡴⢋⡈⠟⣿⠣⣤⣤⣀⣶⣆⠀⠀⠰⢦⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠲⣼⣾⣿⣿⢻⣷⠰⢿⣿⣆⣰⠟⣹⠇⣀⣀⢰⡌⢿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⢼⡿⠀⡆⢰⠀⠙⠀⠐⢦⡌⠃⠈⢿⣇⠈⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠁⢀⠞⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣦⡀⢸⡟⣁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⡀
⠀⠀⠀⠈⠙⠻⠌⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠙⢏⡇
⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⡆⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠞⢛⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠸⡆
⠀⠀⠀⠀⠀⣿⡥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢾⡧⣿⠴⡧⢼⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠓⠒⢻⡀⠀⠀⠀⠤
⠀⠀⠀⠀⣸⡏⢉⡺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⡗⣿⠒⡗⢺⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⡖⠒⠒⢧⠀⠀⠀⠶
⠀⠀⠀⠠⣿⣿⣧⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇
⠀⣀⣀⣀⣀⣤⣤⣴⣶⡞⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⢹⠋⠉
⠀⠻⣿⣿⣿⣿⣿⣿⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⢠⣤⣄⣼⣿⡁⢹⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣽⣄⣀⢀⣀⡀
⠀⠀⠈⢻⣿⠿⠟⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⢨⣭⣯⣿⣭⡅⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⢡⣏⣺⣯⠽⠛⠉⠁
⠀⢰⡟⢳⡴⠖⠻⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣼⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢳⣿
⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠓⢾⡇


⠀⠀⠀⢀⣀⣤⣄⣀
⠀⣠⡾⠋⣤⣶⣶⠍⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣭⣤⣦⡔⣠⡀
⢠⡟⠀⠀⠘⢿⠏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣆⣀⣀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣵⣿⣷⡀
⢸⡇⣶⣶⣶⠎⢶⣶⣶⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⢹⣿⣿⡗⡀
⠀⢻⣜⠿⠋⠀⠈⠻⢟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣉⣿⠻⠟⠃⢻⣧⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣇⣺⣿⣿⡇⡇
⠀⠀⠉⠳⠶⠴⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠷⠝⠿⣿⡯⠜⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⢙⡯⠛⠂⠀⠂⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣀⠀⠀⠀⠀⠀⢠⠊⠄⠐⠆⠘⡅⣄⠀⠀⠀⠠⠀⡼⠀⠄⠀⢀⡀⠀⠀⠀⠈⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡄⠀⠈⡶⠉⠀⠐⠒⠲⢸⡀⢀⣤⠀⢀⣼⠁⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠈⠉⠐⠂⢲⠀⠀⢙⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠁⡼⣤⠄⠀⢐⠀⠀⠀⢀⠀⠀⢗⣠⣦⣔⡺⠃⠀⠀⠀⢀⣀⠤⠤⠤⢄⡀⠀⠀⠀⢻⡾⠛⠆⡀⠈
⠀⠀⠀⢀⠀⠀⠁⠜⠶⣶⠃⠀⠀⠈⢃⡀⠀⠀⠀⠀⠜⡹⠷⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠘⢆⢀⡀⡀⠁⠀⢠⡜
⠀⠀⠀⠁⠀⡐⠁⠀⠀⠈⠀⠀⠀⠀⢀⠔⠊⠉⠁⠀⠢⡀⢀⠀⠀⠀⠂⠀⠃⠀⠞⠀⠙⠒⠀⠀⠠⢸⠋⠀⢰⣚⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⡆⠀⠄⠀⠁⡤⠀⠀⠀⢆⣀⠀⡄⠀⡆⠀⠘⣤⣤⡇⠀⠀⠀⣸⠛⠁⠀⠈⣠⠠⢤⡀
⠀⠸⠁⠀⠀⠀⠀⠀⠀⠊⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⢄⡘⠤⡲⠃⣈⡙⠢⠔⠃⠾⠁⠀⠀⠀⢆⣀⢀⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢇⣀⠀⠲⠆⠀⠀⠀⢠⠾⠅⠀⠀⠘⠉⠑⠠⠥⠥⠤⠴⠒⠁⣀⣤⣀⡀⢄⠙⠛⠛⠇
⠀⠀⠀⠠⢃⡀⠀⠀⢀⠔⠊⠉⠉⠳⣤⡑⠒⠶⠦⠴⠂⡠⣞⠀⠀⠸⠶⠢⠤⢀⡀⠀⠀⠀⢀⠀⡜⠠⠘⠲⠈⢢⣣⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠁⠠⠀⡎⠀⠀⠈⢺⡆⠈⣏⠋⠒⠒⢿⠁⠀⠀⠠⠀⡠⠂⠅⠈⣐⠋⠛⠀⠐⠚⠘⠂⠐⣶⣶⠀⢰⣿⡶⠴⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣸⠤⡟⠂⠀⠡⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠚⠓⠦⢺⠇⠈⢯⡅⠈⢌⠧⡔⣿⣯⣦⢾⡿⠀⠜⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣑⡐⠒⠒⣠⠔⠓⠒⡄⠀⢹⣄⡀⠀⡀⢸⠀⠀⢀⣀⠀⠀⠀⠀⣆⠀⠀⠑⠒⢡⣭⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈⠁⠉⠋⠀⠀⠀⠚⠏⠛⠀⠀⠀⢠⣀⠢⡄⡈⠏⣀⣀⠼⡵⠓⠁⠀⢀⠐⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠎⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠥⠤⠖⠺⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⢠⡞⢭⣱⠂⠀⠀⠀⠀⠀⣿⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⢻⡿⠆⠀⠀⠀⠀⢀⡴⢯⣍⡢⠁⠀⠀⠀⠀⠐⠛⠻⣿⠟⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠞⠣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡈⠳⠃⠀⠀⢀⠤⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠳⠎⠀⠀⠀⠀⢠⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡋⠁⠀⠀⢎⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⠂⠀⠀⠀⠀⠀⡔⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠢⢄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡄⠀⠀⠀⠀⠀⣤⠰⠃⠑⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠈⠢⣄⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⣔⠲⠈⢃⠿⠟⠀⠀⠀⠀⠀⢙⣀⠤⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠓⢄⠀⠀⢈⠀⠀⢸⠀⠀⠀⢀⡤⢤⠀⠙⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠈⠢⡀⠀⠑⠚⠙⢄⣀⠤⡈⠻⢸⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⣴⣿⠙⠬⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠙⡆⡹⠶⠃⠀⠀⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⣴⠛⠫⣸⡿⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢀⣼⣿⣿⣿⣿⣦⡀⠰⠿⠟⠣⡀⠀⠀⠀⠀⢂⠀⢀⡄⠀⠀⠀⠀⠘⠺⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣴⣿⣿⣿⣿⡿⠋⠁⠈⠲⢄⠀⠀⠘⢄⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣠⣾⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣶⣿⣦⣤⣨
⠀⠀⠀⠀⠀⠀⣼⡿⠁⢀⣼⣿⣿⡿⠋⠁⠀⢀⣠⣴⣾⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⢰⡟⠀⣴⣿⣿⠟⠁⠀⣠⣴⣾⣿⡿⠟⠋⠉
⠀⠀⠀⠀⢠⡟⣠⣾⡿⠋⣁⣤⣶⡿⠟⠛⠉
⠀⠀⠀⢀⣿⣼⢟⣩⡴⠟⠛⠉
⠀⠀⠀⣾⠿⠛⠉⠁


⣿⣿⣿⣶⣶⡿⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣶⡿⡶⠿⡶⠶⠾⣶⡶⠶⠾⠶⠶⠾⠿⡾⠷⠿⠶⠿⢷

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠄⡀⠀⢤
⠀⠀⢏⢀⠀⠀⠀⠀⠀⠒⠁⠀⠀⣀⠀⠀⡼⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠠⠘⠆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠙⣆⠀⠀⠀⠠⡠⡄⠀⠀⠀⠘⠉⠂⠀⠀⠀⢇⡠⠀⠈⠉
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠅⠤⠒⠁⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠂⣤⠁
⠀⠈⠀⠀⣴⠀⠀⢀⡀⢰⡆⢢⠀⠀⢠⠀⠀⠀⡤⠠⡀⢰⡄⣀⢀⠀⢤⠄⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠙⡀
⠀⠀⠀⠀⡟⠀⠃⣼⢡⠀⡇⠁⡆⠀⠈⣧⠀⠀⢿⠐⠄⢸⠀⣿⠀⠀⢸⠀⡏⢀⠸⡆⠀⢠⠄⢳⡐⠀⠀⠄
⠀⠈⠀⠀⠁⠀⠘⠃⠀⠀⠁⢠⡇⠈⠀⠇⠀⠀⠸⠤⠂⠈⠀⠟⠀⡀⠈⠀⠃⠀⠀⠃⢠⠟⠂⠀⡇⠀⠰
⠀⠀⠀⠈⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠆⡄⡈⠀⠐⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⡄⠀⠁
⠀⠈⠀⠀⠀⠆⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢗⡂⠨⠈⠐⢱⠀⠀⠀⠎⠑⠊⢁
⡀⠀⢀⠀⢀⠖⠁⠤⡀⠀⠀⡤⠀⠀⠈⠂⠐⠄⠄⠀⠀⠀⠀⢠⣤⠴⠦⠒⠛⠁⠀⠀⠈⠢⠠⠁⠀⣀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣿⡯⠍⠀⡭⣙⠙⠀⠀⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡽⠾⢿⣿⠛⠁⠀⠀⠴⠀⠈⠁⠲⣄⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⠅⢀⣴⣿⣃⣠⣄⣀⡀⠀⠔⠀⠀⠀⠈⠛⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⡤⢫⣿⣿⠏⠀⠀⣉⠙⠳⢦⡀⠀⠈⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠫⠐⡴⠃⢠⣿⡏⠀⠀⠘⠛⣆⠀⠈⠻⢶⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠠⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢟⠀⠀⣸⡟⠁⠀⣿⣿⣄⢘⠂⠀⢠⠃⠀⠀⠃⠌⡿⣶⡇⠂⠐⠲⠀⢷⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣆⠀⡼⢻⣿⣿⠁⠀⡴⢦⡞⢉⣾⠄⠀⠒⠈⠻⣶⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣗⠀⣿⠀⢸⣿⠀⣦⠀⣾⣥⣾⣿⢿⣶⣴⢀⣴⣻⠿⣾⣶⡆⠀⣻⣦⠀⢀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢏⡀⣿⠀⠸⣿⣿⣇⠀⣇⠈⢉⡡⠾⣿⣿⣧⣸⠁⠸⠟⣿⠃⠠⠃⡆⠀⡏⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠐⣿⣄⡀⠈⠛⢿⣷⣿⣧⣾⣷⣤⣿⣿⣿⣿⣤⣤⣴⣟⣤⣖⣨⠃⣘⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢻⣟⣫⣿⣦⡈⣠⣭⣿⣽⣿⣿⣉⢻⢿⣿⣿⣿⣿⣿⣿⡏⣈⢧⡀⠟⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠻⠋⠉⠉⠛⢻⣾⡿⣛⢻⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣧⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠛⠿⠿⠟⠷⠷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⠅⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠄⠀⠀⢘⠟⠋⣿⣧⣿⣿⡿⢽⡿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠈⠀⠘⣭⡾⢶⣿⡻⠟⠋⣰⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣉⣁⣄⣠⣬⠋⠀⠀⣽⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣟⠋⠁⠀⠀⢀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⣨⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢚⡀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠈⠉⠁⠀⠀⠰⠾⠭⠭⣄⣸⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢃⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⣁⠠⠀⠉⠀⠀⠐⠡⠀⠀⢤⣶⣚⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠒⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠋⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠼⠇
⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⢤⠟⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠖⠓⠒⠒⠠⡀
⠀⠀⠀⠀⢐⡂⠉⠀⠐⠀⠰⡃⠀⠀⣴⠒⠉⠀⠀⠀⠀⢀⠔⠁⠀⠈⠢⡀⠀⢊⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠪⡇⠈⠉⠀⠐⠂⠰⠅⣀⡂⠠⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⢄⠀⠀⠀⠀⠀⢈⡄⡽⠍⠍⠉⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠅⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠒⠂⠤⡀⠔⠀⠀⠐⠀⠀⢀⠀⣠⠎⠀⣹⠄⠉⠁⠀⠋⢋⢀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠁⠀⠀⠀⠀⢸⠉⠐⠂⠀⣞⠇⠐⠀⣸⠁⠀⠀⠀⠐⠁⠑⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⣾⠀⠀⠀⠀⡇⡈⠀⠀⣼⠕⠀⠀⠀⠨⠀⠀⠨⡏⠁
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠠⠊⠀⣠⠞⢽⠀⠀⠀⢠⠷⠤⠴⠤⣼⢔⢥⠀⠀⡠⡢⢤⣼⣇⡀⠠⠤⠄
⠀⠀⠀⠀⠈⠐⠠⠀⠐⠀⠰⢸⡶⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⠒⡛⠫⠀⠠⢺⢀⠀⠀⠠⠤⠠⠄⠤⢾⢤⣤⡀⠀⢝⣵⢟⣾⡷⡾⠿⣛⣒⣂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠣⢀⡀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠄⠄⠐⡀⣸⠅⠄⠀⠸⡓⠚⠐⢶⠟⣿⣛⠗⠐⠑⢑⣿⠟⠉⠉⠑⠤⠀⠀⠒⢓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠃⠥⠄⠀⢈⠠⠀⡠⠀⢀⠀⣼⢄⠀⡀⠸⠀⠀⡼⠃⠀⠀⠉⠁⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠔⠁⣡⠅⣜⠁⡈⠄⠘⣠⠜⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⡀⠊⠨⠁⣠⠏⠙⠛⠳⠼⠯⠀⠀⠀⢀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂⢈⠀⢄⢄⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠄⢰⣿⣧⣸⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠠⣾⣯⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⡆
⠀⠀⠀⢠⣾⣿⣿⡟⠀⠈⠹⣿⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣴⣶⣶⣶⣦⡀
⠀⠀⠀⣼⣿⣿⡟⠃⠀⠀⢀⠟⣿⣿⣿⣿⣿⣿⣿⠆⠀⡀⢠⣤⣀⣤⣤⣦⣄⡀⠀⠀⠀⠀⣴⣾⣿⠟⡁⢀⠉⠀⠉⠙⠛⠷⠆
⠀⠀⢰⣿⣿⡟⠛⠳⠀⢠⢶⣦⣿⣿⣿⣿⣿⣿⠟⣳⣿⣄⣾⣿⣿⠿⣿⡿⣿⣿⣂⣀⢠⣾⣻⣿⣷⡟⠀⢊⣄⠀⡀
⠀⠀⢰⣿⣿⠃⠀⠀⠀⠄⠀⠈⠀⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣭⣽⣿⣿⣿⣯⢀⣴⣿⢿⣿⣄
⠀⠀⢸⠉⣿⣧⡀⠆⠴⢦⣄⣾⡆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⢿⣿⣛⠻⢷⣄⡄⡀⢰⡂
⠀⠀⠀⠀⣸⠟⢿⡀⠂⢀⣬⣤⡴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡑⣍⡉⠀⣾⠏⠸⠏⣛⠁
⠀⠀⠀⠀⠹⣦⡈⠓⢶⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢤⣠⢽⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠙⣿⣦⣄⠀⠙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⠻⠿⠿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⢿⣾⡧⠀⡈
⠀⠀⠀⠀⠀⠀⠙⢹⣮⣶⣶⡄⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⠀⠈⣉⣉⣁⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⡠⠁⡀⠳⡀
⠀⠀⠀⠀⠀⠀⣠⡞⠀⠙⣿⣿⣄⢹⣿⣿⣿⣿⣿⠿⣿⠻⠿⠛⠃⠀⠐⠿⠿⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡀⠀⢠⠀⠀⣴⡇
⠀⠀⣀⡀⠀⠀⣀⣀⣤⡄⢻⡹⣿⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⠁⠀⠀⠀⠀⠙⢷⡀
⠀⠀⣀⣽⢿⣶⣯⣍⣩⠒⠈⡙⢻⢯⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿⣿⣿⣿⣿⢙⡟
⠀⠰⣿⣿⣿⣿⣥⠿⣍⣾⣦⣤⣛⡛⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⢿⣶⠟⠃⠀⠀⠀⡼⢁⣾⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠉⠛⠛⠓⢾⣯⣯⣿⣿⣿⣿⣿⠿⣟⣿⣿⣿⣿⣿⣆⡀⢐⠒⠲⠒⠒⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠹⠙⠛⠿⢿⣽⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⠛⠋⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⠶⢶⣶⣦⣤⣀⡀⠈
⠀⠀⠀⠀⠀⢦⠰⣶⠀⠀⢠⣽⣻⣿⣿⠿⠿⠉⠉⠙⢿⣿⣿⣿⣶⣶⣶⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣶⣿⡇⠀⠀⠈⣿⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠻⡟⢋⡀⠀⠀⠀⢰⣶⡀⠀⢸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣙⣿⠀⠲⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠻⠟⣶⠄⠀⣸⣏⣇⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠜⢣⡀⣼⠀⠀⠀⠀⢀⣴⣾⣤⣄⣴⣤⣤⣾⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠐⢗⠀⢀⣤⣴⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠙⠄⣘⠇⠀⠀⣄⣴⣶⣾⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡀⠀⠀⣼⣷⣌⢿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠁⠉
⠀⠀⠀⠀⢰⠀⠀⢀⢌⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⣿⣿⣿⡀⠠⢭⣛⣛⢓⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠀⠀⠋⠈⢿⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⢛⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠠⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⡗⢰⡆⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣨⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⣤⠀⣀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣽⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢉⡏⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠿⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠛⠿⠐⠿⠟⠀⠁

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⢸⣿⣶⡦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⢸⣿⣿⠗⠀⢰⣤⣤⣤⠀⢠⣤⣤⣤⠄⠀⣤⣶⣶⠆⠀⠹⣿⣿⡇⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠈⣿⡿⠃⠀⠀⢻⣿⡏⠀⠀⠘⢿⡿⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣶⣄
⠀⠀⠀⠀⠀⠀⣰⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠆⠀⠀⠀⠀⡶⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⣾⣷⠆⠀⠀⠀⠹⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠸⡿⠀⠀⠀⣴⡯⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢰⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢿⠇⠀⠀⢠⣿⡄⠀⠀⢸⣷⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣼⣄⠀⠀⠀⣼⣤⠀⠀⠀⣰⣇⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡄⠀⠀⠘⠿⠇⠀⠀⠀⠛⠃⠀⠀⠀⠉⠃⠀⠀⠀⠛⠋⠀⠀⠀⠿⠿⠀⠀⠀⣴⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⡀⠀⠀⠀⠀⠿⠋⠁⠀⣿⣶⡆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠻⣿⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⢹⡿⠋⠀⢻⣶⡶⠀⢰⣶⣤⠄⠠⣤⣶⠆⠀⢶⣾⡇⠀⠙⢿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠀⠀⠀⢿⠏⠀⠀⠹⡟⠀⠀⠈⠛

⠀⡀
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡤⠀⠀⢸⡇⠀⠀⢠⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡀⠀⠈⢹⢿⡟⠂⠀⢸⡇⠀⠐⢻⡿⡏⠁⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠈⠻⣦⡀⠈⢷⡀⠈⠁⢀⣾⠁⢀⣠⠞⠁⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⣿⠧⠀⠀⡀⠈⠁⠀⠘⣷⡀⢀⣾⠃⠀⠈⠁⢀⠀⠀⠼⣿⡿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠳⢶⣤⣤⣿⣿⣿⣿⣤⣤⡶⠞⠛⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡁⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⡴⠾⠛⠛⣿⣿⣿⣿⠛⠛⠷⢦⣤⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⡖⠀⠀⠁⢀⡀⠀⢠⡿⠁⠈⢿⡄⠀⢀⡀⠈⠀⠀⢲⣿⣷⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⢀⣴⠟⠁⢀⡾⠁⢀⡀⠈⢿⡀⠈⠙⢦⡀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠁⠀⢀⣸⣾⣧⠄⠀⢸⡇⠀⠀⣼⣷⣇⡀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠓⠀⠀⢸⡇⠀⠀⠘⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡄⠰⠶⠀⣀⢀⣤⣄⠀⠐⣀⠀⠀⠀⣀⡀⢀⣤⡄⠀⡤⢤⣤⠀⠀⠀⠀⠀⡸⠛
⣶⠀⠀⠀⠀⠀⠉⠉⢁⠀⠀⠀⠀⠀⠀⠙⡿⠁⣾⢶⡏⠀⠀⠈⠟⢑⢘⡫⡅⠀⣥⡽⢤⣿⡷⠀⡀⠀⠀⠀⠰⡿⠃
⠩⣿⣶⠀⠀⢀⣺⡗⡈⡇⠀⠀⠐⠀⠀⣠⣤⡌⠛⣈⡀⠀⠀⠀⡀⡀⠿⣀⠀⠀⡿⡅⢀⠛⠀⠀⠟⠀⣤⣀⡎⢀⠀⠀⢰⠂⣧
⣤⣾⣿⡧⠀⢠⡅⠀⢃⡀⠀⠀⠀⠀⢸⣿⣿⡿⣠⠈⠀⠀⠀⠀⣿⠇⠀⠀⠒⠠⠇⠀⢘⡃⠀⣿⡀⠀⠈⠟⠛⠋⠁⠀⠀⠐⠚
⠉⠉⠀⢀⡀⠀⣧⣾⣿⣿⠀⠀⣠⣤⣤⣛⠋⢁⣾⡄⠀⠀⠀⠀⠑⣊⣤⡀⢰⡇⠀⢀⣿⣿⠧⠙⠿⠀⠀⠀⣀⣺⣿⣤⢄⣀⡠
⠀⠀⠀⣿⣅⠀⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠤⢸⡏⢈⣀⡎⠁⠛⠿⢿⠁⠀⠀⠀⠀⢸⠟⠋⠁⠹⠿⠀⠉⠳
⠀⠀⠀⠉⠻⡞⠉⠙⣿⣶⣿⡟⠉⠉⣝⠋⣩⠇⠀⠀⠀⠀⠀⢠⡀⠉⠛⠉⠁⢀⠀⠀⢠⡀⠀⠀⠀⠀⢈⠛⠘⠷⢠
⠀⠀⠀⠀⠘⠃⠀⠀⠙⠛⠋⠀⠀⠚⠛⠛⠋⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠋⠀⠀⠘⠛⠃⠀⠀⠀⠈⠀⠀⠀⠙

⠀⠀⠋⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠂⠑⡄
⠀⡀⠀⠀⠀⠀⠁⠈⠉⠐⠒⠂⠤⠤⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠔⠒⠂⠀⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡏
⠀⠀⠀⢃⠈⠑⠦⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⡄⠴⢺⠁⠀⢰
⠀⠀⠀⢸⢀⡀⢸⠀⠀⠀⠀⠉⠐⠒⠠⠄⣀⠀⠐⢀⡀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠰⠖⠂⠁⠀⠀⠀⠈⣄⡀⢸
⠀⠀⠀⣼⠖⠱⣢⠀⠀⠀⠀⠀⡀⠀⡀⠂⡈⠀⠀⠀⠙⣀⠀⠘⡄⠀⠀⠀⠀⡠⠁⠀⠁⠀⠀⠀⠀⠀⠹⡕⢾⡀
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣀⢈⣀⠀⠀⠀⡁⠀⠀⠀⠀⡀⢣⡀⠈⠢⡠⠔⠊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠑⠄⠀⣁⠴⠃⣉⡀⢉⡈⠋⢦⠘
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠈⣀⠃⠔⠉⠀⠀⠀⠀⠑⢌⢱⡠⠂⠉⠈⠉⠒⣄⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠗⡈⠀⠀⠀⢀⡀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡰⠠⡁⠀⣀⣀⣀⣀⣀⣤⠀⠐⠀⠀⠀⠀⠀⠀⡰⠀⠀⠘⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢠⡘⠋⠁⠈⠉⠁⡰⠇⠀⠀⠀⠀⣠⠖⠁⠀⠀⣠⠼⣳⢄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⡊⠀⠠⠆⢤⡒⣛⠓⠂⢲⣄⠀⠀⠀⠑⠂⠀⢃
⠀⠀⠈⠉⠐⠢⣀⠘⠀⠀⠀⠐⠗⢀⠀⠀⠀⣀⠀⠋⠂⠀⠀⠈⠒⠢⢄⠲⠐⠲⠡⠞⠁⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⢀⠖⠲⠒⠶⠦⠱⢶⡆⠡⠀⢀⠘⠠⠄⠠⠐⠤⠀⠷⠃⠀⠀⢤⠤⠔⢉⠀⣀⠄⠒⣀⢘
⠀⠀⢀⠀⠀⠀⠀⣇⢼⠀⡠⠀⠀⡀⠀⠘⡰⠆⠀⠀⠆⠀⠀⠰⠄⠀⠄⠀⠉⠛⢳⠊⢲⠚⠖⡳⡴⠶⢦⡉⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⢹⡶⡄⠺⠀⠁⠐⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⢣⠈⠹⡆⢠⣇⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠈⠀⠀⠀⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠀⠤⢺⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠐⢊⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠈⠄⠀⠙⠂⠤⡀⠀⢀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢰⠀⠸⡀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠒⠦⣄⡀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠈⠐⠠⢀⣉⡐⠂⠤⠤⠤⠤⠐⠊⠁⣀⠤⠊⠁⠀⠀⠀⠉⠓⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠇⠀⠀⠀⠀⠩⠉⠉⠋⠛⠃⠐⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⡀⠤⠀⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⣶⠀⠀⠐⢁⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠴⠙⢦⡀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠊⠀⠀⠀⠉⠒⠒⠊⠀⠀⠀⠀⠀⠈⠢

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣀
⣿⣛⣛⣛⣛⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣽⣿⣯⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⠀⠀⠀⠀⢠⡄⠛
⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠈⢀⠂⠀⠐⠀⠀⠀⠦
⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁
⠠⠠⠄⠋⠀⠲⠹⣦⣄⢀⣀
⠀⠀⠤⠀⠀⠀⠀⣹⣿⣿⣧⣤⣄⣴⡶⢲⠆⢀⡄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠀⠀⣽⡝⠈⢦⡌⣻⣧⣤⠀⠀⣬⣟⡞⠉⢳⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠔⠀⠀⠀⠀⠉⠁⢀⣸⣤⣉⡛⠿⡄⠀⡡⠟⠉⠀⠀⡈⠀⠀⠀⠀⠀⠄⠀⠀⢀⣴⣿⣿⡏
⠈⠁⡀⠁⠰⠆⠀⠀⡄⠀⣻⠉⢘⠢⢄⣷⣻⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⡰⠏⠀⠀⠀⠀⠰⣤⡀
⣤⣄⣈⣠⣄⣤⣤⣤⣤⣤⣿⣶⣦⣤⣄⣨⣿⣦⣄⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣠⣤⣴⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⡀⠀⢰⣄⠀⣾⡅⢀⡤⠀⢀⣿⣷⠂
⠀⠀⠀⠀⠰⣿⡀⠀⠀⢀⢴⣶⣾⠛⣴⡆⢀⣿⡇⠀⣼⣄⣰⣇⣀⣻⣏⣀⣿⣇⣼⣧⣀⣾⣿⣿⣄⣀
⠀⠀⠀⠀⢰⣿⠟⣳⣀⠈⠈⠠⣤⣀⣽⣷⣾⣿⣿⡿⢋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢀⣤⣤⡶⠟⢻⣿⣿⡦⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠘⠛⠉⢀⣶⣾⣿⢿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣴⣾⠛⡿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⡋
⠀⠀⠀⠠⠙⣿⣭⣴⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⡈⣿⣿⢿⣿⣿⣿⡿⠿⡻⢿⣿⣛⣿⠟⠛⠿⣿⠿⢏⡀
⠀⠀⠀⠀⠀⠙⠿⣿⠿⠉⠉⠹⠛⠉⠁⠀⠀⠉⠑⠀⠘⠩⠋⠁⠀⠀⠀⠻⣏⡍⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀⣀⠀⣠⠤⠶⠤⣄
⠀⠀⠀⠀⣠⠚⠉⠉⠉⠙⠢⠤⢤⡞⠑⠞⠁⠀⢸⠁⠀⠉⡡⠤⢤⡀⠈⢳⠲⠤⣄
⠀⠀⠀⢰⠁⢀⡤⠒⠦⣀⣄⡀⠀⠓⢤⡀⣠⠒⢉⣰⠉⠉⠀⠀⣀⣱⠀⠸⣄⠀⠈⠣⢤⡀
⠀⠀⠀⢸⡀⢺⠀⠀⠀⠉⠀⠃⠀⠀⠀⢱⣇⠀⠏⠀⠀⠀⠀⠘⠁⠀⣳⠀⠈⠳⠤⡀⠀⠙⠦⠲⢄
⠀⠀⠀⠀⢳⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⡶⠒⠲⠤⠒⠢⢤⡀⠀⠁⠀⠀⠀⠀⢸⡤⠔⠒⠤⡼
⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠙⠚⠉⢦⡀⠙⣄⡀⠀⠀⠀⡴⠲⠔⠉⠉⠳⡘⡆
⠀⠀⠀⠈⣇⠈⠉⠉⠱⣄⠀⠀⣀⢔⣒⣦⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠰⢣⡃
⠀⠀⠀⠀⠈⠑⠒⢤⣀⠴⣍⠉⢁⡜⢲⠚⡖⢻⠒⠒⠒⣿⠒⠒⢺⠓⡞⢲⣾⣦⣀⣤⣄⣀⣀⣀⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⡏⣏⢹⠉⠉⠉⣿⠉⠉⢹⠉⡏⣟⣏⣻⣛⣛⣻⣛⣛⣿⣹⣛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣀⣀⣖⣆⣯⢿⢹⠉⠉⠉⣿⠉⠉⢹⢹⢋⣧⣯⢼⠤⠤⣼⠤⠤⣯⣼⡼
⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣹⢸⢸⡇⠀⢠⡛⡄⠀⢸⢸⢸⢹⣷⢸⠀⠀⢸⠀⠀⡇⣸⡇
⠀⠀⠀⠀⠀⠘⢦⢤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣸⣇⣠⡻⠋⢞⣆⣼⣸⣼⢸⣿⣸⠀⠀⣸⠀⠀⣇⣻⡇
⠀⣀⣀⣀⣀⣀⣸⢸⣽⢼⢽⣭⡯⡯⣯⡽⡿⢸⡵⣿⣧⠀⣼⣯⢿⠘⡿⣼⡏⢹⠉⠉⢹⠉⠉⡏⢹⣇⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣸⣺⢺⢺⣒⡗⡗⣗⡇⡇⣼⡝⠉⢉⣿⡉⠁⢻⣣⡇⡟⡇⢸⠀⠀⢸⠀⠀⣇⢸⢻
⠀⠀⠀⡏⢉⣉⠉⣉⠉⣉⠉⣉⠉⣉⣹⢡⠿⣼⠷⠶⠾⣿⠷⠶⢾⡧⢧⢹⠃⡎⠀⠀⢸⠀⠀⢸⠘⡜⡄
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⣿⡏⡸⠀⡇⠀⠀⠀⣿⠀⠀⠈⡇⠸⡈⣦⣇⣀⣀⣸⣀⣀⣸⣄⣧⣷
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⡿⢳⠗⢒⠗⠒⠒⠒⣿⠒⠒⠒⢷⠒⢷⠻⣄⣀⣀⣸⣀⣀⣀⣇⣘⣆⣧
⠀⠀⠀⢧⣸⣿⣤⣿⣤⣿⣤⣿⣴⠧⡼⠤⣼⠤⠤⠤⠤⣿⠤⠤⠤⠼⡤⠼⡦⢵⡤⠤⢼⠤⠤⠤⢼⡤⠽⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡾⠒⢲⠗⠒⠒⠒⠒⣿⠒⠒⠒⠒⢷⠒⠺⡖⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠆⠀⣀⠀⠂⠀⠀⠈⢀⡤⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠻⣥⠓
⠀⠀⠀⠐⠀⠀⠠⠄⠈⠁⠄⠀⠀⠐⠹⠀⠀⠀⠀⣀⢀⠂⠐⠲⠀⡠⠀⠁⠀⠀⠀⠀⠝⠀⠍⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⣀⡀⠀⠘⠚⠉⠀⠀⠐⢬⠇⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠘⠀⠉⠀⠀⠰⠄⠀⡀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠗
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⢴⠇⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠰⣶
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⠀⣶⡶⠸⡆⠀⣸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⢦⡀⠀⢻⠟⠀⠙⢦⣽⣥⠾⠁⠀⣦⠀⢀⣇⠀⢰⠆⠀⣦⠀⢀⣆⠀⠀⠀⢠⡄⠀⣠⣇⠀⣾⠀⠀⢰⣀⠀⠀⣀⠀⡀⠀⠀⢀⣄⠀⢀⡆
⠀⠈⠀⣀⣻⣋⣠⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⢦⣙⣟⣤⠟⠀⠀⠘⢦⣙⣟⣠⣄⡀⠀⠹⣦⣙⣯⡴⠃⠀⠀⣙⣿⣤⠴⠋⠀⠙⠶⣤⣘⣟⣠⠞⠁
⠀⠀⢸⡍⣿⣿⠀⠀⠀⠀⢀⣼⠋⠻⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠙⠂⠀⠀⢹⣿⡇⠀⠀⣞⠹⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡇⢀⡀
⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⡾⠁⠀⠀⠙⣧⠀⠀⠀⣿⢻⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠙⠀⣿⠻⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠐⠀⠀⠐⠠⠌
⠀⠀⠀⠀⢠⡾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣄⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⣿⢋⡿⠋⠙⠁⠀⠀⠀⠀⠀⢐⣯⣽⡛⣿⡏⠛⠁⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠳⠀⠘⠀⢰⡃
⠀⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⠛⢷⣄⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡄⠄⠀⣠⣤⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⡀⠀⢈⣻⡆⠘⢿⣿⣿⣿⣷⡿⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠟⠁⠀⠀⠀⠀⣾⣿⡄⠀⠀⣾⣿⣇⠀⠀⡌⠻⣷⣶⣸⣿⣿⣏⣀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⣦⣤⡻⢿⣋⣠⡄⢟⢆⢸⡿⣿⣻⡟⣿⣿⣿⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣯⡿⣧⣬⣭⣥⣴⡶⠟⠋
⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⣿⣟⣯⣴⣮⣥⣼⣿⢿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⢙⣛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣻⣷⣸⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⡷⠶⠶⠾⠀⠀⠸⠶⠶⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⠙⣿⣹⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⣿⣿⣿⢸⣿⢸⣿⢹⣿⢻⣿⠟⠘⠿⠘⢛⣿⠟⣿⡏⠁
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⠁⠉⢸⣿⢸⣿⢸⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠉⢸⣿⢸⣿⠀⠀⠀⠀⠐⠿⠃⠿⠃
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿

⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⡉⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠂⠀⠀⠙⠒⠀⠄⡀
⠀⠀⠀⢀⡠⠴⠛⠛⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⡏⠀⠀⠀⣀⠔⢲⣿⠭⠥⠔⠓⠒⠀⠀⠀⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢳⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣰⠋⠀⠀⠀⣀⣠⡤⠶⠖⣒⣈⣉⣩⠭⠉⠒⠲⣄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢿⡀⠀⣀⡻⠮⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁⠂⠆⠀⠀⠋⠈⠀⠇
⢈⠟⠋⠁⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠰⠶⠶⢋⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣿⠀⠀⣀⠤⠶⣚⣛⣯⠥⠶⠒⠚⠃⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⡄⠁
⠙⢦⣀⣀⡴⠋⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠴⠋⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢀⡞⢡⡞⠀⠀⢀⡤⠶⢶⣽⡋⣩⠟⠉⠋⠛⠢⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠸⡀⠀⢀⡿⢱⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁
⢸⠀⣀⣈⣩⣭⠤⠼⠤⠤⠤⠤⠧⠤⢤⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠠⠁
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠼⠀⠀⠀⠀⣸⣄⣀⣀⣀⣴⠁
⠀⠀⠘⢦⠤⠄⠲⠶⠒⠒⣶⣒⣒⣲⡒⠲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠤⢀⠃
⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⢀⣀⣀⣀⣀⣂⣉⣭⣽⡇⢈⠆
⠀⠀⠀⢼⠃⠀⢤⣤⣤⡤⠤⠤⠴⠶⡒⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⣀⣀⣈⣭⣤⣵⡶⢈⠆
⠀⠀⠀⣼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠝⡓⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣐⣢⣭⣭⣥⢈⠆
⠀⠀⠀⢼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠿⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠉⠉⠉⢉⣩⣭⣥⣶⡎⣈⠂
⠀⠀⠀⠘⢧⣀⠀⠐⠒⠒⠒⠺⣋⣗⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠉⡭⢛⠜⠁
⠀⠀⠀⠀⠀⠉⢻⠛⠛⠛⠛⡿⢹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡛⣛⣷⠞
⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⠷⠾⠼⠶⠧⠿⠼⠼⠧⠧⠾⠼⠶⠧⠷⠾⠼⠶⠧⠷⠼⠼⠧⠷⠾⠼⠼⠧⠷⠾⠼⠶⠧⠷⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢻⡹⡏⠉⠉⠋⠙⢟⢻⠉⠉⠉⠉⠛⡟⡟⠉⠉⠉⠉⢻⠻⡏⠉⠉⠉⠉⠛⡟⡟⠉⠛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣠⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢠⠞⣽⢸⠀⠀⠀⡠⢋⡇⡇⠀⠀⢀⡔⣹⡇⡇⠀⠀⢠⢞⡵⡇⣿⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣰⠣⠎⣸⢸⠀⠀⡼⠱⠃⡇⡇⠀⢠⠎⠜⣹⡇⡇⠀⣰⠣⢎⠐⡇⣿⠀⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢰⠃⢂⠎⢾⢸⠀⡼⠐⣰⠃⡇⡇⢀⠏⠐⡼⢹⡇⡇⣰⠃⢃⠎⠞⡇⣿⢀⠎⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠇⢀⡄⠈⣼⢸⣼⠁⢠⠀⢁⡇⣧⡞⠀⡤⠀⣹⡇⣧⠇⢀⡄⠈⡜⡇⣿⡞⠀⡤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠏⠀⠀⠀⠘⢹⣸⠃⠀⠀⠀⠊⣇⡟⠀⠀⠀⠀⢻⣇⠏⠀⠀⠀⠘⠁⡇⡿⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣤⢞⡩⣍⠲⡤⣬⢏⡔⣒⢢⣀⡁⡸⠃⢂⣀⡄⠈⢀⡟⠐⠂⢀⠀⠉⢰⠏⠐⠀⡀⠀⠁⣀⡟⠐⠂⢀⠀⢹
⠀⣠⠞⠀⠀⢯⣏⢀⡀⠀⠀⠈⠛⠙⠀⠁⠉⠉⣧⡯⡾⠶⣄⣢⠎⡰⣣⠃⠋⢐⡷⢃⡜⡼⡐⡁⠘⣠⠟⡰⣣⠃⠋⠀⢻
⠀⢧⠀⠀⡔⠋⠁⢏⠙⠋⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢳⣴⣵⣳⣳⡷⠋⣠⢞⣜⣝⣝⣽⠟⢁⣞⣵⡵⣱⣳⢣⣾
⠀⠀⠭⠭⠭⠭⠉⠉⠉⣭⣭⡍⠉⢉⣉⠉⢉⡉⠉⣉⠩⠭⡉⠉⠹⠿⠏⠉⠉⠉⠩⠭⠭⠭⠉⠭⠉⠩⠭⠭⠭⠉⡩⠭⠉
⠀⠀⠠⠬⠭⠉⠉⠥⠤⠀⠰⠆⠀⠐⠒⠒⠒⠀⠀⠐⠲⠈⠉⠉⠀⠉⠉⠩⠍⠉⠉⠡⠄⠀⠀⠒⠒⠂⠘⠛⠦⠌⠵⠶
⠀⠀⠀⠀⠚⠛⠓⠀⠀⠀⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠶⠄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣠⣀⣴⠇⠀⠀⠀⢀⠀⣤
⠋⠐⠀⠀⠀⠀⠀⣸⣏⠀⠠⡐⠀⣴⢠⡆⠀⠀⠀⠀⠀⠀⡰⠶⠶⣿⡉⠀⠂⣀⠀⣠⡀⠟⠈⠀⠀⠀⠀⣼⠿⠛⣃
⣀⡄⠀⠀⠀⠀⠐⠉⣉⣀⡀⠀⠀⡆⠘⠀⠀⠀⠃⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⠁⡙⠀⠀⠀⠀⠀⠀⢰⣧⣴⠿⠛
⢸⡇⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⣤⣿⠿⢦⣤⣤⣀⠀⠀⠀⠀⠐⠆⣴⡇⠀⠀⠀⢠⣅⣴⠞⠃⠀⠀⠀⢿⣭⡏
⠀⠀⠀⠀⠀⠀⣾⣻⠋⠁⠀⠀⢾⠾⣾⡿⠟⠛⠛⢦⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⣿⡉⠀⠀⠀⠀⠀⠈⠁⡁
⠀⠀⠀⠀⢰⣶⣍⣍⠀⠀⠀⠀⢠⣤⣿⡇⠀⠀⠀⢸⠀⠀⢠⣀⣌⡁⠀⠀⠀⠀⠀⢨⠱⣶⣿⣿⣿⣿⣷⣦⣿⡀
⠐⠃⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠘⠛⠋⠃⠀⠀⠀⠘⠒⠚⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠊⠀⠈⠙⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢠⣤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⣾⢷⡀⠹⡀⢸⡘⡆⠀⠀⡟⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⢹⡈⣧⠀⠀⠀⢷⡇⠀⠀⢀⣀⠀⠸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⣤⠀⠱⡀⠈⢧⢸⡄⠀⠀⢸⡇⠀⢰⠃⣿⠀⠀⢰⢻⠀⠀⢀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠙⣷⡄⠀⠀⠈⣆⣇⠀⠀⠘⠁⢀⡏⢠⡏⠀⠀⣞⡞⠀⣰⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡓⢦⣄⠀⠀⢻⡀⠀⠀⠈⢿⣄⠀⠀⠘⣿⠀⠀⠀⠀⣸⠁⣾⠁⠀⢸⡟⠁⠀⠁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⣷⣄⠀⠻⣄⠀⠀⠀⢻⣆⠀⠀⠘⣧⠀⠀⠀⣿⣼⠇⠀⢠⠟⠀⠀⣠⡾⢛⡇⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢷⣄⠀⠀⠻⣦⠀⠀⠈⠀⠀⢀⣿⡏⠀⠠⠋⠀⣠⡾⠋⢀⡞⠁⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠉⠳⣦⡀⠹⣧⠀⠀⠀⠀⢸⡟⠀⠀⠀⣠⣾⠟⢁⡴⠋⠀⢠⠞⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⠭⠷⠶⠤⠀⠀⠀⠉⠳⢼⣷⡀⠀⠀⠟⠀⠀⣠⡾⢋⣡⡴⠋⠀⠀⠀⠀⢀⡤⢞⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠖⠂⠈⠑⠀⠀⠀⠴⠿⠟⠛⠉⠁⠀⠀⠀⣀⣴⣞⣭⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠀⠀⣀⣀⣤⣤⡶⠚⠁⠀⠀⣰⠂⠀⢠⠀⠢⣀⠀⠀⠀⠐⠒⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢛⣋⣩⠅⠂⠁⠀⠀⠀⣠⣾⠁⠀⠀⠀⣧⠀⠈⠳⣦⣄⡀⠀⠀⠀⠠⣤⣤⣤⣴⣚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⡀⠀⠀⣀⠜⡱⠃⠀⡄⠀⠀⠸⣷⡀⠀⠈⠻⢍⡓⠶⣤⣀⠀⠤⣄⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⣠⠞⢁⡼⠁⠀⢀⣧⠀⠀⠀⢳⠙⣄⠀⠀⠀⠉⠓⠦⢌⣹⣶⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⣴⡟⢁⣴⠏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠣⡈⢧⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⢠⡆⠀⠀⢼⢸⡇⠀⠐⣄⠀⠀⠾⠆⠀⠈⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠸⣿⠁⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣤⡶⠾⠛⠛⠛⠛⠛⠲⠶⣤⣀⣠⡴⠶⠚⠛⠛⠛⠛⢿⡄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⢀⣀⣀⣀⡀⠀⣠⠾⠋⠁⠀⠀⠀⣀⣀⣀⣀⣸⡇⠀⠀⣿⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣤⠶⢻⡏⠉⠉⠉⣹⠟⠁⠀⠀⣠⡴⠞⢿⡉⠉⠉⠉⣿⠀⠀⢰⡏⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⣴⢿⡇⠀⠀⢻⣄⠀⣼⠏⠀⠀⣠⠟⢧⡀⠀⠈⢻⡄⢀⣼⠃⠀⠀⣾⢷⣄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⣾⠃⠀⢀⡾⠁⠀⢻⣆⠀⠀⠙⢾⣏⠀⠀⣼⠃⠀⠀⢳⡄⠀⠈⢿⡞⠁⠀⢀⡾⠃⠀⠹⣆⠀⠀⢻⡆
⠀⠀⠀⠀⢰⡏⠀⠀⣼⠃⠀⠀⠀⠙⢷⣀⠀⠀⠉⠻⠶⣯⣤⣤⣤⣬⣿⠀⠀⢸⡇⢀⣰⠟⠁⠀⠀⠀⢻⡄⠀⠈⣷
⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢘⣿⠟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⢳⡶⠶⠶⠶⠶⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢿⡄⠀⠀⣸⠇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⠻⣤⡼⠋⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠙⠳⣦⣄⣀⠀⠀⠀⢻⣦⠀⠀⠈⠻⢦⣤⣾⠃⠀⠀⢀⣀⣤⡶⠛⠁⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠉⠉⠙⠛⠛⠉⠉⠳⣦⡀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠁⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣠⣤⡴⠾⠛⠳⠶⣤⣄⣀⣀⣀⣀⣤⣤⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠸⠄⠀⠈⠈⠀⠀⠀⠶⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⣤⢀⠀⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠑⠖⠀⡁⠀⠠⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠁⠂⠀⠁⠀⠂⠤⠄⢀⠀⠂⡀⠈⠀⢀⡀⢀⠚⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡔⠆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠄⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⠀⠘⠉⠀⠀⠒⠁⠀⠀⢀⣠⠄⠈⠀⠀⠒⢃
⣶⣶⣶⣶⢶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠋⢻⣿⠉⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣩⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠋⠀⠈⠉⣿⣿⡟⠉⠉⠙⠿⠟⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠀⠀⠀⠀⠀⣸⡿⠏⠐⠆⠤⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⢿⣿⣿⢡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠡⢠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣉⣉⣈⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⢰⣉⠂⠀⠀⠀⢰⠀⠀⠀⠀⡆⠘⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣾⣿⡟⠀⠀⠀⠀⢶⣧⡀⠀⠀⡇⠀⣉⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⢠⣆⢸⣿⡇⡀⡇⡇⠀⢀⣀⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⡄⠀⢸⣿⣮⣿⣧⣿⣿⡇⠀⠀⢨⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠶⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠂⠀⠀⠘⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠲⣄⠀⠀⣠⣤⡀⠈⣧⡇⠀⢀⣤⡄⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢳⡀⠸⣆⠙⣄⠸⠇⠀⣾⠋⢹⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠈⠛⢧⠀⠈⢷⡸⡀⠀⢸⡏⠀⣸⠀⠀⠀⣴⢿⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢶⣄⠀⠀⠀⠀⠹⡇⠀⢸⡇⠀⡏⠀⠀⣼⢋⠞⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⣄⡈⠛⠷⣤⡈⠳⣄⠀⢤⡀⠀⠀⢸⠁⡸⠁⠀⣸⡷⠋⠀⠀⠁⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠙⠷⣝⣆⠀⠙⡄⠀⢸⢠⠃⠀⠀⠋⠀⢀⣠⠖⣛⣭⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢯⣭⠭⠿⠶⠦⠀⠀⠀⠀⠙⢧⡀⠀⠀⣸⠇⠀⠀⠀⣠⣴⣿⠶⠛⠉⠀⢀⣠⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠋⠀⠀⠠⠚⠋⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⡤⠶⣺⠿⠋⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐⠶⠾⣭⣉⣉⣩⡿⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⣁⡴⠋⠁⠀⠀⠀⣠⡶⠀⠀⠘⣿⣄⠀⠀⠀⠀⡀⠀⠀⢠⣀⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣾⠟⢁⣤⠞⠉⠀⠀⠀⠀⠀⣴⢻⠇⠀⠀⠀⢹⡌⢳⡀⠀⠀⠹⡗⢦⣄⠈⠻⣗⠦⣄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⣀⠀⠀⠀⢠⠏⠀⣸⠃⡼⠀⠀⠀⠀⠀⢿⡄⠙⡄⠀⠀⠈⠳⣬⠇⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⣠⠀⠈⠀⢰⠇⢀⠇⠀⠀⢀⡄⠀⠈⢿⣄⠸⡄⠐⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠏⠀⠀⠀⣾⠀⡸⠀⠀⠀⢸⣿⡄⠀⠈⠻⢿⠇⠀⠘⢌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡜⠀⠀⠀⠀⢹⣴⠃⠀⢠⠀⠘⣇⣷⠀⠀⣄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠐⡍⠀⠀⠋⠃⠀⠀⠀⡤⠠⠀⠀⠀⠀⠨⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢤⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠦⢤⡄⠀⠀⠀⡀⠀⠀⠄⠉⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⣄⠀⠀⠀⣠⠐⡀⠀⠀⢀⠔⠁⠐⠀⠀⠀⠀⢀⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢄⠁⢂⡤⠐⠀⡆⠀⠘⠉⡐⠂⠤⡰⢶⣀⠈⠒⠃⠀⠂⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠚⡌⠀⠀⠀⠐⢡⠀⠀⠀⠁⠀⠐⠚⠀⠐⠐⠃⠀⠊⣀⠀⠀⠘⠁⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⣀⠠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢁⣀⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⡀⠀⢠⠀⠀⠀⠑⣀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠉⠀⡀⠈⠈⠀⠀⠀⢀⡤⠤⠀⠉⠀⡀⠙⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⠞⠋⠛⢦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡟⣰⠋⠀⠀⠀⠈⢷⣘⣧⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡤⠶⠶⠶⣾⢠⣏⣙⣳⡶⠶⢛⣉⣭⣤⡶⠶⠶⠦⣍⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢰⡇⣼⠿⢋⣡⠶⢾⣉⠻⢿⣄⣧⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⣠⣾⠇⣿⠞⠋⠀⠀⠀⠈⠛⢦⣌⠻⢦⡀⢀⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⢿⣡⣾⠀⡏⠀⢀⡴⠖⢦⡀⠀⠘⡏⢻⣦⣹⠟⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣦⡙⢿⠀⣇⠀⠘⢧⣀⣼⠃⠀⢠⣇⣼⠟⣡⣾⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠙⢿⡆⣿⢦⣀⠀⠀⠀⢀⣤⠾⢋⣥⠞⠁⠈⢷⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠸⡇⢻⣦⣍⡛⠶⣾⣋⣥⣾⠋⡟⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⠶⠶⠶⢿⠘⣟⣩⡽⠷⠦⣬⣙⡛⠺⠷⠶⠶⠶⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠛⣇⢹⡅⠀⠀⠀⠀⡽⢩⡟⠛⠓⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⢦⣀⣠⠞⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣬⡤⠞⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⣿⣼⢒⡯⠁⣯⡷⢼⢫⡌⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠀⠉⠁⠁⠉⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢸⠇⠀⢺⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢸⣷⣢⣼⡷⠀⠀⠀⠈⢻⡇⠀⠀⠌⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⣄⣼⡀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⣌⣷⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣞⣷⣦⠀⢀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣀⣀⣿⣇⠀⠀⣼⣿⣿⣾⠀⠀⢀⡄⣹⣶⣍⣿⣦⡀⡀⠀⠀⠀⠀⡘⠁⠀⠀⠹⣧⣼⡏⠔⠘
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢁⠀⣿⣯⠍⣙⢷⣿⣿⣏⣽⣿⠀⠀⣸⣇⣬⣌⣿⣿⣿⣿⣧⠀⢀⠀⠴⢀⢸⣷⣷⠀⠻⣿⡏
⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠟⡿⠀⢸⣏⠀⢘⣿⣿⣿⣏⠉⢻⠁⠀⣿⡏⠀⢿⣿⣿⣿⣿⣿⡃⠸⣿⣶⣿⣾⣿⣿⡇⠀⠈⠐⠁
⠀⠀⠀⠹⣦⡙⢿⣿⣿⣿⢃⣴⠃⢀⣈⣉⠀⢀⣭⣝⢿⣿⡀⣸⣦⣸⣿⣿⢀⣼⣿⣻⣿⣿⣿⠗⠀⠻⣿⣿⣿⠿⡿⠟⠓⠀⡄
⠀⠀⠀⠀⣿⣿⡦⠁⠀⢨⣿⣿⣠⣿⣿⣿⡆⠸⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠺⢿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣷⣀⣶⣿⣄⣤⣤⣿
⠀⠀⠀⠀⣿⣿⣿⣷⣶⣾⣿⣿⣿⣻⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇
⠀⠀⠀⠘⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠘⠛⠛⠛⠋⠉⠋⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡈⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⠇⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣇⡟⠀⣾⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⢌⢳⡀⠀⠀⠀⠀⠀⢇⠀⠀⡆⢸⣿⡇⣸⡇⣰⡏⠀⠀⠀⠀⠀⠀⣠⠚
⠀⠀⠀⠀⠀⣀⠀⠀⠉⠲⣄⡀⠀⠀⠀⢈⠳⣹⣄⠀⠀⠀⠀⢸⣄⠀⣧⣾⣿⣧⣿⢡⡿⠀⠀⢀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠈⠙⢶⣄⡤⡀⠑⢼⣿⣷⣄⠀⠘⡄⣿⣶⣿⣿⡿⡟⠿⢿⢇⠀⣠⠊⣠⡾⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣉⠻⣿⣦⣌⣿⣿⣿⡷⣠⣷⣿⣿⣿⡿⢻⢣⢄⣾⣶⡿⠱⣾⢋⡴⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⠟⢉⠻⣿⣿⣯⠹⣿⣿⣽⣿⠇⣿⣿⣾⣿⡿⣡⣴⣿⠟⠀⠀⣀⣤⠶⠚⠉
⠀⠐⠄⠤⢤⣀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠠⢀⣠⣉⠲⢿⡛⢦⠙⢿⣿⡉⠀⣼⠿⣿⣿⣞⣿⣿⠁⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⡟⠲⠶⢾⣿⡿⣷⣿⣷⡀⠀⠉⠁⠀⠀⠘⣩⣿⣿⣯⣶⣿⣯⡄⠄⠀⢠⣠⣤⣤⣤⣤⣤⠴⠶⠶⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⣉⣛⣿⣿⡷⠦⢬⣭⡟⠀⠀⠀⠀⠀⠀⢈⣿⣟⣛⣉⣹⣶⡶⠶⠶⠾⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣲⣿⣿⣿⣿⣿⣿⣧⣶⠤⠶⠒⡀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣈⣩⣍⢀⣠⣴⣾⣷⢿⣿⣻⣟⠀⠀⠀⣄⣴⣄⠀⣀⠀⠀⠉⣽⣟⡓⣶⣤⣠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⡟⠿⠛⠋⠻⣿⣿⢿⣿⣿⠟⣱⢻⡆⠀⣿⣿⢻⣽⣷⡙⠿⣶⣾⣿⣯⣿⣿⣿⣿⣿⡶⣤⣄⣀
⠀⠀⠀⠀⠤⠔⠋⠉⠉⠀⠀⠀⠀⠀⣀⠴⠚⠉⣴⡿⠛⣵⡿⢁⡟⢠⣾⣿⣿⡆⢻⣿⣿⢦⣮⡛⢿⣿⣿⣿⡿⣿⡿⣯⣐⠢⠍⠙⠒⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠞⣡⣀⡾⣿⡗⡜⣤⣼⣿⣿⡿⠃⠀⣻⣿⣆⠉⠻⣶⣷⣎⠀⠝⠲⢍⡂⠌⠛⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣼⣿⠏⣰⣿⡟⢁⣿⣾⡿⠘⡁⠀⠈⢿⡎⢿⠂⠀⠈⠻⣿⣧⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠽⠁⣰⣿⠏⣶⣼⣿⡿⡃⠀⠁⠀⠐⣿⣿⡀⠃⠀⠀⠀⠈⠳⡙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠈⠀⣰⢻⠟⢰⣿⡿⡿⠀⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠂⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡰⢡⠏⠀⣿⢻⢹⡇⠀⠀⠀⠀⠀⠀⠀⢻⡝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⢀⠏⠀⣸⠏⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣇⠀⠀⠀⢠⡾⠁⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣿
⢶⣦⣤⣄⣀⣤⣤⣤⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢀⡿⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⣀⣀⣀⣠⣶
⠀⠙⢦⣈⠉⠀⠀⠀⠉⠻⣦⡀⠈⢷⣄⠀⠀⢀⣴⠏⣀⣀⣀⠀⠀⠘⢷⣀⠀⠀⣠⡾⣡⡾⠋⠁⠹⣆⠀⠀⠀⠀⣰⡏⣤⠞⠋⠉⠉⠉⠉⣡⡟
⠀⠀⠀⠙⠷⣤⣀⡀⠀⠀⠈⠙⠳⠶⣽⣿⣿⡿⠿⠛⠉⠉⢉⣿⠶⠶⢦⣽⣿⣿⠿⠟⠉⠀⢀⣤⢤⣽⣷⣤⣤⣾⡿⠟⠁⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠋⡀⠀⠀⠀⠉⠀⠀⠀⢀⣤⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢸⡋⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠶⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠶⠾⠿⠶⠶⣤⣤⣤⡤⡤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⣎⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠛⡗⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀
⠀⠀⠀⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣒⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠬⠭⠍⣵⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⣀⣠⣋⡛⠒⠒⠖⠴⡇⠀⠀⠀⠀⠈⠁⠛⠃⠀⠀⠀⠀⠀⠉⠲⠤⠼⠾⣀⣀⡄⠀⠀⠀⠀⢠⠞⠉⠀⠉⠙⠢⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡉⠉⡉⠐⠒⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣠⠒⠒⠹⡄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⠡⢀⡤⠤⢷
⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢾⡏⠉⠙⠲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠤⠞⠛⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣸⠀⠀⢠⣶⡄⠀⠀⢸⣧⠀⠀⣀⡗⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣰⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⣰⠃
⠀⠀⠀⠀⡤⠠⢤⣠⠔⠒⢢⠀⠀⠀⠀⣾⡷⠤⠤⠤⡏⠀⠀⣾⠇⢷⠀⠀⠘⣿⠒⠋⠁⢠⡶⠒⠢⣄⠀⠀⢿⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢙⠾⡅
⠀⠀⠀⠀⢇⠀⠀⠁⠀⠀⣸⠀⠀⠀⢐⣿⠇⠀⠀⢰⡇⠀⣼⣯⣤⣼⡇⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠈⡇⠀⠈⣿⡞⠁⠀⠀⠀⣠⢄⣠⢤⠀⠀⠀⠳⣏
⠀⠀⠀⠀⠈⠳⣀⠀⠀⡰⠃⠀⠀⠀⠸⣿⠀⠀⠀⢸⠀⢰⣿⠀⠀⠀⢹⠀⠀⢿⡆⠀⠀⢸⣇⣀⣠⡴⠃⠀⠀⣾⡇⠀⠀⠀⠀⠙⢄⣡⠞⠀⠀⠀⠀⢸⡄
⠀⠀⢠⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⣼⡏⠉⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠻⠃⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣴⡞⠉⠓⢦⠀⠀⠀⢸⣧⠀⠀⣰⡞⠛⠲⡄⠀⠉⠉⣿⡏⠉⠀⣀⠀⠀⠀⠀⢸⡇⠀⠙⢦⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⣠⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣸⠀⠀⠀⣼⡇⠀⠀⣿⡇⢀⣠⠇⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⢸⠇⢸⣷⠀⠀⠘⡇⠀⠀⠀⠀⠈⣿⡄⠀⢠⠇⠀⠀⢸
⠀⠀⢀⡀⠀⠀⠀⢸⣷⠶⠚⠧⣄⠀⠀⣿⠇⠀⠀⣿⡿⣍⠁⠀⠀⠀⠀⣿⠀⠀⢸⣧⣀⣀⣼⠀⠈⣿⠀⠀⢠⡇⠀⣰⣿⡀⠀⠘⣿⣀⡞⠀⠀⠀⢸
⠀⠀⠁⠑⠙⠆⠀⠈⣿⠀⠀⠀⢸⠀⠠⠿⠄⠀⠀⣿⡇⠈⠳⠀⠀⠀⠀⠿⠀⠀⣿⡇⠀⠀⡿⠀⠀⣿⣀⡠⠏⠀⣰⡟⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣠⠞⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢀⡇⠀⠀⠙⠉⠀⠀⣰⡟⠉⠙⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡶⡄⠀⠀⠰⠟⠀⠀⠀⠾⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⡆
⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡉⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠄⠀⠀⠀⠀⠀⠀⣞⠑⠞⢱
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⠉⢳⠦⣄⡀⠀⠞⠀⠀⠠⠖⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣠⠤⠴⢆⠀⠀⠘⢦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠘⡏⠑⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⣋⣉⣩⣤⡤⠖⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠
⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠀⠸⡆⠁⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣁⡨⠤⠔⠒⠋⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠙⠁⠀⠀⠀⠀⢸⡀⢀⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠉⠀⠀⠀⣀⣠⢤⡤⢴⣛⡦
⠀⢀⡤⢤⡀⠀⠀⠀⠀⢠⠗⠋⠀⠀⠀⠀⠀⠖⢦⣀⣀⡀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢸⣓⣮⣽⠯⠽⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤
⠚⠉⠀⠀⠙⠢⠤⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣰⣿⣿⠀⣾⣿⣷⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⣿⣿⡏⢸⣿⣿⣿⡆⢹⣿⣿⡀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠐⠿⠿⠿⠀⠿⠿⠿⠿⠷⠈⠿⠿⠷⠀⠀⠀⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣴⠟⣿⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠶⠟⠁⠀⣿⡇⠀⠙⢷⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⡀⠰⢶⣾⣿⣿⣷⣶⣶⣤⣀⡀⠀⠀⠀⠈⠇⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠⣶⣿⣿⣿⣷⣦⣌⡙⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⣰⣿⡿⢋⣡⣌⠹⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣷⠄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣾⣿⣿⡄⠻⠿⢿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⠋⣰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⣷⡄⢹⣿⣿⣤⡙⠛⠿⠿⠟⢃⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣌⡙⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⢠⡋⢲⠖⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠉⡑⠂⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⣸⠓⣴⠂⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢀⡀⠄⠠⠤⠀⡈⠀⠀⠀⠒⣀⢤⡀⠀⠀⠀⠀⠀⠀⠠⠏⠉⠁⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⢺⣀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠁⢀⠄⡪⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠎⠀⠀⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠀⠀⠀⢊⠤⠒⢉⠀⠀⠤⠈⠑⢄⠀⠁⢂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⡄⢀⢔⠁⡚⠉⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠁
⠀⠀⠀⢀⠀⠀⢀⠄⠂⢘⢟⠛⠒⠐⠄⡅⠀⠀⡂⠄⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢊⢔⠡⢒⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣀⣴
⠀⠀⢀⠊⠀⠔⠁⠎⢔⠕⡱⡪⠂⠡⡂⢀⠀⢈⠔⡨⢂⠄⠀⠔⠁⠞⠝⡐⠀⣾⢐⣡⠎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡌⠋
⠀⠀⠆⠀⡌⠀⠀⠀⠀⠈⠀⠁⠁⠊⠢⠘⣆⠠⢊⠔⡡⡢⡢⡀⠌⠚⢈⣩⠁⠛⠶⣅⠨⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣀⠀⠀⢈⠁⠀⠀⠠⠂
⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢢⡁⠪⠊⢈⠋⠀⠀⠘⠉⠊⢑⠠⠀⠈⠓⡐⠡⠀⠀⠀⠨⡋⠆⠀⢀⡤⡠⠈⠐⢄⠑⢌⠂
⠀⠀⠀⠀⢃⠀⠀⢂⠀⠀⠀⠀⡊⣂⠕⠊⢅⠠⠄⠾⣷⠃⠀⠀⠀⠀⠀⠀⠁⠂⢕⠀⠀⠘⡎⠴⠀⠀⠅⡂⢀⣠⢖⠎⡁⠀⠄⠀⢡⠀⢂
⠀⠀⠀⠀⠈⡄⠀⠐⡂⠔⡠⢀⢀⠂⠀⠀⠀⠠⠐⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡷⠠⠀⠀⠠⠈⠫⣋⠄⡪⢐⢅⠀⠀⠀⡆
⠀⠀⠀⠈⢂⠘⢄⠀⢐⢅⡂⢀⠍⠀⠀⠀⠀⠄⠊⠅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠔⠅⠀⠀⠈⠀⢱⡨⢐⠕⡠⠂⠀⠀⡆
⠀⠀⠀⠈⠢⢈⠢⡑⠤⡁⠂⢐⢧⠀⠀⠀⠀⠁⡂⠅⣣⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣟⠀⠠⠀⠀⠀⠀⠀⣆⠅⡊⢔⢴⠀⠠⠀⡀
⢀⣀⡰⠂⠀⠂⠀⠀⠀⠀⠁⠈⠘⡤⠀⠀⠀⠀⠐⠡⡹⣆⠀⠀⢂⠄⠠⡀⢀⠄⡠⠀⠀⡼⢑⠡⠊⠀⠀⠀⠀⢀⡡⢊⢔⢅⠕⡠⢃⠔
⠰⠧⡨⠛⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⢄⠲⢄⠀⠀⠀⠐⠋⠁⢄⠒⡥⠮⠂⠅⡊⠔⣡⣶⣶⣷⠃⠀⠀⠀⡠⢀⣼⡮⢖⣰⡥⠖⠴⠃⣤⣠⡤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠂⠑⠠⢄⡀⣐⣀⢀⡔⠁⢉⠘⣿⣤⡅⠂⠉⣄⡛⢀⣤⣀⠀⠀⠀⣠⢈⣉⣩⠭⠶⠋⠀⠀⠺⣯⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠇⠎⠀⠐⠀⠉⠃⠁⠀⠀⠁⠩⣤⣤⠤⠴⡠⠂⠀⠀⠠⠐⣋⠉⠴⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⡄⠀⡇⠀⠀⠀⠀⡘⠀⠀⠜⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠘⡀⢁⠀⠀⠀⢠⠁⠀⡌⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢡⠈⠀⠀⠀⡄⠀⠜⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠆⠀⠀⠰⠀⠜⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⢰⡆⠂⡌⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣧⡐⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠳⢸⡆⠀⢰⠃⠀⠀⠀⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⢿⣆⠀⢻⠁⠀⠀⠀⢀⡀⠀⢧⠇⠀⣠⢞⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣧⠈⠀⠀⠀⢠⠏⢻⠀⠟⢀⣜⡵⠋⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠈⢿⡄⠀⠀⠀⠸⣇⠀⣿⠀⣾⠀⡼⠀⢀⠞⠁⣠⡾⠛⢉⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠦⠀⠻⣦⡀⠀⠀⢻⡄⣿⠀⣿⢰⠇⠀⠀⣠⠞⠉⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠸⣇⠸⠀⣿⡎⠀⢀⡼⣁⣤⣾⠟⠋⠁⣠⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠓⢶⣤⣀⠀⠀⠙⢷⣿⠀⠀⡿⠀⣠⣿⠿⠛⠉⠀⠀⢐⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣉⡉⠉⠉⠉⠀⠀⠀⠹⡄⠀⠁⡴⠋⣀⣤⠶⠾⢯⣭⣭⣬⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯⠥⠴⠚⣉⣠⣤⢴⣶⡶⠖⠒⠀⠀⢰⡄⡄⠨⢄⣀⣀⡀⠀⣠⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢉⣡⡶⠛⠁⠀⢀⣴⠀⠀⢸⣷⡘⢦⡀⠈⠻⢭⣳⣦⠀⠙⠲⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⣠⡶⠟⠁⠀⠀⢀⡴⢫⠇⣰⠀⢸⡇⢻⣌⠛⠀⡀⠠⢭⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⢀⣴⠋⠀⢠⠏⠀⡼⢠⡇⠀⠸⡇⠀⢻⣆⠀⠙⡶⣄⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠁⠀⢀⡏⠀⣰⠃⠈⠀⠀⠀⢷⠀⠀⢻⡎⢧⡈⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⣇⣰⡟⠀⠀⢸⡇⠀⠘⣇⠀⠀⢻⡼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⡇⣷⠀⠀⠘⢦⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠈⠛⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⡦⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠉⠀⢩⣷⣦⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠰⣿⠂⠀⢀⣽⡶⣦⡀⠀⢀⡀⠀⠀⠀⢠⡄⠀⠀⠁⠀⢀⡀⠀⢼⣿⣀⠀⣠⣄⠀⠀⢠⠆⠈⠛⠋⠀⣿⣦
⢀⡶⠿⣿⣷⣿⣿⠷⠛⠁⠠⠾⠇⠀⣠⠀⣨⡏⠀⠠⣶⠀⠘⠿⠂⠛⠉⠉⣸⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠛⣿
⣼⡇⢰⡌⠻⠛⠋⠀⠀⢦⠀⠀⠀⣻⠁⠀⠀⣀⠀⢤⣿⣆⡠⠀⠀⠀⠀⠀⠛⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠰⣿⠀⠀⠉
⠏⠀⠛⠛⠀⠀⣠⣶⣿⣿⣤⡴⢰⡇⠀⠀⢀⣿⡆⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠆⠈⣤⡀
⠀⠀⠀⠈⡿⠓⢻⣿⡟⣹⣿⢀⣽⠀⠀⠀⣸⠋⠀⠟⠉⠃⠀⠀⢐⡉⠁⣀⠀⠀⠎⣩⣥⣄⠀⠀⠀⠀⢰⡇⠀⡇⠀⠀⠀⠘⠓⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠈⢷⡀⠀⢠⠀⠀⣿⠀⢸⡇⠀⣿⠀⠀⡄⠀⢀⡾⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⢷⠀⠘⣇⠀⢹⠀⠀⠀⠀⡏⠀⣸⠃⠀⡾⠁⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢦⠀⠈⢧⠀⢹⠀⠘⠀⠀⠀⠀⠃⠀⡏⠀⡼⠁⠀⡴⠋⠀⣀
⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠙⠶⣄⡀⠈⠳⣄⠈⠳⡄⠈⠆⠈⠇⠀⠀⠀⠀⠀⠀⠸⠁⠰⠁⢠⠞⠁⣠⠞⠁⢀⣠⠶⠋⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠈⠙⠦⣄⠈⠳⢄⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⡠⠞⠁⣠⠴⠋⠁⢀⣠⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠉⠒⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠒⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤
⠀⠀⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠄

⠀⠀⠒⠒⠛⠛⠛⠛⠋⠉⠉⠉⠉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣀⠤⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢤⣀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢀⣠⠖⠋⢀⡴⠊⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠑⢦⡀⠙⠲⣄⡀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⣠⠶⠋⠁⢀⡴⠋⢀⡴⠁⢀⠆⢀⡆⠀⠀⠀⠀⠀⠀⢰⡀⠰⡀⠘⢦⡀⠙⢦⡀⠈⠙⠶⣄⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠞⠀⢀⡞⠀⣸⠀⢠⠀⠀⠀⠀⡄⠀⣇⠀⢳⡀⠀⠳⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡾⠀⢠⡏⠀⣸⠀⠀⠀⠀⣇⠀⢹⡄⠀⢷⡀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡾⠁⠀⠘⠀⠀⣿⠀⢸⡇⠀⣿⠀⠀⠃⠀⠈⢷⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣄⣰⢐⣀⠀⢆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⢀⡼⠞⠉⠀⠀⠈⠳⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣀⠜⠋⠀⠀⠀⠀⠀⠀⢠⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⡹⠁⢪⣾⠦⢄⠀⠀⠀⠀⠀⢀⠔⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠤⡰⠴⡆⡀⠘⣿⡇⠀⡇⠀⢀⠴⢊⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠔⠋⠀⠀⠘⢌⣶⡼⠀⢀⡿⣩⢁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠒⠋⡉⡐⠢⣄⠀⢀⡠⠚⠀⢀⠞⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⡠⣢⡿⣞⡻⡿⠾⠒⠉⢀⢔⡤⠊
⠀⠀⠀⠀⠀⠀⡠⠒⠁⡀⢐⠵⠊⠳⢯⣕⡆⠀⢀⣊⠬⠒⠁
⠀⠀⠀⠀⡠⠊⠀⡄⡸⠖⠁⠀⠀⠀⠀⠀⢩⠟⣏⡝
⠀⠀⠀⠰⠀⠀⢈⠎⠀⠀⠀⠀⠀⠀⡠⠒⠁⢎⠜
⠀⠀⠀⡇⠀⠘⠸⡀⠀⠀⠀⢀⠴⠊⣠⡴⠚⠁
⠀⠀⠀⠹⡙⣇⢀⠈⠒⠒⠊⢁⢰⡤⠊
⠀⠀⠀⠀⠈⠒⠥⣱⣒⣰⠤⠖⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡀⢀
⠀⠀⠀⠒⠱⠪⠖⠅⠢⢒⠔⡩⢊⠕⡪⢊⠕⠥⢪⠔⠥⠪⠊⠕⠪⠚⠕⠫⠪⢊⠔⠕⠕⠱⠩⠪⠪⠲⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠨⡆⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⢲⠆⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⡃⠀⠀⠀⢀⡀⢀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠘⣧⠰⣷⢀⡼⠁⣀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⡀⠀⠀⠈
⠀⠐⠀⢸⣷⠀⣸⠃⠀⠈⢹⣿⡏⠀⠀⠹⡄⢴⡷⢀⡏⠀⠸⣄⢰⡷⠀⠀⠀⠻⣄⢰⡷⢠⡏⠀⠠⣷⠄⢀⡴⠀⢦⣀⠀⣾⡆⣠⠏
⠀⠀⣴⢲⣷⡞⠁⠀⠀⠀⣼⠿⣇⠀⠀⠀⠉⣿⣿⠉⠀⠀⠀⠈⣿⣿⡟⠛⠦⠀⠈⢻⣿⡏⠀⢀⡴⣾⣿⠉⠀⠀⠀⠈⣹⣿⡟⠁
⠀⠀⠘⢾⣿⡇⠀⠀⢀⡾⠁⠀⠘⢧⡀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⢸⡿⡇⠀⠈⠇⢸⡿⣆⠀⠀⠀⢠⣿⣿⣿⠀⠃
⠀⠀⠀⢸⣿⡇⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⢸⡇⢹⠀⠀⠀⠈⣿⣻⠉
⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠙⠙⠀⠀⠀⠀⠀⠈⠃⠃⠀⠀⠀⠛⠀⠛⠀⠀⠀⠀⠙⠙

⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⢀⣨⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⢀⣀⠁⠃
⠀⠀⠀⠀⠻⣽⡿⣿⡷⠦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢶⡯⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⠀⢀⠄
⠀⠀⠀⠀⠀⢸⡗⣦⡀⠀⠁⠀⠀⠀⠀⠐⣿⣿⡾⢿⣄⠀⠈⡁⠤⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠀⣀⡁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠙⢷⠀⢸⣿⣷⣶⣦⣿⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠟⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠰⠟⠀⠀⠀⠀⣼⣧⠀⠀⢠⣿⣧⡀⢈⣽⢷⣤⣭⣿⣿⣿⣁⡀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢷⣤⣜⣟⣉⣠⣀⣡⣄⣿⣿⣿⣿⢿⣿⣿⠀⠀⣠⣴⡿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡸⣿⣿⣷⣷⣦⠰⣷⡶⣶⣶⣶⢶⣤⣿⣷⡶⠿⠛⠁
⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡾⣿⣿⡿⢶⣶⣶⣾⡟⣿⡇⣿⣿⣿⣷
⠀⠀⠀⣽⣅⠀⠀⢀⠀⠀⢀⠀⠀⢨⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⣿⣾⣿⣼⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣇
⠀⠀⠀⣿⡟⠙⠋⠉⠀⠀⠈⠙⠛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡇⣿⡇⣿⢾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢹⣿⠻⠇⣿⡇⣿⢸⣿⢸⣿⠀⠈⠀⠀⣿⢸⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠀⠀⠀⢴⠿⠋⠀⠀⣼⡇⠀⠀⠻⠃⠻⢸⣿⢸⣿⠀⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢸⡿⢸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠠⠤⠈⠂⠀⠀⠀⠀⠠⠨⠑⠀⠀⠀⠀⡀⡀⠀⠀⠉
⠄⢀⡀⠀⠀⠀⢀⠔⠊⠉⠐⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠱⠄⠀⠀⠠⢀⠄⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠙⠀⣀⣀
⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⠊⠉⡢⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠲⡎⠠⢐⢬⠀⡄⡄⠀⠈⡉⢄⡀⡤⠀⠀⠂⠀⠀⠉⢳
⠀⠀⢸⡀⠀⠀⠐⠀⠀⠘⠋⣸⢏⡶⠀⡠⠀⠀⠂⢁⡐⡑⣒⣠⢖⠲⠓⢀⠃⢰⡤⠀⢆⠀⠀⡕⠂⢈⠀⢴⡇⠀⠀⠀⠀⠈⡆
⠀⠀⡸⠀⠀⠀⠀⡀⠄⢀⠸⠃⠁⠀⠀⡜⠀⠂⠐⠀⡛⠁⠚⠁⠀⠀⠀⠀⠃⠀⠒⠂⠁⠉⠀⡈⠀⠘⠀⣸⡾⠣⢤⠀⠀⠸⠁
⠀⡐⠡⠀⠀⠀⠀⡡⡀⠀⠁⠂⠀⠀⠰⡡⣒⠉⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠂⠈⢀⠔⠁⡎⠙⢆⠠⠚⠙⢻⡿⠛⢉⠠
⠀⢀⠆⠀⠀⠀⢠⠀⠈⢆⠱⡈⠠⠀⠊⡀⠝⠂⠜⡾⠃⠰⡗⠀⠀⠤⠀⠀⠁⣠⠀⠈⢀⡜⠁⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⢰
⢐⠕⠒⠠⡀⠀⠈⡕⠄⠈⢆⢃⠔⢁⠞⠃⠀⢠⠔⠁⠀⠁⢈⠀⠀⢢⠠⠤⠚⣚⡆⠀⠉⠀⠀⠀⠀⣜⡦⠄⠀⠀⠀⠃⠀⠐⡆
⠁⠀⠀⢠⠇⠀⠀⠃⠈⠢⡀⠀⡔⠁⠐⠀⡰⠃⢀⡀⠀⠀⣠⠃⠂⠸⠀⠀⠀⠀⠘⣈⣋⡗⠒⠒⠈⢻⠧⢼⠉⠑⠂⣶⠀⠀⠁
⠀⠀⠀⡎⠀⠀⠀⡇⢀⡀⠀⠀⢱⠀⠀⠰⠁⠀⠀⠈⠉⠉⠈⠀⠈⠊⠀⢠⣀⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠂⠤⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣠⢀⣴⣸⣷⣿⣆⠀⠀⠀⢀⠠⡾⣿⣶⣄⠈⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢆⣀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⣿⣶⣶⣬⡚⣩⣿⠿⠟⢻⠃
⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣷⣼⣿⣿⢿⣁⣿⣿⠀⣸⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢘⣿⣿⣿⢿⣿⣿⡿⠟⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠃⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣂⣯⣩⣍⣿⣿⣶⣿⣿⣏⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢻⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣍⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⡄⡎⣸⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠁⠈⠉⠛⠛⠛⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂
⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠂⠀⠀⠀⡀⠤⠐⠂⠁⡠⠌⡃⠛⠢⢀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠈⢢⠂⣔⣈⣀⡉⠀⠢
⠀⠀⠐⠄⡁⠐⢂⡄⠣⠊⠀⠀⠀⠒⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠀⠀⠀⠀⠠⠊⠛
⠀⠀⠀⠀⠀⠀⠀⠘⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠔⢀⠼⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠊⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠤⠆⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⡖⠀⠈⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠑⠒⡦⠀⠔⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠐⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸⠀⠰⠄⢀⠀⠀⣀⠀⠠⠇⠀⠐⠂⠀⠐⠠⠄
⠀⠀⠀⠀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠁⠐⠂⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠦⠄⠀⠐⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠄⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡀⢀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠊⠀⠐⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢫⣷⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠄⠃⢰⣷⡀⠀⣰⣆⠀⠀⠀⠈⠛⣷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠌⢀⡐⠠⣸⡇⠀⢠⣿⠅⠀⠀⢹⣦⣀⠀⠈⢘⣻⣦⡄⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⣴⡏⢐⣠⣿⠃⠀⣼⣿⡇⠀⠀⠀⣿⣿⣧⡀⠈⢣⣿⣿⣦⣀⣀⠀⠀⠀⢻⡜
⠀⢰⣧⠀⡠⠶⠶⠀⠀⠾⠋⠀⠰⠿⠿⠿⠛⠛⠿⢤⠴⠿⠿⠿⠄⠀⠀⠼⠿⠛⠛⠀⠈⠙⠟⠻⠿⠿⠦⠤⣀⣸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣀⡀⠀⠠⣾⠁⠀⠀⠀⡀⠀⢀⣶⡀⠀⠀⣿⠀⣠⠀⢀⣀⣴⣿⠃⢀⣀⣀⣀⣀⣠⣤
⠀⠀⠀⢰⣿⣧⡀⠀⠠⠾⠟⣏⣹⡇⣸⢿⠀⠀⣸⣦⣧⣴⣾⣿⣷⣦⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⢻⣏⣭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠀⠁⠈⠉⠈⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠐⠒⠤⡀
⠀⠀⠀⢀⠐⠉⠀⠀⠉⠰⠁⠀⠀⠀⠀⠀⠀⠈⠳⡊⠉⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⡖⠁⠀⠀⠀⠀⠀⠀⠈⢖⠈⠉⠈⠁⠢⣄
⠀⠀⡐⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂
⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡱⢒⠤⠤⠐⢎⡁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠕⠢⠤⠤⠐⣌⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠈⠁⠐⠖⠀⡩⠀⠈⠀⠉⠈⠩⠉⣀⣐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⢰⠂⢈⠡⠀⠀⠀⠁⠈⠏⠡⣀⡒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣇⠘⠉⠣⠀⠀⠀⠀⠀⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠦⠀⠀⠀⠀⠀⡂⠘⠃⢀⠀⠀⠐⠋⠧⡀⠹⠍⠛⠀⠀⠠⡀⠚⠃⡄⠀⠀⠀⠀⢀⠴⢎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠗⠂⢀⠀⠀⠀⠀⢃⠠⢲⣤⠄⠰⠁⢰⠄⢸⠀⢴⠄⠰⠀⢤⡇⠄⠶⠀⠀⠀⠀⠀⡀⠐⠢⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠛⠶⣤⠖⡏⠀⠸⠀⠀⣷⣄⡀⠀⠈⠀⠀⣀⣠⡇⠀⡅⠀⢸⠓⢦⣤⠶⠛⠁⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣄⡀⠈⢻⡇⠀⠙⠉⠈⣿⠏⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⠀⢱⠀⠀⠈⠀⡖⠐⢮⠀⠀⠀⡸⠀⠹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⡆⠀⠀⢀⡇⠀⠘⡆⠀⢠⠇⠀⠀⠙⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠃⠀⠀⠀⠀⠳⣄⣠⠼⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢲⡶⠒⠲⣶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⢸⡇⠀⠀⣿⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⠿⠿⠿⠇⠀⠀⠿⢿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢖⠀⠀⠀⠀⢀⠾⠐⠞⠀⠀⠀⢀⣔⠈⠨⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠘⠉⠀⠀⠀⡰⢅⠙⠊⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⠀⠀⠀⠀⠀⠀⣀⠘⢍⠒⠁⠀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠀⠀⠀⠀⠀⠀⠀⠛⠉⠋⠀⠀⠀⠀⠄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠛⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡴⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠀⠀⠀⠀⠀⠀⠀⢠⠰⣀⠀⠀⠀⠀⠀⢎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠃⠀⣀⠀⠀⠀⠀⠀⢀⠛⠄⡤⠀⠀⠀⠀⠀⠀⠐⠣⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢂⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⠌⢃⠇⠂⠀⠀⠈⠑⡀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠢⡀⠀⢅⢀⡁⠀⠀⢠⡒⡀⢹⠜⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⠀⠈⢄⠀⠀⠈⠲⡄⢆⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⢐⠋⢴⠘⠈⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠁⠌⠀⠀⡠⠂⠀⠑⢄⠀⢄⠶⢆⠀⠀⠀⠠⠁⢈⠀⠀⠀⠀⠶⠅⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠌⠀⠀⡠⠐⠁⠈⠢⣀⠀⠡
⠀⠀⠀⠀⠀⠈⠈⢀⠔⠁⢀⠔⠊⠀⢀⠠⠐⠈⢀⠁⠖⠃
⠀⠀⠀⠀⣠⠀⡠⠂⡠⠐⠀⡀⠄⠂⡁⠄⠂⠈
⠀⠀⠀⣠⢃⢌⠄⢊⠄⡀⠅⠐⠈
⠀⠀⢠⣿⣶⠵⠚⠉
⠀⠀⠉⠁

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

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



⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿