Gift wrap Emojis & Symbols

⠿⣫⢕⣮⣱⢞⣫⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠻⠿⣿⣿⣿⣿⣿⣷⣦⣈⡁⠀⠀⠀⠀⢹⡘⣈⠡⡅⣒⢩⠁⢂⢇⡍⠾⢹⠀⠀⠀⠀⠀⠀⠈⣁⣭⣿
⣿⡶⢜⡭⢾⣯⡰⢟⣣⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⠃⠀⠈⣉⠛⠻⢿⣿⣿⣿⣷⠀⠀⠀⠈⣵⣐⠡⠅⢒⢊⠁⠆⠖⣘⠨⠭⣇⠀⠀⠀⠠⣴⣾⡿⣛⠭
⢥⣚⣱⠷⣌⠵⠚⣷⠾⣫⣄⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠂⢉⠟⠃⠀⠀⠀⠀⠸⣆⣃⣍⠨⡤⡒⡮⠱⣐⠣⠇⢳⠆⠀⠀⠀⠈⠵⣺⣅⢿
⢞⡫⣕⣋⡾⢟⡫⣖⣛⢳⣿⡆⠀⠀⠀⢠⠁⢠⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠏⠟⣘⡨⠅⡒⢨⢩⢠⠆⠇⠞⣘⠀⠀⠀⠀⠈⢩⣞⣿
⣷⡼⣛⢩⣾⡏⢺⣿⠿⠞⠋⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠖⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⢰⠰⢁⣃⡯⠌⠐⠒⠐⠀⠁⠀⠀⠀⠀⠀⠀⢛⡭
⢅⣽⡑⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠸⠄⣀⠀⠸⠂⠀⠀⡀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠈⠁⠀⠀⠀⠀⠀⣴⣿⣧⣄⠀⡀⠠⠀⠀⠈⠿
⣿⠿⠛⠉⠀⠀⠀⢠⣾⣿⣦⡀⠀⠀⠄⢀⠀⠈⠁⠒⠂⠤⢁⠀⠀⠀⡘⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣷⣤⡰⠀⠂⡀⠈
⠁⠀⠀⠀⠀⠀⠀⡨⠛⢿⣿⣿⣦⣈⣠⠏⣠⠀⠀⠀⠀⠀⠀⠈⠐⠒⠁⠀⠰⡲⣄⣧⡋⢴⣤⣤⣶⣄⠀⠀⠀⠀⠀⢀⠔⠀⢠⣤⡌⠻⣿⣿⣿⣆⠂⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⢿⣿⣿⣿⠋⠡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⣻⣿⣿⣿⣿⡿⣿⣯⡀⠀⠀⢀⠜⠁⠀⠀⣿⣿⣧⣤⣌⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⣩⣾⣿⣿⡟⡀⠀⠀⢀⡀⠀⢰⣿⣿⣿⣿⠟⠀⠈⠻⡿⠋
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⢟⣴⣿⣿⡿⢫⣾⣿⣄⠀⠀⠀⠢⡈⠛⠋⠉⠀⠀⢀⠄⠁
⡖⣤⢉⡤⢦⠀⠀⠁⢄⠀⠀⠀⠀⠀⡠⠞⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⣱⣿⣿⣿⢟⣴⣿⣿⡿⢋⣤⠀⠀⠀⠈⠢⡀⠀⠀⠔⠁⠀⣠⣄
⡓⣽⣾⣱⠥⡲⠀⠀⠀⠑⠄⠀⡀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠟⣡⣿⣿⣿⠟⣵⣿⣿⣷⠀⠀⠀⠀⠈⠒⠊⠀⠀⣰⠓⢄⡉⠲
⣍⠻⢿⣗⢍⡡⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣣⣾⣿⣿⡟⣡⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⣅⡙⠢⣌⡑
⢄⡙⠢⣍⠓⢇⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⢋⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡋⠢⣍⢓⢤⣉
⠦⣉⠓⢤⡙⠲⣌⡃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⡉⣿⣶⣥⡑⠣⣬
⠕⡬⣑⠦⣈⢓⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠋⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣉⠻⢧⣬⣤⠸⠿⢳⣬
⣷⣮⣈⢖⢬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠛⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣦⡀⡔⠀⠀⠀⠀⠀⠀⠘⢤⡉⠛⢴⣝⡻⣶⣿⠘⠿
⠙⣋⡙⣿⠂⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⠀⠖⠁⠀⡀⠀⠀⠀⠈⠑⠦⣈⠪⢦⢍⠳⣿
⠻⢿⡧⠁⠀⠀⠸⡈⢣⠊⢀⠇⣠⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⣤⠀⡀⠀⢀⠀⠀⠘⢿⣿⣿⣟⠋⠒⠄⠀⠀⠀⠀⠀⠀⠀⠙⠢⢕⠳⣢
⡑⡠⠁⠀⠀⢀⢠⡑⣼⣧⣾⣿⣿⣿⡿⠋⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠪
⠈⠀⠀⠀⠀⠑⣰⣶⣿⣿⣿⣿⠟⠋⠀⢸⣏⣛⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣄⠀⠂⠀⢀⡀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠐⠲⣆⡞⣀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠋⣅⡀⣸⢩⣝⣹⡇⡶⠷⡄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⢿⣿⣿⡿⣿⣿⣿⢿⡇
⠀⠀⠀⠈⢿⠿⠫⠋⠁⣴⢤⣧⡼⢭⣼⢰⡦⠴⠇⡟⠛⢦⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣤⣤⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣟⣿⣿⣇
⠀⠀⠀⠀⠀⠘⢄⡶⠶⠇⣾⢲⡟⣾⢓⡾⢸⡟⠛⠃⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠈⠣⣾⢙⣋⣾⣩⣏⣿⠉⠙⣁⠔⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋⠀⠀⢐⠉⡦⠒⢄⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣰⠦⠿⠀⢉⠔⠊⠀⠀⠀⠀⠀⠀⢸⠈⢀⠚⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣄⣇⠀⣴⠂⢢
⠉⡦⠀⠀⣠⣄⠀⠀⠀⠀⠻⣀⡠⠒⠁⠀⠀⠀⠀⠀⢮⠑⢄⠸⣼⠇⣌⠔⢊⠇⠀⠀⠀⠀⠀⠨⠲⢤⣼⣿⣼⢁⡠⢊⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣔⣡⣶⣿⠿⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣵⣬⣰⣟⣾⣥⡒⠡⢤⠀⠀⠀⠀⠈⢒⣠⡤⡾⠿⢻⢻⣏⣇⢡⢤⡆⠀⠀⠀⠀⠀⠀⠘⠉⠑⠦
⣿⣿⣿⣷⣿⡷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡿⠶⠶⠶⡶⣶⣶⠾⢶⡶⠿

⠀⠀⠀⠀⠀⠠⠄⢸⠉⣠⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⠄⠀⠀⣀
⠀⠀⠀⠀⠐⡈⠓⠚⣃⡿⣊⢁⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢤⡿⠾⢇⣀⢠⣅⣀⡀
⠀⠀⠀⠀⠀⠁⠊⢹⠀⠰⢄⠀⠁⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⠆⠁⡆⠐⠄
⠀⠀⠀⠀⠀⠈⠆⠚⠂⠇⠂⠀⠅⠒⠂⠀⠀⠀⢀⠀⠐⠴⢶⣆⠲⠶⠯⠤⠤⠤⠤⠤⠄⠀⠀⠠⠄⠀⠀⠆⠂⠆⣸⠲⠐⠆⠶⠈⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⡒⣺⠈⡅⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⢠⠀⠚⠉⠀⠀⠀⠀⠛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠁⠀⠁⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠠⠀⡄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠠⠀⣅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠃⢨⠀⢀⠀⠀⠙⣄⠀⢠⠀⡄⢀⡠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣀⡠⠤⠯⣵⣶⠤⣴⣶⠦⠀⠀⣀
⣠⠄⠁⠤⢀⣤⣤⢤⣿⣴⡤⠤⢄⡈⣀⢀⢪⡀⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡈⠁⠀⠀⡐⠂⠐⠈⠲⠄
⠠⠀⠒⠂⠀⠀⠀⠀⠄⠠⠂⠄⠀⠀⠠⠠⠄⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢺⡜⠀⠲⠐⠒⠂⡧⡆⠀⠋
⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢠⢤⣄⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠺⡏⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⢀⢈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠐⠚⡇⠀⢀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣠⣵⠃⢄⠜
⠀⠀⠀⠀⠘⠑⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠧⠛⠉⠀⠀⠒⠠
⠀⠀⠀⠚⠀⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠣⢈⣴⢁⠔⠁⢀⡠⠄⠀⠀⢀⣀⣀⢉⠀⠐⠒⠀⠠⠀⠀⠂⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠒⠀⠀⠀⠀⠀⠰⠊⣡⠔⠀⠀⠀⠀⠀⠈⠁⠐⠂⠤⢈⡀⠰⠓⠉
⠀⠀⠸⣦⢂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⡀⣀⡀⠔⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠆⡙⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⡃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠
⠀⠐⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠠⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⠀⠀⠀⠀⠁⠈⠆⠀⠀⠀⠄⢀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠈⢠⠃⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠊⠀⠀⢀⡆⣠⠎⢀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡅⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠘⢈⠀⠀⡀⢀⠠⠀⠀⢀⠀⡄⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠌⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠁⠀⠀⠻⠀⣄⠀⠀⠋⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠃⠀⢀⡀⠀⠀⡄⣠⠞⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡂⠀⠀⢱⠂⢀⡀⠀⠈⠃⠐⡄⢀⠠⠀⠀⢠⡟⠀⠀⠀⠀⠀⣴⠀⠀⠌⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤⠀⠐⠃⠀⠀⠀⠀⠈⠀⠠⠤⠀⠀⢡⠀⣰⠁⠀⠀⠧⠔⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠡⠆⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠇⠀⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠸⡄⢃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠓⠠⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⣠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠋⡀⠰⠀⠀⠀⠀⠀⠀⣆⠐⡈⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⡼⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡅⠀⠀⡀⠀⠂⠀⠀⠀⠨⠁⠉⠇⠀⠉⠀⠀⠀⡀⡀⠀⠈⠑⢡⠆⠀⠀⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠣⠈⡄⠀⠸⡀⢂⠀⠀⠀⠀⠀⢀⠀⡀⢁⡔⠀⠀⠀⠊⠀⠀⠀⠐⠁⠛⠀⢚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡏⠂⠙⠛⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠓⠒⠁⠀⠀⢀⠁⠀⡠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠸⠦⠒⠀⢀⠀⠀⠀⠀⣀⠃⠀⠀⠀⣰⠀⠀⠈⠣⢞⠀⠀⠀⠀⢰⡄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠲⠀⠀⢰⡂⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠊⠀⠰⠀⢀⡀⠀⠘⠃⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠁⠸⠆⠐⢐⠄⠀⠐⠃⠀⠃⠀⠀⠀⡀⢀⠀⠀⠀⠀⠉⢑⡀⠀⠙⠰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠋⠀⠀⠀⠀⠀⠀⢀⡀⣄⢀⡜⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠏⠀⢈⠉⠀⢀⡄⠀⠀⠀⠀⠀⢀⡀⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠐⠰⠂⠀⠀⠠⡄⢀⠆⠀⠀⠀⠀⠛⠚⠁⠀⠀⠈⢀⠁⠂⠀⠀⠀⠸⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠎⠀⠀⠀⠁⠀⢀⠀⠘⠁⠉⠀⠚⠃⠀⠀⠀⠀⢄⠀⠀⠀⠁⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠄⠋⠀⠀⢇⠐⡀⠀⠀⠀⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠙⠀⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠛⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠯⠉⠉⠓⠄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠠⠤⠼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢦⡀⠀⠀⠀⢰⠋⠀⣀⠔⠀⠀⠀⠀⠀⠀⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠿⠛⠓⠒⠦⠤⣀⠙⢷⣄⠳⣄⣀⣠⠇⣠⡾⠋⠀⠀⢀⣀⣀⣀⣀⣚⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡁⠀⠀⠀⠀⠀⠀⠈⣿⣦⣝⣧⠿⠤⢾⣰⢃⣥⣴⠾⠿⠟⠛⠋⠉⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠿⣿⠷⠶⠶⠶⠶⠶⢿⣿⣿⣷⣦⣤⣼⣿⣿⣋⣁⣀⣀⣀⣀⣀⣤⡤⠴⢯⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⣶⠞⠀⠀⠀⠀⣠⠴⠚⠉⣉⠟⠉⠛⠛⠻⣟⠛⠛⠯⢍⣉⠀⠀⠀⠀⠀⠈⠐⢤⠼⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠀⠀⣴⣿⣷⣦⣤⣎⡁⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⢉⣁⣦⣀⡄⡰⡸⠘⡆⢸
⠀⠀⠀⠀⠀⠀⠀⣀⡼⢏⠀⠀⠀⢀⣼⣷⣿⣿⣿⡏⠀⠉⠛⠲⣤⣀⡀⢀⣀⣤⠼⢷⠿⠿⠿⢿⣿⡇⠀⠁⠀⢱⢸
⠀⠀⠀⠀⢀⣴⣚⣁⣠⣅⠀⠀⣠⣾⢿⣿⣿⣾⣿⡇⠀⠀⠀⠂⡠⠨⣿⠉⠀⠀⠀⢸⡀⠀⡎⠨⠞⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢀⣼⠿⠛⠾⣧⠙⣿⣿⡇⠀⠀⠀⠐⠴⣿⣿⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⡰⣫⠴⡟⠙⠀⠀⠀⡟⠀⢿⣻⡟⠶⣤⣀⡀⢐⢪⣿⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⡿⣧⠀⢰⣷⡤⡘⣆
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡇⠀⠀⠀⠀⡗⠈⣣⢽⡇⠀⠀⠉⠻⢿⣿⣿⣤⠶⠛⠉⠙⡇⠀⠀⠀⠀⡇⠛⣷⣌⡹⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠋⠸⡇⠀⠀⡐⠁⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠁⠀⠀⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠈⠀⠀⡄⠸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⣇⢀⡀⠀⡇⠀⠀⠀⠈⠀⠠⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⠀⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⣠⣴⣾⡦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠳⢤⣀⠀⠀⠀⢩⡇⠀⠀⠀⠀⣀⣦⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣧⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢜⠁⠀⠀⣀⠐⠒⠐⠒⠈⠀⠀⠀⠀⢠⢀⡄⠀⠀⠀⠀⣀⡖⠚⠀⠀⠀⡄⠀⠀⠈⢣⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⢀⡀⠀⠀⠨⢈
⠉⠀⠀⠀⠀⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⠀⠀⠀⣀⢌⠄⠀⢀⠀⠃⠀⠀⠀⠀⠠⠋⠠⠐⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁
⠀⠀⠀⠀⠀⠀⠁⢐⢶⢄⠀⠀⠀⠐⠂⠸⠀⠀⠠⠚⠁⠀⠀⠈⠜⠀⠀⠀⠀⣀⡀⢀⠀⠐⠀⠒⠀⠀⡀⠔⢁⠀⠀⢀⠀⠀⠀⡰⠒⠁
⢂⠤⠶⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠀⠈⠀⠉⠀⠀⠀⠀⠄⠀⠀⠟⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡢
⠃⠀⠀⠀⠀⠀⠠⠀⠀⠈⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣄⡀⠒⠱⠃⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡐⢋⠔⠉
⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⢺⠀⠀⠀⠀⣦⠀⣀⠀⠀⠀⠀⢄⠰⠀⠀⠀⠉⠋⠋⠑⠀⠀⠉⠀⠀⠀⠀⢀⣀⠄⠀⠠⠀⠀⢘⠑
⠀⠀⠀⠀⠀⠠⣴⠀⠀⠀⠀⠀⠀⠀⠰⠈⢦⣄⡀⠀⠀⠀⠈⠻⠄⡀⠀⠀⠀⡀⠀⠠⠆⠂⠢⠤⢒⠂⠁⠁⠀⠀⠀⠀⠀⠁
⢤⡔⠀⠀⠀⠌⠈⠀⠀⠀⣦⡀⠀⠀⠀⠀⠈⢢⡉⠂⠀⠀⠀⠺⠏⠁⠀⠀⠀⡁⠀⠀⠈⠁⠀⠁⠁⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠
⠈⠀⠀⠠⠐⠀⠀⠀⠀⠃⢵⡈⠀⠀⠀⠀⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠊⠉⠑⠂⠁
⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⢤⡔⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⣀⠀⠤⣀⣀⠀⠀⠘⢁⠀⠀⠀⠴⠂⠄⢄⢀⡀⠀⠀⠀⠈⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡤⠀⠀⢀⠰⠒⠔
⠀⠚⠁⠀⠉⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⢲⠀⠀⠀⢵⣮⠄⢢⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡲⡆⠀⠀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠀⡴⠂⠀⠀⢈⡰⠞⠀⠀⠀⠀⠐⡄⢀⣀
⠁⠀⠀⡀⠀⠀⠀⠁⢴⠀⠀⠀⠀⠀⢈⠝⠁⠉⠀⠰⢈⠀⠀⠂⡇⠀⠀⠀⠀⠑⠐⠁⠀⠀⢀⣀⠔⡻⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉
⢠⡄⣼⡂⠀⠀⠀⠀⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡸⡀⠀⠈⣥⠀⠀⠀⠆⡰⠄⠀⠀⠠⠠⠀⠀⠃⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⣤
⠀⢰⡃⠐⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⠐⠁⠀⠀⠀⠥⠀⠀⠀⠀⡌⡠⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠⠘⠛⠀⠁⠨⠁
⢀⠇⢱⠀⠀⠈⠑⠃⠔⠂⠘⠵⠟⠁⠀⠀⠀⠀⠀⠘⠃⠀⠛⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⢠⡆⠆⠔⠀⢊⡁⠀⠀⠀⠁⠜⠁⠀⠀⠀⠀⣨
⢡⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠌⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⢤⠀⠀⠐⠒⠀⠈⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠊⡄
⢀⠀⠀⠀⠀⠀⠉⠡⡀⠀⠀⠀⠀⠜⠃⠀⠀⢠⠜⡐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄⠀⠀⠀⠀⠁⡀

⡄⢰⡆⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⡀⠉⠀⠈⠁⠳⣬⣿⣿⣿⣿⣿⣿⣦⣀⠈⠙⠳⣄⠀⠀⠀⢀⠾⣷⣦⠀⠀⡇⠀⢰⢾⣿⢟⣇⠡⡀⠀⠂⠐
⣧⢹⠊⠀⠀⠂⠉⠀⠀⠀⠛⠁⠀⢀⢀⠀⡰⠊⠀⠀⢠⡦⣰⠄⠈⠙⠿⡟⠛⠛⠛⠛⠛⠛⢛⠓⠛⣂⢀⣀⣉⣀⣉⣉⣉⠀⡇⠀⢺⣿⣿⣿⣿⣦⣀⣷⣤⣤⣤
⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⠁⢁⠀⠀⠀⠈⠸⠟⠂⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⢈⣹⣿⣿⣿⣿⡿⠛⠛⡁
⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢺⣀⢘⠀⠀⠀⢠⠀⠒⠆⠀⠀⢠⡄⠀⢄⠀⠀⠀⠀⠀⠁⠀⠐⠒⢢⡀⠀⠀⠀⠘⠀⡇⠀⠀⠈⣿⡿⠿⡥⢄⠀⠀⠈⠂
⠂⢸⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣼⣿⣿⡇⠀⠀⠘⠂⠲⠂⠀⠀⠀⠁⠀⠈⠀⠀⠆⠀⠀⠘⠁⠀⠀⠀⠁⢀⠀⠀⢰⠀⡇⠀⠀⠀⠎⠀⠀⢁⠀⠀⠀⣀⣬
⠀⢸⠄⠀⠀⠀⠀⠰⠖⠀⠁⠀⠀⠀⢸⡿⢿⡇⠀⠀⢀⣀⣴⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⢰⠀⣿⠀⠀⠄⠀⠀⠀⢸⡆⠀⠀⠀⢹
⠀⢸⠄⠀⠀⠀⠈⠀⠀⣀⣠⡤⠴⢶⣿⡉⠉⠁⠀⠀⠀⠀⠟⠀⠀⠀⠀⡇⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⣘⡀⢸⢀⠂⠀⠀⠀⢀⣼⣇⠀⠀⠀⣰
⠀⢸⢀⠀⡀⠀⢀⣀⣭⣴⣶⣿⣿⣿⣷⠤⠤⠄⠀⠀⠀⠾⢰⠇⠀⠀⠀⣁⠀⠀⠘⠏⠁⠀⠀⠀⠀⠠⣐⣢⣭⣶⣿⣿⣿⡇⢸⠂⠀⠀⠀⢠⣾⣿⣧⠠⠄
⠀⣿⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠠⢅⠀⠀⠀⣠⣟⠳⠶⠶⠶⠦⢬⠓⠒⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡆⠀⠀⠀⠈⠁
⠀⠙⣞⣛⠛⡛⣛⢛⣛⠛⠛⢛⢛⢛⡛⡄⠀⠀⠀⠀⠀⠀⡉⠢⠔⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠋⠉⠁⢸⣇⣀⣀⣤⣤⣤⣤⣤⣶⣶⣷⣼
⡤⠊⢨⣩⠀⠀⠀⠀⠏⠐⢄⣠⠀⠀⡇⡇⠀⠀⠀⠀⢸⡌⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⣸⠀⠀⠀⠀⠀⡿⠟⠉⠀⠀⠀⠀⠀⠸⠀⢿⣿⣿⡏⣿⡿⣿⢿⡿⣿⠻
⠃⡀⢀⡟⠛⢀⡀⢀⠆⣴⠘⡗⠀⠀⡇⡇⠀⠀⠀⢠⢠⠀⠀⠀⡇⠀⠀⠘⠤⠸⠦⡄⢸⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⣰⠂⠀⠈⠋⠙⠁⠙⠀⠉
⠀⣧⠫⠁⢀⡀⠈⠁⠀⠀⠀⡃⠀⠀⡇⡇⠀⠀⢀⣧⠰⣄⠊⠀⢼⠀⠀⠀⠈⠙⠂⠀⢹⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠈⢙⠂⢤⡀⠀⣀⣠⠤⠤⠴⣶⣶⣾
⡆⠘⠳⢶⣄⠀⠀⠀⠀⠀⢀⣧⡀⠀⡇⠇⠀⠀⣸⣿⣷⣿⠢⠀⠀⠀⠀⢀⡀⡠⠀⠀⢸⢀⠀⠀⢀⣼⠈⠉⠉⠁⠀⢀⠀⠀⢨⠀⠀⢉⣄⣀⡠⢤⠀⢸⣿⣿⣿
⣿⣶⣤⣄⣈⣳⣄⣀⣀⣀⣜⣻⣿⣦⡇⢰⠀⠀⢾⣿⣯⣾⣆⠰⢄⠈⠀⠀⠀⢀⣴⢁⣿⠈⠈⠈⠀⠄⠀⠀⢠⣤⠀⠈⠀⡄⠸⠀⡠⠀⠀⢀⠀⡀⠙⢾⣿⣿⣿
⠀⠤⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⢺⣿⣿⣿⣿⣶⣼⣿⡷⠲⠞⣹⣿⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠠⠉⠀⠀⠀⡿⣡⣟⠀⠀⠈⢹⠤
⠀⠈⠀⠀⢦⠀⠀⠀⣀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠙⣿⣿⣿⡿⠟⠉⠀⠁⡀⠀⡄⠀⠁⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠇⠀⠀⠀⠀⢉⣉⠀⠀⠀⢸
⠀⢀⠀⠀⠀⡄⠀⠈⠈⠦⠀⠀⠀⠀⡇⢸⠀⠀⠀⠩⠟⠉⢣⠑⠄⠀⠀⡈⠀⠀⠀⡐⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣧⣤⣴⠀⠀⠀⣇⠈⠉⠀⠀⠀⢸
⠀⠈⠀⠀⠀⠁⠀⠀⠀⡀⠀⢢⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠐⢺⣟⢹⠏⠀⡇⠀⠀⠀⠀⢀⣀⣀⠠⠀⠀⠐⠛⣿⣿⣿⠀⠀⠀⠈⠈⢉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⡇⢀⠂⠀⠀⠀⠀⣿⠀⠀⠀⢠⠇⠘⠃⠀⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣿⣛⣻⠀⠀⠀⠰⢲⡏⠀⠀⠀⢸
⣶⡤⠀⠀⠀⠀⠀⠈⣀⠀⠴⣂⣠⣥⣶⠀⡇⠂⠀⠀⠀⠀⣾⣿⠄⠀⠠⠔⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠤⢖⣒⣻⣭⣭⠇⠠⠼⠀⠀⠀⠀⡌⢡⠀⠀⠀⠸
⠉⠀⣀⠀⡀⢄⣲⣬⣶⣾⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠽⠿⠛⠒⠊⠀⠀⠀⠘⠀⢀⡇⠄⠀⣂⣠⣴⣶⣾⣿⣿⣿⣿⣿⣏⠉⠹⠀⠀⠀⠨⠃⠍⠀⠀⢀⣴⣃
⠉⠉⣦⠁⠀⠀⠉⣿⣿⣿⣿⣿⣿⠿⠿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣤⣤⣤⠸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠑⠢⣀⠀⡰⠟⠚⠋
⠀⠀⡇⠀⠀⠀⠀⣸⣿⣿⠿⠛⠁⠀⢀⠀⡟⢶⣴⣾⣿⣿⣾⣿⣾⣿⣿⣿⡏⠸⣿⢀⡼⢭⠍⠉⠉⠍⢡⡄⠀⠀⠒⠀⢢⢸⠀⠀⠀⠀⠀⡄⠐⠁⠘⠁
⠀⠰⡇⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⢀⠁⠘⣿⢿⡿⢸⡏⠿⠏⠛⠙⠋⠻⠂⢲⠋⠀⢰⣧⡀⠀⠀⢈⠀⢈⣦⡇⠀⢸⢸⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠄⠐⡄
⠑⢠⡇⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠰⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⡎⢰⢀⠼⠀⠈⠲⢄⠌⠘⠣⠸⠀⠀⢸⢸⠀⠀⠀⠀⡇⠀⢀⡆⠰⠄⠀⠀⠘
⠀⢸⡇⠀⠀⠀⠀⡄⠤⠤⠤⠢⠀⠀⢰⠀⡅⠙⠢⠤⠐⠒⠒⠃⠉⢹⣿⣿⣿⣆⣇⠸⣧⣂⡐⠒⠀⠀⠀⠀⠀⢠⠀⠀⢸⠈⡀⠀⠀⣨⣧⠸⣆⠀⠈⠃
⡀⢨⡧⠤⠤⠤⠖⠁⠀⠀⠀⠀⠀⡆⢈⠀⠀⠀⠀⠒⠀⠐⠉⢦⡐⣻⣿⣿⣿⣿⣿⣄⠈⠙⠻⢦⡀⠀⠀⠀⠀⣼⣷⣄⠀⠀⡇⠀⢤⣽⣿⡿⡏⢃⠀⠀⠠
⣇⢺⠱⠀⠀⠄⠒⠀⠀⠀⠶⠂⠀⠀⠨⠀⢤⠔⠁⠀⢠⣤⢠⡀⠙⠻⢿⡿⠿⠿⠿⠿⠿⠶⠶⠦⠿⠠⠀⠀⠚⠀⠛⠛⠒⠀⡇⠀⢾⣿⣷⣾⣿⣄⠁⣦⣄⣀⣀
⠷⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢸⠀⠃⠀⠀⠀⠘⢱⡿⠄⠀⠀⠀⡇⠀⠀⠀⠀⠄⠈⠈⠀⠀⠉⠀⠀⠉⠁⠉⠉⠈⠀⡇⠀⠚⠿⣿⣿⣿⣿⣿⠿⠻⠉⠉

⠀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⡀⣀⣀⣀⡀⠀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣀⡀⠀⡀⢀⢀⠀⢀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⡀
⠀⢧⡨⢿⢺⣽⣓⣰⠿⡆⢸⠀⣗⣺⣇⡿⠀⣺⠄⡿⠀⠀⠱⠂⠇⠀⠪⠀⠀⠌⠸⠀⠙⠗⠪⠽⠚⠸⠀⠝⠃⠆⠸⠁⠰⠱⠸⠀⠀⠪⠀⠀⠅⠸⠞⠀⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡉⠁⠀⠀⠀⠈⢷⡶⠶⠶⠤⣤⣤⣤⠤⠤⢤⣤⣤⣄⣀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠈⢳⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⡶⢛⣿⠶⠛⠉⠉⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣦⡀⠀⠀⠀⢈⢳⣠⡞⠁⠀⠀⠀⠀⢀⣾⣡⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⠶⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⠛⠿⢦⣄⡐⢌⣦⣻⣄⣤⣤⣄⣀⣤⣿⡫⠄⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⡿⢠⡞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣠⣤⣤⣤⣤⣤⣄⣈⣉⣓⣿⣿⡏⠀⢠⣾⠿⠏⠁⣀⣀⣤⣶⣶⣿⣿⣿⣿⣿⠿⠟⢋⡴⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠀⠀⠠⠴⠶⠒⠒⣛⣻⣿⠿⠟⣿⣿⣟⢿⣙⠛⠛⠛⠛⠛⠛⠛⠛⠿⣯⣉⠁⠀⠀⣠⠞⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⢻⣧⠙⢦⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡴⠋⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠠⣯⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣻⠟⠁⠀⠀⠀⠀⣰⠏⢻⣧⠀⠉⠀⠀⠉⢷⣦⣄⡀⠀⠀⠀⠀⣠⠞⢷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠳⣦⣀⠀⢀⣴⣿⢟⡼⠁⠀⠀⠀⠀⢀⡼⠃⠀⠈⣿⣆⠀⠀⠀⠀⠀⢹⡌⠙⠶⣄⢀⡼⠋⠀⠸⡇⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠳⣿⣿⣯⠟⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⣨⢿⡁⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⢻⡛⠳⠶⢤⣤⣀⡀⠀⠀⣹⠏⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣸⣿⣯⣴⣶⣶⡶⠖⠒⠻⢀⡼⠃⠈⣇⠀⠀⠀⠸⡇⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠉⠛⢲⡿⢤⣄⣀⡀⠀⠀⡾⠀⠀⠀⠀⠰⠟⠛⠉⠉⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢹⡀⠀⠀⠀⢿⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠉⠉⠛⢺⡷⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⣇⠀⠀⠀⠸⣇⡾⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠉⠛⠲⠦⣤⣀⣀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣄⣀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣹⡄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⣀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⢿⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠦⢤⣼⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⢡⠂⢀⣇⣀⣀⡓⠒⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠤⠄⠀⠤⠤⠈⠁⢠⠵⢤⡃⡧⠄⠈⠉⠥⠄⢀⣀⡀⠀⠀⠂⢂⣀
⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠛⠒⠾⠀⠠⠐⠀⠁⢀⡤⠒⡠⠷⣶⠼⣴⣽⠯⢝⠓⠒⠒⠒⠤⠀⠀⢑⡀⠊⠀⠈⠳⣄
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠓⠀⠀⠀⠀⢁⡠⠊⢰⠟⡠⠊⣡⠇⠈⠢⠀⠀⠢⣀⠐⠢⡤⠞⠃⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠐⠒⠲⡀⠀⠀⠀⣀⣀⡤⢻⠀⡗⠊⠑⡄⠀⢀⡈⠀⠀⠈⠑⠢⡀⠙⢄⠉⠁⠀⠐⠒⠒⠒⠓⢄⡀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠱⣄⢀⠞⢁⠖⢉⠜⠀⡇⠀⠀⠈⢂⠀⠑⢄⡑⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠒⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡀
⣿⣯⢽⣟⡻⣻⣛⠛⣻⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡳⠀⢸⡀⠓⣹⣈⣁⡀⠀⣿⣿⣿⣿⢹⢻⡏⠀⣸⠀⠀⡇⠀⢸⠀⡆⠀⠉⠻⣿⠛⠉⠀⢢⠀⢰⠸⡧⠆⠀⠈⠯⠌⣷⣮
⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣸⣸⡇⠀⢿⠀⠀⡇⠀⢸⠀⢳⠲⡦⢺⣿⠲⣖⡲⠎⠀⠰⠤⠧⠄⠀⠈⠉⠀⡋⠙
⡔⡎⠀⠰⢿⣉⣴⣁⠌⠇⠀⠀⠈⢉⣉⠉⢠⢤⠘⠦⠴⠷⠤⠞⠀⠘⠢⡧⢘⣿⠠⣧⠤⠄⠀⠀⠠⠄⠀⠄⠘⡥⠛⡁⢸
⡰⡇⠀⣮⣼⣯⠉⣽⣯⣷⠀⠀⠀⠘⠧⣑⣦⣰⢖⣉⠟⠀⠀⠀⠀⢘⠒⡗⠚⣿⠀⣅⠠⠇⢠⡄⢭⣦⣅⠤⢀⠒⡌⠁
⠛⠁⠀⣧⣵⣬⠀⣥⣤⣾⠀⠀⣏⣉⣉⡉⣉⣉⡏⣉⡉⣉⣉⡄⠀⢈⠑⡖⢈⣿⠂⣤⠔⡇⠸⡄⣃⡅⠁⠀⠀⠙⠀⠓⢛
⠖⣦⠀⣯⣡⣌⡆⣥⣍⣼⠀⠀⢸⠷⣌⠻⣾⠀⢷⣌⠻⣮⡛⠀⠀⢈⠙⠗⢉⣿⠓⡧⠐⡇⣀⣀⠤⡄⢦⠀⠀⠀⣖⠢⡏
⠾⠥⢤⠙⠙⠋⠉⠉⠉⠁⠀⠀⠘⣷⣘⣷⣬⣀⣧⣉⣳⣮⡃⠀⠀⠨⠴⠧⠠⠿⠁⠶⠪⠃⠙⠉⢷⣥⠚⠿⠂⢠⠬⠿⠿
⣀⣀⡼⠀⢀⣰⡒⡔⢢⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⡀⠀⠀⠀⣀⠀⠘⠂⠚⢸⠒⢸⠀⢸⣀⣀⣠
⠀⢸⠀⠀⢘⠋⠱⠶⠏⠈⠁⠐⣠⡘⠀⠀⡐⣒⡦⣀⠴⠆⡂⠘⢘⢘⠘⢇⠙⠆⠠⢊⠜⠀⠀⠂⠚⠚⠒⠊⠀⠀⢹⠀⠈
⠀⢸⠀⠀⢸⠁⠸⢠⠁⠈⠀⠆⠽⠸⠀⢀⠘⠦⣶⣿⡆⠈⢁⠀⠈⠀⠄⠐⠐⠻⠻⠀⠠⠤⠐⠋⣔⣤⣄⡢⠄⠀⢸
⠀⢸⠀⠀⠀⠉⠉⠉⠁⠁⠀⠒⠒⠒⠀⢠⣀⠀⣸⠀⣄⡀⣠⠀⠀⠀⢣⠄⠄⡄⢠⠀⠀⡰⢰⣯⣿⡍⣯⣿⣼⡆⢸
⠤⠚⠀⠀⠀⠀⠀⠪⢥⣸⣠⣹⠵⠀⠀⠀⡁⢂⣙⠀⠤⢐⡃⠀⡀⠀⢀⠀⠀⡇⠀⠀⠀⠀⢸⣤⣤⡅⣩⣦⣵⡇⠘⠦⠴
⣾⢹⠴⣲⠀⠀⠀⣷⣾⣯⢹⣽⣯⣷⠀⠀⣏⢎⣹⢀⡔⣨⡇⠄⠿⠄⠈⠉⠉⠉⠉⠉⠉⠁⢸⣌⣭⡁⣭⣌⣹⠀⠀⠀⣤
⠙⣿⠉⠁⠀⠂⠀⣧⣤⣼⢸⣴⣭⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⠀⠀⡤⠖⠆⣤⣄⠀⠀⠈⡉⠭⢍⡉⠉⣉⠀⠀⠂⠈
⠺⣿⠒⣶⠖⡇⠀⣧⣩⣽⢸⣥⣩⡇⠀⠀⣀⣀⡉⠱⡎⢹⡠⣶⡄⢠⡘⡒⣺⣿⠒⠃⣢⠀⢸⠂⠖⣸⠔⠆⠨⠀⠀⠳⢞
⠘⣿⠢⡧⠚⡇⠀⢉⣉⠉⠉⠉⣉⡁⠀⠀⢳⣏⣙⣦⣶⡏⠀⡉⠀⠘⡶⢶⢾⣿⢲⡶⠊⠀⠘⠋⠯⠻⢛⡄⢻⠀⠀⠰⠤
⢰⣿⠐⠶⢊⡇⠀⠘⢎⠢⠀⠎⡠⠏⠀⠀⣾⠤⠤⡇⢸⠤⠤⠆⠀⠀⣿⢸⢸⣿⢸⠁⠀⠀⠀⠒⠀⡚⠀⠀⠋⠀⠀⠰⠄
⢺⣏⠑⠶⠉⡁⠠⠒⠒⠺⠛⠒⠒⠒⠄⠀⢠⠀⠀⣇⢸⠀⠀⡀⠀⠀⠙⠛⠛⠋⠉⠉⠁⢰⡶⢄⣘⢙⡠⢖⡷⠀⠀⠐⠠
⢺⣏⠙⠛⢉⡇⠰⡤⠤⢤⠀⡦⠤⢤⠃⠀⠀⠉⠉⠉⢉⣉⠉⠁⠀⠀⠀⡄⡠⡲⠀⠠⠀⠀⠙⠲⠿⠾⠶⠉⠀⠀⡄⢛⠢
⠼⠧⠤⠾⠬⠃⠀⡇⠀⢀⡀⡀⠀⢰⠀⠀⠀⠀⢰⡓⢾⢨⡖⣲⠆⠀⢠⢐⡿⢤⠀⢳⠖⣲⠶⣲⡗⢚⣰⠖⣢⡶⠁⠨⠵
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⢁⢉⡀⠀⠀⢠⠖⠚⠻⡿⠛⠓⠆⠀⢈⠀⡇⢈⠀⠸⠞⣡⡾⢋⡅⠸⣋⡾⢋⡽⠀⠀⢀
⠂⠀⢰⠂⣀⠛⢀⡀⠂⠀⠀⣖⢦⣁⠃⢧⠀⢸⣄⣀⣠⣧⣀⣀⡜⠀⠈⠉⠉⣁⠀⠀⠛⠛⠒⠛⠃⠘⠛⠒⠛⠃⠀⠀⠂
⣄⡀⢰⡄⣡⣿⢗⡁⣄⢀⡃⠈⢹⣿⠉⠍⣵⡀⣈⠀⢀⡇⠀⣸⠀⠀⢰⡗⣼⣉⡷⢲⡄⠀⠀⠘⣰⣐⠀⠀⢀⣀⣤⡀⢀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠀⠀⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣥⣀⣷⣁⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠅⠀⢀⣀⡀⣧⣧⠟⠉⠀⠉⠁⠒⠂⠠⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⢀⠔⠋⠁⠉⠁⠈⠉⠁⠀⠒⢠⡴⠊⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠁⠀⠀⠀⢺⠃⠀⠀⠀⠒⠒⠒⠠⠄⣠⠖⠁⢸⡴⠊⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠂⠀⠀⠤⠤⣬⢀⣀⡀⠀⠀⠀⠀⠀⠀⣁⣀⠔⠉⡆⠀⠘
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠘⣤⠎⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠈⠉⠉⠁⣿⠁⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣀⡀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⡀⠀⠀⠀⠟⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠆⠀⠀⠐⠒⠀⠀⠘⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠉⡎⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢐⡒⡆⠀⠀⠀⠀⠇⠀⠀⢍⡻⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡃
⠀⠀⠀⠀⡆⠀⠉⠀⠀⢖⡲⠀⢠⠀⠀⠀⠀⠀⡤⡤⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢣⠎⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⡇⠀⡴⠶⠀⠀⠀⠀⢀⠀⠀⠰⡚⡂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠈⠢⠄⣀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡸⠖⠁
⠀⠀⠀⠀⢁⠀⠘⠊⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠂⠆⠠⠤⠤⠄⠀⢀⣠⠶⠊⠁
⠀⠀⠀⠀⠘⠤⢀⣀⣀⣀⣀⣀⣠⡤⠀⠤⠄⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⡖⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢠⡧⢒⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⡀⠀⠈⠉⠉⠁⠀⠘⡿⡟⠋⠐⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠘⢋⠆⠀⠀⠀⠀⡐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⣤⠊⠀⠀⠀⠀⢀⡴⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⢀⣀⡀⠀⠀⠀⠈⠀⢸⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡤⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣀⣠⣄⣦
⠀⢀⣠⡶⣻⢷⡿⣂⡔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣶⣶⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⣾⣿⢿⣿⣿⣟⡷⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⣿⡿⠀⠀⠀⠀⠀⠀⢀⣾⣶⠆⠀⠀⠀⠀⠀⢠⠄⠐
⠀⢈⣾⡻⣟⡻⢶⢜⣳⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠉⠛⢿⣯⢷⡽⣯⣉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⢨⠂⠀⠘⡁⠀⠘⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠘⢾⡀⠀⠀⠀⠠⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠈⡀⠀⣀⣀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⡀⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⠀⠀⠀⢠
⢡⡀⠀⣈⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠙⢅⣻⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⣼⣿⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠰⠟⢋⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠊⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠷⠙⣮⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⡆⣤⠀⢠⣀⡆⢀⣭⡀⠒⣱⣾⠀⠀⠀⠀⠀⣀⢠⡀⢀⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣿⠏⣀⡛⠁⣅⢸⣏⣤⡄⠀⠁⠀⠀⠀⠀⠀⢫⡀⠶⣔⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣷⣇⡄
⠀⠀⠀⠀⠀⠀⢀⣀⢈⣁⡐⢿⠍⠥⣬⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡝⣻⣟⣵⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠑⠶⠛⠀⠘⠀⠘⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⣿⣎⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠄⠀⠠⣿⠀⢐⡄⠀⠀⠀⠀⠀⠀⣬⣿⢿⠄⠀⠀⠀⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠄⣈⣾⠠⠂⠀⠀⣀⣀⠀⢀
⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⠀⠄⡖⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⡄⠐⠄⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠈⠻⠚⠁⠻⡁⠀⠀⠐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢺⠄⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣅⠂⠇⣥
⠀⠀⠀⠀⠀⠘⠋⢿⡾⠛⠀⠀⠈⡡⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⡗⡁⠀⣠⠳⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡼
⡀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⢀⠀⠴⠶⢆⣠⠄⠀⠀⠀⠀⠀⠘⢡⠀⣠⠎⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠆⠹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⠁⢢⣞⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠷⠀⠀⠘⠃⣿⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣅⠀⠀⠀⠰⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠙⢷⣄⠀⠀⠘⣄⢹⡄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⠤⠒⠛⠓⡶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⠛⠓⠶⣭⣷⣄⠀⠈⢧⢇⠀⠀⠀⠀⠀⠀⡠⠋⢀⠔⠁⠀⠀⠀⡰⠁⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠤⣤⣀⡈⠙⠛⠶⢤⣸⠖⠒⡶⣦⠤⢊⣡⣒⣁⠤⠤⠤⠴⠾⢥⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⠄⠒⠠⠄⡀⠀⠉⠉⠛⠉⠙⠀⢸⣰⠀⠁⡟⠠⢉⠡⣤⣤⣤⣤⣤⣤⣀⣀⠈⢻⡄⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⣄⣐⠲⢤⠤⠤⠉⠛⠛⠛⢛⡛⠿⠿⣿⣦⣤⣧⠀⠀⠹⣆⠠⢤⣤⣀⡀⠀⠀⢀⣼⠥⠖⠛⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣶⠹⣆⢀⣀⣉⣉⡉⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠦⠤⠄⣀⣀⠀⠀⣀⡤⢾⠀⢻⣄⠀⠀⠈⠉⠙⣾⠃
⠀⠀⠀⠀⠠⠀⠀⠊⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⡎⠀⢸⡏⠛⠶⠦⡤⠾⠋⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠴⠡⠤⠶⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⡼⠁⠀⢸⡇⠀⢀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠁⠀⠀⢸⠁⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⡾⢄⡀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣀⡀⠀⢠⡇⠀⠙⢾⠀⠀⠀⡆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠁⠙⡆⣼⠀⠀⠀⢸⠀⠀⠀⠁⠄⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⠀⠀⠈⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡐⢀⠀⠀⠀⡇⠀⠀⠘⡄⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⠁⢸⠀⠀⠀⡇⠀⠀⠀⠑⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⡜⠀⠀⠀⡇⠀⠀⠀⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢤⣄⣀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⢡⠀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⠀⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⡀⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠶⢤⣄⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⣀⣿⣠⠔⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠿⠿⠛⠿⠟⢛⠋⠀⠀⠀⢀⣀⠉⠙⠂⠀⠀⣾⠀⣄⣆⠄⠘⡆⠀⠀⠀⠄⠿⠋⠀⠀⠀⢠⠖⡄⢀⡄⠙⠈⠛⠉⠉
⠀⠀⠀⡸⣄⠈⠒⠀⠀⠀⠀⠀⢀⢸⠟⠙⢻⣀⠀⠀⢀⣿⠚⠭⠒⠀⣰⠇⠈⠀⠑⡀⠀⠐⠬⣁⠓⢼⣴⡿⠭⠄⠀⠀⠀⠀⣄
⠠⡀⡾⠀⠀⠱⣤⠀⠀⠀⠀⠀⠐⣿⡀⢁⣸⠧⠀⠐⠁⢀⠉⠛⠒⠒⠁⢀⠀⠀⠀⢀⡀⠐⠀⠨⠟⡿⠿⡣⡀⠈⠀⠀⠀⠀⡏
⠂⡐⠀⠠⠾⠲⠈⠁⠐⢀⠐⠈⠀⠀⠹⠋⠓⠀⠀⢠⡀⠘⠃⡀⢤⠀⠀⠈⠑⠤⠊⠠⠀⠀⠠⠀⠈⡀⡀⠀⠀⠂⠀⠀⢀⡀⠘
⠙⢇⠀⠀⠐⠆⠀⠀⠀⠁⠈⠀⠀⠌⠀⠲⠉⠆⠀⢀⡀⠛⢲⡟⠂⠤⣄⠀⢀⡔⠁⠢⢀⠀⠀⢀⠀⢈⠁⠀⠀⢀⢸⣦⠉
⠀⠀⠀⠀⡠⣶⣾⣿⣶⣑⣄⡀⠀⢳⡀⡜⠘⠁⢰⠀⠁⡘⠷⢡⡙⢂⠈⠰⠋⠀⠀⠀⠈⡐⠋⣿⣛⠲⣇⠀⠀⢸⠥⠀⠀⠀⠠
⠒⠒⠀⢠⣲⣿⡿⣻⢟⣿⣵⡓⠀⠈⣷⣀⠠⠖⠁⢀⠀⠉⢀⡀⢡⠀⠀⢀⡔⢂⡀⠀⢀⠋⡟⢺⠟⠃⢘⠂⠹⠖⠀⡖⢩⡿⣦
⣽⡷⠄⠀⣭⣿⣿⣿⣷⣾⣿⡧⠀⠰⠃⠀⠀⣆⣶⠧⡗⠠⠀⠁⡀⣀⠀⣕⣿⣿⢎⠀⠈⠙⢟⣣⡬⠙⠋⠀⠁⠀⣰⢿⡿⠳⠿
⣶⠅⠊⠀⠉⠹⡼⠿⣭⠟⠟⢁⣤⠴⠦⢄⠈⢣⢧⡯⣜⡧⠀⢀⠰⠶⠈⠂⠈⠋⠀⠰⡄⠴⠀⠀⢀⡀⢀⡄⠀⠀⠛⠻⣿⣯⣁
⠋⢀⣰⠶⣤⡄⠀⠀⠀⠀⢀⡞⢀⣀⡀⡀⣷⠀⠉⠑⠃⠀⠀⡄⠉⠀⠁⠀⠀⠀⠀⢣⠰⠦⠆⠀⢨⡑⣬⣀⣔⡂⠈⠈⢀⡈⠿
⠀⢤⡇⠲⢀⡦⠀⣰⣷⡀⠸⣇⠀⠩⡛⠧⣼⠀⠀⠀⠀⢀⣾⡇⢀⡀⣠⣤⡴⠂⠙⠄⠶⠄⣛⠁⢠⠔⠉⡏⢱⡍⠀⠀⠀⢀⠎
⡀⠀⠨⡖⠟⠀⠠⣿⣿⠃⠀⠈⠢⠶⠶⠚⠁⠉⠢⠀⠀⢘⠟⣡⣿⣿⠿⠋⠀⠀⠀⠘⡆⠂⠉⠀⠀⠀⠀⠀⠀⠠⣄⡀⠉⡆
⠄⠂⠀⠀⠀⠀⠀⠋⠀⣤⠔⢻⡦⠤⣶⡀⢀⠀⠀⢀⠠⠎⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠛⠛⢀⠠⢲⠊⠀⡀⠂⠛⣷⣷⢋
⠀⠈⠀⢀⢴⣑⡄⡀⠀⠀⠀⠈⠀⠘⠋⠁⡽⠷⡀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⣀⡌⢿⠇⠠⡾⠀⠀⠈⡩⢝⠿⠻⡟
⠂⠀⠀⠨⢻⣿⣻⠁⠀⠀⠀⡠⢢⣴⣶⣴⡄⠀⠀⠀⡰⡫⡥⢿⢟⠛⣠⠀⠀⣿⣶⠀⠀⠁⠀⠀⠀⡀⠤⠄⡀⠀⠂⠀⠘⣀⠄
⡀⣠⠀⠀⠀⠉⠀⠀⠀⠴⢯⣻⡿⣿⢿⣿⡧⢅⠀⠀⡽⠃⣴⣾⣧⢿⡙⢂⠀⢿⣿⠃⠀⠀⡈⠑⠻⢐⡒⢂⣀⠶⠀⠀⠀⠁
⠛⠛⢠⣼⡆⣀⣄⠀⠀⢠⣿⣿⣽⣾⣿⣿⣟⡋⠀⠀⢧⠘⣈⣉⠗⡴⣴⠞⠀⠀⠁⢤⡽⠚⠙⢿⡄⠀⠀⠀⠴⢶⡀⠶⡂⠀⣀
⠀⠀⠈⠁⠀⠛⣫⠉⠉⠀⠻⡿⣟⣻⣿⣹⠛⠂⠀⠀⠈⠙⠫⢓⡺⠖⠃⠀⠀⠀⠀⠾⣇⡈⣡⣟⡉⠀⠀⢤⠠⠶⢀⣿⣍⣀⡉
⠂⠀⠀⠀⠀⠤⠄⣂⡔⢀⣤⠀⠈⠁⠀⡠⢺⠀⠀⠄⠀⠠⠀⠀⠀⠠⢴⣥⣤⢲⠀⠀⠋⠙⠋⠁⠀⠀⣠⡀⠰⠓⢠⣷⠄⢉⠁
⠀⠀⢰⣄⠐⠂⢉⠏⢛⡲⠄⢛⠢⠤⢊⠀⡆⠀⠀⠀⠀⠄⠀⠀⠀⢨⢾⣘⣸⡩⠂⠀⡉⠶⠁⢹⠀⠀⠀⢠⠤⠀⠶⠆⠘⠋⠁
⣴⣤⡸⣿⡇⠀⠈⠀⠀⠁⠀⠈⠆⠀⡞⠐⠓⠠⣄⠀⠀⢠⡤⠻⣤⠌⠙⠝⠓⠁⠔⠀⠓⠰⠀⣼⠀⡀⠠⠀⠀⠀⢀⠤⠀⠹⣿
⠛⠿⠷⠈⣏⠒⠄⢀⣡⡀⠀⠀⠘⣾⠥⠄⠂⠉⠀⠀⠰⠾⡐⠂⡽⠆⠀⡀⠄⠀⠌⠒⠤⣀⣿⠃⠀⠂⠀⢘⠀⢸⣽⣾⢽⠂
⣿⡿⢶⠚⣿⣏⣶⣿⣻⡃⢱⠀⠘⠁⠰⠆⠸⠐⣆⠠⠆⠀⠛⠿⠀⠀⠀⢀⡙⣋⠄⠀⣠⣆⠈⠂⠀⠀⠀⠀⠀⠈⠘⠟⠉⢡⣴
⠀⠀⠀⢣⣶⣉⠨⣍⣹⡿⣏⠀⠀⠀⣠⡀⠶⠤⠉⣄⠒⠀⡠⠒⠒⠦⡄⠀⠀⠀⠀⠀⣿⣿⠆⠠⠢⡀⠀⠁⣾⢡⣴⠀⣠⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠁⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⣇⡀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢤⢀⣸⠒⠈⠀⠀⠀⡆
⠀⠐⠂⢀⠀⠐⢯⠄⠄⢄⡂⢀⠙⠤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠋⡀⢔⡪⠤⠠⡽⠂⠀⡀⠒⠂
⠀⠀⠐⠚⠂⠀⠋⠀⠀⠀⠉⠒⠬⠂⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠐⠥⠒⠉⠀⠀⠀⠙⠀⠒⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠒⠒⠒⠒⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣀⣑⡾⠟⠉⠉⠉⠉⠻⣷⣊⣀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠸⡒⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⢒⠗
⠀⠀⠀⠀⠀⠀⠀⣨⠗⠀⠈⠦⢴⣾⡿⠙⠒⠒⠒⠒⠒⠒⠒⠒⠋⢿⣶⡦⠴⠁⠀⠺⣁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉⠉⠗⢶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢠⣤⣶⡶⢾⡉⠉⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣃⣸⠀⠀⠉⠙⠓⠒⠦⠤⠤⠤⠒⠚⠋⠉⠀⠀⣇⢘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠠⠤⠤⠤⠤⠔⠐⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠀⠁⠒⠒⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⢰⠒⠲⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠖⠒⡆
⠀⠀⠀⣤⣒⠂⢻⠀⠀⢱⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠢⠤⢄⣀⠀⠀⡞⠀⠀⡟⠐⣒⣤
⠀⠀⠀⠀⡼⠁⠈⢷⣶⣦⣓⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣚⣴⣶⡾⠁⠈⢧
⠀⠀⠀⠘⠋⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠉⠙⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⢂⠔⣈⡔⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⣪⢚⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡤⠔⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠰⠑⠁⢼⠀⠀⠀⠀⠀⠀⠂⢀⣶⠶⠞⠺⢿⡖⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⠄⢀⠃⠀⠀⢸⠀⠀⣤⡤⠴⢖⠛⠙⡇⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠈⠰⠠⠆⠼⠶⢯⡇⠀⠀⢸⢸⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⠤⠖⢈⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠉⠀⠀⡘⠀⠀⠐⠗⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠸⠀⢸⡇⠀⠀⢸⠀⢠⣷⠦⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠠⠀⠠⠀⠀⠀⢠⠰⠀⠀⠃⠀⠀⠀⠀⠐⠀⣹⡇⠀⠀⣸⣿⣻⡿⢶⣾⣯⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠂⠐⠨⠀⠀⠠⢰⡈⠋⠉⠙⢹⠀⢹⡗⠀⢨⣿⣿⠿⣧⣾⣯⣽⣿⡇
⠀⠀⠀⠀⠀⠸⡇⠄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⣖⣊⡇⣁⣾⣷⣸⢶⣷⡿⢛⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⡇⠀⠈⠉⠛⡟⡟⠛⠊⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠐⠀⠄⡀⡗⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠂⠤⡤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⣀⣀⣀⣀⣀⣰⣀⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠤⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⠀⡀⡀⠀⠀⠀⠀⠀⣀⠠⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠀⢀⠀⢀⡤⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⡗⣘⡏⠀⢈⢇⣨⠃⣠⡀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠈⠘⠿⣹⠁⠀⠀⣏⡻⠛⠁⢀⣤⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⠌⣷⡀⠀⠀⣹⣓⡶⣞⠉⠀⠀⠀⣺⣯⣶⠾⠂⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠾⠇⠘⢶⣺⣏⣹⣤⣯⣩⣉⡨⠏⠈⠉⣆⣤⠀⠀⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢠⢯⡠⣿⣀⣴⢤⡤⡆⠀⠀⢀⡀⣀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣱⣎⡹⠓⠺⡧⢼⣉⡷⢤⠗⠘⢯⣹⣞⣉⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣰⠟⠀⠀⢀⢬⠂⠉⠐⡵⡀⠀⠀⠹⣆⠉⠚⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⡦⡷⡾⡄⠀⢀⢣⢾⠵⣠⡀⠉⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢐⡟⠐⡥⠀⢨⠇⢩⣂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⢀⡀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠂⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠒⠒⠒⠀⠈⠉⠉

⣶⣶⠶⠾⠟⠛⠛⠛⠛⠳⣝⣿⣼⢸⠇⣿⠀⣿⠀⣿⠁⣿⠇⣿
⣦⣤⣤⣶⣶⠿⠿⠿⠻⠷⣜⡇⡇⣾⢰⡏⣸⡇⢸⡏⢰⡟⢠⡟
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⢷⢣⡇⣾⢁⡿⢀⣿⢀⣿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⢡⡏⣸⠇⣼⠇⣸⡏⣸⡏⠀⠀⠀⢀⣀⠤⣄⠲⣮⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⢸⠇⣿⢠⡿⢠⣿⠀⡿⢥⣶⣽⡪⡕⣎⢳⡌⢷⡈⢿⡄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡸⡸⣇⢿⡘⣧⣸⢿⣚⠭⢿⣛⣻⣿⡼⡜⡆⢿⡘⣷⠘⣷⡈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠽⠿⠿⣟⡫⠵⣚⡭⢖⣫⡭⢖⣒⣻⠵⢷⢹⡘⣧⠹⣧⠸⣧⠘⣷⡀⠀⠀⢀⣀⣀⠤⣤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⡭⠭⠵⣚⣩⠵⢚⣩⠴⢚⣩⡵⠖⠛⢻⢿⣧⡙⢧⡙⢷⣌⠳⣌⡻⢔⣪⠽⠶⠮⡝⡌⢧⢳⡜⢮⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣒⣛⣋⣭⠴⢚⣩⡴⠞⠋⠁⠀⠀⠀⠈⣿⡼⡼⡶⢋⣗⠾⣛⠵⢚⣭⠶⠞⠛⠓⢾⢹⢸⡆⢿⠈⣧⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣇⣿⡭⠗⣋⡵⠞⣋⣤⡶⠿⠛⠛⢾⢸⡈⣇⢸⡇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣸⡖⣋⣩⡴⠞⠋⣁⣤⣶⠾⠿⠷⣼⡇⣿⠘⣧⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣉⣥⣴⠶⠟⠋⣁⣠⣤⣶⣦⣼⡇⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣴⡶⠿⠛⠋⠉⠀⢨⢹⢇⢸⡇⢻⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⡈⣷⠘⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⣛⢌⢧⣘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠚⣛⣩⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠛⠋⢁⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣾⠿⠛⠁

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠎⠀⠀⡃⠀⠀⠀⡆⠀⠀⢨⠀⠀⠀⢐⠀⠀⠱⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣠⣮⣤⣤⣤⣮⣤⣤⣤⣧⣤⣤⣤⣥⣤⣤⣬⣤⣤⣤⣼⣤⣤⣤⣵⣤⣤⣤⣵⣄
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡸⢇⠀⠀⡨⢇⠀⠀⢨⢇⠀⠀⡸⢅⠀⠀⡸⢇⠀⠀⠨⢇⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠀⣠⣱⣪⣥⣤⣵⣪⣥⣤⣭⣨⣤⣬⣅⣬⣤⣤⣵⣊⣅⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣧⣠⣤⣤⣼⣧⣤⣤⣄⣼⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⠿⢿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⢀⡀⣰⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣆⢀⡀
⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢶⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠶⠂⠀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠙⠻⣦⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⣴⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⣦⡀⠀⠘⢷⣄⣠⣾⣿⠁⠤⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠤⠤⠶⠞⠻⢿⣿⣿⣿⣿⣿⣿⣻⣥⣶⣿⣿⣿⣿⣿⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡼⠉⠳⣤⣤⣤⣤⣴⣶⣾⣿⣿⡟⣭⢻⣟⣛⣻⠿⢿⣿⣷⣦⡀⠈⠑⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⢸⣿⣿⣿⡋⠉⠉⢡⣿⣿⣿⡄⠙⠻⣿⣿⣦⣹⣿⣿⣷⡶⠖⠚⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠳⣼⣿⣷⠀⠙⠳⡄⠼⣿⣿⣿⣷⠛⠛⢹⣿⣿⡇⣿⣿⣿⠇⢀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣧⡀⠀⢠⡇⠀⠹⣿⣿⣿⣷⠀⣸⣿⣿⡧⢾⣿⣿⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢨⣿⣿⠈⠳⣼⣧⣤⠤⢿⣿⣿⣿⡏⢽⣿⣿⠀⢸⣿⣿⡅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⠀⠀⠀⡯⠀⠀⣾⣿⣿⣿⠁⢸⣿⣿⠀⢸⣿⣿⡇⠀⣯⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⣿⣿⠀⠀⠐⡇⠀⢀⣿⣿⣿⡏⠀⢸⣿⣿⠀⠀⣿⠻⣇⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢻⣿⠀⠀⠰⠇⢠⡾⠛⣿⠏⠀⠀⢸⣿⣿⡀⠀⠈⠃⠀⠀⡏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⢸⣿⡇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠄⠀⠀⠀⠀⠀⣿⣇⣧⣠⣠⡤
⠀⠀⠀⠀⠀⠀⠠⠶⠄⡆⡇⠀⢸⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠀⠀⠀⠀⠀⢀⣿⣿⣯⣧⣰⡶⠄⢀
⠀⠀⠀⠀⠀⠀⣤⣶⣠⡟⣿⠀⠘⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢀⣇⡉⠾⣿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠈⢿⣵⣬⣧⣘⢷⣤⣿⡇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⣀⣠⢴⣾⣿⣿⣦⠄⠈⠑
⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⣿⣷⣮⣿⣇⡀⠀⣿⠀⣀⠠⠀⢀⣀⣤⣿⣿⣿⣿⡿⣟⡻⠉⡛⠓⠀⠐⢓⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠢⡄⠈⢻⣏⠹⢦⣿⣥⣴⣶⣿⡿⠿⠛⠛⠋⠉⠐⠋⠉⢉⣁⠀⠠⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⢶⡚⠁⠓⠠⣶⡛⠋⠉⠐⠚⠉⡍⠉⠋⠁⠀⠄⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠔⠋⠀⠀⠀⠛


⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠞⠁⣤⣈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠱⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠸⡄⠀⠀⠘⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠙⣄⠀⠀⠹⣇⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠶⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡀⡀⠀⠀⠙⠢⣄⡑⠦⡈⠣⡀⠀⢿⣤⠤⠶⣖⠉⠀⠀⠀⠀⣀⣀⡤⠖⠊⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣒⠒⠈⠉⠉⠉⠁⠒⠢⠤⢍⣓⣤⣀⣈⣦⠼⡏⢆⠈⢊⢳⡒⠋⠉⠭⠁⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠿⢐⣛⣛⣋⠉⠑⣒⣒⢲⠶⠶⠶⣒⣿⠿⢭⣇⡤⢧⢘⠀⡄⠀⣗⡢⠬⢭⣭⣤⣤⣤⣔⣒⣚⡣⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢠⠒⠚⠛⠒⠂⠠⠤⠤⡤⠤⢿⠀⠇⠀⡟⠛⠛⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡘⢀⠀⠀⡇⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠈⠀⠀⣠⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠛⡏⠉⠉⠉⠁⠒⠺⠀⠀⠀⢸⠤⠤⠄⣀⣀⣀⣀⣀⣇⣀⡇⠀⠀⠀⢹⠤⠤⡇⠀⠀⠀⡗⠒⠈⠉⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⡰⠃⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠛⠒⠋⠉⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣀⠤⣀⠀⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠁⠀⠀⠉⠁⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠂⠤⠤⢧⣀⣀⣀⣇⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣀⣀⣇⡀⢀⣀⠧⠄⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠿⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠶⠶⠿⣼⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣽⣷⣤⣄⢀⢄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠁⠀⠀⣷⠢⠎⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢷⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢬⡆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡇⠀⢠⠂⠀⠀⠀⠀⠀⠀⡏⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢐⠄⡸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⠀⡔⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢜⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠊⡀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢎⠎⣽
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⣸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⡐⢈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣧⠀⠀⠀⠀⠀⠀⢀⡾⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠊⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⠦⣄⣀⣀⣠⡴⡟⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⢥⣾⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢪⢺⡆
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠆⢀⠔⠀⠀⢀⠔⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡱⢣⢾⡇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠐⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⡰⢣⠞⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⡡⠃⣧
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡱⠃⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠱⢁⢺⡇
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠳⠦⢼⠇
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠻⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠰⣶⣿⢿⣶⠆⠀⠀⠀⠀⣶⣶⡿⢿⣴⣶⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⣄⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⣼⣯⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣼⣅
⠀⠀⠠⡶⣀⡀⠀⢀⣤⠴⠖⠒⠲⠶⠶⣮⣭⣳⣀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⣈⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⡀⢀⣠
⠀⠖⠔⠁⠠⠁⣰⡯⠖⠒⠒⠒⠶⢤⣄⣀⠀⠉⡿⠛⠻⠶⠶⠶⠾⠛⠋⠀⣠⣿⣧⣶⣿⠃⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⣰⣿⠛⢿⣟
⠼⠚⠀⢀⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⢦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣥⣤⠴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⢻⣶⠞⠿⠃
⠀⠠⠀⠈⡀⢂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⢀⡀⠁⠀⠀⠀⠀⢠⠚⠉⠉⠁⠉⠙⢿⣆⠉⠉⠙⣛⠛⣿⠲⠶⠶⠶⠾⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣆⠀⣤⣿⣛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣠⡾⠋⠉⠓⠀⠙⢋⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⣇
⠀⠀⠀⠀⠀⣿⣥⣼⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡛⢻⣿⠿⠋⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡦⢸⣷⣦⡄⠀⢀⡀⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠋⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⣿
⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⢇⣾⣿⠟⣻⠛⢫⡟⢍⢁⡿⢫⣟⠃⣿⣯⣀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿
⠀⠀⠀⠀⠀⣿⠀⢺⣿⡏⣼⡿⣡⠀⣿⠀⣿⣶⣏⢘⣴⣾⡯⠀⣿⣿⢹⡇⣰⣶⣶⣿⡿⡿⣻⡿⠟⢻⡿⢛⠁⣾⣿⡆
⠀⠀⠀⠀⠀⣿⠠⢸⣿⣷⣬⣾⣿⢸⣿⣾⣿⣿⣿⣿⣿⣿⠇⠐⢿⣿⣾⢰⣿⡿⠁⢸⡇⢱⡏⢨⠄⡿⡁⢏⡄⣿⣿⡇
⠀⠀⠀⠀⠀⠋⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⠿⠿⠛⠛⠋⠹⠃⠀⢸⣿⣇⢸⢟⣴⡇⣿⡇⣾⣿⣿⣌⣴⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣿⣿⣶⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠈⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠁⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⣿⣿⡿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⡁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡶⠟⠛⠛⣧⣴⢦⣤⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠉⢻⡀⠀⠀⡿⠃⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣳⣀⣰⣇⣠⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣤⠶⠚⣫⡿⣿⠉⣿⠳⣄⠉⠻⣶⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠔⣡⠞⠋⠀⣠⠞⠋⠀⣿⠀⡏⠀⠈⢷⡄⠈⢻⣆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢼⡧⣦⢀⣾⡇⠀⠀⠀⣿⠀⡇⠀⠀⠀⠻⣆⣶⠿
⠀⠀⠀⠀⠀⠀⣤⣤⣌⡁⡴⠒⠚⠛⠛⢻⡶⢚⠻⢯⣼⡧⡀⠀⠀⣿⠀⡇⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢠⡾⠁⠰⡈⢹⡇⠀⠀⠀⠀⢸⣇⣽⠀⠀⠙⣿⢟⡛⠛⣿⠀⣟⠛⠻⠟⢿⡟⠀⠀⠀⠀⠀⠀⢐⣒⠲
⠀⠀⠀⠀⢻⡀⠀⠀⠹⣿⣧⠀⠀⠐⠀⣿⣿⠃⠀⠀⣰⣿⠀⠀⠀⣿⠀⡇⠀⢀⠀⢸⡇⠀⣠⡶⠶⠛⠛⠛⠛⢳⡄
⠀⠀⠀⢀⠀⠻⣤⣠⠶⠮⠿⣆⣠⣦⠾⠟⠳⣶⣣⡼⠏⣿⠀⠐⠀⣿⠀⡗⠄⠀⠀⣻⣧⣤⣿⠀⠀⠀⠀⠀⠀⢸⣧⡶⠛⠻⢶⣄
⠀⠀⢀⣀⣤⣤⣿⠁⠀⠀⠀⢠⡟⣧⠀⠀⠀⠘⣿⠛⠛⠛⠷⣦⠀⣿⠀⡇⢀⣤⡶⠟⠁⡦⢹⠀⠀⠀⠀⠞⠀⠈⡟⠀⡼⠀⠀⠙⠻⣦
⠀⠀⣿⠉⠀⣰⠃⣠⡄⠀⢠⡏⠀⠘⣇⠀⠠⠀⠸⣆⠀⠀⢠⣷⠤⣿⠀⡟⢿⠁⠀⠀⠀⢳⡈⣇⠀⠀⠀⠀⠀⢀⡇⣼⠁⠀⠀⠀⠀⣿⢠
⠀⡄⢻⠀⠀⡿⠞⠉⣷⣠⡟⠀⠀⠀⢻⡄⠀⠀⠀⢿⣀⣀⣸⡧⠤⣿⠀⡟⠛⣇⠀⠀⠀⠀⠻⣼⡄⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⢀⣼⠃⠎
⠀⠹⡈⢻⠛⠛⠛⠟⠛⢿⣧⠀⠀⠀⠈⣧⠀⢀⣄⢸⡏⢹⡟⠀⠘⣷⠀⡇⠀⠘⣧⡀⢀⣀⣀⣘⣷⡀⠀⣀⣤⠾⠷⢤⣀⣀⣠⣟⣁⣀⣀⣀⠀⠀⠄
⠀⠀⠃⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣻⣄⡟⠙⢿⡟⢸⡗⠆⠀⣿⣠⡿⠶⠶⠞⣻⠋⠀⠀⠀⣠⠟⠛⢧⡀⠀⠀⠀⠻⣯⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⢸⡇⠀⠐⠀⠀⠀⣿⠀⠀⢀⠀⣽⠿⠁⠀⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⠀⣰⠇⠀⠀⠀⣸⣃⣀⣀⣀⣹⣄⠀⠀⠀⠘⣷⡤⣤⣤⣤⣤⡼⠃
⠀⠀⠀⠈⣯⠀⠀⣀⠀⠈⣿⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⢸⡇⠀⠀⣿⠘⡷⡞⠻⣿⠖⠛⢦⢀⡟⠉⠋⠉⠉⠙⠹⡄⢀⡶⣤⡘⣷⠁⠀⢠⡏
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠰⠁⢸⡓⠆⠀⣿⢀⡇⢹⡄⠀⠀⠀⠈⠛⠁⠀⠘⠃⠀⠀⠀⢻⡞⠀⠀⠙⠻⠂⠀⣽⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢘⠁⠒⠀⣀⣿⣧⣤⣤⣿⣸⣧⣄⣵⣤⣤⣤⣤⣤⣤⢤⣤⣤⡤⠤⠤⠤⠦⠴⠶⠶⠶⠶⠞⠋
⠀⠀⠀⠀⠈⠛⠛⠚⠛⠛⠻⠶⠶⠶⠶⠟⠛⠉⠋⠉⠉⠁⠀⠀⠀⠈⠉⠉⠈⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡖⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣰⣈⠁⡄⢀⡞⣠⠞⢙⣇⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⣦⠱⣤⠐⣤⢔⠔⡴⢯⡜⠁⠀⠸⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⣷⡰⡽⢆⡾⠀⠈⡿⠋⢁⠾⣵⣫⠖⣋⣝⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⣣⡸⠧⢎⢻⡟⢯⡀⠀⢰⣃⣠⡯⢻⡱⣏⠖⠁⠿⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⠃⠀⠀⠀⢯⣿⡘⣶⡔⠋⠡⠈⢧⣜⡳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠀⠀⠀⢐⣼⠿⠷⢴⠖⠳⡶⠗⠺⣼⠥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⢀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣉⣉⣙⣲⡿⠞⠺⠾⠴⠷⠞⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠛⠋⠉⠉⢹⡿⠆⠀⠀⠀⠀⠀⠀⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⠤⢒⡾⠿⠶⠟⠻⠻⠳⠲⢶⢶⡿⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⡼⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠠⣽⣾⣥⡄⠀⠈⠀⠀⠀⣼⣿⣦⡀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠰⠚⢱⠟⠧⠀⠀⢀⡀⠀⠀⠁⠏⠙⠃⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⡠⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢠⢀⢀⣀⠀⠀⠀⠀⠀⠀⢼⣿⡧⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢙⣾⣿⣯⡁⠀⠀⠀⠀⠀⠾⢻⡟⠇⠀⠀⠀⠀⢻⣾⣾⡤⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠈⠉⠛⠀⠀⠠⡄⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⢠⠿⠷⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠒⠶⠶⠶⠶⠶⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠠⠤⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⢶⣶⣾⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣩⣿⣿⣥⣶⠶⠶⠾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡶⢧⡀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⡾⣷⣦⣞⣱⠃⠈⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣟⡿⣿⣟⣿⣿⣶⣇⣀⡟
⠀⠀⠀⠀⠀⠀⢠⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⢻⣿⣿⣿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡛⣾⣿⣳⢿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⡪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡟⢃⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣻⢡⣿⣗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠉⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣛⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⠻⣿⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁


⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡏⢻⠉⠉⠉⠉⠙⠛⠛⠛⠛⠓⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡠⢊⡴⢲⢀⡇⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⣙⣓⠶⣄⡀⡇⢸⡼⡱⠋⡴⢋⠞⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣈⣣⣘⠦⣌⣉⡲⣝⡷⣞⠻⠷⣮⣔⣁⠀⣀⣀⣀⣀⣀⣀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠤⠭⠭⠭⠭⠥⠭⠽⠶⠶⢭⣽⠀⠈⠁⠀⠈⢿⡯⡙⢯⡭⣭⣭⣭⣭⣍⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠛⣆⠀⣨⣶⣇⠀⢳⡘⣆⠣⣀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⡟⢦⡀⠙⠀⠀⢀⡵⠈⠳⣬⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⠞⠀⡇⢸⠳⣄⡤⠞⠉⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡴⠁⠀⠀⡇⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠼⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠞⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⣠⣤⣶⣤⣤⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠒⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⢀⣠⠤⠶⠚⠋⠉⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣈⣭⢿⡆
⠀⠀⠀⠀⠀⢸⡟⠓⠲⠤⣤⣀⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⢦⣤⣤⣤⣤⠿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠚⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⢀⣀⣤⡴⣾⠏⠁⠀⡼⠁⠀⠀⠙⣆⠀⠉⠙⢷⣶⣤⣄⣀⣀⣠⠟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠛⠋⠉⢩⣏⡿⠃⠀⠀⣸⣃⠀⠀⠀⣀⣸⣆⠀⠀⠈⢻⡄⠀⠀⠉⣿⠀⠀⠀⣀⣠⡤⡾⠁
⠀⠀⠀⠀⠀⠀⢹⠛⠒⠶⠤⣄⣀⡀⡿⠀⠀⠀⢠⡟⠁⠀⠀⢠⠏⠉⠙⡟⠋⠁⠀⠸⡆⠀⠀⠀⠹⣄⠀⣀⣿⠴⠖⠋⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⡿⠒⠶⣴⠏⠀⠀⠀⢠⡏⠀⠀⠀⡇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠘⣏⠁⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡧⠶⣶⠀⢠⡿⠦⢤⣄⣀⣇⣀⣠⠴⠖⠋⠻⡄⢠⡟⠦⣜⡇⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣠⠏⠀⠀⠀⠀⠉⡏⠁⠀⠀⠀⠀⠀⠹⣾⠁⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠤⣄⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣈⡥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠤⣤⣀⡀⠀⠀⡇⠀⠀⣀⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠷⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠢⡴⠓⠶⠉⠲⠚⢦⠔⢆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠓⢃⠀⠡⠀⢠⠀⠀⠀⡆⠀⠀⠀⡌⠀⡘⠚⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠺⡀⠈⢆⠀⢂⠀⠀⠀⠀⢐⢀⡀⢀⠁⠐⠀⠐⠀⡠⠁⢀⠗⢦
⠀⠀⠀⠀⠀⢰⠚⠣⠀⠈⠂⠀⠂⣀⠄⠚⠀⠉⠀⠀⠀⠈⠉⠑⠲⢄⡐⠀⠐⠁⡠⠞⠓⡆
⠀⠀⠀⠀⣚⠉⠑⠄⡀⠑⢀⠐⠊⠀⡠⠄⠒⠉⠁⠀⠀⠉⠐⠂⠄⡀⠈⠓⢄⠈⠀⠠⠊⠉⣓
⠀⠀⠀⣺⠁⠁⠂⠄⠈⠠⠊⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠲⡁⠠⠐⠈⠈⣕
⠀⠀⢸⡁⠈⠑⠂⠀⡨⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠱⡄⠐⠊⠁⢈⡇
⠀⠀⣏⠈⠁⠀⠐⢠⠃⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⠀⠈⠁⣹
⠀⠰⡉⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠁⢉⠆
⠀⠰⡋⠉⠉⣁⠀⢩⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⣉⠉⠉⢙⠆
⠀⠀⡏⠉⢀⡀⠀⠴⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡀⠈⢹
⠀⠀⢸⠉⢀⣀⠀⠀⢳⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠤⣀⡀⠉⡇
⠀⠀⠀⣝⠁⣀⠤⠂⠁⠱⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠐⠤⣀⠈⣫
⠀⠀⠀⠀⢽⣀⡠⠐⠁⡠⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢄⠈⠂⢄⣀⡫
⠀⠀⠀⠀⢠⠿⣀⡠⠊⢀⠔⠀⠈⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠋⠀⠢⡀⠑⢄⡀⡍⢣
⠀⠀⠀⡰⢃⠊⠀⠣⢤⠃⢀⠌⠀⠌⠀⠂⠀⠁⢸⠈⠁⠈⡀⠠⠀⢡⠀⠡⡀⠘⡦⠜⠀⠈⠂⠱⡀
⠀⠀⡜⢠⠂⠀⠀⠀⠈⠉⠻⡀⡜⠀⡰⠀⠸⠀⠀⠀⡇⠀⠁⠀⠇⠀⢣⢀⡜⠉⠁⠀⠀⠀⠀⠡⠘⠄
⠀⡈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠱⠤⠣⣀⠦⣀⡤⢀⡔⠤⠎⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⡀
⢰⠁⠄⠀⠀⢀⣀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠄⢀⠜⠁⠘⢆⠈⢀⠀⠀⠀⠀⠀⢠⠤⠤⣄⣀⠀⠀⠀⠂⠐
⣌⣠⠤⠒⠋⠁⠀⠀⠀⠈⡇⠀⠀⠀⢀⠂⢠⠋⠀⠀⠀⠀⢣⡀⢂⠀⠀⠀⠀⡟⠀⠀⠀⠀⠉⠑⠒⠤⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠌⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠂⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡞

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⢌⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠀⠀⠱⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢵⠀⠀⠀⠀⡋⢀⣁⠀⠀⠒⡗⠚⠒⠒⢲⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠈⠈⠀⠈⢩⠏⠉⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠈⠉⠢⡔⠊⠉⠉⠑⢄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢣⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡄⠀⠀⠀⠑⠦⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠃⢠⡿⢹⢶⠃⢳⢴⡎⠕⠀⣰⠀⣾⡱⠀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠖⠙⠷⠋⠘⠶⠃⠘⠶⠒⠀⠛⠊⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠦⣜⡁⢧⣸⠤⣀⡎⠀⡜⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠢⢼⣀⣀⣀⣩⠋⠀⠀⢸⢀⡜⡴⣞⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⢲⠏⠀⠀⢠⠃⢹⣦⠴⡟⠚⠺⠤⠼⡆⠀⢀⠗⠲⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠼⡄⠀⠘⠢⡔⠉⠉⠉⠉⠉⡆⢸⠀⠀⠀⠀⡿⠚⢣⢀⠴⠥⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡏⠉⠉⠑⠒⡾⠿⢿⣭⣵⡖⠒⠒⠦⠔⠣⠼⠖⠲⣮⣭⣓⠶⠾⡗⠒⠊⠉⠉⢹
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⡇⠀⢸⠀⠀⠈⠉⠉⠓⢲⡖⠒⠉⠉⠁⠀⡇⠀⠀⡇⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠒⡇⠀⢸⡥⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⣀⣀⡇⠀⠀⡗⠒⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⠀⠉⠉⠑⠺⡗⠊⠉⠉⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠼⠦⣄⣀⡀⠀⠀⠸⠀⠀⠀⢀⣀⡠⠧⠤⠒⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠚⠓⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠿⠵⠶⠦⢤⣄⣈⣯⠉⠙⠒⠲⡏⠀⠀⠀⠀⢀⣀⠴⡇
⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠾⡉⠐⠒⠒⠒⠒⠈⠉⢹⠀⠀⢀⣀⣿⣭⣿⠛⠛⠋⠁⠀⢷⡢⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⡏⠈⠉⠉⠒⢲⣷⠀⠀⢀⣀⣀⣤⠔⠛⠉⠉⠉⠛⠒⠢⠭⢭⣉⣛⡿⠷⣯⠈⠉⢿⠉⠁⢹
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇⠉⢹⠉⠀⢰⠋⠙⠒⠒⢦⡤⠒⠒⠊⠉⠁⠀⡇⠀⠀⡏⡇⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⡟⠒⠒⠢⢼⡇⠀⡜⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡧⢼⠀⢸⡗⢻⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⡜⢁⡀⠀⡟⠒⠒⠤⠤⣼⣥⠤⠤⠒⠒⠚⠉⡇⠀⠀⡇⠸⣼⠳⠇⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡟⠋⢹⡿⣰⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡆⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⣀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠼⢧⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣧⠤⠖⠓⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠼⠧⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠉⠙⠛⢦⣍⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣇⣼⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⢻⡟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣽⠁⠀⢹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣾⣿⡄⠀⠀⢀⡴⢦⡀⠀⠀⢠⣶⣿⡄⠀⠈⡟⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣛⡛⠁⠀⢠⡏⠀⠈⢷⠀⠀⠘⠿⠿⠃⠀⠀⣇⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡏⠟⠀⢠⡟⠀⠀⠀⠈⢧⡀⠀⠀⠟⢻⡆⠀⣿⠀⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠒⢒⣉⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠋⠀⠀⣿⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣴⣾⠟⠛⠛⠷⣤⡴⠚⠉⠉⠻⣶⡀⠀⠀⠀⢹⡄⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣿⠃⠀⠀⠀⣰⡟⣷⡀⠀⠀⠀⢸⣷⠀⠀⠀⢸⡇⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡆⠀⠀⠀⣿⠀⣸⡇⠀⠀⠀⣼⠇⠀⠀⠀⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⢷⡀⠀⠀⠈⠛⠛⠁⠀⢀⣾⢋⣠⠤⣤⡀⢸⡇⢸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣠⠴⢤⡀⠻⣄⠀⠀⠀⠀⠀⣴⠟⠁⣾⠁⣀⠀⣿⢸⡇⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⣴⡀⣹⠀⠙⢦⠀⠀⣠⡾⠁⠀⠀⠙⠒⠋⣠⡏⢸⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠳⣌⠛⠁⠀⠀⠈⠳⠶⠋⠀⠀⠀⢀⣠⡴⠞⠋⠀⢸⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠓⠶⣤⡀⠀⠀⠀⢀⡴⢚⣉⠀⠀⠀⠀⠀⢸⡏⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣾⠖⠈⢻⠀⠀⠀⣾⠀⠏⠈⢳⡀⠀⠀⠀⢸⡇⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣀⣉⣳⣶⣋⠀⠀⠀⠘⠲⠤⠴⠛⠀⠀⣀⣀⣼⣷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠴⠶⠦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣛⣙⣛⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣶⣿⣶⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠉⢻⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⠀⣿⣛⣛⣛⣻⠀⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣿⠠⣤⣤⣤⠄⣿⢠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⠿⠀⠿⠿⠿⠿⠿⠀⠿⠧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣿⣀⣀⣀⣀⣠⣿⣀⣸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣤⣤⣠⣶⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣤⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠠⠔⢿⣿⣿⣿⡶⠠⠜⠐⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣗⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⢁⡀⠤⠂⢲⡟
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⠇⠀⠀⢀⣀⣤⣤⣦⣶⣶⣿⣿⣿⡏⠀⠀⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣠⣤⣄⢀
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣯⣿⣿⣿⡟⠀⣠⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡀⠀⠀⢀⢤⡟⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣠⣿
⠀⠀⠀⢀⣤⠻⣋⡴⣿⠿⠃⢸⣿⣭⣿⣿⣹⣼⣿⣿⢣⣾⣿⡫⣿⣟⣿⡟⣿⢿⣿⣿⣿⡿⠇⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⢫⡴⢟⣥⣿
⠀⠀⣠⠾⢋⠘⠯⡈⠀⠃⠀⠀⠻⣿⣿⣿⣷⣿⣿⡟⣾⣽⣣⣯⣿⡿⣼⣟⣯⡽⣻⣿⡾⠁⠀⠑⡀⢰⡇⠀⠀⢀⡄⠞⠈⠉⠂⠯⠒⡽⣿⣧⢲⡜⣿⣿⡟
⠀⣔⣧⣰⠛⠀⢈⡴⣂⠀⠀⣠⢀⣿⣿⣻⣿⣿⣿⣻⣿⡿⣻⢷⣝⡽⣿⣯⣾⣿⣿⡿⠁⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣶⡹⣈⣿⠃
⠠⢿⡟⠃⠠⢞⣥⠛⠋⠀⢻⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⢟⣛⣟⣿⣟⣿⠃⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⣻⡼⢿⡟
⡀⠀⠀⠀⠀⠛⠁⠀⠀⠂⠀⢷⣿⣿⣿⣿⢿⣿⣹⣟⡿⣟⣦⡱⣿⣯⣿⡵⣫⢯⡾⠁⠀⠄⠀⠰⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⢑⢛⣵⣾⣿⠃
⡶⣃⠀⠀⢠⡀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣽⣿⣯⣿⣷⠟⣿⣻⣿⡻⣷⣽⣿⣯⡿⡟⠀⠀⠠⠷⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡙⣷⢻⣿⡏
⠘⠉⠀⢺⡞⢃⡀⠈⠀⢀⣤⣿⣿⣿⣾⣿⣿⣿⣿⣗⢟⣿⡻⣿⣿⣹⡽⡻⣿⣮⠃⠀⠀⠀⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢎⣵⣿⠁
⠀⠀⠀⠀⢺⡼⠇⢀⡴⣎⣽⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⣻⣷⣶⣯⣿⣾⣿⡿⠿⠒⠐⠒⣨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣩⡵⣋⣹⡏
⠀⠀⠀⠀⠈⠀⠀⠀⠸⢽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⢾⣿⣿⣯⣯⢭⣿⡿⣿⡁⠀⠔⠂⠰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢠⣕⣾⣿⣿
⠀⠀⠀⣴⢆⠀⠀⢀⡀⣾⡿⣿⣿⣷⣿⢯⣿⢿⡿⣯⣯⣿⣾⢿⣿⣿⣟⣿⡇⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣻⡜⣿⡇
⠀⡼⣇⠹⠟⠀⢸⡿⢷⣿⢿⣹⣿⣿⣿⣼⣿⣻⣿⣻⡿⣿⣿⣶⣿⣿⣻⣿⡇⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡿⠿⣃⣿⣿
⠀⠘⠋⠀⠀⠀⠀⢱⣾⡿⣏⣿⢿⣿⣿⣿⣿⣷⢿⣷⣟⢿⣽⣿⣿⣿⣟⡿⠃⢀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠶⢟⣵⣾⡏
⢀⡀⠀⠀⠀⠀⠠⢸⣿⢷⣿⣿⣿⡿⣿⣿⣿⣿⣻⡿⣿⡿⣞⣷⣕⣾⡿⠁⠀⠈⠄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⣦⢻⣿⣿
⣯⢗⠀⠀⡀⠐⣀⣾⣿⢾⣿⣿⣿⣳⡿⣿⣿⢯⣿⣾⣽⣿⣽⣽⣿⣾⠃⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡜⣣⣽⡇
⢱⡞⡇⠀⣤⡖⣹⣿⡿⡟⣿⣿⡿⣿⣿⣽⣟⣿⣻⣯⢶⡿⣾⢿⣟⡯⠀⠀⠀⠀⠀⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣫⠧⢛⡿
⠀⠁⠀⠀⠹⠟⣿⣿⣿⣻⣿⣿⢷⣿⣿⣿⣿⣻⣽⣾⣻⣯⣷⣯⣯⡃⠀⠐⡀⠀⣦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢀⡛⣥⣾⣿⠇
⣤⠀⡀⢁⡀⢸⣿⣿⣻⣿⣿⣿⣾⣿⣯⣿⣻⡾⣿⡵⣾⣿⣿⡿⢽⠀⠀⠀⠛⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⢻⡜⢿⡿
⡾⠃⢰⣾⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣺⣿⣽⣟⣳⣿⣽⣵⣿⣇⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣵⣾⠇
⠀⡍⠆⢹⣼⣿⣯⣷⣿⣿⣿⣿⣿⣿⢟⣷⡵⣾⢿⣷⢾⣿⣾⠿⠻⠃⠒⠂⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣭⡶⣛⣼⡟
⠀⠠⣲⠝⣿⣿⢿⣾⣿⣿⢻⣿⣿⣿⢾⣿⣟⣿⣯⣾⣿⣟⣿⠣⠠⠔⠊⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⣦⢺⣿⣿⠃
⣦⠈⢎⣶⣿⣿⣟⣿⣿⣟⣿⣿⡿⣻⣯⣿⣿⣟⣿⣿⣿⣾⡷⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣝⢎⣻⡟
⣋⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣷⣻⣿⠿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣣⢾⣻⠃
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣻⣿⢿⠾⠋⢠⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠺⣟⣵⣶⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣦⣌⠃⠘⣡⣴⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣉⠛⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠟⣉⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣉⣩⣭⣤⡈⠻⡟⢿⣏⡁⢈⣹⡿⢻⠟⢡⣤⣬⣍⣉⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⠻⣿⣿⣿⣿⣟⢃⡀⠻⣿⡇⢸⣿⠟⢀⡐⣻⣿⣿⣿⣿⠟⣻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡘⢿⣿⣿⡛⣿⣿⣦⡈⠃⠘⢁⣴⣿⡿⢛⣿⣿⡿⢁⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⠄⣠⣤⣤⠀⣤⣤⣤⠄⠀⠀⠠⣤⣤⣤⠀⣤⣤⣄⠠⣤⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢃⣴⣿⣿⣿⣿⠛⠟⢁⣴⡇⢸⣦⡈⠻⠛⢿⣿⣿⣿⣧⡘⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⣿⣿⠟⢁⣄⣻⡿⠇⠘⢿⣟⣠⡈⠻⣿⣿⠿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⠖⢀⢰⣿⣿⣿⣷⡇⢸⣾⣿⣿⣿⡆⠀⠲⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠈⣿⣿⣿⡿⠃⠘⠿⣿⣿⣿⠃⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣦⣿⡟⣡⣴⣇⣸⣶⣌⣻⣿⣴⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣈⠉⠈⠁⠀⠀⠤⠀⠐⠀⠀⡈⠈⠙⠓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡠⠀⠀⠳⣄⠁⠀⠀⠀⠄⠀⠉⠀⠀⢀⡠⠤⠧⡀
⠀⠀⠀⠀⠠⠂⠉⠀⠈⠐⠤⡀⠀⠀⡎⠠⠈⡄⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠘⣄⣠⠡⠄⠀⠃⠉⠁⠊⢀⠇⠀⠀⠀⣠⠀⠀⠀⠀⡄⠀⠠⠆⠀⢱⣀⣀⡠⠊⠀⠀⠀⣱
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠁⠀⢽⣉⠯⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⡴⠶⠒⠒⠓⢄⠐⠓⠀⣨⠅⢈⡷⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠈⢆⡒⠀⠀⣀⡠⢀⠋⢬⠆⠀⣀⡈⠃⠠⠀⠀⠀⠈⠢⡀⠸⠀⠀⠈⠛⢔⠒⠛⠛⠒⠁⠀⡩⢄⠂⢤⡤⠔⠁
⠀⠀⠀⠀⠀⢠⠃⠉⠉⠀⠀⠀⠰⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠱⢶⠂⠀⢈⡀⢠⡀⠣⠔⠚⠢⣀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠁⠤⠀⠤⠤⢴⠄⠤⡄⠀⠈⢳⡄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠀⠈⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠂
⠀⠀⠀⢸⡀⢀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠉⠃⠀⠘⠒⠒⠒⡚
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⠀⠀⠀⠑⠂⠀⠀⠒⠎⠀⠀⠂⠀⠠⢤⠃
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠐⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠦⣤⣀⣀⣀⡀⠇⠀⠤⠄⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⣀⡠⠤⠘⠒⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈⠉

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣄⣠⣤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡫⣠⣾⡟⠀⠀⢻⣷⣄⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡿⠿⢿⣿⣿⣿⣛⣛⣻⣭⣷⢾⣫⣾⣿⠏⠀⠀⠀⠀⠹⣿⣷⣝⡷⣾⣭⣟⣛⣛⣿⣿⣿⡿⠿⢿⡄
⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⡿⠿⣟⣫⣭⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣭⣝⣻⠿⢿⣿⣿⣿⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣰⠶⠶⠛⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⠉⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠈⠉⠉⠉⠉⣉⣁⡀⠀⣀⢀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⢽⣿⡇⠀⠀⠀⠀⢰⣹⣿⣸⠀⠻⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⣽⣿⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠸⡄⡞⠉⣭⣭⣭⣄⢸⠀⡏⠀⠐⠀⠐⢸⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⣸⣿⣿⣿⣿⠘⡀⡇⠢⠀⢴⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠻⠿⢿⣿⠿⠆⡇⢇⠀⠀⠀⠀⠄⠿⡿⢻⡟⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⢈⣒⣒⣲⠶⠎⢍⣁⣨⠭⠭⠽⠿⠟⠛⢇⠸⡇⠀⠀⠈⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⢠⣀⠤⡀⢸⡇⠀⠐⣄⠐⠆⠀⢸⠀⣷⠀⠀⠰⣶⣿⣿⣿⣿⣤⣤⠄⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⡠⠂⠈⠐⠀⢸⣷⠀⠀⠀⠗⠦⠄⠸⠄⠛⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢻⡇⠀⠶⠇⠀⠈⣿⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⡿⢃⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠘⠦⣤⣤⣤⣶⣖⣚⢉⣉⣉⣩⣭⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣿⣿⠟⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⢸⢀⡤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠐⠂⠀⠐⠂⢸⢸⠈⠁⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠻⠃⠀⢸⠈⡠⠦⠆⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣅⡘⣒⣒⣒⣒⣊⣉⣀⣓⣀⣭⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⠿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣻⡟⠉⠛⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠀⠀⠀⠐⠚⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⠒⠒⠒⣺⣿⢯⡉⠉⠉⠉⠉⠙⣿⡏⠉⠉⠉⠉⠉⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠖⠓⡆⠀⡰⠋⢼⠟⣶⠃⠀⢀⡀⠀⣞⢻⠇⠀⠀⠀⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠲⠒⠁⣰⠁⠀⠈⡩⠃⠀⠀⠀⠁⠀⠈⠁⠀⠀⢰⠚⠓⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⠊⠉⠓⢦⣎⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠘⠦⠴⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠾⣶⣶⡦⢠⠋⠀⠀⠘⠿⠿⠃⠀⠀⢸⣉⡷⠀⠀⠀⠤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡎⠀⠻⠏⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠶⢤⡜⠁⢠⣖⡆⠀⠀⠀⢰⠚⡦⠀⠀⠦⠀⠀⢰⣶⣶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠛⠀⣀⣤⣀⠀⠀⣴⣦⠀⠀⠀⠀⠀⡼⠉⠙⢦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠁⠀⢈⠆⠀⠉⠉⠀⠀⠒⠀⠀⠙⠦⠔⠃⠀⠀⣴⣲⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡴⠋⠙⣆⠀⠀⢰⣳⠆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠃⠀⠀⠺⠞⠁⠀⠀⠙⠦⠴⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣤⡀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡟⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠙⠛⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠉⠀⢀⠀⣘⣛⣀⣀⣀⣀⣀⣓⣊⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣊⣉⡉⠉⠑⠲⢤⡒⠉⠉⠉⠉⠉⠑⠲⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠣⠘⢤⣜⣋⠒⠦⡐⢭⣢⡀⠀⠀⠀⢀⡠⠔⠒⠩⠛⠙⢒⡲⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠾⢗⣦⣄⡀⠈⠉⢙⠛⢆⢱⣱⡄⠒⢮⡥⢀⡠⢴⡾⠭⡉⠉⠓⠢⡄⠀⠉⠉⠓⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠈⠙⠛⠷⠶⣿⡾⢷⣥⣈⠀⣢⠝⠿⢶⣦⡈⠓⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢀⡠⡇
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢩⠔⠋⡶⠎⣿⠿⣧⣭⣂⡀⠈⠙⡄⢀⡤⠊⠉⠒⢤⡀⠀⣠⠔⠊⠁⠀⡇
⠀⠀⠀⠀⠀⢃⠈⠓⠦⣄⡀⠀⢀⡠⠖⠋⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠈⠉⠉⠛⠛⠻⠥⣄⡀⠀⢀⡠⢽⠋⠀⠀⠀⢀⣴⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⢓⠯⠴⣉⡀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡖⠉⠀⢸⠀⢀⡠⠖⠁⢸
⠀⠀⠀⠀⠀⠘⣤⣀⠀⠀⠀⠸⡄⠀⠀⢨⠋⠛⠒⠒⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⣼⢠⢠⣾⠔⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠈⠉⠒⠤⢤⣇⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⢤⡤⠴⠚⠁⠀⠀⠀⣯⠼⠊⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠉⠘⢳⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠤⠚⢹⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠉⠓⠦⠤⣄⡀⠀⠀⢀⡤⠖⠋⠁⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⣻⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⢸⡆⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⣠⡠⠔⠊⠁

⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠛⠛⠛⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⠒⠒⠶⠦⣄⡀
⠀⠀⠀⠀⢠⣾⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⢀⡴⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⣤⣀⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⢀⣠⡤⠶⠖⠚⠛⠛⠉⠉⠛⠛⠛⠿⢤⡀
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠙⣷⠴⠶⠶⢿⣁⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⣿⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠁⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⢻⠁
⠀⠀⢸⠀⠀⠈⠙⠛⠳⠶⠦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠛⠛⠉⠀⠀⣿
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣇⠀⠀⠀⠀⢀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣄⠀⠀⠀⣸⣷⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠖⠛⠉⣡⠞⡿⠀⠈⠉⠉⠉⠁⢸⡆⠀⠙⣟⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠞⠛⢉⡿⠁⠀⢀⡴⠋⢰⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢹⡄⠀⠀⢻⡝⠛⠷⢶⣤⣄⣀⣀⡀⠀⠀⣀⣠⡴⠋
⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⣠⠟⠀⠀⣠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣷⠀⠀⠀⢳⡀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣴⢿⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⣿⡇⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡾⠃⡿⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⣠⡟⠁⣸⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡿⣧⠀⠀⠀⠘⣧
⠀⠀⠀⠲⣶⣶⡶⠒⠛⠋⠉⠀⠀⠀⠀⢀⣼⠏⠀⣠⠏⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⣧⢻⡆⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢻⡟⠀⢀⣴⠟⠁⢀⣴⠋⢀⣀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡌⢿⡄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢋⣠⡴⠟⢁⣠⡴⢛⣡⡾⢛⡟⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢷⡈⢿⡄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⣠⣴⣶⡿⠷⠞⠛⠉⠀⠈⠛⠛⠛⠋⠁⢀⡾⢁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡌⢻⣄⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠙⢦⡙⢧⡀⠀⠘⢶⣤⣤⣤⣤⡽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣀⣀⣀⣹⡿⠛⢷⣄⡈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣿⠙⠉⠁⠀⠀⠀⠉⠛⠷⢶⣤⣭⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠘⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⡬⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣆⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⠁⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⣟⣲⡲⣄⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⠒⠒⠒⠒⠒⠒⢲⢎⡷⠿⠧⠤⢬⣽⣷⣄⣀⢈⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣋⣀⣀⣀⣀⣀⣠⣿⢟⣄⣄⠀⡄⠀⠀⢘⣿⠉⠉⠉⠉⠉⠛⠓⠒⣒⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⡿⣿⡏⠩⠉⢹⠿⣿⣿⠟⠻⠿⠻⠷⠻⠿⠾⢿⡦⣿⣷⣧⣧⣤⣶⣸⣏⠩⡪⢂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠚⠋⢠⡶⣤⠀⠉⡸⠇⠂⠀⠀⡞⣋⡟⠀⠀⢸⣷⢿⡆⢀⠀⢸⣏⢙⣿⡆⢘⢕⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡠⣤⠀⠀⠒⣫⣤⢄⣈⠁⠀⢀⡂⠑⠔⠊⠀⠀⠓⠃⠀⠀⠀⠠⠈⠓⠃⣾⣇⠀⡩⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠧⡾⠀⢀⣾⢋⣥⡈⡙⢷⡰⣷⡄⡆⠀⠀⢀⣀⠀⠀⠠⢊⠀⡐⠄⠀⠁⣿⣿⡀⠪⢀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠓⣲⣾⣷⣾⡷⠾⠷⠾⠿⠶⠾⠥⣤⣤⣯⣴⣆⠀⢀⠠⡑⣣⠃⠀⠺⣿⣘⣇⠀⢕⡹⣇
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⡋⠀⠀⠀⣀⣾⠋⢴⡄⠈⢻⣆⠀⣤⠀⠀⠀⠀⠀⢀⣠⠔⠻⡇⠀⠑⠒⠉⠀⠀⣀⣸⠀⢿⡀⠩⢆⢿⡄
⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠺⠶⢿⣯⣤⣤⣤⣧⣧⣿⣤⣀⣦⣄⣤⣴⣸⣏⠁⠠⡈⣧⠀⠀⠀⠈⠀⢸⢿⣿⠄⠸⣇⠐⠕⠸⣧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢹⠀⠈⡀⢹⣀⣤⠄⢤⡀⠌⠒⢻⠅⠀⢿⡀⠠⠂⢿⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣔⢍⣿⠻⠲⢻⠇⠀⠀⢸⠇⡀⠸⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⡷⠒⢲⣤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠔⡡⣷⠨⠉⠡⠀⠀⠀⢸⡇⠂⠀⣷⠀⢠⠶⠸⣇
⠀⠀⠀⠀⠀⣾⡇⠗⡅⠀⣰⡖⠀⠑⣤⠊⠙⢄⡠⠋⠡⣈⡩⠋⠫⣉⡝⠛⣍⣹⣷⠀⠪⠀⢸⣠⣄⡀⠀⡔⠒⢌⣇⠁⠀⢸⡀⠐⠩⣂⢹⡄
⠀⠀⠀⠀⠀⣿⣅⠀⢈⠾⡁⠈⡢⡊⠀⠑⣴⠋⠑⢄⡠⠊⠢⣀⠴⠋⢄⡠⠚⢻⣿⡆⢀⠀⢸⡟⠙⠁⠀⠷⣷⠞⣿⠀⠀⣼⢟⠻⣻⣿⠿⠃
⠀⠀⠀⠀⠀⣿⢈⠶⡁⠀⡸⢎⠀⠈⣦⠋⠈⠣⣠⠊⠣⣀⡰⠋⢢⡠⠊⠑⢄⢼⣿⣷⠀⠄⡨⣇⣀⠀⠀⠀⠀⠀⣿⠀⣼⣏⣵⡾⠛⠁
⠀⠀⠀⠀⢠⡟⢄⠀⡸⢎⠀⠀⡱⡎⠀⠑⣤⠊⠈⢢⡔⠉⢢⡠⠊⠑⢤⠔⠉⢺⣿⢿⡄⠘⠄⣿⣧⡷⠀⠀⣰⣏⣻⣼⡿⠟⠁
⠀⠀⠀⠀⢸⣇⡠⠛⣄⠀⡱⢎⠀⠈⡦⡊⠀⢱⡔⠁⠑⣤⠊⠑⢤⠔⠁⠑⣤⢺⡿⣽⣧⣴⣇⣼⠛⠙⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⢸⡋⠢⣀⡠⠫⡀⠈⡷⡊⠀⢙⢶⠁⠈⡲⡊⠀⢳⡔⠁⠑⣤⠎⠀⢹⣿⣿⠣⢈⣽⠟
⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠶⠾⠶⢧⣤⣵⣎⣀⡈⣤⠃⠈⢢⡔⠉⠣⡤⢺⣿⢯⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠳⠷⠤⣮⣌⣾⣿⠟⠁

⢠⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣶⣶⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠛⢿⡷⢄⢀⢀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡇⣸⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⠁⠀⡀⠠⠤⢤⡄
⢸⣿⣿⡟⠛⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⢸⣿⣿⡇⠀⢸⣿⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡇⠀⢸⣿⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⢀⢀⣠⠀⠠⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢫⣴⣦⡘⣣⣾⣹⣿⣿⡇
⢸⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠈⠀⠈⠀⡀⢀⣀⣀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠇⣿⣿⣿⠿⣿⡇
⠀⠈⠙⠃⠀⢸⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠉⢻⣿⣿⠋⠉⣉⡉⠁⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⡇⠀⠀⣾⣿⣦⠀⠀⠂⠄
⠀⠀⠀⣤⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⡇⠀⠀⠙⠟⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣯⣿⣶⣿⣿⣿⠀⠀⠸⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⣿⣷⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠁⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠯⣷⡄⠀⠀⠀⠀⠀⠀⠀⡞⡾⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠘⡇⠀⠀⢀⣶⣶⣶⣖⠛⡗⣒⣛⣿⣫⡽⠿⣤⠀⣀⣤⡀
⠀⠀⢸⣿⣏⣉⡉⡏⠉⠉⠉⠉⡏⠉⣹⣟⣿⡿⠛⠻⣿⠋⠉⠁⠉⠀⣰⠦⣿⣺⣧⠀⢹
⠀⠀⢸⠉⠉⠉⠉⠋⠉⠉⠉⢩⣯⣭⣭⣽⣿⣤⣤⡤⢼⠤⠤⠤⢿⣯⣽⣰⡇⠈⢹⡗⠾⣄⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⡇⠀⠀⠀⣸⣀⣀⣀⣸⣾⡀⠙⠷⢤⣸⠁⠀⢀⣩⣷⣦
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠏⠉⠉⠉⠛⠉⠉⠉⠉⠉⡇⠀⠀⠀⠙⠓⢤⡼⡇⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠢⣄⠀⠀⠀⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠙⠦⣄⣿⠗⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠂⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⣀⣀⡀⠀⠀⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢠⠀⢰⠀⡔⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠲⠟⠎⠀⠀⠓⡧⠚⠁⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣸⢆⠀⢀⣕⡤⣔⣇⠀⠀⢼⡡⠴⠂⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠀⠱⠽⢤⠗⢮⠼⡕⠁⠈⠓⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣤⠀⠼⢽⣊⠗⢎⣲⠥⠄⢠⡔⠒⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡹⠃⠀⠀⠕⠉⠁⢇⠀⠀⠻⡉⠓⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⡳⢦⠀⢀⠶⡟⠢⠄⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠘⠀⠘⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⢠⡀
⠀⠀⠀⠀⠀⠒⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠐
⠀⠀⠀⠀⠤⠂⠈⡞⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠾⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠟⠋⢂⠀⠂⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢌⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠂⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠠⣤⣄⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⡉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠉⠐⠒⠒⠤⠤⢀⣀⠀⠀⠀⠀⣟⢠⣧⣴⣇⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣴⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡫⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡥⠴⠶⠶⡟⠛⡟⠉⠉⠉⠉⠉⠁⠐⠒⠒⠒⠂⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⠉⠁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠒⠒⠒⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒⠒⠂⡠⠤⠤⠶⠿⠂⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠠⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠗⠀⢀⣀⠀⠠⠤⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡻⠿⠛⠻⠿⡿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠦⠤⢤⡤⠤⠖⠒⢲⠖⠒⠒⠒⠒⡶⠒⠒⠒⠒⡶⠶⠶⢴⡦⠦⠴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡼⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢳⠀⠀⠀⢧⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡰⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⠀⠀⠀⠸⡄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⢣⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⡆⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠤⠤⠤⠤⠾⠤⠤⠤⠤⠤⠶⠺⠒⠒⠒⠒⠒⠒⠺⠒⠲⠶⠶⠶⢿⠶⠶⠒⢠⠛⠒⠒⡒⠶⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣼⡇⠀⢀⣶⠀⠀⣸⡀⠀⠀⣸⡀⠀⠀⣸⡀⠀⠀⣸⣀⠀⠀⡸⢇⣀⣀⡼⣄⣀⣀⣷⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠋⣿⠋⠉⠀⠉⠉⣹⣉⣉⣉⣀⣉⣉⣉⣀⣈⣒⣚⣁⣈⣉⣉⣀⣸⡁⠀⠀⠀⠈⣷⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣠⡿⠤⣀⠀⠀⢸⠉⠏⠉⠈⠀⠀⠀⠀⠀⠀⡀⣀⡀⣠⢤⠉⣉⠙⠉⠉⡇⠀⠀⡏⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠉⣉⣄⢀⣄⣸⡄⠀⢸⠐⡮⠀⣇⣀⣎⡳⢳⠞⠦⠃⢿⡦⠸⠻⠌⢓⣦⠀⢠⠇⣰⠚⠋⠛⢿⢤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣵⢰⣾⠁⠈⠉⢈⠿⠼⠀⢸⣄⡥⣤⡭⠤⠤⠴⠶⠲⠶⠶⠖⠒⠒⠒⠒⠚⠒⠒⠾⢘⣏⢠⣤⡴⣄⣤⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡶⠸⣄⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢰⠛⡄⠀⠀⣸⡇⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⢁⣀⠀⢠⢦⡀⠀⠀⠀⢀⣠⣤⣀⡤⢤⣄⠀⠀⠀⠀⠀⠀⢀⢶⡀⠸⣼⠀⢻⢲⡖⠋⢇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠛⢊⣙⠒⠓⣤⠿⡴⢲⣀⡀⡧⠴⣏⢀⡤⣀⠹⣄⣀⣀⡴⠶⢋⣦⢷⠴⣄⣴⢺⠜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠑⡦⢣⡠⠇⠐⢇⡤⢤⠈⢁⣽⣅⢖⡌⣻⢶⡚⢀⡏⢀⡟⢥⠀⣬⣹⣄⠀⠁⠸⡄⠀⠡⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠙⠣⠤⣶⠦⠴⠋⣛⠉⣆⢈⣿⠮⣉⡴⣇⣠⠟⡟⣉⠙⠧⣏⠛⠁⠀⣉⢧⣤⡖⠳⠼⠶⣏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⡸⠽⢀⠈⢳⠀⠸⠭⢇⠈⣻⠣⢴⠡⡏⣝⠹⣆⠙⠋⢀⡶⣏⣰⣀⣶⡼⠀⠀⡳⢀⠀⡘⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠚⣇⠀⣸⡟⢛⣶⠞⣆⡸⠉⢳⡠⠾⣆⡑⢚⣡⠋⡵⢚⡛⣿⠀⠀⢠⠿⢶⠀⡀⣱⠊⠒⠉⠑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⡁⣽⠋⠁⠻⢤⠃⢸⡃⢠⣙⣇⢯⡀⣤⠉⢻⣆⠑⠔⠋⡸⠛⣤⣾⣋⡈⠋⠉⣯⣤⠀⡀⢀⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⣸⢯⠿⣤⠜⠳⠔⠓⠶⠋⠈⠒⠬⠤⠠⠜⠀⠉⠉⠉⠀⠀⠀⠀⠙⠦⠚⠓⠁⠘⠖⢹⠇⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⢀⢠⡤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⢤⡤⠤⠤⠤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⠀⠀⠸⡆⠀⠀⢡⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢠⡇⠀⠀⡄⢀
⠀⠀⠀⠒⠒⠉⠁⠉⠙⠁⠓⠒⠚⠓⠦⠤⠼⠆⠒⠒⠚⠓⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠛⠒⠒⠒⠚⠓⠂⠉⠙⠹⠦⠤⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠤⠤⢤⡔⠋⠀⠀⠈⠙⢶⠲⠶⢶⠶⠶⠤⠤⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠲⠄⠀⡴⠋⠀⠀⠀⠀⠀⠀⠈⢷⠀⢸⠀⠐⠚⠁⠀⠀⡄⠀⠀⣭⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠰⡄⠀⠀⣀⡄⠀⠀⡜⠕⠀⠀⠀⣀⣀⡀⠀⠀⠈⡇⢸⡀⢠⡀⠀⠀⠘⠁⠀⡀⠀⢀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠐⡇⠀⠀⠀⠐⢇⠀⠙⢦⠀⠀⡟⢸⡆⠀⠉⠀⠀⠀⠀⠀⠇⠀⠈⠑⠂⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠆⠀⠀⠀⠦⠄⠀⠀⠹⣤⡀⠀⠀⠈⠑⢦⣀⢣⢀⣧⣸⠇⢀⠄⠀⠐⠊⠀⢀⡄⠀⢦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠶⠶⠶⠦⣬⡿⠁⠀⠈⣷⠚⠶⠶⠶⠶⠶⠬⠤⠤⣤⣤⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⢋⣩⡽⣆⡠⣀⣴⣭⣉⠉⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠒⠒⠒⠚⠛⠛⠛⢛⣋⡽⠟⠋⠁⣀⡴⠞⠉⠉⣽⠃⣽⢻⠘⣯⠉⠙⢦⡀⠀⠀⠙⢶⡒⠒⠒⠒⢾
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠆⠀⣀⡴⠞⠋⠁⠀⣀⡴⠞⠁⠀⡤⠀⢰⠇⢰⡇⢸⠀⠈⠳⣤⣠⠇⠀⠀⠀⠀⢳⠀⢠⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠉⢩⣟⣀⡤⠞⠉⠀⠀⠀⠈⠁⣰⠏⠀⣾⡆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠶⠀⠀⣰⠋⠀⣸⠻⡇⠈⣧⠀⠀⠀⠀⠀⠠⠄⣠⠼⠁⠀⠀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠆⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣰⠃⠀⣰⠏⠀⡇⠀⠈⢷⠤⣤⠤⣶⠚⠉⠁⣠⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⣰⣣⣄⣰⠏⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠋⠁⠸⠏⠀⠸⠂⣷⠀⠀⢸⡇⠤⠄⠀⠀⠀⠀⠀⠈⠙⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⠀⠈⠉⠀⠀⠀⡄⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⠈⠓⠀⠀⠀⠀⠚⠀⠀⠀⠀⢤⠀⢸⡀⠀⠀⡇⠀⠃⠀⠀⢀⡀⠀⠈⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠼⠧⠤⠤⠷⠤⠤⠤⠤⠤⠽⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠦⡴⠓⢶⠋⢳⠖⠳⡤⠶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠒⠺⡁⠈⡄⠀⢁⠀⠈⠀⢸⠀⠀⠀⠀⠎⠀⡱⠒⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠉⠙⢆⠀⠡⠀⠘⠀⠈⠀⢠⠀⠸⠀⠸⠀⠘⠀⠰⠁⢀⠎⠁⢹⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠴⢅⠀⠑⣄⠀⢢⠀⢁⣀⠤⠄⠒⠘⠒⠚⠀⠓⠠⠅⣠⠁⠠⠂⢀⠔⠁⢀⠷⢤⡀
⠀⠀⠀⠀⢀⡤⠷⣄⠀⠑⢄⠈⠢⣠⠖⠉⠀⢀⡀⠤⠄⠀⠀⠠⠤⢀⡀⠀⠉⠣⢤⠂⢀⠔⠁⢀⡴⠧⣄
⠀⠀⠀⢠⡴⠧⢀⠀⠑⠠⡀⡱⠊⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠑⢄⡠⠐⠁⢀⠠⠷⣄
⠀⠀⢀⡸⠦⢀⠀⠉⠒⢄⡜⠁⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠣⠐⠊⠁⣀⠠⠮⣀
⠀⠀⢈⡦⣀⣀⠈⠁⠀⡜⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢳⠀⠉⢀⣀⡠⣏
⠀⠀⢫⣀⣀⠀⠀⠁⢰⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⣀⣀⣸⠃
⠀⠐⢏⠀⠀⠀⠈⠉⡉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠀⠀⠀⢈⠗
⠀⠠⡏⠉⠁⢀⡀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣀⠀⠈⢉⡦
⠀⠀⣜⠉⠁⠀⢀⠀⠸⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⠀⠀⠉⢹⡄
⠀⠀⢈⠗⠈⠉⠀⡀⠄⢣⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⡀⠈⠉⠐⣏
⠀⠀⠈⢱⠖⠉⠁⣀⠠⠊⢣⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⢄⡀⠉⠑⢖⠉
⠀⠀⠀⠈⠳⡖⠉⠀⡠⠔⠁⡱⢄⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠑⠠⡀⠈⠑⡶⠋
⠀⠀⠀⠀⠈⢳⡶⠉⠀⡠⠊⢀⠔⠑⠤⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠄⠈⠢⡀⠈⠳⠶⡋
⠀⠀⠀⠀⢠⠎⡹⠲⡊⠀⡠⠊⢀⠜⠀⡘⠉⡒⠢⠤⢄⠀⣀⠠⡤⠔⡆⠙⡀⠐⢄⠈⠢⡀⠈⠶⠚⢣⠙⣄
⠀⠀⠀⡰⢁⠌⠀⠀⠉⢹⣀⣠⠎⠀⡐⠀⠰⠁⢀⠀⠰⠀⢰⠀⢰⠀⢠⠀⠰⡀⠈⢆⣀⡸⠉⠁⠀⠀⠑⡈⢦
⠀⠀⡜⢀⠊⠀⠀⠀⠀⠀⠀⠘⠤⠰⡁⢀⠃⠀⡈⠀⢀⠀⢸⠀⠀⠀⠀⢆⠀⡱⠠⠎⠀⠀⠀⠀⠀⠀⠀⠐⡀⢣
⠀⡘⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠒⠳⡤⠒⣤⣴⠢⣴⠓⠲⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢣
⢰⠁⡌⠀⠀⠀⣀⣠⡤⠤⠴⡄⠀⠀⠀⠀⠀⢀⠊⢀⠞⠁⠀⠳⡀⠑⡀⠀⠀⠀⠀⠀⢀⡦⠤⠤⣄⣀⠀⠀⠀⢡
⣘⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠂⣠⠋⠀⠀⠀⠀⠘⣄⠘⠄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⠃⡰⠁⠀⠀⠀⠀⠀⠀⠈⢆⠈⠄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⣉⠉⠁⠀⠀⢀⡏⢝⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢒⣩⠘⡯⢫⢟⠱⡲⢶⢤⡤⣀⡀⠀⠀⠀⡇⠉⠁⠀⠀⠀⠀⢸⡮⢓⠭⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠘⠂⡯⢔⠥⡪⢖⢕⡠⠪⡪⢙⢝⢗⢲⡇⠀⠀⠀⠀⠀⠀⢸⡪⢐⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢗⠕⣪⣆⠵⠵⠒⠚⠚⠉⢹⢟⡿⢦⣀⠀⠀⠀⠀⠀⣿⡪⠕⣺⠁⠀⠀⣀⠤⠤⠀⠀⠒⣲⡤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣀⡇⠀⠀⠀⠀⡖⡉⠉⠄⠀⠐⠀⠀⠀⠀⠀⣾⠕⡊⢔⠮⣷⢄⠀⠀⠀⡭⣒⠅⡞⠀⠀⡜⢁⣠⡤⢴⣴⣼⣧⠾⠏
⠀⠀⠀⠀⠀⢠⠔⠱⠌⣗⢔⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢍⡪⢔⢺⣇⢕⠀⠀⠀⡯⢒⢭⠇⠀⡔⢁⡞
⠀⠀⠀⠀⠀⠀⢣⠀⠀⢻⣂⣺⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣀⡀⠀⠠⠤⠿⠥⠮⠷⠽⠷⠵⠤⠤⠼⠯⠶⠼⠤⠔⢁⡎
⠀⠀⠀⠀⢠⠊⣉⣍⢭⣍⣩⡉⢉⡥⠤⠤⡤⠤⡄⢀⡴⠖⠒⠲⠀⡖⠒⡶⢖⣶⠀⣶⠚⢛⢛⠀⣰⠞⡺⣶⡲⢀⡞
⠀⠀⠀⠀⠈⠆⠳⣡⠀⠀⢻⢻⡈⣇⠁⠀⡇⠁⠁⢸⣥⠄⠀⢸⠀⡇⢰⡯⣐⡏⢸⣿⢌⠢⡸⠀⣿⠅⣪⡿⢀⡜
⠀⠀⠀⠀⠀⠘⡄⢹⣆⢠⡘⣟⣷⠸⡆⠀⡇⠀⢸⠘⡾⠀⠀⢸⠀⡏⢸⣏⣾⠀⣼⣿⣵⣭⠇⠰⣇⣅⡾⠁⡜
⠀⠀⠀⠀⠀⠀⠘⡄⠙⠛⠓⠛⠛⠁⠙⠒⠓⣒⡁⠀⢉⣉⣉⡁⠀⣉⣭⣭⣁⢀⣤⡤⢤⢦⢀⣤⡶⢦⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⣯⣟⣿⢣⢸⡍⡏⠀⢸⠀⡏⠀⠀⢸⢸⡇⢸⡳⡟⢸⢕⡏⡢⡝⢸⢻⢢⡏⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⡄⢙⢘⡆⣷⠇⠀⠌⠀⡇⠀⠄⡈⢈⠆⣿⣲⠇⣸⣹⣗⣼⠁⣏⣾⡞⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⠒⠂⠃⠘⠓⠒⠚⠀⢈⣀⣉⣁⣈⣙⣉⣉⣄⠬⠭⠥⠤⠤⢤⣤⠠⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣂⣀⣀⢀⣀⣀⣀⣀⣉⣉⣉⡉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⡉⠉⢉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡞⣛⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠹⠛⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣥⣕⡼⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⡽⣦⡆
⠀⠀⠀⠀⠀⢤⡠⢀⠱⣿⣿⣋⢴⠠⢄⠠⣀⠠⢀⠠⢄⠠⢄⠠⠀⣀⠀⣀⠀⡀⢄⡠⢄⠠⡀⠄⡀⢄⡠⣏⡻⠿⢗⡵⡠⣀⠤⣄⣤⡠⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠐⠀⠁⠊⠁⠂⠁⠊⠁⠊⠑⠉⠐⠁⠊⠁⠈⠀⠉⠉⠉⠁⠉⠀⠉⠈⠁⠉⠑⠉⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠡⠀⠳⡄⠀⠀⢀⡴⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠓⠶⠮⣭⣶⣤⣽⠦⣞⠋⢀⣀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢⡀⠀⠀⢶⠒⢢⠄⡀⠀⢸⠇⠀⠀⠀⠀⠀⢹⠉⠛⢻⠿⠶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠙⠶⣄⢸⣠⣧⡞⣝⣆⣿⣤⣄⠀⠀⠀⠀⡜⠀⠀⡎⠀⠀⠀⠀⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣓⣾⣉⣩⠿⣟⠋⠉⠁⠀⢻⣄⣀⠀⠀⠇⠀⢀⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠛⣋⡟⢁⡏⠈⠳⡀⠉⣲⣤⣀⣠⡿⠉⠙⠻⠇⠀⢸⠶⠦⢤⡤⠐⢲⣿⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⢹⠎⠸⠀⠀⢹⣦⡿⠛⠉⠙⣷⠀⠀⢸⠀⢀⠏⠓⢤⡄⠳⡀⢸⡏⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣀⣠⣼⠶⠚⣇⠀⠀⢣⠉⠀⠀⠀⠘⣧⠀⠾⠀⢮⣐⣀⣀⣉⣳⣷⣼⣷⣋⣤⡤⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠈⠉⠙⠛⠶⣼⣄⠀⠈⢆⠀⠀⠀⠀⠘⣧⡆⠀⢘⣀⣀⣤⡼⠿⠛⣿⢻⣹⠄⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣬⡄⠀⠀⢀⣤⡾⠷⠛⠛⠉⠉⠀⠀⠀⠀⣳⢇⠱⡴⠶⠞⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣸⡇⠀⠀⠀⣀⣠⣤⡴⠶⠚⠛⠙⡸⡾⠁⢎⡐⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠓⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠿⣯⣭⣁⣀⣯⣂⣀⣠⣭⣧⣤⣧⣤⡤⠶⠶⠿⠾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠰⡶⢀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢤⡮⣧⣴⡯⢴⡆⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠋⣦⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠦⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⡤⠶⠖⠛⠋⠉⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢩⠀⠀⠀⠀⠀⠀⠀⡀⢻⠂⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⣶⡃⢀⡀⠀⠀⠀⠰⢺⣿⡗⠲⠀⠀⠀⠀⢀⣸⡀⠀⢸⡀⠀⠀⠀⠀⠠⡶⢝⢾⣟⠶⠶⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣈⣾⣧⣿⣵⢿⣃⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡔⠁⠀⠈⣢⠼⠦⣄⠀⠀⠀⠀⠀⠋⣸⡍⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠓⠛⣏⡿⣿⢿⣽⠛⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⡼⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣿⡃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿
⠀⠀⠀⠀⠀⠀⣠⡿⠒⠒⠒⠒⠒⠤⠄⣀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣄⣀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠤⠐⠊⠉⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢼⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠶⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉