Ceylon cinnamon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⢤⡴⣄⢀⣀⢀⡀⣀⢀⣀⣤⡀⢻⣏⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⢿⠃⠈⠣⠁⠿⢿⡷⠛⢿⣿⡻⠳⡏⠀⠸⠋⠁⣶⣆
⠀⠀⠀⠀⠀⠀⢀⣠⢦⠉⠉⠢⡀⠀⡰⠀⠀⠈⡀⠀⠀⠃⠀⠀⠘⡄⠃⠠⠘⠻⠿⠇
⠀⠀⠀⠀⠀⠀⢿⡮⠷⢤⣀⣀⠀⣠⠁⠀⠀⠀⠡⠀⠀⠀⠀⢠⣤⡷⣦⠀⣠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⢄⠀⠀⠀⠀⠱⠀⠀⠀⠈⢫⠿⡁⠀⢸⠃⠯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠢⠀⠀⠀⢰⠀⠀⠀⣀⠊⣠⢬⣣⣶⣤⢄⠀⢀⣤⡄
⠀⠀⠀⢠⣤⡀⣺⡙⠀⠀⠻⣽⢰⣿⠀⠀⠠⡀⠀⢸⠀⠸⣍⣀⢁⡹⢚⣰⠊⠹⢴⠆⡾⠞⠃
⠀⠀⠀⠘⠛⠇⢨⡁⠀⠀⠀⠘⠊⠁⠀⠀⠀⠱⡀⠈⠀⠀⠀⠀⠀⠀⠈⢁⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠴⠆⠐⠀⠀⠀⣀⡀⠀⠐⠀⠀⠰⠀⠀⠸⠀⠀⠀⠆⠈
⠀⠀⠀⠀⠰⣟⣷⢰⣗⣤⣈⠀⣫⣃⣺⠇⠁⠀⠖⡞⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠀⠀⠉⠃⣄⠿⢭⣫⣥⢽⣕⣾⣃⣄⠀⠀⢸⠇⠀⠱⠁⢠⣤⣤⣄⣀⡈⠁⡀⠆⡀
⠀⠀⠀⠀⠀⠀⣴⣥⢚⠷⣛⣛⣏⢿⡽⡟⠻⠆⠀⢸⠀⠀⠀⠀⠼⠀⠐⢦⣀⠄⠙⠢⡀⠈⠲⡀
⠀⠀⠀⠀⠀⢰⣿⠏⠀⣿⣿⠿⣶⡂⣷⢡⠄⠀⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠈⠰⢆⠁⠀⠐⠀⠈⢦
⠀⠀⠀⠀⠀⠈⡈⠀⠀⣾⠃⠀⠈⠙⡈⡆⠀⠀⠀⢸⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠃⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠈⠀⠘⡀⠀⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⢡⠀⠀⡟⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⢀⠘⠀⠀⠀⠀⠀⢃⠀⡇⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⡄⠀⠘⠈⡀
⠀⠀⠀⠀⠀⠀⠈⢯⠀⣥⡸⠀⠀⠀⠀⠀⠀⠈⡄⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢂⡈⠀⠀⠀⢹⡎⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⡏⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠉⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠜⣇⠙⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡰⡀⢓⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠂⢢⡼⢣⣾⣿⣷⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡤⢊⠀⠤⠒⠒⠃⢀⣾⠁⢸⢸⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢀⡔⢉⠒⠀⠀⢀⠔⠀⠠⢀⡟⠀⡌⢸⡿⢸⠿⣿⣿⣿⠽⣿⣾⢿⠧⠿⡆
⠀⠀⠀⢠⡾⠛⠀⠀⠞⠑⠓⠂⠀⠀⠸⢏⢀⠇⣾⣺⠰⠆⠈⠏⠛⠂⣀⠁⠩⡊⠀⠌⠆
⠀⠀⠀⣾⠡⠄⣀⠈⡒⠂⠀⠀⠀⠀⠰⠑⠌⠀⡇⡾⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⣤⣄⠈⣙⣹⠆⠀⠀⠈⣴⠀⢀⣀⡀⠀⠀⢰⡗⠈⠀⠀⠀⠀⣀⠀⠀⠀⡎⠻⠄⡚⢳⡄⠀⠀⠀⢰⡿⠆
⠀⠀⠀⠘⠧⡀⠙⠦⢀⠙⠀⠀⡰⠓⠆⠀⠀⡸⠁⠀⠀⣸⠓⠶⠀⠀⠀⠰⢟⠇⣀⠀⢉⡶⢤⡘⡹⠦⠀⣠⠄⡾⣁⠀⡆⡠⢶⠆
⠀⠀⠀⠀⠀⠈⡷⢩⣥⢵⣆⠀⠁⠀⠀⠈⠃⠱⡄⠀⢀⡾⠋⢱⠀⠀⣀⠟⠠⣦⡘⠃⢱⢲⡟⠋⣠⣄⠀⠁⡀⠂⠙⠃⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠨⠷⠤⣦⡀⡀⠀⠋⠙⣂⢸⡇⠀⠀⠀⠀⢋⠴⢶⡞⢀⠀⢸⡟⠀⠀⢫⠝⠀⣀⣀⢆⡰⢂⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠗⠂⠁⠀⠀⠀⠀⢀⠀⠀⠈⠃⠀⢀⠀⠀⠈⢦⡘⠐⠋⣀⣼⣁⣤⣀⣠⣤⠞⠋⠙⢿⠴⠏
⣤⣤⣤⣄⡀⠀⢠⠔⢁⡀⠒⠀⣌⠐⠀⠀⠀⠀⠀⠐⠀⠁⠐⢀⠀⠀⠀⣿⣠⣾⢛⠛⠛⠋⣠⠌⠉⠙⠛⠃⠀⠾⠋
⠉⠉⠛⢿⣿⢿⡕⣊⠁⠠⠤⢠⠀⢀⡐⠐⠚⠐⣂⣤⡤⢤⡛⣻⡟⠤⡀⣩⠝⠛⣿⣿⡿⠿⣿⠷⣦⣍⣁⠒⠤⢄⡈⠓⢄
⠀⠀⠐⠛⠿⣿⣿⣭⣭⣛⣴⣋⣽⣉⣽⡆⠘⠋⣉⣁⣴⣾⣿⠋⠀⢠⡼⠁⠀⣰⠏⠘⣿⣤⡘⠛⣣⣌⢙⢷⣤⣀⠙⠢⡀⠑⢆
⠀⠀⠀⠀⠀⠈⢻⣿⠳⣯⡍⢷⣝⡐⠓⠒⢛⣫⣭⠃⠉⠀⣏⠀⠀⣾⠁⠀⢰⠋⠀⡼⠋⠙⢿⣦⣉⠙⢾⣤⣌⠙⢷⣄⡈⠢⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣻⣮⠛⢦⣙⠛⢏⡙⠯⠐⠄⠲⠄⠀⢏⠀⢸⡇⠀⢠⠇⢀⡜⠁⠀⣠⡞⠉⣿⣷⣤⡀⠶⣤⣤⠈⠛⢦⡐⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⠣⣎⢹⡛⢊⣀⠀⢋⡀⠁⠀⠄⢸⡄⢸⠃⣠⡟⡠⠏⠀⣠⡴⠉⢀⡼⠋⠀⠉⠻⢶⡾⣟⠻⣾⣤⡙⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⣽⠺⠧⣸⠷⠶⣿⣷⣶⣴⣿⣿⠛⠻⣿⣮⣡⠶⠛⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠉⠓⠻⠾⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠽⠧⠴⠾⠧⠝⠛⠉⠉⠉⣶⠃⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⡌⠁⠉⠉⣵⡶⠄⢀⡄⠸⣟⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡷⠂⢀⠔⠀⢀⡼⠀⣰⠆⠀⠈⢧⠹⣆⡿⠋⠁
⠀⠀⠀⠀⢀⡔⠁⣴⡛⠟⠀⠆⠀⠚⣴⠟⠁⡆⡿⠀⠀⠀⢠⡇⢸⡇
⠀⠀⠀⠀⠌⢡⡞⡻⢀⠈⣡⠂⢠⡞⢳⠂⠠⣿⠇⠀⠀⠀⠘⡇⢸⡇
⠀⠀⠀⣄⠠⢿⠊⡁⢈⡄⠀⠐⠈⣷⠄⠀⢲⡟⠀⠀⠀⠀⠀⡇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⠤⣀⣀
⠀⠀⠈⠉⣰⡟⡄⢠⠎⢠⡋⠑⡀⠁⣰⢤⠏⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⣀⢀⣠⣴⢟⣫⣝⢣⣀⡴⠛⠶⢦⣤⣬⡟⠦⣀
⠀⢀⣟⢩⣿⠤⡴⠋⡞⠉⢃⠄⢀⠐⠠⠋⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⣴⣾⠟⠛⠛⠻⠟⢻⣽⣥⣀⣀⠁⠉⠁⠀⠰⠋⠁⠒⢋⠳⣄
⠀⢈⣸⡿⢣⡾⣡⢾⣏⠴⣉⡴⠛⠤⠀⣤⢤⡤⣤⣤⣀⡀⣤⣇⠸⣷⠏⠀⠀⠀⠀⠀⠀⠙⢿⣫⣟⢙⠛⢶⣀⠀⠀⠀⠀⠈⠀⠀⠜
⢠⡞⣿⢷⣿⢷⣿⢿⠿⠚⣉⠔⠀⠐⢛⡁⠀⢀⡐⣦⠏⠁⠛⢄⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢤⡈⢁⣸⡶⠒⣄⣀
⠈⣘⣷⣿⣷⠟⠉⢀⠔⠚⠁⠀⢴⣶⠋⢠⣼⣷⢱⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠝⠩⣏⣀⠒⠫⢼⣷⣶⡄
⢀⣽⡿⠛⠁⠀⡐⠋⡒⠀⣴⡥⡊⠑⠢⣬⣽⡃⡨⣅⠀⠀⠀⠀⡆⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠥⢾⣶⣆⣀⡉⠁
⠘⠋⠀⠀⠀⠜⣀⠂⡠⢞⠋⠁⠈⣠⡴⢅⠈⢸⢿⡟⠀⠀⠀⠀⠃⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⢀⡘⣠⠂⢐⣜⠋⠀⢨⡶⢿⠄⠈⣰⢻⡞⠁⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠦⠈⢧⣡⣟⡁⢈⡾⢻⠄⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠈⠁⡿⡇
⠀⠀⣸⠄⢘⡰⡏⠀⡴⡛⠅⠁⣤⣴⣯⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⡆⢠⡿⢁⣿⠿⢊⣰⣶⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⡇
⠀⠐⣠⣾⣣⣿⢧⣲⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⣾⣿⣿⠿⠋⠁
⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⣦⠀⢀⣀⣠⣤⡴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⠶⣂⣄⣀⡀⠤⠄⠒⠊⠙⠁⠀⠀⠡⠒⢋⣭⣤⣶⡤⠋
⠀⠀⠀⠀⠀⠀⡀⢞⠛⠋⠉⠉⠉⠉⠀⣤⡾⠏⠛⠉⠀⣀⠀⠄⣤⣴⣶⣾⣴⠷⠿⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠉⢹⣿⢿⣟⣛⣛⣉⣉⣡⣤⣤⣴⡶⠾⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣴⣶⣶⢦⡄
⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠛⠛⠛⣛⢫⣛⠛⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⠴⠿⠟⠛⠿⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡭⠾⠿⠿⠛⠛⠛⠁⠐⠀⠴⠦⢄⡀⠀⣠⠤⢴⣤⣾⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠢⠀⠀⠐⢄⡀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⢂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⣨⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⢰⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠒⠢⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢘⠀⠀⠀⠑⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠲
⠀⠀⠀⠀⠐⠿⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠒⡀⠁
⠀⠀⠰⠃⠀⣀⠋⠩⠀⠈⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⡀⠈⠢⠂⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣄⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠐⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠉⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠁⠃⠃⠃⠁⠀⠀⠁⠁⠁⠁⠐⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⡎⠀⢠⡄⠀⠀⠀⡀⠀⠀⡠⠒⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠉⠓⠐⢬⡡⢴⢈⡄⠰⠋⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠃⡄⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠷⠾⠦⢿⡀⢂⠀⠘⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣶⡆⢠⣆⣴⡜⢂⢠⡽⢱⠎⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⠘⠁⠠⠸⠆⠀⠁⠸⢀⣅⣛⣉⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢈⡋⢠⠀⠀⢀⡀⢃⠀⡟⢡⡌⢉⠛⡙⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⡉⠈⣜⣁⡤⠁⠀⠰⠈⠞⠁⠁
⠀⠀⠀⠀⠀⠀⢀⠀⢠⣀⡀⠀⢀⠀⠐⠀⢸⣿⡟⢱⡄⢀⠀⠉⢁⢤⣢⣈⠉⠀⠀⡐
⠀⠀⠀⠀⠀⢀⡈⠛⠠⠥⣀⠖⠂⠉⠰⠄⠀⠑⠛⠈⡁⠈⠸⠆⠰⢄⠘⠛⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠾⠀⣻⣂⣀⣤⣪⣥⣀⠓⢀⠀⠀⠃⠀⠈⠀⣀⠌⠈⠁⠠⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠚⡀⠛⣭⠿⠋⣁⠀⠛⠛⠉⠀⠈⠉⣀⠄⠊⠁⢤⣤⣤⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡼⣟⣘⣿⠩⣄⣶⡆⠻⣾⠁⠀⠀⠀⠀⠉⠛⠯⡛⠷⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⡠⠀⢻⡿⠹⢿⣤⠇⠙⠀⠀⡟⠲⠶⠴⠤
⠀⠀⠀⠀⠀⠀⢸⣷⣾⠀⠀⠸⣿⣶⢞⣼⡃⡓⠀⠀⡇⣀⣀
⠀⠀⠀⠀⣠⣤⣽⣿⣿⠆⠀⠀⠋⠉⠛⠛⠳⣭⠀⠈⠠⠐⠿⠶⣥⣾⣿⣤⣀
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⠱⣾⠈⡄⣴⣀⠀⠀⠀⠀⠈⠙⠛⢿⣷⠄
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣝⣋⡀⡀⠈⠢⢼⡿⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠃
⠀⣸⣿⣿⣿⢿⢿⣿⣿⡿⠛⠛⠛⠛⠛⢿⣿⣶⣾⣿⣿⣿⡿⣶⣄
⠀⣿⣿⣿⢃⡤⠈⠛⠁⠀⠀⠀⢀⣠⡾⠋⠉⠉⠉⠁⠀⠀⢀⣼⣿⣷⣦⡀
⠀⢹⣼⣷⠎⠀⠀⡇⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠘⠘⣿⣿⣿⣿⣷⣦⢤⡀
⠀⠀⠱⠇⠀⠀⢰⠃⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠈⠀⠀⠑⣿⣿⣟⣿⣦⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⢸⣦⢤⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠀⠸⡇⢹⡧⠜⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⣤⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣳⡄⠀⠀⠀⣿⣧⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⡄⠀⠀⢹⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣈⣶⣶⣄⠀⠀⠈⠢⣀⠇⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠉⠉⠈⠙⡄⠀⠀⠀⠀⠀⣧⡆⠀⠀⠀⢀⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡌⢀⡀⠐⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠶⠄⠀⠀⠀⠀⠀⠈⢦⠀⠀⠔⠁⠘⣧⠱⠄⠀⠀⠖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠄⠐⠒⠀⠤⠬⡇⠀⠀⠀⠀⠈⠴⢿⠀⠀⡀⠉⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣻⡾⠃⠀⣿⣤⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⣘⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⢥⣺⠇⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⡂⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⣀⠂⠐⢀⢺⣿⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢁⣤⡛⣶⣌⣋⣿⣿⣷⣄⡀⠀⠀⡆⠀⠀⠀⡀⠀⠀⣀⠀⠀⢺⡁⠂⠀⣠⡶⠛⠀⠀⠀⣀⡀⠀⠤⠶⠦
⠀⠀⠒⠒⠶⣄⠀⠀⠀⠀⠺⠿⢿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⠀⢀⣴⣿⣿⡘⢿⣄⠀⡜⠀⠀⢰⣉⠰⠊⠀⠐⠀⠀⠀⠈⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠟⠟⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⠇⠈⠹⣿⡄⠀⢲⣆⠀⠀⢀⠀⢠⠀⢀⠀⠊⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣤⣼⣿⣤⣾⣿⠟⠻⣇⠀⡟⠁⢈⠉⠀⠀⠀⠀⠨⣿⡀⠀⢻⣷⡆⢸⣇⢸⣦⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠋⠁⠀⠀⠀⠀⢣⡇⠴⠛⠀⠀⡄⠀⠀⠴⣿⡆⠀⢸⣿⣿⣰⡿⠋⠁⠀⠀⢀⡀
⠀⠀⢀⣀⣀⣀⣀⣠⣤⣄⣀⣁⣀⣀⠀⠀⠈⠀⠀⢭⡇⠀⠀⠀⢀⠋⠀⢻⠀⠀⠀⢰⡇⠀⠀⡴⣿⡇⠀⣼⣿⡿⠋⠀⠀⠀⢰⠆⠜
⠀⠀⣿⣿⣿⣿⣿⣿⡽⢿⡟⠉⢻⡄⠀⢾⣶⣯⣴⡄⡈⢆⠀⠀⠈⠀⠀⢸⡃⠀⢀⣾⣿⡆⠀⠀⣿⠀⢰⣿⡟⠁⠐⠀⠒⣸⠏⠜⡄
⠀⠀⢿⣿⣿⣿⣿⡇⣀⣸⣿⣦⣼⣏⣓⡉⣿⣿⣿⣿⣾⣦⡱⡀⠀⠀⠀⢨⡇⠀⣼⣿⣯⣿⡄⢨⣛⣰⣿⡿⣤⠶⣠⣶⣔⢡⠞⠀⠃
⠀⠀⢠⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⡇⢠⡿⠿⢿⡿⣿⣦⣾⣿⣟⣡⣤⣣⣼⠻⢏⡷
⠀⠀⢿⣿⣶⣿⠿⣧⣼⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⢸⣾⣿⣿⣶⡹⢿⣿⣿⣿⣿⣿⣿⣥⣤⡋⠀⠂
⠀⠀⠀⠙⠻⢷⣶⣿⣧⣰⣦⡛⠁⣼⣿⡟⢿⡿⢿⣿⣿⣿⣿⣿⣿⡆⡀⠀⣿⠘⢿⣿⣿⣿⣿⣿⣯⣫⣭⣌⣹⣯⣽⣿⣿⣷⣄
⠀⠀⠈⠙⠶⣤⣝⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡇⠱⡀⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡁⣙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣄⣉⣉⠛⠻⠿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠙⠢⣻⡏⠀⡰⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⡙⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣎⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡌⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣾⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⡟⠀⠀⠀⠀⠈⢿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠇⠀⠀⠀⠀⠀⠘⣿⣏⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠠⠀⠀⢠⣸⣿⡗⠶⠶⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠒⠿⠠⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⢿⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠌⠋⠔⠀⠀⠀⠀⠈⠡⠀⠀⠈⠀⠈⢀⣀⡀⠤⠤⠀⠀⠀⠀⠄⠀⠺⣥⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡾⡅⠠⠀⠐⠃⠀⠀⠀⠀⠐⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⣖⢟⢱⠀⠀⠂⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⡐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣴⢏⣥⠞⠁⠀⠀⠀⠀⢘⣱⣾⠷⡟⢦⠟⣿⢐⡀⠐⢰⣆⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢁⣴⡤⣀⠀⠈⠀⠈⠁⠀⠀⢀⠀⠈⠀⠹⡷⢶⣠⣿⣻⠷⢆⡎⠀⠸⠉⠅⠀⠀⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣜⠿⠷⡇⢀⡠⠀⠀⠀⠀⠀⡌⠨⡇⠑⢚⠣⠍⠏⣼⢣⡼⢏⡒⡤⢁⡍⢺⠀⠘⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡍⢆⣤⡄⠀⠀⠀⡔⠀⠒⣁⠄⠐⠂⠀⠀⢡⣶⢧⢍⠆⠀⠀⢠⣣⡜⣦⡖⣩⡾⠜⠆⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠁⠰⠞⠞⠆⠀⠀⠛⠂⠘⠋⠠⢄⠐⠂⠀⠎⡭⢊⠄⣀⠀⠀⠐⠭⠴⠭⠵⠋⠅⡞⠀⠀⡇⡾⢷⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠈⡤⢠⠈⠆⠀⠀⢀⢾⣳⡤⠀⠀⠀⠀⠀⢁⠀⠒⠂⠀⠟⡀⠀⠀⠀⠀⠂⢀⠈⠀⠀⠀⠀⠀⠶⠒⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡒⡿⣄⡽⠀⣠⠐⠀⠀⢋⣀⣤⠒⡫⠠⣍⢠⠀⠀⠀⢈⠎⡀⠐⣒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠻⣾⡄⡀⠀⡀⠀⠀⠀⠉⠐⠀⢄⠀⢀⡜⠀⠧⠄⠀⢁⡔⡙⣧⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣑⣣⣟⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠐⠡⡴⠚⡿⣨⡇⠄⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠁⠀⠀⠒⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠑⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣧⡿⣴⢢⠈⠑⠲⡄⠠⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠂⠀⠐⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⣀⣀⣤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⠯⣿⣶⢮⣶⣽⣭⣬⣙⣃⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢤⣤⣄⡀⣀⠀⢸⠄⠧⠰⡄⠶⢡⣆⣌⡜⠻⡿⣮⡙⢛⣻⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡏⠡⢘⠘⠁⠀⠀⠀⢺⠀⠀⠀⠓⠂⠞⠶⠾⠿⢴⠟⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠋⠠⠀⠞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⠀⠸⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⢀⠀⠀⠀⠀⢈⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⢨⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⡀⠀⠀⠀⠱⡀⠀⢸⣇⡞⠀⢀⣠⣴⠶⣚⣛⣻⣿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⠀⠀⠀⠀⠘⣆⢸⡟⠀⡴⢛⣽⣻⠧⣾⠿⢿⣿⣥⢿⡿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⢸⢿⣃⢸⣷⣿⠶⣋⣿⠿⣛⣿⡽⣿⣿⣿⣿⣻⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣛⣽⣷⣿⢾⣾⣿⠁⣸⠏⠀⠉⠛⠻⠿⣮⣴⣶⣹⣽⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣣⣜⣻⡿⣿⣷⡿⣼⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠱⢉⣉⡫⢞⢅⡞⣸⡿⠁⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣑⣻⢫⡟⣯⡎⢨⢼⡿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣴⢶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠆⢺⣛⡟⡙⠷⢗⣻⣶⡕⠊⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣖⡾⢿⣻⣿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠠⠓⣾⣿⣾⣶⠖⣾⠋⣁⠰⣢⡀⠀⠀⠀⣿⡇⠀⠀⣴⡿⢟⣩⡬⣿⣿⣾⣟⣮⣿⣻⣿⡟
⠀⠀⠀⠀⠀⢀⠀⠉⠉⠁⠋⡀⠈⣁⡀⠕⢤⡹⣦⠀⢸⣿⡇⢀⣾⢿⡶⣻⣿⣟⣩⣽⣿⢿⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠀⠘⠁⡠⣈⠑⠚⠋⠽⢓⢶⣿⣼⡇⢸⣿⡇⣾⣿⢟⣿⣽⣾⠿⣏⣭⣷⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠦⣽⢃⣴⣨⣿⠿⠿⠦⣤⣿⣠⠛⠾⠿⣿⣷⣶⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠸⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠤⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠠⠦⠄⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢰⣆⡰⣄⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⢁⡰⡉⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⢐⠶⠁⠀⣟⠔⠉⣹⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢣⠈⠀⠈⠀⠀⠄⠁⠁⠀⠀⠀⠀⣉⣠⢀⡄⡁⠐⠀⠀⠀⠀⠢⡀⣀⡏⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠘⠇⠀⠁⡰⡄⠀⠀⠀⠀⢳⠈⠃⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⠎⠃⠀⠀⠀⢒⠀⠀⠀⢀⡀⠀⠁⡍⠨⠀⠀⠂⠀⠈⢰⡑⠀⠀⠀⠀⠀⠧⠀⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⡐⠀⠀⠀⠀⠀⠈⠀⠒⠀⢀⡀⡀⠀⠀⠀⠀⠁⠀⠘⠅⡔⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠤⠰⠍⠈⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠄⠐⠁⠉⠀⢀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⢀⠀⠠⠉⠀⠀⠀⢀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⠆
⠀⠀⠀⠀⠀⠀⢀⠀⣠⣬⠽⠽⠿⢿⣿⣿⣷⣆⠀⠀⠀⠘⠀⠀⣠⣤⣾⣿⣋⣉⡉⠑⠒⠶⣤⣈⠉⢜⢟⣿⡿⠁
⠀⠀⠀⠀⢠⣾⡟⠛⣁⣥⠶⠞⢻⣿⣿⣿⣿⡿⠢⢄⣀⣤⠚⢻⣿⣿⡶⢶⣤⣀⠉⠙⠲⢤⣄⡈⠛⣶⣜⣿⠃
⠀⠀⠀⣰⣿⣩⡶⠛⢉⣤⠶⠊⢋⣩⡽⣻⠏⠁⠀⠈⠹⡇⠀⠐⠛⢿⡙⠲⣄⡈⠙⠲⢄⣀⠈⠛⢶⣌⠙⢿⣧
⠀⠀⢠⣿⣿⣿⡵⡾⠋⣀⣠⣴⡾⠗⠊⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⣤⠙⠢⢄⡉⠒⠤⣄⡉⠑⢦⣄⣹⣷⣾⣿⣧
⠀⠀⣸⣿⣿⣿⣿⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸⣹⣿⣿⠏⣻⣶⣦⣄⡁⠂⠤⠉⣙⣒⢦⣽⣿⣿⣿⣿⡇
⠀⠠⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⡻⣟⡏⢿⣐⣿⣿⣿⣿⣿⣷⣶⡤⠄⠈⠉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢠⣶⣿⣿⣿⡿⣿⣿⢿⡿⣾⣯⠀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣫⠏⣱⡟⢱⡿⠁⣼⡇⢸⡇⢻⣏⠂⣿⣿⣿⡿⠻⠁⠃
⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⣡⡏⣰⡏⠀⣿⠃⠐⢾⡇⢸⡇⢸⣷⠀⣽⠟⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠁⣺⡏⠀⣸⣿⠀⢸⡇⢸⠫⡆⡏⠑⠀⡰⠁⠀⠀⠀⠀⠀⠀⡀⢀⠐⡀⢠⠀⡄⠀⡀
⠀⠀⠀⢠⡀⣨⠀⠀⠀⠀⡇⢸⡏⠀⣿⠃⡀⣼⡇⢀⣾⠂⣸⠀⣹⡁⠀⠀⠐⠀⠀⠀⣰⠄⠆⡰⠁⢸⠀⡄⠸⢨⠆
⠀⠀⠀⣰⡋⣣⠄⠀⠀⠰⣷⢾⡇⣼⣿⣶⣾⡿⠀⣼⠏⣰⠃⠀⠁⢣⠀⠀⠀⠀⠀⠀⠻⣷⢤⢈⡇⠌⠀⠀⢀⣦⣜⡐
⠀⠀⠀⠘⢃⠸⠀⠀⠀⠀⠿⣾⡯⣿⣿⣼⣿⢃⣼⠏⡴⠃⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠙⠟⠛⣧⠃⠒⡆⠀⠿⠃
⠀⠀⠀⠀⡋⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢣⣿⣫⠞⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄
⠀⠀⠀⠀⢃⠇⠀⠀⠀⠀⠀⠙⣾⣿⣿⣷⣿⠕⠋
⠀⠀⠀⠀⡋⢢⠀⠀⠀⠀⠀⠀⠈⠻⣟⡟⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠁⡀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢠⡄⠀⠀⠀⢠⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠀⢱⠄⠀⠄⠀⠀⠀⠀⠀⢸⣷⡄⢰⣿⣷⠀⠀⣰⣟⣿⠀⠀⣰⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣄⠀⠈⡀⠃⠀⠂⠀⠀⠀⠀⠀⠀⢻⣿⢸⣿⣿⢀⣰⡿⠧⣿⡇⠘⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⠀⠺⣷⡀⠁⣀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠻⣿⣿⢹⣿⣿⣀⣇⡄⡄⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⠀⠈⠄⢈⣱⢞⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⢋⣏⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡔⡄⢾⣿⠟⢋⢀⠴⣚⡋⠤⠶⠂⠀⠀⠀⠀⠀⠈⢻⠃⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⢯⣿⠿⣿⡿⣿⡤⣼⡅⢠⣞⣠⣤⣥⣤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣻⢿⣿⣶⣠⠾⠿⠍⠠⠠⠠⠸⣛⡿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡛⠻⠿⢏⣇⠑⠀⡾⢝⣂⣮⣭⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠭⣍⡙⠿⣿⣿⣿⣾⣯⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⢻⣿⣿⣿⣿⡆⡧⣙⠈⠙⠻⣯⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣨⠍⡿⠁⠀⠀⠀⠉⠙⠛⠛⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⡈⠇⡃⢰⣾⣿⣛⡛⠛⢿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠚⠛⠛⠛⠛⠿⠿⠿⠿⢷⢰⣇⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠐⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠆⠠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠎⠐⠀⢀⠲⡀⠀⠠⡀⢀⠀⡄⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢓⡄⠙⠢⡀⢀⠈⠂⡁⠈⠀⡀⣤⡶⠟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠈⠀⡀⠀⠀⠘⠆⠀⠁⠀⣀⠟⠋⣠⣾⣿⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⠀⢄⡀⢀⠁⠈⢶⡈⠁⣨⠅⡠⠖⠀⣠⠞⠁⣀⠔⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠉⠓⠀⠂⣀⣀⠀⠱⣄⠀⡀⠁⠀⠀⢁⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢈⣫⣿⠯⡁⠀⠀⠘⠀⠀⣤⡠⠚⠹⡇⠀⠀⠀⠀⠀⠀⠀⠊⠀⣀⣴⠶⠃⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⢀⣱⣾⣿⣓⠒⠀⠐⠂⠂⠘⣠⣭⣤⠀⠀⠐⠀⠀⠀⣂⣠⡤⡴⠶⠟⠋⠁⡴⠞⠁⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣟⠉⠩⢤⣀⠐⠦⡀⠀⢻⡟⠛⠲⢀⠻⠀⠀⠃⠬⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⣿⡻⣶⣀⠈⠓⢦⡈⠀⠀⠀⠀⠁⠀⠠⠀⠠⣄⣤⣠⣄⣠⣤⣤⣄⣤⡄⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⡉⠛⣍⡻⣦⣝⠳⣤⣄⡉⠀⠀⢀⠀⠀⣀⢀⡀⢀⣀⢀⣀⣀⡀⣀⣀⣀⣤⣠⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣹⣦⣬⣙⠻⠷⢦⣌⣁⣀⠰⡌⠁⣠⠉⠀⠁⢹⣿⣿⣿⣿⡿⣿⠛⠛⠛⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣄⣈⡑⠒⠿⠿⣧⡜⠠⠟⢤⠀⠀⠘⡿⠛⠻⠦⠶⣤⣌⣙⡈⠓⠴⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡲⠶⣤⣤⣄⢀⠀⡉⠛⠳⢦⣀⠀⠀⠀⠐⡀⠁⣀⡾⣦⠙⠒⢶⣶⣀⣀⠉⠙⠲⣦⡀⠉⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣍⡙⠛⠿⢿⣦⣦⣀⠈⠑⢦⣀⠀⢠⡄⠀⠀⠈⠀⠘⠣⣄⣈⠙⠶⣆⣀⡀⠙⠳⣤⡈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠉⠙⠻⢶⣤⣬⣉⠛⠛⠶⣦⣈⠙⠀⠀⠀⠀⠀⠄⠀⣀⣤⣙⣷⣤⣄⠉⠳⢦⡄⠈⠑⢦⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠷⠽⢆⣸⣏⣻⢿⠿⣶⣶⣤⡬⠵⢶⣶⠀⢠⡤⠀⠀⠀⠔⠢⢤⠿⢿⣿⣦⣄⣉⠛⢤⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠾⠶⠶⠖⠂⠚⠁⠋⠀⠀⠛⠦⠀⠙⠂⠸⠀⠀⠀⠀⠈⠉⠉⠙⠉⠛⠋⠉⠉⠉⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣤⣤⣶⣾⣿⣿⣶⣆⣤⡀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠹⠶⠟⣁⡩⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⣿⣿⣴⣯⣴⣉⣽⢋⡟⢫⠖⠠⢀⠀⠀⠀⡎⠀⡀⢀⣈⣉⣙⡛⣃⠶⠿⣦⣴⣦⣤⣄⣀⣈⡁⠒⠤⢀
⠀⠀⠀⠀⠀⠀⣠⠞⣹⣿⣿⣿⣿⣉⣍⣩⣉⡭⢉⡏⠛⠷⡤⢁⠀⠀⠀⠀⢰⡌⠟⠈⠀⠙⠻⠿⠿⠷⠟⠴⠟⣥⣌⣀⢀⣉⠉⠚⠂⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠊⠀⠞⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠓⠛⠚⠓⠒⠀⠀⠀⠀⠀⢁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠍⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠄⠀⢰⠄⠀⠈⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠆⡆
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠰⠀⠰⡀⠀⢉⢡⠂⠀⢀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠘⠁⠀⠠⡀⢣⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠇⠸⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣄⠀⠀⠀⡀⠠⠾⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠
⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣏⡃⢀⠸⠁⠀⠀⢦⣽⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣅⣠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠈⠙⠻⢧
⠀⠀⠀⠀⠀⠀⠟⠁⠀⣸⣿⣿⡿⠋⠀⢰⡏⢿⣷⣆
⠀⠀⠀⠀⠀⠀⢀⣴⣻⠟⣫⡿⠏⠀⠠⠀⢑⣄⢳⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡖⠉⠘⠀⠀⠀⠀⠉⠘⢿⡗⣳⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣶⡟⠶⡿⢠⣤
⠀⠀⠀⠀⠀⠠⠟⠁⠀⢀⣤⣶⣶⡤⠀⢲⡀⠀⠀⠙⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⡟⡁⢸⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢩⣿⠏⠀⣴⣿⣦⡀⠀⠀⠀⠈⠻⠧⠀⠀⠀⠀⠀⢿⢶⣾⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⡿⠉⠀⠀⣸⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠟⠁⠀⠀⠀⢱⣏⣼⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠲⡖
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠘⠀⠈⠀⠀⠀⠀⡇⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡄⠀⡟⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠐⠚⠂⠀⠠⠀⠂⠀⠀⡴⠀⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⡄⠀⠀⠨⠀⠀⠀⠀⠀⢷⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠈⠉⠠⠀⠀⠈⠈⢹⠀⠀⠒⢀⣀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⡸⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠣⠔⣡⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢀⠙⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠁⣄⠰⢊⣤⠿⠃⠲⠀⠄⠀⠐⢀⡆⠀⡀⠀⣀⣠⣈⣠⣤⣡⣬⡡⠀⡘⢁⣀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⡓⢦⣜⠀⠶⡤⠀⠘⠉⡀⠀⣼⡿⠟⢻⣿⡿⢿⠟⠁⠀⠐⠀⠂⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⠤⢭⠷⣤⡀⣤⠀⢀⠀⡿⢫⣤⣾⣏⣡⠞⠀⡘⠒⠀⠀⠑⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢍⢻⣿⣅⠀⣤⣥⠿⠔⢢⠋⠈⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠳⣬⡿⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠹⡇⠀⢠⡃
⠀⠀⠀⠀⠀⠀⠉⠉⢉⡙⠻⣟⣛⣻⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⢇⠀⡇⢠⠏⠀⠐⠒⠲⢶⠶⡖⠴⠤⠤⠤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠈⠙⢿⣿⣿⣿⣿⣿⣯⣏⣵⢄⡀⠈⣄⣇⡜⢠⣤⣴⣂⡀⠤⠀⠐⠀⠀⠀⠺⢿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠓⠀⢁⠠⠠⠔⣂⣋⣩⣿⣿⣿⡿⣤⣿⣿⠥⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⣀⣐⠶⠞⠉⢋⣴⣿⣿⣿⣇⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⢀⡴⠘⠉⠀⠀⠀⣠⡟⢹⣿⣿⣿⣿⠁⠀⡇
⠀⠀⠀⠀⠀⠠⠀⠀⣀⡶⠋⠀⠀⠀⠀⣤⠾⠛⡠⠛⠿⠿⣿⣧⡀⣀⣇⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⢀⣠⣤⠟⠏⠀⠀⠊⠀⠀⠀⠀⠀⠈⠙⣿⣿⠓⠶⣶⣶⣶⣾⣦⡀⠀⠀⠠
⠀⠀⠀⠈⠀⡴⢋⣀⡄⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠁⠉⠛⠛⠿⣷⣆⣀⡀⠀⠀⠦
⠀⠀⠀⢂⡜⠟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠑⢦⡀⠀⠈⠙⠻⠷⣶⣄⠀⠙⠂
⠀⠀⠀⢎⠄⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣾⣷⣷⣲⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠈⠙⢿⣤⣙⠶
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠿⣤⣿⡿⠟⠁⠀⠀⠀⣀⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠐⠈⠻⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣿⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣆⢠⠇
⠀⠀⠀⣾⡉⠳⡀⠈⠑⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⢀⡜⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣡⡿⣶⢈⣀⣠
⠀⠀⠀⠈⢳⣶⡌⢠⢀⣄⠀⢶⡖⠀⠀⠀⠀⠀⠈⠻⣭⡝⣛⡤⣾⡛⢯⢶⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⡗⣻⣻⣽⢟⠁
⠀⠀⠀⠀⠀⠙⢣⠏⣎⠻⣦⣀⠙⠦⣌⣀⡀⠀⠀⢀⠤⠚⢹⣿⡿⢿⣳⣿⡋⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠠⠊⠾⢋⢹⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢯⡣⣌⠛⣷⣶⡻⣻⣿⣴⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⡀⢀⡀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣳⣾⣝⣫⣿⣟⠛⢂⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠟⢻⡿⣟⡷⠚⠋⠁⢀⠠⢐⡬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠛⠋⠙⠷⠿⠁⠀⠀⠀⠀⢠⡞⣹⠏⠁⣠⡴⠞⡡⠀⢀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢼⡟⠁⠀⠀⣤⣊⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣠⣴⣾⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠔⠃⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢿⣷⣶⣺⣵⢳⢮⡥⣌⡛⠁
⠀⠀⠀⠀⢀⠀⣴⣖⡿⠛⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠠⠄⠐⠀⠀⠄⠀⠀⠀⣠⢺⣿⣿⣿⡟⡏⠿⠾⠙⠉
⠀⠀⠀⠠⠿⣾⣿⡿⠷⡒⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⢀⣁⢶⣾⣋⠀⣀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢠⠟⠊⠉⢿⠇
⠀⠀⠀⠀⠀⠉⠚⢛⡍⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢻⠞⠩⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣶⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠿⣷⣀⣠⣤⠔⠂⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⢠⣚⠉⠈⠀⠘⣿⣿⡵⠿⣿⠅⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠉⢀⣀⣀⣀⣄⡤⠀⢠⠄⠀⣀⣀⣀⡀⠠⣀⡀
⠀⠀⠀⠀⠀⢠⡶⣿⣿⡿⠋⠰⠀⣿⣿⠟⠀⣡⣦⡀⠀⠀⠀⠀⡈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡰⠄⣠⣿⣯⣭⣌⡉⠉⠉⠉⠋
⠀⠀⠀⠀⢀⠞⠁⠀⠉⠀⠃⠀⠀⠀⠀⠠⣾⣾⡑⠀⠀⠀⠀⢸⠏⠉⡙⠟⣻⣿⣿⣽⣿⣿⠛⠁⠈⠀⠠⠀⠉⢉⡛⠻⠿⠛⠙⠳⠂⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⡼⢲⣶⠂⠀⠀⠀⠀⣾⠀⡞⢀⣼⠿⠻⠿⣿⣿⣷⣶⠂⢤⣤⡄⠤⢠⣼⣥⣶⣶⣦⣄⣀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠀⢀⣰⣿⠟⠁⠀⠀⢀⣤⣾⣿⣿⡿⠍⠉⣧⣶⠶⢻⢿⣿⣽⣿⣾⣿⣿⣷⣤⣿⣏⡈⠛⣿⣟⣿⣷⣦⡀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⣼⣿⣿⣤⠴⣞⣿⠿⣿⣿⡿⠅⣀⡤⢨⡝⢷⣦⣴⣾⣯⣿⣿⡟⢿⣿⣿⣿⣿⣿⣷⣶⣿⢿⣿⣿⣿⣿⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠘⣠⠈⠉⢿⠿⢿⣿⣿⣿⣻⣶⣎⣿⣿⡾⢅⣀⢁⠶⠈⢹⣛⣯⡙⣿⢻⣎⣿⡟⢻⣅⣰⡘⣻⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠡⢂⠀⣰⣤⠴⢾⡽⠉⠛⠺⣿⣾⣍⣧⡠⠂⣸⡃⠛⠛⠺⠟⠳⠌⣿⣿⣿⣿⠾⣿⣿⣇⠀⠀⠉⠙⠛⠛⠛⠻
⠀⠀⠀⠀⢠⣶⣿⡀⠀⠀⠀⢠⡿⢾⠏⢰⣆⣈⣀⡀⠀⠀⠀⠙⠻⢿⣵⠖⣋⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡟⡀⠀⣉⣛⣄⡀⢀⡠⠊⠑⠓
⠀⠀⠀⠀⣾⣿⠽⣧⡀⠀⠀⠀⢴⡾⠀⣼⣿⣿⣿⡿⣶⣦⠀⠀⠀⠒⠂⠀⣿⣦⣈⣉⠉⠈⠉⠁⠈⢻⣿⢧⢤⣄⠤⠐⠚⠉⠓⠤⣀⣀
⠀⠀⠀⠀⢻⣿⠄⠀⢫⣤⣄⠀⡸⠁⢠⢿⣻⠟⠙⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠁⠈⠒⠂
⠀⠀⠀⠀⠀⢹⠀⠀⢈⠾⡅⠋
⠀⠀⠀⠀⡠⠻⠀⠀⠈⠀⢁
⠀⠀⠀⠀⠀⡐⠀⢀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⣄⠀⠀⠀⠂⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⡞⣸⣹⣾⠟⣡⣜⣽⡆⠀⠀⠀⠀⠘⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠙⠻⡛⠿⡇⡀⠖⡫⠋⠺⣟⣿⣗⡏⠻⣿⡄⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠈⠀⢾⣃⠎⠀⠀⠘⡜⣿⠯⠀⠀⢻⡇⠀⠀⠈⢄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠀⠀⢶⡀⣿⠋⠀⠀⠀⠾⠧⣤⣤⣀⣈⣉⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢭⣩⢶⣲⣄⣆⣻⣿⣆⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠄⡀⢸⡇⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣽⢯⣿⣿⣗⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠴⠿⠟⣿⣿⣧⡀⢸⡄⠀⠀⢠⡇⠀⢠⠔⣦⡘⠁⠀⠀⠀⠀⣠⣤⣾⣿⣿⠟⠋⠁⡵⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠖⡶⠶⣿⣿⣿⡿⠿⠦⢿⣀⣀⣬⠉⣵⣾⣲⣿⠞⠁⠀⠀⢀⣰⡟⠻⣿⣷⠦⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⣻⡏⠁⠀⠀⠀⠀⠈⠛⠿⠿⢛⣿⣿⣿⣶⣤⣦⣶⠿⠿⣍⣡⠈⢻⡷⠇
⠀⠀⠀⠀⠀⠀⠄⢤⣤⣶⣾⡽⠯⠿⢿⡅⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠏⠀⠈⢭⣿⣿⣶⣦⣦⣤⣤⣶⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⣬⣥⣿⣾⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠿⣽⠛⡿⣿⣿⣿⣷⣿⣛⣇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢻⢁⠁⣼⣡⣿⣿⣿⣿⣿⣿⡟⣿⡅⣰⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⡶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣾⣿⢟⣽⣵⣿⣯⣾⡿⠟⣹⣿⣿⣿⣭⣛⣧⣿⣉⣠⣤⡙⣧⣹⡍⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢿⡿⠋⠉⠀⠉⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣿⣿⡇⠘⠷⣧⣿⣾⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⢿⡙⣇⡇⢹⣿⡿⠁⠀⠀⠀⠉⠻⣷⣌⣿⢹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣦⣧⣿⣇⣽⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠛⠋⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠁⠀⠀⠀⠀⠹⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⣀⣐⣴⠏⠁⠔⠒⣲⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠤⠤⠤⠒⠒⠈⠉⠉⢳⣴⣾⡿⠛⢑⣒⣶⠴⢾⣿⠛⠉⠀⠀⠐⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣥⣄⠠⠀⡀⠀⣠⠤⠄⠒⠀⠀⠠⠶⢻⡘⣧⣻⣍⣡⡤⠆⠐⠋⠉⠁⣀⣠⡤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⡟⣻⣿⣿⣨⣤⠤⠖⠐⠒⠉⠈⠀⠀⣠⣤⣶⠿⠟⢻⡶⢏⣤⣤⡴⠶⠒⢋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⢿⣿⡛⠉⠉⠁⢀⣀⣤⣤⣴⣾⣿⣿⣿⣯⣅⣄⠀⣶⣾⣿⡈⣩⣁⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠈⠡⣿⣟⣤⣼⣿⣿⣿⣷⣾⣿⣾⡿⠟⣛⣛⣿⣿⣿⣿⣿⡿⠗⠒⠉⣈⣤⡿⠟⠋⢁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢢⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣦⠾⠛⠉⠁⠀⠀⠀⢀⣄⠦⠾⠷⠞⠋⢤⣔⣴⣡⡾⠛⣯⡏
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣫⣿⣿⣾⣿⣿⣿⣷⣄⣠⡤⣤⣶⠶⠟⢻⣿⣿⣿⡋⠙⢳⣄⠟⣘⡛⢡⣾⣿⣴⣶⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⢿⣿⢟⣻⣽⣗⣤⣶⣿⢠⡎⠭⣛⠿⣿⣿⣶⣥⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠾⣾⣷⣾⣿⣿⢻⠋⢹⢰⣿⣦⡀⠱⡼⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⢯⣭⣽⣿⣿⣷⣫⣿⣿⣿⣿⡷⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣤⡚⢭⠤⢶⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠼⠷⣷⣿⣼⣵⠿⢨⡆⠀⠘⢠⣔⠠⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡀⠀⠀⠘⣣⠐⣿⣿⣿⣽⢻⣿⣷⡋⢀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣾⢿⡿⠿⢯⣿⣿⣿⢇⣿⣶⣿⣿⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠦⡖⣲⣼⡿⣿⣾⣟⣿⣾⡁⢮⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠩⠡⠟⣾⣿⣿⣿⣯⣅⣻⣿⢤⡦⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡱⠟⠉⣀⠰⡟⠷⠗⠻⡿⣟⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠡⢾⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢣⣤⣤⣶⣦⡆⠀⠀⠀⠀⠰⣶⣶⣦⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣤⡁⠁⣿⣿⣿⣿⣿⣄⣀⠀⠀⠈⠻⠿⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⣿⣿⣿⡄⣿⣿⣿⣿⡿⠛⠟⠀⠀⣀⣀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⣿⣿⣿⠓⠀⠈⠚⠃⠀⠀⠀⢠⣾⣿⣿⣿⣧⣀⡀⠀⠀⠀⣠⡤⠐⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣿⣿⣿⠟⠂⢄⠀⠂⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⡅⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠋⠀⠀⠀⢧⡄⠀⠀⠀⠀⣘⠻⣿⣿⣿⣿⠉⠀⠀⠀⠀⠨⡛⢻⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢀⠀⠀⠀⣼⡇⠀⠀⡀⠀⠐⠾⢿⣿⣿⣿⠿⠶⣤⡀⠾⢀⣷⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣤⡤⠀⣴⡦⠀⠀⢀⠀⠀⠀⠀⢠⣿⣇⠠⠁⠀⠀⠚⣡⣤⣴⣿⣷⣤⠀⠀⢈⠋⠹⠆⢈⣿⣿⡄⠀⠘⣿⠟⠁⠀⠈⠹
⠀⠀⠀⠀⠙⠁⠄⠀⠀⠀⣻⠀⢄⠀⠀⡾⠿⠙⠁⣀⣀⣤⣾⣿⡿⢿⣿⣿⣿⡿⢰⣿⡆⠀⡄⣸⣿⣿⣿⡀⠀⢻⢠
⠀⠀⠀⠐⢦⣤⣀⡀⠀⠀⠼⢷⣀⠁⢴⢦⣴⣿⣿⠿⢿⣿⠋⠉⠅⠈⣿⣿⣿⠟⠈⢻⡇⠀⠿⣿⣿⣿⣿⡇⠀⠈⣧
⠀⠀⠀⠀⠸⣷⣎⣉⣿⣷⣶⣤⣙⣟⠉⣿⣿⣯⣶⣶⣿⢿⠁⠀⠁⠀⣻⣽⠃⠀⠀⠈⠓⠰⠀⣿⣿⣿⣿⡇⠀⠀⠘⠀⢠⣤⠀⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⣛⠛⢛⠛⠛⠿⣯⣝⣻⣿⣿⢧⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠅⠀⢀⣀⣀⠰⠀⡈⠃⡘⠁
⠀⠀⠀⠀⠀⠹⢷⣿⣷⣷⡆⣬⣽⣽⣿⣷⣶⣿⣽⣿⣿⣾⣿⣿⣿⣿⠿⠁⢀⣀⣀⣤⡶⠿⢛⠛⠋⠀⠁⢸⡟⠻⢿⣿⠁⡐
⠀⠀⠀⠀⠀⢀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣶⣾⣿⡷⠀⠀⠀⣸⣿⡷⠺⠿⠏⠉⠁
⠀⠀⠀⠀⠀⠈⠋⡾⡿⢿⣿⣟⠛⠋⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣄⣽⣿⡿⠟⠁⢀⠀⠐⢋⣉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠀⠀⣀⠀⠀⠀⣀⡀⢙⠻⣿⣦⣽⡙⢿⣿⣥⡄⣄⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠠⠐⠠⠀⠦⠈⠡⠉⣠⠂⠠⠂⣐⢓⣧⣴⣾⠇⣼⡙⢨⢯⡏⠹⣉⣁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⡉⠧⠀⢻⠵⣿⢇⡜⢻⣷⣶⣛⣩⡗⠒⡖⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠀⠁⠚⠛⠏⠛⠛⠛⠉⠋⠙⠋⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⡖⣢⣄⠀⠀⠀⠀⠀⠀⠄⠒⠂⡐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢖⣢⣤⣀⡀⠀⣀⢀⡤⢀⣴⡿⠏⠀⠀⠒⡹⣾⠁⠈⢙⠄⣀⠄⠚⠁⠀⠑⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠤⠤⠀⠖⢙⣻⣿⣻⣿⣷⡟⣟⣻⣶⣶⣶⣾⣯⢷⣡⣶⡟⠋⠁⠠⠊⠀⠀⠀⡀
⠀⠀⠀⠀⣤⣶⡆⠁⠀⠁⠀⣀⠀⠀⠀⠀⢀⣈⠭⠞⡔⢻⠯⢌⣺⣿⡏⡹⡓⢧⣯⠀⠘⠉⠓⠪⣽⣧⠀⠀⠀⣐⣀⣤⣲⠁⠀⣀⣀⡀
⠀⠀⠀⠀⢿⣿⣷⡶⠆⠉⢩⠴⠒⠒⠈⣁⣐⣒⠈⠬⠓⢌⣲⠿⢛⡩⢉⠁⣻⢲⣿⠀⠀⠠⠄⢉⡋⠡⠤⠶⠟⠛⠀⠉⠉⠁⠀⢀⡄⠃
⠀⠀⠀⢀⣀⡿⡿⢧⣶⡢⠦⠒⠚⡟⠉⠉⠉⣠⠖⠉⠀⠀⠀⠀⠅⠊⠁⠀⣸⡌⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⢰⣿⣿⣇⢠⣿⣿⣿⠀⠀⢐⣠⠆⠠⢀⣀⡤⠄⠒⠢⠔⠒⠃⠉⠀⠈⢀⡇⣿⠄⡀⠐⠀⠠⠀⠀⠒⠉⠉
⠀⠀⠀⠉⠁⠙⢾⣿⣿⣿⡤⠾⠶⠶⠛⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠄⢀⠠⠴⡱⠛⠉⠁
⠀⠀⠀⠀⠀⢠⢶⣿⣽⡆⠀⠀⠀⠀⠄⠀⢀⠄⠠⣂⠄⠠⠐⠊⠉
⠀⠀⠀⠀⠀⠹⡿⣿⡿⣏⠔⠂⠄⣀⠀⠔
⠀⠀⠀⠀⠀⠀⠈⠢⠴⠓⠊⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠋⡙⠛⠟⠿⢿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⠊⠀⠕⡒⢄⣀⢀⡏⠉⠉⣷⢏⠀⠀⠈⠙⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⡻⣿⣿⡗⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⡀⠀⠀⠪⠂⠄⢈⠱⢶⣦⣬⣾⣽⣶⣤⣤⣶⣛⡻⢻⣶⣾⣿⣿⣻⠟⠹⠻⠿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠐⠀⣸⣿⠕⡛⠛⠉⠍⣼⣽⢹⠏⢻⣿⡏⠭⠹⡝⢄⢢⣁⣀⡀⠀⠀⢉⣀⡀⠀⠈⠉⠉⢹⣿⣿⣿⣿⣿
⣿⣿⣷⣄⡀⠀⠉⠉⠙⠙⠻⠷⠦⠄⢈⡛⠁⠠⡀⠀⠀⣿⡆⣿⠈⠨⢙⠻⢿⣖⡣⠮⠅⣐⡂⠬⠅⠒⠒⠠⠤⡕⠂⠰⣦⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠠⣿⢣⡇⠀⠉⠒⠍⠀⠀⠀⠀⠑⠢⣈⠉⠉⠛⢞⠳⠶⠶⢄⣲⡼⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣄⠀⠀⠀⠠⣿⢸⠉⠁⠀⠈⠒⠢⠴⠒⠂⢀⣀⣀⠁⠄⠠⡈⠆⠀⢀⣾⣿⣷⡆⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠾⣦⣤⣿⣿⣿⣷⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⣁⣈⡢⠀⢠⡀⠀⠠⠀⠀⠀⠀⢠⣯⣻⡾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣀⡀⠢⠒⠄⣻⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣶⣼⣦⣤⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠖⠚⠉⠉⠉⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠶⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⢀⣀⣀⠴⠞⣚⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠤⠤⠴⠶⠒⠒⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⠠⠤⠄⠒⠒⣈⠁⣠⣤⣤⣶⣷⣾⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠤⠤⠐⠒⠒⠈⣉⣩⣉⣀⣀⣤⣤⠤⠶⠚⠓⠚⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡋⠉⠉⠉⠁⣀⣉⣉⣉⣴⣤⣶⠤⠴⠶⠖⠚⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⠤⣤⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠂⠀⠒⠒⠀⠂⠀⠀⠐⠒⠒⢀⢒⣂⠐⢀⣀⡐⠀⠄⠂⠂⠿⠿⠛⠒⠒⠋⠩⢽⠋⠙⠟⢦⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠒⠓⠀⠀⠀⠁⠀⠂⠀⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢼⣷⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣔⣐⣶⣌⠻⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠚⠳⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠮⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠸⡡⠤⠀⠀⠀⠁⣀⡐⠒⠀⡠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠑⠒⠂⠀⠐⠒⠶⠤⠦⠤⠤⠤⣤⣉⣉⣉⠐⣐⠒⢒⡒⡀⢒⣀⠀⠀⠀⠠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠉⠀⠈⠉⠉⠩⣷
⠀⠀⠀⠀⠀⠀⠀⠠⠤⣥⣖⣒⣒⣦⣬⠤⢄⣰⣂⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠒⠀⠀⠀⠀⠐⡀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠶⠶⠿⠷⠯⠽⠿⠿⠶⠤⠾⠶⠿⠾⠶⠶⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠰⣎⢘⢦
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣠⠤⠠⠤
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠁⠀⠀⠀⠀⢀⣄⡀⠀⠀⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⢀⡀⠀⠀⠀⠀⠠⢤⣼⡧⣱⡄⠀⠀⠀⠀⡰⡿⠪⡉⢠⣼⣿⠗⣀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠉⠙⠐⠠⠄⠄⣀⡇⠘⣍⠉⠣⠐⠤⠤⠽⡆⣔⡀⢠⣜⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠢⠌⡀⠀⠀⡀⢾⠛⢳⣶⡵⣷⡶⣟⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠳⠵⠪⣿⡿⣾⡇⠿⠤⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣷⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣦⠞⢐⠑⠀⢵⠊⠗⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠘⣴⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⣦⡝⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⢄⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀⠀⢡⠈⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢈⠁⠀⢧⠀⣶⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢠⡤⠄⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠑⠤⠀⣣⡅⣤⡠⠤⠀⢒⠀⠀⠒⠚⠋⠑⠙⠈⠀⠀⠁⠀⠀⠀⠀⣃
⠀⠀⠀⡆⡨⡛⠛⠛⠛⠛⠛⠋⠛⢉⠓⠀⠈⢉⢹⠋⢣⠀⠀⢀⠀⠈⠦⠀⠀⠲⡲⠖⠶⠶⠓⠈⠉⠁⣀⣤⣈⠦⠠⠤⠀⠀⠀⢀⠀⠤
⠀⠀⠀⢷⣅⣉⣥⠀⠀⠀⠠⠶⠶⠧⠀⠒⠀⠡⠘⠂⠈⢡⡆⠤⢀⡀⡜⠣⣠⠤⠤⠄⠐⠀⠈⠀⠁⠀⢀⡙⠄⠁⢀⠀⠀⠀⢔⡁⠀⠁
⠀⠀⠀⣀⠉⠉⣁⣀⣨⣴⣻⣭⣤⡤⠴⠶⠒⠚⠛⠋⠉⢱⠸⢦⡀⠈⠇⠀⢡⠀⢀⢤⡀⠀⠀⠀⠀⠈⠫⡉⠚⢦⡀⢂⠀⣦⣿⢃⢂⠀⢀
⠀⠀⢪⠈⢝⡄⠀⣿⠋⠜⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡙⠢⡐⠘⢀⠆⠠⢞⣁⠀⠠⢄⣠⠤⠶⠭⠴⠦⣽⣦⣟⣿⣿⣭⣄⠒⠉
⠀⠀⢩⡁⡸⠇⠀⣯⢄⢎⠢⢿⡇⠀⠀⢀⣀⣀⣀⣐⣷⡤⢤⣀⣀⠀⠛⣆⡌⠠⠴⠣⠄⠀⠀⠙⢽⣉⣓⣶⣖⣲⣶⣿⣿⡻⢟⡻⠿⠿⠒
⠀⢀⠈⠙⠛⠀⠀⠘⠷⣽⡶⠿⠛⠛⠛⠛⠋⠉⠉⠁⠈⠻⠦⣄⡿⠪⢂⣿⢦⣯⠳⡐⠀⢰⠄⠀⠀⠉⠉⣉⠭⠁⠒⢺⡇⠱⡀⠑⡀
⡄⡝⢇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠶⢲⠏⢀⡠⣾⣿⠀⢚⣇⠘⠈⠁⠀⠀⠀⠈⠁⢠⣄⣀⣤⢼⢰⠀⡋⠢⠇
⢻⡷⠇⢀⠀⡀⡀⣀⣀⣀⣀⣀⣠⣤⢶⢖⠻⠛⠉⠉⠈⠀⠸⠗⠋⠀⣟⡏⢰⠇⠸⢂⠋⠀⠀⢀⣀⡴⠾⠛⠋⠁⠀⠀⠱⣆⠃
⠀⠉⠙⠋⠉⠉⠉⠉⠉⢹⠏⣩⣙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⣿⠞⠉⠀⣘⣣⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡇⠈⠳⡘⡆⠀⣀⣠⡤⠶⠚⢋⣭⢴⣋⡽⠷⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣵⣄⠀⠻⠛⠋⣩⣤⣴⣶⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣶⣤⣤⠴⠖⠛⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠄⢀⣤⣠⡿⠁⠐⠚⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠤⠀⠄⠀⠒⠒⠒⠋⠉⠈⠀⠀⣽⢾⢿⣛⣉⠽⠽⠗⢚⣿⣏⠁⠀⠐⠈⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⣶⡄⠇⠀⠀⠰⢒⣓⠈⠀⠀⠐⠋⢹⣌⣧⣽⢤⠶⠚⠂⠉⡀⣀⣠⡤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⣿⡿⠷⠖⠒⠋⠈⠁⢀⣀⣀⣠⣴⠾⠛⠛⠉⣻⡏⡦⡶⠾⠛⢉⣩⠄
⠀⠀⠀⠀⠀⢀⢀⣠⡄⠙⣿⣫⣽⣯⣀⣠⣀⣠⣤⣾⣶⣿⣿⣿⣿⣿⣿⡆⢒⡬⠿⠿⣇⣦⡶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠘⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣭⡴⠿⠿⠟⠻⠟⠛⠉⣡⣀⣲⡿⠛⡉⢠⢄⣀⣤⢴⠆
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡋⠁⠀⠀⢀⣄⣠⣴⣶⣳⣯⣭⣥⡀⢳⡞⣷⡿⢁⣼⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠑⠾⣿⣿⣿⣿⣿⣿⣷⣶⣯⠿⠛⠋⠁⠘⣿⣿⣿⡦⢤⣛⢃⣑⡖⢀⠿⢿⣿⣿⣭⣉⡤⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠟⠋⠉⠀⠀⢀⠀⠀⢀⣽⣻⣗⣺⣿⣾⣿⠿⣧⢻⣌⠁⠪⣙⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⣻⡿⡿⢿⣿⣿⣠⢇⣽⣿⣷⣤⣙⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠿⠗⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⣒⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⡤⠤⣀⣀⡀⠀⠀⠀⣠⠖⣋⠴⠊⢁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⡥⠖⢲⡆
⠀⠀⠀⠀⠀⣇⠞⣳⡀⠀⠘⠉⠭⠭⢥⣾⣁⣰⣞⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⡥⠚⢁⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠟⢓⣶⠶⠶⠤⢤⣍⣉⣉⠉⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣚⠵⠚⣡⡴⠚⠉
⠀⠀⠀⠀⢠⣖⣦⢤⣄⢀⣤⠞⢫⣄⠀⢰⠟⠀⢀⣠⡌⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠐⢉⣠⠶⠋⠁
⠀⠀⠀⠀⠘⠦⣽⣢⠾⠋⠁⢀⣸⡟⠐⠀⣂⠀⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠾⣟⡓⣦⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣟⣲⢮⡄⣉⢈⡉⢒⣻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣿⣈⣼⡲⣾⣧⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠹⣿⠃⠉⠁⠉⠁⠀⠀⣤⢾⡿⣻⠟⢻⣿⡿⣯⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢻⣎⡻⠦⠬⠴⢚⣛⡴⢯⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠈⠛⢷⢭⣭⣽⣟⣩⣭⣭⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠀⠀⠃⠈⠙⠇⠀⠀⠀⣹⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣴⡾⢟⣥⡖⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠷⠶⢶⣤⣤⣾⣶⢚⠙⠄⠁⡈⣿⣁⡽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠈⠉⣴⣾⡟⠠⠄⠰⠀⠶⠀⣳⢴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡑⣏⡽⠖⢊⠽⠻⣯⡟⢲⡴⢆⢖⣀⣶⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⢮⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣖⢧⣠⣀⠀⣠⡴⢻⣿⣿⣯⣻⣤⡗⠿⠿⠿⠄⠀⠀⠀⠀⠀⣠⣤⡴⠞⣫⡥⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠘⢮⣙⣖⡽⠟⠁⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡧⠖⠉⣠⡤⢞⣁
⠀⠀⠀⠀⠀⣠⠤⠤⢤⣤⣄⣈⣳⣄⣙⣦⣑⣄⡀⠀⠀⣠⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⣻⣟⢊⠁⠄⠀⠌⠿⠟⠉⣩⠇
⠀⠀⠀⠀⣴⠒⠒⠒⠒⠒⠒⠲⠶⠶⠦⠄⠀⠀⠀⢠⠼⣷⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣀⡀⠀⣥⣶⣏⣰⠆⠰⠂⠒⠠⠾⡾⠗
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢶⡶⠿⢮⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⡦⢼⣌⣻⣄⣽⠞⠫⠟⣷⡏⣻⡴⠃⡽⣄⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠶⢤⣒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣭⢴⡯⣽⠿⢤⣀⣤⠾⣿⠿⢥⣹⡶⡟⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣯⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠬⠯⠞⠋⠀⠀⠀⠀⠀⠙⠻⠃

⠀⠀⠀⠀⠀⠀⢠⣾⣷⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠖
⠀⠀⠀⠀⢀⣥⠼⢻⡿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡄⠀⠀⠀⠐⢻⣿⠟⠉⠉
⠀⠀⠀⠘⠆⠟⢠⣾⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⠀⠄⠀⠀⠀⢹⡫⢿⣿⡇⢀⣴⠏⠀⠀⠁
⠀⠀⠀⠰⡐⡦⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⢃⣾⣿⣷⣼⣿⣄⣠⣄⣀⠠
⠀⠀⠀⠀⢋⣀⣤⣤⠀⡀⠀⠀⠀⠀⠀⢀⠀⠶⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⡿⢏⡉⠉⠉⠉⠚⠛⠀⢠
⠀⠀⠀⠀⠆⠈⢳⠉⠶⠃⠀⠀⠀⠄⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢤⡀⠀⠀⠀⠀⠃⣤⣹⣤⣠⡄⠰⠆⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⢲⡀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣶⡀⠀⠀⠀⠀⢀⡞⠁⠀⠸⠀⠂⠀⣀⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠁⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠉⣿⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠘⠃⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⢠⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣦⠀⣰⣶
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⢸⡇⠀⠀⢀⣠⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠆⠈⢡⡶⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠀⠸⣿⣿⣷⡄⡀⠃⠀⠀⠘⢿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠹⢿⣦⡀⠀⠀⠀⠀⣠⡴⠃⠀⠀⣸⡶⠃⠙⠇
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣿⣿⢹⣿⣿⡇⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⠄⠀⠀⠀⠉⠐⢦⡄⡀⢈⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢠⣼⡿⢹⠀⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠂⠁⢀⠈⢁⡀⢉⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⢿⡇⠀⠀⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⣵⠿⠂⠤⠿⠟⠉⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣷⠀⠀⣶⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⠈⠠⠖⠈⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠰⢾⡷⠀⡈⠁⠛
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⠘⠀⠀⠀⡄⠀⣾⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠄⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠎⢹⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⡇⠀⢹⠀⢀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠲⠶⠛⣉⠁⢀⡀
⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠘⠀⠼⠄⣸⠆⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣸⠀⠀⠘⠄⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡚⢛⣿⣿⠟
⠀⠀⠀⠀⢠⡯⠙⠁⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⠀⠈⠉⠿⠉⣠⡤
⠀⠀⠀⠀⠼⠖⠂⠀⠀⠀⠀⢠⣠⡄⢸⠀⢸⠀⠀⠀⣷⠈⢳⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣲⠆⠘⠀⠀⢀⡀⠀⣩⣴
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢾⠀⣿⣧⣸⠀⡆⠀⠀⠀⢩⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⢘⡇⠀⠀⠀⠀⣶⣶⣤⣄⠀⠀⠀⠀⠀⠈⣿⠿⠆⠀⠀⠀⠀⠙⣾⠟⡁
⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡿⣿⣷⢂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢹⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢣⡘⠁⠀⠀⠀⠀⠀⢸⠟⠻⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠇⠀⠀⠀⡀⠸⠇⡀⠀⠀⠀⠀⠀⠀⠛⠖⡉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠠⠄⠷⣤⠀⡀⠀⠰⠀⠀⠀⢸⠀⠀⠁⠀⡄⠀⠀⠀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⢠⣶⣏⠉⠃⠀⠀⠀⠀⠀⢨⡇⢰⠀⠈⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢾⠿⡏⢰⣷⣷⣔⣀⠀⠀⠀⠀⠀⢺⡇⠘⠀⠀⠀⠀⠀⠀⢀⡛⢗⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠛⠾⠟⢻⣿⣯⣀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⣀⠈⢱⣎⣹⣇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡟⠉⡄⠉⣶⣦⡀⡿⠁⠜⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⣹⡆⠰⢃⠀⠠⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠘⠂⠀⠀⠀⠀⠃⠀⠁⠸⢿⣈⣄⣷⠞⠛⠀⠀⠀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠷⠒⠞⠳⠶⣦⡀
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣄⣀⣏⢈⣀⠀⠚⠀⠀⠀⠀⣿⠀⠀⠀⣀⢠⣴⣾⣷⠒⢠⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠉⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙⣏⠛⠃⣴⠆⠀⠀⠀⡟⠀⠀⠀⢫⣶⣯⣽⡏⠐⢀⡽⠻⡇⣸⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠄⠀⢀⠀⠄⠀⣀⠄⠀⠀⠀⠀⠀⠘⢶⡸⠇⠀⠀⠀⠀⠃⠀⠀⠀⢣⣾⡿⡏⢙⠀⠹⠀⠀⠀⢉⠀⠀⠀⠀⠀⠠⠿⡿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⣴⠃⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⡰
⠀⠀⠀⠀⠀⠀⠉⠀⠐⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠜⠓⠠⠰⠇⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⡀⣀⣀⡀⢀⣀⣀⣀⡀⣀⠀⢀⡀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⣀⠀⢀⣀⢀⣀⢀⣀⣀⣀⣀⡀⢀⣀⠀⣀
⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣜⣋⣻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡘⠳⡄⠶⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠒⠿⠀⠀⠀⢘⢃⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡷⠾⠀⣾⢠⢦⠙⡄⢦⠟⣱⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⡁⠀⠂⠛⠀⢀⡀⠿⣘⣜⣏⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠀⠀⠀⠀⣄⠘⡀⢠⠋⣤⠀⡹⠋⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⣠⣎⣠⠄⠡⠀⠄⢰⠍⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⡿⢟⠙⡆⠀⠀⠀⠉⣠⣴⡀⡚⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠒⠀⠈⠐⠀⠀⠀⠉⠁⠋⠀⠁⡇⢀⠌⠈⠛⠷⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢀⣙⣁⣄⣤⣤⣤⣀⠁⢀⣀⠀⢰⠀⠈⠀⠀⣈⡡⠃⠈⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠈⡠⠈⡥⠛⠋⣀⠀⠚⠉⠉⠉⠉⠉⢀⡠⠀⠉⢤⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡠⣏⣘⣾⠣⣆⢴⡆⠺⣶⠋⠀⠀⠀⠀⠙⠻⣿⣿⣿⣟⠻⢿⡄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢹⡟⠹⢳⣄⠅⠈⠀⠀⡾⠠⣤⣤⣌⡀⠀⠀⠀⠉⠙⠻⢦⡀⠀⠐
⠀⠀⠀⠀⠀⠀⢻⣧⣎⠀⠀⠀⣿⡶⢖⣼⣂⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⣀⣀⣿⣿⡿⠀⠀⠀⠉⠉⠛⠛⠧⣇⠀⠐⠠⠨⣿⢴⣒⣴⣶⣄
⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⡀⠠⡖⠘⡀⡤⡀⠀⠀⠀⠉⠙⠻⢿⣿⣦⡀
⠀⢠⠟⠛⢽⡿⣫⣾⢿⣿⣿⠏⠛⠁⠀⠀⠑⠄⣳⡿⠟⢂⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⢴⠟⠛⠛⠆⢃⠾⠛⠛⠛⠛⠛⢿⣶⣤⣼⣷⣶⣶⣷⣄
⠀⡁⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠴⠚⠉⠉⠛⠉⠉⠁⠀⢿⣿⣦
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠚⢿⣿⣿⣿⣦⣄⣀
⠀⠀⠔⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠉⠒
⠀⠀⠀⠀⠀⠀⡆⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢻⠉⢹⠏⡛⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⢳⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠸⣆⡛
⠀⠀⠀⠀⠀⠀⠘⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠒⢢⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠔⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠴⠆⠘⠉⠀⠑⢀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠉⠉⠀⠀⠀⢀⣤⠤⠀⠈⡀⢠⣱⡄⠀⠀⠀⠀⢀⡀⡤⠴⡒⠉
⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠀⠀⠄⠀⠀⠙⡁⡀⠍⠖⢐⡮⠟⠉⠀⠀⠀⢹
⠀⠀⠀⠀⠈⠐⠀⠈⢦⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⣀⣨⡴⠂⠁⠀⡠⠴⠺⣥⣀⠀⢀⠀⡈⠔⠁
⠀⠀⠀⠀⠀⠀⢠⠐⢐⡀⠔⠊⠉⠀⠀⠀⠀⠀⣀⠤⡒⠮⠚⠉⠀⢸⣤⠖⠋⠀⡆⠀⠁⠀⠠⠐⠁
⠀⠀⠀⠀⢀⠄⠑⠐⣸⡲⡆⠀⠀⠀⣀⡤⠶⠍⠂⠁⠀⠀⢀⣠⠖⢻⡇⠀⠀⠀⣇⠀⠄
⠀⢀⡔⠊⠁⠀⠀⣢⣄⡠⠇⠔⡒⠝⠋⠁⠀⠀⠀⢀⣤⠞⠋⠀⠀⢸⣅⠌⠐⠚⠁
⠀⠀⠈⠆⠀⠄⠊⠁⠀⡠⠒⠀⣄⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⣠⡴⠋
⠠⠀⠒⠉⠡⠀⡀⠀⢸⠀⠀⢀⡀⢀⣀⠔⠋⠀⠀⢀⡤⠒⠉
⠀⠑⢄⠢⣤⡌⣴⠠⠊⠣⡀⠑⠠⠞⣁⠀⢀⠤⠊⠁
⣀⣀⣀⣁⣒⣋⣁⣀⣀⣀⣀⣀⣠⣥⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⠀⠀⠀⠤⠀⣶⣾⣿⣿⣿⣤⡖
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⢷⣄⠀⠐⢇⢹⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠙⢿⡄⠀⡐⢛⡻⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠟⢤⡀⠀⠀⠀⠈⠃⠀⠈⠀⠁⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⢦⠀⠀⠀⠠⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠤⠀⠄⠠⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⠀⠀⠀⣠⣤⣦⣴⣤⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠁
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡴⢀
⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠐⠳⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠷⠃⠈⠿⠟⠷⣤⡄
⠀⠀⠀⠀⢸⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⣸⡟⠛⢢⡤
⠀⠀⠀⠀⠀⠠⠙⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣷⣠⠀⡀⠀⠀⠀⠀⠀⠌⣡⠈⠛⠀⢀⠄⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠻⡇⢠⠀⠆⠀⠀⠀⢀⡄⢀⢸⡟⠃⠐⠛⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⡆⠀⠀⠀⠀⠀⢾⣠⣿⠦⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣀⠶⣿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠛⣿⡏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⣏⢛⣛⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣘⣠⡄⠀⠀⣤⠀⡀⠀⠀⠀⠀⠐⠋⢈⡯⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣂⠀⣄⡀⠀⠀⠀⠂⠀⠀⢸⣆⢠⡿⠀⠇⠀⠀⠀⠂⢀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡾⣟⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⢠⣿⡼⠃⠀⠀⠀⠀⠀⠀⣼⣟⣧⣶⣶⣠⢶⠟⠠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢬⣿⢰⣿⣿⣿⣿⣿⣾⣷⣇⡆⠉⠀⠀⠀⠁⠀⠀⠀⣀⠂⠀⠀⠛⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠹⠦⠀⢸⡞⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠀⠀⠀⠀⣀⠀⠘⢧⣄⣁⡀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⢽⣿⣿⣿⡋⢨⣿⣯⡀⠀⠀⠀⠀⠀⡀⠐⠃⠈⢻⣿⡅⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠈⠁⠉⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠋⠹⣿⡀⠀⠀⠐⢂⠀⢠⣽⠟⣻⣷⣿⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠠⣼⡟⣾⣿⣿⣿⣷⣌⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠱⠀⠀⠀⠀⠀⠼⡿⠛⠿⣿⣿⣿⣿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠛⡻⣦⣤⣤⣄⠀⠀⠠⣤⣤⡤⠡⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠌⣀⠀⠋⠀⠛⠁⠀⠀⠐⢶⡿⢛⣿⢉⣼⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠴⣿⣿⡣⠙⢧⣄⠐⠈⢻⣿⣷⣤⡀⠀⠀⠀⢀⣤⠞⠛⠛⣰⠛⠃⡀⣀⡠⠞⠀⠄⠤⣀⣀⢈⣙⠂⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡳⠛⡀⠘⠃⠀⠀⢘⠇⠘⢿⣶⡙⢠⡀⠈⠀⠇⠄⠀⠚⠀⠀⢐⠛⢧⡄⠀⠀⠀⡉⠉⠈⠛⠲⣦⠈⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠟⠗⠀⠁⠀⠀⠀⠀⠸⠀⠀⠜⣿⡷⣀⠁⠀⢀⣠⡴⠶⣶⣬⣄⠀⠀⠀⠀⠀⠄⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⡉⠂⠀⠀⠉⠀⠈⠉⡉⠿⠆⠀⠶⠶⣶⣗⡀⠛⠶⡾⠹⠒⣶⠂⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠸⠛⣷⡄⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠻⠙⠿⡟⠙⡿⠻⣟⠿⢛⣻⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣶⣷⣾⣷⣶⣿⣶⣾⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠁⠈⠦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠐⠂⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⢀⣠⠤⠒⠈⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣦⡤⠔⠂⠉⢀⣠⡤⠔⠊⠉⠀⠀⠀⠀⠀⠀⣀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠐⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠟⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠩⢤⣅⠢⡀⠀⠀⠀⠀⢀⣽⡿⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢒⣤⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣱⡼⠀⠀⠈⠉⠉⠀⣀⡴⠿⠛⠉⠀⠠⣀
⠀⠀⠀⠀⠀⠶⣿⣶⡶⣴⠏⣴⣦⡀⢀⠤⠒⠂⠁⠀⠀⠀⠀⠀⠀⠈⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠐⠛⠳⢶⠀⠛⣻⠇⠈⢰⠛⠳⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠚⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠂⠰⡶⢿⡇⠀⠀⠀⢀⣤⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⠀⠀⢠⣾⡿⢟⡕⢰⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣄⡀⢤⠂⠀⢀⡜⠀⣀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠉⠉⠈⣹⣬⣭⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣤⣤⠭⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⡀⠀⣠⡟⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠰⢄⣀⡀⠀⠀⠂⠸⡆⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠇⠀⢿⡑⡈⠁⢒⢨⣿⠃⠀⠘⠫⣼⣭⣭⡻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣶⡾⠇⠀⠀⠁⠙⢻⠋⠋⠀⠀⠀⢠⣶⣯⣿⣿⡄
⠀⠀⠀⠀⠀⢺⠤⢄⡀⠈⠈⠀⠂⠀⠀⠀⠀⢰⡆⠀⢰⣧⡀⠀⠉⠙⡏⠛⠁⠀⡤⠓⠀⠀⠀⠀⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠐⠀⣜⡳⣶⣤⢀⠀⠀⠀⠀⠀⠀⡇⢀⣺⣾⣧⡄⠀⠠⠀⠀⢤⠒⠻⣀⣀⣻⠿⢟⠟⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢥⠈⠙⠿⣧⠀⣄⠀⠀⠆⢳⠀⠈⠇⣷⣆⠀⣈⠰⡖⠻⢇⣴⠌⣋⡵⣂⠱⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠐⡮⣷⣝⠿⠁⠀⢻⣦⡄⠈⠿⣗⣠⡟⠉⣡⣾⣿⣿⠯⠅⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠔⠀⠛⠀⠿⢿⣦⢻⡧⠀⢚⣿⣿⣴⠿⠿⡙⣭⣿⡶⣯⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⡀⠀⠠⢂⣀⣶⣮⣝⣿⡂⢨⡿⢟⣾⣭⡎⠄⠩⠜⠙⠀⠙⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣈⣍⠉⣲⣿⣿⡏⠃⠀⣿⣿⣿⣿⣿⠾⠶⠶⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠙⠛⠓⠛⠛⠋⠙⠛⠃⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡷⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠇⠈⢢⠔⡝⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠣⡀⠑⠠⡘⡄⠈⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠲⢄⡀⠙⠆⣿⢀⠂⠀⠀⢀⣀⠀⠠⢤⠤⡔⠶⡲⡘⠏⠫⠙⠈⠃⠀⠀⠈⢣
⠀⠀⠀⢀⠤⠤⡤⣤⣤⣤⣤⢤⡤⢤⡶⢦⣀⠀⠀⠡⢿⡯⣜⠛⠉⠁⠐⠒⠤⡀⠀⠁⣀⣀⣀⣀⣀⣤⡄⠀⠤⠄⠐⠒⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢂⡔⠱⣴⡄⠀⣀⡈⠈⠀⠀⣠⠊⠀⣀⠀⠔⢸⠁⠈⠤⠀⠀⠒⠀⠀⢩⡉⠀⠈⠫⠑⠉⣙⠉⠈⠠⠤⠄⠒⡾⡓⢏⡁⠉⠑⠢⡀⢀⠤⠂⠙
⠀⠀⠀⠘⠷⣶⣶⣖⡒⣒⣒⣒⣛⡉⠩⠉⠀⠀⠀⣈⣉⣀⣤⣀⠛⡉⠒⠢⢤⠉⡙⡖⠂⠒⠈⠁⠀⠀⠀⠀⠀⢠⠤⣇⠱⡀⠀⠄⠀⠀⡘⣡⡆⢀
⠀⠀⢀⣠⣀⡀⠀⠀⣤⢴⣾⣽⡶⠶⠶⠒⠛⠋⠉⠉⠉⠀⠀⠈⡀⠛⢦⡀⠈⠆⢃⠸⠀⡠⠐⣦⠀⠀⠀⠀⠀⠀⠑⢄⡈⠙⢦⡈⢆⢘⣾⣿⣡⠃⠤⢀⡄
⠀⠠⡏⣆⠢⣡⠀⢰⡏⠃⢊⠭⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠅⠀⣠⣍⢷⣜⡈⢄⠏⠠⢞⣅⡀⠤⠐⣒⣶⠒⠛⠓⠚⠲⠦⢽⣾⣽⣿⣯⣥⣔⣀⠁
⠀⠀⢨⣍⢀⢻⠀⠸⣇⠀⢎⡲⣸⣧⠀⠀⠀⡀⣔⣀⣀⣀⣷⡶⠤⣄⣀⡀⠉⠛⣇⡌⠀⠐⠾⠠⣀⠀⠀⠙⢬⣉⣛⣻⣒⣒⣶⣾⣿⣿⠻⢝⡛⠿⠿⠟⠢
⠀⠀⠀⠑⠛⠓⠂⠀⠹⠦⣽⣶⠾⠷⠓⠛⠛⠛⠛⠉⠉⠁⠈⠻⠦⣌⣸⠞⡨⢊⣯⣦⣿⠙⡔⠂⠠⢦⠀⠀⠀⠉⠉⢉⡉⠭⠅⠒⣿⠀⢣⡀⠱⡅⠈⠀⠉
⡐⡩⢯⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⣾⢃⠌⣠⣞⣿⠈⠌⢧⠈⡖⠊⠁⠀⠀⠄⠒⠈⢁⢀⠀⢀⣀⡇⢇⠈⠑⠤⡇
⠇⣯⣶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⢶⠾⠫⠙⠙⠀⠠⣷⠴⠊⢹⡿⡏⠀⡦⢙⢦⢰⠒⠈⠀⠀⠀⣠⣤⠾⠞⠛⠉⠁⠘⢼⢀⠁
⠈⠻⠴⠶⠷⠾⠶⠶⠾⠷⢿⡶⠛⠻⢿⡫⠑⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣷⣼⠶⠌⠀⠶⢀⣀⡤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⡞⠓⢦⡙⣆⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⣻⡭⢼⣟⣁⣤⠴⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢇⠀⠀⢳⣼⣄⣤⠴⠞⢋⡉⣀⣤⢞⣫⠵⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⡄⡈⠉⠁⢐⠲⠮⣓⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⣪⣌⠢⣤⡤⠤⠖⠒⠉⠉⢉⣀⡀⠤⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠐⢦⣀⣀⣀⣠⣤⡒⠂⣤⡶⠛⠋⠉⠉⠁⠼⣀⠇⠀⣀⣀⡤⠒⠊⠉⠀⠀⠀⢎
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⠶⠶⠖⠒⠚⠛⢋⣩⣭⠿⠷⡒⣿⣂⣻⣿⠬⠭⣝⣛⠲⠾⣗⠛⠉⠉⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⡴⣋⡙⡏⠁⠀⠀⠀⣁⣀⣀⠀⠀⢀⣀⡠⠤⢴⠣⡞⠀⣀⣾⣜⣁⠬⢟⣏⠖⠉⠁⠀⠉⠑⠛⠁⠀⠀⠀⣀⣠⣴⣾⣿⠀⣀⣀⣀⣀
⠀⠀⠀⠻⣿⣵⣷⠶⠏⠉⠁⠀⠀⠀⣉⣁⣠⣤⠤⠶⠚⠢⠌⠩⠓⠁⠀⠀⠀⠘⣻⣼⠀⠀⠀⣀⣠⡤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠁⠀⡖⠚⠁
⠀⠀⢀⣤⣼⣯⠭⠤⢴⡶⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡤⠤⠔⡟⣿⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠁
⠀⢠⣿⢿⠑⠀⠠⣠⢶⡕⡄⠀⠀⠀⠀⠀⣀⣀⣤⠠⠤⠖⠒⠋⠉⠉⠁⠀⠀⠀⡇⣿⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠒⠋⠉⠁
⠀⠀⠙⠋⢷⣀⠀⣿⣝⣣⠥⠶⠔⠒⠚⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣤⣇⠿⠀⠒⠊⠉⠉
⠀⠀⠀⠀⠀⣬⢿⢉⡙⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠾⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠸⣤⣾⣼⣿⠀⠀⠀⣀⣤⠴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠈⢿⣉⣡⡧⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣾⣿⣿⠟⠋⠛⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠶⠶⠒⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠁⡀⣻⣿⣿⠄⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠈⠈⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠐⣿⣿⡟⠀⠀⢀⣠⠶⠛⡩⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣀⣠⡶⠷⠶⣾⣿⣿⠇⠀⠀⠀⠀⣸⣿⣿⣶⠶⠛⠉⠀⠈⠟⠠⠐⠀⠙⢦
⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣴⡿⠋⠀⠀⣴⣿⡿⢻⣯⣴⣶⣾⠿⠛⠉⠀⠀⠀⠄⠀⠂⠀⠀⠀⢀⡀⠐⣈⣷⡄
⠀⠀⠀⠀⢀⣿⣿⡿⠉⠀⠉⠻⣿⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⢸⡇⣾⡟⠀⢀⣱⣾⣯⣿⣿⠿⢿⠏⠁⠁⠀⠀⠀⠀⠀⡀⠄⠴⠀⠀⣀⠠⠉⠉⠄⣉⣻⣇
⠀⠀⠀⠀⠸⣿⣿⣷⣤⡀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣦⣤⣀⣘⣷⣿⣿⣿⣿⣿⣿⣝⠉⢁⡚⠂⠀⢀⣀⣀⣠⣴⣈⣀⣤⣴⣶⣤⣾⣶⡶⠾⠿⠛⣛⡛⠛⠷⣄
⠀⠀⠀⠀⠀⠹⡻⣿⣿⣷⣶⣦⣤⣤⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⣿⣷⣾⣷⡶⠿⠟⠛⠛⠛⠛⠉⢉⣥⠄⠀⠈⡀⠭⠓⠒⠋⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠛⠛⠻⠛⠛⣋⣽⣿⣿⣿⣿⣷⣿⣾⣿⠟⠻⠛⠩⠛⢿⣿⣿⣿⣷⣤⡄⠴⠒⠚⠉⠁⠀⠀⠁⠀⠀⠀⢀⣀⣀⠠⠄⠒⠂⢩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⣿⣿⠿⣟⣿⣿⠿⠿⠷⠒⠀⠀⠀⠀⢀⡀⠄⠀⠙⡿⣿⣿⣌⣉⠁⠀⠀⠤⠤⠐⣒⡋⠭⠟⠉⣋⣀⣉⣥⣤⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣟⡟⠛⠁⡚⢍⣓⡞⠋⠉⠁⢀⣀⠠⠄⠲⠒⠂⢀⡤⠄⠒⠚⠉⠅⠐⠸⠿⣿⣿⡃⣐⣀⣛⣩⣭⠵⠶⡾⠟⡻⣿⠉⠉
⠀⠀⠀⠀⠀⣠⡾⣫⣥⣤⣤⣍⡛⢦⡀⠀⠈⠀⣀⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⡉⠙⢣⡐⠨⠔⠱⠃⣐⣯
⠀⠀⣠⠶⡺⣿⢸⣿⣿⣿⣿⣿⣿⣎⢳⡀⢀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣤⣤⣴⡶⠾⠟⠛⢛⣵⣾⡿⠋⠙⠛⣿⡿⣿⡥⠂⡡⠀⡀⠄⣊⡽⠃
⢠⡾⣡⡊⠂⢽⣄⠛⠟⣡⡟⣡⣬⣿⡌⣧⢀⠀⠀⠀⢀⣀⣤⣤⣾⣿⡿⡿⢋⡑⠊⣶⣬⣶⣿⢛⠅⠴⠃⣀⡼⣻⣿⣿⡟⠳⣂⡤⠖⠋⠁
⣾⢰⡟⠛⠿⢦⡛⠙⢿⠿⣧⠹⣿⣿⢇⣿⣩⣤⣶⠟⢛⣻⠿⣟⠋⣥⠂⠀⢊⣤⡾⠿⢻⠇⣠⡶⠀⡠⢚⠡⢐⣿⣿⣿⣿⠛⠁
⢸⣆⠻⣿⠆⡈⣧⠔⠀⠞⠈⣷⢬⣥⣾⡿⠿⠷⠶⣶⣏⣁⠀⠁⣠⣷⣮⣶⣯⣭⣧⣶⣤⠊⢁⠁⠀⠀⠉⢂⣠⣿⡿⠿⠋
⣾⢡⡄⢶⣾⢧⠇⣤⠖⣀⣪⡵⢾⡿⢡⠖⣻⣿⣷⣎⢻⣧⣰⢞⣽⠟⣋⡙⢻⣿⣷⡍⣿⠋⠙⠁⣀⣴⡾⠟⠋⠁
⢻⣜⠧⠼⣫⣞⣨⡴⠾⠛⠉⠀⢸⡇⣿⢸⣿⣿⣿⡿⣸⡟⣡⣹⠇⡞⣽⣿⠀⣿⢿⠇⣿⣡⣴⠟⠋⠁
⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢷⣜⠷⣭⣭⣭⠴⣋⣾⡵⠿⡄⢧⣭⣥⣾⠟⣣⣾⠟⠋

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⠘⠃⠀⠀⠀⠀⠀⠀⡘⠆⠀⠀⠀⢀⣠⣼⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠒⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠱⡀⠀⠀⠃⠀⠀⠀⠀⠤⣙⡠⠀⠀⠀⠰⠵⢞⣯⠉⠃⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⣣⠀⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠰⠆
⠀⠀⠀⢓⡀⠀⢰⠃⠀⠀⠀⠶⠆⣮⡄⠀⠀⠐⣄⠀⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⢠⣐⡾⠶⠀⠀⠀⢠⣿⣿⡿⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⢀⣁⡋⠀⠀⠀⠸⡆⠘⠀⢠⠆⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⢄⠀⠾⠇⢸⠀⢿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⢰⠈⢅⣀⠀⠀⠀⢻⣄⢠⠃⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⠙⣆⠀⢘⡶⠀⢀⡞
⠀⠀⠀⠀⠠⣼⠎⠀⠀⠀⠪⡛⡚⠀⢙⠦⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠈⣇⢸⠃⠀⠘
⠀⠀⠘⢃⠔⡻⠁⠀⠀⠀⠀⠁⠍⠡⠂⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣴⣾⣿⠒⠲⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠈⠸⠅⠀⠀⠀⠀⠀⠀⠀⢻⠘⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠘⠃⠀⠀⠀⠀⠀⢸⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡶⡀⠀⠸⣷⣿⠀⠀⠀⠀⠀⠲⠞⠂
⠀⠀⠀⣠⣤⣄⡀⠀⠀⠈⢲⣇⡂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⣾⣶⡄⠀⠀⠀⠀⠸⣛⣿⠏⠀⠀⣿⡏⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠼⠿⣿⣿⡇⠀⠀⠐⠀⠉⠵⠀⠀⠀⠠⣴⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠄⠛⡉⣶⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⢡
⠀⠃⠀⠀⠸⠻⠤⠀⠀⠀⣠⠁⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠉⡀⠉⠀⠀⠈⠀⠀⠀⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⢀
⠀⠂⢠⡶⣶⡶⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠑⠤⠤⠀⠀⠀⢶⣧⠄⠀⠀⠀⠀⠀⠀⠤
⠀⡀⠘⣾⠿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠅
⠀⠄
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠴⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣄⢀⠀⠀⠀⠀⠠⠦⠦⣐⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢰⣆⡰⣄⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠐⢁⣸⡋⢀⠀⠀⠀⢠⢴⠀⡉⠀⠀⠀⢀⠀⠀⠀⠀⠐⠶⠁⠈⣿⠖⠉⣹⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⢧⠈⠀⠈⠀⢀⠄⠉⠃⠀⠈⠁⢀⡉⣠⣀⡄⣃⠐⠀⠀⠀⠀⠢⡀⣠⡏⠀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠀⣀⠀⠑⠄⠈⠠⠀⠀⠀⠀⠀⠐⠀⠀⠘⠘⠏⠀⠁⡰⡄⠀⠀⠀⠀⢳⡈⠣⢼⣿⡟
⠀⠀⠀⠀⠀⠀⠁⢂⠀⠈⠑⠟⠃⠀⠀⠀⢚⠀⠀⠀⢀⡀⠘⠃⣇⠸⠈⠀⠂⠀⠈⢰⠓⠀⠀⠀⠀⠈⢧⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠄⠞⠂⠀⡛⠀⠀⠀⠀⠀⠈⠀⠒⠀⢀⣀⡤⠄⠀⠀⠀⠁⠀⢸⠥⡖⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⢤⡽⡟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠤⠐⠇⠉⠀⢠⠁⠀⠀⠈⠢⠐
⠀⠀⠀⠀⠀⠀⠼⠆⠀⠀⠁⢀⢀⡀⢀⠀⡠⠉⠀⠀⠀⢠⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⠆
⠀⠀⠀⠀⠀⠀⢀⠀⣢⣭⡿⠿⢿⣿⣿⣿⣷⣆⠀⠀⠀⠘⠀⢀⣠⣤⣾⣿⣏⣉⣉⠛⠓⠶⣤⣈⠋⢽⣿⣿⣿⠁
⠀⠀⠀⠀⢠⣶⡟⠛⣉⣤⠶⠟⣻⣿⣿⣿⣿⡿⠢⣤⣠⣤⠞⢻⣿⣿⡶⢶⣤⣈⠉⠙⠲⢤⣄⡈⠛⣶⣽⣿⠃
⠀⠀⠀⣸⣿⣫⡶⠛⣉⣤⡶⠛⢛⣫⣽⣿⠏⠡⠀⠈⢹⡇⠀⠘⠛⢿⡙⠲⣤⡈⠙⠲⣤⣀⠈⠛⣶⣌⢻⣿⣦
⠀⠀⢰⣿⣿⣿⣵⣾⢃⣠⣤⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⣇⢀⣀⣠⣤⡙⠲⣄⡉⠲⢤⣄⡉⠛⢦⣄⣹⣷⣾⣿⣧
⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⣿⣿⣿⡟⣻⣶⣦⣍⡑⠂⠤⠉⣛⣒⣮⣿⣿⣿⣿⣿⡆
⠀⠠⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⡿⣟⡏⣿⣼⣿⣿⣿⣿⣿⣷⣶⡦⠄⠉⠉⠙⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⢿⡿⣾⣿⠀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⡿⣻⠟⣽⡿⣳⡿⠃⣽⡇⢾⡗⢿⣏⡧⣿⣿⣿⣿⢿⢁⡆
⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⣡⡟⣴⡏⢠⣿⠇⠐⣿⡇⢸⡇⢸⣿⢀⣬⠄⣅⡥⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⣿⠁⣿⡏⠀⣸⣿⠀⣼⡇⢸⠿⣆⡖⠒⠟⡺⠛⠃⠀⡖⠀⡆⡡⡗⢀⠐⡏⢰⠂⠶⠐⡇
⠀⠀⠀⢠⣀⣨⠀⠀⠀⠀⡏⢸⡏⠰⣿⠃⡀⣿⡇⠀⣾⠂⣼⢀⣻⡁⠀⠀⠁⠀⠀⠀⣳⠀⠆⣷⠅⢺⠀⡆⠰⢨⡆⡀
⠀⠀⠀⣼⡋⢡⠀⠀⠀⠰⣗⣾⣇⣿⣿⣶⣿⡿⠀⣾⠏⣰⠃⠀⠁⢧⠀⠀⠀⠀⠀⠀⠻⣷⣦⠈⡇⠌⠀⢰⢀⣦⣞⠜
⠀⠀⠀⠘⢃⠹⠀⠀⠀⠀⢿⣾⣿⣿⣿⣾⣿⢃⣼⠏⡴⠃⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠙⠟⠓⣿⠃⠲⡞⠘⠿⠋
⠀⠀⠀⠈⡋⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢻⣿⣫⠞⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠃
⠀⠀⠀⠀⣧⠇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⡋⢳⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡼⠓⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⡒⢂⠈⠤⠁⠀⣀⠊⠀⢶⠀⠀⢸⢃⡀⠀⠀⠠⡄⠀⠰⣙⠈⢽⡃⠀⢀⣸⣇⡀⢀⣀
⠀⠀⠀⠀⠀⠈⠑⣬⠦⢠⡄⠀⠀⠀⠢⠊⡀⠀⡸⠆⡅⠀⢰⠆⣄⠷⠀⣡⡷⢂⡁⠐⣡⠅⠶⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠂⢶⠀⠀⠀⠉⠀⡇⠀⠀⠐⠃⢴⠞⡀⢀⡟⠀⠈⠝⢠⣀⡬⢒⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡎⣉⣤⣾⣷⠢⠴⠾⣁⡀⢫⠏
⠀⠀⠘⠛⠻⣷⡶⠆⠐⡊⠀⠀⢀⠈⢠⢀⡀⣀⠠⣄⡲⠆⠘⠻⠿⣾⣶⣴⣶⣤⣀⠀⠄⡀⠀⢄
⠀⠀⠀⠀⠐⠛⢿⣿⣷⣥⣤⣽⣮⡶⠀⣃⡉⣰⠿⡞⠁⢠⠎⠀⣰⠁⣻⣄⡙⢲⣍⠳⠦⣀⠑⢄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣏⡻⣦⠻⢴⡉⣭⠥⠓⡀⠀⡇⠀⠏⠀⢠⠁⡰⠁⠈⡿⢦⣀⠓⢠⡈⠳⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⡤⠛⠂⠐⠀⠁⠀⠈⠀⢑⢸⡇⢠⢃⠔⠁⣠⠞⢁⡞⠉⠻⢮⣽⣷⣦⣍⠺⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⠇⠦⠷⠒⣿⠶⣴⣿⠟⠻⣿⠤⠔⠊⠀⡠⠋⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠈⠀⠀⠀⣿⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠒⢀⣤⠄⣀⠐⡏⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⠀⠀⠀⣰⠃⣴⠀⠈⢊⠣⡞⠋
⠀⠀⠀⠀⠀⠀⠔⡠⠟⠉⠀⠀⣀⣞⠁⣢⡃⠀⠀⢸⠰⡗
⠀⠀⠀⠀⠀⢀⡼⡔⠐⡀⠈⠄⢦⠀⢠⡾⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠀⣀
⠀⠀⠀⠀⢈⣁⡞⠀⠜⡀⡋⠀⠀⡴⠔⠁⠀⠀⠀⢸⠀⡇⠀⣀⣀⣠⣴⣟⣭⠓⠤⠔⣒⠧⢬⡛⠢⣀
⠀⠀⠀⠀⢣⣼⣂⠎⣰⢀⠔⣠⠀⠈⠀⠀⠀⠀⠀⠘⠀⣟⠾⠋⠉⠉⠉⢽⡿⣦⣤⣀⠀⠀⠀⠀⠉⠊⠱⡄
⠀⠀⠀⢰⡾⣵⣯⣾⣿⠗⢚⠁⠀⠚⠉⠉⡹⡽⠛⠫⡀⣿⠀⠀⠀⠀⠀⠀⠙⢿⣴⡈⠋⣠⠄⣀⡀
⠀⠀⠀⣰⣷⣿⠟⠁⠀⠐⠁⣀⢶⠉⢰⣾⢴⠃⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠉⠊⠉⣯⠄⡛⠼⢶⣆
⠀⠀⠀⡶⠋⠀⢀⠀⠀⢀⠿⠀⠀⢱⠚⢣⣤⡄⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠶⠦⠄
⠀⠀⠀⠀⠀⠀⢢⠂⢘⠓⠀⣠⢼⠉⢀⢴⡟⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠣⠝⣴⠏⣀⡟⠧⠀⣤⣾⠞⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠜⢠⡞⣣⡼⠉⣀⣴⡾⠇⠁⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⣠⣿⣾⢋⡄⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⢰⣿⠿⠋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⠠⠤⠆⠉⠓⠠⠤⢒⣚⠷
⠀⠀⠀⠀⠀⠀⠀⢠⠶⠟⠛⠛⠛⢉⣵⠾⠛⠊⠁⢀⣀⣠⣤⣤⢤⠶⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣈⣿⣟⣛⣩⣥⣌⣤⠤⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⣄⣺⣯⣤⣥⡄⠀⠀⢀⠀⠀⠀⣀⣀⣀⡤⠂⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠁⢉⠙⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠛⣤⡀⠀⠀⣠⠜⠁⠀⡄⠀⢿⣗⡄⣤⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⢿⣿⢦⡀⠱⢀⠀⠙⠻⣞⡡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠷⣽⢤⣈⠂⠤⠀⠈⠑⡟⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⡗⢄⡀⠀⠀⠈⠣⡜⡧⢀⣀⠴⠐⠃
⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⠀⠀⠀⠀⠀⠀⣧⠀⠙⣦⡀⠀⠀⠈⢃⣀⠀⠀⣀⠠⣴⡛
⠀⠀⢀⠆⠈⠀⣈⠉⡀⠤⠄⡀⣀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠹⣶⣄⠀⠈⠀⠀⠈⠀⠀⠈⠙⠲⢤
⠀⢀⡰⠀⡠⠞⠁⠀⠀⡀⢠⠇⠀⠀⠀⠀⠀⠡⡰⡃⠈⠁⠀⠀⠀⠈⢠⡀⠐⢤⠀⠀⢀⡨⢿⣆⠀⠀⠀⠐⠀⠀⠠⠐⠀⠀⠀⠈⢲⡀
⠀⡎⠀⡸⠁⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⠀⢀⣀⣹⠙⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠉⠉⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠸⠁⢀⠃⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⢱⠋⠈⢤⠀⠀⠀⠀⠀⠀⠀⠈⠰⠒⡲⠒⠀⠁⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠈⠣
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡾⠀⠄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠆⠀⡌⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⡿⠀⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⡄⠀⢏⠀⠀⠀⠀⠀⠀⠑⣄⠠⢄⣠⣄⠈⠉⠙⢄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⡂⠀⣤⠀⠈⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⢀⠘⠦⠄⣀⠀⠀⠀⠀⠀⠀⠀⡟⠠⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⢀⣀⠀⢸⡇⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢁⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⢀⡴⠦⠀⠀⣤⠀⠀⢠⡄⣠⣄⠀⠀⢠⠄⣠⣄⠀⠀⢠⠴⢲⠀⠀⢠⡄⣠⡄⢀⣤⠀⠀⢀⡴⢶⣤⣤⡄⢀⣤⡀
⠀⠀⠀⠀⠀⢸⡁⢀⡤⠚⣧⣀⡴⠻⠞⠁⠻⣤⠔⢻⠞⠀⠻⣤⠴⣏⡠⠿⡤⠔⢻⡞⠁⢷⠎⠘⠧⠴⣏⣀⡼⠁⠸⠷⠃⠸⢧⠴⠋
⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣀⣀⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⠀⠀⢠⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠙⠀⠀⠀⠃⠀⠀⡆⠀⠀⠀⠀⠴⠆⢀⡈⠁⡀
⠀⠀⠀⠐⠃⢠⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣀⠀⠙⠋⠀⠁
⠀⠀⠀⠀⣰⠘⠃⠀⠀⢀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡀⠀⠀⠀⠟⠁⠀⡄
⠀⠀⠀⠀⠪⠈⠀⠀⠀⠈⠀⠀⠀⠘⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⢠⢀⡄
⠀⠀⠀⠈⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⣈⠂
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠹⠀⠀⠀⠀⠙⡄⠀⠆⡔⡡⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠆⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡆⣾⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⣮⠤⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠘⡿⠀⠠⠀⠀⡐⠀⠀⠀⢀⡨⠖⣯⣱⠘⠆⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠘⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠆⢰⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠐⡄
⠀⠀⠈⠀⠀⠠⠀⠀⢀⠠⠁⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠀⠀⠀⠀⠱⣦
⠀⠀⠀⠑⠆⠀⠀⠀⢀⠤⠘⢶⡷⠃⠀⠀⠀⣾⡻⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠠⡄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠘
⠀⡂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉⠑⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠁⠀⠀⠀⠁
⠀⡀
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⢀⣼⡷⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⢀⣰⠟⠋⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣞⠉⠙⠒⢤⣀⠀⠀⣠⠴⠚⠉⠀⠀⢀⠤⡲⠟⢓⣤⡤⢤⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠓⠲⣄⣀⡬⠟⠋⠀⠀⠀⣀⠤⠊⣡⠞⠁⣠⠞⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠴⠊⠁⠀⠀⠀⣠⠔⠊⠁⣠⠞⠁⢀⠔⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⢀⡠⠖⠉⠀⠀⢠⠞⠁⢀⠔⠁⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⢀⠔⠁⠀⡠⠊⠀⠀⢀⠔⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠰⣄⠀⣀⡤⠖⢋⠋⠀⠀⠀⢀⠔⠁⠀⠠⠊⠀⠀⠀⢠⢮⣄⡀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⠊⢙⣧⠸⠛⣛⠲⡀⠁⢀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠈⠉⢒⣢⣄⠎⣡⠭⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠯⢵⡇⣎⡩⣳⠈⡇⢀⡨⠃⠀⢀⣴⠇⠀⠀⠀⢠⠾⢄⡀⠀⠀⣠⢪⠴⢬⢡⣻⡆⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⢦⣀⠀⠓⠖⣟⠝⢀⣶⠯⢄⣀⣴⣉⠀⠀⠀⠀⡴⠁⠀⠀⠉⠢⢄⣀⠸⣺⠯⠜⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠌⡉⠋⣉⣡⠔⠋⠡⢊⡦⡋⡴⠶⡕⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⣉⡛⠉⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠃⠱⠬⣿⠃⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠉⠅⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠘⡀⡀⡀⢀⢀⢀⢀⠀⡀⡀⡀⣀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⠇⠇⠇⠆⠸⠸⠰⠰⠀⠃⠇⠇⠄⠆⠸


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡛⢷⣤⡟⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠻⡿⣿⣻⢿⡀⣏⢀⢙⣁⣀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣿⡇⣿⢰⢷⡟⡄⣾⢏⣿⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣙⠴⠃⠛⢾⣤⡤⢯⣹⢬⣍⣍⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣽⡁⠾⠀⠼⣤⡙⡇⢼⡃⣶⠁⣿⢱⡟⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠌⢚⠀⢈⡡⢔⠆⠚⣀⣑⣼⣯⣤⠇⢀⣠⠋⠽⢛⣻⠐⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⢷⡴⡓⠬⢆⣈⡗⠀⣿⢿⡍⣶⠀⣄⡀⠁⢴⣾⣇⣍⡰⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠌⡁⢒⣦⣜⣛⠐⡉⠃⢀⠀⣙⠁⢸⠠⠀⡟⠀⢪⣈⣋⣟⠀⣼⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠰⠞⡓⢨⣏⣤⣴⣾⣥⣤⣉⣳⣽⣇⣚⡄⠘⠁⣠⠤⠴⠁⠤⠦⠌⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡴⢿⠟⢛⣡⣤⣚⡟⠉⠉⠉⡡⣏⡤⠊⠉⠲⢦⣶⣶⣿⣿⣷⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠀⢰⣾⣧⣽⣯⢿⣴⣿⠉⢻⡇⠤⠀⢀⠀⠈⠙⠻⢿⣿⣿⣏⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣠⠄⠈⣿⡛⠟⣷⡆⢉⠏⠀⢸⠓⠶⠶⠷⠖⠀⠀⠀⠀⠀⠉⠻⣧⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠠⠀⢺⣿⣟⣷⣿⣀⠀⠀⠈⠀⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡟⠂⠀⠈⠁⠉⠙⠛⠳⡄⠀⠓⠒⠻⠟⠿⣿⣿⣷⣦⣔
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⠄⠻⡇⢁⢸⣢⣀⠀⠀⠀⠀⠈⠉⠻⣿⣳
⠀⠀⠀⣸⠟⢿⣿⣿⣿⣿⣿⣿⣿⣓⣉⣀⣀⣀⠐⠂⣿⢋⣀⣦⡀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⢸⡟⢿⣻⣿⡿⠟⠉⠙⠉⠉⠉⣿⣿⣶⣿⡿⢿⠿⢿⣦⣄
⠀⠀⠀⠀⠄⠉⣠⠛⠉⠋⠀⠀⠀⠀⣠⡶⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢤⠜⠁⠀⢈⣀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⠛⡿⢿⣿⣿⣷⡖⠠⢀
⠀⠀⠀⠀⠿⠀⠀⠀⡏⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠈⠣⠀⠀⢠⡚⠃⣿⢾⡆⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠃⠀⣆⢠⣍⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣾⣿⡏⣾⡯⠀⣼⡓⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢁⠀⠀⣀⠀⠀⠀⠰⠄⠀⠀⠀⢰⠃⢀⣾⠁⠀⢰⡏⣼⠏
⠀⠀⠏⢹⣿⡆⣿⡇⣰⣯⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠉⠀⠀⠀⢀⡾⢀⣼⡏⠀⠀⣾⣧⣿
⠀⠀⠀⢺⣿⠀⣿⢠⣿⣏⣿⠃⠀⡀⠀⠀⢰⠀⠀⢀⡀⠀⠘⠊⢔⢀⣁⠨⠗⠀⠀⠀⠀⢨⣿⣝⣿⡷⢢⣴⢾⡿⡿
⠀⠀⠀⠘⣿⠓⣿⣿⣿⣿⡏⠀⠀⠋⠀⢀⠾⠀⠐⢀⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠞⣷⣷⢻⣇⣿⣿⢷⣎⠡
⠀⠀⠀⠠⣿⣶⣿⣿⣿⡟⡀⠁⠀⠈⢁⡈⠀⠙⡐⢌⠀⠀⠄⠀⠀⠠⠀⠐⠀⠀⠀⠀⣸⣋⣖⣿⣿⣾⣿⡛⠿⢿
⠀⠀⠀⠀⢻⣿⣿⡯⠏⠀⠂⠀⠀⡇⠀⠥⠤⡄⢀⠚⠀⠀⣄⢠⠈⠂⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⣿⣾⡾⣿⢿⡶⠄
⠀⠀⠀⠀⠀⠹⡿⠁⠀⠀⠀⠲⠂⢀⡰⡜⢀⠀⢈⠈⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⣿⢻⣻⣿⣿⣿⣿⡶⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⠶⢤⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⣾⡏⠰⢧⣿⣿⣿⣿⠇
⠀⣠⡾⠋⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠄⣀⠀⠀⠈⠀⠀⠀⢠⣀⣴⡿⠀⠀⣯⡥⠋⣸⡞
⡾⠫⠀⠀⠀⢀⣰⣿⡿⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠾⢻⡄⢠⣿⡇⠀⠀⠀⠀⢀
⠊⠀⠀⠀⢀⡜⢻⡿⠛⠻⣶⣤⣀⠈⢙⢳⣆⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⢹⣿⣅⡀⠀⠀⠈⠙⠻⢿⣧⡻⣽⡯⢜⢦⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⢋⠔
⠀⠀⠀⠀⠀⠿⣿⣭⣙⠳⢶⣤⢄⣠⣍⣛⢻⣽⣷⣿⢿⣿⣶⣄⠀⠀⠀⠂⠠⡀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠋⠠
⠀⠀⢀⣡⡀⠀⠀⠉⠙⠻⣶⣿⡾⣽⣿⣿⣿⣾⠟⣿⣿⣿⢯⡉⠛⠿⢶⣦⡼⠃⠀⢠⣬⣿⡿⠛⢁⠀⠂⠁
⡴⠞⠉⠙⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⣵⣿⢃⣿⣾⣿⣿⣿⣷⣼⣡⣀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢐⣬⣶⣄⠀⠀⢀⠀⠀⠀⠀⠀⠉⠺⠿⢽⣿⣿⣿⣟⠯⠵⠿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠋
⡥⠴⠞⠛⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠼⢷⣶⣤⠌⠀⠀⠀⠀⠀⠀⠠⠤⠶⠒⠚⠉⠁⠀⠀⠠⠄⢀
⠀⠀⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣆⠀⠠⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣤⣠⣀
⠀⠀⠀⠀⠀⢐⣻⣿⣿⣿⣿⣯⠀⠀⠂⠀⠀⠀⣠⣾⣿⡿⠿⠿⠿⠿⠿⠿⢿⣷⣶⠄⠀⠀⠀⢀⣤⣤⣀⣄⣀⣀
⠀⠀⠀⠀⠈⣿⡿⣻⣿⠇⣿⣿⠀⠀⠀⢀⠀⢼⣿⣿⡶⠶⠶⠶⣶⡶⣚⣿⡿⠟⠁⠀⠀⠀⠀⢸⠾⠷⣿⣿⣤⣿⣀⣀
⠀⠀⠀⡀⣾⣿⢰⣿⡃⢠⣿⣿⠀⠀⠐⠀⠀⠀⠈⠻⢿⣷⠿⠟⠛⠛⠋⠁⢀⠐⠀⠀⠀⠀⠀⡌⠀⣹⡇⠀⠀⣿⢻⣿
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣟⣿⣟⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠁⢰⣶⠀⠀⠀⣄⡄⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⢠⢤⠀⠂⠀⠀⠀⠇⠀⠀⠀⠐⠀⠂⠈⠁⠀⡄⠀⠀⢀⠀⠂⡀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠊
⠀⠀⠀⠈⠉⠀⡴⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⡄⠀⡀⢠⠧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡴⠢⣄⢀⣎⣼⣿⣆⣰⠚⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⡎⠸
⠀⠀⠀⠀⡀⢀⠀⠘⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢠⣇⣠⣽⣿⠟⠛⢿⣿⣿⣿⣿⡇⡄⠀⠂⠀⠀⠠⠀⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢾⣤⣦⣿⣿⢛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣶⣒⣦⣤⣂⢲⠀⠀⠀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠱⢪⣿⣿⣿⣿⣍⣼⣿⣿⡷⢀⣤⣤⠀⠀⠠⣿⣿⣿
⠀⠀⢸⠋⢀⡄⠙⡇⠀⢀⣼⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣀⣀⢀⣰⣾⣿⣿⣿
⠀⠀⠙⠦⣌⠁⠠⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠻⠿⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⢉⣩⠈⣿⣩⡛⣿⠿
⠀⠀⠈⠀⠉⠁⠀⢸⣿⣿⡏⠁⣹⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢟⣿⣼⠿⣿⣿⣶
⠀⠀⢀⣀⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠠⡿⢿⣿⣿⣿⣿
⠀⠀⠈⢱⣄⣾⣶⢳⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿
⣴⣷⣶⡶⢿⣿⠛⣿⣿⡧⡬⢭⣛⠻⠿⠿⠿⠿⠛⣭⡾⠓⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠈⠉⢹⡿⢿⣿
⠉⠛⠛⢷⣞⣯⣼⣛⣦⠙⠗⠪⠋⠹⠆⠠⠀⠤⠬⠠⢄⠀⠀⠀⠀⠀⠀⠺⡼⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉
⠀⠀⠠⣶⢹⣿⣿⣿⡗⠐⠒⠒⠒⠒⢢⠐⠀⠒⠒⠒⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⢸⠀⠸⠿⠿⢿⡟⠀⠀⠀⠀⠒⠀⠐⠀⠐⠐⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠘⠷⠀⠀⠀⠘⠋⠈⠈⠈⠉⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙

⣠⣤⣀⣀⣀⠀⠀⠀⣀⣄⣠⠤⠤⠄⠰⠲⠶⠲⠶⠶⠖⠲⠖⠒⠖⠖⠖⠶⠶⠾⠒⠒⠲⠶⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡦⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣠⠞⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁⢀⣬⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢰⠏⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠂⣀⠤⠒⠁⠀⠀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⢀⠎⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡰⠃⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⣀⡤⠄⠊⠁⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠐⣰⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡲⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠠⢀⠜⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⠔⠚⠀⠀⠀⣀⡔⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣰⠋⠀⠀⠀⣐⠏⠀⠀⠀⠀⢰⡷⣲⣮⣤⠴⣫⡄⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡤⠁⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⢈⢁⢼⣹⣷⠀⣿⣿⣆⠀⡠⠖⠩⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢀⡜⠁⠀⠀⠀⡜⠬⠁⠀⠀⠀⠀⠀⠈⢷⣄⠈⠧⠔⢉⣼⡟⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⢐⠟⠀⠀⠀⠀⠜⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠤⠟⠛⠉⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⢌⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡀⣡⠃⠀⢀⠔⠋⢀⡰⠒⠀⢀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢊⡮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠎⡰⠁⢀⠔⠁⣠⠴⠋⠀⠀⢀⠔⠀⠀⠀⡀
⠀⠀⠀⡠⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠀⠀⣤⠀⠀⠀⡠⠃⢠⢃⡔⣡⠞⢁⡠⠞⠁⠀⠀⣀⠖⢁⣀⠤⠚⠉⠙⡆
⠀⠀⠐⠁⢀⠀⠀⠠⣠⠃⠀⠀⠀⠀⠂⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠀⢰⠏⠀⢀⠜⠀⠀⢀⣾⠚⢁⡴⠈⠀⠀⠂⣠⡾⠅⠚⠉⠀⢀⣠⣴⠬⡄
⢀⡤⠔⠀⢤⡀⢁⡕⠋⠠⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢽⠀⡟⢠⡟⠀⡠⠃⢀⠂⡠⠟⣡⣴⠋⠀⠀⠀⠠⠞⠉⠀⠀⣩⡴⠖⢋⣡⠤⠔⠛
⡎⢰⠟⡻⣇⢡⡼⠤⢀⣁⠀⠀⢀⡜⠀⠀⠀⢀⡶⠛⠉⠉⠉⠉⠙⠳⣦⠀⢸⣠⣇⣞⢀⡔⠁⣐⢡⣊⡴⠊⠁⠀⠀⢀⡴⠊⠀⢀⡤⠖⠋⣡⠴⠚⠉⠀⣀⣠⠴
⢫⣴⠀⡴⢏⢮⡶⠿⡻⣎⢱⢀⡞⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢲⣬⣿⣿⣧⣾⣂⡴⡿⠟⠁⠀⠀⠀⢀⡴⢋⣴⢖⣋⣭⠖⠋⠉⠀⢀⣠⠴⠛⠉
⠀⠻⣑⠪⣛⠚⠁⠀⢈⠏⣰⠜⠀⠀⠀⠀⠀⠻⣤⣄⣀⣀⣀⣤⣤⡤⠤⠤⢿⣿⠽⠛⢹⣿⣾⡅⠀⠀⠀⢀⣴⣫⣾⠿⠟⠛⠃⠀⠀⣠⠤⠒⠉
⠀⠀⠀⠁⠂⠬⢑⣎⣡⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠙⢿⣤⠞⠉⠙⣧⠙⢶⣤⠶⠟⠋⠉⠀⠀⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⠁⠀⠀⢀⡴⣿⡇⠀⠀⠀⢸⣧⠜⢿⡄⠀⠀⣀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⠋⠁⠀⠀⠀⠀⣠⠔⠁⠀⠸⠇⠀⠀⡠⠞⣿⠀⢀⣿⠖⠋⠁⢀⠀⠀⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠐⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⢀⡴⠋⣀⣠⣿⠛⠛⠁⠀⠀⠀⢸⡀⠢⣀⡞⣄⠘⡄⠀⣀⠄⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢿⣿⣧⣿⡀⣀⡴⠋⠀⠀⠀⠀⠀⢀⣰⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠸⡅⠛⢀⠷⡀⢤⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡻⣇⢸⣧⣻⣿⣷⣿⣿⣷⡐⠃⠀⣀⣴⣿⡿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣲⣄⢹⣠⣶⣂⣤⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⡄⠈⣽⣟⡉⠻⣿⣿⡇⢰⣿⡿⠋⣸⡑⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⡒⠉⣄⠄⠁⣝⣿⣿⣿⣟⠉⠠⠌⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠂⠸⣻⡍⢿⡤⠿⡿⢟⣽⠟⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠭⠟⠽⠟⣻⠿⣿⡋⠙⢥⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣖⣠⣿⣿⣦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣤⠰⡿⢠⢻⣧⣘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠭⠋⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡡⠞⢷⠈⣾⠈⠙⠓⠲⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣋⣀⣀⣈⢣⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⣞⠋⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡜⡁⠁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣡⠏⠛⢁⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢂⣋⣭⠴⠶⠋⠉⠈⢡
⠀⠀⠀⠀⠀⢀⡀⢀⠼⡅⠀⣰⠋⠀⠀⣀⣀⡤⠔⣚⣩⣤⣶⢶⢿⠋⠉⠁⣀⣀⡤⠶⠚⠋
⠀⠀⠀⠀⣠⠍⣰⡏⠊⢀⡾⠁⣤⡶⢟⣭⣥⣾⡿⠋⠉⠀⢈⣀⣠⠶⠖⠛⠉
⠀⠀⢀⡀⢃⣜⣉⡄⣤⠟⠀⠀⣿⣿⣤⡾⣿⣓⣠⠴⠖⠚⠉⠁
⠀⠀⢻⣏⣏⣉⡈⣶⠏⠀⠀⠀⠈⠻⠯⠙⠋⠁⠀⠀⠀⣠⣤⠤⠀⠀⣶⣶⠶⢶⣶⣒⣒⣲⣶⣶⠶⠶⠶⢦⡀
⠀⠀⠻⢿⣿⣟⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡿⠿⠟⠛⠛⠟⠋⠋⠀⠂⣀⣀⣈⣈⡡⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠒⠓⠒⠒⠋⠈⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣬⣴⣖⣶⣆⣔⡄⡤⣶⣆⡴⡵⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠁⠀⠉⠁⠋⠀⠈⠉⠉⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣑⠀⠀⠐⠂⠐⠀⠀⠀⠀⢸⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⣄⠀⡸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠸⠃⠀⠀⠀⠀⠀⠀⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠉⠀⠁⠒⠒⠁⠀⡄⠐⠀⠀⡠⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠲⠀⠀⠀⢸⠀⠀⠀⢤⡀⠀⠀⢀⠀⢤⠀⠀⠈⠃⠀⠀⠀⠀⠸⡾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡘⠀⢀⠐⠉⠁⠄⠀⠈⠉⢉⠂⠀⠐⠊⣠⡀⠀⠀⠀⢤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢼⠀⣰⠂⠀⠀⠄⠀⠀⠀⠄⠀⠀⠂⠤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠂⠀⡈⠋⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠊⣠⣀⠞⣥⡾⠇⠰⠄⠔⠁⠐⠂⣂⠀⣀⢀⢠⣀⣠⣠⣤⣦⣤⣥⠄⢠⠋⣀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢤⡛⢦⣨⠒⠶⢶⡀⠀⠋⠁⠀⣰⢾⠿⢻⣿⣿⢟⡿⠋⠀⠀⠂⠘⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠐⠀⠀⠙⠢⡭⠿⣶⡄⢤⡀⠀⡀⣸⢻⣿⣴⣞⣍⡴⠋⠀⠓⢂⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠺⢍⣻⣿⣧⠀⣆⣯⡾⠷⢻⡜⠉⠀⠀⠈⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠉⠹⣤⣿⠋⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⣿⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠉⠉⢍⡙⠻⢟⣏⡻⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⢡⠀⣿⠀⡾⠉⠀⠒⠒⠶⣶⢶⠤⠤⠤⠤⡠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠹⢿⣿⣿⣿⣿⣿⣿⣽⣷⡦⡀⠀⢢⣿⡸⠁⣌⣤⢖⣀⠡⠤⠄⠂⠒⠐⠐⠿⣿⣿⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠓⠒⠈⡠⠬⠥⢘⣛⣿⣿⣾⣿⠿⣦⣼⣿⡧⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⡶⠶⠛⢍⣭⣿⣿⣿⣇⡂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⢀⡤⠘⠋⠁⠀⠀⣠⡾⢻⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠠⠊⠀⣀⠶⠋⠀⠀⠀⠀⢠⡼⠟⣩⠚⠿⠿⢿⣿⡀⢀⣿
⠀⠀⠀⠀⠀⠀⢠⡽⠋⠀⠀⣀⣠⠾⠫⠁⠀⠊⠁⠀⠀⠀⠀⠈⠙⢿⣿⠟⠶⢶⣶⣶⣶⣶⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠁⣰⠋⣀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠹⡈⠙⠛⠿⣿⣶⣂⣀⠀⠀⠢⢄
⠀⠀⢸⢂⡜⠷⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠘⠦⡀⠉⠀⠙⠛⢿⣷⣤⡀⠈⠷
⠀⠀⠀⢜⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣷⣶⣶⡀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⠀⠀⠀⠉⠻⢧⣈⡳⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣥⣿⣿⠟⠁⠀⠀⠀⢀⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠊⠙⣷⣜⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿

⢷⡆⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⣤⣤⠸⠂⢿⠙⡀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⡟⠈⠐⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠤⠂⠀⠘⠒⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠰
⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⡶⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢶⠎⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠰⡄⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃
⠀⢀⡇⠀⠀⠀⠁⠀⠈⠖⠫⢇⣤⡴⣯⠤⠐⢄⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠤⢤
⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠴⠏⠉⠁⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⡠⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠢⠀⠐⠒⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠀⣰⡄
⠀⠀⠀⠀⠀⠀⢄⢀⢀⠇⠊⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠾⡆⡾⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢋⡤⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡌⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠠⠈⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣐⣀⣤⣄⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⢽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠉⠒⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡀⢄⠀⠔⠀⠀⠀⠀⠀⠀⢀⣼⣿⡣
⠀⠀⠀⢱⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠘⠂⡁⠀⢁⠄⠀⠀⠀⢤⣿⣿⣟⣅⠡⠂
⠀⠀⠠⣕⣲⣿⣿⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠀⠀⠀⠀⠀⠩⡷⠀⠀⠀⠀⠠⠬⣀⠾⠀⠀⠀⠀⢀⣹⣯⣿⣿⣩⣶⠥⠄
⠀⠀⠨⣓⣿⣿⣷⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⠡⠔⠀⠀⠀⠲⣿⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⢉⣹⣿⡿⣯⣤⠵⠖⢒⣀⡀
⠀⠀⠀⠤⣿⣿⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠅⠀⠂⠀⠀⠀⠀⠁⠂⠀⠈⣙⣓⠦⣽⣿⣡⠴⠖⢛⣉⣁⡀
⠀⠀⠈⠽⣿⡲⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠨⢇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣶⡶⡼⣻⣯⣭⠥⠖
⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⣹⣿⣫⡶⠶⠖⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡧⠄⠀⠀⠀⠀⠀⠀⢠⡃⠀⠘⠻⢷⡴⠀⠀⠀⠀⢀⣉⣉⣁⠾⣛⣋⣉⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⣉⣉⣀
⠀⠄⠀⠀⠁⠀⢰⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⣰⣇⢀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠀⠁⠀⠰⣄⠀⠀⠀⢠⡆⠀⢠⣴⣤⠀⠀⠁⠈
⠀⠀⠀⠀⠀⡐⣾⣯⠀⠀⠀⣿⠄⠀⠀⠀⠀⢨⢉⡁⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠘⢻⡍⠀⠀⠀⠀⣤
⠀⠃⠀⠀⠀⢸⣿⣷⠀⠀⠀⡿⠀⠀⠀⠀⠀⠠⠀⢀⠲⠃⠀⠀⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿
⠀⡊⢸⠀⠀⠈⢸⡇⠀⠀⠀⡇⠀⠀⣾⡀⠀⠀⠀⠀⠁⠀⠀⠰⠿⢤⠄⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣪⠀⠀⠀⠀⠟
⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠐⠘⡇⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⡀⣸⣿⡜⠰⣆⠀⠀⠀⠀⠄⠀⠀⠀⢠⣯⠙⣩⡃⢶⣴⡄⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⢤⢰⡶⠔⢤⡝⠛⠉⠀⣆⠈⠀⠀⠀⢀⢠⡄⠀⠂⣿⠷⠿⢈⢥⢸⡿⠵⣏
⠀⠀⠀⠀⠀⠐⠛⢦⡀⡀⠿⠛⠀⢨⣧⠈⣦⣐⡇⠀⡘⠋⠀⠀⠀⠠⡾⢘⠁⠀⢠⣾⠓⠲⠆⣿⠿⠆⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠎⣣⡁⠐⢀⡀⠆⠉⠐⠀⡌⡗⠀⠃⠀⠀⡀⡄⠀⠀⠀⢀⣀⠀⠉⢨⡄⣸⣗⣶⠦⠀⣿
⡀⠀⠀⣀⠀⣠⠀⣹⠋⠁⢻⣿⣏⠁⠀⠀⠀⠁⠃⠀⠀⠀⠄⢁⣗⣰⣄⣠⣤⣼⡄⠘⠋⣠⢁⣙⣿⣿⠆⣿
⠁⠀⠝⢻⡇⠁⢠⣟⣶⡆⣸⣿⠉⠁⢸⠀⢳⡀⠀⠀⠀⢰⠀⢸⣿⣽⣿⣿⣏⠈⡗⣶⣰⠃⣘⠛⣿⣿⡿⣿
⢀⡀⠀⠀⢁⣴⠏⡜⠀⡿⢿⠛⠀⠢⣽⠀⠀⢷⢀⣄⠀⠐⡀⢉⣽⣿⣿⣹⣿⣷⡀⢠⣷⡔⠟⠀⢻⡉⠃⣿
⠃⢐⣃⠀⡸⢿⣀⡁⠀⣈⣭⣄⣠⣶⣿⠀⢰⢶⠚⢳⣿⢀⣁⣾⣿⣿⣿⢉⡿⡏⣧⣿⣟⠁⠘⠀⣸⣾⡆⣿
⠀⠈⠏⠲⠤⣾⠅⣼⠎⢩⡏⠙⢿⡿⡇⠀⠀⢸⠷⢣⣿⣄⠉⡿⠎⠟⠁⣿⠃⢠⣿⣽⣯⣿⣿⣿⣯⣭⣧⣿
⠀⠀⠀⠀⢰⣿⡈⣿⠀⣿⠁⠀⠀⣆⡇⠀⠀⢠⠞⡱⠘⠋⠀⠀⠀⠀⠀⠁⠀⢡⠟⢻⡿⣿⣿⣿⣷⣿⡇⣿
⠀⠀⠈⠉⠉⠁⠉⠈⠉⠉⠁⠀⠀⠉⠉⠂⠒⠊⠒⠙⠒⠒⠒⠓⠐⠒⠂⠐⠐⠋⠐⠃⠖⠚⠟⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣿⣠⡶⠟⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢰⣿⠟⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⣿⠏⠀⠀⢀⣾⣋⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⣾⠃⠀⠀⣴⣿⠟⠛⠉⠉⠀⠈⠉⠛⢷⣄⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠘⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣴⠶⠀⠀⠀⠀⠀⠀⠀⣿⣶⢶⣦⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣠⡆⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢈⣿⠀⠛⠛⠋⠁
⠀⠀⠀⠀⢸⣇⠀⠀⠀⣻⣶⣶⡾⢿⣦⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⣠⡾⠋
⠀⠀⠀⠀⠈⢿⣄⠀⠀⠛⠁⠙⠃⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠛⠉⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢻⣶⣶⣶⡶⠿⠃⠀⠀⣀⣽⣷⠀⠀⠀⢀⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⢷⣦⣤⣤⣾⣯⣥⣤⣴⡶⠿⠛⠋

⠀⢀⣠⣤⡄
⠀⠹⠿⠿⠛⠀⠀⠀⡀⠀⠀⣤⡄⣀⢠⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠋⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣴⢿⣿⣿⠻⣇⠀⠀⠀⠀⢂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⢀⣴⣤⣿⠯⣼⣿⡂⠀⠀⠀⠘⠀⠀⠀⠀⠈⢣⡴⢤⡀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠟⠉⠸⠃⠤⣊⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠴⠆⠈⠀⠀⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⢒⣾⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠐⠂⡸⡇⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠖⠂⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠈⠛⠿⠗⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⠀⡲⢄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢋
⠀⠀⠀⠐⠀⠀⠀⠀⠁⠛⢠⣳⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠉⠛⠰⠆
⠀⠀⠀⠈⢑⡀⠀⠀⠀⠷⡄⢄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠞⠋⠀⠀⣀⠀⠀⠀⠒⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠛⠠⣄⠀⠀⠀⠢⡍⠀⠙⠀⠀⠀⠒⠁⠀⠀⠀⢀⡀⠀⠀⠀⠘⣤
⠀⠀⠀⠘⠛⠆⠐⠂⠀⠀⠀⠀⠀⠀⡀⠉⠠⠀⠀⠀⠀⠛⠃⠠⠄⠀⠀⠀⠐⠈⠁⠀⠀⠐⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⠟⢠⡄
⠀⠀⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⣋⣩⡭⠭⠭⣍⢉⣓⡒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣴⠏⢉⣤⠶⠶⠶⠶⠦⣌⠙⢲⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡏⠀⢼⡇⠀⣿⣁⠀⠻⢿⣿⡆⠈⣷⠀⢿⣷⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢘⣇⠀⢸⣇⠀⠘⠻⠿⣿⣶⡿⠓⢀⣿⠂⠀⣿⣷⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠐⣿⣆⠀⢿⣧⣄⣀⡀⠀⠀⣀⣰⣿⡟⢀⡤⣵⣿⠀⢺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠠⠘⣿⣄⠀⡙⠻⠿⠿⣿⢿⠿⠟⠋⣠⣮⣼⣿⠃⡰⢸⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠻⣿⣮⣤⣐⣤⢀⣠⣤⣄⣤⣶⣿⠟⢀⡴⣑⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠙⠟⠛⠻⠛⠛⠛⠋⠉⠥⠐⠊⢑⢽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢆⣖⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⣭⣤⣽⣷⣾⣶⣷⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣆⠀⣠⣷⠀⠀⢠⣾⡅⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⢀⠂⠁⠈⠀⠀⠀⠀⠀⠈⣿⡆⣿⣿⡆⢀⣾⣛⣧⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠀⠘⢷⡄⠀⠀⢀⣠⠀⠀⠀⠀⠀⠘⣷⣿⡟⣷⣿⠉⣎⠉⢀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢙⣶⣿⣿⣷⠆⠀⠀⠀⠀⠀⠈⢻⣶⣿⡟⢛⣹⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡴⠰⣿⠟⢋⡠⢖⣚⠥⠖⠂⠀⠀⠀⠀⠈⢹⡇⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣟⣟⣿⣷⡴⠠⢀⣮⣴⡶⠶⢖⣒⣤⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣿⣿⢶⠟⠛⣂⣐⣐⣰⠭⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢤⡤⣤⠤⢤⣶⣬⣭⣍⣾⠀⣀⣤⣤⣴⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠬⣿⣿⣿⣿⡆⣝⠿⠻⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠉⡛⣿⠋⠀⠀⠘⠛⠻⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣶⣦⣄⠃⠈⢠⣶⣶⡒⠛⢿⣿⣶⣮⣅
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠛⠛⠛⠛⠛⠛⠿⠿⠄⣆⠀⠀⠀⠁⠀⠉⠛⠛⠛⠛⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠤⠤
⠀⠀⠀⠀⠀⢀⠔⠒⠒⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⣉⡁⠀⡒⢒⣄⣼⣿⠂⠒⠢⠤⠦⠀⠤⢤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⢉⡼⡟⠋⠁⠊⠒⠛⠓⠒⠒⠒⠒⠐⠒⠐⠊⠁⠀⢠⠶⠰⣞⢌⠂
⠀⠀⠀⠀⠀⠀⡘⠊⠒⠲⠬⠴⣄⣠⣄⣀⣂⠀⠠⠀⠀⣴⠎⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣼⡆⢸⡤⢨⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢇⣀⢀⣀⠀⠀⠀⠈⠉⠉⠉⠒⠚⠙⠿⡿⢠⣿⣿⣿⣥⣶⣷⣒⣐⣒⣶⣦⣴⣤⣤⣄⣴⣀⣒⣆⠹⠶⠟⣠⡀⠀⠐⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢤⣀⡠⢄⣀⡀⢤⠀⡇⠘⠀⠀⠀⠈⠉⠐⠉⠉⠉⠛⠛⠋⠋⠛⢻⣒⣮⠵⣖⣚⣲⠟⡙⣶⢆⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠧⢇⣸⣤⣆⣲⣤⠴⣒⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣡⣦⣽⠶⠃⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠚⠋⠭⠤⠶⣂⣓⣒⡢⠄⡁⠻⠯⠐⢚⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠈⠁


⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠈⠁⢠⣦
⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⢨⡋⠀⣤⠀⣠⣄⠀⢠⣄⢀⣤⡀⠀⢀⣤⣀⣄⠀⢠⣤⠀⣠⣄⠀⣤⡄⠀⣠⣄⣤⡀⢠⣄⠀⣠⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⢸⣿⡾⠁⣿⠀⣼⣿⡏⢸⡇⠀⣿⠃⢹⣿⠁⢸⣿⡼⢻⣿⡼⢹⡏⢸⡿⠘⢺⡧⢾⣿⡜⢹⡿
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢀⡀⣿⡇⢸⣿⠇⢸⣿⠀⣿⡿⠀⣼⡇⢸⣿⠀⢸⣿⠀⢸⣿⠃⢸⣿⠁⣿⡇⢸⡇⠀⢸⡇⣾⡿⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠧⠤⠿⠃⠻⠧⠾⠟⠀⠘⠿⠔⠿⠇⠀⠸⠧⠴⠿⡤⠚⠿⠄⠸⠿⠀⠸⠏⠀⠻⠧⠘⠳⠀⠾⠁⠻⠇⠀⠿⠧⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢦⣄⣀⣠⣄⠚⠁⡀⣊⠀⠀⡆⣀⠠⠀⠀⢠⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣄⣐⡀⢀⠰⣤⢀⣦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⡹⣷⣞⠛⢋⣡⣼⣯⠴⣠⣀⣴⣷⣾⠥⣤⡴⣶⣶⣋⠀⠀⠀⠀⠀⠸⡀⠉⢙⠿⢿⣼⡥⠟⡟⠀⠀⢀⡀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢌⠣⠈⠻⣟⠺⡿⢿⣿⡿⠃⠙⢿⣟⠛⠲⠦⠑⢄⠈⠀⠉⠀⠀⠀⠀⠀⠈⠙⠋⠀⠩⣭⣥⣤⡘⠛⢉⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠈⠐⠀⠀⠈⠻⡎⠀⠀⠹⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠶⣤⣇⠈⠙⢢⠀⠠
⠀⠀⠀⠀⠀⠀⠛⠄⠠⠀⠐⠀⠠⠄⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⠘⣗⠒⠒⠴⠚⠉⡩⠖⡎⢹⠻⣄⣀⢀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠘⣧⣀⠁⢀⡜⠁⣸⠇⢠⣿⠅⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠈⢻⢀⣿⣆⣴⣿⣝⣿⣷⣶⡽⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⡾⠋⢠⠗⡄⠀⠀⠀⠀⠂⠂⠒⠆⠁⠒⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⢻⣿⠟⠉⠀⠀⠈⠱⠆⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠈⡉⠹⣧⣀⣈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⢧⣀⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠇⢀⠀⠁⢄
⠀⠀⠀⠀⠀⠉⣀⢀⠴⠒⠬⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠂⠀⠀⣀⣙⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠈⠑⠉⠁⠀⠠⠀⠀⣴⣇⡀⠀⠀⠀⣠⡆⠀⡷⠀⠀⣸⣿⢛⠈⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⢐⠀⠀⠹⣦⣀⠉⠄
⠀⠀⠀⠀⠀⠚⠃⠈⣬⡀⠀⠀⠁⠀⣹⠇⡀⠀⠀⠀⢻⡑⢾⣥⠄⠀⣉⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠓⠾⡆
⠀⠀⠀⠀⠐⠻⠛⡹⠿⢿⡀⠀⠏⠛⠁⠀⠀⠀⠀⠀⠙⣍⡀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡴⠉⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠆⢲⡶⠶⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⣿⡀⠀⠀⠀⡀⠀⠀⡔⡄⢠⡀⣠⠤⠂⠔⠂⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠈⠀⠠⠤⠀⠀⢠⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠙⠃⠀⠀⠈⢇⠀⣴⠏⡇⢸⡾⠋⠐⠀⠄⠀⠀⠀⠀⠨⠆⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣤⠀⠀⠀⠁⠀⠀⠀⢰⠄⠀⡆⣻⠏⢸⡇⣸⣅⠈⢀⠀⠀⠀⠀⠀⠀⠂⠀⠲⠓⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠔⠋⠙⠀⡁⠀⠀⠀⠀⠀⠀⣬⡄⠀⠀⡿⢀⣾⡧⢿⢁⣀⣤⣀⠶⠋⠁⠀⠢⠈⠀⢢⡀
⠀⠀⠀⢰⡆⢄⣀⠀⠀⠀⠀⠀⠀⢀⡆⡄⢠⠄⠀⠐⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⡇⢺⣿⡷⠛⠁⢁⡠⠜⠀⠀⠀⠐⢀⡄⡀⢀⢠⣴⡲
⠀⠀⠀⢐⠀⠢⠀⠉⠐⣄⠀⠀⣄⣸⡧⢠⡞⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⣿⡄⠁⢹⣿⢋⣠⠴⠚⠋⠀⠀⠀⠀⠐⡶⠟⠛⡠⠛⣈⠉⠶⠂
⠀⠀⠀⠀⢦⠀⠁⡆⣀⢸⡆⢸⣢⡈⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠘⣇⣠⣼⣿⠛⢁⠀⠀⣂⡐⠞⠀⠀⠀⣀⡞⠀⠁⠞⢁⠀⡀
⠀⠀⠀⠀⠈⠻⢶⣿⣿⣿⣿⡀⢻⡷⣿⣿⣤⣦⣤⣤⣄⡀⠀⠀⠈⢧⡁⠄⠈⢿⣏⣷⣿⡷⢞⡿⠀⠀⠀⠀⠀⠐⠈⡉⠈⡸⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⣻⣿⣿⣿⣿⣿⡟⠙⠛⠯⡉⠖⠀⠀⠳⣿⡄⠀⡸⠛⠛⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠏⣁⢌⣉
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⢘⣉⢸⣻⡿⢋⣝⠶⠄⠊⠀⠀⠀⠀⠀⠘⢿⣦⡃⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠐⠁⠒⠂
⠀⠀⠀⢀⣾⡿⠛⠛⠉⠉⢙⠛⠋⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⠀⢠⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣿⣿⣿⣿⣿⣿⣾⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢳⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣿⣿⠀⢠⣿⣿⣿⣿⠯⠽⠿⠿⠿⢯⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⣿⠀⠸⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡏⣹⣏⠟⠀⠚⠺⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠲⢧⣺⣟⣿⡿⠋⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠠⠤⣄⣀⣀⣀⣀⣀⣠⣤⡾⠿⠟⠋⠁

⠀⠀⠀⠀⣠⣀⠀⠀⠀⢤⣀⣠⡤⠤⣀⣠⣤⠴⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⠠⣤⣤⡀⠀⣠⣤⣄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢐⣿⣿⣷⣶⣦⣄⣉⠙⠛⢭⣄⡀⠀⠈⠉⠙⠛⠋⠉⠁⢀⢀⡤⢊⡴⠋⠀⠀⣿⣿⣿⡗⣀⢀⡟⠀⠀⣦
⠀⠀⠀⠀⢉⣀⣤⠾⠛⠉⢉⡭⠛⠲⠿⠿⠟⠀⠐⠻⠿⠷⠖⢀⣀⣤⣾⡴⠟⢤⣤⣶⠀⠙⢿⡉⢻⣼⣾⠇⠀⢠⣿⡄
⠀⠀⠀⠀⠚⣩⣤⣤⡀⠀⢸⡇⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⠴⠾⠟⠛⣰⠏⠈⠻⣄⣹⣿⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⢧⣙⣦⣷⠀⠂⢸⣿⠈⠛⠛⢛⡿⣿⡿⢻⡿⠋⠀⠀⣠⡄⠀⢀⣤⣶⣶⡄⠙⣿⡿⢀⠆⠀⠋
⠀⠀⠀⠀⠀⢈⠛⢿⣤⡈⠻⣿⡆⠀⠘⠟⢠⡾⢠⣨⣴⠋⣠⡞⠁⣠⣾⡿⠋⠀⣴⠟⢻⣿⣿⠏⣀⢸⡇⢸⣧⡠
⠀⠀⠀⠀⢠⡟⠀⠀⣨⣉⡻⢿⣿⠀⢧⡀⢈⠀⣿⣿⣿⣿⠋⠀⠐⠋⠀⠀⣠⣾⢁⣴⣏⡤⠀⢰⠏⣼⠁⠸⣏⠳
⠀⠀⠀⠀⠀⢠⣾⡆⠀⠛⢿⡄⢹⡇⠸⣟⠲⣔⠈⠛⠋⣁⣤⡤⡤⠴⡶⠾⠿⠿⠿⠻⠻⠖⠲⠶⡄⣿⣿⡇⠙⣆⣣⠄
⠀⠀⠀⠀⠀⣠⣿⡇⠀⢀⣤⣤⡀⢿⣀⣉⠻⢦⣱⡖⠀⠿⠿⠧⣠⣤⣤⡶⠒⠂⢀⣀⡀⠀⢀⡀⠀⠉⣛⣁⣀⠘⠛
⠀⠀⠀⠀⠀⣺⣿⣧⠀⣾⣿⣿⣧⠘⣿⣿⡄⢀⣙⣋⠀⠀⣠⠾⡫⠖⠉⠂⠀⢀⡄⠉⠉⣀⣙⣛⠲⣌⣉⣉⣩⣭⣄⡀
⠀⠀⠀⠀⠀⢻⣿⠏⢸⡟⠹⡏⡀⠀⣀⣄⡀⠀⠘⠿⣧⠘⠛⠮⣐⣤⠶⠋⠀⠘⢷⡀⠈⠙⠉⠛⠓⠌⠙⢷⡖⠚⠿⠃
⠀⠀⠀⠀⠀⠘⣿⠆⢸⡇⣸⣷⣷⠞⠉⠀⠀⢶⣿⣦⡀⠀⠠⠞⢋⠁⣠⣤⣄⠠⠤⣿⣦⠈⠀⠐⠲⠶⠄⠀⠙⠆
⠀⠀⠀⠀⠀⢀⠈⠀⢸⣿⡿⠋⠀⠀⢠⣤⣤⣀⣻⡁⠹⣦⠀⢠⡾⠸⣿⣿⣿⡛⠛⠛⢻⣷⣤⡘⢢⣤⣤⣄⡀⠄⢀
⠀⠀⠀⠀⢀⡾⠁⣠⡿⠋⡠⠄⢀⣴⠀⠛⣒⠬⣍⣻⣆⠙⢷⣦⣤⣤⣬⣝⣛⣛⡛⠛⠛⠛⠛⠷⣄⠘⠳⠶⠦⢭⣽⡆
⠀⠀⠀⠀⢀⣴⠟⢁⣤⣾⢃⠀⠘⣁⣀⣤⣤⣀⣀⠂⠉⠳⡀⠹⣿⣦⣤⣀⣹⣿⣿⣦⠈⢻⣷⡄⠈⠳⣤⣵⣆⠲⣆
⠀⠀⠀⠀⠺⠿⠓⠙⠇⠛⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠻⠓⠂⠉⠛⠿⠛⠀⠀⠈⠉⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀⣠⣿⠀⢹⣇⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢺⣏⠉⠛⠋⠉⠀⠀⠀⠈⠉⠛⠋⢉⣿⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠛⠶⠶⠶⣤⣤⡟⠀⠀⢀⣿⠃⠀⠀⣠⡴⠶⢶⣤⡀⠀⠀⢻⡇⠀⠀⠀⢿⣤⣤⠶⠶⠶⠛⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠇⠀⠀⣾⠋⠀⠀⠀⠈⢻⡄⠀⠀⠿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢿⣤⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣤⣿⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⢷⣄⣀⣠⣴⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠧⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠾⣧⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⠟⠳⢶⣤⠀⢠⡴⠾⠛⠷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⢿⣤⣤⣤⠿⠈⠙⠳⣦⣤⠶⠛⠉⠸⣧⣤⣤⣼⠇⠈⠛⠶⣤⣴⠞⠋⠁⠿⣤⣤⣤⠿⠀⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⢀
⣿⡟⡋⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⠐⠌⣽⡶⠀⠀⠀⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠆⠰⡅⢸⢃⣠⡠⢆⣟⠈⢀⣁⢈⡀⠀⠀⠀⠀⠀⠀⣰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⡈⠉⠉⡕⠦⢷⠒⣾⡥⠜⠁⠀⠀⡄⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠀⡇⠀⡼⢿⡈⠏⠶⢿⠄⠀⠥⣀⡀⠀⢙⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⢈⠧⣀⠤⡀⡀⠤⣈⠘⠣⣺⠄⠀⠀⠁⠀⢨⢤⡴⣀⡙⠃⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⢶⣿⣾⣿⣙⣞⡡⢈⣽⠤⣦⣶⣶⣾⣶⣷⣾⠞⡸⣡⢤⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠒⢆⠀⠀⠄⠙⢯⣿⣯⣿⣷⠚⣼⣾⣿⣿⣿⣿⣿⢿⣧⠈⠱⣌⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠻⣽⣿⣧⢸⣿⠿⢿⡟⠋⠁⠈⠉⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠙⣾⠃⠀⡜
⠀⠀⠀⠀⠀⠶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠈⠆⢹⠀⡼⢒⡤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣷⣌⣻⣿⣿⣿⣿⣿⣿⣶⣄⠘⣾⡴⢳⣵⣶⣿⣭⣿⠿⠿⠛⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢜⣛⠭⠴⣒⣻⣿⢿⣿⣿⣿⡗⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇
⠀⠀⠀⠀⠀⢀⠔⠁⣠⡴⠞⠋⠉⣠⣾⣿⣿⣿⡇⢸⡇
⠀⠀⠀⢀⡴⠋⣀⠾⠋⠀⢀⣤⠾⢫⠞⠻⠿⢿⣄⣼⣇⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⢀⡾⢁⠞⠉⠀⠠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠉⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⣼⣧⣏⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⢹⡇⠀⠀⠀⠀⠀⢀⣶⣶⣿⣶⣦⠀⠀⠀⢰⡟⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠛⠁⠀⠀⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠻⡄⠀⠀⠀⣠⢠⡿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⣿⣤⠀⡀⢽⣾⠁⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢉⣻⣦⠀⢸⡝⠀⡀⢠⣤⣍⣉⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠹⣷⢸⡇⢀⣠⣶⣤⠉⠙⢧⣀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠤⠀⠀⠀⠘⠀⢠⡀⠚⠀⠀⠰⡾⠶⣶⠟⠒⠿⣿⣿⡿⠃⠀⠀⠀⣿⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⢀⡄⠀⠀⡇⣴⣖⠁⠀⠀⡀⣠⣈⡿⠗⠀⠀⠀⠀⢀⠀⠀⢸⡶⣸⢿⡟
⠀⠀⠀⠀⠀⠀⢵⣠⠀⣼⠇⠀⠀⠁⠀⠀⠀⢸⠁⡧⠔⠙⣿⣤⣿⣿⢇⣄⠀⠀⠀⣀⠀⠀⠀⢠⡿⠃⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢻⡄⡋⠀⠀⠀⢃⠀⠀⠀⢘⡾⠂⠀⢹⣿⣿⣿⣿⡿⠄⠀⢠⡀⠀⠱⢄⡀⣰⠇⣾⠛⠁
⠀⠀⠀⠀⠀⠀⢀⠘⣿⣀⠀⠀⣀⠀⠀⠀⢠⠸⡗⠓⠀⠨⠿⢿⣿⣿⠗⠊⠀⢈⣷⡀⠀⠀⠀⣿⢰⡿⠂
⠀⠀⢹⣶⣶⣦⣇⣜⣿⢿⠂⠀⠙⠃⠀⠀⢀⣷⡠⠄⠼⠷⢦⣴⣻⣿⠀⠲⠲⠈⠟⠒⠀⣶⠃⡸⠛
⠀⠀⠈⢿⣿⣿⣿⣿⡿⢼⠂⠀⠓⠀⠓⠺⠍⠙⠙⠛⠢⠄⠀⠶⠟⢷⠶⠄⠊⠘⠂⠰⠀⣝⠋
⠀⠀⠀⠀⠻⢿⣿⣿⡇⠸⣇⡀⢀⠐⠒⢄⡀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠞⠉⠁
⠀⠀⠀⢀⡈⣑⠶⡬⠣⡀⡙⣧⡘⢿⣧⠀⠀⠉⠉⢹⡍⠉⠀⢠⣄⣤⣠⠀⠀⠀⠴⠃
⠀⠀⠀⢨⠿⠇⠀⠃⠀⠃⠊⠙⣻⣦⣄⢀⣤⣤⣤⣤⣾⣤⠈⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠹⣿⠿⠛⢻⣿⡗⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣦⣴⣤⣬⢿⠛⠟⠢⠀⢸⡟⠁⠀⠀⣠⣤⣶⣿⣿⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠙⠃⠘⠀⠀⠀⠃⣼⠃⠀⢀⣼⣿⡿⠿⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢀⣸⠟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⢽⢠⠶⠒⠀⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⢷⣬⡄⠔⠲⣦⠀⠀⠀⡀
⠹⢘⣫⠂⣀⡀⠄⠄⠐⠒⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠈⠻⣷⢀⢚⣡⢆⠀⠂
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣶⡀⣀⠀⠀⠀⠀⠃⣠⣤⠳⣠⣄⠀⠀⠀⠐⠀⠚⠁⠀⠀⠀⠀⠠⡄⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠚⠓⠒⠛⠀⠀⠀⠀⠉⠁⠈⠉⠉⠈⣉⣁⡩⣴⡟⠀⠀⠀⠀⠈⠓⠰⠺⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠙⠂⡀
⠀⠀⠀⠀⠀⠈⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⣀⠀⢿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡠⠳⠶⣀⠔⠀⠀⠀⠀⠀⢀⠤⠀⠴⣤⢀⠀⠀⠒⠈⠉⠀⠀⠀⠰⡀⠀⠀⠀⠁⢄
⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑
⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⣠⡴⢦⣄⠀⠀⠀⠀⠀⠀⢺⡧⢽⣧⠔⠒⠋⠁⠀⢀⣤⢴⠊⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠈⠦⣄⠠⣤⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡈⠰⢿⣿⣧⣤⢀⠕⠉⢏⡇⠀⠀⣀⠠⡶⠛⢛⠇⠀⣆⡀⠢⠐⠊
⠀⠀⠐⢄⢠⣛⣦⡭⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⢊⡽⢧⣄⠀⣨⠧⢚⢓⣚⠉⠀⠀⠀⠐⠯⣠⡴⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⢿⣿⣮⣷⢰⢾⡎⠋⡹⢳⠰⢂⠠⠐⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠒⠀⠄⣀⡀
⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠈⢋⣻⣅⢼⣣⣾⣟⠭⠲⠶⠛⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠤⣀⣀⠀⠀⠀⠀⣆⠀⠐⡀⠀⠀⠀⠀⠈⠉⠁⢼⡿⣾⢯⣥⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⢸⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡀⠤⠀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠠⠀⡀⡤⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠤⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡀⠀⠀⠀⠀⠠⠼⠶⠁⢘⡷⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡹⣃⢵⢶⡆⠀⠀⠀⠐⠚⠃⠨⠞⠥⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣂⠴⢤⡀⠀⠀⣀⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠃⠘⠦⠠⠰⢊⠔⠒⣦⣠⠄⠀⠀⠀⠀⢀⠄
⠀⠀⠁⠈⠉⠀⠀⣶⡟⠶⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠈⢟⠦⠄⣶⠀⠀⠠⠀⠈⠀⢀
⠀⠀⢀⠀⠀⠀⡼⡟⣇⠀⠀⠀⠀⠀⠀⣤⣞⢷⠆⠀⣠⣾⡇⠂⠀⠀⠀⠀⠀⠀⠁⠐⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⠀⠀⠀⠀⠀⠈
⣀⠀⠀⠈⠉⠻⠛⢱⠿⠆⡄⠀⠀⠀⢨⣔⠀⡑⠂⠛⢿⣿⠄⠒⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠉⠒⠂⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦
⠀⠈⠁⠈⠐⣾⡀⠈⣦⠀⠉⠀⠈⢙⣫⡫⣘⡷⣀⢞⣧⣽⡆⡀⠀⠸⡀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠘⠏⠉⠉⠠⢀⡐⠀⣙⠧⢁⣯⣳⣑⢿⠛⣷⢚⠃⠀⠀⢣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠇
⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠋⢺⢿⣿⣿⡌⠓⠋⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⢀⣁
⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠏⠛⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠔⠒⠋
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⡀⠀⠒
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠄⠀⠀⠀⠀⠀⠀⣶⡆⣤⠖⠈⠁⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⡱⢤⠀⠀⠀⢀⡴⠒⢦⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⠞⣰⠃⠀⢀⠔⠁⢀⣠⠞⠉⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣠⠋⡴⠁⣠⠞⠁⣀⡴⠋⠁⠀⠀⢀⡴⠃⠀⢀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡇⠀⠀⣴⠀⠀⠀⢠⠞⠀⡰⢁⡞⣡⠞⠁⣠⠞⠋⠀⠀⠀⣠⠖⢁⣀⡤⠒⠉⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⣸⠏⠠⠂⡴⠁⢀⠔⢠⡿⠞⢁⡤⠚⠁⠀⡀⠀⣠⣾⠥⠚⠉⠁⠀⢀⣤⣖⠭⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⡇⢰⡇⢠⡟⡐⢠⠞⠀⡰⠊⡰⠋⣠⣴⠟⠀⠀⠀⠀⣠⠞⠉⠀⠀⢈⣡⡴⠞⠛⣉⣠⠤⠚⠲⡀
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠛⠉⠉⠛⠻⢷⣄⡀⢘⡇⣸⢣⡟⡄⡰⠃⢀⠞⡠⢊⡤⠞⠉⠁⠀⠀⢀⡠⠊⠀⠀⣀⡤⠞⠋⣁⡤⠖⢋⠍⠀⢀⣠⡤⠃
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢵⣄⣿⣿⣿⣉⣼⡅⢀⣾⣿⠞⠋⠀⠀⠀⠀⢠⡴⢋⣠⣴⠶⢛⣡⠴⠒⠋⠁⠀⢀⣠⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣿⣿⣿⡿⢿⣷⣩⡞⠁⠀⠀⠀⠀⢀⡴⣫⣶⣿⡯⢶⡛⠉⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⠶⠒⠚⠛⠛⠛⠛⢋⡩⣿⣟⠁⣠⠼⢿⣟⢿⣄⠀⠀⣠⣶⣿⠾⠛⠋⠁⠀⠁⡀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠀⢸⣿⠞⠁⠀⠀⠻⣆⠙⣿⡞⠋⠉⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⣀⠴⢻⣿⠀⠀⠀⠀⢐⣿⡞⠙⢿⡄⠀⢀⣠⠴⠊⠉
⠀⠀⠀⠀⣠⣤⡒⠋⠉⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠈⠿⠀⠀⢀⡠⠞⢿⡇⠀⣸⡷⠚⢉⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⢰⣿⣿⣿⣆⠐⠅⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣤⡶⠋⢀⣀⣬⡝⠛⠋⠀⠀⢸⡑⢤⡀⢠⣾⡅⢱⡄⠀⠀⢀⣀⡄
⠀⢀⣀⡬⣿⣿⣯⣿⡆⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⢀⣴⣟⡴⠚⠉⠀⠈⠀⠀⠀⠀⠀⢸⣷⢀⡁⣉⢉⣁⢸⣇⣠⠞⣫⣽⡇
⣰⡿⣟⡆⢼⣏⠿⣿⣇⣾⣿⣷⣄⠰⠁⠀⠀⣠⣴⣿⡿⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣄⣁⢩⣼⢈⣈⣉⠀⣉⣍⠉
⢿⣿⣵⣗⠊⠛⢻⣿⠛⢿⣽⣿⣿⡄⢠⣶⣿⡿⠋⡿⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠹⢭⣿⣄⣿⣼⣿⣥⣾⠿⠥⠤⢀
⠸⣿⣿⣿⣀⣴⢿⠿⣿⡆⢰⣿⣿⣧⢞⣽⠏⠀⣼⡵⠁⠀⠀⠀⠀⠀⠀⠀⠶⣬⡉⢠⣤⣒⣀⣰⣭⣿⣿⣿⣟⣁⣀⠲⠒⣐⣺⠞
⠀⠉⠉⠉⠀⠸⣼⣇⣺⣷⣉⠛⢛⣵⣿⡃⠀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠭⠭⣵⡾⢛⣿⠿⣿⡛⢝⢳⡤⠭⠒⠁
⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣯⡧⢾⣿⣟⡟⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⡡⢺⡿⢀⢻⡿⡘⢆⠡
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢚⡴⠻⡇⠙⣼⠉⠛⠷⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⠹⣄⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠉⠛⢻⣿⣷⣿⢿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⡿⣛⣵⣴⣦⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⠿⠟⣷⣿⣿⣿⣿⣦⣀⡀⠀⠀⢽⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣿⠅⠒⠄⣶⣍⡻⢿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⣿⣿⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢼⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣧⠀⠀⠐⡟⢡⡿⣻⣿⣿⣿⣿⣿⠶⣄⣀⡲⢿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠆⠀⢘⢆⡾⣱⣿⣿⣿⠻⣿⢿⠑⠈⠹⣙⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣏⡿⠃⡭⡸⣿⣿⡿⠋⠙⣿⡝⠧⡄⣰⡀⣻⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡞⣹⡇⢠⡶⠐⠻⣿⣿⣧⣶⢹⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣹⣿⣿⣿⠟⠁⢹⣿⠜⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡟⠉⠀⠘⣸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠯⠀⠀⠀⠀⠿⠼⠻⠿⠿⠿⡿⠿⠿⠿⡿⡿⠿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉