Corner Emojis & Symbols

⠠⡆
⢀⣀⠠⠄
⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢠⡄⠣⣔⠋⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⢀⠉⢀
⢸⡇⣀⣀⡙⠢⡀⠈⠃⠶⠀⠆⠀⠀⠀⠱⡄⠀⡀⠙⠁⠉
⠀⠀⡉⠉⢡⣄⢸⡄⠀⠀⠀⢀⡤⠒⣚⠛⠋⢁⡆⠠⣄⣀⢀
⠻⠀⠙⠂⠻⠷⠞⢳⠷⢶⠠⣏⣰⡄⠈⠳⡄⣼⠃⠀⠙⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠀⠴⡁⠔⢁⣶⠸⡀⢙⠛⠁⠶⢀⣀⢀⡈⠛⠓⠈⢧⠀⠐⢂⡀⠋
⠀⠤⢤⣤⣤⣀⣀⡀⠁⠀⠑⠘⠀⠀⠆⠈⠋⠘⠇⢠⣾⢃⣼⠀⠀⠈⠁⠚⠀⠀⠀⢠⡀⠀⠀⡤⠀⣴⠆
⠀⣐⣀⣀⠂⠀⠩⠉⠛⠓⠶⠤⣤⣀⠀⠀⠀⠁⢀⡤⠉⢉⡹⠶⣤⡀⣤⠔⠒⠲⠤⣤⣇⣀⠀⠰⠆⣀
⠀⠀⡉⠉⣉⣉⡙⠒⠲⠤⢤⣀⠀⠍⠙⡳⢦⣄⡀⠀⠈⢁⣶⠀⠇⠸⣧⣶⠀⠹⣆⠀⢠⡔⢀⠀⠀⠈
⠀⠀⣿⡆⠁⡀⢹⡆⠀⢠⡀⠀⢉⠓⠢⢄⡀⠈⠙⠳⣤⡈⠁⠀⠀⡆⠈⠡⠦⠀⠉⠰⠋⠀⢸⡖⠢⠄
⠀⠀⣻⠇⠀⠈⠉⠀⢤⣌⢿⠀⣾⠃⢀⡀⠉⠓⠦⡀⠀⡙⠳⣄⠀⠀⠀⠆⠐⠿⢀⡄⠙⢷⠀⢧
⠀⠀⠁⠀⠔⢢⣶⡀⢢⡙⠈⠀⠡⢞⣋⠁⠀⣠⠤⣌⠓⢤⡀⠌⠓⢤⡀⠀⠀⠄⠘⠁⣴⣶⠀⡜⠀⢠⠄⠀⣠
⠀⠀⠀⠰⠿⠂⡍⠰⠷⠡⠸⠃⣀⠙⣋⠁⠀⠧⠄⠈⠃⠀⠙⢦⡐⠀⠹⣄⠀⠀⠤⠄⠙⠷⠞⠁⠀⠀⠶⢀⡁
⠀⠱⣄⠀⠰⠶⠰⡶⠀⠲⠦⠀⢴⠆⢰⣤⠄⠀⢀⣴⠿⠛⠁⠀⠙⢦⡘⠈⠳⡄⠀⠀⠶⢀⠛⣧⡀⠀⠀⠈
⠀⡀⠀⠑⠀⠀⠠⠐⣡⡀⠀⢶⠆⠲⢨⣅⠸⠀⠸⢁⣴⣶⠁⣰⡆⠀⠑⣄⠃⠙⣆⠀⠾⠋⡔⠉⣵⢚⡒⠒⠦⣀⢀⠆⠀⠀⣤⠀⣀⡀
⠀⠄⠉⠍⠙⠒⠲⢤⣌⡀⠐⠄⠘⠃⠈⠉⠀⢀⡀⠈⠛⣡⡾⠟⠁⠈⠳⡌⢦⠀⠈⢧⠀⠀⢁⡄⠻⠿⠃⢸⣇⠈⠛⠤⠀⠠⣦⠀⠉⠁
⠐⠒⠒⠂⠤⢌⣀⠀⠄⠙⠳⢤⡁⠒⠠⠄⠂⠈⠁⠀⠀⣀⢀⠀⠀⠧⠼⠃⠀⢣⡈⠈⢧⠀⠈⠀⡀⠚⠂⠀⢃⣤⠾⠋⡠⠀⠀⠘⠃
⢰⡄⠀⠀⠀⢀⣀⠈⠒⢤⡁⠀⡝⠢⡀⠛⠁⡇⠀⢰⣶⠀⣶⡆⠀⢀⡄⢀⡄⠀⢳⡐⠈⢧⠀⠀⠁⠐⠛⢀⠀⢢⡄⢠⡗⠢⡀
⠸⢱⠟⠒⠀⠘⠋⠀⠀⠀⠈⠲⣄⠠⠘⢦⡀⠀⠀⣶⠄⠒⢰⣦⢸⠸⢇⡾⢁⣀⡀⢣⠐⠘⡆⠀⠀⠐⠀⠛⣀⣀⠛⢸⠃
⠀⠈⠀⢦⡆⠀⢠⣴⡆⢰⣷⡆⠈⢢⡀⠀⠱⡀⠀⢄⡘⠋⢀⠀⢁⣤⠀⢘⣋⣉⠀⠈⡆⠐⠸⡀⠀⠢⠤⠘⣿⣋⣠⠎⢀⡀
⠀⣈⣲⣾⣏⠉⢁⠀⠰⠌⣁⣀⠀⠀⠱⡄⠔⠹⡀⢠⡤⠀⠈⠇⢐⡢⣄⠲⣭⠛⠓⠀⠸⡀⠄⢇⠀⠑⠤⠄⣤⡉⠀⠀⣨⡅⠠⠆
⠀⣤⣀⡈⠓⢍⡻⣷⠆⠀⡿⠋⠀⣀⡀⠹⡀⡀⠱⠀⢠⠃⢶⠆⡙⢃⣄⡀⠈⢀⡤⣄⠀⡇⢠⠸⡀⠰⠾⢃⠸⣷⣀⡀⠀⠶
⢸⠀⠂⣉⠲⣄⠹⡜⣦⣸⣇⡀⠀⠙⠋⠀⢡⠀⠄⠃⢠⠀⢶⠆⣩⡌⢋⠇⠀⠘⠆⢈⡇⢹⠀⠀⡇⠀⠔⣡⢰⣯⣭⠉⠳⣄
⠉⣠⣿⠟⠀⠘⡆⠸⡟⢿⠀⠃⢈⣇⠀⠀⠀⡄⡀⢸⠀⢢⠀⠀⠙⠁⠉⢀⣤⣤⣤⣌⠀⢸⠀⠀⣥⠀⠈⠁⠀⣍⠁⢠⡇⠘⣦⠞⠀⠀⢀
⠠⠈⠁⠤⠤⠄⠁⠀⠃⠀⠁⠈⠩⠥⢦⠀⠀⠇⠀⠸⠀⠀⠙⠂⠀⠀⠀⠉⠀⠀⠈⠉⠁⠸⠀⠁⠘⠀⠀⠐⢀⣈⠀⠘⣁⣀⣬⠑⠀⢠⡍⠀⣤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾⢿⠶⢾⣿⣿⣶⣶⣶⣾⣷⣶⣶

⠀⠀⢰⣶⣶⣄⣴⢶⢶⡶⠀⠀⠀⢀⣄⣠⣶⢄⠄⠀⠀⠀⡶⣲⣤⣖⣒⣒⡒⠀⠀⠀⣶⣠⣶⣶⣶⣶⠶
⠀⠀⠘⢿⣿⣟⣧⣽⢿⠆⠀⠀⠀⣹⡟⠍⠉⠻⠃⠀⠀⠀⣻⣿⡟⠃⠀⠀⠀⠀⠀⠀⣾⢿⣷⠉⠉⠁
⠀⠀⢰⣟⣝⣿⢻⣶⢻⠀⠀⠀⠘⢟⣧⡀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗
⠀⠀⢸⡿⠿⠗⠋⠒⠒⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⣲⣴⣒⣒⡒⠒⠒⠀⠀⢰⣲⠶⢀⠒⠒⠒⠂⠀⠀⣿⣟⢿⠯⢽⣛⣳⠋⠀⠀⠯⡧⣮⢵⡏⠉⠘⠁
⠀⠀⢰⢻⢻⣶⠋⠀⠀⠀⠀⠀⢸⢇⡏⠉⠀⠀⠀⠀⠀⠀⡾⡟⢢⣼⠽⠋⠁⠀⠀⠀⢦⣏⠃
⠀⠀⢸⢸⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⡶⠋⠀⠀⠀⠀⠀⠀⡏⠉
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠭

⠀⠀⢀⡀⢠⢀⣠⣤⣤⣤⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢨⣝⠞⢻⣴⡶⠂⠀⠀⠀⠀⢸⡷⢶⠏⣻⠏⣻⡤⠶⠚⠃⠀⠀⢰⡿⡟⣣⡾⣶⣻⣬⣿⠞⠋
⠀⠀⢰⢫⣷⡝⠆⠀⠀⠀⠀⠀⠀⢸⡗⣿⢉⣽⠾⠃⠀⠀⠀⠀⠀⠀⢘⣶⣟⣹⠿⠊⠉
⠀⠀⢸⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠁
⠀⠀⠘

⠠⡦⠄⡀⠀⣠⢾⠋⠀⠘⣟⠲⣤⢶⣷
⠀⢳⠳⣮⣿⡇⢺⠀⠠⠀⢸⠀⢹⡿⠞⣩⠿⢂⣠⠤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⢀⠷⠿⠿⣧⠈⢇⠀⣀⢸⠀⡞⢠⠞⣡⠞⢉⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠰⠗⠒⠒⠦⣄⡑⣸⡦⠟⠚⠶⣶⢃⡜⢁⣴⠟⠁⣀⣤⣶⣾⣟⣛⣛⣛⣒⡲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⡔⡽⠚⣋⣉⠛⠻⣍⠉⠉⠉⠉⠉⠁
⡀⠀⠀⠀⠀⢢⣼⠏⡴⠋⠉⠳⡌⣾⠀⣾⠁⣴⠿⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠷⠾⠿⢷⣦⡤⢀⠀⠈⠛⠃⠘⣄⠧⣀⣀⣈⡷⠀⣸
⢻⡒⠶⠒⠒⠒⠺⡄⢧⡀⢀⡴⢃⡏⠀⡇⢸⡇⢰⡟⠻⣷⡄⠀⠙⢿⠿⠛⠉⣀⢤⡶⠖⠒⠒⢬⡹⡏⠐⠢⠬⢍⣒⣚⠓⠊⠉⣁⡠⠔⠋
⡠⢛⣷⡶⠚⢁⠼⢉⣶⣬⠥⠶⢿⣷⠀⢳⡀⠻⢶⣬⣴⠿⠃⠀⠀⠀⣠⣴⠏⢡⠎⠀⠀⠀⢰⡋⠇⡜
⠙⠒⠺⣠⠞⣡⠞⣉⣤⠴⠶⠶⠤⣌⠁⠀⠙⢦⣄⣀⣀⣀⣠⠤⠲⠿⠉⠁⣰⠃⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠸⢃⡞⢡⡾⠋⢀⡴⠖⠒⢦⡈⠳⣄⠙⣦⣉⠛⢿⣿⣇⠀⣶⠄⠀⣴⠃
⠀⠀⠀⡞⢠⡿⠁⢀⡞⠁⣰⠶⡄⣷⠀⢸⣦⠘⣿⣿⣶⡤⠭⢍⣭⡴⠞⠁
⠀⠀⢠⡇⢸⡇⢀⢺⡇⠀⢿⣄⣤⡿⠀⢸⣿⣷⡘⡟⠟⢬⡁⠒
⠀⠀⢸⡀⢾⡇⣼⣾⣧⡀⠀⠉⠉⠀⠀⡞⠉⠉⣧⢻⠘⡀⠘⠦
⠀⠀⢸⡇⣿⡇⣿⣿⣿⣿⣶⡆⠀⠀⣼⡇⠘⠷⢋⡾
⠀⠀⢸⡅⣿⡇⢹⢹⣿⣿⡿⠀⠀⣼⡇⠁⢀⣤⠞⠁
⠀⠀⢸⡇⢹⡇⢸⣼⣿⣿⠃⠀⡼⣁⡴⠚⠉
⠀⠀⢸⡇⢸⡇⠈⣇⣿⡿⠀⣸⠛⠁
⠀⠀⢸⡇⢸⡇⠀⢸⡸⡇⢠⠇
⠀⠀⢸⡇⢸⡇⠀⠀⢳⢧⠘⣆⣠⣄
⠀⠀⢸⡇⢸⡇⠀⠀⠈⡞⣧⣈⣓⡸⠁
⠀⠀⢈⡇⢸⡇⠀⠀⠀⢸⣻
⠀⠀⢸⡇⢸⡇⠀⣶⣶⠈⡏⡇
⠀⠀⢸⡇⢸⡇⢀⡬⠷⢄⣿⢡
⠀⠀⢸⡇⢸⡇⣮⠞⠉⢦⡿⢸
⠀⠀⢸⡇⢸⡇⢻⠸⣂⣿⡇⡜
⠀⠀⢸⡇⢸⡇⢸⢦⣉⣁⡜⠁
⠀⠀⢸⡇⢸⡇⣿⠀⠉⠁
⠀⠀⢸⡇⢸⡇⣿
⣀⣀⣸⣇⣸⣇⣻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⠀⠄⡄⡀
⠀⠀⠀⠀⠀⠀⣁⠌⠃
⠀⢰⠀⠀⠀⠀⠀⡀⡁⣀⣺⣦⡶
⠀⢸⠀⠀⠀⣠⣊⠀⠀⠈⢹⠟⠷
⠀⢸⠀⠀⢀⠉⠉⡥⠒⠒⠲⢄
⠀⢸⠀⠀⠘⡄⡞⠀⢀⠴⡄⠀⡇
⠀⢸⠀⠀⠀⢳⣇⣄⠈⠦⠤⠴⠁
⠀⢸⠀⠀⢰⣌⢏⠉
⠀⢸⠀⠴⠚⠓⠪⣆
⠀⢸⠀⠀⠀⠀⠀⣿⣷⢀⣤⣶⡶
⠀⢸⠀⠀⢠⣴⣶⣾⣿⣾⡿⠋
⠀⢸⠀⠀⠀⠉⣋⣽⣿⣿⣿⣷⡄
⠀⢸⠀⠀⢠⠎⠠⣿⣟⢹⠀⠉⠁⠠⠀⢄⠀⢀⣀⡀⠀⠀⣀⣄⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⣤⣠⡄
⠀⢸⠀⠀⠈⢆⣈⣀⡜⣸⢀⢁⠢⠣⠬⠀⠀⠀⢿⣿⡆⣾⣿⠏⠀⠀⠀⠀⢰⠃⢀⡀⠉⢆⠰⢾⣿⠶
⠀⢸⢠⠚⠉⠑⢦⡀⢀⠃⠐⠠⠞⠒⢉⠭⢭⣽⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⡀⠓⠶⠃⠀⡸⠀⠀⠹⢀⠠⢀
⠀⢸⣇⠀⠉⢳⠀⣧⡖⠋⣉⠑⡄⠀⢏⠠⠼⠛⡻⢹⣿⡯⠙⠛⠛⠖⠤⣄⣿⣀⣀⡤⠞⢁⣦⢀⠂⠀⢰⢀⠃
⠀⢸⠈⠓⣖⣯⡰⠋⣠⣏⠈⢀⡇⠀⠈⠒⠒⠚⠁⠈⠻⠃⠄⠀⠀⣸⠻⠆⠈⠙⠒⠒⠂⠚⠋⠁
⠀⢸⡀⠀⠘⠻⠁⢨⢿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⢀⠴⠊⠉⠉⠉⠙⠻⣦⡂⠀⠀⡀⠠
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠰
⢸⡀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢹⡄
⠀⢣⡀⠀⠀⢀⡴⠁⢧⠀⠀⠀⣷⠂⡠⠐⢀⣀
⠀⠀⠈⠑⢊⣭⠤⠤⣌⣷⡀⠀⣯⡴⠒⠉⠁⠈⠙⢶⡀
⠀⠀⠀⢰⠋⠤⠶⢤⡀⠹⣿⡀⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⡀⠀⠀⢀⡇⠳⣝⣿⠁⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠙⠶⠶⠋⠀⠀⣿⣿⠀⠀⡠⠖⠒⠶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⠀⡈⠀⡀⠈⠁⠈⡇
⠀⠀⠀⠂⠀⠠⠖⣀⢀⡠⠀⢺⠁⠈⢀⠡⣀⣀⡠⠃
⠀⠀⠀⢀⣀⣀⠀⠀⠀⢑⡆⢙⠊⢖⠉⠃
⢀⡀⠤⠒⠒⠢⢭⠗⠒⢩⡄⢯⢦⣉⡇⠐
⠈⠀⠀⢀⢀⣠⣬⣄⢀⡔⠢⢲⠤⠛⢄⠂⠀⠠
⠀⠀⠀⠖⠈⠁⡀⠨⠭⢌⡀⠸⠀⠀⠀⠀⠂⠀⡀
⠀⠀⡠⠤⠢⢬⡀⠀⠀⠀⢀⠀⠄⠀⠒⠐⠠⢀⡀⠀⠀⠀⢠
⠀⠎⢠⠀⠀⠀⠹⡄⠀⠀⠀⠑⣆⠈⠱⠂⠠⡊⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠠⠀⢠⠖⠉⠉⠑⢆
⢸⡀⠸⣄⠀⠀⣠⠇⠀⠠⠤⡅⠈⣱⢒⠔⢊⠡⠠⢄⠀⢄⠀⠀⢰⠀⠀⠂⠀⠀⠀⢂⠀⠀⠀⡀⠈⡇
⠀⢣⡀⠈⠙⠋⠁⠀⠀⠐⠀⠘⡉⠀⡁⠉⢢⠀⠀⠂⢀⡌⣖⠐⡦⢄⣈⠤⠀⠀⠀⠀⠁⠒⠊⠀⣰⠃
⠀⢤⡙⠦⣤⣀⣀⣤⠴⠀⠴⠊⠀⠁⡑⠀⠁⠑⠢⠀⠘⡤⠬⣒⡤⠰⠅⠀⠀⣛⠶⠤⠤⠀⣠⠞⠁⠀⠀⣀⡤
⠀⠀⠢⡹⠶⠶⠶⢐⣡⡤⠠⠀⠀⠀⠉⠈⠀⠀⠄⢠⠔⠢⢴⡈⣱⠔⠉⡳⠂⠲⠲⠶⠿⢿⣶⣶⣍⠉⠉⠉
⠀⠀⠀⠀⠀⠱⠚⠉⢌⡜⡎⠀⢠⠔⠢⡀⢁⠀⠀⠀⠀⠀⡎⠁⠀⠣⠀⢀⣀⡀⠀⠀⠀⠀⠈⠙⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢦⠀⠡⣄⡴⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠈⠳⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠄⠒⠀⠀⠦⢀⠠⠞
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠖⠛⠳⣄⣶⣶
⣰⣶⣦⠀⠘⠻⠏⠃
⠙⠟⠋⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠐⢛⣡⡄
⢠⣴⡄⢀⣴⣿⠟⠁
⣼⡟⢑⠛⢋⠁⢀⡆
⢿⠊⠀⠀⠀⠀⠢⠙⠉
⡆⢀⣴⣶⣦⡀
⡇⠀⠀⠉⠉⠁⠀⠠⠀⣀
⠱⡀⠀⠀⠀⡀⠔⠁⣻⣿⠶
⢰⣷⣄⠀⣠⡀⠀⠀⡩⠬⢅
⠈⢛⡿⠧⡙⣿⡄⠈⣴⣶⠈
⡜⠁⣈⠑⠵⡈⠇⠀⠙⠛
⠁⠀⠛⠁⠀⢱⠀⠀⡀⠀⢀
⠀⢀⣄⠀⠀⢸⠀⠀⠩⠒⠏
⠀⠘⣿⡇⣠⢊⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⡤
⠀⠀⡼⠞⠛⠛⠛⠋⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠓⠀⠀⣤
⢠⠎⠀⠀⠀⠀⠀⠀⣾⢿⣃⣀⣀⠀⠀⠀⠀⡴⠊⠉⠀⠈⠐⢤⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠘⠀⠀⣠⣾⡯⠉⠉⠛⠫⢟⠛⠿⠿⠆⠀⠀⢣⣤⣤⡀⠀⠀⠀⢻⠀⢀⣴⡿⢃⡴⢞⣋⣀⣀⠈⠓⠂
⠀⠀⠐⢋⣵⣾⣿⣿⣶⠀⠸⣿⡒⢄⡀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠆⢰⠟⠉⠀⢉⣠⣈⠉⠉⠋⠀⢀⣶⣦
⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠙⠿⠀⠈⠒⠤⠀⠀⠀⠀⠤⠒⠁⠀⠀⠀⠀⠀⠸⡟⠋⠀⠀⠀⠀⠊⠿⠿

⠀⠀⠀⣇
⠀⠀⠀⢸⡀
⠀⠀⠀⠈⣇
⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠸⣿⣆
⠀⠀⠀⠀⠀⣿⣿⣦
⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦
⠀⠀⠀⣾⣷⣼⣿⡇⢻⣿⣿⣷⣄
⠀⠀⠀⢿⣿⣿⢿⡇⠀⢻⣷⡈⠻⣷⡀
⠀⠀⠀⠀⠉⠀⢸⡇⠀⠈⣿⣷⠀⠘⣿⣦
⠀⠀⠀⣴⣶⣄⣼⡇⠀⠀⣿⣿⣇⠀⠘⣿⣧
⠀⠀⠀⣿⣿⣿⡿⠁⣰⣿⣿⣿⣿⠀⠀⢹⣿⡇
⠀⠀⠀⠈⠉⠉⠀⠀⠹⣿⠟⢸⣿⡄⠀⢸⣿⣿
⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⣾⣿⠀⠀⢸⣿⣿
⠀⠀⠀⣴⣿⠟⢻⣿⣿⡆⢰⣿⠏⠀⠀⣸⣿⣿
⠀⠀⢸⣿⡇⠀⢿⣿⣿⠇⠈⠁⠀⠀⢠⣿⣿⡏
⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠹⣿⣿⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣄⡀
⣼⣦⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠛⣹⣿⣿⡿⠋⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⠛⢿⣦⡀
⣿⣿⣷⣦⣄⣀⣀⣀⣤⣴⣶⠋⢰⣿⣿⠋⠀⠀⠀⢠⣶⣿⣿⠿⠿⢿⣿⣷⣶⣦⣄⣀⠙⢿⣦⡀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⡏⠀⠀⠀⣀⣤⣤⡀⠀⠀⣴⣿⣿⣿⠛⠛⠻⠿⣿⣶⣿⣿⣶⣄
⠀⠀⠀⠉⢉⣡⣿⣿⣿⣿⠀⠀⢹⣿⣷⠀⠀⢸⣿⣿⣿⣿⡆⠀⠉⠛⠋⢁⣀⣀⣀⣀⣀⡉⠛⢿⣿⣿⣷⣤⡀
⠀⣿⣿⣿⣿⣿⠟⢹⣿⣿⡄⠀⠈⢿⣿⣧⡀⠀⠉⠉⣹⣿⡇⠀⠀⢰⣿⣿⡛⠛⠛⢛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣄⡀
⢠⣿⣿⣿⣿⡏⠀⢻⣿⣿⣿⣦⡀⠀⠛⢿⣿⣷⣶⣿⠿⠛⠀⠀⠀⢻⣿⣿⡿⠀⠀⠸⣿⣿⣿⡆⠀⠀⠀⠉⠉⠙⠛⠻⠷⢦⣤⣀⡀
⠸⠿⠿⠿⠟⠃⠀⠈⠻⣿⣿⡿⠟⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⢿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠄⢸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠹⣿⣦⣤⣾⠿⢱⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⣄⠉⣉⠁⠀⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⣈⠀⢿⣧⡀⠁⠀⣼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠠⢘⣿⠘⢿⣷⢸⣿⣷⣠⠘⠁⡶⠚⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⢠⣤⡈⠿⣿⣿⡿⣄⡀⠁⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⣿⣿⡇⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠃⣿⣿⡇⢀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⢹⠀⠀⡀⣿⣿⠁⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣀⣀⣠⡴⠁⣿⡟⢀⡴⠿⠿⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣍⠉⠁⠀⢸⣿⢁⠀⠀⠀⣾⠛⡙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠻⣿⡄⢀⣾⢷⡏⠀⣠⣄⡹⢷⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠉⣠⣿⠇⣼⠏⠸⣇⠈⠁⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣦⣄⠛⠻⠿⠟⠋⣸⡏⠀⠀⠙⠷⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⣿⠋⣁⠙⣿⣆⠀⠀⠀⠀⣿⡀⠚⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⣹⡇⠀⠀⠀⠀⡎⠀⠀⠹⣦⠸⣿⣦⣀⣠⣿⠋⠀⠀⠀⠀⠘⢧⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠈⠛⠛⠋⢀⣀⡀⠀⠀⠻⠶⠆⢀⡿⠀⠈⠙⠛⢛⣥⡶⠟⠛⠛⠳⣄⠀⣨⣴⣿⣾⣷⣤⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣷⢿⣷⣆⠙⠧⠀⠺⣿⣦⡈⠻⠿⢦⡄⠀⢀⡠⠞⢁⣀⣤⣴⠾⠛⠉⠀⠀⣾⣀⣠⡿⢰⣿⡟⠉⠈⠙⢿⣿⠆
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠄⠈⣿⡇⠰⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⢋⠟⠋⠉⠛⠷⣄⠈⠉⠉⠀⢸⣿⣇⠀⠋⠀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠙⣿⣦⣤⣾⡿⠁⢀⣀⠉⠛⠛⢿⣿⠿⠟⠛⠛⣉⠁⠀⣴⠃⠀⠀⢠⡞⠀⠀⢹⠀⠀⠀⠀⠀⠻⢿⣷⣶⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⣾⡿⠋⠁⢀⣤⠆⠀⠈⢳⡄⠀⣴⡇⠀⢸⣿⢀⣤⣶⣤⡙⠲⠐⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⣾⠋⠁⠀⣿⠀⠿⠃⠀⠈⠁⢸⣇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠑⠀⣆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠟⠀⠀⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢞⡷⣆⡼⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡠⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⢿⣷⡄⠀⠀⠀⠀⠀⢿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⢅⠀⣹⠇⠀⠀⠀⠀⠀⢸⣿⡇⡆
⠀⠀⠀⠀⠀⠀⠐⡿⠦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⢺⣿⣿⣿⠀⠀⠉⠁⠀⠀⠠⢀⠀⠀⠀⢻⣧⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⣤⡀⠀⣡⡀⠀⠀⠙⢿⣿⣤⡀⠀⠀⣀⣀⠀⠀⠀⣀⣠⣘⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠐⠃⠀⠀⠀⠘⣳⠦⢄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⢿⣿⣦⣠⡑⠦⠀⠀⣀⣙⣿⣷⣦⣔⣟⣛⠃⢀⣾⢏⣁⡈⠉⠳⡄
⠀⠀⠰⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢼⢰⣶⠀⠀⠉⢀⣲⣶⡶⠖⠓⠒⠐⠒⠒⠺⣽⠻⣿⢛⡛⠉⠉⠙⠛⠺⠭⠭⠭⠭⣅⣘⣿⣾⣿⣿⡊⢷⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠙⠛⠁⠀⠾⠃⠰⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠆⠀⠀⠀⠠⣦⡀⠀⡀
⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠲⠦⣤⣤⣤⣤⡶⠶
⠀⠀⠘⣷⠛⠹⠟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣴⣷⣶⣶⣿⣿
⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣶⣿⠿⣟⣿⣿⣿⡿⠿⠷
⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡈⠿⠀⢀⠠⣪⣴⡿⠟⢉⠔⣿⠟⠋⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣀⠘⠤⡀⠀⠀⠀⠀⠀⠀⣀⣨⠶⣚⣵⡾⠟⢉⡀⠀⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣦⣀⠀⠁⠀⠀⠀⠉⣉⣭⡴⠿⠛⠁⠀⣶⣿⠇⠀⢸⠃⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⢀⡤⠎⠙⠀⠀⠘⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⣿⡈⠢⢤⣀⣀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢶⢆⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢧⣿⡆⠀⠀⠀⢐⣶⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⡀
⠀⢀⣞⡀⠐⢦⢻⡶⠿⣀⡀
⠀⢸⣿⡷⠶⢿⢛⡄⣴⡏⢁⣠⡀
⠀⠰⣿⣿⣷⣽⣟⣯⣸⠿⠞⠦⠉
⠀⠘⠅⠙⣦⣩⡸⣿⣏⠙⢀⠁
⠀⠀⠀⠀⡿⠹⠆⠈⠈
⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⠒⡄
⠀⠀⠠⠶⣿
⠀⠀⣦⣴⠟⠘⠃
⠀⠀⢈⠵⠂⢰⣶⡄
⠀⢠⠃⢠⠁⠘⠛⠃
⠀⠈⠀⠿⠇
⠀⢠⢀⡀⢠⡀
⠀⠘⡌⠁⠈⢤⡄
⠀⠀⠀⠘⠃⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠘⠷⠈⠁
⠀⠀⢠⡄
⠀⠀⢠⡅⢀⣠⣀⠄
⠀⠀⠐⠂⠘⢙⣿⠀⠠
⠀⠀⠀⠀⠀⠉⠀⢀⡄⠰⡄
⠀⠀⠀⠈⠀⠀⠺⠟⠁⢀⠁⠀⡀
⠀⠀⠾⠀⠀⠀⠀⠀⠀⢻⠇⠀⡄
⠀⠀⠀⠀⠠⣇⡶⣄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠗⣽⡙⠋⠀⠀⠀⣼⠃⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⡜⠯⠶⠄
⠀⠀⠀⣤⣄⠀⠀⣀⣴⣿⣿⣶⣶⣶⣶⡶⠂
⠀⠀⠀⠘⠿⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠠⠄⠀⠐⠄⠀⠀⣴⡄⠀⡄⠀⣠
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠘⠇⠀⠇⠀⠙⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢛⡿⣦⠀⠀⠀⠀⢀⠀⣼⣿⣀⢀⣾⣤⡼
⠀⠀⠀⠀⠦⡴⠀⠀⠀⢀⡀⠳⠀⠀⠀⡄⠑⠄⢩⡤⠾⠟⠋⣁⣤⣤⣤
⠀⠀⠀⠈⠛⠶⠦⠀⠀⠀⣤⠀⠀⠀⣀⠀⠐⢦⣄⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠠⠀⢀⠀⠀⠰⣦⣾⠏⠀⠀⠀⠉⠃⢀⠀⢿⠟⠛⠿⣶⠒⠒⠀⠀⠀⡀
⠀⠀⠸⣶⣾⠃⠀⢼⡿⢋⠀⣠⠀⠀⢀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⢀⡀⠘⠟⠀⣀⡀⠐⣤⠀⠀⠀⠀⠛⣿⠏⠀⠀⠀⡀⠶⠞⠋⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢁⡴⠊⠉⠁⠀⠘⠦⠀⠀⠀⠀⠈⠁⠀⠀⠰⡄⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢴⡀⢀
⠀⠀⠘⠀⠀⣴⣶⠀⠀⠀⢸⡿⠿⠿⠿⠿⠁⠀⠂⠀⠀⠀⠀⢀⠚⣼⢻⡄⠀⠀⡇⢸⠃⠙⢁⣀⣤⠄
⠀⠀⠀⠀⠀⠻⠤⠄⠀⠀⣸⠁⠀⠀⣤⡤⠀⡀⢀⡆⠀⠀⠀⠀⠣⠼⠌⠀⠀⠀⠀⠋⡠⠐⠋⠉⠏⣀⡀
⠀⠀⠠⣤⠀⠀⠀⠀⣀⠀⠿⠁⠀⠈⠛⠛⠛⣡⡾⠃⢠⡄⠀⠀⠀⠀⠀⣤⣴⡶⠓⢁⠀⢴⣶⢋⡈⢿⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⠉⠀⠈⠓⠈⠁⠈⠁⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⣤⣄⠰⣦⠁⣠⡴⣶⣶⣶⠄⠀⢠⣒⡠⢄⡀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠴⣶⡶⢹⣅⠫⠞⠋⠉⠀⠀⣀⠀⠉⠈⠓⠦⣕⠂⠤⠄⢀⣠⣔⠁
⠀⠀⠀⠀⠀⢀⣴⣪⢌⡅⢬⣻⣦⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠛⠁
⠀⠀⠀⠀⠀⣿⢟⡡⠸⢃⠠⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠀⣴⠄⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠂⠀⠀⠀⠚⠥
⠀⠀⠀⠀⠠⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣹⠿⠁
⠀⠀⠀⠀⠀⡸⠣⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⣷
⠀⠀⠀⠀⣾⢣⠁⢠⡆⢠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠙⢳⠀⠀⠸⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡀⠀⢠⣥⣤
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⣵⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠣⠁⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢨⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠷⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠂⠀⠐⠐⠆⠠⣤⣄⣀⠀⠀⠀⣄⢀⣾⣿⠀⢰⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⢀⡀⡀⠀⠀⠀⠀⠀⠤⠤⠻⣿⣿⣶⣤⣟⠚⣽⣧⣊⠀⢀⠞
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠢⢴⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡀⠀⠵⠁⠀⠀⠀⠁⠀⢀⠀⠀⠈⠙⠛⡃⠿⠟⡻⢿⣏⡐⠛
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢢⠀⠀⠥⠀⠀⠀⠀⢀⡤⠀⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣞⣵⠻⣦⠻⠷⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠩⢆⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⡋⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣻⣿⣿⣿⣿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡘⣿⡏⣼⣥⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⣿⣿⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠉⠉⠛⠿⠿⣻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢀⣴⣶⣤⣿⡿⠋⠁⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡀⣾⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣦⡸⣿⡻⣿⣿⠁⠀⣀⣴⣿⠿⠛⣽⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣿⣿⡾⣷⣶⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⢠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢟⣿⣿⣷⣿⣯⣟⡛⠛⠉⠀⠀⠘⣿⣿⣿⣿⣿⡇⢀⣠⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⢣⣿⠻⣟⣮⡙⠋⠀⠀⠀⠀⣰⣿⣿⣿⣿⢟⣊⣁⣀⠀⠀⠘⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠈⠋⠀⠙⠿⣿⣶⣦⣴⣶⣿⣿⣿⣾⣿⣿⡿⠿⢿⣿⠟⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠻⢿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢠⠔⠒⠤⡀⠀⠀⣀⣠⣦⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠈⠙⣷⢤⠀⢠⠇⠀⠀⢀⠇⠀⠀⠀⠃⠁⠀⠀⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢸⡇⠀⠀⠀⠆⡀⠀⠘⡆⢳⢸⠀⠀⣀⣴⠶⠾⠿⠿⣓⠒⠤⣤⡀⠀⠀⠃⠀⠀⠀⠢⡄⠀⣠
⠀⠀⠀⠀⣠⠴⣏⠟⣆⡀⠀⠳⣄⠀⠀⡠⠃⠀⢄⡇⢸⢏⣴⠚⢁⢀⣀⠀⠀⠀⠀⢣⠀⣀⠽⠶⢤⣀⠀⠈⠀⣀⠇⠀⠈
⠀⠀⠀⠈⠻⠭⡙⢷⣭⡽⠂⠀⠀⢩⠉⠀⠀⢀⡾⢠⡿⠛⠁⠂⠀⠋⠉⠀⢀⣀⡠⠊⢰⠁⠀⠀⠀⢹⠉⠛⠛⠡⠶⠒⢋
⠀⠀⠀⠀⠀⠘⢯⠞⢻⡲⢤⣈⣀⡜⣀⣀⣴⣯⡾⠅⠂⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢐⡋⣀⠀⠀⠀⠀⠀⡀
⠀⢠⠖⠉⠉⠑⡄⠀⠀⣷⠀⠀⠈⠉⠻⣍⠉⠀⠀⠀⠀⡌⠀⠐⠀⠿⠀⠀⠀⠀⠀⢰⠁⠀⠀⠒⠰⠟⠯⠀⠀⠀⠠⠐⠁
⠀⣞⠀⠀⠀⠂⠣⠀⢀⡏⡇⡰⠌⠃⠄⢸⡇⠀⠀⠀⠀⠐⠠⠄⠐⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠸⣄⠀⠀⠀⠀⣠⡞⠀⢸⠰⢄⣀⣠⠞
⠀⠀⠈⠙⠒⠒⢋⠁⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⡁⠀⠀⢀⡿⠈⠀⠀⣐⣀⡀
⢀⣤⡀⡀⠀⠀⠈⠒⠒⣸⡇⠀⢠⠊⠀⠀⠈⢳
⠀⠙⠙⠆⢀⣠⣤⠶⠋⡏⢇⠀⠈⠢⠀⠀⠀⢨⡇
⠀⢀⠴⠚⢩⠋⠀⠀⢸⠂⠈⢦⣀⠀⠀⢁⣠⠞
⠐⠁⠀⠀⠀⠁⠀⠀⠈⡇⠀⠀⠙⢍⠉⠉
⠀⣀⠀⡀⠄⠠⢄⠀⠀⣧⠀⠀⠀⢸⠄
⠀⠉⠐⠀⠀⠀⠀⠁⠀⢸⠀⠀⠐⠋
⠀⠀⠸⡀⠀⠀⠀⠀⢠⢟⡴⠚⠛⠢⡀
⠀⠀⠀⠉⠒⠦⠴⠒⢁⣾⠀⠀⠀⠀⢱⠀⠐
⠀⠀⠀⠀⠀⢀⣠⡴⠋⠈⠂⠄⣂⠀⡄
⠀⠀⢀⡤⠒⢁⡞⣀⡀⠀⠀⠲⣿⠛
⠀⢠⠊⢀⣄⢸
⠀⠀⠀⠀⠁⠈⢦⣴⡦
⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠏⣤⠘⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢠⠀⣠⠞⠀⠀⠂⣰⣄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⢶⣿⡄⡀⠀⠀⢿⡀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣮⠁⠀⠀⢀⡿⠀⠀⠀⢀⡈⠗⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡄⠀⣇⠷⣤⠀⠀⠨⠀⠀⠀⠀⠸⠁⣀⣁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⣾⣟⣏⢲⣿⠐⠄⠰⠀⠀⠀⠀⢠⠠⡤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢠⡟⢟⠙⠛⣅⡿⠀⠀⠀⢦⠀⠀⣰⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢸⡇⠀⠀⠀⢨⡄⣤⡿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⢸⡇⠀⠀⠀⣈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢁⣤⠬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⢰⡶⠈⡄⠪⠛⡃⣙⠀⢠⡀⠀⠀⠀⠄⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡠⡁⣶⠑⡏⠡⡘⢋⠿⢐⠙⠞⠳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠌⠀⢴⡮⠺⠇⠚⠁⠋⠠⠋⢁⡰⠦⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⡀⣴⠤⡄⠀⠁⣩⡿⠳⣦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⠊⠀⠢⠀⠀⡀⠙⠛⠳⢶⡀⠀⠸⠟⣅⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠁⢸⡷⢴⡶⣤⠙⣶⡛⠀⢀⡄⠈⠃⠀⠀⢠⠄⣴⡆⠽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠆⠀⠰⢟⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⣿⣿⡀⠈⠀⢠⠀⠀⣰⢿⡜⢿⣀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⡀⠈⠃⣀⠀⠀⠠⢠⠀⠀⠀⠀⡘⠁⠿⠛⠉⠉⠓⠴⣠⢞⣥⣾⣿⣾⣿⣷⠀⠀⠓
⠀⠀⠀⠀⢀⣔⣡⠄⠀⠀⠐⣄⠀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⠳⣷⢶⡾⡰⠆⠀⠀⠀⠀⠀⠀⣤⣛⡟⠀⠉⠈⠉⠉⠀⣤⠊
⠀⠀⠀⠀⠻⠿⠛⠀⠀⠰⣶⡌⠀⠰⠊⠀⠀⠼⠃⠐⠁⠀⣠⠋⠀⢀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⠀⢀⠸⠆
⠀⠀⠀⠀⣄⠀⠀⣀⢠⠶⠋⠀⠀⢴⠄⠀⠀⠀⠀⠀⢡⡶⠀⣠⠶⠉⠁⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡀⠀⠀⡿⠃
⠀⠀⠀⠀⢸⣉⣋⡹⠏⠀⠀⠀⠀⠘⢧⣀⣁⠂⠀⢠⡘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⡀⢡⠟⠀⣀⡠⠟⠁
⠀⠀⠀⠀⠀⠙⠈⠋⠀⠀⠀⠀⠀⠀⠀⢨⠹⢳⣦⣨⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡤⠚⢩⣵⣦⢰
⠀⠀⠀⠰⠀⠚⠉⠉⠉⢠⣄⠀⠀⢀⠰⠏⢙⣁⡉⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⢀⡅⢨⣿⠼⢦⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⢤⣉⡷⠾⣯⣼⡷⣤⡜⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠆⠛⣋⣙⠳⠻⠷⠄⠡⠂⠈⡙⠂
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠛⠲⠚⠋⡁⣐⠂⠨⠷⢴⡋⠙⠂⠙⠙⡶⠄⠀⠀⠀⠀⠀⠀⠀⣼⡆⠁⠀⠁⠉⠉⠀⠁⠀⠀⠀⠃⠀⠁⠘
⠀⠀⠀⣀⣤⠄⣎⡀⠉⢙⡂⡴⠚⣂⠐⠛⢲⠾⡀⠀⠀⢂⠤⣤⣐⣀⣼⠀⠀⠀⠀⠀⢀⡴⠂⠉⠠⠆⠀⠀⠠⠀⠠⠄⠀⣀⡀⢠⠁
⠀⠠⠂⠉⠀⡰⠀⣑⠟⢈⠁⠆⠘⠁⢶⡎⠀⠃⢁⡀⡤⠉⣧⢘⣀⡅⠸⠀⠀⠀⠀⢀⠢⠄⣸⠀⠠⠤⠤⠤⠤⠤⠤⠤
⠰⠀⡀⠀⣰⠃⣔⠉⠖⠉⠀⠀⠛⠂⠒⠠⠠⣆⠀⣄⠁⠀⢀⡜⢿⠌⢀⠦⠀⠀⠀⡜⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⢀⠀⡙⠲⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠷⠚⠂⢿⠤⠶⠌⠀⠈⠂⠰⠁
⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠡⠤⠤⠤⢀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣐⣒⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⣄⠀⣠⠄⠒⠂⠀⠀⠐⠒⠒⠈⠉⠀⠀⠀⢡⠀⢀⠖⢉⠤⠄⣉⡑⡄
⠀⠀⠀⠀⠀⢀⠤⠊⠀⢀⣤⠶⠒⠂⠘⡖⢂⠀⠀⠀⣀⣠⣀⠀⢀⡤⠶⠤⣄⠀⢸⠀⢸⠀⠇⠀⡠⠚⣉⢝⠠⢄
⠀⠀⡠⠔⠊⠁⠀⣀⠀⠸⠀⢀⣤⠤⠄⠘⡌⡄⠀⠚⠁⠀⠈⠁⠈⠀⣀⣀⡀⠀⢨⠔⠁⡸⠀⠀⢧⡞⣊⠥⠒⠉
⠀⢎⠀⠀⠀⣰⠟⠉⠁⠀⠀⠸⠁⠀⢀⡀⠘⣷⠀⢠⠶⠛⠓⠄⠀⠘⠉⠉⠉⠀⡖⠒⠊
⠀⠈⠢⡀⠀⠃⠀⣴⠞⠃⠀⠀⡀⣠⠎⢱⠀⢹⢃⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠈⡶⢄⠀⠁⠀⠀⣀⡭⠞⠁⠀⠸⠀⢸⠈⢆⠀⣠⢶⣒⠛⠿⠟⠻⠄⠸
⠀⠀⠀⢠⠀⠎⠑⠤⡀⠙⠤⣀⣀⣀⠔⠁⠀⡌⠀⠈⢦⡉⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠈⣼⡀⠀⠀⠈⠒⠤⠤⢀⣀⣀⡠⠔⠁⠀⠀⠀⠉⠢⣀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠈⠫⣁⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣈⠆
⠀⠀⠀⠀⢐⣉⡁⠬⠄⠒⠊
⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠀⠀⣠⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠤⠤⠤⠴⠒⠊⠉⠀⢀⠀⠀⠻⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡆
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠛⠛⠁⠀⠂⠀⠀⠀⠀⣴⠓⣦⠀⠀⠀⠠⠀⡊⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠆⡀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⢀⠀⠠⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⢸⡏⣛⢛⡛⡧⠀⠀⢰⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠉⠈⢰⡇⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⡀⠀⢰⡄⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡾⠃⠀⢠⠆⡆⣀⣀⣀⠀⢤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⣠⣶⣇⡀⠀⠀⠀⠀⠀⢀⣠⣴⢺⣿⡏⣿⣿⢻⣦⡀
⠀⠀⠀⣿⣿⣿⣿⣦⣀⣥⢴⣿⣿⣿⣿⣸⠿⠷⠿⠿⢼⣿⡏
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠉

⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦
⢸⣿⡿⠻⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⢣⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠙⢦⠀⠀⢸⣿
⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣀⣀⣞⢲⣶⣶⣶⣶⣶⣾⠟⠢⣀⠀⢸⣶⣶⣾⣿
⢸⣿⣿⡿⠋⠉⠙⢿⣿⠛⠛⠻⢿⣿⣿⠿⠛⠿⣿⣿⣿⠟⠉⠉⣹⣿⣿⠉⠉⠉⠉⣿⡟⠉⠀⠙⢻⣿⣷⣄⡈⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣧⠤⠤⠤⠼⡇⠀⠀⠀⢸⠿⠧⠤⠤⠤⠼⣿⣏⠀⠀⠘⡕⢨⡧⠤⠤⠤⠼⢿⡀⠀⠀⠀⢀⣿⣿⣛⡻⠿⠿⣿⣿⣿⣿
⣸⣿⣅⡠⠤⠤⠴⠂⠱⢤⢤⡤⠊⡔⠉⠉⠉⠉⣲⣨⣿⣿⣿⣛⣷⡊⡰⠒⠒⠒⢒⣤⣕⣀⣀⣀⣺⣩⠒⠒⠒⠒⠒⣆⣹⣿⣉
⡧⠤⣁⠉⡆⠀⢰⠊⣉⣉⣉⣙⣒⠒⠢⡀⠀⡎⢡⠤⠤⠤⠤⠤⠤⣍⠙⠆⠀⡎⠁⣀⡀⠤⠤⠤⢄⠈⢱⠀⠀⡰⠉⣠⠤⠤⡼
⡇⠀⢸⠀⡇⠀⡇⢰⠁⠀⠀⠀⠀⢹⠀⡇⠀⣇⢰⠀⠀⠀⠀⠀⠀⡜⢸⠀⠀⠇⢸⠁⠀⠀⠀⠀⠀⡇⡸⠀⠀⢇⢸⡁⠀⠀⢣
⠑⢄⣸⣀⣯⣷⣷⣈⡆⠀⠀⠀⠀⡎⢸⠀⠀⠸⡀⢇⠀⠀⠀⠀⢠⠃⣾⡆⠐⣾⣈⣆⡀⠀⠀⠀⡰⢡⠃⠀⠀⠘⡄⢣⠀⣀⠼
⣶⣶⡶⣷⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⠶⠒⠚⠛⠛⠓⢒⣶⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢋⠳⠕⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⣻⠞⠉
⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⣼⠋⢧⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⣤⣦⣤⣤⣤⣤⣤⣀⣀⣙⣳⣄
⠀⠀⠀⠀⣼⠃⠀⠈⢷⠟⠁⠀⠀⠀⠀⠀⣀⣤⣴⢶⠻⣿⡻⡉⠣⡀⠐⡐⡀⠡⢀⠀⠀⠐⠀⠠⠁⠇⠀⠀⠁⠉⣽⠹⡇
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⢏⣙⠌⠢⣓⣌⣿⠾⠷⠶⠶⠶⠷⠖⠒⠓⠒⠚⠒⠒⠚⠒⠶⠶⠴⠤⠥⡴⠁
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢠⣶⣟⡛⠭⢵⣲⠴⠓⠉⠁
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠸⣭⣿⠿⡽⠋⠁
⠀⠘⢦⣄⣀⠀⠀⠀⠀⠀⠀⢷⣬⣉⡃
⠀⠀⠀⠑⠿⣝⣷⣲⣶⢦⡤⣤⣿⡭⣓⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠺⠶⠷⠮⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠉⠉⠙⠛⠻⠿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠦⣤⣤⣸⣷⣤⣀⣀⣀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠛⢛⢿⠏⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠆⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠐⠀⠺⢽⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⣀⠀⠀⠀⠀⣄⡶⡀⢠⣀⠙⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠛⠋⢉⡙⠿⣿⢿⣿⣿⣿⡀⣤⠀⣰⣿⣿⣷⣿⣿⠿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢘⢿⠁⣤⠴⠒⢋⣉⣩⣝⡳⣝⣿⢿⢷⡜⠢⣿⣿⡷⢛⣁⣘⠢⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠉⠃⣨⣤⠶⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠀⡿⠿⣿⣿⠿⠟⡁⠒⠀⠀⠀⠀⠈⢻⣿⡿⠟⠛⣻⡏
⠀⠀⠀⠀⠀⣴⠟⠟⠓⠄⠙⡀⠀⠈⡆⠀⠀⡀⠄⠊⠀⣠⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡛⠿⣿⣧
⠀⠀⠀⠀⠀⢿⣇⠀⠀⢠⠀⠃⠀⢀⠧⠀⠀⠀⡀⠴⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡵⡤⡸⣿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⢀⣠⠔⢁⡠⠔⠂⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⣀⣀⠀⠀⢸⣷⡸⣿⣿⡇
⠀⠀⠀⠀⣼⣉⠙⠧⡀⢸⡿⢁⡔⠉⡗⡀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⣿⣿⣦⣼⣿⣿⣻⣿
⠀⠀⠀⣼⡟⡟⠓⠄⠘⢌⡇⣼⣀⣠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢿⣿⡟⣿⣿⡏
⠀⠀⠀⢰⣵⣇⠀⠀⠐⠪⡿⣛⣿⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣴⣋⣍⠳⡶⣻⣯⣠⡉⢷⣽⠟
⠀⠀⠀⠘⣿⣿⠀⠀⠀⢰⠳⣾⣷⣄⠈⢆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠿⠛⠛⠉⠛⢿⣾⠛⠿⣿⢟⡿⠁
⠀⠀⠀⠀⢹⣻⣦⠀⠀⢸⠀⠘⡿⣿⣷⠈⢢⡀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢤⣀⣀⣀⣘⣿⣤⣾⣿⣼⠃
⠀⠀⠀⠀⠘⣿⡽⣄⠀⡀⠃⢁⡇⢿⣧⢠⡀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⠿⣿⡿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢾⣷⣤⣿⡤⠞⠀⠘⣿⢦⣕⢤⡀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢷⣿⠉⠁⠀⠀⠈⠛⠷⣦⣤⣄⣀⠀⠀⠀⠀⡀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠿⢻⣿⠿⠿⠿⣿⡛⠛⠷⠶⢦⣤⣀⡀
⠀⠀⠀⠀⣠⣴⠾⠛⠉⡉⠀⠰⢶⠆⠙⠶⣦⣤⣤⡴⠟⠀⣳⠆⣠⠄⠉⠛⠷⣤⡀
⠀⠀⠀⣼⠏⠀⣀⣠⣤⣄⣉⡑⢒⣤⣶⢶⣿⡏⣿⣿⣶⣤⡚⠉⣠⣔⠶⣶⡲⢬⡹⣆
⠀⠀⠀⢿⣄⠻⣯⣭⣛⣉⣭⡿⠸⢿⣿⣼⣿⡇⣸⣸⣿⡿⢃⡀⠻⣤⣬⣥⣤⡾⢃⡿
⠀⠀⠀⣼⠛⢷⣤⡀⠉⠍⢡⠖⣠⠂⣩⠿⣿⣿⠿⣏⠉⡘⠪⣉⠛⠢⠀⢀⣠⣴⡿⣧
⠀⠀⠀⢿⡀⠸⣌⣙⢳⣶⣦⣤⣄⣈⣿⣷⣯⣷⣾⣿⣣⣬⣤⣬⣤⠶⣾⣿⡭⠾⢃⡿
⠀⠀⠀⠈⠻⣦⣀⣼⠟⢙⣿⣤⣿⠟⣫⡿⠿⠿⢿⣍⡉⠉⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣤⣾⣿⣥⣀⣈⠳⣤⣀⣀⣤⣼⣇⣠⣠⣤⣤⡶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡿⣿⣶⣤⣬⣍⣉⣛⣛⡛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠉⠉⢻⣿⠿⠿⠿⢿⣿⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⢷⣼⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠉⠉⠙⠛⠻⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣼⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⣶⣶⣶⣿⣤⣤⣴⣿⡿⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠩⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠉⠀⠀⠀⠀⣿⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣰⣿⡿⠋
⠀⠀⠀⠀⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣴⣿⠿⠋
⠀⠀⢀⣴⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣴⣿⡿⠛⠁
⠀⣰⣿⠋⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠁
⣸⡿⠁⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣾⡿⠟⠋
⣿⡇⠀⠀⠀⠀⢸⣿⠀⢀⣴⣿⠟⠋
⣿⣷⡀⠀⠀⠀⣸⣧⣼⡿⠋⠁
⣿⣿⣿⣦⡀⣠⣿⠿⠋
⣿⠉⠻⣿⣿⣿⣇⡀
⣟⠀⠀⠈⠙⠿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⣯⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉⠉⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣤⣤⣤⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠎⢀⡴⠀⣠⠏⡀⠀⢄⣀⠒⠦⠤⣄⣀⣀⣀⡤⠤⠀⠀⢀⣀⡠⠤⠀⠙⣆⠀⢢⡀⠑⢄⡀
⠀⠀⠀⠀⣀⠴⠋⣀⡴⠋⣠⡞⠁⠀⠉⠲⢤⣀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⢀⣠⠴⠊⠁⠈⠳⣄⠙⠦⣀⠙⠦⣄
⠀⠀⠀⠀⠀⠠⢚⣡⡴⢾⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⢤⣤⣤⣤⡤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠈⡗⢦⣌⣓⠆
⠀⠀⠖⠒⠚⠋⠉⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠉⠙⠛⠒⠒
⠀⠀⠀⠀⠀⠀⢰⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡀⠀⡆
⠀⠀⠀⢰⠀⡸⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢧⠀⡇
⠀⠀⠀⡘⡰⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢧⢡
⠀⢀⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⡀
⢀⢛⠩⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⡍⡙
⢸⢸⠀⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⠀⡇
⢸⢸⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⠀⡇
⢸⠀⠀⢁⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠸⠀⠁
⠈⠀⠀⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢸⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠻⣾⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣼⣧⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⢹⣆⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡄⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣇⢀⣀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢉⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠢⡐⠂⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⢢⠀⠀⠀⠉⠐⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢑⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠄⢖⡶⠀⠀⠀⠀⠀⠠⠊⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢴⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⢀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠔⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠔⠁
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⢀⠈⠀⠀⢀⡠⠂⠁
⠀⠀⢠⠃⠀⣠⠔⠁
⠀⠠⠁⡠⠊
⢀⠁
⣷⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⠳⡄⠐⢦⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄
⢀⣀⣠⣇⠀⢸⠇⠀⠀⠀⢰⡆⣋⢉⡀⡀⣀⠀⠀⠀⠀⢀⣀⣤⠖⠀⠀⠀⠀⠀⣤⣶⣋⣻⣟⠒⣦⡀⠀⢀⣀
⠀⠈⠉⠛⢳⣿⣦⠤⡀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣯⣤⡿⠷⣿⣉⣹⣇⣴⠿⠿
⠀⠠⢤⣄⣸⠟⢿⣀⠃⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢰⣶⡶⣶⠠
⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⢠⢠⡄⡄⣤⠀⠀⠀⠀⠀⣿⣷⣿⣷⣿⣇⠀⠀⠀⣤⣤⣤⣶⣿⣶⣄⣀
⢀⣴⢏⢞⣹⣿⣷⣦⠀⠀⠀⢸⢸⡇⡇⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠁
⠈⠻⠿⢿⣿⣿⣿⡿⠀⠀⠀⠘⡏⡇⡇⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⠿⠶⠟⢻⣝⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀
⡞⠲⠶⠤⢤⣤⣤⡤⠤⠶⣶⠒⠛⠉⠉⢻⠀⠀⠀⠀⢸⠀⠀⠀⠉⠁⠀⠀⠀⣠⣾⣿⣿⡟⠛⣿⣿⣿⣦
⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⠀⠀⠀⢀⣼⣀⣠⣤⣤⣼⣤⣄⣀⣀⠀⠀⠀⢠⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⡇
⠘⠲⠦⠤⣤⣧⣤⡤⠤⠴⠿⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠸⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⡇
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⢠⣴⡤⠀⠀⠻⣿⣿⣿⣧⣼⣿⣿⣿⡟⠁
⣠⡏⠉⡟⠉⢻⣆⠀⠀⣲⡀⠀⠀⠀⠀⢀⣰⠀⠀⠀⢹⣿⡃⠀⠈⣿⠇⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⣏
⣿⡇⠀⠀⠀⣉⣿⠀⠀⣿⠈⠙⠒⠒⠊⠁⢸⠀⠀⠀⢸⣿⠁⠀⠀⢻⠀⠀⠀⠀⠜⢹⠃⠀⠀⠈⠏⠘
⠙⢿⣷⣶⣿⡿⠋⠀⢀⣿⡀⠀⠀⠀⠀⠀⣸⡀⠀⠀⣼⣿⡆⠀⠐⣿⡆⠀⠀⠰⣦⠄⠀⠀⠀⠀⠀⢶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣠⣀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠙⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠘⢿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣟⠛⣛⣛⣛⣙⣛⣻⣛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣟⣿⣿⣿⣿⣟⣛⣿⣛⣿⣟⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠞⠁⠀⢀⣠⣤⣽⣦⠀⠀⢠⣾⣥⣤⣀⠀⠀⠙⢦⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡞⢀⣠⣾⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣦⣄⠈⡇⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣠⠴⣶⣶⣶⣦⣀⠉⠉⠉⣡⠔⡪⣉⠉⡩⢖⢤⡉⠉⠉⢁⣠⣴⣶⣶⡶⢤⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡜⠁⢀⣿⣿⣿⣿⣿⣦⠀⣰⠃⠈⠠⠘⠀⠣⠜⠀⠱⡀⢠⣾⣿⣿⣿⣿⣧⠀⠙⡆⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡃⠀⢸⣿⣿⣿⣿⣿⣿⠀⡇⢎⢉⠆⢰⣶⠰⢰⠉⡂⠁⢸⣿⣿⣿⣿⣿⣿⠀⠀⣻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⢧⠀⠘⣿⣿⣿⣿⣿⡿⠀⢳⡀⢀⠔⢌⢉⠕⢤⠉⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⢀⠏⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠑⠦⣽⣿⣿⠿⠋⠀⢀⡀⠙⠬⡒⠈⠀⠑⠊⠀⠀⣀⠀⠈⠻⠿⣿⣿⡧⠔⠋⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣇⠈⠻⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡿⠋⢀⡇⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⡀⡄⣤⢠⡄⣀⣀⠈⢢⡀⠀⠘⢆⠀⠀⠉⠛⢻⣿⢿⣳⠆⢾⣻⣿⣟⠋⠁⠀⢀⠜⠀⠀⣠⢾⡤⡤⢤⢤⣄
⠀⠀⠀⠀⣴⡞⡏⠁⠀⠀⠀⠀⢸⠀⠀⠁⠈⠉⠃⡿⠲⢤⡄⣙⠒⠶⠖⣿⢏⡀⣇⠀⠀⠀⠈⡟⠛⠸⢞⡧⣤⣞⠛⠉⠀⠀⠀⢸⡇⣹⠂
⠀⠀⠀⢸⠛⠀⢻⠀⣀⣀⡤⣶⠾⠹⠏⠛⠰⣶⠶⣧⡀⠀⠀⠉⣾⠱⠶⡧⣨⣗⡙⠘⠋⠛⡴⠳⣤⣀⠀⢨⡏⠘⠓⠛⢶⡲⠆⠾⠽⡟⡁
⠀⠀⠀⠘⢆⡠⡼⠟⠋⢹⡇⣿⠀⡀⠀⢠⠆⡟⠀⠀⢹⣦⡄⣀⡟⠀⠀⠀⠈⢸⠋⠛⠶⠰⠇⢦⢿⡟⠺⠾⣧⣠⣀⣀⢸⠀⠀⠀⢀⣧⡇
⠀⠀⠀⠀⠸⡷⣆⣤⣀⢸⡀⠈⢸⡃⠉⣹⣴⡇⣄⣶⡟⠀⠈⠁⠛⠱⢆⣤⣀⣸⠀⠀⠀⠀⠀⢸⣨⡇⠀⠀⠀⠈⠉⠑⠛⠙⠋⠛⠚⠉
⠀⠀⠀⠀⠀⢧⢸⡆⠉⠙⠓⢻⠟⠛⠛⠛⠚⡟⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠓⠰⠆⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠛⠵⣆⣤⣄⣸⡀⣀⢀⡀⣼⠳⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡏⢉⣉⣉⣉⣉⣉⣉⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢰⡶⠶⠶⠶⠶⠶⠶⢶⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⠘⣧⠀⣉⣁⣠⣤⣤⣤⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡍⣧⠸⣿⠿⠿⠿⠿⠛⠛⢻⡄⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⡆⢻⡄⢉⣀⣀⣤⣤⣤⠤⠌⢷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢻⡄⢻⣿⠿⠿⠟⠛⢛⣛⣳⡈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢷⡈⢿⡄⠉⣁⣠⣤⡤⠶⠶⠊⠻⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡘⣿⡌⢿⣾⠿⠿⠛⣛⣋⣩⣷⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢷⡀⠻⣆⠉⢀⣠⣤⠶⠖⢛⣃⣩⣷⠦⠀⠀⠀⢸⣿⣿⣿⣿⣷⡘⣿⣄⠻⣾⡿⠟⢛⣋⣩⣥⠿⠗⢈⣛⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢳⣄⠙⢷⣤⣤⠶⠾⠛⣋⣩⣥⠤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣥⡌⢹⣧⣈⠛⢛⣋⣭⣤⡶⠾⢛⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡙⠿⠟⢛⣋⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠁⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠂⠐⠈⠁



⠀⠀⡀
⠀⠀⠀⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠡


⠀⠀⠈⠀⠀⠂⢀
⠀⠀⠀⠀⣀⣀⡸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⣀⣀⡀
⠀⠀⠘⠋⠃⠀⠀⠀⠀⠲⠠⠖⠐⠀⠄⠄⠒⠺⢛⣿⠟⠛⠛⢿⡛⠛⠒⠠⠄⠖⠒⠐⠂⠐⠀⠀⡀⠠⠀⠋⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⡄⡀⠈⠉⠀⠀⠀⣄⣾⠁⠀⠀⠀⠈⢱⣄⠆⠀⠀⠈⠉⠀⡀⡎⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⡆⣠⡍⠀⠈⠉⠀⠈⠉⠀⠘⣤⢀⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠛⠒⠒⠶⠶⠦⠤⠴⠶⠶⠒⠓⠚⠒⠤
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⠶⠾⣿⣟⠛⠉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⠾⠻⢿⣟⠋⠛⢿⣄⠈⠙⢷⣄⠈⠙⢷⣄⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠙⢷⣄⠀⠙⢷⣄⠀⠙⣷⣄⣠⣽⣷⣴⠶⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣠⣤⣽⣷⡶⠶⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⢻⡿⠛⢛⣿⠟⠛⣻⡿⠛⢛⣿⠛⠛⣻⡟⠛⢻⡿⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣴⠟⠀⣠⡾⠃⢀⣼⠏⠀⣴⡟⠁⢀⣾⠋⢀⣴⡟⠁⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠇



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⠤⠶⠶⠖⠒⠛⠛⠛⠉⢉⣉⣉⣛⣲⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡒⠛⠛⠉⠉⠉⠉⠀⠀⣀⣀⣀⣠⣤⣤⠤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠉⠛⠻⢯⣝⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⡛⠶⢤⣄⡀⠰⢾⣋⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠖⠚⠛⠉⠉⣀⣀⠀⠈⠉⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡟⠓⠶⣬⣉⠓⠶⣬⣉⠓⠶⢤⣤⡤⠴⠶⠚⠛⠉⠁⠀⢀⣀⣠⡤⠶⠖⠚⠋⠉⠁⣀⣠⣤⠄⠀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠧⣄⣀⠀⠉⠙⠲⢦⣌⡙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣀⣠⡤⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⠤⣶⡞⠋
⠀⠀⠀⠀⢰⡟⠷⠦⣬⣽⣳⣦⣍⡛⠲⢤⣄⡀⠀⠉⠛⠶⢤⣌⡙⠓⠶⣤⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣠⡤⠶⢖⣚⣻⣭⣷⣶⣿⣿⣅⡀
⠀⠀⠀⠀⢸⠇⠀⢰⠶⢤⣬⣉⣙⠛⠷⠶⣬⣙⠓⠶⣤⣀⠀⠈⠉⢻⠆⠀⠉⠛⠶⣤⣄⣀⣠⣤⣴⣖⠛⢯⣭⡴⣾⣻⣵⣾⣿⣿⠿⠛⣋⣩⠴⠛⠁
⠀⠀⠀⠀⢸⣀⠀⢸⣄⣀⠀⠈⠉⠙⠓⠶⢤⣉⣙⠳⠦⣍⡛⠶⢤⣼⠀⠀⢰⠖⢦⡀⢸⣟⣊⠩⣤⣲⣾⣷⣾⣿⡿⠿⢛⣋⣥⣴⣾⡿⠟⢓⣶⠄
⠀⠀⠀⠀⠀⠉⢹⡶⢦⣍⣙⠓⠶⢤⣄⣀⠀⠀⠉⠉⠛⠚⠿⢷⣦⣄⡀⠀⠹⣤⡼⠃⠈⣿⣲⣿⣷⠿⠟⠛⣉⣠⣴⣾⣿⣿⠿⢛⣩⠴⠚⠉⣉⡶
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣬⣍⡓⠶⣤⣉⣙⠓⠦⣤⣄⡀⠀⠀⠀⢸⡋⠛⠶⣤⣀⡀⠠⡟⢉⣁⣠⣴⣶⢿⣿⣿⠿⢛⣩⠴⠚⢉⣀⣤⢶⡏⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠈⠙⠛⠶⢬⣍⡛⠷⢶⣬⣍⣛⠳⠶⢼⠇⠀⢰⡏⢹⡏⠛⣿⣛⡿⢟⣯⠿⢛⣩⡴⠞⢋⣠⣴⣞⡯⠗⣊⣽⣷
⠀⠀⠀⠀⠀⠀⢸⡗⠶⣤⣙⠳⠦⣄⣀⠀⠈⠙⠓⠶⣬⣍⡛⠿⢷⣶⣦⣤⣌⡓⠚⠁⠀⣿⠾⢛⣩⡴⠞⣋⣠⣴⡾⠟⣛⣥⣴⣾⣿⣿⠿⠟⣛⡶⠄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣉⡙⠶⢤⣉⡛⠲⢦⣄⡀⠀⠈⠉⠛⠶⢤⠉⠙⠻⠯⣽⣓⠲⠷⣚⣫⣥⣶⢿⣛⠭⣔⣾⣿⣿⣿⠿⠛⣉⡤⢶⡋⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠉⠓⠶⣬⣉⠛⠶⣬⣙⡓⠦⣤⣀⠀⢸⠀⠀⣠⠶⣄⠈⢹⡿⣝⣫⢗⣊⣥⣶⣿⠿⠟⢋⣡⠴⣞⣫⣵⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠘⠧⣄⡀⠙⠶⣤⣀⠀⠉⠙⠳⢦⣌⣙⠳⠦⣍⡙⠛⠀⠀⣿⡀⣿⠀⢸⡿⣽⣾⡿⠟⠛⣉⣤⣴⣟⣹⣶⣿⡿⣟⣿⣿⡿⠟⣙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡶⢤⣉⠙⠲⢤⣀⡀⠀⠉⠛⠲⢤⣍⡛⠲⢤⣈⡙⠁⠀⣽⠛⢉⣡⡴⣖⣿⣯⣿⢿⣻⣯⣵⣿⡿⠛⢋⣡⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢈⣿⣷⣦⣌⡙⠓⠦⣄⡀⠀⠀⢹⠀⠀⣈⣉⡓⠲⣾⣶⣿⣷⣿⢿⣻⣽⣲⣿⠿⠛⢉⣀⡴⠞⠋⠉⠛⠦⣄⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣚⠉⢹⣄⠀⠸⣇⠀⠉⠛⢿⣟⡶⣤⣉⠛⠶⢾⠀⢰⡇⠈⣷⠀⣿⣟⣫⣵⣾⣿⠟⠛⢉⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⣀⣠⡭⠿⠂
⠀⠀⠀⠀⠀⢸⡇⠈⠉⣙⣳⣾⣿⣶⣬⣛⠶⣤⣀⠈⠙⠻⠿⣿⣷⣶⣤⣄⡙⠛⠁⠀⣿⡷⠿⠋⢉⣠⡴⠞⠋⠁⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⡏⠉⠉⠛⠳⠮⣭⣙⡲⣭⣓⢦⣄⡀⠀⠉⠛⢿⠟⠿⣷⡶⢤⣿⡤⠶⠛⠉⢁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⡿⠖
⠀⠀⠀⠀⠀⠀⣧⣀⠀⠷⣤⣀⡀⠀⠀⠀⠈⠉⠛⠛⠷⢮⣽⣳⣦⣄⣸⠀⢀⣤⣝⠳⢦⣤⣴⣶⣿⣿⣿⣿⣿⣿⠿⣟⣻⡭⠟⣛⣡⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣬⣙⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠉⠛⡾⢭⣀⠸⣇⣿⠀⢸⣿⢿⡿⢻⣯⣿⠿⠷⣚⣋⡭⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣬⣉⡛⠶⢤⣄⡀⠀⠀⡇⠀⡽⠳⣿⣅⡀⢸⡿⠖⢛⣉⣥⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢮⣽⣛⡶⠃⠀⠻⣴⠇⠈⣟⠻⢟⣻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⣤⣀⣿⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢢⠰⠀⡆⠦⠰⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡆⢰⢠⠆⡄⠴
⠀⠀⠈⠀⠀⠆⡆⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠨⠘⠀⠅⡇
⠀⠀⠠⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠁⠀⠃
⢀⣠⠂⠄⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⢄
⠀⣿⣿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⡻⣻
⠀⠘⡠⢂⢋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠐⡙⢾
⠀⡀⡀⠈⡌⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠃⠃⢀⣸
⠀⠉⠘⡂⢄⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⢐⠆⠘
⣈⣉⠉⠦⠮⣀⡀⠲⠖⠩⡉⡱⠶⠀⠠⡀⡶⠊⠉⢉⣲⡆⠀⠀⢰⣖⠈⠉⠑⢦⣀⠀⠀⠶⢆⢉⠉⠲⠤⢄⢀⠱⠶⠨⣉
⠈⠁⢲⡔⠀⠉⠁⠀⢢⡄⠉⠁⠀⠐⣤⠉⠁⠀⠀⠲⡟⠀⠀⠀⠀⢻⡄⠀⠀⠈⠙⣤⠂⠀⠈⠉⠲⡔⠀⠈⠉⠀⢢⡄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⠛⠛⠛⠓⠲⠦⣄⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠚⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⣠⣧⣀⠀⠀⠙⢦⠀⠀⠀⠀⡴⠋⠀⣴⠶⠶⠶⣤⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣟⠀⠀⠈⠇⠀⠀⠈⣧⠀⠀⣼⠁⠀⠛⣿⠛⠛⠛⠛⣿⠃⠀⢻⡀⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠓⠶⢦⡀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠉⣿⣉⣉⣉⡽⠋⠁⠀⢸⡇⢈
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣇⠀⠀⢀⡿⠀⠀⢀⡟⠀⠀⢻⡀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⣼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠙⡟⠉⠁⠀⣠⠞⠀⠀⠀⠈⠳⣄⠀⠻⠀⠀⠀⠀⠀⢀⡼⠃⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠶⠚⠉⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡈⠙⠲⠦⢤⣤⣤⣤⣤⡤⠴⠖⠋⢁⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠤⠀⢀⣀⣀⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢨⠀⠀⠈⠉⠉⠉⠀⠀⠒⠂⠠⠤⠠⣄⢀⡎⠀⠉⠑⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠠⠖⣒⣒⠂⠀⢠⣤⠀⢀⣀⢠⢻⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠧⠭⢴⡄⠀⠀⣈⠭⠭⠅⠀⢸⠀⠢⣮⣂⢄⠔⡀⡀⠀⣠⣁
⠀⢃⢀⢖⠂⠤⢀⣀⠀⠀⠀⠀⢀⠌⠀⠬⠗⣒⠆⠀⠀⢀⣀⢈⡉⠁⢀⠆⠀⠀⠀⠈⠙⠪⢮⣔⠀⡗⠾⠋⠲⢤⡀
⠀⠀⠀⠈⠳⢕⡔⡠⡈⢉⠐⠒⠣⠤⢤⠿⠕⠂⠀⢄⣤⣭⢐⡂⠀⢀⢎⠄⠔⠀⠀⠀⠀⠀⠀⡨⠟⡳⣬⣋⣛⡵⡬⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠳⠥⣮⣊⣀⢔⠔⠵⢄⡠⠬⠽⡄⠈⢀⡠⠔⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠑⠡⡪⢂⢔⠥⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⠘⠛⠚⠛⠓⠈⠉⠁⠀⠀⢀⠔⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠁⠑⡪⠣⢂
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⢉⠠⠦⡼⠟⠛⠓⠒⢲⠤⠤⠤⣐⣊⣡⣔⡷⠒⠀⢈⡉⠒⠤⠤⣀⠀⠀⠀⠀⠀⠈⠓⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡘⠂⠤⠄⣀⠀⠈⠀⠀⡀⠄⣤⠍⡛⠍⠉⣂⣀⣉⣉⠉⠀⣠⠤⣺⢟⠻⠒⠀⢀⠏⡐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢀⠈⠁⠀⢀⡤⠊⠉⠀⠀⢀⣀⣀⠉⠉⠒⠒⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡄⣀⠀⠀⠈⠑⠢⠊⠀⠀⠀⢀⡠⠊⣠⡤⣍⠉⠐⠒⠤⠤⣎⡉⣩⡩⠁⢒⠀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠱⣶⠩⠲⢤⢀⠀⠀⣀⡠⠔⣉⣐⠾⠖⠂⠀⣀⡛⠍⠒⠂⢀⣽⣀⡀⠀⠒⠊⠉⣠⡤⠖⠗⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢥⣡⢢⠈⠝⡲⣖⠒⣢⠄⢀⡰⠤⢍⠑⠂⠀⢀⡤⣛⠭⠁⡤⣀⠀⢀⣾⣥⣀⡑⡀⡐⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠾⣜⡜⡻⢤⣚⣁⠊⠉⣀⣠⣤⠶⢛⠣⠁⠠⢼⡛⠀⢀⠎⠀⠐⠋⠉⢙⡒⠟⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠒⡒⠦⣀⠈⠉⠓⠚⠚⠛⠛⠛⠭⢍⣋⡀⠀⠊⠍⠒⠂⡠⠋⠀⢀⠃⣘⡚⠉⠀⢀⢫⡅⠂⢈⡷⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⡀⢤⡒⠬⡐⠬⠒⠀⣉⣲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⢊⣀⠀⠀⢸⢀⠒⠒⡄⢀⣐⠊⠀⠀⡿⣴⣩⣧⢱⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠒⢅⣈⠀⢀⠠⢄⡙⠲⣤⡤⠔⣛⣲⣤⣀⡀⠀⠀⠀⢯⠙⠒⠂⠤⠥⣀⣠⡃⠢⠼⠴⠁⢔⣒⠫⠄⠀⠇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠂⠭⠒⠌⢁⠴⠚⠛⠷⣔⡈⠈⡝⢦⡀⠀⠈⢷⡡⢂⢄⠀⡀⡀⠈⠉⢳⠀⢈⣁⠂⠉⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠙⠻⢴⣄⡇⠀⠀⠀⠉⠓⠧⢎⣔⡱⢡⠊⡸⣦⠥⠂⠉⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠂⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠾⠷⠦⠔⡪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡀⠀⠀⡀⢀⡀⡀⣀⠄⡠⠄⡀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⢀⠀⡀⢀⠄⡀⢀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠈⠒⠕⠪⠔⠝⠩⠐⠕⠨⠊⠔⠊⠔⡩⠪⠔⠀⠠⠪⠎⠥⠊⠔⠡⠎⠔⠡⠚⠵⠨⠒⠅⡪⢊⠔⡠⡢⢀⠔⠔⡠⠠⠤

⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠸⠿⠉⣿⡏⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⣀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⣰⣿⣷⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣼⡿⠃⠈⠙⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣶⣦⣄⣀⠀⣼⡿⠁⠀⢠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠈⠉⠛⠿⢿⡿⠁⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠃⠀⠀⢀⣿⡟⠀⢀⣴⣿⣷⣶⣤⣄⣀⣼⡿⠁⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣾⡟⢀⣴⡿⠟⠁⠀⠉⠙⠛⠿⠟⠁⣠⣴⣿⠟⠋⠉⠁⣀⣀⠀⠈⠉⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⣾⡿⢻⣷⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⣴⣾⠿⠃⠘⠿⣿⣦⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⢸⣿⠃⢠⣿⡿⠀⠀⠁⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⢀⣶⡿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⣿⣦⡈⠻⠿⣷⣶⣄⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⣹⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⡄⠙⣿⣇⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠘⢿⣷⣤⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⣀⡀⠀⢾⡿⠃⢀⣿⡏⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠙⢿⣷⡆⢰⣾⡿⠋⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⢻⣷⣾⡿⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⡈⠁⣀⣀⣠⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠙⢷⣦⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡿⠋
⠀⠀⠀⠀⠰⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠿⠖⠶⠶⠶⠶⠶⠿⠿⢶⣆⠀⠀⠀⠀⠀⠀⣠⡾⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡤⡄⣠⢤⡀⣤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⢤⠄⠻⡤⠇⠏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠄⠘⠇⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠛⠟⠋⢠⣄⠀⠀⠀⠀⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠘⠋⠁⠀⠀⠀⠀⠉⢠⣴⣶⣦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡶⠄⠀⠀⠀⠈⠉⠁⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢀⣤⣤⣄⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣀⠀⠀⠀⠀⣤⣤⣤⡀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣤⣤⡄⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠄⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣆⡙⠻⣿⣶⡄⠄⠀⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡐⠺⢿⣷⣤⡙⠿⠟⠂⠉⠀⠀⠀⠀⠀⠀⠁⠠⠼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢶⣶⣤⡉⠻⡿⠷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠒⢢⡙⣋⣉⡀⣀⣀⡀⢀⣀⣀⠀⣀⣀⡀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠃⣳⣿⡏⢠⣿⡟⢁⣼⡿⠁⣰⣿⡟⢀⣼⣿⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⣙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠈⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⣿⣦⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠘⠛⠛⠛⠛⢻⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠻⣷⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠸⠷⠶⠶⠾⢿⣷⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⣀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⣶⠀⠀⢸⣿⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠺⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠟

⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠐⠒⠺⠗⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠨⠷

⠀⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠤⠤⢶⠦⠀⠀⠀⠳⠤⠤⠤⢼⡦⠀⠀⠀⠤⠤⠤⠤⢾⠆⠀⠀⠀⠤⠤⠤⠤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣦⠤⠀⠀⠀⠠⠤⠤⠤⠤⡦⠀⠀⠀⠤⠤⠤⠤⢼⡦⠀⠀⠀⠤⠤⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣀⣀⣠⣀⣠⡄⠀⠀⠀⠀⠀⣀⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣀⣀⣀⣀⣄⡀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠉⠟⠀⠀⠀⠈⠉⠉⠉⠙⠛⠀⠀⠀⠉⠉⠉⠙⠁⠀⠀⠀⠀⠛⠛⠉⠹⠛⠁⠀⠀⠀⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠐⠒⠛⠂⠀⠀⠰⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠒⡺⠃⠀⠀⠀⠒⠒⠒⠒⠛

⠀⠐⠒⠒⠒⢾⠖⠀⠀⠀⠐⠒⠒⠒⣿⠶⠀⠀⠀⠐⠒⠒⠒⢚⠗⠀⠀⠀⠀⠀⠐⠒⠾⠆⠀⠀⠀⠒⠒⠒⠺⠷

⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠠⠤⠤⠤⡂⠤⠀⠀⠀⠤⠤⠤⠤⠤⡦⠀⠀⠀⠤⠤⠤⠤⣽⠆⠀⠀⠠⠤⠤⠤⢴⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠥⠀⠀⠉⠠⠔⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡄⣀⡐⣲⢦⣔⢭⣟⡣⠯⠅⣀⣠⡔⣚⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢂⠀⠐⠛⠙⠛⠋⠉⠉⠉⠉⠁⠉⠉⠈⠀⠀⠀⠈⠋⠹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣢⡋⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠪⢇⣀
⠀⠀⠀⡐⠀⠀⠀⠈⠻⢦⣄⣀⣀⠀⡀⠘⠀⠀⠀⢀⡝⠀⠀⠀⠈⠻⣆⣀⢸⡁⣆⢄⠀⠉⠓⠀⠒⠠⠄⡀
⠀⠀⠀⠈⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⢴⡿⠃⠀⠀⠀⠀⠀⠈⠛⠿⠀⠉⠛⢿⡲⣄⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠙⠻⠏⣰⣟⣧⣤⣁⠩⢵⠛⢊⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡀⠀⠀⠀⠉⠻⣷⡢⡀⠀⠀⣶⣖⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⢠⠒⠠⠠⠊⠀⠈⠳⣄⠀⠀⠀⠀⠈⠑⢽⣦⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⢀⢞⡃⠀⠀⠀⠀⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣀⠀⠀⡰⡒⣄⡀⠀⡰⠁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⢠⣀⠀⢀⡜⡄⠿⡖⠅⡼⠉⠺⢯⡡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠚⠁⠉⠛⠋⠋⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⣠⡄⢐⣵⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢁⢤⣄⣀⠀⣀⣀⡀
⠀⠀⠀⠀⣀⠔⠁⠀⣴⠏⠙⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠌⠀⠀⠆⠀⠉⠁⠀⢃⠈⠙⠻⡷⠶⢶⣦⣤
⠀⠀⢀⠜⠁⠀⢠⣾⠏⠀⠀⠘⠋⠀⠀⢀⠤⢶⡫⠭⠹⠛⠛⠋⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠰⢾⣽⣍
⠀⡰⠁⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⢠⣚⡠⠊⠁⠀⢀⡀⠠⠤⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⣠⣄⠀⠈⠻⡝⡄
⠀⢧⣀⣀⢀⢳⡿⠀⠀⠀⠀⠀⡴⣻⠋⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠂⠀⠀⣗⠇
⠀⠀⠙⠛⠿⠿⠇⠀⠀⠀⠀⠀⠘⠻⣶⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠀⢀⣠⠆⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠴⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿
⣻⣿⣿⣿⣽⣟⠾⣭⣭⡿⢟⣿⣟⠶⣿⣽⡷⣿⣿⣿⣻⣿⣿⣿⣽⣟⠾⣭⣭⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠯⣭⣯⢿⣿⣟⢮⣭⣭⣿⢟⣿⣿⢿⣿⣿⣿
⢾⣿⣿⠿⡋⢙⠿⣳⣶⣻⢿⡋⣛⢟⣿⣾⡻⠟⠉⠻⢷⣿⣿⠿⠋⠙⠿⣳⣶⣺⠿⠋⠻⢟⣾⣿⡿⠟⠉⠻⢿⣿⣿⠿⡋⢙⡿⣶⣶⡾⢟⡉⣻⢟⣶⣾⣻
⣷⢰⣿⣿⡇⣾⣿⢰⣿⢰⣿⢠⡿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠘⣿⡐⣿⡐⣿⡇⢹⣿⣷⠀⣿
⡏⢸⣿⣿⢁⣿⡇⣾⡇⣾⠇⣼⢣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⣇⢻⣇⢻⣇⢻⣿⠸⣿⣿⡄⣿
⡇⣸⣿⡟⣸⣿⢰⡿⣰⡟⣸⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⡌⣿⡜⣿⡘⣿⡆⣿⣿⡇⢻
⠃⣿⣿⢁⣿⢇⣿⢣⡿⢡⡟⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢿⡜⣷⡹⣧⢹⣷⠸⣿⣧⢸
⢸⣿⡏⣼⠏⣾⢣⡿⣱⠟⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢻⡜⣷⡹⣧⢻⣇⢻⣿⡘
⣾⡟⣼⢏⡾⣣⡟⣵⠯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡻⣌⢷⡽⣧⢻⣎⢿⣇
⣟⣼⣫⣞⡵⣫⣾⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡻⣾⢷⡻⣎⢿
⣾⣿⡿⣫⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣷⢿⣾⣿
⣛⡹⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣝⣛
⣭⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣽
⣿⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿
⣹⣽⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣹⢿⢿
⣇⣧⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⡟⡿⣾
⣿⢸⡸⡞⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣸⢱⢇⣿
⣿⡎⡇⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡟⣼⢸⡿
⢿⡇⣿⢹⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢹⡇⡏⣾⡇
⢸⣿⢸⢸⡟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⢸⡇⣿⡇
⢸⣿⢸⣇⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣸⢠⣿⢰
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⠛⠋⠉⢳⡄⠀⠀⡰⠊⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠂⠀⢇⠀⠀⠀⠀⡇⠀⡼⠁⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡜⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠘⡇⠀⣀⠀⢨⠆⠀⣤⡤⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⣿⠟⠛⠻⣿⣦⠐⠁⠈⡞⠉⣴⠶⣷⣯⣿⠶⢦⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣀⠀⣠⣿⣿⠾⠿⠿⠛⠷⠧⠤⢾⠭⠟⠤⠤⠿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠈⠻⡿⡿⠿⠛⠁⠂⠀⠐⠀⠀⠂⠀⠀⠐⠀⠀⠂⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣠⢶⡛⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣮⠉⣳⠦⣀
⠀⠀⠀⠀⣴⣯⣾⣿⡇⢸⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⣿⣿⣮⡷⡄
⠀⠀⠀⠀⣋⡿⣿⣿⡇⠸⠿⠗⢄⡀⠀⠀⠄⠀⠀⣀⡤⢞⣻⣜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢺⣿⣯⣽⡳⠿⣏⣉⣩⣩⡤⡦⢶⣺⡉⣴⡿⠟⠋⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈⠑⠳⢮⣙⡿⣿⡇
⠀⠀⠀⠀⣾⣿⣿⣿⡇⢰⣶⣶⣶⡆⢰⣿⣿⣿⡗⠁⠀⠀⠚⠃⠛⠀⠐⠢⠘⡀⢀⠂⠔⡃⠀⠂⠀⠃⠀⠀⠈⠓⢯⡅
⠀⠀⠀⠀⠑⢟⡻⢿⡇⢸⣿⣿⣿⡇⢸⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠁⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠲⢥⣜⣛⡛⢛⢃⣜⣋⡭⠵⠚⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠈⠀⠀⠀⠈⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀⢀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠨⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠉⠀⢀⠀⠐⠠⠁⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠁⣂⠑⠒⠤⢄⡀⠀⠀⠀⠀⠀⡀⠴⢿⢯⡮⠯⠁⣀⣈⣉⣩
⠀⠀⠀⠀⠀⠀⠀⠰⢂⠂⠉⡀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠀⠀⠀⢀⠀⠀⠀⠨⠁⡀⠀⠀⠀⠀⣀⡴⡚⢅⠢⠐⠁⠀⠀⠀⠀⣢⠄⠊⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⢅⣌⡢⠐⠀⠀⠀⠀⣀⣴⣿⣁⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠘⠠⣘⠀⠀⠀⠌⠸⠑⡒⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠲⡙⢕⠈⡢⠑⠀⠀⠀⠀⣀⠔⣪⠞⠃⠁⢀⡠⢖⡫
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⣢⠤⣀⠀⠀⠐⠁⠠⠁⡁⡉⠑⡐⡒⠒⢗⢖⠫⡣⢑⠄⡢⠑⠈⠀⠀⢀⠤⠒⢉⡴⠎⠀⣀⠤⣚⠥⢖⡩⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢙⠀⠀⠘⠉⠃⠢⣄⣀⡀⠁⠈⠈⠈⠢⠪⠢⢑⠵⠪⠂⠁⠀⢀⣠⠔⠊⣁⡤⠚⢉⣠⠔⣫⢕⠪⠓⠝⣩⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠵⡲⠠⠄⡄⣀⡀⠉⠓⠒⠤⢤⣀⣀⠀⠀⠀⢀⡤⠴⠊⠉⣀⠴⠊⣁⠤⢒⡩⢒⠩⡀⢁⡠⠖⠫⣂⠅⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣈⣐⡀⠀⠀⠀⠀⠈⠈⠉⠃⠒⠶⢦⢤⣌⣉⡉⠋⠀⠀⣀⠴⠊⡡⢔⣫⠕⢊⢅⠈⣀⠴⢚⠍⡂⠕⠨⣐⣬⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡵⠲⠨⠬⠭⢉⣛⣒⠒⠤⠄⣀⣀⡀⠀⠁⠁⠐⠉⠉⠙⢈⡠⠖⡩⠖⢋⡔⢈⣡⠔⠋⠕⠠⣐⠄⢲⡳⠫⢓⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡉⠁⣐⠂⠌⠉⠉⣒⠒⠦⠭⢭⢒⡲⠤⠤⠤⢖⡩⢖⣩⠴⣍⡭⡖⠋⢊⢤⡮⢖⣫⠵⣛⡭⡴⢗⣫⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠬⢁⠀⠀⠀⠈⠉⠀⠐⠀⠤⢉⣓⠒⣡⢔⣭⣤⠊⢀⣂⠔⠟⣊⡽⡚⠕⣃⠽⣊⡭⢞⢏⡥⣾
⠀⠀⠀⠀⠀⠀⠀⠀⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠠⠄⠀⣀⠀⡴⣛⠛⠁⣢⣡⡴⠖⣫⠅⠜⠐⣡⠴⠛⢁⣬⠖⣫⠃⣿⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠀⠀⠀⠒⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡾⣧⣶⡾⣫⡩⡶⢚⠡⠲⢛⠊⣀⡡⣮⡪⠖⣈⠠⡢⣿⣈⠉⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠉⠐⠒⠠⠄⣀⢀⣿⡿⣋⠬⡊⢄⠠⡀⠅⣠⣔⡼⠊⠉⠀⡢⣀⣠⠾⠛⠃⠀⠀⠀⠠⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠤⠐⠢⢄⣀⠉⠐⠠⠄⠀⣈⣀⠷⠋⡀⠔⡈⢑⣨⢴⠾⠊⠑⠈⠠⣀⡼⠚⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣄⡀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠁⠒⠀⠀⠂⠠⠤⡓⠥⢂⠡⠒⡩⡐⢁⡌⢂⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡀⠉⠀⠀⠀⠁⠀⠤⡀⠄⠀⠀⠀⠀⠤⢀⡤⠤⠔⢜⠡⡀⢁⠠⣖⣽⣞⠛⠓⠉⠉⠀⠄⠀⠀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⣀⡀⠀⠈⠉⠂⠤⠀⠀⠀⠀⠐⠀⠠⠐⢀⣀⣷⠚⠋⠀⠀⠀⢀⡀⣀⣀⣀⡂⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠈⠐⢀⡁⠂⠀⠀⢰⠘⣨⡷⠛⠉⠉⠉⠀⠀⠂⠀⠀⠀⠀⡀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠸⠿⠅⠤⠌⠭⠭⠭⠭⠍⠩⠶⣂⣂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⡄⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡜⢙⢁⣤⠤⣶⣾⣀⡴⢴⠦⣒⡨
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⡴⡶⣧⣦⠼⠃⠀⢈⡤⠐⡵⠃⠀⢙⣥⣦⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠒⠁⠀⠚⠚⠛⠛⠛⠛⠐⠁⠘⠛⠑⠊⠀⠐⢼⡇⠉⠙⠳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠢⠀⠀⢀⣴⣶⣦⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣶⣿⡏⣿⣿⡟⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣸⣿⠀⠀⠀⠤⠀⠤⠀⠠⠀⢀⣤⣴⣾⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠘⠃⣸⣤⢶⣾⣿⢹⣿⣿⣿⣿⣿⠷⠛⠋⠉⠉⠉⠙⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⣴⣿⣿⢸⣿⣿⢸⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠈⠉⠉⠉⠛⠀⠀⠉⠉⠉⠟⠀⠐⠛⠛⠺⠃⠀⠐⠒⠒⢺⠗⠀⠐⠒⠒⡿⠂⠀⠀⠒⠒⠶⠀⠀⠀⠖⠲⠗⠀⠀⠐⠒⠒⠿⠂

⠀⢠⣤⣤⣶⡄⠀⢠⣤⣤⣴⣦⠀⢠⣤⣤⣦⡄⠀⠐⣶⣤⣴⡄⠀⢰⣶⣾⣦⡄⠀⢰⣶⣶⣦⡄⠀⢰⣶⣶⣶⡄⠀⢰⣶⣶⣶⣦
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠉⠀⠀⠈⠉⠙⠁⠀⠀⠈⠉⠙⠁⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠉⠁
⠀⠀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⢠⡀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⣀
⠀⢀⠕⢕⠗⠀⠀⠀⠿⠿⠃⠀⠀⠀⢀⡽⠂⠀⠀⠀⣨⢯⡿⠂⠀⠀⡽⣪⢯⠗⠀⠀⠀⣨⠗⠀⠀⠀⠀⣸⡿⠂⠀⠀⢀⡽⣪⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⢀⣄⣤⣦⡀⠀⢰⣤⢰⣄⠀⠀⢰⣶⣤⡀⠀⠀⠀⢲⣤⣄⠀⠀⢠⣶⣄⠀⠀⠀⢠⣤⣿⣤⠀⠀⠀⢀⣤⣴⣦⠀⠀⣀⣈⠙⣷
⠀⠀⠀⠈⠋⠀⠀⠘⠁⠘⠁⠀⠀⠘⠋⠁⠀⠀⠀⠀⠛⠉⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠩⠟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠛⠛⠁
⠀⠀⠤⠀⢄⠀⠀⠀⠤⡀⢄⠀⠀⢀⣤⣤⡄⠀⠀⠀⠤⡀⠄⠀⠀⠀⠄⠀⢄⠀⠀⠀⠤⡀⢄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠠⠶⣦⡄
⠀⠘⣀⠘⡡⠀⠀⠘⣛⠟⡀⠀⠀⠘⣷⣼⠟⠀⠀⠀⢀⠚⡈⠀⠀⠘⣀⠛⡰⠀⠀⠀⣀⠜⡠⠀⠀⠘⢧⡜⠃⠀⠀⠈⣷⣆⣉⡛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⣰⣶⡄
⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠉⣿⣿⡍⠛⣿⣿⡆⠀⠀⠀⠀⢰⣿⣷⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⡀⣿⣿⡄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃
⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡟⠿⣿⣿⣆
⠀⠀⢠⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣶⣶⣆⠀⠀⣿⣿⡅⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⢀⣿⣿⣿⣿⡟⢿⣿⠇⠀⠀⠀⠀⠘⣿⣿⣦⣄⣿⣿⣄⣤⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠘⠿⠏⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⢤⣀⡤⢤⢠⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠷⡤⠘⢧⠼⠸⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠉⠻⣶⣄⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⣾⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣶⢶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣀⣀⣀⡀⠀⠀⠘⢿⣴⡿⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⠀⠀⣿⡇⠀⢸⣿⠀⠀⣴⡶⠶⣶⡆⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠶⠾⠿⣶⣶⡿⠷⠶⢾⣿⡀⠀⣿⣧⣴⡾⠿⠶⣶⣿⡀⠀⢸⣧⣴⠶⠿⠶⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢀⣾⠟⠁⣀⣴⣦⣄⡈⠻⣦⣿⠋⠀⣠⣴⣶⣄⠉⢻⣦⡿⠋⣀⡀⠀⢀⣄⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⣿⡇⠀⠰⣿⣹⣏⡉⠀⠀⢹⡇⠠⣾⣿⡦⠀⠉⠁⠀⢻⡇⠀⠈⣿⣤⣿⠃⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣄⣿⡇⠀⠀⠉⣻⣟⣿⠄⠀⣸⡇⠰⢿⣷⠶⠀⣀⠀⠀⣼⡇⠀⠀⣹⣿⣏⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⠉⠉⢿⣄⠘⠛⠻⠟⠋⢀⣰⡿⢷⣄⠈⠛⠷⠾⠟⢁⣴⠿⣷⡀⠀⠉⠿⠉⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣶⣶⣶⣿⣿⣶⣶⣶⠶⠟⠋⠀⠈⠙⠷⢶⣶⣶⠶⠟⠁⠀⠈⠛⠷⢶⣶⡶⠾⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢠⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣦⣄
⠀⠀⠀⠀⣿⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣿⡇⠙⢿⣷⣄
⠀⠀⠀⠀⣿⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⡇⠀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⣿⣿⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⣿⣇⠀⠀⠀⠀⠈⠻⢿⣦⣄
⠀⠀⠀⠀⣿⣿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣷
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⣿⣿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⢀⡐⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡙⢿⡿⠋
⠀⠀⠀⠀⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⣿⣿⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⣿⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⣿⣿⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠻⣿⣿⣿⣿⠟⠀⠀⣠
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣌⠻⠟⠁⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⢿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣻⣛⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠛⠻⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⢹⣿⣧⣀⣠⣿⡿⠿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣿⣿⠟⠛⢿⣿⣅⠀⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠈⣿⣿⡇⠀⠀⠀⣿⣿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⣷⣤⣤⣴⣿⣿⡀⢀⣼⣿⣶⡶⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠐⣿⣿⣿⡏⠀⠈⣿⣿⠋⠉⢻⣿⣿⣿⣇⣠⣿⣦⣼⡟⠻⣦
⠀⠀⠀⠀⢀⠀⢰⣶⣷⡄⠈⢿⣷⡄⠈⢿⠿⣿⣶⣾⣿⣿⣦⣤⣾⣿⣿⣏⢉⣿⡇⠀⢸⡿⠛⣿⠄
⠀⠀⠀⠀⠘⣧⢀⣿⣿⣿⡄⠈⠛⠉⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠘⢿⣿⠛⣿⡟⠻⣿⣶⡟
⠀⠀⠀⠀⠀⢹⡿⣿⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⠀⢸⣿⠀⠈⠛⠿⣿⣷⡾⠿⠋
⠀⠀⠀⠀⠀⢸⡟⢃⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⣸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣁⣀⣀⣀⣠⡇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣶⣾⣿⢢⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⣿⣿⣿⡟⢼⠿⢟⡛⠃⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣷⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠶⠶⠶⠖⠒⠀⠀⠐⠖⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠖⠲⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠁⠉⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇





⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣵⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⣿⠉⠉⢹⠉⠉⢹⡏⠉⢹⡏⠉⠉⡏⠉⠉⡏⠉⠉⣿⠉⠉⣿⠉⠉⢹⠉⠉⢹⡋⠉⢹⡏⠉⢹⡏⠉⠉⡏⠉⠉⣿
⠀⠀⣿⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⣿
⠀⠀⣿⠀⠀⢸⣀⣀⣸⡇⠀⢸⣇⣀⣀⡇⠀⠀⣇⣀⣀⣿⠀⠀⣿⣀⣀⣸⠀⠀⢸⣃⣀⣸⡇⠀⢸⣇⣀⣀⡇⠀⠀⣿
⠀⠀⢻⣄⣀⣼⠋⠉⠹⣇⣀⣸⠏⠉⠙⣧⣀⣠⡟⠉⠉⢿⣀⣀⡿⠉⠉⢻⣄⣀⣼⠋⠉⠹⣇⣀⣸⠏⠉⠙⣧⣀⣠⡟
⠀⠀⣾⠈⠉⣦⠀⠀⠀⠈⢉⡅⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢨⡉⠁⠀⠀⠀⣴⠉⠁⣷
⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⣿⠀⠀⡇⠀⡖⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢲⠀⢸⠀⠀⣿
⠀⠀⣿⠀⢸⡇⢠⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡄⢸⡇⠀⣿
⠀⠀⣿⠀⣼⠁⣼⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣧⠈⣧⠀⣿
⠀⠀⣿⢀⡟⢰⠏⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠹⡆⢻⡀⣿
⠀⠀⣿⣸⢣⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣜⣇⣿
⠀⠀⣿⣉⣉⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣉⣿
⠀⠀⣿⠀⣧⢿⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡿⣼⠀⣿
⠀⠀⣿⠀⢹⡎⢷⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡾⢱⡏⠀⣿
⠀⠀⣿⠀⠈⡇⢸⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⡇⢸⠁⠀⣿
⠀⠀⣿⠀⠀⡇⠈⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠁⢸⠀⠀⣿
⠀⠀⣿⣀⣀⣃⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣘⣀⣀⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣀⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀
⠀⠀⠀⢸⣯⣿⣽⣏⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⡷⠆⠐⠀⠈⠀⠦
⠀⠀⠐⠋⠛⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡠⡤⠤⡄⢠⡀
⠀⠀⠰⡭⠡⠤⠈⠤⢩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⡇⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈

⠀⠀⠀⠲⣶⣶⣶⣦⣦⣄
⠀⠀⠐⠀⣨⣭⣭⣭⣭⣭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠠⠀⠂
⠀⠀⠀⠚⠋⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣤⢤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠀⣀
⠀⠀⠘⣟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢨⠂⠀⠀⠄⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠐⢒⡀⠀⠦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⠀⠠⠄⣀
⠀⠀⠘⠛⢛⣛⣓⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠗⠀⠀⠀⠄⠀⠛
⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⢠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢳⠔⠀⠀⠤⣀
⠀⠀⠙⠷⠾⠷⠾⠶⠷⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⣰⠆⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢛⣭⣵⣶⣶⣶⣮⣭⡛⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⣰⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⢰⣿⣿⡟⣴⣿⣿⣿⣿⢟⣭⢀⣭⠻⣿⣿⣿⣿⣧⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣾⣿⣿⢱⣿⣿⣿⣿⣿⡸⣿⢌⣿⣷⣿⣿⣿⣿⣿⡎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⢠⣭⠻⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⢻⣿⣿⡜⣿⣿⣿⣿⣿⡹⣿⣔⣿⢇⣿⣿⣿⣿⣿⢡⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠈⢿⣿⣿⡜⢿⣿⣿⣿⣿⣶⣀⣶⣿⣿⣿⣿⡿⢣⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣧⠤⠤⣶
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣭⣭⣭⣭⣭⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏
⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⢀⡞⠁⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣄
⠀⠀⢠⡯⠤⠤⡶⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⣫⣴⣾⣿⣿⣿⣿⣷⣮⣝⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣡⣿⣿⣿⣿⠿⣛⣛⡻⢿⣿⣿⣷⣝⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣰⣿⣿⣿⡿⢡⣾⣿⣿⣿⣦⣿⣿⣿⣿⡎⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣶⠆⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⡿⠂⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡹⣿⣿⣿⣷⣜⢿⣿⣿⣿⢟⣽⣿⣿⣿⢃⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡝⢿⣿⣿⣿⣷⣶⣵⣶⣿⣿⣿⡿⣣⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣝⡻⠿⣿⣿⣿⡿⠿⢛⣭⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠆⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠟⠛⠋⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢰⣾⢶⣸⡀⢷⢾⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣴⣿⣿⠇⣿⣿⣷⣤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣙⠛⠉⠀⠈⠙⢛⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠰⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢛⣡⣤⣄⠀⢀⣤⣤⡙⠛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠻⢿⣿⡇⣿⣿⠿⠛⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠔⠂⠀⣸⠀⢀⣑⠠⢀⣀⢏⠍⠉⣙⠒⠦⠎⣉⣈⡵
⠀⠀⠀⠀⠀⡃⠀⡉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⣉⣙⢣⢀⣆⣠⠓⠰⠄⣈⡁⠀⢸⠉⠓⠂⠤⠄⠔
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡰⠁⠀⠀⠁⠀⠐⠀⠀⣀⣀⠀⠀⠣⠄⣏⠀⠼⠀⠀⠀⠀⠀⠈⠉⡁
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⡖⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⢶⣿⡦⠄⠈⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⢀⡐⠀⠃⠀⠀⣀⠋⢠⡁⠘⢂⠂⡀⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠈⠻⠿⠟⠂⠀⢀⣀⣤⠀⣰⣶⡟⢀⣾⡇⠀⠀⠀⠀⠄⠐⡄⠀⠀⣀⠀⠀⠀⡀⠠⠠⠐⡄⡂
⠀⠀⠀⠀⠀⢶⣿⣿⣟⣛⣥⠀⣰⣶⡟⢀⣾⣿⣧⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⡦⠀⠄⠠⠀⠀⣀⠀⢀⠀⠀⡥⡤⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡘
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠁⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⢻⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⢸⡇⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠈⣧⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢻⡄⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⡇⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠁





⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⡠⠤⠒⢶⠖⢳⡄⡠⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠑⡄⠀⠀⢨⠀⢎⠀⠀⢠⠏⢠⢊⠞⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠘⡄⠀⠘⡄⢸⠀⠀⠸⣀⡷⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣀⣠⣄⣀⠀⢹⠀⣰⠁⢸⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⢟⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠉⠲⢄⡠⠴⢺⠁⠀⠀⠀⠀⣠⡶⠖⠒⠀⠈⠀⠀⣠⡶⠶⠖⠀⠘⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠀⠑⢤⡚⠣⡀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣤⠞⠋⠀⠀⠀⠙⢦⡑⣄⠀⠀⠀⢠⡾⠛⠙⠁⠀⠀⢀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠃⠀⠀⣴⠞⠋⠀⠀⠙⢮⡦⡀⠀⠋⠀⠀⠀⠀⠀⠒⣋⣤⠔⣛⡻⠆⠀⡇
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⠀⠐⡏⠀⠀⠀⣰⢄⠀⠑⣞⢦⡀⠀⠀⠀⢀⡴⢟⡭⠖⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠒⠦⣄
⠀⠀⠀⡴⠃⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⢀⢀⡏⠀⢣⠀⠘⡄⠙⢦⡀⠀⢿⠞⠁⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡴⠻⡀⠹⡄⠀⠀⠀⠀⠑⡄
⠀⢀⠎⠀⠀⠀⠀⡟⠀⠀⣠⡶⠒⠀⠀⢀⢄⡾⠁⠀⠀⡆⠀⠰⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡘⠀⠀⠹⡄⠙⣄⠀⠀⠀⠀⢸
⠀⠘⢄⠀⠀⠀⠀⠇⠀⠀⣿⠁⠀⠀⠀⣡⠞⠁⠀⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠁⠀⠀⠀⠀⣠⣖⠉⡆⠀⠀⠘⣄⠘⢆⠀⠀⠀⡸
⠀⠀⠀⠉⠒⠤⣄⣀⡀⠀⠁⠀⠀⢠⣞⣁⣀⣀⣀⠴⠃⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠈⢆⠘⢆⠀⠀⠈⢦⠈⠳⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠉⣑⠂⠤⢄⣀⣀⠈⠀⠈⣀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⢢⣈⣳⣀⣀⣀⡳⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡀⡿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⣀⠀⠀⠀⠀⠀⣀⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⣄⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡤⢚⣥⡮⡓⢄⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠤⠤⠀⣈⣣⠀⠀⠀⠀⠀⢀⡠⢎⠀⡠⢒⢥⡺⣟⠥⣊⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⡩⠋⠀⠀⢀⡠⠖⠉⠀⠈⢦⠻⣅⠛⣊⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠁⡠⠖⠉⠀⠀⣠⠴⠉⠀⠀⠀⢀⡠⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠋⠀⠀⣀⠴⠊⠙⢄⠱⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁


⣿⢿⠿⠿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠋⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⣡⠀⣤⣬⣽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⢀⣀⣿⣿⣿⣷⣄⡉⠀⠻⠿⣿⣿⣿⣿⡇⠀⠀⢀⠶⡀⠀⠀⠀⡎⠀⠀⠘⡄
⠒⠒⠒⠒⣄⡴⠒⠒⠒⠋⠀⠘⣄⡴⠒⠋⠈⣿⣿⣿⣿⣿⣿⠀⣶⡄⠈⣿⣿⣿⡟⢆⢀⠎⠀⠙⠒⡄⡸⠀⠀⠀⠀⠘⠒⠒⠒
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣧⣭⣍⠀⣩⣤⣶⣿⣿⡟⠀⠘⠎⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉







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

⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠶⠶⣿⣿⡷⠆⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠠⠶⢾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⡤⣤⣤⢤⡤⣼⣦⡀⠀⠀⢶⣶⣾⣿⣦⠀⠀⢀⡀⠀⠐⢤⣄⡀⠀⠀⣀⣀⣀⣀⣸⣦⣄⡀
⠀⠀⣿⣟⣿⣿⣸⣟⣟⣿⡿⠂⠀⣨⣿⣿⣿⣿⠇⠀⢸⠿⠃⠀⣀⡽⠿⠓⠀⠿⠿⠿⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠋⠙⠹⠿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⡀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠤⠤⠀⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠒⠂⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⢁⣀⣤⠤⢴⣖⣿⣿⣟⠛⠙⠛⠛⠛⠻⠿⣻⣷⣶⣶⣦⣤⣤⣀⣈⠁⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⣤⣶⣿⠭⠥⠒⣋⣴⢡⣿⣿⣿⣟⡒⠒⠒⠒⠊⠉⠭⣿⣿⡙⠛⡇⠙⣿⡻⠿⠷⢦⣤⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣠⣾⣿⣿⣏⡙⠛⣛⡫⠝⡡⠻⣿⣯⡫⣈⠉⠑⠒⠂⠈⢑⡿⢟⣿⣷⣄⠙⠦⣈⠉⠙⠛⢋⣹⣿⡄⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⣰⣿⢿⣷⣼⣯⣬⣭⣥⡔⠋⠀⠀⠙⢿⣷⠄⣈⣉⠉⠂⠈⡡⠴⣿⠟⠁⠀⠙⠦⢄⣉⠉⠉⢈⣁⣽⣿⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡯⣿⢺⠇⠀⣄⠐⢸⠟⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠀⠀⠰⠒⠊⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⣯⣿⠛⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡿⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡟⢻⠏⣿⠀⠻⢻
⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⡗⢄⠀⢀⡿⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⡇⢸⠀⠈⡇⠀⡇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠃⢸⠀⡿⠀⠂⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠇⣿⠀⢸⡇⢀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢠⠀⢠⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢸⢿⠀⣿⠀⣼⠀⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠀⢸⢸
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⣿⢀⡿⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⡄⠈⡀⢸⣸
⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⢠⡟⢸⡇⢰⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇⢠⡇⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⢸⠁⣼⢀⡏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⢱⠘⡇⣦⢻⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣾⢀⡇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡀⣇⢹⣼⠃
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣷⣾⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⢺⣟⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢿⡇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢸⡇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⣷⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⡀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠋⠉⠁⠈⠁⠈⠉⠉⠋⠉⠉⠙⠉⠁⠉⠁⠉⠉⠉⠸⠀⠀⣸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⢠⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣿⣿⠀⡄
⠀⠀⠀⠀⠀⠤⠠⢦⠼⠿⠘⠛⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠙⢻⣤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⡀⢐⠀⠀⠀⡐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠣⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠘⢄
⠀⠀⠀⢀⠤⠊⠁⠦⠀⠀⠀⠀⠀⠠⡀⠀⢀⠄⠀⠤⠄⠄⠀⠼⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⡀⠀⠀⠀⣈⢢
⠀⠠⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠄⠀⠀⢀⠀⠄⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠢⡀⠀⠤⠤⠤⠤⠤⠤⠤⠃⠀⠘⠤⠤⠤⠤⠤⠤⢤⠀⢀⠄⠊⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⣠⣴⣿⣿⣷⣶⣶⣶⣶⣶⣶⡄⠀⢠⣶⣤⣦⣤⣴⣶⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⠿⠷
⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⢤⣤⣿⣿⣿⣿⣦⡤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠈⠛⢿⣿⡟⠛⠛⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣇⣀⣀⡀
⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠛⠛⠛⠉⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉⠉⠛⠛⠋
⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢀⣾⣿⣿⡟⠁⣀⡈⢙⣿⣿⣿⡄⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⡀⠙⢿⡿⠁⣨⣿⣿⣆
⣴⡄⢸⣿⣿⣿⣧⣀⠉⠛⠿⣿⣿⣿⣷⢠⣤⡀⠀⠀⣾⣿⣿⡇⠀⠀⣠⣤⢰⣿⣿⡟⠛⠀⠈⠀⠐⠛⢿⣿⣿⠀⣤
⣿⣿⠸⣿⣿⣿⡋⠛⠿⠇⠀⣿⣿⣿⡟⢸⣿⠃⠀⠀⣿⣿⣿⡇⠀⠀⢻⣿⠈⣿⣿⡷⠶⠶⠀⠰⠶⠶⢿⣿⡿⢰⣿
⠘⣿⣆⠹⣿⣿⣷⣦⡀⣠⣾⣿⣿⡟⣡⣿⡏⠀⠀⠀⣿⣿⣿⡇⠀⠀⠈⣿⣧⡙⣿⣷⣶⣶⡀⢠⣶⣶⣾⡿⢁⣾⡿
⠀⠘⢿⣷⣌⡛⠿⠿⣿⡿⠿⠛⣩⣴⣿⠋⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⢻⣷⣬⡙⠻⠿⣿⡿⠿⠟⣋⣴⣿⠟
⠀⠀⠀⠙⠻⢿⣷⣶⣶⣶⣾⡿⠿⠋⠀⠀⣠⣤⣤⣤⣿⣿⣿⣧⣤⣤⣤⡀⠀⠈⠛⠿⣷⣶⣶⣶⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣾⣷⡄⣶⣷⡆⠀⠀⠀⠀⠀⠀⢠⣎⣏⢳⣰⣩⣍⡆⠀⠀⠀⠀⢠⣾⣿⣦⣠⣾⣿⣦⠀⠀⠀⠀⠀⡴⣴⢦⣠⢶⣶⡄
⠈⣻⣟⣁⣙⣟⡁⠀⣀⠀⠀⠀⠀⠈⠳⣷⣊⣘⣾⡷⠃⠀⠀⠀⠀⠸⢿⣿⠟⠹⢿⣿⠟⠀⠀⠀⠀⠀⣫⣿⣝⣘⣩⣯⠃
⡇⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣶⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿
⠀⠙⢻⣿⣿⠛⠁⠀⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠃⠈⠁⠀⠀⠀⠀⠀⠛⢿⣿⠟⠋⠉⠛⠀⠀⠀⠈⢛⣛⣛⣛⣛⡛⠋⠉⠙
⠀⠀⣼⢿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡁
⠀⠰⠃⠸⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠘⠇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠇⠳

⠀⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⣀⣤⣀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⣠⣤⣤⣶⡖⡄
⠀⠀⠀⠀⠀⢸⣇⢀⣽⠇⠀⠀⠀⣰⣾⣶⣸⣿⣿⣿⡷⠀⠀⠀⡾⢧⡿⡼⢳⣸⢳⡾⣶⢻⡄⠀⠀⠀⣿⣿⣿⣿⡇⡆
⡶⠒⢲⡒⠒⣦⣿⣿⡇⠀⠀⠀⠀⠘⣛⣋⣈⣛⣛⡛⠁⠀⠀⠀⠹⣏⣻⣿⣾⣾⣾⡝⣩⠟⠀⠀⠀⠀⢻⣿⣚⣿⡯⠄⠀⣠⣄
⣇⣀⣻⣇⣀⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⠀⠀⣿⣿⣿⣿⣧⣿⣾⡇⢘
⠉⠉⠉⠉⠉⠁⠻⠿⠃⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠁⠈⠉⠀⠀⠀⠀⠀⠉⠭⠽⠉⠁⠀⠈⠉⠉⠀⠀⠿⠿⠿⠿⠧⠍⠉⠳⠞

⢀⣀⣀⣀⣀⣀
⠈⢫⣯⣉⠉⠙⣷⠀⠀⠀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠴⠶⠦⠀⠰⠷⠶⠶⣶⣀⣀⢀⠀⠀⠀⠀⠰⡶⢶⣦⡀⣀⡀⣠⣤⣤⣤
⠀⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⢸⡏⣶⣶⣶⢹⣿⣷⣶⣿⠀⠀⠀⡞⣿⣽⣭⣭⣽⣧⣤⣴⡆⠀⠀⣿⣿⣿⣿⣿⣿⣶⣾⡇
⠰⠤⣟⠙⠛⠛⠛⠛⠉⠉⠛⠀⠀⠘⢳⣶⣶⣶⠞⠋⠁⠀⠉⠀⠀⠀⠣⢿⣭⣭⣭⣽⠟⠉⠙⠇⠀⠀⠛⣺⣿⣗⠛⠉⠁⠉⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣠⠖⠉⠈⠉⠁

⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⣶⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⡦⣿⣿⣯⣤⣤⣤⣤⣴⣶⣿⡅⠀⠀⢸⡏⣭⣯⡍⣿⣶⣦⣤⡆⠀⣶⠆⣿⣿⠿⣿⣿⣧⢠⣴⡆⠀⠿⠿⣿⣗⣾⣷⣶⡄⣀⣤
⠀⣿⣿⡟⠛⠛⠛⠟⠿⣿⣿⡃⠀⠀⠘⠷⢿⣿⣷⣿⠿⠟⠙⠃⠀⠀⠀⠿⣿⣶⣿⣿⠿⠘⠻⠇⠀⠀⠸⣿⣿⣿⣿⣿⡇⠿⣿

⠀⠀⠀⠀⠀⠀⢀⣼⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⣠⠟⠁⣿⣿⡏⠀⠀⠀⣀⣀⣤⠤⠤⠴⠶⠖⠒⠒⠒⠛⢻⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠢⡀
⠀⠀⠀⣠⡾⠁⠀⢸⣿⣿⡧⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣀⣀⠀⠀⡠⠋⠀⠀⢀⣴⡾
⠀⢀⡼⠋⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⢸⠉⠻⠷⠊⠀⠀⢀⣴⠟⠁
⡴⣿⣅⠀⠀⠀⠀⢠⣶⣿⡋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠷⠶⠶⣶⣶⣶⠿⠛⠁⠀⢸⠁⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠉⠛⠶⣄⡀⠀⢷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣀⣀⣀⠀⠰⢶⣧
⠀⠀⠀⣀⣀⣀⣉⠓⢮⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋
⠀⡴⠋⠉⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣗⠢⠄⣀
⠰⡇⠀⠀⣀⣀⡀⠀⠀⠙⢦⣀⡀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢧⣾⠆⠀⠀⠈⠉⠒⠢⢤⣄
⠀⣇⣴⣿⣿⣽⠿⠷⢄⠀⠈⠓⠾⠚⠁⠀⠀⢀⡖⠻⣟⣲⣄⠀⠀⠙⢦⣀⡀⠀⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠉⠻⠿⠋⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡞⢾⡞⠉⠁⠉⠑⡄⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⠀⠀⣠⣞⣷⠟⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣠⣞⢧⠀⡠⠊
⠘⣷⣶⡤⢤⣤⣄⣀⣀⣀⣀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⠤⠚⠁⠈⠛⠋
⠀⠘⣎⠋⠄⠀⠀⠀⠉⠉⣹⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⠿⣷⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠽⠛⡟⢲⣦⠄
⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠶⠶⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⢿⢸⣿
⠀⠀⠀⠀⢌⣦⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠈⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡀⠀⠀⣀⣤⠴⠶⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠿⠋⠁⣠⠞⠋⠀⠀⣀⣀⣀⡀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣴⠟⠋⠉⠉⠛⠆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠴⣾⡷⠶⠶⠶⠆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢻⣟⠛⠛⠛⠃⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠙⢷⣤⣤⣤⡶⠆⠀⣠⡟
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⢀⣠⡾⠋⠀⡄
⠀⠀⠀⠀⠀⠀⠘⠀⣠⠾⠋⠁⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢰⡟⠛⠛⢷⠄⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸⣇⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⣿⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣼⣯⣤⣄⣀⣤⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠉⠁⠈⠉⠉⠁⣠⡴⠋⢀⣠⣶⣠⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠖⠛⠉⠀⠀⠈⠛⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⡆⠀⣀⣴⡿⣟⡉⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡿⢫⣾⣿⣿⣦⡀⢰⣿⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⣠⣶⣮⣿⣿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣭⣄⣀⣀⣀⣰⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣠⣤⣶⣶⡽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢹⣿⣇⣤⢸⣿⣿⣦⣤⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⠏
⠀⢀⣴⣾⠟⠛⠉⠁⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⢀⣠⣿⣿⡾⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣉⣻⣿⡟
⢰⣿⠋⠀⠀⠀⠀⢀⣀⣀⣀⠀⠙⠿⣿⣿⣶⣾⣿⣿⢟⣾⠀⠀⠈⣿⣟⣁⡀⠀⠀⠈⢻⣿⣿⣿⣿⢿⣤⣄⣀
⠘⠿⣷⣶⣶⠾⠿⠛⠛⠛⠻⢿⣦⡀⠀⠉⠙⠛⠉⠁⠈⢿⣧⡀⠀⠘⣿⣿⣿⣷⣦⣄⡀⣿⣿⠿⠃⠀⠉⠙⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠈⠻⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣠⣴⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣤⣤⣴⡖

⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⡿⣿⢿⡿⣿⣿⡿⣿⡿⣿⢿⣿⢿⣿⢿⣿⣿⣿⢿⣿⡿⣿⡿⣿⣿⣿⣿⣿⡿
⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣾⣿⣾⣿⣿⣾⣿⣿⣷⣿⣾⣷⣿⣿⣷⣿⣷⣿⣶⣿⣾⣿⣾⣿⣿⣿⣾⣿⣷⣿⣷⣿⣷⣿⣷⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠬⠽⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣛⣛⣛⣻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣓⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣤⣴⣶⣶⣦⣭⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿
⣿⡿⣿⣸⣾⢸⢫⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⢸⣾⢸⡿⣿
⣿⣧⡇⣯⣇⡟⣼⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⡏⠟⡏⠿⢻⢻⢹⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⢷⢸⡇⡟⡏⡇⣿
⣿⣿⢷⣹⣹⢱⣿⣱⣿⣿⣿⣿⣿⣿⡿⣿⢻⠃⡇⢸⠀⡇⠀⡇⠀⢸⠸⠘⡇⠃⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⡜⣇⣧⣇⣇⣿⣿
⣿⣿⡿⣿⢧⣿⣷⣿⣿⣿⣿⣿⣿⡿⠇⢻⢸⠀⠃⠘⠀⠁⠀⠀⠀⠘⠀⠀⠃⠀⠀⢸⢸⡏⣿⣿⣿⣿⣿⣿⣿⣽⣽⣹⢿⢹⣿
⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⣿
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⣿⣿⡿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⣿
⣿⣿⣇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣧⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠃⠚⠘⠐⠃⠘⠚⠃⠃⠃⠘⠘⠐⠚⠂⠃⠛⠘⠀⠃⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣼⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⡏⠩⣍⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢓⡿⠋⠁⠀⠀⠈⢳⠜⣧⡄⣀⢤⡔⠶⡖⠊⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠁⠐⠀⠀⠀⠀⠀⢧⠾⠷⠟⠓⠛⠉⠉⠻⡤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣿⡿⠿⠔⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠺⢳⣿⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠐⣿⣿⠀⡄⠹⢶⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠘⠣⢤⣁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠀⣀⣀⠈⠳⣜
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡀⠆⠀⠀⡍⡇⡇⡀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠂⠇⠀⠀⠀⠀⠁⠇⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⡀⡀⣀⣠⣀⣀⣤⢀⣦⣴⢤⣦⣶⣶⣾⢾⣳⣖⣙⣿⠡⢍⡢⠀⠀⠸⠀⢰⢮⠰⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢟⣄⣤⣦⣴⣶⣷⣻⣶⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡓⢤⣀⠅⡘⠹⠸⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠉⠙⠻⠛⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣑⠾⣢⡄⠰⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠟⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⣶⣽⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠰⠶⠠⠖⠀⠀⠒⣚⣘⣂⣉⣀⣋⡿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠁⡈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⡀⠀⢀
⠀⠀⠀⠀⠀⢠⠠⠂⡄⠀⠀⢀⠀⠀⠀⠠⠉⢁⡶⠂⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠰⠈⠆⠀⠀⠐⢀⠂⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠂⢃⠀⠀⠈⣀⠀⠀⠐⢄⠘⠋⠀⠀⠀⠀⠀⠂⠀⠀⢱⠀⠒⠀⠀⠸⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠞⠀⣴⠁⠀⠀⠀⠈⠓⢄⠀⠀⢀⡤⠂⠀⠀⠀⠀⡀⢁⢠⡀⠄⢀⠀⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠁⠠⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠈⠀⠠⠀⠂⢰⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠐⠒⠶⢶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠗⠳⣿⣶⠒⠀⠀⠒⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠛⠛⠿⠿⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀
⠀⠈⠛⠲⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⠿⠿⠿⠟⠛⠁⠈⠳⠟⠁⠈⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠠⢄⣠⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣾⣿⣿⣟⠁⠀⠀⠠⢤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⣿⣿⣿⣿⡋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠃⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠠⢤⣴⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢶⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣚⠁⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠒⠻⠝⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⡂⡐⠀⠀⠠⠆⠀⠂⠸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢗⣟⣿⡓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣁⠐⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠂⣌⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣦⣤⣘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠉⠉⠛⢻⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣿⣷⣦⣤⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣁⣀⠀⠀⠀⣈⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠙⠛⠻⠿⣿⣿⡷⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣦⣤⣀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⠁⠀⠈⠙⠛⣿⡿⠛⠁⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠖⠲⣾⣿⣯⡀⢸⡀
⠀⠀⠀⠀⠀⣠⣤⣔⠻⠿⣿⣿⣶⣶⣤⠶⠛⣁⣀⡠⢤⣴⣶⣖⠉⠉⠉⠻⣿⣿⣦⡀⠀⠈⠛⢿⣿⣦⡇
⠀⠀⠀⠀⠘⡷⣶⠀⠉⠓⠢⢬⣟⡛⠛⢿⣿⣷⣄⠀⠀⠙⠿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣦⣀⡤⠤⠟⢻⠋
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⣳⡦⡝⢿⣿⣷⣄⠀⣀⣈⡿⠿⠷⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠸⣀⣤⡀⠀⠀⠀⣀⣀⣽⡥⠾⠴⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠚⠛⢳
⠀⠀⠀⠀⠀⠀⠛⠿⡖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠶⠖⠚⠛⠉⠉⠁⠀⠀⣀⣀⣠⣤⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣀⣀⣤⣤⡴⠶⠖⠛⢻⡏⠉⠀⠀⢸⣇⣀⣤⡤⠴⠶⠚⠛⠉⠉⠉⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠉⠁⠀⠘⣇⣀⣠⣤⠴⠷⠖⠛⠛⠉⠉⠁⠀⠀⢀⣀⣀⣤⡤⠶⠶⠚⠛⠉⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⠶⠒⠛⠋⠉⠉⠀⠀⠀⣀⣀⣠⣤⠤⠶⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣤⡤⠴⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠖⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠒⠚⠉⠉

⠀⠀⠀⠀⠀⢀⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣤
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⢀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣾⣿⣷
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠰⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⢠⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⡀⠀⣿⡇⠀⢸⣿⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠿⢷⣦⣤⣀
⠀⠀⠀⣀⣤⣴⡾⠿⠛⠉⠁⠀⠀⠀⣿⡇⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⢸⣿⠀⠀⠀⠈⠉⠛⠿⢷⣦⣤⣀
⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷
⠸⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⣿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⢹⣧⠀⠀⢠⣤⣶⠾⠛⠉⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠛⠷⣶⣤⡄⠀⠀⣼⡟
⠀⠀⢻⣇⠀⠈⠁⠀⠀⢀⣀⣤⣶⡾⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⣿⢷⣶⣤⣀⡀⠀⠀⠈⠁⠀⣸⡿
⠀⠀⠈⣿⡆⠀⠀⣴⡾⠟⠛⠉⠀⠀⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣿⠀⠀⠉⠛⠻⢷⣦⠀⠀⢰⣿⠁
⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣀⣠⣴⡶⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿⢶⣦⣄⣀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠹⣷⡀⠀⠰⠿⠛⠉⠁⠀⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⣿⠀⠈⠉⠛⠿⠆⠀⢀⣾⠏
⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢀⣀⣤⣶⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿⣶⣤⣀⡀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠐⠛⠋⠉⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⠉⠙⠛⠂⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢀⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠙⠉⠁⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠉⠋⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠉⣉⣩⣽⡿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⢿⣯⣍⣉⠉⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣠⣴⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣦⣄⣼⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢠⡄⡤⠈⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠄⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠈⠀⠀⠀⠀⠁⠂⠂⠀⠀⠀⠀⠀⠠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘



⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀
⣤⡤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣴⢘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡋⡔⢷⢇⣳
⠻⣿⡿⡻⡻⢛⢛⣛⡿⡻⠛⢟⠟⡻⣻⢛⠛⡛⠛⢓⠷⣒⠒⠖⡲⣲⢖⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠕⠁⡀⢈⠞⠁
⠀⠈⠻⣞⢔⠅⠙⡁⠊⢂⠔⡡⠊⢈⠄⡡⠈⠀⠀⡁⠈⡁⠀⠨⢚⠕⡡⣾⠁⠀⠀⠀⠀⠀⠀⣠⡞⠁⠆⠀⢀⡼⠋
⠀⠀⠀⠙⠾⠞⠾⠶⠷⠮⠾⠾⠵⠧⠤⠴⠤⠮⣬⣀⣀⣠⣌⣀⣀⣊⡐⣿⠀⠀⠀⠀⠀⢀⡴⠏⠀⢂⠀⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⢀⡴⢋⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣴⠋⡰⠁⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠿⠐⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡿⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⠀⠀⠀⠀⠀⢰⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣟⣀⣀⣀⡀⠴⠹⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⣀⡀⣸⣿⣿⣟⣿⠿⡿⠍⠉⠁⠀⢠⣄
⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⡍⢁⣿⠿⣿⠋⠁⠀⠀⢲⣄⠀⠀⠀⠹⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣶⠞⠁⠀⠘⠇⠀⠀⠀⢸⣿⣰⣾⠀⠀⠘⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣆⠧⠀⠀⣀⠀⠀⠘⣿⣿⣿⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣆⡀⠙⠀⠀⠀⠙⢀⣠⣴⣿⣿⣿⣿⡿⠁
⣿⠉⠉⠉⠉⠀⠀⣠⣿⣿⣿⣿⡇⠀⠛⠀⠀⠀⠈⠉⠉⠉⠻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠟⠉⠉⠛⣿⣿⡿⠿⣿⣿⣿⣿⡿⠗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣷

⠀⢀⣀⣤⣀⣀⣄⣀⣤⣤⣀⣀⣠⣤⣤⠤⣤⡤⠶⠦⢤⡤⠴⢦⣤⠤⠶⠶⠶⠶⠚⠓⠶⠶⠶⠒⠶⠤⠶⠶⣦⡤⠤⠶⣤⣤⣤⣄
⠀⢿⡏⠉⣿⠁⢆⠈⢉⣀⣀⣡⢹⡀⠠⠠⡀⢀⠐⠤⠤⢒⣴⡶⢸⡀⢠⣠⠀⢦⡀⣁⣀⣁⣠⠄⢀⣾⠇⣰⠧⠤⠖⡀⠀⡠⠀⡾
⠀⢸⣷⠀⠘⢧⡈⠢⣄⣈⣁⣠⡼⢷⡀⠁⢙⠦⣍⣛⣛⣋⡭⢶⡿⢣⡀⠙⢷⣤⣉⠙⠛⠋⠁⡠⠞⢁⣴⡋⠙⠛⠉⣀⠀⠀⣼⡃
⠀⢸⣿⣷⡀⠀⠙⠂⠀⠉⣩⣅⣶⠿⠛⣦⣄⡁⠂⠒⠂⠐⢊⣡⣴⣿⣿⣶⣤⣀⣉⣉⣉⣀⣀⣤⣶⣯⣙⠛⠛⠛⠋⢁⣤⣾⣿⡇
⠀⢸⡇⠘⠛⣷⣦⣤⣀⣀⣀⣠⣤⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⡛⠻⣿⡿⠻⣿⡍⢹⢸⣧
⠀⢸⡇⡇⠀⣿⠀⠀⡟⠉⢹⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⡇⠀⠿⣇⠀⢻⠀⢸⠘⣿
⠀⢸⡇⠀⠀⣿⠀⠀⠇⠀⠸⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣷⠀⢸⠘⠀⠘⠘⠸⠀⣿
⠀⢸⡇⠀⠀⡟⠀⢸⠀⢀⢃⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢻⠻⡏⡟⣿⡇⢿⣿⣿⣿⣿⣿⣧⠀⢫⢂⠀⣇⠆⠀⠃⠰⠀⣿
⠀⠸⡇⠀⢀⡇⠀⡀⠀⡘⡐⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢛⠈⠀⠈⠀⠀⠀⡇⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⢎⠀⠸⡼⠀⠀⢰⢠⡿
⠀⠀⣷⠀⢸⠇⢰⠃⢠⡱⢀⣾⣿⣿⣿⣿⣿⡇⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⡿⣿⣿⣿⣿⣿⡄⠈⢆⡀⠃⣣⢸⣟⡸⡇
⠀⠀⣟⠲⠾⣀⡏⢠⡿⠁⣾⣿⣿⣿⣿⣿⠏⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⠈⣿⠤⠟⣋⣥⠾⣧
⠀⢀⡿⢿⡷⣶⣮⣭⣭⣘⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⢹⣿⣿⣿⣿⣥⣶⢾⡿⠻⣿⡀⢻⡄
⠀⣼⠁⢸⡇⠈⡅⢹⡏⢻⣿⣿⡿⣿⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢹⡇⢸⡇⠀⢿⣧⠘⣧
⢰⡟⠀⣾⠀⠀⠇⠈⣧⠀⢿⣿⣷⡟⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣾⠃⠸⠇⠀⠸⢿⠀⣿
⣸⡇⠀⢿⠀⠀⢰⠀⠋⡄⢸⣿⣿⡅⡸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⠀⣷⠀⠀⢸⠀⠈⠘⡇⢸
⣿⠃⠀⢸⠀⠀⢰⠀⢠⠁⠀⣿⣿⡇⣧⣶⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⠀⡁⣿⣿⡏⠀⠈⠀⢸⢸⠀⠀⡇⡇⢸
⣿⠀⠀⢸⠀⠀⢸⠀⠘⢸⠀⢿⣿⣷⣿⣿⢠⢸⡇⣡⡆⠀⡄⠀⢠⠀⠀⡄⠀⡆⢰⣸⠀⣿⠀⡇⣿⣿⡇⠠⢠⠀⢨⠈⡀⠀⡇⡇⢸
⣿⠀⠀⡎⡀⠀⢸⠀⠀⢸⠀⢸⣿⣿⣿⣿⣾⣾⣷⣾⣧⣶⣷⣶⣾⣶⣾⣷⣶⣿⣾⣿⣷⣿⣶⣿⣿⣿⡃⠀⠘⠀⠈⠀⠁⠀⡇⡇⢸
⢹⡇⠀⠀⠃⠀⢸⠀⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣛⣛⠿⠿⠛⠛⠿⠿⠿⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⣀⠁⣁⣼
⠈⠻⣤⣤⠤⣤⡤⠴⠶⣤⠴⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠋⠉⠉