Floristry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⡔⠒⢁⡬⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣬⠀⠀⠀⠀⠀⠀⠀⠀⢠⡨⣽⣿⣿⠂⢀⠀⠈⠃⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠠⠔⠂⢀⡄⠀⠀⠀⢿⣻⣈⣻⣿⣯⡀⠀⠀⡖⠉⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⢈⣃⠀⠀⡀⠀⢛⠿⡿⠈⠈⠿⠠⠄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣉⣀⠞⠀⠀⠀⠀⠀⠀⠠⠀⢵⡄
⠀⠀⠀⠀⠀⠀⡀⢀⣤⢀⡀⢀⣠⠀⡀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⣰⠁⢠⣧⡒⡀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠄⠐⠁⡸⠐⢾⣦⣴⣷⣴⣃⠠⢲⣿⣿⣿⡋⠀⣽⣷⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡿⣤⣿⣿⣿⣿⡿⠁⠛⠛⠿⢿⣦⠶⠉⢌⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢉⠙⡿⢿⠏⠀⢀⣀⣀⠀⠀⠙⠧⠀⣄⠀⢠⣠⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⠈⢛⠋⣀⠈⠀⠠⣀⠀⠀⢠⣿⣿⣽⣃⠀⣦⣀⣻⡂⠼⣀⡄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢻⣾⣯⠀⠀⢨⣹⣆⢔⢜⣿⣿⣿⡿⣅⣝⣣⠟⠃⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠿⠟⢳⠛⣼⠙⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢻⡄⢙⡀⠀⠀⠉⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣇⠌⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡏⠀⣤⠀⠔⠀⠞⠀⠻⠯⢍⡀⠢⠀⠀⣤⣤⠀⢀⠆⢀⡙⠛⢻⣿⠁⠀⠀⠱⣾⣿⣿⣿⣶⠀⠑⢤
⣿⣿⣹⣿⣿⣿⣿⡛⠫⠉⣹⡿⠇⣤⠤⠰⠀⠀⡠⢧⣠⣆⠀⠀⠀⢀⣿⡆⢙⣤⡚⠓⠈⠁⠀⠘⣿⠀⠀⠀⢹⣿⣧⣼⣿⡿⠂
⣿⣿⡿⠁⠁⢸⣿⣧⠀⠀⠀⣵⠒⣯⣿⠄⠐⢀⣵⠀⠁⢾⣶⣤⣌⡞⠉⠁⠛⠀⢴⣶⣄⣀⠀⣀⠋⠀⠀⠀⠀⠛⠛⠻⠋⠋⠀⣀⡀
⣿⢻⡇⠀⠀⣼⣿⣿⣷⠀⠾⠿⠿⣿⣻⣿⣾⣟⠁⠀⢰⣿⣿⣝⣿⠀⠀⠀⠀⠀⢈⣿⡻⣿⣿⣽⣤⣞⣄⣀⡀⠀⣀⢀⠀⠀⠀⠈
⠀⠀⠉⢠⣼⣿⠛⠩⠉⠃⠀⠀⠀⠙⣿⣿⣿⠻⡀⠡⣶⣿⣿⣾⣿⡇⠀⠀⠀⢀⣼⡿⢿⣿⣅⣾⣿⣿⣿⣿⡿⣟⢿⣦⣤⠴⢏⡀⠰
⣀⠀⠀⠀⠿⣷⢭⣐⠀⡠⠒⠓⠒⠄⣸⣿⣿⣿⣶⣿⢛⡿⠿⢙⢿⡇⠀⠀⠙⠻⣿⣶⣿⣿⣿⡟⢍⠻⠿⡟⠧⣤⣬⣻⣿⡘⢈⢻⣿
⣿⣿⣷⣜⣠⣷⣿⣿⣎⣠⣄⠀⢱⡼⠿⣟⣻⡏⠻⡏⠀⠀⠀⠘⢏⡿⠲⣤⠄⢀⣽⣿⣿⠟⣋⠉⢀⡵⠀⢷⠌⡆⢛⣯⣟⢁⣤⡰⢻
⠿⠿⠋⢿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣴⣾⠟⣰⣇⣸⣧⡀⠀⠀⢠⠞⠃⠤⢙⡃⠌⠆⠀⠙⠀⠉⣀⠀⣇⠀⣀⠀⠀⢼⠡⠬⢮⣠⢟⣿
⠀⠀⠀⢺⡏⠻⡝⣧⣿⣿⣯⣿⡄⣿⠛⠞⣩⣽⡿⡝⠷⢀⣴⡇⠀⠘⢀⢺⡋⣀⡶⠤⣾⣿⣶⣿⡢⣌⢀⡹⣆⢰⡆⣁⠔⠺⢡⣌⣉
⣦⡀⡲⢮⣧⠀⣁⢈⣢⠛⡻⠞⠙⠰⣶⠄⣿⣯⡆⠿⣦⢠⣤⣤⣤⣜⠙⣡⡌⠉⠁⠀⠘⠃⠰⢮⣽⣾⣿⣿⢮⣯⣿⣿⠓⠽⠈⠙⢿
⠉⠁⢻⣌⣸⣯⢀⣹⣯⠧⣄⢧⣈⢁⡀⠀⣘⡈⠃⣾⣷⣦⣠⣿⣿⣿⡟⠋⢰⣾⣂⢴⠀⢀⡐⠈⠀⠀⡀⠙⠻⣭⣹⡇
⣶⡖⠾⠁⠈⠉⠿⠉⠀⢰⢫⡿⣿⠃⢼⡇⣙⠋⠖⠉⠉⠀⠁⠈⠙⠻⢷⡆⡀⣸⣿⣿⣿⣿⡤⠀⢀⣺⣷⣶⣾⡿⣿⠁⠀⠀⣀⡷⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣦⣿⣽⠁⠀⢀⠄⢠⠀⠀⠀⠀⢈⣷⣿⣿⢿⣿⣿⣿⣇⣀⡨⢿⣿⣿⣼⣧⣸⣧⠀⢠⡛⠀⣈
⣆⡀⠀⠀⠀⠀⢠⠀⢀⠀⢀⢀⣼⠷⠞⠻⢿⡶⠀⠀⠀⠀⠀⠐⣷⣴⠾⠛⠑⠀⣀⠈⠉⠛⣭⣾⡟⠋⠹⡿⠉⠛⠘⠁⠈⠿⠁⢠⡯
⠀⠈⠳⣤⣀⠀⢸⣆⡌⣰⡌⠛⣭⠒⠂⠓⢺⡇⠀⠀⠀⠀⠀⠀⣿⠁⢂⣀⣤⢤⡁⠀⠀⢀⣿⡏⠀⠀⠀⢀⠀⢨⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠈⢿⣷⣿⢿⡟⠉⠀⠀⢡⠀⢠⡤⠻⢧⠀⠀⠀⠀⢀⣤⣃⣼⠟⠁⠀⠀⢀⣀⠛⠉⠛⠳⣤⣆⡠⠊⢰⡷⣄⠀⠀⠀⣴⣇
⣴⠋⢀⠠⠼⠿⠖⢿⠁⠀⠀⢠⣿⠀⠀⠀⢀⣠⣷⣄⠀⠀⡺⡗⢿⣁⣤⠆⠀⠀⠈⠙⠻⠂⠲⠆⠙⠋⠀⣀⣍⠀⠁⠀⣦⣤⣞⠉⠰
⠏⠀⠀⠐⠀⠀⢀⡦⢀⡰⠖⠛⠻⣄⠐⢤⠈⠉⠩⠋⠀⣹⡋⣎⢵⠍⣃⠠⠀⠀⠀⢀⠄⠀⣆⠀⢘⣶⣿⡿⠋⠀⠀⠀⠉⠈⠘⢣⡀
⠆⢀⣀⣁⡶⢶⣾⣷⡀⠀⠀⠠⠀⢈⣷⡾⠳⣄⣀⠀⠀⠀⢆⣎⠶⠾⠖⠂⠀⠀⣶⡗⠀⠀⠀⠀⢸⣿⣯⣄⠀⠀⣠⣤⣤⠀⠀⠀⢀
⢲⣟⢿⣶⣾⣧⡿⠛⢿⣷⣦⣠⠞⠁⠈⠀⠀⠀⠙⠛⠃⠄⡘⠁⠠⠔⠶⠶⠛⠿⠷⢶⣾⣧⣴⣶⣿⣟⣠⠀⢸⣿⣿⣿⣿⣧⣀
⣿⠏⠈⠋⠽⢏⠀⠀⠀⢻⡿⠏⠀⠀⠠⠤⠀⠀⢀⣤⡴⠖⠛⠠⣄⠀⠀⠀⠀⢀⡒⠀⠈⠻⠘⣅⢆⠠⢛⡆⢸⣿⡏⠀⠉⠓⣿⣇⡶
⠐⠀⣯⢈⢀⣙⡀⢦⠀⠚⢶⠂⣠⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠈⠙⢻⡆⠺⠛⠀⠀⠀⠀⣻⡿⠿⢿⣿⣿⣾⣇⠀⠀⠶⢠⡞⠛⠶
⠀⠐⢧⣮⡛⠇⠙⢮⣷⠀⠘⠁⠀⠀⠃⢀⣾⣻⣿⡄⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⡄⢀⠛⠿⡟⠰⣄⣸⠀⠛⢴⠃
⠰⣦⠃⠁⢀⡐⢲⣾⡥⢘⣋⣠⡄⡈⠐⠠⣴⣯⣿⠗⠀⠀⠀⠀⠀⢀⣿⣕⠀⠀⠀⠀⠀⣠⠖⢹⣿⣄⣨⣔⡄⠀⠠⢽⡇⠰⡤
⢓⣠⣽⣶⠞⢃⠾⣷⢎⡉⣁⠀⠀⠉⠃⣠⣾⣿⠗⠀⠀⢠⣤⣤⠴⠸⠿⠇⠀⠀⠀⠛⠻⢁⣠⣿⣹⣿⣥⣬⣷⣤⣤⡼⣿⣿⢿⣂⠖
⡁⠀⢀⣽⠉⡿⠖⢀⡀⠶⠁⠉⠀⠻⣾⠁⢻⣿⣶⣖⣤⣿⡿⠁⠀⠀⠀⣷⢀⣀⡤⢀⣴⠂⠀⠀⠀⠈⣭⣽⣿⡟⠁⠀⠀⠀⠀⡉⢦
⠀⠈⠉⠁⢀⢀⠀⠉⠀⡀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⣿⣷⣟⣤⠖⢢⣼⣿⠋⠻⣷⣅⠀⠀⠀⠀⡀⣷⣽⣿⠀⢐⡀⠀⠀⠀⠀⠆
⠀⢀⡔⠀⠋⣸⠆⠀⠀⢠⡐⠄⠀⣀⣀⣠⡿⠿⡿⢿⠻⠷⣄⡻⣵⣧⢞⣡⣉⣉⣴⠻⠛⠃⢠⠀⠀⢑⣦⣙⡿⠔⠛⠷⠀⡀⢀⣄⢀
⣶⣿⣷⣄⣠⣿⣧⠀⠁⠀⢸⡛⢶⣿⣿⣯⢀⠀⠀⠀⠀⠀⢈⡿⢻⣿⠟⠁⡸⠟⠃⠀⠉⠛⡤⢰⣶⠋⢰⣭⢄⠀⢦⡀⠀⠈⠂⠥⣀
⠸⣿⡿⠿⣿⠏⠁⠹⠂⠀⠈⠁⠀⠣⠀⣹⠅⠀⠰⣦⣤⣄⣈⢑⣸⠃⠀⠈⠀⠠⣀⠀⠀⠀⠴⡀⠉⠻⢿⡿⠚⠱⠂⠈⢀⡙⡛⢔⣿
⠞⠋⠀⠀⢻⠀⠀⠇⠀⠲⠋⠁⠀⠀⠀⠙⡀⠀⠈⣼⡿⢿⣿⣿⣿⡷⣄⠀⢤⣖⣿⡁⣼⡟⠀⣖⠃⣀⡠⠀⠘⠀⠀⢀⡈⠃⣴⡟⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⠏⠉⢁⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠷⠶⡏⢛⡍⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠁⠀⠀⠀⠠⢿⣏⣿⣦⠀⠀⠀⢰⡄⠀⠀⠸⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠿⠛⠀⠀⠀⠨⣥⡆⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⠀⠸⣥⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠⠈⡀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠹⡀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⢦⡝⣞⠀⢩⡄⢰⢠⠀⠀⡀⠀⣰⠋⣀⣸⠇⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⣣⡰⢀⠘⣤⠏⠀⠀⠀⢙⣂⣿⣶⣿⣾⣇⣠⡏⠀⠀⠀⡠⠖⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⢀⡀⠀⠐⠿⠊⢁⣉⠐⠿⡄⠀⠀⠀⢈⣠⣽⣿⣿⣿⣿⠿⣏⠛⡠⠂⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠀⠂⠀⠀⠀⠀⠁⠀⠀⢱⡀⣄⢁⡸⠁⠀⠹⠟⠻⠏⠀⠈⡿⠁⠀⠀⠀⡄⠀⡀⠀⠀⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣨⣷⣷⣄⡉⠙⣜⣿⣷⡄⢣⡜⠀⣠⠀⠖⠀⡀⠀⢰⣷⡄⢡⡆⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡁⠙⣿⣿⡿⠦⢠⣤⣿⠄⣠⣼⣿⡀⠈⠋⠀⢾⣥⠘⠿⠂⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⢦⣽⣆⠉⡉⠃⡀⠀⠛⢃⠀⠉⢻⣿⡗⢛⡴⢁⠀⢠⣶⣄⣀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠈⠉⠉⠍⠣⡞⠛⠋⠀⡀⠘⣷⣠⢤⠿⢄⣧⡼⠯⣀⡼⠿⠿⣦⡈⠛⠯⢉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠲⣀⠀⠘⠂⠀⠀⠀⠺⣿⣟⡀⢰⣿⣻⠇⣄⠫⣄⠉⣇⣈⣙⠿⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⣶⣶⡄⠀⠀⠀⠀⠀⢲⣶⢿⣿⣿⣾⣿⣤⣿⣿⠆⠠⠀⠛⢛⣋⣤⣶⣷⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⡿⣿⣿⣿⡀⠀⠀⠀⠀⠈⣯⣿⣷⣯⣼⣿⢭⣭⣿⣶⠴⡈⢳⣶⣶⢷⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠘⣻⣷⢿⣾⣿⣹⣾⢿⣾⢥⠘⠛⢿⡿⣽⢳⣿⢶⣾⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠿⠿⠛⠋⠉⠻⣿⣿⡄⠀⠀⠀⠀⠉⣹⡷⢉⣧⣿⡿⠏⠉⠠⣥⠀⣀⡉⢟⢺⡾⢿⣟⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⣴⣶⣶⡟⠋⠡⠀⢰⠀⠀⣀⠐⠉⠈⠛⠩⠃⠀⢰⣴⣞⣀⣉⡡⠚⢻⣽⠉⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢋⡙⢹⡿⠁⠀⠠⣴⣫⡶⢯⢀⡀⢀⣤⣄⣴⡦⣾⣿⣿⣿⣿⣿⣻⣷⡄⠁⠀⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠛⢿⣿⡀⢠⣤⡽⣿⣿⠶⣛⣿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⠇⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣁⣼⠇⢀⣽⣴⡾⢻⢸⣷⣿⣿⣿⡿⢿⡿⣯⢩⣿⣄⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠍⠺⣏⣹⠟⠙⠂⠹⠟⢿⠿⢿⠟⢻⣿⣿⣿⢿⣷⣧⣿⡀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⡍⠀⠀⠀⣴⣟⣧⠈⣠⡄⢹⣿⣿⣿⣿⣿⣿⡿⠋⠈⠁⠑⠂⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡔⠀⠀⠀⠀⠉⠉⠉⠀⠻⠋⠀⠻⣿⣿⣿⣿⠟⠣⠠⠄⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣴⣿⡶⠀⠘⠢⢀⣀⡀⠿⠋⠉⡐⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠸⠟⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⢸⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠆

⠟⠿⡇⠀⢀⣾⣿⣿⣟⠂⠛⠛⢟⣿⣿⣿⢿⣏⣀⡀⢸⣿⣿⢭⣿⡀⠀⠀⠀⠀⢨⡿⣛⣿⣿⢿⣧⣯⣤⣤⣆⡀⣀⡠⠀⠀⣀⠈
⠀⠀⠈⢲⣾⡿⢉⠡⢀⡁⠀⡀⠀⠙⢿⣿⡿⣛⠄⢸⣶⣿⣿⣿⣿⡧⡀⠀⢀⣠⣾⠟⣻⣿⣦⣺⣿⣿⣿⣿⡟⠿⢻⣷⣶⢖⢧⣔⣐
⣄⣀⡀⠈⠛⡷⣦⣌⣀⠴⠋⠙⠛⢂⣼⣿⣿⣿⣿⣿⠫⠿⠛⢏⣿⡇⠀⠀⠉⠙⡿⣷⣿⣿⣿⣟⠢⠙⠛⡟⠁⠶⣦⣽⣿⡌⠠⠩⣿
⣿⣿⣿⣎⣴⣿⣿⣿⣦⣴⣬⣀⣰⠞⠻⢏⠹⡇⠙⡏⠀⠀⠀⠈⢣⡏⠱⣶⡂⣀⠾⢿⣿⠋⣁⡄⠠⡿⠀⠷⠆⠧⢙⡯⢭⢀⠶⣐⣻
⠻⠿⠉⢯⣿⣿⣿⣿⣿⣯⣻⡿⠿⣾⣾⢋⣴⣧⣸⣷⡀⠀⠀⢰⠛⠁⠢⣍⣅⠌⠓⠀⠈⣂⢁⣠⠀⢃⠀⢄⠀⠀⠺⣀⠒⢇⣤⢯⣽
⠀⠀⠀⢻⡇⠹⡜⢧⣿⣿⣶⢿⡄⠟⠉⠛⣴⣼⡿⣏⠳⢀⡴⡇⠀⢈⢠⣻⣍⣀⡗⢖⢻⡿⠷⣾⣓⢬⣀⣜⢦⢰⣇⣀⡞⣚⢡⣮⣤
⣦⢀⣒⢺⣦⢀⣱⣨⣆⡋⡙⡏⢍⡸⡾⠄⢿⢶⡖⠟⡶⠰⢤⣶⣶⣮⠉⣵⠆⢐⠁⠀⠈⠇⠘⢶⣿⣷⣿⣿⣿⣿⢽⡿⠋⠳⠁⠈⠻
⠉⠈⢻⡬⣼⣧⣠⣽⣯⠳⢆⣧⣈⡠⠄⠀⣮⡌⠃⣿⣿⣷⡴⣯⣿⣿⡟⠁⠰⢮⣅⡲⠀⢠⣜⡁⠀⢀⡀⠈⠛⣧⣼⡇⠀⠀⠀⢀
⢿⠕⠛⠀⠀⠈⠟⠁⠀⠸⠳⠿⣿⠓⢾⣁⣭⡉⠒⠀⠁⠀⠀⠀⠈⠻⢿⡆⠄⣸⣿⣿⣿⣿⠦⠀⢨⣙⣷⣾⢿⡽⣿⡁⠀⠀⣄⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣿⣼⠁⠀⢠⠀⠠⠀⠀⡀⠀⢀⣿⡿⠿⠿⣿⣿⣿⣧⡬⡴⢾⣿⣾⣼⡷⣼⣷⠀⢰⡟⠀⣨
⠦⣀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⣾⠒⠋⠛⢿⡞⠀⠀⠀⠁⠀⠈⣷⡴⠛⠋⠉⠀⡄⠀⠉⠩⣴⣿⡟⠉⠘⠟⠈⠙⠚⠃⠀⠻⠀⢠⡿
⠀⠈⠳⣦⣄⠄⣸⣦⡇⣸⠌⠙⡥⠛⠃⠉⣻⡆⠀⠀⠀⠀⠀⠀⡿⢁⣁⣀⡤⠶⠄⠀⠀⣀⣿⡏⠀⠀⠀⢀⡀⢸⠁⠀⠀⠀⠀⠸⠁
⠀⣀⠀⠈⢿⣿⣿⣻⡟⠉⠀⠀⣡⠀⠰⠆⠛⢧⡀⠀⠀⠀⢀⣄⣣⣼⠏⠀⠀⠀⢠⣄⡉⠉⠉⠳⣤⣆⡤⠚⢰⠿⣦⠀⠀⠀⢴⣦
⣶⠁⠀⠤⠾⠛⠛⣿⠁⠀⠀⣰⣿⠀⠀⠠⢠⣤⣿⣄⢀⣀⡺⢟⠿⣥⡴⠂⠀⠐⠈⠉⢛⠂⠒⠒⢉⠋⢀⣠⣥⠀⠀⠀⣶⣤⣾⠉⠐
⠄⠀⠀⡀⠀⠀⢠⠗⢄⠰⠛⠛⠻⣄⠀⢦⡀⠀⠁⠋⠁⡺⣋⢜⠫⠪⡁⠄⠀⠀⠀⠀⠤⠀⡦⠀⢘⣷⣿⠟⠉⠀⠀⠀⠈⠀⠈⠃⡄
⠦⢤⣠⠤⠿⠷⣷⣷⡄⠀⠀⠀⠀⣈⣿⡟⠓⢤⣠⡀⠀⠀⢎⡯⠯⠖⠛⠀⠀⠀⣾⠇⠀⡘⠀⠀⠰⣿⡿⣆⠀⠀⣠⣶⣤⡄⠀⠈⠠
⣾⣿⣻⣶⣾⣷⠿⡛⢿⣿⣦⣴⠋⢀⠀⠀⠀⠀⠙⠛⠁⠂⡈⠀⠐⠒⠲⠾⠙⠻⠿⠶⣿⣧⣴⣾⡿⡟⣠⠀⢸⣿⣿⢿⣿⡷⣄
⢿⠋⢘⠓⡽⣏⠀⠀⠀⢻⠿⠓⠀⠀⠰⠄⠀⠀⣀⣤⡶⠚⠋⠲⣄⡀⠀⠀⠀⣠⡏⠀⠀⠻⠘⣅⢆⠐⣙⣇⢠⣿⠏⠀⠊⠙⢾⡯⠐
⠒⠀⣇⢈⢀⣉⡀⢆⠀⠛⢺⠀⡤⠀⠀⠀⣤⣴⣿⠇⠀⠀⠀⠀⠀⠉⢻⡖⠚⠓⠀⠀⠀⠀⣹⡿⡿⢿⣿⣿⣾⣟⠈⠀⠲⢰⡞⠙⡓
⡀⠐⢧⡮⠙⠆⠙⢾⡷⠀⣊⠀⠀⢈⠁⢀⢮⣻⣿⡄⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡄⢠⠘⠻⠿⠐⣄⡼⠀⠋⠲⠁
⠴⣶⢁⠂⣰⡈⢳⡾⠡⣈⡁⠤⢄⣉⠐⠢⣾⣯⡿⠓⠀⠀⠀⠀⠀⢀⣿⣥⠀⠀⠀⠀⢀⣠⠞⣹⣿⣄⣈⣄⡄⠀⠠⢼⣇⣐⡥⠈
⣓⣤⣽⣾⠛⣡⠾⣿⢪⠍⣁⡀⠀⠈⠁⣠⣿⣿⠓⠀⠀⣰⣤⣤⠴⠐⠛⡇⠀⠀⠀⠋⠩⠁⣠⡟⢜⣿⣤⣬⣷⣦⣤⠼⣿⣿⠫⣆⠞
⡀⠀⣀⡽⠉⠟⠚⢀⡄⠾⠀⠀⠀⠻⡟⠀⢻⣿⣿⣶⣤⣿⡿⠁⠀⠀⠀⢷⢀⣀⡴⠀⡴⠂⠉⠀⠀⢀⣥⣭⣿⠟⠁⠀⠀⠀⠀⠌⠣
⠀⠈⠉⠀⣠⢠⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣶⠒⢠⣼⣿⡋⠹⣷⣄⡀⠀⠀⠀⡀⣷⣾⣿⠀⢐⡄⠀⠀⠀⠀⠂
⠀⢀⡞⠈⢁⣼⡆⠀⠀⢠⡐⢄⠀⢀⣀⣰⠿⠿⠿⠿⠛⠷⣄⡻⣼⣧⣞⣡⣨⣩⣵⠛⡛⠙⢠⠀⠀⢑⡶⣙⡿⠖⠛⠻⠀⡀⠀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠱⠂⠄⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡆⠀⣃⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢢⡌⠓⢀⢀⠈⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠈⠠⠀⠙⡧⢆⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢺⡆⢸⠦⠈⠱⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠋⠀⣴⠼⠻⢤⠄
⠀⠀⠀⠀⠀⠀⠀⡤⢠⠆⠀⢇⣸⠅⠀⠀⠀⠅⠐⣦⡀⠓⢄⡀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣌⣲⣦⠀⠀⠀⠀⢷⣉⣾⢶⣷⡽⢁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠞⠂⣤⣦⣶⠿⣿⡯⢿⣖⣿⣷⣆⠠⠀⠀⠀⠔⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣠⣈⣅⠀⢺⣷⣿⣿⠀⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⣿⣞⣥⡞⣿⠑⢤⣤⣿⣿⣿⣿⡏⠀⠠⡀⠀⠀⠆⠀⠀⠀⡠⢖⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡦⣼⣿⣿⣟⠟⠋⠀⠀⠀⠘⠊⡁⡄⠄⠐⡀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⣟⠉⠀⠹⠝⠖⠈⣷⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⡥⠁⠀⠀⠀⠻⠂⠶⠈⠀⠀⠀⠀⢆⣀⠀⢠⠀⠀⠀⠙⠄⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡐⠘⠁⠁⠀⡅⠀⠀⢄⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⠀⠀⠀⠀⠀⠀⠖⠀⠀⣀⣀⠀⠀⠀⠀⠤⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⡀⠙⠛⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⢠⠀⠀⠀⠂⣈⠀⢣⣀⣤⣠⡔⠀⠀⠏⠈⠘⠓⠆⠀⣠⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⣄⠂⠀⠄⠂⠤⢈⡀⠈⠹⠆⠉⠀⠠⣶⣄⠀⠀⠄⠀⠀⠀⠀⠀⠉⠘
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡘⠀⢀⣤⡄⡤⠘⠛⠃⠒⠓⢤⣠⠀⠉⠉⠀⠀⠂⠀⠐⣴⣶⣤⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⡈⢠⡀⠘⠁⠀⠀⠀⠀⠀⠤⠀⠁⠀⢀⡀⠀⠀⣠⠀⠀⠉⠙⢩⣿⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠐⠀⠈⢆⡀⠀⠀⡆⡅⠀⠀⢀⣴⠶⡶⠀⠀⡀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠙⣩⣀⣠⠀⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⢠⡀⡴⠊⠁⠀⠀⠀⠖⠀⠀⣺⠉⢿⡷⢠⣤⠁⠀⢀⣾⣿⣧⣬⣿⣿⠷⠒⠌⠀⠈⠀⢈⠂⠀⣄⠬⠁⠒⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠉⠉⠐⢄⠀⠀⢺⡀⠀⠑⣆⣀⢀⠨⠅⠀⠀⠉⠈⢻⠿⠿⡿⠉⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⢀⣨⣧⣴⣦⠈⠁⠀⠈⡈⡄⠀⣶⣠⣦⡄⡀⠀⠀⠀⢠⡀⠠⣆⣠⣴⣤⡄⠀⠀⠀⢠⢧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢠⠊⠉⢿⡿⢻⣷⣮⡀⠠⠀⡁⠀⢸⣇⠀⣈⡂⠈⢀⢠⡔⠉⠀⡠⣿⣿⡏⢻⣿⡄⠀⠀⠀⢷⠄⠀⣀⣀⠀⠀⠒
⠀⠤⠂⠒⠀⠀⠄⠀⢀⠀⠀⠀⢀⡄⠀⠐⠄⠀⠾⢿⣿⡟⢀⡻⠃⠀⠀⡤⠀⠈⠀⠀⢸⠟⠶⠀⠃⠀⠉⠀⠹⢿⣿⣿⣿⠁⠀⠀⠰⠖⠁⠀⠈⠉⠗⠂
⠀⠀⠀⠑⠀⠀⠀⠠⣄⢠⣀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠈⢡⡾⠃⠀⢀⠀⠓⢀⣤⣾⣶⣧⠀⠀⠙⢶⠦⢀⠀⠀⢨⠉⠋⠀⠀⠀⠀⠀⠛⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠤⡈⠁⠀⠴⠂⢀⡁⢀⡀⠀⠐⠀⠖⣋⠀⠀⠴⡎⢠⠀⢸⣿⣏⣹⣿⡇⠀⢀⡋⠀⠘⣀⣠⡾⢆⠀⢀⠀⢀⠟⡂⢊⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠿⠂⠀⠀⢉⣄⠈⠑⠀⢤⠀⢀⠜⠛⠿⣿⠿⠓⠂⠀⣃⠀⣤⣳⣷⡱⣋⠻⣶⣿⠿⢷⡎⠓⠑⠊⠀⠋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠠⠀⢰⠛⠀⠀⠀⠋⠙⢷⣄⢳⠀⠀⠲⣿⠀⠀⠀⠈⣣⣀⣀⠘⠋⣾⢪⣿⣿⣿⣿⣞⣵⠀⠀⠀⢡⠤⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⢀⡀⠀⢀⣠⣴⢟⡽⣿⡇⢄⢀⠀⢘⠖⠀⠒⠉⠁⠀⠀⢤⢾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⣍⡿⡴⠃⠀⠈⠻⣿⣳⣿⣷⣼⣿⡀⠀⢢⡂⠐⠒⣶⠲⣿⣷⠆⣿⣻⣿⣿⣿⡍⠁⠐⠒⢖⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⠆⢁⠋⠁⠢⠙⠐⠀⠀⠀⠀⠁⠹⠟⠃⠀⢱⡀⠀⢘⣤⣤⡤⢝⣆⠀⠃⡐⣻⣧⣀⡀⠀⠀⣲⣀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⢀⠐⠴⠆⠀⠀⠤⠌⢳⣠⡆⠁⠉⠀⠀⠈⠁⡵⠙⢦⣤⠀⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠀⣦⢀⣤⠠⡄⡌⠉⠁⠀⠀⢤⣀⠀⠀⠀⠀⢌⡉⠑⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠐⠀⡀⣾⡇⢰⢠⠆⠁⠀⠀⢴⡱⠮⠿⠀⠡⠰⣤⣷⡀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠆⠤⠄⠀⠊⢁⣾⡥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠑⠂⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠚⢠⣖⣀⣱⠀⠀⠀⠂⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠞⣻⡴⠩⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⠀⠚⠁⠐⠁⠂⠆⣐⠋⠐⠉⠏⠀⠈
⠀⠀⠘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠉⠉⠄⠀⠀⢠⣸⣯⠟⢀⠆⠀⠈
⠀⠀⠀⠀⡀⠀⠰⠇⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠄⠀⠀⠀⠀⠀⠀⠳⠀⠛⠁
⠀⠀⠀⠀⠀⠀⣤⡄⠐⢠⡿⠂⠀⠰⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠤⠐⠀⢀⣶⡓⠀⠀⠒⣦⢀⡀⢀⣶⠆⠀⢠⣄⠀⡠⠀⠰⣦⠰⠄
⠀⠀⠀⠀⠀⠀⠐⠋⠁⠈⢿⡀⠐⠾⠿⠛⠒⠋⠛⢠⡴⢋⠁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢤⣀⡤⠖⢈⡉⠀⠤⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⡟⣿⠳⠈⢻⢿⡆⠀⣠⢚⣿⠟⡷⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⡖⣷⠘⡂⠀⠈⣼⢨⣤⢋⡯⠋⡸⢱⣇⢠⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣿⣿⣤⠀⢣⠀⠀⢹⣼⣿⣞⢁⡶⣡⣿⣿⠟⠖⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⣿⠄⠀⢳⣦⠈⣾⣿⣿⢛⣵⣿⣿⣵⠂⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣽⣿⣿⣿⣾⣷⣿⣿⣿⣿⣯⣾⣿⣿⣝⣦⣤⣾⣿⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⠻⠿⣿⡿⠟⣋⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣦⣀⢀⠀⣰⠆⠈⢿⡟⠀⠀⠀⠀⡀⠀⠀⣶⣿⢻⢻⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡒⢄⣙⣿⣯⠀⠻⣇⡀⠀⠻⣤⡀⢰⣿⠏⠀⠰⣿⣿⣬⣼⣾⣿⠟⠀⠀⢀⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣫⣭⣷⣿⣿⡿⠛⠛⠛⠛⠛⠓⠺⢿⣿⣇⡀⠈⠁⠈⢹⣿⡟⠙⢁⡴⢃⠁⡸⢁⣰⠤⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡀⠀⠀⡾⠁⠁⣰⣿⡁⠀⡰⠀⠋⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⡲⠤⠤⠀⠠⣄⡀⠙⣇⠀⢰⠀⠀⣰⣿⡯⣷⣾⣁⣀⠀⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⣶⣶⣶⣶⣷⣄⠀⠀⢰⣿⠁⠀⢻⣦⣸⡇⠀⢿⠹⣿⣇⣠⢅⣤⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡞⠛⣸⣿⣻⢻⡿⠄⠀⣼⣿⠀⠀⠈⣯⣿⠇⣴⣣⣿⣶⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⣾⡇⢠⠟⣿⣟⣿⢿⣆⣼⣿⠋⠀⠀⠀⣿⠋⣼⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⢶⣿⣿⣿⣯⣾⣿⡋⠀⠀⠀⠀⠀⢿⣿⠃⠀⣠⢶⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣴⣒⣾⣿⣿⡟⢉⣥⡟⣼⠧⣤⠀⠀⠀⢸⣿⢠⣴⡟⣄⠃⠰⣽⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠟⠉⠀⠀⠙⣇⢸⣿⣶⣯⣌⣽⠀⠀⠀⢸⡇⠨⣿⣧⣿⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⣿⠛⠟⠋⠀⠀⠀⣸⠁⠀⠀⣽⡿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⣦⠀⠸⣆⢻⡀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⡄⡟⣆⠀⠈⢩⣷⠀⣰⣫⠄⢰⣏⣠⠞⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠶⣻⣇⣻⣷⣤⣄⣹⣧⡟⠁⠀⡞⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣤⣼⣿⣿⡿⠋⠙⠻⣷⣀⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡶⠏⠙⠌⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣰⢃⣿⣿⣿⣦⣠⣾⣿⣿⡄⠀⣏⠉⣽⣤⣤⡄⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⢀⣧⣾⡿⣿⣿⠈⣿⣿⣿⣿⣇⡀⢯⠀⢹⣿⣧⡷⠀⢀⣀⢀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠘⣿⡿⠍⢻⣿⣿⣿⣿⡿⠿⠛⠟⠻⠷⠖⠛⠛⠛⢤⣿⣽⣫⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣟⣀⢈⣿⣿⣿⣝⣠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠤⣽⣿⣏⣿⣿⡯⢸⠇⠀⠀⠀⠀⠀⠀⠀⠽⣿⣷⡄⠉⢁⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⢕⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣄⣤⡞
⠀⠀⠀⠀⠀⠀⠈⡏⠻⣿⣿⣿⣿⣿⣿⣿⡇⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣛⢿⣿⣿⣿⣿⣥⣾⣿⡷⠀⠀⠀⠀⠀⣶⠲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⢻⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣰⣾⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠿⢿⣿⣿⣠⣦⣶⣿⣿⣿⣿⣷⡈⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠈⠉⠋⠉⣲⣿⣟⠻⢿⣿⣟⡛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣾⣄⡉⣉⣛⡻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⢋⣿⡟⡟⠉⠉⠙⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠁⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠾⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⣖⠉⠆⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣈⣆⠀⠀⠈⠀⠀⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣺⡭⢷⠶⠀⠀⠀⡺⠀⠂⠘⠃⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣜⡥⠠⣔⠈⠐⣆⠀⠘⢅⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢦⡀⠈⠉⠻⣁⠈⢀⠀⠁⠐⠒⢄⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠲⣤⠀⠀⢠⠀⠀⠙⢦⠀⠀⢈⣦⠀⠀⠄⠀⠀⠸⠀⠀⠀⢠⢡⠀⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠄⠀⠀⠠⣠⡄⠀⠣⠀⠀⠈⠂⠐⢎⠒⣂⠀⠀⠀⢠⣸⡙⠀⠈⠒⠤⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠁⡀⠀⠀⠀⠈⠂⠀⠀⢣⠀⠀⠀⠀⠈⠄⠛⢦⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣌⡀⠀⠤⠔⠂⣐⠦⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠎⡀⣀⠄
⠀⠀⠀⠀⠀⠀⡀⠁⢁⠀⣉⢭⠭⠘⡂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡾⠅
⠀⠀⠀⠀⠀⠀⠡⠀⠛⠈⠁⠉⣀⢤⠖⠒⠒⠒⠛⣧⡀⠀⠀⠀⡖⣶⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠀⠀⡀⡤⢂⡀⠀⠈⠁⠐⠀⠀⠋⠛⠁⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡠⠤⣠⠄⠀⠀⠀⠀⠀⠐⡁⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣈⣿⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⢠⠀⠀⠂⠀⢃⡀⠀⠀⠀⠀⠀⠁⠉⠃⠀⠁⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⠂⠀⠀⠈⢃⡀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠀⠀⠀⠀⠀⠀⠁⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡀⢀⠈⣀⠄⠀⠀⠡⡈⢤⠀⠀⠘⠋⠀⢀⣠⡄⠀⠀⣦⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠒⠈⠱⠊⣄⣁⠈⣁⠀⠋⠁⢠⡵⢢⡅⣀⣲⢻⡿⠃⠀⠀⢯⣹⡟⠉
⠀⠀⠀⠀⢀⠄⠀⠀⠂⢀⡀⠀⠀⡀⠤⠀⠂⢂⣉⠛⠠⠚⠃⣵⡄⠁⠀⠻⢿⣿⢆⣷⠀⠙⣦⠈⠁⠀⠄⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠲⠀⠁⠀⠀⠀⢀⠈⠙⠨⣉⠖⠀⠂⡀⢈⠙⠆⠀⠀⠀⢙⣀⠙⠀⠂⠁⠀⠀⠄⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠠⠤⣶⡈⡙⢁⠀⠀⠀⢰⠂⡥⠡⣔⡶⣄⣀⡴⠎⠁⠀⠀⢰⣆⡀⠀⠀⠄⠀⠉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⣙⢄⣿⣳⣧⡶⠀⠑⠘⠀⠰⡿⠁⠀⠈⢹⠀⠀⠀⡀⢙⠣⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠘⠛⠛⠀⠀⠀⠀⠀⡠⠁⠠⡘⠀⠈⢀⠀⠠⠈⢻⡄⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⠂⠈⠀⠀⠀⠀⠀⢰⡀⠀⠀⠂⠆⠠⡌⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠻⠹⣦⣠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡶⠙⣦⠀⠀⠀⠀⢀⡀⣾⠛⠙⠻⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣧⣉⣙⣿⡆⣠⣴⠟⠛⠋⠋⢀⣠⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⡿⣿⡀⢀⡠⢴⣿⢫⠻⣿⣿⣿⡁⢸⣭⣿⣣⠴
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠈⠀⣿⣿⣭⣾⣿⣿⠏⠙⠛⢻⣿⣟⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢀⣉⣡⣼⣿⣿⣧⣶⣿⣧⣌⣻⣿⣿⣿⢟⡀⠉⡄⠀⠈⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠛⣿⠟⠙⠿⢿⡿⠿⣿⣿⣿⣿⠃⠀⡁⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⣡⣤⣀⠀⣀⣀⠐⠒⢻⣿⣾⣿⣤⡀⠁⠈⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠈⠙⠛⠟⠛⠻⣦⣼⡿⣿⣿⡯⣄⢀⣀⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠀⠀⠀⠀⢀⣶⣶⣾⣿⠀⠉⠘⠧⠈⠉⠉⠀⣀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⠐⠤⠀⢰⣿⡃⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⠞⢩⠞⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡭⠁⢀⡤⠂⣹⣿⣿⢏⣿⣿⣴⡶⡞⠁⣸⡿⠇⢀⡋⡄⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⡇⢠⣿⣿⣶⣿⣿⣿⣧⣄⠀⠀⣿⣷⠀⣼⡸⢲⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣻⣆⠄⢻⣾⡻⣿⣿⣿⡿⣿⢿⡹⣧⠀⣿⡗⢠⣯⣜⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⡷⢤⣽⣷⣿⣷⣻⣿⣿⣿⡿⠁⡏⠀⠁⠹⣷⡈⢻⣼⣿⣾⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⡟⠙⠋⠀⠀⠀⠀⠀⢴⣇⡸⣻⣷⡎⢿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠛⠀⠀⢠⣤⡠⢤⣄⠈⠛⣿⣿⣿⣧⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠙⠶⢤⡀⢹⠟⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣄⠹⣧⡀⠀⠻⡆⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣤⠈⣿⣤⠀⢻⠀⠀⠀⢸⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⡜⢻⣧⠸⣇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣽⣷⣿⣦⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠙⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡤⣤⣰⡶⢾⡾⠿⢿⣻⣤⣀⠀⢀⡜⠀⠀⠈⠛⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⣙⣡⣠⣰⣼⣤⣧⣀⡹⢟⣿⣇⣼⠆⠀⠀⠀⠀⠀⠀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠤⢤⡀⠀⠀⠀⠀⣠⣼⣿⡆⣇⣶⣿⣿⣿⣿⣿⣿⣿⣤⣌⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⢀⣿⣷⣷⢊⢽⣿⠟⣩⡿⠾⠳⢦⣝⣿⡟⣬⣽⣿⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⣹⣿⣿⣞⡙⣷⣇⣄⣄⣈⣴⡼⢟⣧⢻⣿⣋⣀⠴⠛⠉⠁⠀⠀⠀⠀⠐⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠖⠀⢀⠀⠀⠀⠀⠀⠈⡿⢟⣿⣯⣾⣹⣯⣽⡹⣼⣦⣾⣿⠿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠰⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠹⡿⠿⠿⠿⠿⢯⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⡂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣆⠀⠀⠀⠀⠀⣿⡷⠂⢤⣀⢀⣤⣿⣟⣛⠛⠛⠛⢅⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠀⠈⠀⣀⣴⡁⠙⢆⠀⣀⣀⡈⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠦⡀⠁⠠⢤⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠽⠞⠁⠀⠀⠀⠈⠃⠀⠐⠀⠠⠿⠿⠟⠠⢐⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣅⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠉⠙⢻⣿⣿⣿⣾⡟⣿⣿⣿⣿⣦⠐⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠸⣯⠙⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠠⠨⣆⡘⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢾⣿⣯⣹⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣢⢤⣀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠀⠙⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠐⡿⠂⠠⣤⠿⠀⠀⡀⠀⠀⢉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠀⠈⠁⠐⠃⠰⣴⡅⠀⠀⠀⠁⠀⢄⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠻⡀⠀⠀⢀⠀⠀⠄⠀⠀⠀⡜⣆⠀⠀⠀⠀⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠠⣸⣂⣾⡀⠀⠀⠀⠃⡘⠇⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠿⠁⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠾⡿⠛⠁⠀⠠⣴⡶⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢤⣶⣿⡟⠀⠀⠀⠙⢄⠀⠀⠀⢻⡇⡠⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠤⠤⠵⠶⢤⠀⢩⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠖⠋⢁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢠⠀⠒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠠⠠⡄⠀⠐⠙⣤⣀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⠀⠔⠁⠀⠓⠀⠀⠀⠀⠀⠀⢠⡀⣀⣤⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣿⣿⣟⢋⡉⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⢁⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠀⠀⠀⡠⠀⠀⠀⠀⢀⡴⡿⠁⢹⣯⠀⠀⠠⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠑⠠⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄

⠀⠙⣄⠀⠀⠠⡄⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠥⣽⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠉⠢⠀⢀⣤⣄⡀⣻⣆⣀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⣰
⢀⡀⠀⠀⠀⠀⠀⠀⡠⣤⣅⣄⣼⠀⠀⡀⠀⠈⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠂⠀⠀⣠⠟⠶⢘
⡞⣂⠀⣀⠀⠀⠸⠬⠄⠀⢏⠙⢿⣧⣄⡇⠀⠀⠀⠀⠀⢀⣗⣫⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢠⠀⠀⠀⠀⠀⡌⠄⢱⣿
⠑⠉⠀⠛⢯⠂⠀⠀⠀⠀⠀⠨⢤⣿⣿⠇⡆⢀⠀⢠⠀⠀⠈⠙⠁⠀⠀⠰⣿⣷⠀⠀⠀⠘⠆⠀⠙⠉⠀⠀⡦⠀⠀⠀⠀⠃⠰⠎⠓
⠀⠀⠀⠀⠁⠀⠄⠀⢀⡀⠀⠀⠀⠿⣿⡖⡱⠏⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠙⠉⠀⢀⠀⠀⠑⢀⠄⠀⠀⡀⠀⠀⠀⠰⠦⡀⠀⠈⢢
⣴⣶⡷⠀⣀⣄⠀⠀⠘⠓⠀⠀⠀⠚⠉⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⢀⠀⠀⠑⡀⠈⢻
⢿⣇⠀⠈⠉⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢰⠌⠁⠀⠀⠀⣾⣥⠀⠀⠀⠀⠘⠄⠀⣄⡀⣧⡄⠈⠑⡄⠁⠠⠔⠀⠀⠻⠇⠀⠀⠉⢲⡀
⡄⠈⠀⠀⢀⡀⠈⠁⠀⠀⢷⡄⢀⠀⠀⡰⠀⠀⠀⠀⠀⠹⣼⠃⠀⢀⡠⠀⠐⣦⣿⣿⣿⣷⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠀⣸⠉
⠠⠄⠂⠐⠋⠍⠀⠀⠀⢤⠀⠐⠊⢀⡜⠁⠀⠀⢀⣀⠀⠈⠁⠀⠀⠏⠀⠐⠲⠾⣿⠟⢽⣻⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⠃
⣀⠀⠀⡀⠁⢒⣤⠀⠀⠀⠤⠄⠠⠚⠀⠀⠀⠈⠰⣩⡭⡖⣢⣀⠀⠈⠀⢰⠀⡀⠀⠛⠛⠋⠀⠀⠀⠀⢰⡏
⠲⠍⢻⣻⠿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⢹⠃⢵⣿⠷⣬⠀⠀⠈⠁⠰⠇⠀⠀⠠⡀⠀⠀⠀⠀⠸⠇⠀⠀⡃⡀⠐
⠀⠀⡜⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⠀⠎⣹⣉⡘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠸⠀⢀⡗⠁⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠊⠋⠁⠾⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⡄⢀⣴⠀⠀⠀⠀⠀⠀⡈
⠈⠀⠀⠀⡄⢀⣤⠀⠀⢳⠀⣰⣿⣟⠀⣼⠂⠀⠀⠀⠀⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠛⠁⠀⠀⠀⠀⢀⠀⠀⠂⢀⡀
⠀⠀⠀⠀⢰⡘⠻⠂⠀⠀⠀⢻⣿⠿⠛⠃⠀⠀⢤⡄⠀⠀⠀⢁⣀⠀⠀⠀⢠⠀⠀⠀⢀⣓⠀⠹⠀⠀⠀⠀⢌⠸⠃⡾⣿⠓⠀⠈
⠀⠀⠀⠀⠀⢠⠆⠀⠈⠀⠀⠀⠁⠀⢀⠆⠀⠀⠀⠀⠀⠓⠀⠀⣀⡀⡀⠀⠈⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⢿⠄⣞⠙⣋⠁⣗⣲
⠐⠀⠄⠰⠂⠀⠀⠀⠀⠀⡐⡞⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠰⣿⣡⡷⠂⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣔⢿⣹⣁⣿⣹⠇
⠀⡇⠀⠀⠀⢰⣶⣾⠁⠀⠌⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⣠⣶⡄⠀⠀⢸⣇⠀⠈⠉⠑⠓⠁
⣼⡗⠂⠀⣻⠾⠟⢿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠀⣱⢶⡃⠀⠀⢸⣿⡀⡀⠀⠀⡀⠀⠀⠈⠐⠲
⠘⠛⢄⠀⢉⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠙⠷⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣦⠈⢿⢧⣤⣿⣼⣿⠷⠶⠂
⠀⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠦⢀⡐⣄⠀⠀⠀⠀⠀⡀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣼⠞⠙⠉⠉⠉⠀⠀⠀⠀⢀
⠀⡇⠀⠀⠘⣧⡄⠀⠀⠀⠀⠀⠘⢁⣄⡏⣥⣭⠀⠀⠀⠀⠀⢰⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⣀⠀⠀⠀⢠⠖
⢠⡶⣃⠀⠀⠙⢿⠀⠀⠀⠀⠀⣞⠻⠭⠟⢢⡄⡅⠀⠀⠀⠀⠈⠁⠀⣤⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠁
⠀⠇⠉⠀⠀⠀⠈⢆⠀⠀⠒⠂⡩⠀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣄⢠⣄⠀⠀⠀⠀⠖⠀⠀⠀⢀⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣴⣞⣋⠁⠒⡶⠴⣶⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⣞⣉⣒⣒⣛⣫⣽⠷⢀⣸⣷⣾⡝⠛⠚⣶⠓⠺⠄⣀⣶⡶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⣴⡶⠻⡟⢉⢴⡾⠻⢤⣴⡴⣷⣿⣿⣿⡊⢦⣽⣭⣭⣥⣤⣤⣹⣍⣓⠾⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡀⠈⢷⣤⡿⢾⢿⡷⢷⢞⣫⣾⢏⣇⣀⣌⡹⠢⣿⡟⠛⡣⡘⣿⣿⠟⠲⡿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡿⣧⠉⢭⣶⡾⣿⣄⠊⣨⣃⣀⣼⣽⣠⣽⣿⣥⡏⢀⣴⣿⣶⣶⣿⠿⢯⣓⣲⡶⠷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⣿⣃⣼⡇⡜⠿⣿⠿⣿⣿⣟⠋⠠⠭⣽⣷⣾⣧⣾⠋⣿⠿⢿⣼⣦⣾⣿⡿⢟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠁⣰⣿⣿⡮⠍⠳⡶⣏⢀⡡⢏⣿⠇⠨⠛⡿⢿⡳⣅⡉⢝⡿⠀⠈⠛⢉⣻⣿⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡝⠋⡟⠠⠙⣋⣿⣧⣡⣿⣦⣴⣾⣤⢿⣶⡾⡶⣬⠇⠀⠤⠴⠾⣿⣶⣶⡴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠱⢤⣭⠛⣿⢋⣾⣿⣿⣿⣍⠐⠒⣣⣿⠞⠃⠀⠀⠀⣀⣤⣬⣽⠧⢸⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠴⢟⢹⣿⣷⡞⡟⣹⣿⣿⣿⣠⣹⣿⣁⣾⠀⠀⠀⠀⠘⢯⡉⢸⡿⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⣤⣹⡱⡈⢻⡣⡙⠿⠞⣿⣽⠷⣤⢿⣍⠀⠀⠀⠀⠀⠀⠉⠉⠁⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⣿⣷⣧⡜⠑⡦⣍⣁⣼⡟⢾⣁⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⢁⠢⣉⣺⡾⡃⠌⠉⠁⠠⣤⡝⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣶⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣿⣶⢿⣧⢰⠟⠀⠀⡦⠀⡈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣶⣶⣉⣶⣿⠋⠀⣴⠀⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠆⣠⣴⣿⠆⠀⠀⠀⠈⠦⣀⡀⠉⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣆⢸⡟⠃⣢⠃⠀⠀⠀⠀⠈⠹⡛⠶⣦⣖⣈⠉⠁⠀⠀⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀⢈⠉⠿⢷⠟⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⣀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣀⠁⢙⢹⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⢘⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠓⢌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⢀⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣤⠉⠀⣬⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠾⠦⣤⣀⡀⡆⠴⡊⠀⠀⠀⠀⠀⠀⠀⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⣄⠀⠠⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠟⠛⠻⠿⣿⡿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠻⠿⠿⠛⠛⠛⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠇⣀⠀⠀⠀⣿⠀⠀⠀⣀⣂⠀⠙⢁⠂⠀⠰⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢆⠀⣋⣛⣺⣛⣿⣿⣿⣟⠛⠻⢿⣦⢫⠀⠀⡂⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡔⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠿⠟⠒⠒⠲⠒⠒⠶⠿⠆⠀⠀⠀⣶
⠀⠀⠀⠀⢀⠠⢼⣄⠀⡇⠀⠀⠉⠻⠙⢻⣿⠿⠛⠛⠿⠷⠿⣿⡿⣭⣭⣤⣼⣾⣶⣤⣄⣀⠀⠀⠀⠈⠴⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢰⣿⣷⣿⣿⣷⣷⡄⠀⠀⠀⠀⠾⢿⠐⠐⠒⠂⠐⠰⠤⠦⠤⣧⣴⣦⠤⢭⣍⣩⣩⣹⣿⢟⣿⣾⣿⣿⣿⣭⣽⠂⠀⢀⣤⡲⠾⡟
⠀⠀⠀⣿⣿⣭⣝⣿⣿⣷⠀⠀⠀⠀⠀⠐⠸⡄⠀⠀⠀⠀⠀⠀⣀⣸⣇⣿⠃⣶⠈⡁⠈⠡⢸⣿⢿⣽⣸⡇⣽⣿⣿⣼⠀⠀⣿⠙⢲⠀⣇
⠀⠀⠀⣿⣿⣿⣝⣿⡟⠻⣇⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⣿⡇⡀⠞⠀⠀⢸⣿⣽⣯⣼⡇⣨⣽⣿⣿⣶⣿⣿⣼⣍⣠⣥⣾⣷⣦⣄
⠀⠀⠀⢻⣿⣿⣹⣿⣧⠀⢻⣧⣶⠆⡀⠀⠀⠀⠀⠀⠀⢀⡴⢯⣥⣤⣭⣭⣽⣿⣷⣦⣴⠀⢸⣿⢸⡿⢚⡇⣸⣿⣿⢻⣿⣯⣭⡛⣿⣿⣿⣿⣿⣿⡀⠇
⠀⠀⠀⢸⣿⣿⢻⡟⣿⠒⢹⣟⣿⣄⡹⠁⠺⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣽⡟⠉⠉⢸⣿⠀⢸⣿⢹⣿⣽⡧⣾⣿⣿⣾⠋⠛⠿⣻⣿⠟⢿⣿⣿⣿⡓
⠀⠀⠀⠈⣿⣿⡟⠃⣿⣾⢎⠛⠺⠯⣝⣿⠐⠰⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣤⡾⢹⣆⢸⣿⣿⣿⣿⡟⣿⣿⣿⣗⠰⡶⠀⢸⡇⠀⠀⠹⢿⣿⣷
⠀⠀⠀⠀⠹⣿⣿⣾⣿⠇⠀⠉⠂⢠⡀⠈⠛⢻⣿⣿⣿⣿⣿⢫⡆⠂⠸⣿⣿⣿⣾⣶⣿⣟⣿⣯⣿⣿⠿⠷⠿⠟⠛⣿⣧⣤⣄⣿⣷⣶⡄⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠈⠀⢀⣿⠿⠿⢻⣿⡿⢃⠁⠰⢀⠹⣧⢿⣿⣿⣿⣿⣜⣷⢔⣒⣀⣞⣶⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⠁⢨⣹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⡄⠀⠶⢬⢆⣿⠘⣿⣿⣿⣯⣿⣿⣿⣿⡿⣿⠛⠛⠉⠉⣁⣠⣬⣤⣿⡿⠇⠀⣼⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡠⣾⣾⡇⡧⢾⡇⣿⣿⣿⣿⣇⣸⣼⣿⣃⣿⠷⠾⠛⠋⠉⢿⣿⣿⣥⣀⣠⡴⡏⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢒⠈⡿⣿⠦⢸⡇⣿⣯⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡎⢠⠁⠐⠀⣼⡇⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡙⢑⢄⢀⡿⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣯⣡⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡴⠒⠒⠒⠒⠜⠉⠈⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠛⠳⢤⡤⠀⠀⠠⠀⠠⠇⠀⠀⠠⠤⠤⢀⡴⠒⠒⢂⣺
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣀⠀⠉⠀⠀⣠⠴⢿⣯⡄⠀⠀⢠⠉⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⡻⠶⣤⣤⣤⡄⠀⢠⣤⠤⡀
⠀⠀⠀⠀⠀⠀⢀⢠⣽⠃⠀⢹⣷⠀⠀⠀⠁⠐⠀⣟⣇⣠⢤⣔⣛⣓⢶⣤⣀⠀⠀⠀⢀⠃⠀⣸⣿⣾⡄⠉⡉⠉⠉⢙⢿⣇
⠀⠀⠀⣀⣴⣾⣷⣿⣿⣆⣂⣼⣿⡆⠀⠀⢧⣠⣤⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣿⠀⢠⣷⣿⡧⣻⠀⡂⠀⣸⠉⢸⣿⣧
⠀⠀⢠⡿⠿⣰⣿⣿⡈⣿⣿⣿⣿⡇⠀⠀⢾⣿⣧⣿⣋⣠⣼⠟⠋⠉⣉⣙⢿⣿⣿⣿⣿⠀⣼⢿⣿⠋⢺⠀⠁⠀⣷⡀⣹⣿⣿
⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣾⣿⣿⣿⣿⡟⠁⠀⠠⠜⣓⣮⡅⢹⣿⣿⣿⣧⣻⣷⡈⢠⣿⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⠀⠀⢠⣷⢿⣫⢞⢿⠀⣿⡿⠿⢿⣿⣯⣿⣾⠿⢛⣉⠩⠔⣶⣿⣼⠁
⠀⠀⠀⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠠⢷⣿⡿⢻⠼⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠠⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣷⡿
⠀⠀⠀⠀⠑⢄⡱⠈⢛⣛⣿⠟⠁⠀⠈⠉⠉⠉⠉⠉⢃⠀⠀⢀⣧⡎⠃⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⢎⠋⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠭⠓⠉

⣿⣿⡿⢟⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣄⣿⣾⣶⣿⣿⣟⣠⣴⣶⣆
⣿⠿⣿⢻⣯⣥⣄⣀⡀⠍⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠠⣾⣿⠿⠻⠿⠟⠿⠟⠿⠿⣿⣷⣶
⠃⠀⡏⠈⠿⣿⣿⣿⠉⢳⣦⣹⣿⠃⠀⠀⠀⣀⣀⣐⠋⠁⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠆
⠀⠀⠆⠀⠀⠈⠛⠫⠄⠈⠙⠋⠀⠀⣴⣿⣿⡿⠟⢻⠇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⢣⠀⠀⠀⠐⠲⠖⠃⠀⠀⠀⠀⡝⣿⣯⢙⣷⠋⠀⠀⠀⠀⠀⠀⢸⣧⢴⢯⣵⣦⣄⣀⣺⣯⣭⣦⣬⡅
⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⢭⡌⠁⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠁⢈⡟⠻⠀⠉⠀⠈⡽
⣧⠀⠀⠹⡄⠀⠀⠀⡄⠉⠁⠀⠀⢰⠀⠙⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⡫⡇⠀⠙⠒⠒⠊
⣿⠁⠠⢤⣘⣦⡀⠀⠻⣿⣿⣦⣤⣴⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⢈⠃
⡇⠀⠀⠀⢈⣻⣿⣦⣤⣜⣿⣿⡿⣰⡿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡿⠂⠋⠁⠉⠳⠀⢀⣀
⣿⣶⠖⠀⠀⢨⡙⠿⣿⣯⣿⣿⣷⣿⣥⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠺⣿⡇⠐⡣⠸⠃⠀⠀⠄⠀⣸⣿⣿⡶
⣿⣿⠓⠀⠀⠚⠻⢶⣤⣌⣭⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⣠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣶⣛⠋⠙⢟⣿⣶⡄⠀⠈⠁⠈⣀⢀⢀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠠⢄⢄⣼⣿⡏⠁⠀⠀⠈⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⠃⠀⠁⣤⣿⣿⡏⠁⣿⣷⡄⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠦⠤⠎⠹⣿⣿⡇⢸⣿⣿⡗⠀⠀⠀⠀⡄
⠀⠀⠀⠒⠂⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠒⠂⢀⠒⠒⠐⠒⠈⡃⠀⠀⠈⢀⠙⣿⢡⡼⢿⢿⡛⢺⣅⠘⠉⡃
⠀⠀⠀⣄⠀⠤⠤⣤⡤⣀⣀⣤⣤⠤⡤⠀⠀⢣⡤⠄⠤⣤⣤⣜⣦⣠⣴⠦⢾⠁⠀⣷⡀⠀⠈⣻⣿⣢⣴⡇
⠀⠀⠀⢩⠀⠀⠀⠀⡶⢈⠉⣡⡀⡾⠇⠀⢀⣤⣿⡎⢶⣰⣤⣿⣦⢟⠉⠀⠀⠀⠀⡟⠻⣆⠀⢹⡟⢿⣿⣿⡟⡉⠉⠛⠉⠍⠛
⠀⠀⠀⡾⠀⠀⠀⠀⠘⠃⢀⡴⠛⠀⠀⠀⢨⡟⣛⡶⢿⣾⣯⣿⠷⡈⠁⠀⠀⠀⠔⠁⠀⢟⡀⠀⠂⣿⣿⣿⡦⠕⠒⠀⠀⠀⠒
⠀⠀⠀⠷⠶⠶⠷⠶⠦⠶⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢶⣄⠀⠀⠀⠿⠧⠂⠈⢻⣿⣿⠧⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢰⠘⡇⠀⠈⡱⠊⠁⠀⠀⠀⠀⢀⣠⣾⣿⡤⠄⠀⠀⠀⠀⠀⢴⣷⣿⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣼⣂⠷⣌⡀⣿⡀⠀⢀⣀⣠⣶⣿⣿⣿⣯⣉⠢⢀⠀⠀⠀⠀⠀⣸⣿⣿⡦⠢
⠀⠀⠀⣶⣴⣦⣴⣶⣤⣤⣤⣤⣴⣤⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣥⣤⣨⣲⣶⣴⣾⣿⣿⡟⡛⠣⠄⣀⡀⠠
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣾⡿⣿⣿⣿⣿⣷⣦⣤⡀⠙⢚
⠀⠀⠀⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡝⢯⢉⣨⠇⠁⠀⠸⠀⢘⡛⣿⣿⣿⣤⣿⣿⣓⣈
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⣡⡿⠟⠋⠠⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠁⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠅⠀⠰⠞⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣿⡏⢻⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠶⠋⣿⣿⣿⣿⡿⠿⣧⡝⠿⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡇⣸⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⠛⠀⢀⠉⠀⠀⣠⣿⠇⠀⠂⠀⡀⠀⠘⠃⠰⢀⣀⠀⢀⡀⠈⡄⠐⠀⠀⣠⡼⠁⣿⡝⣿⣿⣿⣿
⠀⠀⠀⣭⣴⢿⣿⣿⣿⣾⠛⢤⡖⠊⠀⠀⠀⣺⡙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠩⣿⠾⠋⠡⠀⠀⢀⣾⣿⣇⢠⣼⣼⣿⣿⣷⣿
⠀⠀⠈⣿⣿⣿⢧⣬⠝⠻⣷⣎⠓⣦⣴⣶⣌⣿⡿⢄⡀⠀⢀⠀⠀⠀⠀⠀⣠⡼⢿⢛⡢⠠⢤⣾⣿⡷⣾⣿⣿⡟⠹⢿⡿⠩⢈
⠀⠀⢸⣿⣿⡏⠀⠈⠷⡄⠈⢻⣿⣿⣿⣷⣼⣿⣽⣿⡗⣲⠮⣟⣛⣋⣋⣒⣳⣤⣤⣴⣅⣰⣿⣿⡿⢷⣿⣷⣿⣽⣷⣿⣿⠀⠸
⠀⠀⠘⣿⣸⠇⠀⠀⢀⡅⠀⠀⠙⡿⢛⣽⣫⢽⣿⡻⢿⣤⡿⡿⡟⠛⠿⠿⣿⣿⣿⣯⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⡋⣿⣄⣠
⠀⠀⢰⡿⠁⠀⠄⣠⣿⣷⠞⠛⠛⣷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢻⣡⣿⣿⣿
⠀⠀⠀⠣⣴⣤⣾⣿⣿⠧⠴⠤⢦⠽⠶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉
⠀⠀⠰⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢴⣶⣤⠀⠀⠀⠀⣀⠻⠀⠀⠀⠀⠀⣤⣾⣿⣷⣦⡀
⠀⠀⠀⠀⢂⣽⠄⠀⠀⠀⠀⠀⠈⠲⣯⢆⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⠀⢻⣽⠏⠀⠀⠀⠀⠴⠎⣔⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢰⠇⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠀⠀⠀⠀⠀⠀⠴⠀⠀⠐⠂⠀⢭⡄⠀⠀⠀⠙⠛⠿⠛⠋
⠀⠀⠀⢰⢯⢟⡈⢇⠀⠀⠐⠀⠀⢀⡔⢀⡀⢴⣴⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡎⢀⢀⠀⠀⠀⡀⠙⠂⠴⢂
⠀⠀⠀⠸⠀⡘⠿⠞⠁⠀⠀⠀⠀⡸⠀⠀⣀⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢤⠰⣅⠈⠗⠀⠀⠀⠹⣧⠀⣶⣿⡟⠂
⠀⠀⠀⡀⡄⢀⢠⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠤⢙⣤⣥⣀⠀⠀⠀⠀⠀⠰⠈⠋
⠀⠀⠀⠀⠂⠘⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣔⡷⣿⣄⠀⠀⠀⠢⠤⠂⠀⠀⠀⠀⠀⠀⠀⣦⢢⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠲⠀⠀⢹⡍⠆⠀⠀⠸⠿⡿⠋⠀⠀⠀⢣⡠⠀⠀⠰⣿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠪⡽⠿⢿⠃⠀⠀⠤⡀⠀⠈⠀⠁⠐
⠀⠂⠀⠀⠀⢠⣾⣗⠀⠀⠀⠀⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠶⠉⠀⠀⢀⣀⣄⠀⠀⠈⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠢⢹⣧⡞⠀⠀⠀⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣷⣆⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣤⣤⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠈⣿⣿⣿⣿⣿⣿⣦⠙⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣽⠋⠙⠿⣿⣿
⠀⠀⠀⠀⠀⣿⠟⠋⠀⣻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢰⣿⠟⠏⠉⠛⠁⠘⣿⣿⣿⣿⢻⣿⠄⠀⠀⢹⡟
⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⣿⠟⠉⢀⣰⡄⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢠⠈⠻⣿⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣾⣿⣿⣿⣷⠀⠀⠀⠀⠛⣿⠠⠀⣰⣾⣿⣶⣧⡸⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⡀⠉⠻⠀⢿⣧⣛⣿⡟⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢰⡄⠲⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠉⠋⠂⢠⠏⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠠⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⣼⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⠇⠀⠀⠀⠀⠀⢀⠀⡁⠀⢰⠀⠈⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣊⡞⠀⢀⡶⢀⣰⡿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣀⢠⡿⢁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣧⡀⠀⠀⢀⣼⣿⠟⣻⠇⠙⠉⠈⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁⠚⠛⠛⠁⠐⠠⣴⣾⣿⣿⣿⣤⣴⣿⠿⠻⠞⠁⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣥⠀⠁⠀⠀⠀⢀⣾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠆⠀⠀⠀⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⡆⢲⣶⣷⣤⠦⣤⡀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⡎⣼⣿⣽⠀⠈⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣿⣿⡿⢿⣦⡀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣟⡀⠈⢉⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢄⣷⣆⣠⠏⠀⠙⢷⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢶⡶⠶⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠸⠶⠄⢶⡯⠁⠀⠶⣿⣶⣹⣷⡏⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⣠⢄⣠⣤⣤⠤⣾⣿⣷⣶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠳⣾⣿⣿⣿⣿⣿⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⣴⠟⠉⣀⣠⣶⠛⠟⣿⣿⣿⣓⣀⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⢋⣿⣿⣿⡏⢨⠛⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣼⠿⠞⡫⠟⣯⡷⠟⠛⠛⢿⢿⡏⠉⠙⠿⢿⣷⡖⠚
⠀⠀⠀⠀⢀⠀⣠⡴⠂⠀⠀⠸⣏⣿⣿⡟⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⢀⠐⠀⠀⠀⠉⠀⠀⠀⠀⢨⢸⣧⠀⢰⡄⠤⣿⣿⠃
⠀⠀⠀⠈⠁⠀⠀⣤⣀⢠⡀⢠⣼⣿⣿⡇⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠷⠄⠀⠀⠀⠀⠀⠀⠀⠻⠀⣿⠀⠀⡷⠀⠿⠟
⠀⢀⠀⠀⢀⡴⢷⣻⡿⣿⣿⣿⣹⣽⣿⡟⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠘⣇⣿⠗⠶⢷⣤⡀
⠀⢀⣠⣾⣟⣿⡂⣹⣿⣿⡟⠋⣠⣿⣿⡟⠀⡷⠀⣀⢀⠀⠀⠀⠀⢶⡀⠈⠀⠀⠀⢠⡀⣀⠤⠒⠊⠀⠘⠉⠀⢸⣧⣷⡄⠀⢸⡌⣻⣆
⠀⠈⢿⣟⣻⣿⣧⣿⣿⠋⣹⣿⣯⣽⣿⣷⡀⢢⠀⠈⠉⢠⣤⣴⠖⠂⠁⠀⠀⠀⠉⠹⡗⠀⠀⠰⠦⠶⠖⠒⠒⢺⣿⠿⠷⠶⢼⠄⠘⠛
⠀⠀⢿⢯⣹⣥⣿⡿⠃⠀⣧⣸⣿⣿⣿⣏⡀⠠⣷⣾⠖⣤⣉⡙⠋⠀⠁⠀⠀⠀⠀⠀⢆⣀⠤⠀⠀⢘⣀⣤⠀⣨⣿⣀⠀⠀⠰⡆
⠀⠀⠙⠉⣠⣿⣍⡁⠀⢺⣥⣿⣿⣿⣿⡟⢹⣤⣿⣿⣶⡤⠈⠀⠀⠤⠀⠀⠀⠐⠶⠒⢿⠃⠀⢠⠾⢟⣉⣀⡀⢹⣿⠉⠉⠐⠤⠀⠂
⠀⠀⢀⡾⠋⠀⠨⠿⠛⢿⣽⣿⣠⣿⣿⣷⠿⣻⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢂⡀⢶⣴⡟⣿⠛⣁⣿⣿⠀⠀⠀⠀⠀⠈⢲⡀
⠀⡠⠞⠃⣀⡴⠖⠒⠒⠒⢰⡟⠘⢻⣿⣧⡀⣹⡇⠀⠀⠹⠷⢤⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣧⣶⣶⣼⡿⠘⠛⣿⣿⠀⠀⠀⠀⠀⠀⠈⠃
⢀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⣷⠀⢻⣿⣧⠼⠟⠛⠻⠶⣤⣄⣀⣀⣤⣀⣤⠀⠀⢈⠹⢟⣻⠿⣟⢻⣟⠁⠀⠀⣿⣿
⠀⠰⣦⣤⠤⠶⠅⠐⢤⣀⠀⡿⢀⣽⣿⡇⠀⠀⠀⣠⣶⣿⣿⠋⠉⠉⣹⢟⡙⣏⠙⠟⠋⠻⣄⠘⡿⣏⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠈⠛⠋⠈⠛⠀⠈⠉⠁⡿⢸⣿⣿⠓⢀⣾⠿⠛⠓⠛⠁⠀⠀⠰⢃⣈⣙⣛⣦⣀⠀⢰⣈⡟⠀⣿⠀⠀⢠⣿⡇⠀⠀⠀⢀⣠⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⡔⡋⠀⠀⠀⡀⠀⠀⠀⠀⠰⣿⠿⠛⠙⠿⣿⠃⠈⢿⣿⣤⡟⠀⣀⣺⣿⡇⢀⣤⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⣉⣿⡟⠁⠀⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⠀⠀⠘⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠀⣀⠻⣦⣶⣾⣿⡏⠀⠀⠀⠀⠀⠈⢛⣠⣤⠴⠶⠶⠶⠶⣤⣄⡀⠀⠀⠈⣿⣿⣤⣶⣿⢿⣿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢝⣻⣿⡿⠛⠻⠇⠀⠀⠀⣤⣤⠶⠋⢩⣄⢀⠀⠀⠲⠄⠀⠈⠛⢶⣤⣼⣿⣿⣿⠛⠁⠀⠋⠀⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡅⠀⠀⣀⡀⠀⣾⠟⠁⠀⠀⠀⠘⠻⠇⠀⠀⢀⣀⣀⣴⣾⣿⣿⠿⣯⠀⠀⠀⠀⠀⠀⢸⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⢿⡃⢰⠾⢿⢿⣿⡏⠀⣧⠀⠀⠀⢀⡀⠀⠀⢀⣼⣿⣿⡿⠟⠋⠀⠀⢹⡄⠀⠀⠀⠀⠀⢈⡼⠃
⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⣿⣿⠀⠀⢸⣿⡏⠀⠀⢹⡇⠀⠀⠹⠿⣠⣾⣿⡿⠟⠉⠀⠀⢀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢻⠿⣧⡀⠀⢹⣿⡇⢀⣀⣾⣿⣿⣯⣄⠀⣀⣀⡀⣘⣿⣆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⡇⠀⠈⠻⣦⣠⣾⣾⣿⠟⠋⠉⠉⠉⠛⣶⠛⠋⠉⠙⠛⠻⣷⣤⡀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠁⠀⠀⣀⣼⣿⣿⢟⡁⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢸⠀⣠⣾⣿⠿⠋⠁⠀⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡟⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⠖⠛⠙⠛⠋⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣶⣿⣷⠆⠀⠀⠀⠀⠀⡀⢄⣶⡄
⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣀⠤⢓⣼⣼⡹⣿⡄
⢀⣾⢦⣀⠀⠀⠀⠉⠛⠻⠿⠂⠀⠀⠀⠀⢰⣿⣶⣰⣠⡠⠠⣀⡄⠄⡄⣦⣇⢁⡈⢿⣇⠸⡿⣿⣔⠸⣷
⣸⠧⣿⣷⢰⡖⠀⣀⣀⠀⣀⡀⣀⣔⣾⡆⢸⡿⢰⣾⣿⡗⠀⣿⣿⣿⣶⠼⣿⡼⡀⡸⣿⡎⣷⣿⣿⣃⢹
⣿⣲⣿⡟⣾⡇⣱⣿⢴⣲⣿⡄⡿⣷⢼⡇⢸⡧⠄⣿⣷⣯⠀⣿⡿⣿⣟⠁⣿⣷⠋⠀⣿⣷⢺⣽⣿⢠⡌
⡇⣼⣯⣗⣿⠀⢹⡿⠸⢟⣿⡇⣿⣿⠐⡇⢸⡇⢰⣿⡏⣵⠀⣿⣇⣧⣴⡄⢹⣿⣴⠑⢸⣿⣈⡛⣿⡇⠤
⠐⢸⣯⢽⣿⢸⣾⡇⣴⣾⣿⠃⣷⣿⠃⠇⠀⠀⠄⢹⣿⢿⡁⢻⣿⣴⣿⠷⠸⣿⡇⠗⡘⣿⡧⣿⣿⣷⡆
⠘⣿⡿⣿⣿⡈⣿⡇⠻⣟⣿⢰⣿⣯⠈⠀⠀⠀⢄⠸⣿⣷⣷⠸⣿⡎⣟⣩⡀⣿⣇⡔⡀⣿⣗⣏⣿⡸
⠀⠘⣿⣿⣿⢼⣿⣷⣿⣿⣟⣾⣿⠅⠀⠀⠀⠀⠀⠀⡞⢿⣿⣧⣹⣿⣿⣿⣷⣿⣿⠗⢁⣿⣟⣿⡟
⠀⢀⠘⠏⢿⣄⣿⣏⠿⢿⠿⡟⢛⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⣿⠷⢹⡿⠽⣉⠿⣿⡀⠼⡿⠘⣋⠀⣘
⠀⢐⠀⡂⢐⠀⡂⠐⠀⢀⠀⠄⠨⠀⠀⠀⠀⠀⠀⠀⢐⡂⠀⣒⠀⢐⡂⠀⡒⠀⢐⠀⠀⡂⠀⡒⠀⡒
⠀⠀⠀⠂⠐⠀⢠⠀⡆⠨⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠰⠆⠀⠂⠀⢐⠀⠀⡆⠀⢰⠀⢀⡂⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢻⣿⣦⣶⣾⣿⣿⡿⢿⣊⣥⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣧⣯⣹⣿⡊⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠃⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠘⡀⡀⢀⠀⠀⠀⠱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠿⠿⠛⠻⠿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠂⡁⡎
⠀⠀⠄⠀⠰⡃⠇⠀⢀⠄⡀⢰⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⣟⡤⠟⠀⠀⠀⠀⠀⠀⠀⠐⠀⢜⠀⣀⡄⠀⠀⢃⡇⠀⠠⠂
⠀⠀⠀⠀⠀⠁⢠⡄⠀⠀⠉⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠈⠁⠀⠀⡆⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢈⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⠟⣿⣿⡇⠀⠀⠀⠈⠻⠿⠿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⢀⣠⣶⣟⣿⣿⣿⡟⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢿⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⡀⠀⣀⣠⠞⠋⠓⠀⣈⣁⣴⠿⠀⠀⣾⣻⣿⡁⠀⠀⠀⠀⣠⠀⠀⠀⠸⣦⣤⡀⡀⠉⠉⠹⠷⣤⡀⠀⡄⠀⠀⠀⠀⡺
⠀⠀⠀⠀⠀⡆⠀⢠⡀⠘⠃⣾⠟⠁⠀⢀⠤⠊⠀⢻⣇⠀⠀⠀⣿⢏⠁⣿⠂⠒⠓⠀⡇⠀⣡⠀⠀⣿⣟⠂⠀⠑⠠⡀⠀⠈⠻⣆⠀⠀⡤⠀⠀⠆
⠀⠀⡀⠀⠀⠀⡄⠀⠁⠃⠘⢡⠀⢀⠔⠀⠀⠀⠀⡾⠻⣦⠀⠰⣿⠈⠀⠉⢄⡤⠂⢈⠀⢀⡟⠀⢸⡇⠹⡆⠀⠀⠀⠀⠂⡀⠀⡈⠀⢀⠀⠀⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠠⠄⠅⢠⡞⠀⢠⣟⡾⠁⠀⠀⠀⠀⣔⠧⠴⡏⠀⠀⣿⣧⠀⠀⠏⠀⠀⠀⠀⣸⣇⠀⠀⣗⠄⠗⣄⠀⠀⠀⠀⠘⢧⣱⡀⠀⠳⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣞⣹⠁⠀⠀⠀⣠⣾⢿⣴⣾⠃⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⢹⣵⢴⡟⢳⣄⠀⠀⠀⠸⡇⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠑⡣⠆⠐⠂⠀⠳⣥⣼⡽⠃⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠹⣮⡧⠼⠃⠀⠀⠒⡒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠁⢼⠇⠀⠀⠀⠀⠀⠸⠁⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⢻⣆⠀⠀⠈⠀⠀⢷⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠠⠔⠆⠀⡀⠎⠀⠀⡆⠀⠀⠠⠁⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⢿⣧⡀⠈⢿⣿⣄⢀⡇⠀⠸⠀⠄⠠⠐⠐⠂⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣷⡀⠀⡌⠻⣦⠁⠀⠐⠂⠁⠈⢁
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠐⠀⠀⣴⠁⠀⠀⠠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⠀⢹⣧⡄⠐⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⢹⡄⠄⠀⠀⢠⢠⣴⣃⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠹⣿⣧⠀⠀⠘⡄⢻⣇⢄⠀⠀⠀⡄⣿
⠀⠀⠁⠸⠀⠀⡈⠃⣠⠀⠀⡈⠉⠠⠏⠖⠑⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⠀⠙⢿⣧⡠⠀⠀⢾⡇⠌⣀⠀⢀⢀⠋⡁⠐⠙⠐⠁
⠀⠀⠀⠀⠇⠰⠈⠛⠹⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣼⡟⣿⣆⠀⠀⠹⣿⡄⠄⢺⠇⡀⢹⠀⢘⠘⠃⠙⠀⠇
⠀⠀⠀⠀⠀⣄⠀⠈⠀⢁⠈⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡿⠁⣿⠹⣧⠀⡆⢹⣧⠀⠘⡅⡇⠀⡄⠛⠉⡁⠀⡀⠀⡀
⠀⠀⠀⠀⠢⠈⡀⠈⠀⠘⡏⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣼⡇⠀⣿⠀⣿⡆⠁⢸⣿⠀⠀⢸⡇⠀⠜⠀⠀⠀⡀⢐⠂⠁
⠀⠀⠀⠀⠐⠸⠃⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣷⠀⣿⠀⠹⣿⡆⢸⣿⠀⠀⠠⠑⠰⠀⠀⠀⠀⠑⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠁⠀⠀⠀⠀⠀⠀⢻⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⣿⡏⠀⠘⠀⠹⣿⡟⠀⠀⠀⢱⠂⡄
⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⢁⡔⠈⠀⠀⠀⠀⠀⠀⠈⠳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣯⣿⠀⢄⠀⢠⡿⠃⠀⠀⠀⠈⣀⠁⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠸⡇⠀⠀⠈⢀⠉⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠈⠑⢢⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠰⡏⠀⢈
⠀⠀⠁⠀⠀⠀⠆⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠄⠀⠐⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠂⣼⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠐⡿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠚⠂⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⢧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡿
⠀⠀⠀⠀⠉⠉⠐⠀⠀⠴⠆⠀⠀⠀⠀⢱⡀⢀⣠⣤⣤⣤⣦⣀⡄⠀⠀⡠⠂⠀⠀⠘⠃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡊⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠒⣿⡿⠂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⡿⠟⠛⠉⠈⠣⡀⠀⠀⠀⠀⠀⡀⣽⣦⡄⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢖⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⡀⠛⢳⡿⣿⣿⡧⠀⠐⠃⠀⠀⠀⠀⣠⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠿⢳⡀⠀⠉⠈⠀⠈⠤⣀⣀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⢼⣶⡐⠁⠘⠁⢡⣾⠀⠈⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠁⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣿⣇⡀⠀⢠⠆⠘⢀⠀⠀⠀⠀⠀⣎⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣾⢷⣖⠀⠊⠉⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⠀⠘⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠒⠒⣲⢲⡶⠚⠓⠛⠒⠂⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢷⣾⣷⣶⣿⠿⢿⣿⣷⣶⣶⡦⠹⢉⣤⣤⡔⣂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢸⣿⠀⢹⣷⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⣷⢹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⢠⣝⣧⣤⡼⣧⣤⢌⣫⢽⣿⣥⣴⣶⣤⡖⠀⠶⣠⠦⠸⠈⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠋⠁⣤⡀⠀⢀⡆⠛⠁⠀⠀⠈⠁⢀⠀⠀⠀⠠⠷⠄⠀⢀⡀⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠾⡃⠙⠀⠀⠀⠒⠁⠐⣺⡅⠀⠀⢀⡴⠾⣿⡏⠙⠒⣤⡀⠀⣀⣀⠀⢁⡄⠀⢈⣵⣄
⠀⠀⠀⠀⠀⠀⢰⢱⡆⢘⠄⠆⠀⠀⠀⢱⠇⣿⠁⠀⠀⠡⣦⠀⢺⠇⠀⣼⣿⣿⣿⠣⠤⣿⣿⠁⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣌⣓⠠⠬⡄⠤⢄⣀⣠⣼⣤⣿⠠⠤⢤⡔⣀⣒⡁⠀⢰⣿⠋⢿⣿⡖⢲⣿⡿⠀⠀⢸⡿⢻⡇
⠀⠀⠀⠀⠀⠷⣿⣿⢧⡾⠿⠿⠿⠿⠿⠿⠿⡿⠿⣴⠿⠹⢶⡾⠷⡶⢻⣟⠀⣿⣿⣿⣿⣿⣇⣀⠀⣼⠃⢸⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⠶⣶⡶⠦⠚⠾⣷⣶⣶⣿⣿⣿⣿⣿⡗⢸⡏⢠⣿⣿⣽⣿⣿⠟⣿⡿⢿⡄⡸
⠀⠀⠀⠀⠠⠤⠽⠿⠿⠿⠷⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣾⣿⣾⣿⣾⣶⣶⣶⣶⡶⠶⠾⠿⠿⠿⠧⠤






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠀⢠⢀⣒⠓⣤⡞⠋⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⣶⣾⣾⣿⣿⣦⣽⣶⣁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⣿⣶⣿⡧⢿⣿⣿⣿⣿⡿⢚⣇⡠⡤⣄⠾⠂⠀⠀⠀⢲⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡗⢠⢻⣿⠀⣿⡿⣿⣧⢼⣿⣿⢿⡿⠲⢺⣾⠭⠁⠍⠀⠀⢀⠄⠀⣸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⡅⠀⠰⠄⠰⠐⢠⠄⠄⢻⠄⣸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢻⡹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣤⣤⡀⠄⠀⠀⢸⠉⢹⣿⣷⡀⠄
⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡗⢀⣼⣿⣿⣇⠀⠀⢂⣾⠤⣾⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠘⣾⣷⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢵⣾⣿⣿⣟⣿⣦⡄⠀⢸⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⣹⣿⣶⣶⣶⢻⣿⣿⣿⣿⣿⢻⣬⠟⣯⣿⣿⣾⣿⣿⣿⣛⣋⣉⣉⣠⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⡏⠀⣿⣿⣿⣻⣿⢸⣽⣧⢿⣷⣿⣿⣿⣿⣿⣹⣹⣛⣟⣻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠐⢤⣿⣿⣿⢹⡟⠚⠛⠶⠾⠹⠿⠺⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⣟⣼⣿⣄⠐⢶⣒⢲⠤⡀⢁⠀⠀⠀⠀⠀⠀⠚⠒⣾⣿⣿⣿⣾⠄
⠀⣄⣻⣿⣿⣿⣿⣿⣿⠃⢰⣾⣿⢿⣿⣿⣿⣟⣿⣦⠀⢻⣿⣆⢹⣆⠁⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣄
⢀⣿⣿⣿⣿⣿⣿⣿⢋⣶⣿⣿⣿⣾⠋⠡⣼⣿⣿⡿⣷⡀⠙⣿⣠⣿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢿⣿⣿⣷⣿⣷⡄⠈⠛⠛⠛⠿⠄⠡⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠿⠿⣟⢧⣼⢿⣿⣶⣶⣶⣶⣶⣶⣶⣼⣤⣶⣶⣶⣶⣶⣾⠿⠿⠿⠿⠿⠂
⠀⠀⠀⠐⠲⠤⠄⣀⠉⠉⠉⠉⠙⠻⠛⠚⠿⣦⣠⣶⣷⣾⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠛⠿⠿⠿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣡⣀⣀⣀⠀⠀⠀⠀⣠⣤⣭⣶⣶⣤⡀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠀⠙⠻⣿⣿⢿⠃⠉⠉⠉⠁⠀⠀⠀⠀⠀⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣿⠁⠀⠀⠀⠀⠀⢀⣠⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠼⣻⣿⣿⣿⣿⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣾⣶⣤⣀⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡟
⠀⠀⣀⣄⣀⠠⡀⠀⠀⠀⣙⣻⣿⡿⡻⠋⠉⠙⠳⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣀⠠⠈⢻⣿⣿⣿⡷⠶⢶⣿⡿⠿⡿⠿⠋⠀⠀⠀⠀⢀
⠀⣾⣿⣿⣿⣷⣏⣧⣀⣾⣿⣿⣿⣏⡇⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣿⠀⠀⠀⠈⣿⠟⠁⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢾⣧⠀⣿⡄⠀⠀⢀⡀⠀⠀⠀⢸⡇⠸⡿⠀⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠀⠆⠀⠀⠈⠤
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⢽⡄⠀⠀⠘⢿⡆⠹⠧⠂⢰⣿⣿⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠺⢿⣟⣿⡿⠟⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢀⣤⣀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⣾⠈⠀⠀⣰⣦⣤⣤⣤⣴⣶⣶⡄⠁
⠀⠀⠠⣴⣶⣶⣶⣶⣶⣿⣦⡀⠀⠏⠙⣿⣶⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⡋⣠⣴⣶⣿⣿⣿⣽⡿⢿⠛⠛⠃⠚⠒
⠀⠀⠀⢹⡿⠿⠛⠛⠙⠛⠛⢿⣿⣮⣀⠀⠀⣛⡛⣵⡄⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⠟⠀⠀⠱⡄
⠀⠀⢀⠂⠀⠀⡠⠄⠀⠉⣽⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣦⣀⢀⠄⠐⠀⣀⠠⢀⣤⣴⣾⣿⣿⣯⠟⢫⠎⠙⠿⠿⠿⠟⠋⠁
⠀⠀⠨⡀⠀⠜⠀⠀⢀⡀⠘⠿⣿⣿⣿⣿⣿⣿⡟⠙⢿⡏⡠⠀⠀⠠⢀⠀⠀⠀⢙⡿⠿⠟⠋
⠀⡀⠀⠀⢰⠀⠀⠐⠁⠀⠀⠀⠀⣉⠉⠉⠉⠁⠱⠀⠈⢧⡀⠀⠀⠐⠁⠊⠀⠀⠀⠀⠄⠀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢢⠀⠆
⠀⠀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠄⡑⠀⠀⠘⠄⠀⠀⠀⠆⠀⠰⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣾⣿⣿⡿⠆⡀⠀⡤⢀⡀⠀⠀⠀⠀⠀⣠⣶⣦⡝⠀⠀⠀⢀⣀⣁⠀⠀⠀⠀⠀⠀⠠⢄⠂⠀⣤⣤⣤⣄⣂⣀⣀⠀⠀⠀⣤⣴⣶
⠀⠱⣿⣿⣿⣦⣌⠈⣠⠊⠀⠑⢄⢀⠀⠈⠿⣿⣿⣷⡄⠠⠊⠁⠀⠀⠈⠓⠄⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⡏
⠀⠒⠛⠻⢿⡿⠟⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠀⠀⠈⠉⠁⠢⡄⠀⠀⠀⢸⠀⠈⣿⣿⣿⡟⢻⠟⠃⠰⣎⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠹⡿⠟⡡⠂⠀⠈⠰⣿⣿⣿⣿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀
⠀⣀⣀⣀⣠⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⣀⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⢀⠁⠀⠙⢿⣿⣿⣿⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⢄⠉⠛⠙⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠀⠰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣷⡀⠀⢀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢹⣧⠾⠟⠛⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢢⣄⠀⠸⢠⣾⡆⠀⠁⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⢰⡿⠃⠠⣾⣿⠿⠋⠀⠀⠀⠀⠀⣠⠞⢋⣉⡙⠻⢦⡀⠀⢿⣷⢀⣿⢫⣴⣿⣿⣿⡿⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣃⠤⠤⠤⢄⣈⡁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢿⣿⣿⡄⠀⢻⡄⢸⣿⡟⢧⣿⣿⣿⣿⣿⠃⠀⠛⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⡀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠻⣄⣀⣉⡿⢡⠢⣌⡇⠘⠿⣠⡈⠻⣿⣛⣫⣴⣿⠆⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠉⠉⠙⠛⢶⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⠇⠀⠀⣱⣶⣶⣬⣍⣉⠉⠐⠒⠚⠋⠉
⠀⠀⠀⢀⡞⣁⣤⡶⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢠⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠐⠲⣤⠀⠉⠛⠿⠿⠿⠷⠆
⠀⠀⠀⣾⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⠇⢰⣮⠙⣶⠤⠤⠤⠶⠛⠁⠀⢠⣤⡿⠃
⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠻⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣲⣿⣿⠇⠈⠈⠙⠀⠀⠂⠀⠀⠐⠁
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣿⡟⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⡿⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⠄⠒⠀⠂⡀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣿
⡋⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠒⠉⠉⠐⠄⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⣀⣀⣄⣄⢀⣤⣾⣿⡋
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⢦⠀⠊⠙⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⣿⣯⣤
⠦⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⡠⠄⠀⠀⣻⡿⠜⢻⠻
⠀⠀⠀⠀⠈⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠱⡦⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠑⠀⠀⠀⠐⠈⠻⠆⠀⠀⠀⠀⠤⢤⣾⣿⣷⠀⣿⣀⣠⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠤⠾⠿⣿⣾⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⢀⠃⠀⣀
⠀⡄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠉
⠀⠀⠼⢆⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡂⡬⠞⡉⠀⠉⢧⡀⠀⠀⠀⠐⠂⠀⠄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠎⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠷⠶⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠢⠄⠤⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣤⠀⠀⢀⣴
⠀⠀⠀⡃⠒⠂⠴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢆⣠⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⣤⣿⣶⣿⠿⠁
⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⣿⣧⡀⢠⠋⠀⠀⣠⣶⡥⠀⠀⠀⠀⠀⠀⣸⡿⣿⡁
⡀⠀⠤⠀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠒⠤⡀⠀⠸⣿⣿⣤⡆⢀⣾⣿⠋⠠⠀⠀⠀⠀⠐⢀⠂⠀⠀⠙⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⣀⣈⣠⣤⣤⣙⠛⠠⡘⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⠒⠒⠉⠭⠛⠛⢛⡿⡿⢉⣤⠚⣽⣯⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⣿⣆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠰⠀⠀⢀⠀⠁⠀⠐⠃⡸⠀⠙⠄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⢐⣾⣿⡦⠄⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡞⠀⠁⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⡤⠂⠀⠀⡴⠻⢷⡟⠀⣰⠀⠀⠀⠚⠁
⠀⠀⠀⠀⢀⡀⣀⠀⢀⣼⣿⠛⠁⠀⠀⢲⣦⣤⠈⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠉⠀⠀⠄⠹⠋⢦⣼⠀⢀⡏⠁⠀⡘⠛⠹⠀⠀⠀⠀⣄⣴⣄⡀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⡞⠀⠀⡜⠀⠀⡌⠀⠀⣤⣾⣿⡏⠉⢳⡄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⢰⣿⠋⠈⠀⡀⠈⠋⠀⠀⠘⠳⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠴⠆⠀⢁⡠⣀⡄⠁⠀⠀⠀⠆⠘⠋⠀⠀⠀⡀⢀⣾⡄⠀⣷⡄
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⡉⠚⠃⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣤⠿⡙⠂
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠰⠀⢻⠆⠀⢸⣷⢠⡄⠀⢀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢸⠈⠙⠃⡀⢋⠀⠸⣇⢲⡿⠷⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢠⠙⢿⡀⠀⣏⡞⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠀⣷⡄⡟⢀⣶⣇⠀⠀⠀⠐⠂⣤⣁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⡄⣇⠉⡄⠸⣿⠋⡀⢀⣃⠀⠀⠛⠛⠋⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢳⣿⡁⢻⡀⠁⠀⠋⢀⠷⠟⣿⠏⣀⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢻⠁⢸⡁⠀⠀⣀⣼⣶⣶⠠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⡇⣸⣵⣧⣾⡿⢋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠓⠀⠀⣧⡟⣿⣩⣤⣶⣼⣿⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⢹⠇⣿⢀⢙⣿⣿⣿⣷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠛⢦⣀⠀⠀⣿⡰⣿⠏⠿⠿⣿⣹⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠻⣦⠀⣿⣷⡇⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⢀⣧⣤⡔⠒⠒⠂⠐⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠟⠁

⠀⠀⠀⢻⣦⡀⢀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣤⡦⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢘⡏⢻⣿⠩⡇⠀⠀⠈⢃⣤⣷⣾⣥⣜⠃⠀⠘⠻⣾⣶⣶⢷⡞⠃⠀⠈⢿⡿⣧⣴⢿⣿⠃
⠀⠀⠀⢸⡾⠁⠀⢡⣟⠀⠀⠀⠺⠽⠋⠙⠯⠿⠀⠀⠀⠺⣿⠊⠑⢿⠿⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣶⣀⡰⠇⠀⢠⡀⠒⣢⣖⠖⠂⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠁⠘⠇⠀⠂⠀⠀⠀⢿⣰⡟⠿⣆⡽⠀⠀⠀⠙⢟⡻⢟⡻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠔⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣆⠂
⠀⠀⠀⠸⣲⠺⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠘⣯⣿⢿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⠐⠀⠀⠈⠠⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠰⠀⠜⢚⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠁⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠑⣦⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⢀⠀⠄⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠐⠀⢀⡄⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢢⡄⠀⠀⠀⠀⠀⠀⠠⠋⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⠀⠀⠀⠰⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠻⠁⠠⡇⠀⠀⠀⠁⡆⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⢰⡏⡇⠀⡇⣿⠀⣿⣹⠀⠀⢸⡇⠀⢸⠙⡇⢀⣏⡃⠀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠧⠏⠀⠣⠟⠀⠿⠹⠀⠀⠸⠧⠀⠘⠶⠃⠈⠷⠇⠀⠧⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⡈⠂⠠⠄⡠⠀⠀⠀⠀⠀⣠⣠⠄⢠⠄⡀⠀⠀⡄⢐⡀⠀⢀⠀⠀⠀⠀⢨⠀⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠾⠃⠀⠀⡀⠀⡎⠀⠹⠶⠆⠙⠀⠀⠀⠀⠠⠐⢀⠀⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠠⠀⠀⣦⠐⢆⠀⠀⠉⠀⠀⠀⠠⡀⠀⠈⠙⠃⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⠀⠀⠀⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⣿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠄⠀⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣦⣄⡀⠀⠀⣠⡤⣤⣤⣤⣀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠩⢶⣶⣤⣽⣿⣿⣿⡿⠏⣳⣾⣿⣿⡞⣿⣿⣿⡟⢈⡿⢛⡛⣿⣿⣿⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠤⢤⣭⣭⣿⣿⣿⠿⣉⣴⣿⣿⣿⣿⣿⡇⣯⣿⣿⡷⠘⣇⠻⢆⡟⠁⠀⣌⠿⠋
⠀⠀⠀⠀⠀⠀⣀⣉⣭⣭⣽⣿⠟⢡⣼⣿⣿⣿⣿⣿⣿⢟⣲⠽⠟⠀⠑⢄⠈⠉⠁⠀⠀⠘⠑⠶⢴⠄
⠀⠀⠀⠀⠀⠀⠊⣉⣩⣾⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠲⠄⠀⠀⠀⠉⠦⠀⠀⢠⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠚⠍⢿⣿⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠄⠀⠀⢀⠰⢄⣀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⢴⢾⣿⠏⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢙⣄⠀⠀⠐⠍⠉⠲⣦⠼⠋⠁
⠀⠀⠀⠀⠀⢀⣼⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠈⠖⠀⠠
⠀⠀⠀⠀⠐⠹⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠠⢾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣄⣤⠖⠒
⠀⠀⠀⠀⢀⣴⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⡆⢠⣖⣰⣶⣿⡿⠃
⠀⠀⠀⠀⠉⢙⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⡽⡼⣾⣟⠯⢮⣰⣼⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠋⢣⢸⣿⣿⣿⣿⣿⣿⣿⣯⠘⠆⠘⠷⠻⠶⠽⠋
⠀⠀⠀⠀⠐⠀⢿⡀⣿⣿⣿⣿⣿⣿⣿⡷⢁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠘⠃⠀⠷⠹⣿⣿⣿⣿⣿⣿⣜⢠⠌⠀⠀⠀⠀⠀⠀⣰⠾⠛⠋⠉⠉⠛⠻⢮⡳⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠘⣏⡐⢇⣹⣿⣿⣿⣿⣿⣿⢫⣖⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠫⠻⣽⣆⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠸⣧⡘⢁⢻⣿⣿⣿⣿⣿⣿⣎⠄⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠏⣧⣇⠀⠀⠀⠀⠀⢠⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠉⣷⣸⣯⠙⢿⣿⣿⣿⣿⣿⣳⡂⠰⣾⣟⣟⣡⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⠀⠀⢀⢀⣴⡏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡯⠸⣧⠹⢿⣿⣿⣿⣿⣟⣄⠀⠉⠀⠀⠙⠛⠚⠀⠀⠀⠀⠀⠀⠀⠂⠀⢋⣌⣿⣶⣶⣿⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡻⢳⢪⣭⠻⢿⣿⣿⣿⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣼⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠙⠪⣟⠃⡀⠉⠻⠿⢿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣤⣶⣥⣤⣠⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠶⠦⣭⣩⣭⣿⣻⣿⣟⣿⡿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⡆⣀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠻⠟⢀⣿⣿⣿⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣿⠖⠒⣿⡅⣰⠂⠐⣦⡼⠋⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⡏⠉⠙⢧⣀⣴⣋⣹⣮⣴⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣉⣹⡿⢿⣶⡖⠛⢣⡀⠈⣿⣯⣭⠅⠴⢾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⠛⠛⠆⢰⣿⣧⣤⣾⣿⠟⣿⣿⣿⣛⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⢀⣾⣿⣿⡿⣿⡷⠂⢘⠋⢹⡟⠻⣨⡧⠴⣿⡿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣿⡿⠉⢰⣄⣸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡈⣻⡁⠉⣿⠀⢹⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠶⣿⣿⣷⡤⠷⠶⠾⣿⣿⡟⠛⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠈⣻⣿⣿⣷⡄⣠⣿⣿⠿⢄⣯⣶⠟⣠⠿⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠛⠿⠿⠛⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⢠⠃⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⡴⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⣀⠜⢋⣉⣽⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠋⠈⠛⠿⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯

⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⡾⣷⣶⣠⡍⠀⠀⠀⢻⣿⠇⢀⡀⢀⠀⠤⠤⠼⠶⣿⣿⣠⠶⠶⠶⠾⣿⡿⠟⠋⠉⠉⠛⠿⡷⠄⠀⠀⠀⡀⠀⢀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢙⡼⣟⠁⠃⠀⠀⠀⢸⠹⡀⡉⠁⠘⠀⠀⠀⠀⠀⠘⠉⠀⠀⢄⢀⠀⡀⢀⠀⠀⠀⡀⠀⠀⠐⢀⠂⠀⠀⠀⣠⡴
⡁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠬⣷⣤⣀⠀⠀⠀⣠⣿⠁⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⢀⠸⣿⣿⣿⡶⠶⣶⣿⣥⣀⣀⣀⣷⡄⠀⠀⠈
⠁⠽⠟⠉⠷⠀⠀⠀⠀⠀⠀⠀⣀⣜⢹⡿⠟⠛⠛⠛⠻⠳⡖⠲⡾⡄⠃⠀⠀⠀⠀⠀⢰⣌⠀⠀⠀⠀⠹⠿⠳⠛⢦⣴⣮⣿⣿⣿⣿⣿⣿⣷⣄⠀⡤⡀⢠
⠀⣼⡆⣿⠄⠀⠀⠀⠀⣶⠀⠉⠉⢹⠿⣶⠊⠑⠀⠀⠀⠀⠃⠀⠀⢆⠀⠀⠀⠀⠀⢢⣼⡿⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⡻⠿⣿⣿⣿⣾⣛⡠⡀
⣼⠟⡼⠃⠀⠀⠀⠀⠸⠁⣀⡤⢶⠧⣄⣘⣿⡶⠶⠶⢶⠏⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⣶⣿⣿⣿⡟⣿⣿⣿⡍⠩⢙
⠃⣴⠀⠀⠀⠀⢢⣼⡿⠟⠉⠀⡘⠀⠈⢧⡀⠀⠀⠀⠀⠀⠠⠒⠀⢙⠃⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⣿⣷⡿⢻⣿⣿⣧⡿⣿⣿⡿⣧⣿⣿⣿⠉⢀⣴
⣤⣿⠖⠒⠒⠒⠚⢻⢤⣀⡀⠀⣧⠀⠀⠈⢻⣦⡀⠀⠀⢤⡂⡀⠀⢻⡀⠀⠀⠀⠀⠀⢻⢆⠀⠀⠀⢀⣸⡿⠀⠃⣼⣿⣿⣿⣷⣾⣷⣷⣿⣿⡿⢁⣠⣾⢧
⠀⡟⢣⡀⠀⠀⠐⠀⠀⡈⠛⢿⣿⣆⠀⠠⠀⠙⠛⠻⠲⠛⠁⠀⣀⠨⠛⣶⠂⠀⠰⠄⠄⣠⣴⣄⡦⣼⣿⠃⢠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⠿⢿⡛
⠀⠀⠀⠙⠦⣤⣀⠀⢀⡹⠀⠀⠉⠉⡉⠀⠀⠀⠀⠀⠀⡀⢠⣶⢋⠹⡖⠀⠀⠀⠠⠐⠒⠻⢿⠿⡿⢿⣿⣄⠢⣿⣟⠑⠛⡻⢟⣻⢿⣏⣻⣷⣤⣄⠀⠁
⣶⠀⠀⠀⡘⢯⣭⣀⢹⣦⣤⣴⣴⣿⣅⠀⣼⣦⣄⠀⢸⣷⣿⣿⣿⣶⣧⣾⣯⣵⣾⢶⣤⣤⢤⡤⠀⠀⠀⣿⣷⣤⣿⣤⣀⡐⠋⠀⠈⠟⣿⡿
⠙⠆⠀⡰⠀⠠⣽⣿⣿⢫⠍⣹⣿⡿⠛⢷⣾⡿⠿⣶⣿⣿⣽⣥⠀⠉⠛⠛⠛⠉⣷⣿⣇⣠⣄⠀⠉⠀⠀⠿⠇⠙⢘⣿⠛⠣⠀⠀⠀⠀⠿⠃
⠴⣻⣿⣯⣤⣶⣿⣿⣇⢸⣴⣿⣿⣿⣿⣳⣿⣧⣨⡟⠋⢉⡿⣿⣄⣠⣶⡞⣀⡤⠻⣿⣿⣏⠁⠀⣠⠁⠀⠧⡀⠛⠁⢨⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢂⣏⠉⠉⠈⡻⣿⣿⣟⣿⣿⣿⣿⣹⣿⣿⣿⣿⣧⣿⣷⢾⣿⣿⣿⣿⢿⣿⣿⣿⡷⣿⣿⡷⠄⠐⢿⠀⠀⠀⠀⠲⠶⢶⣿⠿⠿⡷⣤⣤⣤⡄⠀⠀⠀⠂⠈
⢹⣟⠀⢀⠠⢿⡏⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣠⣿⠙⠀⣰⣧⠀⠀⠀⣀⠤⠴⠒⠉⠀⠀⠀⠹⠏⡆⠀⠜⠁⠀⠀⢰
⣷⡟⠀⠀⠀⠀⠙⢶⣤⢽⣿⣿⣿⣟⠙⠿⠻⠗⠀⠀⠙⣿⣿⣿⣿⡧⣼⣿⣿⡀⠄⣽⡿⠀⠀⣿⣿⣮⠖⠋⠀⡠⠄⠀⠀⣰⣶⠀⢲⣇⠀⢠⡆⣀⢔⣾⢿
⣻⡔⠀⠀⠀⠀⣰⡿⠛⡟⣹⣿⡿⡟⠛⢳⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣻⣿⣾⡟⢀⣤⣾⣿⡭⠔⠀⠀⠤⣪⠗⠀⣰⠟⠁⢙⡟⢿⣤⠿⠋⢹⣸⠛⠛
⢿⣷⠀⠀⠀⠀⢻⠁⠠⣹⢇⠏⢸⡁⠀⣞⢀⣠⣦⣤⣀⠿⣻⡏⣹⡿⣹⣿⣿⣿⣿⣣⣊⣉⠙⠿⢷⣦⣶⡚⢋⣠⣶⣌⣁⣠⣤⣴⡿⡦⠀⠀⣄⠸⣿
⣭⣿⠀⠀⠀⠀⠘⣇⢠⡏⢸⣧⣴⠦⣶⣿⠛⠑⠁⠋⢿⣷⣯⢿⠛⠿⣿⣿⢻⣿⣿⣿⣿⣿⠿⢿⣶⣬⣻⢆⠛⢿⡉⠉⠉⠠⠀⠀⠐⡈⠀⠠⣿⣷⣿⠂
⣿⣿⣧⡀⠀⠀⠀⠙⣿⡧⡼⠋⠁⠼⠙⠋⠀⠀⠀⠀⠀⠀⢹⡀⢇⠀⢘⣿⣽⣷⡿⠟⠿⣧⡀⠀⠈⠁⢍⣺⡖⠉⠙⢦⡀⢠⡦⡀⠀⠀⢦⣄⣛⢿⡅
⠚⠛⠿⢿⣷⣶⣴⣶⣾⡗⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣾⣿⡿⠷⢄⡀⠀⢉⠀⠀⠀⠀⠙⢄⠀⡇⠈⢻⣿⡇⢈⠀⠠⢄⡙⠿⣿⣿⡄
⠀⣠⣶⡿⢋⡵⠛⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣶⣿⡿⣿⣿⠿⢇⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⠀⠀⣻⣷⠠⣄⠀⠀⠀⠀⣒⣾⡇
⣤⠞⠋⣠⡟⠀⠀⠘⢛⡿⣿⣶⣄⡀⢀⡀⠀⠀⢀⣇⣴⠾⠏⣹⠟⠁⢻⣟⠀⠈⠄⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢀⣰⠶⠟⠛⠻⣆⠙⠃⠿⢾⣾⣿⣿⣧⡀
⠀⢀⡼⢿⡀⠀⠀⠀⠀⢊⣾⣿⣿⡿⣿⠛⠛⠛⠛⠉⢧⠠⠘⠁⠀⠀⠀⢹⠀⠀⠀⠀⣠⠔⢉⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠨⠭⢾⣿⣷
⠀⠌⠀⠘⢳⠀⠀⠀⢀⠎⢨⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠀⠠⠒⠈⠈⠀⠈⠀⣰⣶⡐⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣧⠐⢀⠀⠀⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⢆⠁⠀⠀⠂⣠⣴⠡⠈⠋⠁⠐⠒⠒⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣀⣭⠿⢋
⠇⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡱⠒⠒⠈⠁⣭⠀⠀⠀⠀⠀⠀⡠⢠⣶⢋⠝⡆⠀⠀⠀⠀⠚⠉⠀⢠⢾
⢀⡀⠀⠀⡀⠀⠀⠀⣦⠀⢀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠻⣵⣤⣸⣷⣤⣦⣼⣿⣧⠀⢠⣷⣴⡀⢰⣿⣿⣿⣿⣶⣾⣶⣿⣭⣿⢖⣤⣴⢧⡼
⠠⠟⠓⣢⡈⠃⢀⡀⣿⠀⠀⠀⠀⢠⡾⠋⠁⠀⠠⣄⠀⠀⠀⢀⣀⠂⠀⠮⣿⣿⠋⡔⢙⣿⣿⢛⣻⣾⡿⠟⣷⣾⣿⣯⣇⡀⠈⠉⠘⡙⠉⢹⣿⣇⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣥⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⢀⣤⠴⣤⠿⠿⠛⠉⠻⢆⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣠⠄⠶⠏⡉⢶⠏⠀⠀⠀⠀⠀⠀⠀⢾⡕⢤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠉⡏⠙⠉⠉⢡⣤⠚⠃⠀⣠⠀⢀⣀⣀⠀⣠⣀⡀⠀⠿⣗⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠈⣧⣴⣴⡄⢜⣿⠀⠀⣼⡅⠀⣻⣿⣿⣿⡏⠈⠀⠀⠶⡌⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⣿⣿⣷⣾⣿⣿⣿⣿⣵⣿⡟⠁⣠⣦⣴⣆⡊⣈⣠⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⡟⣯⠙⡇⠉⢰⣋⣼⣷⣤⡎⢿⣿⣿⣿⣿⣿⢯⢣⠈
⠀⠀⠀⠀⣀⣠⣀⡀⢸⠀⠀⢠⣠⠆⠈⠉⠇⢸⠆⣷⡖⣿⠉⢰⡏⢿⠿⣎⢙⡿⣿⣿⣿⡂⠔
⠀⠀⠀⠀⠀⠰⠄⠁⢸⣆⠀⠚⡙⠀⠀⠀⠄⠸⡆⢹⣧⢸⣷⣻⡇⠀⠀⣿⠸⣿⣿⣟⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣼⣷⣀⠀⠀⠀⠀⠀⣀⠹⣎⡙⠿⢿⡰⡿⣿⣷⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠉⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⣁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠋⠀⠸⠋⠀⠀⠀⠀⠀⠀⢶⣼⣿⣷⣿⣿⡉⢁⣀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠸⣿⠗⠂⠀⠰⠒⠀⠀⠀⠀⠀⠈⠛⣻⡏⢹⣿⣾⣿⡿⠌⠁⡟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⢠⣄⣠⣼⠷⠶⠓⠒⠂⠀⠀⠀⠀⠀⠀⣾⠉⠻⣭⣋⣵⣯⣥⣞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠠⠀⠋⠋⠟⠙⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠒⣟⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠐⠀⠹⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⢀⠀⠀⢤⡀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠘⢆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠔⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠂⡀⠀⠀⠙⠠⠀⠀⠀⠐⢤⡀⠈⢆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣠⠆
⠀⠀⠀⠠⠄⠈⠀⠈⠃⣉⠘⠇⠀⠀⠈⠀⠀⠤⢀⣀⣀⠠⠀⠀⠈⠓⢾⣆⣤⠀⣀⠴⠶⠶⠤⠤⢀⠀⠀⢀⣧⠼⠟
⠀⠀⠀⠀⢀⡄⠊⠁⠀⠀⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⡼⠁⠠⡄⠁⠀⠀⠀⠐⢤⣾⣯⣀⠀⡀⠀⠀⡰⠞⡀
⠀⠀⠀⠂⠁⠀⣠⡶⢂⠀⠀⢀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣭⣭⡻⠟⠈⠁
⠀⠀⠀⠀⠀⠂⢑⠀⠹⡆⠀⠈⢣⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⠿⣯⡋⡀⠁
⠀⠀⠀⠀⠀⠀⣈⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠈⠣⢄⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣤⡀⠀⠀⠀⣀⣴⣶⣦⣄⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠇⣀⣴⣿⣿⣿⣿⣿⣿⣦⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠛⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣋⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠉⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⣶⣶⣿⡿⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⣾⡿⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠟⠛⠉⠀⠀⠀⠀⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛⠀⠀⠈⠙⠁⠀⠀⠀⠀⢘⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣍⡉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣦⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡵⠤⣟⣛⠛⣛⣛⣛⠛⣋⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠞⠀⠀⠀⠻⠀⠛⠂⠀⠀⠀⢠⣦⠀⠀⠹⡟⠁⡡⡌⡟⢟⠖⠿⠀⠒⠇⠀⠐⡿⣀⡼⣧⠠⡄
⠀⠂⠀⠠⣄⢄⠀⠤⣴⣆⠀⠉⠋⠀⠀⢰⠟⣉⠃⢼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠐⡌⠙⠛⠀⠀⡘⣤⠃⠈
⢀⠀⠀⠈⠉⠀⠀⡘⠘⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⢱⣾⡆⠀⠀⠁⠀⠐⠀⠀⠀⢠
⠈⠀⠃⠀⠀⠈⠂⡛⠀⠀⣸⠇⢐⡰⠧⠆⠀⠀⡄⢀⠀⠀⠐⠋⠀⠈⠉⢁⡀⠀⠀⠀⠀⠀⠀⠂⣤⡀
⠀⢲⠄⠈⠈⢀⠀⠀⠀⡀⣿⢆⠿⣧⣾⡇⠀⠬⢿⡿⠅⠀⠀⠀⠐⠃⡀⠈⠁⠀⢠⡆⠀⠀⠀⠈⠰⢠
⠀⠀⢀⠀⠀⢸⡆⠀⢸⣿⣿⢠⣷⢼⣿⡄⠀⠀⠂⠀⠀⠀⠘⠀⠠⠆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠰
⠀⢠⠈⢷⣄⠀⠀⢄⠘⠛⠹⡶⠋⠺⠿⠃⠀⠀⠐⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠈⠂⠀⠒⣌⠂⠀⢰⡄⠀⠀⡄⠀⢰⠃⠉⠀⠤⠖⢛⡇⠀⠢⠄⠀⠀⠀⡐⠀⠀⠀⠠⠀⠅⠀⠄
⠀⠀⣄⠀⠀⠀⠂⠌⣻⣆⠀⠀⠀⢰⠃⢀⡟⠀⢀⣠⠄⠀⠉⡇⠀⠀⠈⠀⠰⠵⠞⠖⠀⠄
⠀⠀⠀⠃⠀⣤⣤⣀⠈⢻⣧⠀⢠⠎⠀⣾⡠⠾⠋⠀⠀⣀⠀⠸⡒⠀⠀⠰⠖⠀⠀⠀⠀⠀⣠⡤⠀⠀⠠
⠀⣤⡄⠐⠀⠈⠍⠉⠁⠀⢻⣧⠈⡀⡤⠁⠀⠀⠀⠀⠂⠈⠀⠆⠙⠀⠀⡀⠀⠠⠆⠀⠀⣼⡗⠁
⠚⠋⠀⢀⣴⣶⡅⠀⢳⡤⠈⢿⣆⣽⠇⠀⠀⠀⢸⠆⢀⠀⠀⠀⠀⠀⢀⠁⠂⠀⡶⠀⠀⠈⠀⠀⠞⣻⣄
⠀⠀⠠⠈⠙⠛⠃⠐⠁⠉⠀⠘⣿⡿⠀⠀⢀⡀⠀⠀⠹⠃⠀⠐⠂⠀⠙⢀⣀⠀⠃⢀⢶⣴⣀⠀⣄⠈⠛
⣾⣷⡀⠀⠼⠀⡀⠀⡠⠈⢣⡀⢹⡇⠀⠀⠉⠁⠀⠀⢀⡤⠀⣶⠀⠀⠀⠈⢀⠀⠆⠈⠻⠻⠛⠀⣄⣥⠄
⠛⠛⡁⢀⡀⣧⢀⡆⠀⢀⠀⢡⢸⡇⠀⠀⣠⣾⣯⠸⠎⠏⣀⣀⣀⣶⣤⠀⠀⠵⠁⠀⠄⠀⢠⡾⠋⠓
⢠⡀⢁⠰⡁⠹⢊⠀⠀⠊⠀⡀⢿⣿⡀⠀⣿⣿⣿⣶⣆⢸⣿⣿⣿⣿⣍⣧⠀⣠⣄⡀⠀⠤⠈⠀⠀⣤⠔
⠀⠁⣼⠊⣸⠾⠃⡀⠀⠀⠀⠘⢾⣿⡃⠀⠻⠿⠿⠿⢏⠁⣿⣿⠋⠉⡉⠁⠀⠺⢯⠵⠀⠀⠴⠶⣶⣯
⢠⡀⠠⡀⢨⠷⢀⠀⠀⠲⡖⠀⠈⣿⡁⠀⠀⠀⣠⡄⠀⠚⠋⠀⢼⠺⠛⠀⢀⣈⠈⠀⠀⠀⡀⠀⠊⡋⡀
⢀⠁⠀⠘⣟⡆⢀⠀⠀⠁⠀⠀⠀⠙⠀⠀⣀⢰⠻⠃⠀⣤⡀⠀⠀⠈⠈⠀⢊⣽⠛⠋⢄⠸⢿⠅⠀⠈⠁
⠈⠉⠐⠬⣻⡟⠁⠀⠀⠀⠀⠐⠀⠀⠀⣴⡌⣿⠿⢶⣾⣿⠗⣴⠀⠀⠀⠀⠐⢢⠀⠠⠛⠓⠂⠁⠀⠀⠂

⠟⠿⡀⠀⣸⣿⣿⣟⡀⠛⠛⢿⣽⣿⣿⣇⠀⡀⢿⣿⣯⣿⡀⠀⠀⠀⠀⣿⣟⣿⡿⢿⣾⣵⣤⣤⣀⣤⠄⠀⢀⡄
⠀⠀⠈⢿⣿⠡⢐⠠⠀⣀⣀⠀⢹⣿⣿⣝⣀⣽⣿⣿⢿⣿⡇⠄⠀⣤⣾⡟⣹⣿⣦⡷⢿⣿⣿⡟⠋⠹⣷⡖⡙⢾⣬
⣦⣤⣄⡌⣹⣽⣶⠀⠊⠀⠠⣀⣼⣿⣿⡿⣿⡏⠘⠉⠡⣽⣧⣀⣀⠀⢉⣿⣿⣿⠿⠏⠂⡍⢙⡠⡛⢷⡾⡿⢀⠂⣻
⣿⣿⢿⣾⣿⣿⣿⣿⡿⣶⣴⣏⣍⡵⢚⡇⢸⡅⠀⠀⠀⣹⠇⡘⠧⠐⢮⠙⠻⡀⠖⠀⢹⠁⠈⠁⠁⣸⢋⣳⠊⡱⢼
⠀⠀⠠⣿⠻⡹⣏⣿⣿⣸⣇⢹⠿⠶⢛⣻⣿⠻⡄⢀⡔⠀⠲⡀⣞⠊⢠⣄⢴⣶⣤⣷⢄⠆⡸⣆⢀⡄⢂⠤⠞⣉⠛
⣄⢀⠤⣯⡀⢡⢘⡍⠛⡷⢟⠂⣤⡄⣽⣭⠤⢷⡤⣍⣥⣤⣜⠚⣩⠉⠙⠀⠘⡇⠨⣽⣷⣽⣿⣾⣾⢿⡿⠺⠄⠙⠻
⠉⠘⣧⣉⣿⣅⣱⣯⢧⣴⣅⣁⢤⠀⣨⡘⠃⣿⣾⣀⢿⣻⣿⡞⠁⠶⣗⣰⠄⢠⣐⠈⠀⣀⠉⠛⣯⣽⠃
⠿⠔⠃⠀⠀⠻⠁⠀⠜⠺⢿⡗⠲⣇⣬⡉⠂⠈⠀⠀⠀⠈⠻⢿⡄⣀⣿⣿⣿⣷⠆⠀⣄⣻⣶⣿⡽⢿⠀⠀⢠⡼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣽⣮⠀⠀⠄⢀⠂⠀⡀⠀⣸⣿⠿⠛⠿⣿⣿⠧⣄⣚⣿⣿⢷⣿⢾⠇⢀⡾⠁⢠
⠓⢄⡀⠀⠀⢀⡄⠀⢀⢤⡼⢏⡉⢈⣻⠏⠀⠀⠀⠀⠀⣿⠞⠉⠀⠀⠰⠀⠀⠘⣾⡿⠁⠀⠙⠀⢈⠉⠀⠈⠃⠀⡟
⠀⠀⠙⢷⣦⣼⣷⣧⠞⠀⠘⠀⠀⡀⣼⡄⠀⠀⠀⠀⠀⡝⣠⡶⠚⠋⠃⠀⠤⠴⢿⡄⢀⠀⢠⢆⣼⡀⠀⠀⠀⡀
⣠⠒⠀⣨⣿⡿⣿⠃⠀⠀⢰⡇⠀⠁⠀⠑⣄⠀⠀⢠⣧⣾⠋⣀⠄⠀⠐⠛⠦⡄⢠⡌⠻⠊⠀⣘⠉⠃⢀⣀⣈⡿
⠋⠀⠀⠀⠀⠀⡬⠀⣠⠶⠿⣇⠀⢄⠈⠙⠟⠃⢨⡿⠘⢜⢛⠁⠀⠀⠀⠀⣀⠀⡀⠀⢶⣴⣿⠟⠀⠀⠀⠋⠋⠧⣀
⡄⣀⣀⣰⠶⣾⣷⡈⠀⠀⠀⠈⣳⡾⠷⢀⣀⠀⠀⠬⣚⠦⠔⠗⠂⠀⢢⡶⠀⠀⠀⠀⣼⣿⣅⠀⠀⣠⣤⣤
⣶⣟⣷⣶⢿⡿⠛⢿⣶⣤⡖⠉⠀⠀⠀⠀⠙⠋⠐⢄⠁⠐⠒⠶⠖⠛⠿⠶⣾⣧⡶⣾⢿⢣⡄⠘⣿⣿⢿⣿⣦⡀
⠿⠁⡈⡸⢛⡀⠀⠀⣿⠟⠃⠀⠐⠂⠀⠀⣤⡶⠖⠋⠑⠦⣀⡀⠀⣀⠬⠀⠀⠹⣸⣔⣄⣊⣧⢠⣿⠃⠀⠈⠹⣿⠘
⠉⢠⠆⣤⡬⢤⡳⣀⠉⣫⠠⠂⡀⠀⢶⣾⡿⠀⠀⠀⠀⠀⠈⣻⠋⠉⠁⠀⠀⠀⣿⡛⡟⠻⢿⣿⣯⠀⠈⣃⢿⡉⣍
⢂⢨⢛⠓⡁⣄⣹⠏⢠⠄⠀⠠⠄⡀⢛⡾⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣨⣿⡟⠀⢄⠉⠋⠘⣶⡇⡀⠈⠃
⠌⠛⣦⣴⠷⣸⣿⡸⠶⠂⠉⠰⠄⠈⣿⣿⡋⠀⠀⣀⡀⣀⢰⣿⠇⠀⠀⠠⢴⠞⢁⡾⢿⣖⣓⣧⣀⠈⣹⣷⣮⠄⣠
⠊⠉⢙⡗⣶⢿⠉⠈⣤⠓⠀⠠⣴⠊⢻⣿⣄⣀⣸⣿⠟⠁⠀⢀⡇⠀⢀⠀⣠⠄⠚⠉⠈⢛⣻⣿⡿⠋⠉⠉⠁⠙⢇
⠀⠘⠋⠀⡀⠀⠘⠁⡀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣶⣦⠦⢤⣹⡿⠻⣆⣁⠀⠀⠀⢀⢹⣽⣿⠃⢀⡀
⠀⢠⠆⠘⣠⡇⠀⠀⢠⠠⠀⢀⣀⣠⠾⠿⠿⠟⠿⢍⡹⣽⣦⣚⣉⣉⣱⠛⠟⠃⠀⠀⠈⣦⢟⣿⠔⠚⠇⢀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠛⢲⡛⠻⠭⣍⠀⠉⠉⠙⠲⣄⠀⠀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⢤⠀⣀⠀⡀⠈⢣⡘⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⢞⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⣀⠈⡏⠉⠓⢾⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣟⡵⠋⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠑⣾⣀⡀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⡿⠉⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣦⣞⣁⣤⡴⠚⠒⢬⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⢀⣉⣦⡑⣄⣠⠆⠀⠀⠰⣄⠜⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠈⠈⠙⣌⢏⠀⠀⠀⠠⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠁⠈⠈⠉⠉⠓⠤⣤⠀⠀⠘⣮⢆⠀⠀⢆⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠘⣮⠆⠈⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⡏
⠀⠀⢀⡠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠴⡤⠤⠄⠀⠀⣀⠀⠀⠈⢣⡀⢙⢈⣄⠛⠀⠀⠀⠀⠀⢀⠴⠖⠉⠀⠀⢿
⠀⠀⠀⠁⠢⢤⣠⡤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠲⢄⠀⢷⠀⣄⢹⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢜⡇⠸⠸⠂⠀⢀⡐⠋⠀⢀⠀⡠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢖⠰⣄⣀⠀⣀⣀⣤⠴⠒⠒⠘⠿⣄⡀⡆⠀⡞⠀⠀⡀⢈⠞⠁⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⣈⣧⣁⣸⠁⠀⠀⢳⡍⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠉⠙⠳⠤⠤⠶⢤⣀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⢠⣀⣞⢀⣠⡤⠤⠤⣄⡀⠀⠀⠀⠀⠈⠳⣄⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⡿⠉⠉⠉⠀⠀⠀⠀⠀⣹⠦⠒⠒⠒⠒⠢⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠞⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⢶⡧⠤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⡃⠀⠀⢀⣀⣀⠀⠀⢀⡞⢸⡏⣵⡖⠙⣶⣇⡄⣀⡴⠒⠀⠀⠠⣶⣋⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⢧⡀⣀⡾⠀⠈⢳⣴⠟⢿⣌⠻⠦⣠⡟⠁⠹⡜⠁⠀⠀⠀⠀⠀⠀⠀⠉⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⠿⠋⠀⠀⢠⡟⠁⠀⠀⠈⢻⣆⠟⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⠤⠐⠒⠤⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡟⠀⠀⢀⡴⠒⠒⠒⣤⡀⠀⣠⠶⠶⠋
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠛⣀⡴⠋⢀⡴⠋⢧⡀⠀⢰⠏⠙⠳⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⣤⠿⢛⡶⠛⠉⠉⠀⠀⣰⠏⠀⠀⠀⠉⠒⠋⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣤⣀⠀⠀⠀⠀⠈⢉⣻⠟⠁⠀⣈⣴⡶⠤⠤⠶⢟⠣⠄⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣆⠀⠀⠀⠀⠈⠉⠁⠉⠉⡜⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠙⠲⠶⠦⠶⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⣤⢖⣛⣉⣛⣒⣦⣄⡀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⢦⠤⠀⠀⠀⠀⠀⣀⠦
⠀⠀⠀⠠⣤⡀⠀⠠⠀⠀⠀⢹⣯⣿⣨⠗⠂⠀⠠⠤⣿⣿⠗⣤⠀⠀⠀⣀⣴⣆⡀⠀⠀⠀⠀⠀⡀⠐⡄⠀⢀
⠀⠀⠰⠐⣛⣣⣶⠖⠁⠀⠀⠘⠒⠚⠁⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠸⠛⢿⡃⡈⠀⠀⠀⠀⠀⣌⠶⡋⠁
⠀⠀⠀⠈⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠈⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⢧
⠀⠀⡄⢸⡄⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⢠⢤⠦⠈⠸⣷⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠀⠀⠀⠀⠀⢀⠡
⠀⠀⢷⠈⡃⠀⠀⡶⠀⠈⡱⠈⠀⠀⠀⠀⠈⡁⠀⠀⠙⠀⢀⣤⣦⡾⣡⡆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣞⣯⠁⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡞⢲⣶⠀⠀⠀⠰⠐⡎⠁⠀⠀⠀⣯⠛⣿⡗⠀⠀⣠⣀
⠀⠀⣶⡷⠰⠀⠀⡰⣶⣾⠀⠀⣤⣙⠃⠀⠈⠻⡄⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁⠈⢀⠛⠀⢠⣶⡂
⠀⠀⠀⠀⠊⠀⠀⠘⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠶⢻⠂⠀⠀⡀⠀⠀⡀⠀⠐⣄⠀⠀⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠋⠁⠀⠀⠀⠀⠀⠀⠈⣤⡀⠀⠀⠀⠁⠀⠀⡨⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠳⢶⡟⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠛⠳⣄⣠⠾⠛⠉⠉⠛⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⢸⣧⣤⣄⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⡶⠋⠁⠀⠈⠙⣶⠶⠶⣿⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⣠⡴⠶⠛⠳⠶⣤⣴⠞⠛⠛⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠛⠋⠙⢶⣤⣤⣤⠾⠃⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⣠⡶⠛⠉⠙⠛⠲⣾⠋⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢀⣤⠾⣧⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣴⠟⠁⠀⠙⣦⣀⠀⠀⢀⣠⡾⠛⠳⠶⠶⠛⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣸⠷⣄⡀⠀⢀⣀⣴⠏⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢀⡟⠀⠈⠉⠛⠋⠉⠻⢦⣤⣀⣀⣠⣤⠶⠋⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⡄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⢋⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⢀⣠⡾⠃⠀⠈⢻⣆⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢻⣆⠀⠀⣾⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠉⠉⠙⠛⠛⠶⢦⣄⡀⠀⠀⠀⢻⡄⢰⡟⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠈⣷⢸⡇⣰⠟⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣹⣿⣾⠋⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣀⣀⣀⣹⣿⠃⠀⣀⣀⣀⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠿⠛⠋⠉⠉⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀
⠀⢰⡷⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣧⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣽⣿⣿⣿⣿⡿⠋
⠀⠀⢀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⠀⠀⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣻⡟⠀⠀⠈⠉⠉⠉⠋
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠘⠛⠛⠻⠀⠀⠘⠻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⣏⣛⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣿⡗⠀⣴⣿⣿⣿⣧⣄⣀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢹⡿⠛⠛⠛⢿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣿⣧⠈⠙⢿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⠀⠀⠀⠀⢸⡏⢉⣩⡉⠀⣠⣿⣿⣿⣿⣿⣿⠁⠙⠛⠋⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⠇⣠⣤⣾⣆
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡟⢰⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣙⣷⣿⣿⣿⠇⣾⢡⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠿⠹⣿⣿⣿⠟⠛⠋⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣸⣿⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⡛⣻⡿⣿⣿⣿⡿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣭⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⠀⣀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠈⠀⠐⠂⠃⠀⢀⠠⠄⠐⠤⠄⠈⠡⠂⠠⠀⠂⠀⠀⢠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠴⡤⠈⠁⠀⡀⠢⡀⠀⢠⡀⢈⠀⠀⠀⠰⠀⠀⠄⠐⠀⠁⠀⢤⠁⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠱⠄⡔⠀⢠⠀⢀⠤⠆⠀⢰⡈⢂⠈⠉⠀⠂⢀⠄⠈⠀⠀⠀⡀⠀⠀⡀⠁⠀⢀⣦⠠⠈⠂⠄⠐⠁⠀⠀⡅
⠀⠀⠀⠀⠐⠂⢰⠀⠀⠤⠬⠤⡀⢀⠒⠪⠀⠁⣐⡀⠁⣀⠤⠀⡠⠀⢈⡉⠈⠃⠀⣠⢀⠀⠈⠀⠐⠒⠗⠒⠀⢈
⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠰⠀⠁⢀⡀⣄⠀⠚⠙⡁⠀⠀⣐⣖⢈⠀⢄⠊⠑⠂⠙⠉⠃⢠⠀⠀⠀⠀⠶⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣔⡁⠔⠈⡂⢐⠀⠀⠀⠉⠀⠁⠀⠀⠈⣄⠀⠀⠀⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⢀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⢀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠸⠀⡄⠀⠀⠀⠀⡀⠐⠀⠐⠀⠀⠀⠐⠒⠂⠄⢀⡀⠀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢇⠀⠒⠀⠀⠐⠄⠀⠀⢀⠖⠀⠠⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⠀⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣀⠀⣰⠆⢰⡄⡀⢨⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠿⠟⠃
⣿⣿⣿⣿⣿⡿⠟⠠⢄⠈⠙⠧⠘⢡⠀⠧⠓⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀
⣿⣿⣿⣿⠟⠁⠀⠀⠀⣀⠰⠦⣄⠈⠀⢠⡀⡇⣰⡅⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣀⡠⠴⠃⠀⢀⣠⣴⣶⣿⣿
⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⢿⠃⢸⠇⡤⣿⠀⠀⣠⠁⠀⠀⠒⠺⢿⣿⠿⠶⠶⠶⠶⣿⣏⡽⠿⣯⣯
⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⡀⠀⠈⢤⡈⠀⠀⠈⠀⠀⠀⠀⣠⠈⡠⢚⣟⠃⠀⠞⠀⡠⢼⣿⣿⣿⣷⡄⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⠀⡀⠀⠀⡾⢭⠈⣤⡄⣠⣤⣬⣷⣇⣰⣷⡎⣽⢀⠀⠀⠀⠁⠈⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣷⣶⢿⣮⣿⣿⡟⡛⡳⢾⠿⠁⣾⣿⠁⠊⠀⠀⡠⠰⡒⣒⡶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⣿⣿⣿⡿⡿⢿⠿⣿⢶⡶⣟⣛⢇⣶⠀⠾⠿⣿⠓⠀⢀⠘⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣿⣿⣿⣿⡆⢺⠿⡤⣷⣿⣿⣟⡷⣬⣋⠑⣦⣽⣈⣳⢶⣷⠏⠀⠀⡀
⣄⡀⠀⠀⠀⠀⠀⢀⣿⣿⠀⣿⣿⣿⣟⠻⣧⡞⢹⣽⡛⠯⣏⣹⡾⠛⢿⡏⠠⣟⠉⡝⠁⠀⠀⠀⠀⠘⠀⠀⠃
⣿⣿⣦⡀⠀⠀⠀⣸⣿⡿⠀⣿⣿⣿⣿⢀⣿⣱⣧⣰⡿⠰⣯⢈⣷⢶⣤⣿⣠⣿⠿⠅⠀⢥⠀⠀⠀⠀⠀⠈
⡿⢻⣿⣿⣶⣄⠀⢸⣿⡇⢀⣿⣿⣿⣡⡾⠨⢯⣯⣀⣿⣴⣧⣼⡷⢤⣾⠟⣩⡇⠀⠀⠁⠂⠀⠀⠀⠀⠄⠀⠀⠀⠒
⠂⠉⠹⣿⣿⣿⣷⣾⣿⡿⣿⣿⣿⣿⠋⠀⠀⠐⠘⠿⠿⣿⣾⡻⣷⡿⢻⣾⡇⠀⠄⢐⠘⢁⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠸⠛⡿⣿⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠀⢣⣴⡿⢊⣽⣿⣷⡤⣎⠀⠁⠀⠀⠀⠒⠁⢀⠀⠁⠀⠀⠈⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⢿⣶⣯⠟⠁⣿⣟⣦⠀⠀⠀⠂⢀⠀⠀⠀⠐⠀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠈⠉⠉⠠⠀⢸⡾⠛⠛⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⣤⣴⠀⠀⠀⠀⠠⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⡾⠇⢻⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⣿⣿⣿⣿⣿⠁⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣦⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠈⠄⠀⠀⣀⠎⣀⣴⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣧⣆⡀⡀⠈⢦⣦⢻⣆⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢉⠿⡮⡇⡛⣺⡇⣴⠋⡿⣭⠔⡂⠄⡲⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⢾⡳⢷⠾⡠⢻⣿⢡⡟⣫⣔⠄⠨⡶⠿⠄
⠀⠀⠀⠀⠀⢠⣀⢰⠟⠥⣤⣼⣧⣳⡴⡑⣿⣿⣾⣿⡗⠛⠋⠁⣀⣤⢄⣀
⠀⠀⠀⠠⣶⡎⣿⣯⣠⣀⣸⣿⡿⢛⢷⣿⣸⣏⠳⡟⣤⢖⣽⠟⠁
⠀⠀⣠⣶⣭⣿⣿⣿⣿⠦⠖⠀⣿⠲⡙⢿⣿⣿⡗⠻⢟⡩⠊
⠀⠘⠋⠹⣿⣿⣿⣿⠛⠀⠒⠷⠸⣆⣾⣧⢭⣿⣷⣯⣠⠿⢯⣀⠄
⠀⠀⠀⠘⢿⡛⣿⣿⡞⡁⠀⠀⠀⣨⢟⢻⣼⣷⡹⡙⣤⣾⠠⠁
⠀⠀⠀⣈⡟⣿⣳⣿⣷⡡⠀⠀⠀⣬⠸⣏⣿⠿⣧⣷⣻⣿⡤⣮
⠀⠀⠀⣽⣷⣿⣿⣿⣹⡔⠀⠀⢀⣤⢷⣿⣿⣄⣽⣿⣿⠾⣦⠁
⠀⢀⣼⣿⣽⣽⣿⣿⣿⣿⣜⠑⠟⣤⣿⣍⣿⣧⢿⣿⣹⠼⡏⠁⢀
⠀⠉⠁⠈⠉⠙⠛⠛⠉⠁⢁⣀⣤⣶⢻⣿⣿⣿⡎⠟⣬⢸⣿⢛⡁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡫⣽⢹⣿⢻⣧⢹⢳⡀⢻⣆⢿⡈⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣿⢾⢏⠸⣿⡄⣾⣇⣟⣿⣿⣷⣿⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣿⢿⣿⣾⣮⠄⣾⣿⣿⣻⢻⣿⡿⣏⢻⣿⡆
⠀⠀⠀⡠⡀⡤⠠⠴⢤⡤⣶⣿⣿⣿⢇⡏⣷⣼⣿⣿⣿⣾⣿⣹⣿⣾⣿⡷⡀
⠀⠀⠀⠙⣿⣀⠔⣩⠜⠛⣟⢏⠫⠻⣿⣽⣿⣿⠸⣻⡟⣿⣿⣿⣿⣿⣿⠟⢋⠉⠛⠷⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄
⠀⠀⠀⠀⠻⣿⣠⡇⠀⣠⣿⣸⣰⣣⠿⠈⠙⡿⣿⣿⣷⣿⣿⣯⣿⣿⠁⢰⠁⡜⠀⠀⣼⢸⠀⡎⣷⠀⡠⠀⢀⠤⢄⢪⡁
⠀⠀⠀⢅⠠⣑⣾⣄⣾⣋⣯⡍⠨⣋⠈⣻⣾⣷⣿⣿⠻⣿⣿⡿⣿⠿⢧⣿⠼⢇⣠⡼⢇⣼⣴⣷⡿⣴⣿⣟⢿⣥⠘⠛⠁
⠀⠀⠀⠀⢺⣻⡟⡉⣹⠉⠀⠈⢦⠘⣮⣯⣧⣙⣅⢁⡀⢜⠻⢣⣵⡏⠑⠀⠫⣿⠩⢵⣾⣿⠿⣻⣷⣶⣦⡈⠳⠟⠈
⠀⠀⠀⠀⠀⠀⡇⢣⣸⣄⢷⣤⣼⣟⡙⣿⣎⣤⣴⣯⡼⢿⠛⠒⠋⠁⠀⠀⠀⠈⠈⠉⠉⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠈⠊⠿⠿⠓⠎⠀⠺⠿⠏⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠂⡘⣹⢷⣶⣾⣧⣤⣶⠶⠤⠘⠓⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠷⢾⣿⣿⣿⣯⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⡘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣐⣺⣿⣿⠿⠛⢉⢀⡀⠉⠉⣹⣭⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠁⠀⠀⠀⠀⠀⣴⣿⣿⠟⢉⣀⣤⠖⠋⠛⠿⢿⣿⣿⣿⣿⠛⠛⠛⠉⠛⠛⢿⣿⣤⠉⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⣿⠿⠿⠿⣾⣷⣶⣾⣿⣿⣿⡿⣿⣆⣤⣦⣄⣀⣀⠀⠀⠙⢦⣄⡀⠀⠈⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⣴⣿⣿⣿⣿⣏⣴⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣈⡛⠿⣿⣿⣿⣯⠉⠁⢳⣦⡀⠀⠈⠉⢿⣦⠈⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣥⣾⣿⣿⣿⡿⠿⠿⣿⣷⣮⣿⣿⣧⡀⣠⡌⢿⣿⣆⠀⠀⠈⣿⣧⣀⢠⣽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⡄⠘⣹⣿⣿⣿⣿⣿⠻⡇⣿⣿⣿⣿⣿⡿⠋⠁⣸⣿⠥⠶⣚⣽⣿⣿⣯⡙⠛⠻⠿⣿⣾⣿⣿⡄⠀⢰⣿⡿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⡷⢰⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⠟⠁⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣷⣦⠀⠈⢻⣿⣿⡇⠀⢸⣿⡷⠘⢿⡟
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⠀⣿⣿⣿⡇⠀⣿⣿⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣿⣿⣇⢿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣸⠋⢻⣿⡅⠀⣿⣿⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⣿⠃⠸⣿⣿⣿⣿⣾⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⣷⡿⠀⠀⠙⣷⣳⣿⣿⣿⡇⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣧⣀⠂⠈⢿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠁⠀⢸⣿⠇⠀⢤⣀⣿⣿⣿⣿⣿⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣷⣦⣬⣳⣄⡀⠙⠻⠿⠿⠿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⣤⣿⠏⢀⣴⣿⡿⢹⣿⣿⣿⠏⠀⠀⠀⠀⣦⠉
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠻⣿⣿⣿⣇⠘⠿⣿⣿⣷⡌⠻⣿⠿⣦⣤⡖⠛⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⢰⠟⠀⣠⣿⣿⣿⣿⠀⣿⣿⡏⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠿⣿⣿⣿⡄⠀⠀⠙⠻⣿⣦⡈⠂⠀⠛⠿⣦⣬⣛⣿⣿⠿⠋⠁⠀⣠⣾⣷⣶⣿⣿⣿⣿⣿⡗⠀⢿⠇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠊⠙⢷⣄⠀⠀⠙⠿⣿⣿⠀⠀⠀⠀⠈⠻⢿⠆⠀⠀⠀⠀⠉⠉⠙⠳⢦⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⡏⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠈⠙⢿⡀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣀⣀⣤⡴⠖⠒⠾⠾⠿⢿⣿⠿⣿⣿⠟⢁⣀⣤⠶⢋⣄⣠⣤⣦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠳⠄⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣶⢦⡤⢤⣤⣬⣥⣤⣾⣶⣿⣿⣿⠿⠚⠋⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⢦⣄⣀⠁⣚⣲⣶⣶⣶⠔⢀⣀⣚⡉⠉⠀⠈⠓⠺⠧⠀⠀⠀⠀⣩⣿⡿⠛⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡫⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠈⠙⠛⠿⣿⣿⣿⣶⣤⣤⣀⣀⣀⣠⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⡿⠛⠉⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣒⠤⣑⣆⡀⠀⣄⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⡂⠒⢀⠂⡉⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠈⠹⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠐⢌⠓⠢⠕⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠑⠏⢢⢪
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠡⠖⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⢄⠀⠺⠿⠇⠁⠀⠀⠀⡄⠀⠑
⠀⠀⠀⠀⠀⢱⣷⡤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢰⠐⠀⠀⠃⠃⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠁
⠣⠑⠀⠠⡴⠊⠙⠓⢆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣷⡄⣀⡤⠤⠂⠘⢂⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⢤⠠⠁⠀⣀⠀⣈⠈⠂⠀⠀⠀⠀⠀⠠⣄⢂⡀⢄⠀⠀⠀⠹⢿⠀⠀⠈⠂⣔⢰⡀⡑⠄
⠀⠀⠀⠀⢸⠘⠋⠅⠀⠰⠄⠀⠀⠚⢭⣑⡂⢖⢲⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠘⡈⣉⠲⠀⠀⢀⢀
⣿⡶⠀⠈⠉⠀⠑⠗⠘⠑⠖⠘⠀⠀⠀⠈⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡁⡜⠂⠀⠀⠀⠀⠀⠀⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠈⢂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⢼⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠡⠀⠀⠂
⠀⠀⠀⠀⠀⠰⣤⣤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⢠⠐⠆
⠀⠀⠀⠀⠀⠐⠛⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⡾⢱⡀
⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠰⡀⠀⠀⡀
⠀⠙⠀⢆⣐⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠁⢀⠀⠀⠢⡀⠀⣐⠀⠀⠀⠁⠀⠀⠙⠋⠒⣾⣿⡇
⠀⠀⠈⠑⡍⠪⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡜⡘⠁⡃⠀⠐⠈⣹⣿⣷⠆⠠⠄⠤⢢⠄⠀⢀⢹⠇⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠜⠒⠠⠐⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡈⠈⡁⠀⠄⣲⡆⢀⠀⠀⢠⣆⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠁⠀⠰⠀⠀⠀⠀⠀⢀⡀⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡌⠀⢀⡄⠀⠀⠀⠀⠀⠂⠄⠀⢸⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⢳⡖⠁⠀⠀⢀⠀⢀⣠⠔⠂⢄⣸⠁⠒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢨⡄⡐⢁⠀⠘⠤⠀⠀⡀⣀⣤⢁⢠⣐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⠀⠙⣄⡇⠀⠀⠀⠈⠑⠒⠉⠁⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣮⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠑⠀⠁⠀⠑⢾⠀⠀⢦⠀⠀⠀⠀⢠⣠⠟⢠⡔
⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠀⠀⢀⠀⠀⠢⠀⠠⣄⠈⢠⣘⢛⡕⠀⣴
⠀⠀⠀⠀⡇⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢤⣄⠀⢡⣤⣀⡀⠀⠈⠇⡀⠈⠻⣷⣵
⠀⠀⢀⢀⠃⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⢆⣃⠀⠀⠀⠈⠀⠀⠀⠾⠶⠤⣽⣯⡠⢠⠂
⠀⠀⠈⠓⣺⢧⡀⠀⢡⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⠉⠐⠀⠀⠠⠄⣀
⠀⢀⠠⠲⠄⡀⠀⠀⠺⠃⣀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠖⠛⠻⠶⠤⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⣄⠀⠂⠣⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠤⠤⣤⣤⠤⠤⠒⠒⠒⠒⠀⠀⠚⠂⠘⠉⠉⠉⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠲⡀⠀⠀⠀⢴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣖⠢⠿⣿⣿⡮⣿⣟⠳⣝⢤⣦⠀⣿⣿⣶⢀
⠀⠀⠀⠀⠀⠀⠀⣸⡶⢶⣏⣤⡾⠆⢴⣷⣶⣬⣿⡷⡌⠠⡙⣷⡙⠻⣿⡿⠀⠀⣀⣤⣦⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣣⣾⣿⢿⣷⣴⣷⣜⣻⣿⡻⢷⡜⢆⠀⢸⣧⠀⠙⣷⡆⣰⣿⣿⣿⣿⣿⣿⢿⠿⢷
⠀⠀⠀⠀⠀⠀⠀⣯⠈⡻⠿⢷⣭⢿⣿⣿⣿⣗⢻⡆⢻⣼⣧⣶⣿⡀⠀⣿⣿⣽⣿⣿⣯⣍⡀
⠀⠀⠀⠀⠀⢀⣴⣯⣼⣷⣶⣿⣥⣴⣿⣿⣿⣿⡗⣿⡎⣿⢹⡿⢿⡇⠀⣿⣿⡏⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢾⢿⠟⣭⣵⣾⣿⣿⣿⣿⣿⣿⡏⣄⢿⣿⣿⣞⣡⢾⣿⣆⣿⡏⠀⠀⠀⠈⠙⠻⠿⠿⠦
⠀⠀⠀⠀⠀⠘⣾⡌⡅⠈⣽⡿⣿⣿⣿⣿⡟⢀⡿⢸⡿⡛⢸⠟⣾⣿⣿⡇⠇
⣦⣄⣀⠀⠀⠸⢿⣇⣱⠟⣛⠛⠞⢛⣻⣿⣇⣾⣷⡿⣰⣤⢠⠏⣿⣿⣿⡿⠀⢀⣴⡆
⢻⣿⣿⣿⣦⣤⡈⠻⠿⢷⣄⣉⣻⣯⣿⡿⠟⡉⠛⣫⣿⡿⢋⣰⣿⡿⠋⣤⣴⣿⣿⠇⠀⠀⢀⣀⡀⣀⣤
⠘⢿⣿⣿⣿⣿⣿⣄⢀⣤⢉⣋⣙⣉⣩⣤⣢⣴⣿⡿⢿⣳⣿⠉⢸⡇⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠈⢻⣿⣿⣿⣿⣿⣾⣿⣷⡌⢛⣿⣇⠙⠙⠉⠁⣀⠸⣿⡟⣰⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⠇⠉⠉⠉⠓⢹⡄⠀⢹⣷⣼⡿⢃⣀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⢀⣴⣾⣿⣿⡿⠻⡟⠋⠀⣠⣴⣶⡆⠀⣷⢀⣼⣿⣋⣀⠻⣿⡟⢀⣿⣿⣿⠛⠛⠛⠉
⠀⠀⠸⣿⣿⣿⡟⢁⣀⠙⢦⢰⣿⣿⣿⠁⢀⣷⣾⣿⠿⠿⠿⡍⠉⠻⣯⣌⠙⠿⣿⣿⣷⣦
⠀⠀⠀⢿⣿⡿⠁⠘⣿⣷⣜⣟⡿⠛⠁⣄⣼⠟⠉⠀⣀⣀⣀⡄⠀⠀⣿⣿⣷⡀⠈⢻⣿⣿⡧
⠀⣄⡀⠀⠙⠷⠀⠀⠙⢿⣿⣿⣿⣇⢀⣿⣯⡄⣰⣿⣿⣿⠟⠀⠀⢀⣿⣿⣿⡇⠀⠀⠙⣿⡗
⠀⠘⣿⣷⣆⠀⠀⠀⣴⣿⣿⢿⣿⡟⣼⢏⣿⣇⣿⣋⣁⣀⠀⠀⠀⣾⣿⠿⠛⠁⢀⠀⠀⠈⠃
⠀⠀⠉⢿⣿⡆⢠⡄⠋⠁⠀⢠⣬⣾⣿⠟⣱⠟⢻⣧⣄⠉⢳⡴⢺⣿⣿⡿⢷⣦⡄⢱
⠀⠀⠀⣀⣉⣻⣾⡇⢀⠀⢰⡆⢻⣿⠇⣼⠋⠀⠈⣿⣿⣠⡎⠀⢼⣿⠋⠉⣠⣼⣿⣻⠠⣤⣤⣄
⠀⠀⣾⡿⢋⡀⠉⡙⠺⣇⣼⡷⢸⣿⣸⣧⣤⢤⡀⠨⣧⡿⡃⢀⡿⢞⠶⣾⣝⣻⡿⣿⣆⠙⠿⣿⣧
⠀⠀⡻⠁⣸⣿⡌⠙⠳⣿⣿⠁⣼⡟⠁⠀⢀⣴⣿⣿⣿⣦⡆⣿⠁⢿⣰⣿⣿⡿⣧⣝⠳⠀⠀⠈⠻⡇
⠀⠀⠉⠀⢻⣿⡿⠀⠀⠸⣷⣾⣿⠁⠀⢀⣿⣿⢿⠿⢿⣿⢇⣿⣿⡈⣿⢿⣿⡾⣿⢻⣥
⠀⠀⠀⠀⠈⢻⡇⠀⣠⣾⣿⣿⣧⣤⡀⠈⡿⠋⠀⢠⣼⣿⡿⣿⠙⣿⣿⡄⠹⠞⣡⣶⣅⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠋⢹⣿⠏⠈⠉⠛⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣌⣛⣩⡉⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣠⣿⠋⠀⢠⣿⠟⠆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⢹⣿⣿⣿⣧⡈⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠹⠁⠀⠠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠈⠀⠀⠸⣿⡿⠈⠻⢧⡀⠙⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠙⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠐⠀⠀⠀⠀⠀⡀⠄⡉⢁⠀⠀⠀⠰⣿⡆⠀⢀⠀⠀⢴⡺⣷⠄⠀⠀⠀⣤⣤⡀⠀⠀⢀⠀⠙⠛⠁
⠀⠀⠄⡀⠀⠀⢀⠀⢹⡷⠃⠈⠀⠀⠀⠀⢀⣀⡀⡘⠱⠀⠈⠛⠈⠁⠀⠀⠐⠿⠿⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠹⠆⠛⣀⠀⠀⠀⠀⠀⠀⠹⠿⠉⠀⠀⠀⠀⠰⣆⣀⠀⢀⡀⠀⠀⠀⠀⠀⢴⡀
⠀⠀⠀⡂⠑⠀⠀⢤⣠⠈⠻⠀⠐⠃⣤⡈⠁⠀⠀⠀⠀⠀⠀⢂⠀⠉⠙⠀⠀⢀⠀⠀⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠠⡀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠒⠀⠀⣤⠀⠀⠄
⠀⠀⠈⠂⣀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⢓⡀⠀⠀⢀⠀⡠⢀
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⣠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢴⡶⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⡀⣼⠀⡇⣾⡜⡴⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⠀⢠⣼⣦⣡⣷⣶⣼⣷⣿⣤⣥⣣⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠰⣿⣿⡟⣵⡿⢛⣷⣟⢿⣿⡏⣀⣤⣴⢶⠿⠋⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢⣤⣀⠀⠀⠀⠉⠛⢿⣿⣇⡀⠈⠉⠈⠁⣹⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠘⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠁⠀⠙⠻⢿⣿⣿⣷⣶⣾⣿⡿⠟⠋⠃⠀⠀⠀⠀⠠⢄⠀⠀⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡔⠉⠉⠉⠙⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⡿⠛⠛⠻⢧⡀⠀⠀⠀⢀⠀⠈⠰⡄⠀⠀⠀⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⣶⣶⣾⡇⠀⠀⠀⠀⠀⡄⠀⠀⢿⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⡄⠀⠀⠀⠐⣿⠁⠀⠀⠀⠀⢀⠘⠛⠉⠉⠃⣀⠀⠀⠀⢰⣿⡦⠤⢼⡷⠀⠀⠀⣠⣦⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢏⡧⠀⠀⠀⠀⢈⢠⣤⣤⣤⣶⠟⠀⠀⠀⠀⠀⠈⠀⠀⣀⣾⣿⠃⠀⠀⢀⣤⣿⣿⣿⣿⣶⠶⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠉⠀⠀⠀⠀⢠⣴⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⣉⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⣿⣿⣟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄⠀⢀⠀⠀⠀⠙⢿⣿⠀⢡⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠃⠀⠀⠀⠀⠙⠿⣦⣳⣤⣀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⣤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠐⠛⠉⠛⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢠⣸⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣿⡇⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣈⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⢁⡐⠀⠀⠀⠀⠀⠀⠀⠛⠠⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⢧⣼⣧⠀⠀⠀⠀⠀⣰⡟⣀⣼⣡⣴⣟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣾⣿⣬⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠛⣉⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣉⠉⠉⠙⠛⠛⠻⣿⣿⣿⣷⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⡻⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⠀⣀⣀⣤⣤⡤⣶⠊⠻⢿⣯⣙⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠋⠉⠉⠉⠋⠀⠈⢳⣄⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡐⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣿⣋⣈⣿⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠛⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢄⣀⣤⣀⣀⡀⠀⠀⠀⣀⣤⣴⠶⠂⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⢄⠀⣶⠤⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⢴⢸⡷⢻⣿⡏⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⣿⡿⣿⠏⠛⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⢾⣋⣿⠟⠁⠀⢰⣶⣶⣆⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⠋⠁⠀⠋⠰⠋⠀⠀⠂⠹⠋⠀⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⡟⣿⣿⣤⡴⠋⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⠶⣶⣶⣶⠀⠀⢴⣶⣄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣸⠇⢸⣿⣯⠀⣴⡟
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠈⠃⠀⠀⠀⠀⠀⣴⣀⣀⣠⣿⠋⢠⣶⠋⠀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠓⠚⣿⠾⠛⠋⠁⠀⠈⠙⠿⢿⡀⣿⠃⠀⣾⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠁⢀⣾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢀⣿⣿⣿⣯⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣾⡿⣽⡇⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣿⡟⠁
⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡴⠶⠒⠛⠀⠀⠀⠀⠀⣀⣤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⠛⠛⣋⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⢀⣤⣶⣶⣾⡿⠷⢄⠀⠀⢀⣤⢿⣴⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠻⣿⣶⡀⠀⢠⣾⠿⠟⢻⣿⣿⣿⣧⠀⠀⢠⣿⠏⣴⡏⠀⠀⠀⠀⠀⠀⠀⡤⠀⣶⣡⠶⡄⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⣀⣴⣿⣿⣿⣿⣿⣧⣐⣟⡁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢙⡢⣿⠉⠢⠄⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢿⣿⣿⡿⢿⣿⡛⠿⣿⡯⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣡⣴⡿⠋⠙⠁⢺⠙⣷⠀⣤⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠛⠉⠀⠀⠀⠀⠸⡇⢹⣇⠀⠁⣤⡾⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢠⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢿⡄⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣿⠇⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⡀⠀⠀⠀⠀⢈⣉⣽⣿⣶⠆⣤⣀⣀⣀⣤⠶⠋⠀⢠⡾⠋⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡀⠀⠀⠐⢛⣻⣿⡿⠋⠚⠛⠛⠉⢉⣴⣾⣦⣌⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣴⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⢸⢿⣿⠃⠿⠀⠀⠀⠀⠀⢸⡏⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠾⠿⢿⡟⠳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠟⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡙⠿⠿⠷⠍⠿⠿⠷⠤⠤⢤⡀
⠀⠀⠀⠀⢀⣴⠂⣿⣿⣿⣿⡄⣧⣄⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠙⢦⡀
⠀⣶⣦⣤⡌⠻⢠⠀⠈⠙⠛⢇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣄
⠀⠉⢿⣿⠿⠀⠀⠁⠀⠛⠧⠸⠈⠿⠿⠟⠛⠛⠛⠋⠉⠩⠿⢶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀
⠀⠀⣾⠻⡄⠡⠂⠀⠀⠀⠀⠀⠀⠐⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⡿⣿⣿⣾⣭⡙⢿⣷⣦⣀⡀
⢴⣶⣿⢾⣿⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠿⣿⣷⣶⣍⡻⢿⣿⣶⣄
⠀⠉⢿⡘⣿⡑⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠒⠠⣄⣀⠀⠀⠁⢀⡀⡀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠻⣿⣿⣿⣦⠙⢿⡿⣗⠤⣤⣼
⠀⠀⠀⠙⠛⠛⠿⣿⣿⣿⣶⣤⣀⠀⢠⣾⣷⣤⡀⠀⠉⠒⠢⣄⠉⠀⠀⠀⡀⠀⠀⠋⢀⠀⠀⠀⠈⠀⠀⠀⠉⠀⢀⣀⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣞⡿⠉⣹⣷⡄⠀⠀⠘⣿⠁⠀⢀⣠⡆⠀⢰⣴⣏⠀⣀⣀⣠⣤⣤⡶⢶⣿⣿⣶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡇⣿⣿⣿⣿⣦⠀⠀⠛⠒⢲⣿⣛⣛⣥⣤⣬⣭⢽⣿⣿⠃⠀⣿⠀⣠⣌⠙⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢿⣿⣾⣿⣿⣧⣴⡠⡀⡀⡀⠀⠀⠀⠀⠀⠴⠊⢻⣿⣶⣶⣎⢻⣿⣿⣇⣤⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⢿⠿⢻⣿⣿⣿⣻⢷⣷⣷⣷⣿⣧⡀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣽⣭⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣭⣿

⠀⠀⠀⠀⠀⢀⠄⠒⠂⠠⡀⠀⡠⠀⠄
⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡀⠌⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠤⣷⣄⡀⠀⣀
⠀⠀⠀⢀⡀⠁⠐⢄⠴⣞⢷⢦⠄⠐⠚⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠻⡿⠄
⠀⠀⠊⠀⠀⠀⠀⢸⠃⠒⠻⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣾⡀⠢⠀⠀⢀
⠀⠀⡀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢯⠁⠀⠈⠉⠈⢢
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠑⠀⠉⠠⠀⡀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡔⠄⠀⠀⠁⠀⠐⠀⠀⠀⢀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠉⠀⢢
⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⢀⠀⢄⠀⠃⠀⠀⠐⢽⣆⡀⡀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⡈⡀⣀
⠀⠀⠀⠀⢰⣿⠗⠂⢤⠄⠁⠀⡬⠀⠀⢀⠀⠀⠼⠻⡍⠀⠀⠀⠀⠀⠜⠁⠀⠉⠢⡀⠀⠀⢐⣬⠄⠀⠉⠒⢄
⠀⠠⠀⠀⠝⡇⠀⠀⢠⣀⣠⣼⣦⠠⠤⠐⠃⣁⠀⠀⠹⡀⠀⠀⢠⠁⠀⠀⠀⠀⠠⠀⠩⣽⣿⣷⠖⠶⠀⠀⠐⢄
⠀⠀⠀⠈⠐⡁⠀⠂⠁⠀⠘⠻⠓⢄⠀⠀⠀⠀⠓⠀⠠⠁⠀⠀⠘⢂⠀⠀⠀⢀⡀⠄⠊⢐⠇⡌⢃⠀⢀⠀⠀⠀⢁
⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠆⠁⠀⠀⠐⠁⠀⠰⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠠⠄⠊⠀⠀⠈

⢠⡆⠀⠤⠀⠀⣀⠀⠀⠀⠈⢢⠉⠘⡀⡠⣄⡜⠀⠀⠀⢄⢈⡠⠀⠀⢀⠀⠀⠂⠲⠀⠰⠄⠠⠀⠀⠀⡠⠂
⠀⡀⠈⠀⢀⠀⠈⢳⣏⢈⡤⠐⠀⠆⠁⢐⠞⠗⠀⠀⠀⠒⠉⢆⠀⠘⠀⡘⠁⠈⢳⣴⠀⠆⠐⠚⢒⢶⠒⠒⠦
⢤⣠⡤⠄⡉⡀⠀⠎⠀⡁⠠⡀⠴⠀⠀⠉⠈⠁⠈⠀⠀⠀⠁⠀⠇⠀⣰⢔⠉⢀⡈⡘⠀⠀⠀⢠⠎⠀⢇⡀
⢠⡜⠃⠀⠀⣁⣀⣀⠭⠄⠐⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣠⠆⣀⠃⠀⠒⠀⡝⡀⠀⠈⡆
⣏⠈⠀⠀⠒⡿⡞⠀⠀⠆⠀⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⠀⠀⠒⠀⠁⢢⠐⠀⣀⠀⠈
⠠⡜⠀⠀⠀⠀⠀⢀⢀⡈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡈⠠⠠⣁⠠⠌⢀⠓⠰
⣰⠊⢁⡀⠣⡜⠢⠒⢬⠀⡶⠀⠀⠀⢀⡤⡀⡤⣄⢀⣄⢀⡤⣀⡤⢄⡤⡀⢀⠘⠀⠀⠀⠁⠠⠡⡄⠢⠀⣸⡓
⠼⠓⠈⢉⡆⢁⡈⡆⢪⣀⡐⠄⠀⠀⠸⠤⠖⠟⠧⠼⠻⠄⠏⠹⠧⠤⠭⠆⠀⠀⠀⠠⠐⢁⠀⠀⠆⠄⡎⢸⡙
⠐⠀⢸⢁⠌⢀⣅⠠⠈⡰⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣣⠀⠃⣀⠀⠀⠀⡧
⠀⠀⠋⠈⠬⡀⢉⠓⢠⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢀⣠⠮⠀⡁⠵⠆⠀⠀⠀⡵
⠀⠀⡀⠀⢠⠁⣪⢐⡈⠉⠙⠀⠀⠀⠌⠓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠚⠁⠰⠶⠂⣄⠀⠀⠄⠀⠂⣈
⣄⠀⠀⢠⠇⠀⡆⢠⡌⢠⠀⠀⠀⠀⠄⠀⠌⢀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠰⠁⣤⠀⠘⡆⠀⠀⡱⠋⢀
⠄⠀⡠⠋⢀⠀⠀⠋⢀⢈⡰⢄⠤⡍⠀⠔⠴⢄⠀⠀⠀⢠⡄⠃⠘⠀⠀⠆⠑⢢⢂⠆⢦⠐⠁⠩⠀⡩⢀⡠⠇
⠜⡸⠀⠠⠀⢄⠈⠡⠄⠠⡄⠐⢀⠀⠂⠀⠈⠂⢄⠀⠀⡂⡀⠇⡐⠚⡅⠐⠠⠂⠁⡼⠈⡈⠁⠲⠢⠀⠈⢀⠬

⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⢀⠀⢀⢀⠀⢀⠀⠀⠀⡀⢀
⠀⠀⠃⠘⠁⠙⠢⠘⠐⠂⠂⠘⠉⠄⠛⠀⠚⠃⠱⠐⠄⠣⠀⠀⢰⡀⢀⠄⠀⠀⡀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⣲⠠⡔⣂⠆⠰⠒⢦⢴⣰⠀⣰⠶⠲⣂⠀⠀⠀⠀⠀⠀⠀⠀⣇⡞⠆⠹⡀⠉⠀⢳⢠⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⡏⠀⠰⡀⠁⠆⠠⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⡅⠀⠀⠉⠙⢄⡀⠚⠁⠀⡇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠇⠀⠀⡀⠀⡀⠠⠄⠲⡀⠀⢀⡀⠀⠀⠔⠣⡄⠃⠠⠂⠀⣠⠄⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠁⡄⠤⠀⠀⡀⠀⠰⠄⣀⠊⠀⠀⠂⠀⠀⣀⢠⠞⠂⠀⣈⠾⠐⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠠⠀⡤⠀⠈⠃⠀⠠⢠⠄⠂⢄⠀⠢⣀⠀⠀⡗⢀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠓⢀⠀⠋⠀⠈⣆⠒⠁⠂⣏⠀⠀⢀⡆⠂⠉⠢⠈⠁⡠⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡀⠀⠀⠚⠸⡀⠀⠀⠁⠁⠒⠁⠃⠀⠀⡰⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠁⠀⠁⠀⠀⢁⠔⠈⠉⢄⠀⠀⠠⠠⠀⠀⢀⠜⠉⠐⢖⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠢⣄⠀⢢⣀⢀⠔⠁⠀⠀⠀⠀⠀⠉⢄⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢀⣀⣀⣬⡴⢞⠉⠉⠉⠀⢀⢄⠀⠈⠉⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠡⠛⠉⠀⠘⠄⡀⠠⠗⠁⠀⠑⠧⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⢀⣌⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⠉⣿⣿⣿⡿⣷⣤⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣿⣿⣿⣿⡙⠻⢷⣼⣻⣧⣤⣶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⠇⠻⠆⠀⠘⢿⣿⡿⠛⠛⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢉⣭⡍⠙⣿⠀⠀⠀⢀⣀⣿⡋⣠⣶⣶⣤⣉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣏⣁⠀⠀⢹⣦⣄⣰⣿⣏⡉⠉⠈⠉⠛⠿⣿⣷⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠙⢿⣷⣦⣿⣿⣿⣿⣿⣿⢿⣦⣤⣄⣀⡀⠀⠈⢻⠇⠀⠀⡀⢸⡗⠀⠈⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠈⣿⣿⣿⣧⡿⠋⠈⣿⠀⢻⠿⡿⠟⣛⣟⠀⣀⡀⠀⣰⠇⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⣄⣿⡿⣿⣿⣇⣼⣁⣿⣧⣼⠗⠀⠘⠿⠛⢿⣿⡟⠀⡏⠀⠀⠀⠀⠀⠀⠘⣧⣤⡀
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠿⢷⣆⠀⠀⠀⣿⣷⠘⣷⢼⣿⣿⣿⡿⢋⡙⢉⠀⠈⢦⡀⠀⢈⣿⣇⠀⡁⢰⠀⠀⠀⠀⠀⣸⡃⠸⠛⣀
⠀⠀⠀⠀⣴⣶⡿⢿⣦⣀⡀⢻⣇⠀⣼⡟⣡⣶⣿⣼⠟⣩⡄⠀⣌⠁⠀⠁⠀⠀⠀⠰⣾⡿⣿⠀⠷⠘⠀⠀⣴⠀⢠⡟⠁
⠀⠀⠀⠀⠈⠛⢿⡄⠙⢻⣉⣿⠿⢉⣀⣠⣦⡌⢿⣷⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣼⠷⠶⢶⣤⡀⢉⡴⠃
⠀⠀⠾⠛⢷⣆⡀⠈⠐⠒⠈⣛⠷⣼⣿⣿⣿⣷⣿⣿⣿⣿⢿⣷⡄⠀⠀⠀⠀⠀⠐⠂⠰⣾⣏⣴⡟⣶⣌⢛⡁⠐
⠀⠀⠀⠀⣼⠿⠿⠿⠶⠟⢋⣽⣯⣿⣿⣿⣿⣿⠻⣦⣥⣀⣠⡈⠁⠀⠀⠀⠀⠀⠠⣶⡶⢿⣿⣿⣿⣿⣿⣶⠀⠚⠃⠀⠀⠀⠐⠿⠂
⠀⠀⠰⠆⠀⢶⣿⡾⠿⠟⢉⡾⠟⣿⠛⣿⣿⣝⠳⣄⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣉⣿⡟⣿⣿⣅⠻⠁
⠀⠀⠀⠘⣷⣮⣅⣀⡤⠔⢋⣤⠞⠁⣠⠀⣻⣿⣄⡈⠛⠂⠀⠛⠐⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠛⠳⠍⠳⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠛⠛⠛⢡⣤⣯⣥⣴⣶⣿⣧⡈⠛⠏⠀⣠⣴⣾⣿⣷⡎⢱⣿⣧⠀⠀⠄⠰⠿⠛⣁⡀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢋⣙⠿⡿⠻⣿⣿⠗⠀⠛⠋⠀⢹⡟⠀⠸⣿⣿⣶⣶⣤⣄⣀⣀⠉⣉⣉⡉⠛⠳⢀⠰⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠄⡀⠹⣟⣤⠀⠀⠀⠀⣾⠇⠀⠀⠈⠹⠻⣿⡿⣭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠙⢿⣷⣀⣀⣠⣬⣄⠀⠀⠀⠁⠀⠁⠀⢀⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⣦⣀⣿⡟⢫⣭⣤⣝⢳⣄⡄⠈⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠻⣦⡈⠙⢿⣿⠿⠿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠻⠿⣯⣾⣷⣼⣿⣸⡿⠂⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣀⣹⡗⠲⠾⠿⣶⣤⣽⣷⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⠙⣢⣤⣶⣿⣿⣿⣿⣿⣿⣧⣴⠄⠀⠀⠀⠀⠈⠛⠉⠻⣿⣿⣷⣷⣮⣭⣽⣿⣶⣶⠿⠶⠛⠛⠛⠻⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠛⠋⠿⢿⣿⣷⠘⠉⠻⠆⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡻⣿⣧⣤⣬⣭⣿⣿⣆⣲⣶⡷⢞⠒⣻⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠛⣤⠋⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠻⠿⠿⣿⣿⣛⣿⣿⡻⠿⣿⣿⣿⣿⣶⡿⠛⣫⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠠⢦⢤⣀⣹⣿⣶⡷⠀⠀⠀⠀⢘⠃⠀⠀⢰⡏⢸⣿⣿⣿⣿⡿⠿⠿⣿⡯⠥⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⢹⠟⠁⠀⠀⠀⠀⡀⠀⠀⢠⠟⠀⠸⠿⠿⠛⠏⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠐⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢰⡇⠀⢀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠰⠃⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈