Tentacle Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠄⣀
⠀⠀⠀⠀⢀⠏⣭⡡⢀⣴⠏⢀⣠⣀⠀⠑⠄⠀⠀⠀⣰⣤⣤⠀⠀⠤⣶⢶⣢⢤⠂⣰⢦⢄⢄⣀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠉⠙⠱⠶⣄
⠀⠀⠀⠀⠘⡄⠡⣀⣾⠇⢠⠋⠀⠀⡳⠀⢀⠀⠀⠀⣣⣼⣿⣆⠀⠀⠀⠀⠀⢈⣁⣉⢉⠐⠓⠦⠵⣄⠀⠀⠀⠀⡀⠀⡀⣒⠢⣄⠀⠀⡞⣇
⠀⠀⠀⠀⠀⠹⣆⣘⣿⡅⢸⣀⠠⠐⠁⢐⠆⠀⠀⠀⢻⡬⣿⣏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠐⢤⡙⢷⡀⠀⠀⠀⠄⣑⠉⠀⡼⠀⢀⡷⣾
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣄⠳⢦⡖⠊⣁⠀⠀⠀⠀⠹⠿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠾⠇⣭⠀⠀⠀⠀⢀⣠⠔⠉⢀⡤⠾⢘⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣷⢤⣀⣄⠤⢤⠀⠀⠀⣟⢷⣿⢞⠀⠀⠀⠀⢀⡤⠒⢤⠀⠀⠘⠄⣉⡔⠔⠁⠀⠀⠀⠀⢀⣔⣴⣙⡶⠟⠋
⠀⠀⠀⠀⠀⡠⣤⣴⠂⠀⠉⠺⠟⡻⢿⢲⠏⠀⠀⣰⣙⣻⣿⡋⠀⠀⠀⠀⡏⡞⣿⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣶⠛⠋
⠀⠀⠀⣠⢒⡖⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣷⣾⣿⠋⠀⠀⠀⠀⠀⢇⠙⢶⣞⣦⣀⠀⠀⠀⠀⠀⠀⠐⡧⠛⠁
⠀⠀⡰⠛⡊⣧⠞⢠⠇⠀⠀⠀⠀⠀⠀⢀⡔⢉⢶⣿⠛⠁⠀⠀⠀⢁⡀⠀⠈⠣⣄⠀⣃⢿⣷⢦⢄⡀
⠀⢀⠞⣚⢥⠞⣠⠏⠀⠀⠀⠀⠀⠀⢀⡏⢠⣻⡿⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠑⡦⢍⡛⢾⣛⣟⡦⡀⠀⠀⠀⠀⠡⡀⠀⠀⠰⡀
⠀⢠⢶⡁⡜⢨⠏⠀⠀⠀⠀⠀⠀⠀⠸⡇⢮⢿⣥⡀⠀⠀⠀⠀⠀⠀⠀⢉⣾⡁⠀⠀⢱⠀⠙⢦⠻⠠⠽⣷⡀⠀⠀⠀⠀⠈⢄⠀⠀⠱⡄
⠀⢸⠞⡡⠚⣌⠠⢂⣉⠀⠀⠀⠀⠀⠀⠈⠓⠬⢍⡛⠳⢤⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⢣⡀⠀⡇⢐⠺⡹⣇⠀⠀⠀⠀⠀⠈⢱⡀⠀⠸⡄
⠀⠈⢲⢑⠄⠱⣄⣾⠍⢱⢈⡀⠐⢍⣠⣄⡀⢄⡀⠈⠳⡄⢹⡀⠀⠀⠀⠀⠀⠨⣿⡄⠀⠀⠑⠒⢡⡇⠻⣉⠏⠀⠀⡠⠒⠉⠑⢄⠣⠀⠠⢱
⠀⠀⠈⠲⣼⣢⡈⠛⠐⠀⡴⠃⠀⠀⠀⠀⠈⢦⠑⠀⠀⡘⢸⡇⠀⠀⠀⠀⠀⠀⠣⣝⠶⣤⣤⡴⢆⢘⣎⣻⠁⠀⠀⡇⠠⡯⠷⣸⢜⠀⠈⢻
⠀⠀⠀⠀⠈⠑⠛⠗⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠣⠤⠬⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠣⣤⠤⣿⠯⠗⠁⠀⠀⠀⢱⠀⠹⠿⡥⠎⠀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣚⡏⢍⣛⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⡀⢀⣐⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡴⠋⣤⡿⠜⠯⢽⡿⣷⣦⢬⡝⠲⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⡀
⠀⠀⠀⠀⠔⢉⢠⡉⡀⠀⠇⠀⡐⢀⠃⠀⠀⣄⠀⠀⣠⠞⢠⡶⠉⠀⠀⠀⠀⠈⠉⠫⠽⣲⣿⣤⣄⣽⣧⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠚⠀⠻⣌⡁⠃⢀⠀⠀⠁⡨⠀⠀⠀⠈⠉⠋⠒⠚⠁⢀⡤⣴⠶⠴⠤⣄⡀⠀⠀⠀⠉⠈⠁⠙⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⢈⢂⠀⢇⠀⠀⠀⡸⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠐⡐⢂⢤⡉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡖⠛⢧⡀⠈⠁
⠀⠀⠈⣀⠂⡀⠑⠒⠋⢀⠔⢠⠌⠀⠀⠀⠠⣄⣀⡤⠚⠁⠠⠆⠉⠁⢉⡟⣩⡝⡾⣣⠘⡄⢀⠄⢀⠄⣀⠀⠀⢀⠜⡇⡄⠀⠻⣉⠆⢲⡇
⠀⠀⠀⠀⠣⢍⠀⠒⠒⡁⠰⠀⠀⢰⣿⣂⣀⢀⡀⡀⠠⠌⠁⠀⠀⠀⠈⣧⡙⠪⠶⠏⡰⠁⢠⣙⣋⣿⣿⣽⣿⣿⣿⡻⠴⣆⣄⣠⡻⠗
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠘⠂⠯⠁⠦⠄⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠋⠀⠀⠀⠈⠁⠀⠉⠛⠛⠋⠁⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣿⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⠛⠋⠻⣧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢷⡄
⠀⠀⡾⠁⠀⡀⠀⠀⠀⠀⠀⠀⣸⣯⣥⣄⡀⠶⠟⠀⠀⠀⣸⣿⠀⣴⠿⣦⣀⣾⠋⠁
⠀⠀⠛⢦⡄⠁⠀⠀⠀⠀⠀⠀⡯⡏⠀⠈⣿⠀⠀⠀⠀⣐⣿⡏⢸⡇⠀⢹⣟⠚⠧⣤⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⢀⣿⡄⠠⠀⡰⢴⡟⠀⠈⠃⢀⣾⠧⠀⠀⠰⡕⣦⠾⠋⠉⠙⠻⣷⣆
⠠⣿⣿⣿⣦⡀⠀⢀⣴⣶⣶⣶⣾⣷⣞⡭⢛⠁⠀⢠⢱⡟⠀⠀⠀⠀⢎⠒⢁⣾⢿⣛⣃⡷⠀⠀⠀⠀⠀⠉⣿
⠀⠀⡩⢛⢿⡗⠀⣼⣿⡿⠛⠙⠋⠉⠉⠳⣯⡙⢷⠃⢸⡇⠀⠀⣄⠛⡦⠀⣼⣳⠎⠉⠁⠀⠀⠀⠀⠀⠀⢀⠐
⡰⢨⣍⠷⠛⠀⠰⠛⣿⣧⡀⠀⠀⠀⠀⢠⡿⢃⣸⣁⠐⢇⠀⠲⠎⣿⠃⣼⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙
⢿⣿⣤⡄⠀⠀⠘⠛⢲⣉⠿⢷⡄⢠⣶⣏⣱⠞⢧⠘⠷⡻⡄⢛⡖⣿⡀⣿⢸⡁⡄⠀⠀⠀⠀⠀⣀⠀⣀⢲⣾
⠀⠹⣿⣿⢴⠄⠀⠀⢈⡉⢶⢞⢿⣿⣧⢸⡏⢠⠈⡗⠻⠖⢷⡉⣹⡸⣷⣸⡆⢷⡼⢆⣀⠀⠀⣮⣙⢂⣼⠿⠁
⠀⣠⣿⠛⣾⢛⠀⠀⢨⡎⠸⡗⢻⣿⣷⡴⢷⡼⢧⡽⠞⣷⠞⢷⣥⢴⡞⢿⣿⣈⣷⣈⠷⡀⢬⣥⣭⢸⡇
⣴⣿⣉⣼⡋⣷⣀⣴⣾⣷⢸⡇⢸⣿⣿⣷⡞⢷⡈⣿⡶⢿⡦⢼⣿⣴⢳⣏⣿⣿⣤⡿⣶⣹⣿⣤⢯⡸⣿⣄
⣿⣯⢽⡿⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣂⣻⣥⣭⣭⣭⣤⣥⣬⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠎⠁⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⢨⠀⠠⠀⠀⠀⠠⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⢀⠤⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠠⡀⠂⡁⢄⠀⠀⠀⠈⠙⣦⣄⠀⠀⠀⠀⠀⡈⠀⢀⠰⠊⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⢐⢤⠃⠹⠥⠜⠥⡀⢄⡀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⢊⠀⠀⠈⠀⢠⠄⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠃⡁⠀⢀⠀⣆⠉⠀⢀⡀⠀⠲⠄⢠⣲⠀⠀⠛⠇⠀⠀⢀⠀⠀⠀⡜⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠈⡆⠶⠉⠀⠟⠀⠀⢨⢡⠶⡄⠈⠀⠇⠀⠀⠁⢈⠄⡛⠀⠀⠀⠀⡁⠀⠀⢠
⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⣀⠌⠃⠛⠀⢴⡀⢠⠀⠈⡎⡐⢀⠀⡠⠃⠁⠀⢀⠾⡀⢀⠀⠀⠀⢨⡕
⠀⠀⠀⠀⡜⠀⠀⠀⠀⡾⠁⣄⡘⠀⢠⠘⠫⢌⠀⠀⡷⠁⣨⠆⠂⠁⠀⠀⢀⡞⠀⣭⡄⢀⢀⡞⠁⠀⠀⠀⠃
⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⣹⠁⠰⠡⠁⠀⠀⠀⣠⠁⢰⠁⠀⠀⠀⠐⣠⠼⠀⠐⢀⡼⠉⠍⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⢁⠀⠀⠀⢺⠀⠀⠸⠀⢠⢈⠀⠀⠀⢸⡀⠀⠸⠀⠀⠀⠀⠀⣇⠀⠀⢰⠁⢀⢀⠀⠀⠀⣠⠚⠁
⠀⠀⠀⠀⢸⠘⠀⠀⠀⢦⠀⠀⡛⢿⢽⠀⠀⠀⠀⠣⡀⢤⠀⠀⠀⠀⠐⡁⠀⠀⢈⠆⢀⠀⠀⠀⡘⠁⠀⠀⠀⢰
⠀⠀⠀⠀⢸⠀⠀⠠⠀⠘⡇⠐⡄⡈⢻⡸⠀⠀⠀⠀⠈⢻⠀⠀⠀⠐⠀⢹⡉⠀⣎⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⢷⠀⠈⠁⠀⠳⡄⠀⠁⠀⠀⠈⡆⠀⠀⠀⠀⠘⣅⠀⣺⠀⠀⠀⠄⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⡿⠀⠀⠁⠀⠀⣿⡖⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢇⠣⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⣾⣦⣄
⠀⠀⠀⣾⠹⠯⣶⠿
⠀⠀⠀⠻⣷⣤
⠀⠀⠀⠀⠙⢿⣿⣤⡀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣸⡿⣫⣷⣿⣿⠿⢿⣿⣷⣆⠀⠀⠀⣄
⠀⠀⠀⠀⢠⣫⣾⣿⡟⠉⠀⠀⠀⠈⠻⢷⣵⣀⣶⡼
⠀⠀⢀⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣶⣾⣿⣿⣿⣿⡟⡃
⠿⣿⡿⢿⣿⣿⡇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢷⣦
⣀⣶⣶⣿⣿⣿⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧
⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠
⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡾⢿⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢀⠔⢁⣴⣿⠇
⠻⠛⠻⢿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠘⠛⠻⣿⡿⠿⠿⠛⠉⠁⠀⠉⠉⠳⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠅⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢦⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠋⠛⢷⣦⡀⠀⠀⣿⣛⡂⢐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠹⣿⣆⠀⢸⣯⡖⣦⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⣿⠯⣝⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣆⢣⢬⠀⠀⠀⠀⠀⣀⣀⣤⠤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⣸⣿⡉⠦⠦⠀⠀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣤⣰⣾⣿⡟⠁⢠⡹⢿⣤⣝⠐⠇⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⣿⣆⠰⠥⣊⣻⣧⠐⡉⠛⠎⢿⣿⣦⣤⣶⠟⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠈⠲⡄⠀⢀⣼⠙⣛⣿⠏⠀⣿⡿⠖⢚⣁⡟⢿⣤⠈⠑⡺⠄⢹⣿⣻⣧⣄⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⢹⢀⣶⡖⢋⣙⡏⢀⣼⣿⠷⠚⠠⣽⡇⢸⣅⡠⡑⠖⢷⣿⡟⠹⣝⠚⠡⠄⠀⢀⡔⠈
⠀⠀⠀⠀⠀⠀⠀⣼⣾⣤⡞⣟⣻⣿⣿⡿⡷⠄⠪⣂⣿⠀⣸⣄⣠⠋⠦⢾⣿⣧⠀⢻⣉⠀⠲⠀⡏
⠀⠀⠀⠀⠀⠀⣸⠇⣿⠤⢞⣥⣽⣿⠋⢰⠤⠔⢀⣈⣿⠀⣿⣀⣀⠂⠦⠴⣿⣿⣦⣼⠤⠀⡉⡃⣧
⠀⠀⠀⠀⠀⡰⢻⠀⣷⠔⠺⣳⠷⠿⣄⣧⠤⡘⡀⢈⣿⣸⣟⠈⠁⠰⢄⢤⡏⣿⣿⠗⠒⠀⢄⡅⢹⣆
⠀⠀⠀⠀⠀⠅⠹⡀⠸⣶⠖⡓⢹⣋⣹⡥⠤⡆⠈⠉⣿⡟⠉⢈⠀⣄⣀⣨⢀⣿⡟⠁⠀⠀⠠⠄⠈⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣿⣷⡶⠩⠂⢨⡅⠀⠄⢈⣽⠟⠋⠉⠁⡀⠀⢀⡏⡼⡏⠁⠁⠀⠒⠞⠀⠀⠇⢱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣧⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣉⠻⣦⠖⣤⣰⢮⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠋⠳⠄⢙⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠈⠀⠀⠓⣠⡟⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⢀⣀⣠⠞⠁⠘⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢁⣐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⢋⣼⢣⠠⡄⠲⣦⡀⠀⡤⣾⣉⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⢸⠏⠙⣿⣟⡅⣓⡊⢻⣿⣿⣿⣿⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡀⠸⣄⣀⣈⣉⢹⣯⣿⣏⣿⣿⣿⢃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠹⣆⠀⠀⠉⠉⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣿⣆⡘⢷⣄⣠⡈⠛⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠂⠀⠀⠻⣿⣿⣿⣷⣤⡍⠛⢦⣠⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠻⣦⣄⠺⣾⣿⡿⣿⣿⣿⣿⣿⣷⡎⢳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣟⡿⣾⡟⢀⡼⣿⣿⣿⣿⣿⡷⢈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠞⠀⠘⣿⣿⣿⣿⣵⣿⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣣⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠗⠈⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠠⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡥⢈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠷⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠐⡀⠐⠄⠀⢀⡀⠀⠄⠀⠀⠀⢰⠀⠀⠔⠂⠀⠀⠠⠀⠁⠘⡘⠀⠀⢀⡤⠔
⠀⠀⠀⢠⠀⠀⠁⠁⠀⠍⠁⠀⠠⠀⠀⠢⠤⢀⠤⠑⢀⡀⢰⢀⡀⠀⢠⠀⠀⠐⠈⠀⠀⢀
⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⡰⠁⠈⢀⠁⣼⠀⡀⠀⢀⠂⠀⠀⠀⠀⡌⢀⠀⠀⠈⠀⠀⠎⠂
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⢇⠈⠀⠀⠀⢀⠀⠀⠠⡀⠀⠈⠁⠀⠰⠈⠀⠀⠀⠰⠄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢧⠀⠀⢱⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢸⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠜⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⣄⣀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣤⡤⡛⢻⣿⠿⡿⠿⠿⣿⡹⠥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠂⣸⡟⠿⠟⠀⡔⢩⡙⢺⣇⣛⣀⣿⠛⣿⣻⣍⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣈⠐⠒⢛⡽⢣⠖⡀⠐⣷⣤⡴⠋⠉⠉⠀⠈⠛⠖⢻⣎⢩⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡿⠏⠛⠋⠀⠸⠦⢈⣁⣼⢆⣀⣀⡄⢀⣀⠀⠀⠀⠀⠙⢤⡯⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⣰⣃⠤⠂⠤⠖⠲⡄⢸⣿⠿⠿⠿⣿⣿⣿⣿⣳⣛⣶⣤⣀⡀⣧⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢿⡛⠁⣾⣦⠀⠚⠓⢈⣿⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣤⠄⢀⡷⣀⠙⠿⣶⣤⠶⢊⡇⠀⠀⠀⣠⠒⣿⣥⠿⠞⠛⠛⠛⢧⣿⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣴⣿⡿⠃⠐⣡⠌⠀⠂⣸⡃⠀⠀⣠⣯⡶⠋⢀⡤⣴⢶⣶⣄⠀⠱⣼⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠉⠉⠛⢷⡀⢀⣿⠀⠃⠃⢸⠄⠀⢸⠃⣻⠇⠀⡞⢀⣿⠻⣿⡿⠃⠀⣻⣽⢹⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠂⠀⣷⠎⠻⣦⡀⣰⣾⡆⠀⠸⢿⡉⠀⠀⡇⢈⣿⣄⠀⢀⠀⠠⣿⣿⣼⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⢋⡶⢛⡻⣿⣯⢹⡇⠀⠱⣆⣿⠀⠀⠱⡞⢹⠟⠛⡿⣿⣷⡿⠁⣧⣄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢉⡉⠙⢮⠻⡟⢡⠊⠀⠀⠙⢿⡇⠀⠀⠨⣟⡳⡄⠀⠈⠻⠀⠰⠟⠛⠋⢠⣏⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⢋⢀⡀⠀⢡⢧⣄⠀⠑⠀⠀⢸⠇⠀⠀⠀⠙⣡⣿⠟⢶⣤⡀⣀⣀⣠⠤⢾⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⠞⠁⠀⢸⠆⠙⠦⣤⣤⣴⣿⠀⠀⠀⠀⠀⠈⠓⠶⠆⠬⠿⣤⠼⠆⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠤⢤⡤⠋⠀⣠⣾⣗⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⠓⠳⣽⣠⣪⠷⠂⠀⠀⢽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢈⡉⢲⡝⢹⠃⠀⢠⠖⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠘⠛⢀⡟⠘⣧⣄⣀⣀⢤⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣖⣧⣀⠘⣷⣉⡭⣉⡙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠬⠙⣿⣧⣿⠁⡀⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠈⠉⠀⠉⠓⠚⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⣠⠖⠃⣩⣬⡿⠽⣶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⡏⠀⠀⠀⠀⣠⡾⣝⣳⡮⠶⠿⢷⣦⡼⠿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣿⣶⣤⣶⡿⠏⣲⡼⠊⠀⠀⠀⠀⢹⣿⠲⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⠧⠿⠴⠒⠋⠀⠀⠀⠀⣀⣴⠟⡅⠱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠿⠽⠉⢩⣤⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠍⠁⣴⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡏⠑⣤⣮⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⣴⣾⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⡈⢠⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡝⠂⣼⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡏⠀⣙⣏⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢳⡄⢟⣻⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣵⠁⢸⡭⠟⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣏⣿⠝⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢟⠻⣶⣟⢋⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠯⠼⠉⠉

⠀⠀⠀⠀⡀⠀⣀⣀⣀
⣀⠄⠀⠁⠀⠀⠀⠀⠀⠉⠒⣄⣀⢀⠀⠀⠀⠀⠀⠀⡠⠒⣠⠠⣔
⣿⣤⡤⠠⡴⣀⣰⠴⠓⠉⠁⠀⠀⠀⠀⠁⠂⢀⠀⡎⠀⡴⠁⠉⡖
⣯⡍⠉⠙⠟⠛⠁⠀⠀⢀⠠⣴⢀⢰⣦⠠⣄⡀⠈⠣⢴⣇⣀⣀⡼⠷⠒⡂⢀⣂⣄
⠏⠀⠀⠀⠀⠀⠀⣀⡒⢫⠖⡶⡦⢯⡆⠴⣕⠠⣗⣖⣤⠨⣍⢠⣴⣿⠶⣿⡛⠉⠛⢷⣦⣤⣤⠔⠁
⣧⡀⣀⡀⠴⠶⡌⣳⡉⡛⢋⠻⣅⣻⠀⡀⠈⠢⣼⡬⠿⠚⠉⡸⠉⡅⠀⠀⠹⡇
⠏⡠⠬⣤⠵⠚⠒⠦⡼⠦⠞⠀⠘⡮⠄⡠⠠⠀⠀⠀⢀⡴⠊⠀⠀⠸⣄⠀⠀⠹⣄⡀⠀⢀⡀
⣄⠴⡾⠁⠀⠀⠀⠀⠙⠧⡾⡼⡓⠈⢄⠈⢁⠶⢛⠛⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠡⠟⡬⢠⡉⠁⡄⢬⠑
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠫⠄⠗⠒⠊



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡉⠤⠤⡀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢅⣀⠀⠈⡆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⢀⡰⠃⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠂⠉⣀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠒⠒⠦⣄
⢀⠠⠤⠤⠤⢄⡀⠀⠄⡀⠀⠀⠀⠀⢀⠴⠊⠁⢀⡤⡶⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠤⠶⠤⣄⡀⠈⠳⡄
⠁⠀⠀⠀⠀⠀⠈⠻⡓⠀⠑⢄⠀⠠⠃⠀⠀⣞⠟⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⠹⣆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⢰⠇⠀⢀⠞⠁⠀⠀⠀⠀⢠⠏⠀⣠⣤⣀⣑⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢹⠀⠀⡇
⠑⢤⣤⣤⣄⠀⠀⠀⠀⠀⠳⣄⣿⠀⠀⢸⣯⡀⠀⠀⠀⠀⢸⠀⢸⠇⠎⠉⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⢀⡟⠀⢰⠇
⠀⠀⠻⡉⠙⠻⣦⡀⠀⠀⠀⠈⢿⠀⠀⠹⣾⠈⠢⣄⣀⠴⠃⢀⡏⠀⠠⠀⣤⡖⠀⠀⠀⠉⠒⠤⠐⠚⠋⠀⣠⠏
⠀⠀⠀⢱⡀⠀⠌⠟⢂⡠⡀⠀⢸⡀⠀⠈⢏⡆⠀⠀⠀⢀⣀⡜⠀⠀⠀⣼⡿⠁⠀⠑⠢⣀⣀⡀⠀⣀⡤⠞⠁
⢱⡄⠀⠈⣇⠀⠀⡀⠀⠙⢆⡀⢸⡇⠀⠀⣿⡷⡖⠶⠖⠋⠁⠀⠐⢶⣼⡟⠁⠀⠀⠀⠀⠀⠈⠉⠉
⣾⡃⠀⠀⢸⡀⠀⠄⠀⠀⠀⠑⠾⣷⠀⠀⢼⣷⣆⠀⠀⠀⠀⢀⣠⡾⡟⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣄⡀
⣧⠸⡆⠀⠈⠻⣄⣄⢀⣀⣀⣀⡀⠸⠀⠀⡼⣿⠻⠦⠒⠊⠈⠀⡏⠸⣇⠀⣠⣧⠀⢠⠞⠉⣴⡶⠺⠿⢴⣭⢳⡀
⢜⣿⡙⢶⠀⠀⠙⠻⠅⣀⣀⣀⠿⠁⠀⢀⣷⠿⡁⠀⠀⠀⠀⠀⠙⢤⣉⣉⡥⢃⡴⢃⣴⡛⠁⠀⠀⠀⠈⣷⠀⡇
⠀⣉⢻⡞⣗⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠞⠉⠁⠂⠠⠄⣀⡀⠀⣀⣠⠐⠋⣐⡯⠃⠀⠀⠀⠤⣀⣒⡡⠟
⣿⡯⢿⣯⡙⣗⡿⣮⣱⣶⣞⣳⡴⠷⡿⠧⠋⠙⠲⢳⢄⢤⡀⣀⠈⢉⣁⣠⢤⠿⠉
⠿⠟⠉⠀⠀⠀⠁⠐⠛⠃⠬⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠛⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠛⠛⠻⠗⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢄⠠⢄⠈⠄⠠⢠⡀⠐⠄⡀⠀⠀⢸⡇⢸⡶⠀⠀⠈⠅⢻⣆
⠀⠀⠀⠀⣄⠀⠸⣧⠘⢁⠀⠄⢱⡀⠨⠀⠛⢦⡈⠁⡬⠷⡀⠈⠂⡀⠀⠉⣉⣄⢀⡀⠀⠀⢀⢹⡧
⠀⠀⠀⠦⠁⢰⠆⠈⢧⠡⠄⢤⠘⣧⡄⠐⢢⡈⢑⡄⠉⣘⠸⣄⠀⠁⡀⠀⠹⣁⣹⠁⠀⠀⠀⠁⣷⡆
⠀⠠⠁⣠⠜⢃⡀⠀⢸⠐⠂⠲⢀⠿⣷⣄⠀⠀⡌⢻⡄⠀⠀⢸⡄⠀⢡⠀⠀⠨⠙⢸⠇⠀⠀⠀⢹⡇⢠⢖⠋⣉⣍⠢
⠀⠀⡀⠘⠘⠓⢁⡆⢸⠀⠀⠆⢸⣅⣈⡟⠴⠄⠂⢼⡇⠀⠀⢀⣁⠀⠀⠀⠀⠀⠈⡕⠰⠀⠀⠀⠒⢧⢸⣇⠀⠃⠓⠂
⠀⠀⠘⠢⢴⣦⢞⡡⠃⠀⠀⠁⣾⡅⠀⠄⠄⢒⡠⢺⣇⠀⢠⠉⣧⠂⠀⠣⢀⠀⠀⠈⠒⠁⡄⠀⠨⠘⣼⣿⠀⢈
⠀⠀⠀⣠⠶⢚⣋⠁⠀⠀⣠⣼⠟⠛⢷⡶⠞⠋⠀⠀⣿⡆⠈⠐⢻⡶⠶⠢⠤⣉⠐⡄⠀⠉⠗⢢⠀⠁⠘⠃⠀⣠
⠀⠀⠐⠀⡔⢡⣦⢱⠚⢋⠕⠚⠓⠀⠐⠤⢔⢀⡀⠀⢨⣿⡂⠀⢀⣀⣠⠄⠀⣷⢡⠀⠀⠀⠀⠙⠻⡤⣀⠀⢴⠋
⠀⠀⠀⠀⠑⠚⣁⠟⠀⣮⠰⣏⣩⡑⢦⣀⣀⣀⣀⣠⡼⠋⠙⠏⣁⣀⣀⢀⡠⢯⡉⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉
⠀⠀⠀⠐⠒⠚⠁⠀⠀⠙⠾⣤⣊⡠⠞⠉⠉⠉⠁⠀⣘⢓⣀⠞⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡄⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡃⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⢈⣷⣽⡀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠉⢻⣷⣄⠀⠀⣿⡵⣆⠈⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣧⠀⢸⣾⣯⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠈⣿⠟⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢸⣏⣱⢒⠀⠀⠀⠀⢀⣠⣤⠴⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⣠⣿⣿⠇⢀⣼⣿⡤⣗⠛⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢶⣤⣾⣿⣿⠏⠀⡤⣜⢻⣦⠯⣙⢛⢸⣿⣿⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⣿⣦⠴⢴⣉⣽⣷⠔⢩⠛⢧⠻⣿⣷⡤⣾⠟⠛⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠙⢦⠀⠀⣠⢟⢹⣛⡿⠃⢠⣿⠿⠖⢻⣠⡟⣿⡤⠆⡉⠛⠇⢸⣿⣿⣿⣦⣀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⡇⣸⡶⠚⣉⣻⡇⣤⣿⡿⠗⡋⠂⣽⡇⣹⣥⡤⣉⠒⠺⣿⣿⠙⢯⣓⠃⠦⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⣸⣷⣷⢶⢻⣋⣿⣿⣿⢿⠷⠖⠡⣀⣿⠀⣼⣄⢠⠈⠶⠶⣿⣿⡀⢸⣏⡀⠒⠆⢸⠃
⠀⠀⠀⠀⠀⢠⡿⢸⡦⠴⣫⣬⣿⡟⠁⡶⠤⠚⣀⣘⣿⠀⣿⣀⣀⢈⠶⠤⣿⣿⣷⣸⠧⠄⢊⣙⢸⡇
⠀⠀⠀⠀⢠⢿⡇⢸⡦⠖⢏⡶⢾⢷⣰⣦⣤⠺⡀⢈⣿⣸⣟⠈⠉⢐⢤⡤⡎⢿⣿⡿⠒⠂⠠⣩⠀⣿⡄
⠀⠀⠀⠀⠸⡝⣇⠀⣷⡶⢚⠋⣻⣛⣿⣄⣤⠢⡈⠉⣿⡟⠩⠉⠀⣄⡀⢠⡁⣾⣿⠃⠀⠀⠀⡴⠀⢸⡷⡀
⠀⠀⠀⠀⠈⢄⠈⠳⢸⣿⣶⡞⠁⠃⢹⢀⢀⡄⠉⣹⠟⠛⠙⠋⡀⠀⠈⡸⣸⣟⣉⠉⠅⠒⢲⠃⠀⢸⠳⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⡏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⢀⡀⠠⠤⢤⣀⠀⠀⠀⠀⠸⠤⠞⠀⠀⠀⣴⣿⡌⠀⠀⠀⠀⠀⠀⢤⣠⡰⣿⠉⠀⠀⠉⠛⢲⡄
⠀⠀⠀⠀⣳⣴⠾⢟⡟⣻⢷⢦⣀⠀⠀⠀⣀⣠⣦⣟⣿⠋⠀⠀⠀⠀⠀⠀⠹⡴⠧⠚⠑⣂⣀⠀⣀⣀⡴⠇
⠀⠀⢠⣿⠋⠀⠀⠀⠁⠻⣻⣦⡬⣿⣶⣿⣿⢛⣋⠑⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢴⣿⣿⡿⣛⣿⡋⠄
⠀⠀⢸⣿⠀⠀⢀⠀⠀⠀⣀⢯⢷⣽⢋⣴⣞⣛⠀⠠⠤⠆⠴⠖⣚⣭⠗⢀⠴⢀⡄⢸⣛⣼⡟⠋⢏⣷⡀
⠀⠀⠘⣿⡄⠀⢸⠀⠀⢠⢭⣟⣿⡔⠙⠻⢿⣯⣽⣷⣤⠴⠶⠞⢋⢁⡴⠋⠀⣻⢇⣠⠫⣿⣛⠒⣶⢺⣧⣤⣤⣄⡐⠂
⠀⠀⠀⢿⣧⠀⠈⢧⠀⢨⣽⠶⣽⢁⢔⣊⢭⣅⣛⣀⣤⣤⣤⣴⡾⠋⠀⢀⠾⠿⣤⣏⣾⢿⢛⣷⡿⣸⣿⣅⡀⠉⠙⠲⡄
⠀⠀⠀⠀⠻⣷⣄⣸⡇⠱⣾⣟⣿⣿⣿⣻⠟⢋⡟⠁⢨⡿⢡⡟⠠⠀⢰⠏⠀⠀⡼⣰⡿⣼⣧⣖⣷⣧⠀⠈⠙⢳⣴⠀⢹
⠀⠀⠀⢀⠀⠈⠛⠛⠁⠀⠻⣷⣜⣿⣯⡰⠶⢻⣆⣴⠟⠁⢸⠁⠀⠀⠀⠀⠀⢀⣗⣺⠇⠈⠉⠻⣏⠍⠳⡄⠀⠀⣿⡆⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣻⣿⠷⠿⠶⠒⠊⠁⠀⠀⢹⠀⠀⠐⠷⣄⣀⡾⣚⡏⠀⠀⠀⠀⠘⢷⡱⡍⠄⡸⣿⡇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠿⣧⡀⠀⠀⠀⠀⠀⠀⠘⢖⡂⠀⠀⣰⢟⣠⡟⠁⠀⠀⠀⠀⠀⠈⣇⠁⢺⡽⡽⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠑⢌⠻⣷⡄⠀⠀⠀⠀⠀⠀⢈⣙⠒⡚⣷⣚⣋⢀⢀⣀⣀⡀⠀⠀⠀⡟⡇⣸⢟⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢶⣦⣄⠑⢬⠹⣧⡀⠀⠀⣠⣶⣿⠿⠻⠿⠿⣿⡿⠿⢾⣽⣿⣻⣽⣟⣿⡴⣡⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⠀⠀⠀⣜⡇⠀⠐⢟⠿⣆⠀⠏⣼⠁⠀⠀⠀⣀⣀⣈⠉⡑⢶⠶⠶⠛⠛⢭⡬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠈⠀⠀⠀⠈⢣⣿⡄⠈⢢⠤⣤⠞⢋⡉⣀⢀⣀⣁⣀⣨⡬⠿⠒⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡐⢄⡀⠀⠀⠀⢀⣠⢪⡿⠀⠀⠀⣱⢬⣛⢿⠿⠛⢉⣩⣤⠤⠤⠀⣠⡶⠶⣦⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢉⣈⣉⣻⠵⠟⠀⠀⠀⠀⢘⣾⠁⠉⠉⠉⠉⠉⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⣀⠀⢀⣀⣀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣋⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⣽⣿⣿⣿⣿⣿⣿⡿⣀⣸⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠺⣮⣽⣿⣿⣿⣿⣿⠟⠉⠀⣀⣀⠄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣿⣦⣉⠛⠻⢿⣿⠟⠁⢀⡀⢺⣿⣿⣿⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⢠⠏⠠⠀⠘⠀⠀⠙⠟⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⢋⣁⣀⠈⡟⠀⠀⠀⢿⣦⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢿⣿⣟⣿⣣⡇⠀⣀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡛⠃⠉⢠⢧⠐⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⢐⠇⠀⠑⠈⢧⠀⠀⠀⠀⢈⠉⠀⠈⠛⠉⠻⡿⠛⠛⠉⠉⠉⠉⣁⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠐⢴⣸⠀⠉⡹⠛⠒⠒⠤⢄⡀⠀⠀⠁⠈⠙⠻⡏⠉⣀⡙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣽⣦⠎⠀⠀⠀⠀⠀⠘⠁⣲⡄⠀⠀⠀⠘⢤⣿⡿⢟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡤⠚⠉⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠐⠀⠆⠀⡾⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⠔⠉⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡿⠀⢀⠀⠀⣀⢀⠈⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠆⠈⠀⢸⣃⡴⣢⠀⠠⣿⣿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⢀⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢈⡁⠀⠀⣠⣶⣿⠿⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡂⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⡦⣄⣿⣿⣏⠀⠀⠊⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠈⠧⢸⡄⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⣿⡿⠛⠁⠀⠀⡌⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡄⢉⠅⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⢈⠒⠋⠀⠀⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣶⡀⠸⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠒⣩⠉⢢⠁⢐⡏⠀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠇⠀⠀⠀⠀⡤⠀⣈⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢛⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣤⣤⣤⣤⡀⠀⠙⠚⠋⢙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⡓⠋⠁⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⣿⡆⠀⣠⣶⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢼⣧⣤⣴⡓⠋⠀⠀⠀⣸
⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣠⡶⠛⣲⣶⣿⣿⣿⣶⣿⣿⡅⣀⣤⣶⣶⣶⣦⡀⠰⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣼⡿⠋⠉⣹⣷⠀⠀⠀⠀⣿
⠀⠘⠷⣶⠛⠛⢿⣷⡄⣸⡿⠷⠀⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣻⡿⠛⢻⣿⣿⣶⣶⠟⠀⠀⣀⣠⣶⣶⠤⠀⠀⠀⠀⠀⣴⠋⣴⣿⣟⣀⣴⣾⣿⠿⢀⣀⣔⣶⣿
⠀⠀⠀⠘⣷⣤⣾⣿⣷⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣦⣀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⠀⢿⡀⠀⢷⣼⣿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿
⣶⣾⣶⣴⣿⣿⣿⣿⣼⣿⣇⠈⠛⠚⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⠻⣿⣷⣶⣿⣿⣿⣉⣙⣻⣿⡿⠷⢟⣉⡳⠀⢹⣿⡀⢲⣿⣿⣿⢿⣿⣿⣷⣿⣿⡻
⣿⣈⠙⠛⢛⣿⣿⣿⣿⣿⣿⣷⣤⠀⠙⢛⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣎⣻⡿⣿⣿⣷⣿⣿⣽⡿⡇⢰⡏⣉⣡⣤⣨⣿⣷⣾⣿⣷⣻⣹⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢋⣿⣿⣛⣿⣿⣿⣿⣧⣠⣿⣿⣿⣻⣷⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⢋⣿⣾⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣇⣀⣥⣤⣿⣿⣛⡛⢿⣿⢿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡻⠛⢿⣿⣿⣿⣿⡿⢩⡇⣠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣉⠻⣦⡴⢠⣐⢮⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠗⠻⡄⠘⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠁⠀⠲⢄⡾⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⢀⡴⠋⠱⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡇⡀⣤⣮⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢏⡽⣋⢀⠀⢤⣄⠀⠀⣀⣶⢲⣴⣶⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⣴⡿⠷⣯⣾⡃⡴⠟⣷⡶⣷⣿⣿⡿⢻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠧⠀⣯⠀⠀⠛⠛⢶⣛⣶⡞⣿⣾⣿⠏⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠘⣧⠐⠀⠊⠛⠻⣿⣿⣹⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣟⡠⠈⢷⣄⠀⠀⠒⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠹⣷⣯⣿⣷⡀⡙⠻⢦⡀⢀⡹⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⠇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣳⣤⣽⢯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢣⣄⠀⠀⣦⣼⣿⣿⣿⣿⣿⣿⣿⣄⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢿⣦⣝⣿⡿⠙⣿⣿⣿⣿⣿⣿⣆⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣿⣿⣂⡼⠉⢿⣿⣿⣿⣿⢯⣴⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⡄⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢞⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣣⣄⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇⠘⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡖⢠⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢡⠀⠀⠀⣐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⣒⠂
⠀⠀⠀⠀⠀⢠⡰⠐⠑⠚⠚⠔⡄⡄⠀⠀⠀⠀⠀⠀⣾⠀⠔⡢
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠈⠐⠅⢅⠈⠀⠀⢴⠂⠠⠁⡂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢘⣆⠀⢐⠃⣀⠍⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⡢⠃⠈⠩⠀⠀⢈⡀⠀⠀⠀⢀⡠⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠁⠀⠂⠀⠈⡋⠀⠀⢐⠀⢀⣂⠀⠀⠀⢴⠋
⠀⠀⠀⠀⠀⢀⠀⠀⡸⠀⠀⠀⠀⠀⢐⡒⢐⠂⠔⡀⠐⠀⠀⠀⠂⠄⡐⠁
⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⢐⠀⢨⠀⠁⠆⠀⡂⠀⢈⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠀⠅⠈⠅⠀⠄⠀⠀⠐⠀⠀⠨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠗⢐⣾⣿⣿⣿⣿⣿⢟⠹⣫⡼⠛⣿⣰⣬⡻⢿⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠃⠈⠋⠟⠉⡅⠋⣵⡏⣴⡿⠀⠀⢸⣿⣿⢻⣄⢳⣌⠿⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢡⣆⡀⢠⣆⣼⣧⣸⢻⣿⣿⠃⠀⠀⠀⣿⢻⠀⢻⣿⣿⣧⣠⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢸⣿⣟⠀⠀⠀⠀⢻⣸⣀⠀⢻⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢹⡇⠏⠀⠀⠀⠀⠀⠨⠉⠉⠙⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠇⣀⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡧⠉⣈⣿⣿⠄⠀⠀⠀⠀⠀⠀⣸⣿⣿⠙⢬⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠙⠟⠛⠀⠀⠀⠀⠀⠀⠀⠙⠛⠊⠀⢈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠹⠏⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡆⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⣠⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣾⠿⢿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣀⠀⢀⢀⣀⣀⣀⢀⡰⢇⡀⡀⠀⠀⢐⠿⣿⡿⠿⣇⠀⠀⡀⣀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠿⣿⢿⣟⡀⠀⡐⢀⣁⠀⡘⣀

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣾⣥⡀
⠀⠀⠀⢀⣾⣻⣟⣍⣿⡇
⠀⠀⠀⠸⣧⡈⠈⠉⠉
⠀⠀⠀⠀⠹⣿⣾⣄⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣿⡿⣫⣶⣿⣿⣿⠿⠿⣿⣿⣷⣄⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢰⣫⣾⣿⣿⠋⠁⠀⠀⠀⠈⠻⢿⣾⣐⣀⣶⣼⠆
⠀⠀⠀⢀⣴⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣠⣤⣴⣿⣿⣿⣿⡿⡟
⣿⣿⣿⣿⣽⣿⣿⡇⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⣙⠛⠛⣋⣽⣿⣿⣧⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⣿⣧⡀
⣀⣼⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰
⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⣿
⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣠⣤⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣭⣭⣯⣽⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠐⢋⣠⣶⣿⡿⠁
⠉⠁⠀⠙⠻⣿⣿⣭⣿⣯⡼⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠉⠉⠓⠻⡿⠟⠻⠟⠉⠀⠀⠀⠀⠀⠀⠙⠛⠿⣽⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅
⠀⠒⠈⠀⠀⠒⠀⠀⠐⠂⠀⠂⠀⠂⠰⠄⠂⠂⠐⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⡀⠒⠀⠀⠀⠀⠀⠀⠐⠿⠿⠙⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢷⡙⣥⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠄
⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡋⠌⢣⠠⣿⠀⡇
⣦⡆⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠈⢁⡄⠀⡄⢡⠉⡌⠀⣍⠃⠸⠆
⣿⡷⠀⠀⠀⠀⠀⠶⠁⠀⠘⠀⠀⠀⣐⠀⠀⠀⠀⠁⠐⠈⠀⠀⠀⠀⠀⠰⠐⠂⠰⠀⢹⡄⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠁⠀⠘⢗⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢡⠀⢂⠀⢣⡄⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⠀⡌⠁⠎⠡⡄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠃⠀⠀⠅⢄⠀⠀⠀⠀⠀⠀⢀⡓⢬⡀⢐⠂⢘⠳⠄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠄⠀⡘⢲⠖⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠈⡅⠰⡇⠈⠄⠈⠦⣸⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠪⡐⡀⠐⣤⢉⡌⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⠁
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠨⣤⢤⣄⠀⢳⡐⠐⠂⠀⠀⠀⠀⠀⠀⠐⠃⣤⠀⠶⠀⠉⠐
⡈⠖⠛⣄⠀⠈⠅⠀⠀⠀⠀⠀⢀⢀⡈⠀⠀⠙⠀⠈⢃⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠁⠆⢠⡏⠓⠠⠄⠀⠉⠀⠰⠠⠄⡀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠑⢢⡄⠰⠓⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡄⢦⣀⠻⡄⠸⢄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡠⡀⣀
⠀⢤⠁⠠⠄⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠄⠀⢐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣉⣨⡓⠙⢻⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⡓⠀⠘⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⢀⢠⡏⠈⠀⠀⠀⢀⣼⠋⢧⠀⠀⠀⠀⠀⠒⠀⠉⠀⠀⢀⣄
⠀⠈⠱⠀⠙⣌⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡷⠄⠀⠃⠀⠠⠀⡰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠰⠀⠙⢀⠀⠠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣲⣢⠄⣢⠴⠋
⠘⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡰⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛⠌⠙⠙⠢⠀⢱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠲⠄⠀⠀⠀⠀⠀⢀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡋⠒⢈⠤⣱⠂⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥⠓⣀⡟⢀⣽⡦⡞⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣠⠯⡍⠻⠴⠛⢋⡍⠹⢇⠠⡉⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣩⣇⠀⠀⠀⠀⢀⣨⠋⠀⢸⠖⠂⠊⢿⠀⠀⠀⠉⡧⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⡁⠀⠀⢠⠊⠁⣆⠀⠀⢀⠐⠂⡠⠊⠀⠀⠀⢀⠃⠀⠁⠢⢀⠀⠀⠀⡠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠇⠀⠀⠘⣆⠀⠠⣀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠣⡔⠁⢾⣤⣕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠠⠼⢁⣀⠀⠈⣦⠀⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⡀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠙⠦⣐⢃⡽⢀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠕⠒⠒⠒⠒⠠⢀⠈⠀⠀⠀⠀⠑⢄⠀⠀⠆⠀⡜⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⣸⡌⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⣠⠤⠤⠄⠀⣀⠀⠀⠀⠈⠳⠤⠤⢒⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠘⢆⠀⠀⠀⠀⢀⠼⠁
⠀⠀⠀⠀⣀⠠⠤⠤⠤⡀⠀⠀⠀⠀⠀⢀⠜⠁⡠⠂⠀⠀⠀⠀⡀⠠⠀⢀⡀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠚⠋⠁⠀⠈⢄
⠀⠀⡠⠊⠀⠀⣠⣤⠦⣌⡀⠀⠀⠀⡠⠋⠀⠠⠁⠀⠀⠀⡴⠃⢄⠰⠠⠀⠈⡐⡄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⠀⠀⠀⠢⡈⠛⠓⠋⠀⣀⡤⠊⠀⠀⢠⠁⠀⠀⠀⡜⠀⠀⠀⠂⠈⠀⠀⠄⠎⢂⠀⠀⠈⠢⣀
⠀⠀⠣⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⣼⠀⠠⠀⠀⠘⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠈⠓⠠⠤⢀⣀⣀⣀⠠⠄⠄⡺⠁⠀⠀⠀⢰⠃⠑⢤⡉⠀⠀⠀⠈⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⡠⠂⣶⢢⣤⡀⡠⠊⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⢹⠀⠀⢠⢠⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⢸⠀⠐⠛⠛⠋⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⡄⡄⠀⠐⠀⢀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠉
⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠀⠀⢀⠈⠂⢸⠉⠉⠉⠙⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢂⠀⠀⠀⢐⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢂⠀⠀⠀⠉⠈⢀⠀⠀⢀⣤⠎⠓⡒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠐⠒⠀⠀⢄⠃⠂⢿⣴⠋⠭⠓⠄⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠳⢦⣀⡀⠐⠂⠈⠀⠀⢄⡦⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠠⢤⡄⠀⡄⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣇⢀⠔⠋⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠰⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠘⠄⠀⣀⡀⠀⠋⣁⢴⠊⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠂⣀⢡⣴⡾⠁⡞⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡘⠁⡸⠀⠀⣠⡍⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⡰⠀⠀⠈⢈⡀⠀⠀⠀⠀⠀⠀⠄⠛⠁⠆⠀⠀⡄⠀⠀⠀⠀⠰⢠⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋⠁⠀⠀⠀⠀⠀⢰⠆⠀⠀⠃⠀⠀⠀⢠⠂⠀⠀⡆⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠈⠀⠀⠀⢀⠂⠈⠀⠰⠀⠀⠀⠀⠂⠀⠀⣀⣀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⢠⠊⠀⠀⠀⢠⠎⣠⠀⢠⠃⠀⠀⠂⠀⣠⠞⠋⠉⠁⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⡀⢀⡴⠁⠀⠀⠀⢀⠜⢀⠁⢀⡏⠀⠀⡄⠀⢰⠃⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠁⣠⠋⠀⠀⠀⠀⠀⡎⠠⠋⠃⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢳⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠁⢂⡜⠁⠀⠀⠀⠀⠀⠦⠁⡄⠄⠀⡇⠀⠀⠀⠐⠀⠀⢀⢄⡀⠠⠊⠀⠃⣌⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠔⠀⢠⡞⠀⠀⠀⠀⠀⠀⣸⠀⠀⠁⠀⢰⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠁⣠⠃
⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⢀⠶⢀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠰⡆⠀⣄⠄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡜
⠀⠀⠀⠀⠀⢸⠀⠀⠐⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠡⠀⠐⠢⡴
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣆⠈⡀⠀⠀⠀⠀⠀⠀⣨⠀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢴⠀⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠔⠁⢄⠔
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠠⠃⡀⡉⠘⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⡹⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡌⠀⢀⠋⠀⡀⣠⠎
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠒⠀⡄⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡱⠀⢀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠎⡰⠇⠀⢀⠄⢀⡇
⠀⠀⠀⠀⠀⠈⣧⠀⡈⠄⢰⡄⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣡⠀⡌⡄⢀⠀⠀⣧⠀⠀⠀⠀⡴⠀⠑⠀⠀⠀⢘⡃
⠀⠀⠀⠀⠀⠀⠹⡆⠐⠤⠀⠀⠀⠐⢇⠀⠀⠀⠀⢁⠀⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠸⡀⠀⠃⠈⠀⠐⢹⡄⠀⠀⢰⠆⠄⠀⠀⠀⠠⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢤⠀⠀⠱⡄⠀⠀⠈⡆⠀⢠⠀⠀⠢⠀⠀⠈⢧⡀⠀⠀⠀⠇⠀⠀⢄⠰⡀⠃⣷⡀⠀⢐⡄⣀⡁⠀⠀⠂⣡⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠤⠀⠈⠄⠙⢄⠘⠄⠀⠀⠁⠀⠀⠠⠤⡀⠡⠀⠀⠑⠷⣄⠀⠀⠸⠄⠀⠻⡀⢡⠀⠼⣷⡀⢸⡇⡄⢰⠀⠀⢢⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⠶⣦⣄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⢠⡾⠛⣿⣦⠀⠀⠀⢠⣶⠉⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠙⢀⣿⡿⠀⠀⠀⠈⣿⣧⠀⢀⣴⡾⠟⢁⣤⣶⣶⣦⣤⡀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣴⣿⠁⠀⠀⠀⠀⢠⣴⣿⠋⠀⠀⠀⢀⣼⣿⠏⢠⣿⠋⠀⠀⢸⣿⣿⠁⠀⢻⣿⡆⢸⡅⠙
⠀⠀⢠⣶⣻⣭⣽⣫⠖⢿⣿⠟⠋⠀⠀⠀⠀⠀⡏⣿⣿⣧⣤⣤⣶⣿⡿⠋⠀⢸⣽⣧⡀⠀⠘⣿⣿⣦⣀⣸⣿⣇⣸⣿⠄
⠀⣨⣼⡿⠛⠛⠻⣿⡴⣎⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠛⢿⣿⣯⣳⣮⣛⠿⢿⣿⣿⡿⠿⠋
⠀⣿⣿⣧⣀⣠⣤⣼⣧⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠛⠉⢿⣿⣿⢛⠀⠀⠀⠈⠛⠿⣿⣽⣷⣾⡿⠃
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣬⢯⡛⡱⢖⡠⠤⢤⣤⡀⠀⠈⣿⣿⣦⣴⣿⣿⢇⡞⠀⠀⠀⢀⣴⣾⡿⠿⠛⣯⢳⡄
⠀⠀⠀⠉⠉⠉⠉⠘⣿⣿⣶⣦⣭⣬⣓⣹⡛⢙⣗⠟⢲⣿⣿⢿⣿⣿⣿⠛⠀⠀⠀⠀⣼⣿⠿⠁⢀⣤⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⢿⣿⣿⣷⣞⢻⣿⡿⠟⠹⢾⡛⣿⣦⡀⠀⠀⢻⣿⣿⢹⡟⢹⣿⢏⣽⠇⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣠⣾⣿⣿⣿⠇⣿⣿⣤⣤⣤⣤⣿⣛⣿⣷⠀⠀⠀⠉⢛⣿⣷⣾⣿⣼⣷⠾⠟⠁
⠀⠀⠀⠀⡠⢴⣿⣿⣿⣿⣿⣿⣛⣙⣽⣿⣿⡿⠿⣿⣿⣻⡟⢛⡿⣿⣿⣿⣿⣿⣦⣄⠀⣰⣿⡟⢿⣿⣿⣿⣦
⠀⠀⣠⠾⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⢀⣀⣑⣾⣿⡹⢶⢧⡚⣻⣿⣿⣿⣟⠈⢻⢿⣿⡀⠀⠹⣿⣿⣿⣧
⠀⠈⣕⣰⠀⣿⣿⣿⡿⠛⠉⠁⠀⠀⢀⡴⠚⣿⣿⣿⣿⣿⣿⣿⣿⠽⣾⣿⣿⣿⣿⣀⣸⣦⣿⣿⣶⣶⣿⣿⣿⣿⣀⣀
⠰⡺⢩⡏⢰⣿⣿⡟⠁⠀⠀⠀⠀⣴⣏⣴⣼⣿⣿⣿⠟⠛⠉⠁⠀⢀⣼⣿⣿⣿⣿⣿⡟⢀⣽⣿⣿⣿⣿⣿⣿⣯⣽⠿⣗⡤⡀
⠠⣙⣬⣿⡀⢿⣿⣧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣿⡿⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠏⢠⠋⠀⣿⣿⣿⣿⡿⢿⡿⢿⣿⠾⣶⠣
⠀⠩⡃⠠⡹⣾⣿⣿⣦⣀⠀⠀⣿⣿⣿⣿⡿⡌⣷⢳⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⣯⣴⣾⣿⣿⣿⡟⠀⠈⣇⣨⣟⠈⣸⠁
⠀⠑⠴⣷⠖⢻⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣘⢻⣝⢫⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⣸⣿⣿⣿⡟⣿⡍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⡀
⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⢤⣤⣰⢠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠰⡚⠟⣧⠛⢿⣖⠲⢶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣁⣽⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠹⡆⠀⢠⣏⠎⠀⡈⠀⢢⣬⣄⠀⠀⠀⠀⠀⣀⣴⡞⠱⠄⢂⡜⠁⠐⠃⠒⠂⠱⢬⡑⠃⢛⣿⡶⣄⡀⠀⠀⠀⠀⣰⡏⡩⠈⠛⠉⠉⠉⠅⠀⠂
⠀⠀⠀⠀⠀⠀⢟⡀⢈⠻⡀⠎⠀⠀⠀⠈⠋⣇⠀⠀⢠⠞⠎⠹⠈⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⣑⣹⡿⣢⡀⠀⢠⡟⢋⠁
⠀⠀⠀⠀⠀⢀⣎⠃⠘⢞⣧⡀⠀⠀⠀⠢⢀⡀⠆⣰⠃⠤⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⣸⠿⣢⣼⠛⠆
⠀⠀⠀⠀⢠⠾⡍⠀⠀⠈⠻⣄⡢⣀⡀⠀⠀⠀⠰⢯⡠⠤⠂⠀⠀⣀⣴⠖⣠⣤⣶⠶⠧⠾⣲⣤⠀⠀⠀⠀⠀⠀⠀⠐⠬⠬⢞⣤
⠀⠀⠀⠀⡟⠒⠀⠀⠀⠀⠀⠈⠙⠫⢄⣞⠵⢠⡍⠸⡠⠀⠀⠀⣾⣿⣧⣦⠎⠁⠀⠀⠀⠀⠠⠉⢶⣦⠀⠀⠀⠀⠀⠀⢀⡆⡬⣹⡆
⠀⠀⠀⠀⡟⣣⠐⣮⠿⣭⣢⠀⠀⠀⠀⠀⠙⢺⢟⠃⢈⠀⠀⠀⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⣧⠀⠀⠀⠀⢀⡼⠳⠠⣀⡾⡀
⠀⠀⠀⠀⢹⢹⣟⣤⣐⣯⠟⠀⠀⠀⠀⣀⣠⣬⠾⠁⣼⣦⣄⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⣾⣧⡄⢡⡍⢫⡇
⠀⠀⠀⠀⢀⣸⠀⠈⠁⠀⠀⠀⢀⣰⣾⠕⠘⢻⢨⠌⠉⠹⡍⢆⠙⠻⣿⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣤⣯⠀⠈⠀⠘⢘⢋⣑
⠀⠀⠀⠀⠈⢈⢣⡀⠀⠀⠀⣰⡟⠋⠁⠀⠀⠘⣯⡆⠀⠀⢸⣿⡇⠁⠀⠀⠻⢻⡓⢤⡀⠀⠀⠀⠀⠀⣘⣷⢌⠈⠙⠃⠀⠀⠀⠘⡿⢿
⠀⠀⠀⠀⠀⠈⠋⣙⡶⢤⣴⣻⢃⡀⢀⣀⣀⡤⢿⣟⢲⣶⠼⣦⡄⠀⠀⠀⠀⠀⠉⠉⢿⣦⣠⡤⢶⡎⠙⣿⠘⠂⠀⠀⠀⠀⠀⢠⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣿⣧⣀⣹⣏⣀⠻⠋⠈⢿⣑⠘⣟⡿⣩⣷⡄⠀⠀⣀⣴⡏⠈⣝⣃⣀⡁⠇⠘⠛⣧⡀⢀⣠⣦⣶⡇⣎⣙⣆⡀
⠀⠀⠀⠀⠀⠀⡀⣠⡶⣶⣴⡿⢯⣬⣯⣄⠠⠀⣠⣼⣿⢻⡛⡔⠀⠙⢌⣷⠾⠛⡻⠗⠘⢻⣍⣷⠀⠀⠀⠀⣹⣷⣿⠟⠛⢩⢐⢈⡿⠉⢽⡗
⠀⠀⠀⠀⠀⢴⣾⠛⠁⡿⠜⠄⠀⠀⣉⣹⣿⡒⠙⢮⠛⠻⣿⣉⠀⠀⡼⠙⠱⡏⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⡾⢿⣿⣤⣀⠈⣪⡿⠁⠀⣸⣻⡀
⠀⠀⠀⠀⠀⠠⠁⠿⢶⣟⠉⢾⠋⡛⠛⠎⠛⠙⠫⡰⡄⠀⠈⠲⡿⣾⠿⡖⠱⢿⡀⠀⠀⣜⣞⡏⠀⠀⠀⢸⣻⠂⠈⠛⢷⣮⣭⣥⣤⣴⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠻⡢⠀⠀⠀⠀⢀⣀⡄⣗⣼⣤⣀⠀⠀⣻⣄⣿⣾⢻⡇⡴⢾⣹⡟⢀⣠⡼⢹⣟⡿⣶⣠⣆⣰⣽⠋⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠃⣦⠀⢀⣴⡌⠋⠁⣧⠿⠛⠝⡷⣄⢹⣉⢍⢙⣷⡿⠛⠛⠁⢀⣼⡟⠁⠀⢯⣗⡀⠉⣽⣿⡣⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣠⠌⠆⣸⣟⠀⢀⣼⣭⠆⠀⠀⠁⠙⡆⠙⠤⡿⠞⠀⠀⠀⠀⢸⣾⠁⠀⠀⢘⠟⢡⣺⠟⠱⣿⣧⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠑⠀⠀⠛⠛⠟⠓⠈⠀⠀⠀⠀⠀⠹⣾⣄⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⢐⣆⣽⡇⠀⠀⣸⠇⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢶⢪⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⠸⣽⠀⠀⢌⡺⡿⠻⠛⠿⠾⡿⠊⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⠜⡀⠀⠀⠀⠀⠀⡴⠟⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡝⠀⠸⢋⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⠃⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠈⠻⡋⣶⡀⠄⡀⠀⣀⢀⣠⡌⠅⠀⠸⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠈⠲⠿⠖⠚⠟⠂⠋⠈⠀⠀⠀⣮⣨⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣽⡷⣤⣀⠀⠀⠀⢀⣠⣿⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠘⣏⡿⣛⣿⣻⠿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠉⢽⣿⣿⢻⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠈⠉⠙⠚⠉⠛⠛⠉⠛⠓⠋⠛⠛⠙⠋⠓⠟⠛⠛⠛⠙⠙⠋⠛⠛⠋⠛⠛⠛⠻⠟⠿⠟⠟⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⢠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⣶⣿⣿⠙⢿⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠢⡄⠀⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⣿
⣿⣿⢰⣯⣽⣿⣦⣼⡟⠀⠈⠟⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠑⢄⠑⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿
⣿⣟⠸⣿⣿⣿⡉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠱⢄⢠⣦⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠁⠻⣿⣅⠀⠀⠀⣆⡠⠀⣀⡠⡴⢶⣂⣲⣶⣿⣷⣶⣶⣲⣶⣦⣽⣷⢠⡾⡟⣿⡆⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠸⣿⠉⠀⠀⠀⢨⠴⠉⠁⠀⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠛⠀⠀⠀⠚⠀⠀⠀⢩⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠠⣴⡆⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⣼⢋⣧⣴⣶⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢠⡄⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠘⣿⠛⢻⣿⡟⠛⢛⣯⣿⡿⠿⢿⣟⡛⣷⣶⣾⣷⡾⣿⣿⣿⣿⣿⣿⡟⠉⠘⠃⠀⣿
⣿⡇⢀⣴⣄⡀⠀⠀⠻⣷⣿⣿⣿⣼⣿⣽⣿⡧⠺⠿⠿⠷⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⡴⠀⠀⣿
⣿⡇⣼⣿⣏⢻⣶⠂⢄⠙⣽⣿⣿⢻⢹⣿⣿⠇⠀⠀⠀⢠⡉⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣇⠛⢔⠀⠀⣿
⣿⡇⠉⠛⣿⣿⠀⢀⢁⣼⣿⣿⠿⢤⣄⣍⣉⣠⣤⣤⡴⣦⢴⣭⣭⣷⡎⣻⣿⣿⣿⣿⣿⣿⢩⢀⠆⠀⣿
⣿⡇⣶⡄⣿⡏⠂⣛⣼⠟⢫⠀⣀⢴⣦⣤⣭⣬⣶⣶⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣦⠀⣿
⣿⡇⣿⣷⣿⢳⣾⢟⡥⡅⢶⣶⣿⢿⣯⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⢶⢻
⣿⡇⣿⣿⣿⣿⡟⣾⣾⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠉⠉⠉⠉⠉⠉⢉⠌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠈⣉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠘⠁⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠢⠀⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⣠⠄⠈⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠒⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠤⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠁⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠰⠀⠀⠀⢠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣖⣦⡀⠀⠀⢠⣌⢆⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣉⠙⢛⣇⠀⠀⡟⣉⡀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠈⠉⠉⢙⡇⠀⠀⠀⠀⣠⣶⠇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠋⠁⠀⠀⠠⣀⣀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠠⡤⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠱⡈⠉⠛⠒⠐⠉⠉⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠒
⠀⠀⠀⠈⠆⠀⠀⠀⠀⠉⠲⢶⠾⠄⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⣀⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡴⠖⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠘⠦⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢀⣀⠀⠈⠑⢀⠀⠀⠀⠀⡘⠉⠀⢀⣤⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⣫⡃⠀⠀⡌⡇⠀⠀⡀⠁⠀⠠⣫⡅⢡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠇⢹⣧⠀⠀⣱⠃⠀⠀⢻⡇⠀⠰⣿⠀⠇⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣦⡠⣽⢀⠼⠁⠀⠀⠀⠀⠙⢤⣀⣧⣠⢾⠝⠁
⠀⠀⢀⠔⠀⠉⡀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⡼⠃⠙⢛⣤⠄⠀⠀⠀⡄⠀⠀⠀⠉⠉⠹⣾⠀⠀⠀⠀⠀⠀⢀⠄
⠀⡔⠁⠀⢨⡤⠖⠐⠤⣀⠀⠀⡄⠀⡠⠔⠁⠀⢀⡤⠾⠁⠀⠀⠀⠀⡀⠀⠀⠠⣦⠀⠀⠈⠣⡀⠀⠀⢀⠄⠁⢀⣠⠤⢒⡲⠤⡀⠀⠀⡀
⡘⠀⠀⢰⠃⠀⠀⠀⠀⠘⠂⠀⠘⡞⠁⠀⠀⣠⠏⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⢄⠀⠀⠠⠽⠶⠶⠃⡀⡴⠉⣠⡿⠛⠙⠳⣮⢀
⡇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠰⠀⠀⢣⠀⢀⡴⠁⠀⠀⠀⠀⠀⢀⣠⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⠀⠀⠀⠀⠈⣷
⠰⡀⠈⠠⠅⣲⢀⣀⣀⠤⠚⠇⠀⠈⢀⡾⠁⠀⠀⢀⣤⣤⣶⣿⣿⠿⣟⣦⢤⣤⣠⢤⢤⠤⠖⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠐⠁⣤⣿⣿⢿⠗⠀⠈⠻⣽⠺⠾⣌⣮⣦⠢⡔⠓⠒⢦⣈⢣⠀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠲⢄⠀⠀⠀⠀⠀⡰⠀⠰⠛⡇⠀⠀⠀⠀⢀⡁⠘⡟⡸⡇⠀⠀⠀⠘⠀⠀⠀⠈⠁⠤⠙⡄⠀⠀⠻⣸⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠒⠏⠊⠀⠂⠀⣀⡇⠀⠀⢀⠀⡎⠀⡼⠁⢣⣻⡀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠤⣀⠀⠀⠀⡏
⠀⠀⠀⠉⠁⠀⠁⠀⠀⠁⠀⠁⠀⠀⢳⡀⠀⠀⢢⣣⡞⠁⢀⡌⠣⡱⡄⠀⠀⠀⠀⡘⡔⠉⠀⠀⠎⠀⠀⢠⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠌⣇⡀⠀⠀⠈⠙⠲⢉⡀⠀⠁⡝⣆⠀⠀⠀⡅⠳⣄⠀⡄⢀⣰⠀⠈⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠈⠲⡇⢸⢸⡆⠀⠀⡀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠐⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣆⡀⠀⠘⡯⠞⠀⠀⢀⠁⠠⠄⠀⢀⠀⠀⠠⢤⣈⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠀⠀⢹⡇⠀⠀⠗⠀⠀⠄⠀⢀⡀⠀⠀⡀⠀⢀⡀⠀⠈⠑⠛⠛⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠄⠀⠀⢀⡀⣼⡇⠀⠀⠆⣄⠀⡐⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠐⢁⣠⡟⠀⠀⢌⠀⠙⠀⠰⠦⠤⠤⢴⠞⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⠖⠋⠀⠀⠠⠂⠀⠳⢄⠀⠀⠉⠁⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣧⣤⣀⣀⣀⣀⣤⣾⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠛⠉⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠋⢉⣉⣉⣉⣉⣉⣉⡉⠉⠛⠛⣸⣧⡀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⠶⠶⠶⢶⣶⣶⣶⣤⡼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⣉⠛⠛⠛⠻⠿⠿⠿⠿⠛⣛⣤⣾⣤⡀⠁⠀⠀⠀⠀⠈⠻⠷⢦⣤⣤⣤⣤⣀⣀⣀⣠⣤⠴⠛⠑⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⡿⠀⢀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⣨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⠶⠶⠶⠶⠶⠶⠶⠶⠦⠀⠀⠀⢀⠴⣿⠀⠀⢰⣿⣿⣿⣟⣛⣉⣉⣉⣉⣉⣉⣉⣉⣻⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣷⠀⠉⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠀⢙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⢉⣉⣡⣤⣤⣤⣤⣤⣤⣭⣉⠻⠿⠟⠉⣀⠀⠀⠀⠀⢀⣤⣴⠶⠶⠟⠛⠛⠛⠛⠛⠛⠲⢦⣄⣀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⣉⣉⡉⠉⠉⠉⠉⠉⢉⣁⣀⣤⢴⡾⠃⠀⠀⠀⠀⠈⠛⠻⠿⠶⠶⣶⣶⣶⣶⣶⣶⠾⠿⠿⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠛⠛⠛⠛⠛⠻⢿⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠉⠁









⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⣶⣶⠶⢶⡶⢶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⠀⠀⠀⡀⠒⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠙⠢⢍⣒⠾⢦⣀⠀⢀⡒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⢤⣼⣦⡀⠀⠀⠑⠢⡈⠱⡀⠙⣆⢠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣙⣤⡀⠀⠈⣙⣦⠀⠀⠀⢱⡀⡷⠀⡈⢀⠀⢠⡔⡝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡢⡀⠈⠑⣩⠅⡙⣃⠀⠀⣸⣿⠅⡰⢣⡇⡐⢠⠈⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⢹⠀⠀⣏⣧⡆⣿⠀⣴⣟⣥⣾⡥⠞⡿⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠸⣸⡀⠀⢤⣿⠿⢼⡟⠋⠉⠀⠀⠳⣄⠑⠄⣰⡧⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⠳⢤⠏⠁⠀⠀⠀⠀⣀⣠⣤⣤⡈⣇⢟⠱⠞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣦⣤⡀⠀⠀⠀⣾⣋⣝⣿⡗⠈⢻⣆⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⣿⣆⢀⡀⠿⠋⣩⠟⠁⠀⢸⣿⡤⠶⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢷⠤⠈⠈⠁⠀⠀⠀⠀⠀⢀⣿⠿⠇⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠉⡁⠀⠉⠻⣧⣀⠀⣼⣷⣶⠀⠀⣀⡾⠁⠱⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧⠠⡀⣄⠢⢅⠓⠂⢸⠻⣷⣮⡛⠋⣠⡾⡿⢒⡲⣅⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⢻⡆⠉⠂⠉⠀⠢⢍⠉⢻⣟⣛⢉⣠⣿⠶⠆⣈⠆⠀⢺⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢾⣧⣱⣤⣬⣧⡀⠀⠀⠀⢀⡀⢀⡩⠿⠶⣞⣡⣤⣤⣴⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣤⣀⠀⢹⠏⣠⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢻⣿⣿⣿⡿⠿⠿⠿⠷⠺⠾⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠈⢿⣫⡔⣠⠀⡀⢀⣤⣶⣦⣄⠀⠀⠀⠉⠉⠛⠻⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠠⠂⠀⡉⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠴⢞⣡⠞⠁⠋⠙⠛⠛⠻⠟⠛⠉⠀⠀⠉⠙⠲⠦⢤⡀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣾⣿⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣀⣰
⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⣯⡉⠙⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠀⣠⣿⣿⣿⣻⣿⠀⢀⢀⣴⣷⣿⣿⣿
⠀⠀⠀⢠⣿⣿⠏⠸⡁⠀⠀⠀⠘⣿⡀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⢀⣴⣿⣿⣿⣿⡿⣁⣴⣿⣿⡿⢿⣯⣭⣿
⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⢟⣿⣿⣥⣾⣿⣬⣾⣿⣾⣾⣿⣿⣿
⠀⠀⠀⠈⢿⣿⣦⣤⣤⣤⣴⣾⠟⠁⠀⠀⣠⣿⣟⣿⣃⣀⣀⣀⣀⣀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠟⢩⣿⣿⣿⣿
⠀⠀⢀⣀⣀⡈⠉⠋⠉⠉⠉⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⠟⣻⣿⡿⡿⠋⠁⢠⣿⣿⣿⣿⣿
⠀⣴⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣿⡿⣟⣸⣿⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿
⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣅⠀⠀⣀⣀⣤⣾⣿⡟⣛⣿⣵⣿⣿⣽⢿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⢿⣿⣻⣿⣧⣾⣿⣿⣟⣟⢾⣟⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠘⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⡿⠟⠁⠀⠘⠿⠿⣿⣿⣿⣿⣿⣟⣻⣿⠍⠊⠀⠉⠻⡿⣿⣿⣟⣻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠿⢿⣿⢿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⣿⡟⠁⠀⠀⢀⣠⡶⠚⠛⠛⡟⠛⠻⠛⠛⠛⠋⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⣤⡶⠟⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⢈⠉⠳⠉⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⡠⠀⠀⣸⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢶⠁⠄⣠⠃⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠀⠚⣉⣃⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣍⡀⢉⡉⠘⡭⠂⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠉⠁⠀⠛⠉⠙⡲⠀⠠⡜⠳⠖⣿⠃⠀⠑⢤⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠁⠂⠒⠁⠀⠀⢀⡼⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠦⣈⣒⣂⣀⠀⠀⠀⠊⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢳⡀⠀⠀⠀⠀⠸⡀⠀⠀⣀⣀⣀⡈⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠑⣤⣀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠈⠑⢶⠔⠊⠁⠀⠀⠙⣦⠂⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⢸⡧⠜⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢛⣛⡷⠴⠚⠃⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠠⢞⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠤⠤⣅⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣌⠀⠦⠀⢌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠳⠶⡽⠟⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣀⡴⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⢀⡞
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠝⠲⠦⠤⠴⠋
⠀⠀⢸⠁⠀⠀⢀⠔⠄⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋
⠀⠀⠸⡄⠀⠀⡚⠘⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠤⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢧⠀⠀⠸⣸⠏⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⣀⣠⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⢂⠀⢰⠏⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⢀⡾⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡟⣈⡀⠨⠉⣙⠓⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⣈⡀⠀⣈⣙⣳⡶⠶⠶⠦⠼⠷⠤⢤⣀⡀⠀⠀⠀⠀⢱⡀⠀⠀⣀⣠⠤⠴⠶⠤⠶⠤⣄⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠙⠶⠦⠬⠴⠴⠿⠞⠛⠶⢶⣄⠙⢦⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⡸⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠂⠈⠁⠈⠀⠀⠀⡰⠀⠭⢹⠟⠦⣄⠀⠀⠀⠈⠳⢄⡀⢀⢀⡀⠀⠀⠀⠀⣀⡼⣋⠜⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠊⣡⣞⣷⠋⠀⠀⠈⠙⠒⠂⠀⠀⠀⣐⡒⠩⠥⠤⠴⠶⠟⠋⠉⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠦⠥⠄⠐⠒⠒⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣮⣷⣷⠾⠛⠓⣚⡋⠭⠖⢢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⠤⠤⢴⣴⡞⣵⣾⣿⣞⣿⠇⠀⠀⣐⡒⠀⠠⡐⠀⠈⠐⠫⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣉⠁⠠⠴⠒⠂⣰⠋⡞⣼⣿⣿⣳⣾⡿⠁⠀⢐⣒⠤⠀⣐⠀⠀⠀⠀⠀⠀⠀⠫⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠐⢀⡠⠀⠐⠚⣉⡁⡼⠁⢸⢹⡿⠿⣿⣟⣿⣿⡻⣶⡲⠮⢭⣀⡢⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠐⠀⠀⡠⠄⠀⣩⠥⡾⠁⢸⠈⢸⣟⣟⣒⣲⡯⣽⣧⢹⠹⣄⠀⠈⠙⠳⢦⣀⠀⠀⠀⡀⠄⠀⣐⢮⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣩⡤⠶⢻⡇⢸⠸⠀⠈⣇⠀⠀⠈⠉⠓⢿⢸⠆⠘⣆⠀⠀⠀⠀⠈⠳⢦⡰⠌⠂⡐⢌⠃⠠⡜⢿⣦
⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢂⣤⠶⠋⠁⠀⠀⢸⡀⡜⡆⠀⠐⠹⡄⠀⠀⠀⠀⡾⡘⡾⡀⢹⡄⠀⠀⠀⠀⠀⠀⠙⢦⡑⣌⠂⠠⡱⡜⣎⢿⣇
⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⢸⣧⣱⠠⠀⡀⠃⠹⣄⠀⠀⣰⠃⠁⠇⣷⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⢁⠱⡹⡽⣞⣾⣿⡆
⠀⠀⠀⣾⣏⠀⠀⠀⠞⡠⢂⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢧⠁⠠⠀⢆⠳⡌⢦⣰⠋⠀⠈⠰⣹⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣳⣱⣽⣿⡹⣿⣧
⠀⠀⢰⣯⡿⠠⢀⠆⡔⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⠰⠀⠲⣜⡾⠁⠀⠀⠠⠀⢃⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⠧⠁⣿⣿
⠀⠀⢸⣧⣇⠇⡞⣼⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢠⡰⣌⡶⠋⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡟⢠⣸⢧⡇
⠀⠀⠀⣿⡽⣼⢣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⣟⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡾⣣⣿⠁
⠀⠀⠀⢻⡿⣝⢾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢮⣝⡓⠮⣭⣓⣲⡶⢤⣤⣤⣤⠤⠴⣖⠛⠅⠈⣼⠃
⠀⠀⠀⠀⢳⡜⢳⣬⣙⠓⠶⠤⠤⠤⠤⠤⠶⠶⠚⡋⠉⠤⠒⣀⠄⠀⠁⠄⢀⠀⢀⠀⣠⡾⢭⣙⡲⢬⣍⣛⡲⠮⣭⣭⣍⣉⣛⣉⡅⠠⠥⠀⣡⡞⠁
⠀⠀⠀⠀⠀⠹⣎⠑⠋⠙⣛⣒⣒⣒⣒⣀⣐⣉⠉⠤⠖⢒⣠⠄⠘⢉⠴⢂⡀⣀⡵⠟⠳⢭⣓⠮⣭⣓⡶⢯⣭⣟⣛⣛⣒⣒⠒⢂⡐⠃⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣌⡓⠂⡨⠭⠭⠭⠭⠴⠶⣒⣂⣀⠁⠐⠚⣡⢤⣀⡽⠞⠉⠀⠀⠀⠀⠈⠙⠓⠾⢭⣽⣟⣛⣓⣒⣒⣂⣴⡦⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣌⣹⣿⣿⣿⣭⣭⣶⣖⣺⣭⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡿⡟⢿⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣳⢹⢏⠳⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢁⠠⠀⣼⣿⣷⣌⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⢿⣿⣟⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣧⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⣴⣿⣿⣿⡟⠘⣿⣿⣷⠉⠛⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣷⣾⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢰⣿⡏⢸⣿⡇⠀⠘⣿⣧⡀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⡏⣿⣿⣿⣷⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⣷⠀⢿⣷⣀⣾⡿⠛⣿⣦⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣳⣟⣿⣿⣿⣧⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠸⣿⠀⠀⣹⣿⣯⠀⠀⠈⢿⡇⠈⢿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⠀⠀⣿⠇⠻⣧⠀⠀⠘⣷⠀⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣾⠋⠀⠀⣿⠀⠀⢻⡄⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢻⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⡁⢀⠀⣙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢾⡸⡜⢣⡹⡾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣳⣷⣮⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⢸⡏⠉⠉⠉⢉⠉⠉⠉⠉⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⢸⡇⠀⢀⡞⠉⠙⣦⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠰⠀⠶⠶⠶⠶⠀⠀⠀⠀⢸⡇⢸⡇⠀⠘⣧⡀⣠⡟⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠲⠶⠀⠲⠶⠶⠶⠶⠶⠶⠶⠶⠀⢸⡇⢸⡇⢠⠞⠉⠉⠉⠙⢦⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⢸⡇⠸⠷⠿⠶⠶⠶⠶⠶⠾⠶⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢿⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢸⡇⢠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇⠸⠷⠋⠀⠀⠠⢴⣶⣖⣛⠛⠉⠉⠉⢛⣛⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢸⡏⠉⠛⠚⠛⠉⢹⡇⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠶⠦⠤⠶⠖⢻⡇⠘⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠘⣇⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠤⢤⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⡤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢤⣤⣤⣤⣤⠀⠀⠀⠀⣿⡋⠉⠉⠉⠉⠃⠀⠀⠀⣀⠴⠻⣏⠻⣄⣀⣠⠟⣹⠟⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⠉⠓⠶⣤⣀⠀⠀⢀⡾⠋⠀⠀⠘⢧⡀⠉⢠⡾⠃⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣄⣠⡄⠀⠀⠀⠀⣿⣀⠀⠀⠀⠉⠙⠲⠋⠀⠀⣠⠀⠀⠀⡽⠿⣯⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⡟⢋⣬⣥⡙⣷⠀⠀⠀⣿⠉⠳⠆⢀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠳⠤⠞⠀⠀⣶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⡄⢺⡅⢾⣀⣈⡇⣨⠗⢠⣤⠟⠀⠀⠀⠈⠛⠦⣄⣠⡴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣦⣉⣉⡴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⢈⡏⢹⡁⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠤⠤⠤⠤⠤⠤⠤⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⢿⡇⢸⡿⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇



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

⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⡶⢿⡉⠛⠛⠷⢦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠛⣿⣄⣀⣠⢬⡆
⣔⣹⣞⡼⣞⣣⢧⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡄⣠⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣴⡾⠕⠉⠀⠀⠀⠀⠀⠀⠰⠏⠆⠃⠂
⠀⠀⠐⠀⠃⠀⠀⢨⠀⠀⠀⠀⢀⣀⣀⣀⠀⠛⠉⠋⠉⠉⠁⠠⠰⡷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⠀⠀⢀⡀⢈⣐⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠆⠀⠀⠈⠀⠚⠯⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠠⡀⡀⣅⠀⠀⠀⢸⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣟⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠀⠀⠁⠉⠈⣌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡎⢸⣿⣿⣿⠟⡠⠖⣻⠀⠀⣠⣀⠀⠀⠀⠀⠀⠘⠄⠀⡄⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡆⢸⣇⣼⣿⣿⢱⢉⣴⠞⢻⠀⡜⢁⣎⡤⣄⡀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⡰⡋⢧⣮⡿⠟⠛⠛⢨⠋⣡⣴⣋⠜⢠⢻⡸⢷⠋⡽⠂⠈⠁⠀⡂⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠜⢠⠃⣿⠇⠀⢀⣤⣤⣼⡏⡸⢛⠏⡰⠁⠀⠀⠣⠊⢰⢳⣶⠿⣾⠵
⠀⠀⠀⠀⠀⠀⢠⠀⠎⡠⢡⢋⠀⠀⠀⢡⣶⣿⡀⡇⠈⠋⣒⣁⠀⠀⢀⣀⣀⡀⠰⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⡄⢰⢁⠃⡘⠀⠀⠀⢸⢷⣆⣠⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡿⠂⠄⣀⠀⠀⠀⠀⢀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⢡⠘⠎⡐⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠑⠶⠤⢼⡏⠉⠈⢉⠹⠟⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡤⠖⠚⠛⠉⠛⠒⠶⣤⡀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⢩⠟⠁⠀⢀⣤⣴⡶⠖⠲⠶⣄⠙⢦⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠀⠀⠀⣿⠀⢸⡀⠀⠀⣠⠬⡷⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠸⡀⠀⠀⢻⡀⠈⢧⡀⠀⠿⣭⠵⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⡶⢿⣦⣄⡀⠱⡄⠀⠈⢷⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⢋⠅⠂⠀⠀⠀⣀⠈⠙⣦⠘⠢⣀⠀⠙⢦⡀⠈⠛⠦⣄⣀
⠀⠀⠀⠀⢠⡞⠁⡔⠁⠀⠀⠀⠀⣨⠿⠿⢦⠈⡇⠀⠀⠉⢦⠀⠈⠑⠒⠤⠤⢈⡉⠉⠙⠛⠛⠛⠛⠛⠒⢦⡀
⠀⠀⠀⣰⠏⠀⡜⠀⠀⠀⠀⠀⢸⠁⠀⠰⣾⡴⠃⠀⠀⠀⡸⠡⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢠⡟⠀⢠⠀⠀⠀⠀⠀⠀⠈⠳⡶⠶⠋⠀⠀⠀⣠⠞⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⢹⡀
⠀⠀⣼⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢻⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣠⡴⠖⠲⣤⡀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠖⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠸⣇⠀⠀⠀⠈⠢⡀⠀⠀⠀⣰⣋⣄⡀⠀⠈⠻⣄⠀⠀⡸⠀⠀⠀⣴⠏⠀⠀⢀⣀⣻⣆⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠉⠢⣄⢰⣿⠋⠈⠹⣦⠀⠀⠙⣧⣴⠃⠀⢀⡾⠁⠀⢀⡴⠋⠉⠹⣿⡄⠀⢀⠂⠀⢰⠇
⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢀⠘⣧⠀⠀⠈⢷⡀⢀⡾⠁⠀⠀⣾⠁⠀⠀⠀⢹⡇⢀⡞⠀⢠⠏
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢻⠅⣴⠟⠉⠛⢿⡆⠀⠀⠈⢷⡞⠀⠀⠀⣸⡿⠋⠉⠳⣄⢸⣧⠎⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠸⣶⡇⠀⠀⠀⠈⢻⡄⠀⠀⠈⠀⠀⠀⢰⡟⠀⠀⠀⠀⢿⣼⠃⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⠳⣤⣀⣿⡇⢀⣀⡀⠀⠈⢷⡀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣀⠀⣸⣯⣾⣿⢟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⠿⠿⣿⣟⠉⢻⣿⡿⠾⣷⣤⠀⠀⣤⣿⠷⣿⣿⠟⠙⣻⣿⠿⠿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠲⣌⠲⣄⣀⣤⢀⣼⠷⠀⠀⠿⣄⣠⣄⢀⡤⠞⡡⠂⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠈⠑⠠⠤⠐⠊⠀⡤⠃⠰⠄⠈⠑⠢⠤⠔⠊⠀⠀⣠⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠃⠀⠀⠀⢻⣦⣀⠀⠀⠀⢀⡠⠊⠑⡄⡠⠈⠢⢀⠀⠀⠀⠀⣠⣼⡏⠀⠀⠀⠘⠳⣤⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢸⣷⡡⢌⠉⠉⢀⡀⡀⢀⠀⢀⡀⣀⢀⡀⠉⢉⡠⣠⣾⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢿⡪⠔⣋⣉⠁⠀⠀⠙⠋⠀⠀⠉⣁⡛⠮⢓⡟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⢫⠐⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠄⢂⡍⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠈⠁⠚⠛⠒⠒⠛⠛⠈⠁⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣤⣤⣤⣤⣤⣤⠶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣀⣀⣀⣀⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⣠⣤⠶⠚⠛⠉⠉⠉⠀⠀⠀⠈⠉⠉⠙⠛⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠈⢧⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠸⡆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣷⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠤⣶⣾⠿⠛⠁
⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠉
⠀⣰⠏⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡦⣄⠙⣆
⣰⡿⠞⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡼⢻⠀⠀⠀⠀⠀⠀⡾⠸⡆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⠳⣽⡆
⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡏⠀⠀⢀⡼⠁⢸⠀⠀⠀⠀⠀⣼⣁⡀⢻⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⢿⡀⠈⢿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⣷⣟⡇⠀⣠⠞⡇⠀⠸⡇⠀⠀⢀⡾⠃⠋⠙⣿⡆⢸⢻⡄⠀⠀⠀⠀⠀⠀⢸⠀⢳⡀
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣠⠏⠀⣿⠹⢷⡴⢏⢘⠇⠀⠀⢻⣀⡴⠋⠰⡀⣀⡠⡇⣧⡟⠀⢧⠀⠀⠀⠀⠀⠀⣾⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣴⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠣⠤⠔⠁⢸⠇⠀⢸⡆⠀⠀⠀⠀⢰⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⣼⢣⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⣧⠀⠀⠀⢠⡟⡄⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⣼⠀⠀⢀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁⠀⠀⡞⢿⠀⠀⣠⡏⠈⠌⢦⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢸⠁⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢰⣇⣼⢀⣼⡋⠘⢆⠈⢎⢳⡀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡏⠀⠀⠀⠀⢩⡿⠶⣤⣀⣀⣀⣀⣤⡤⠖⣻⠇⠀⠀⠀⡾⠀⠸⣿⠏⠉⠛⢶⣆⠀⢣⠱⡄⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸⠃⠀⠀⠀⢀⡟⠀⠀⡾⠉⠉⠉⣽⣇⠀⢠⠏⠀⠀⠀⣸⠃⠀⣼⠋⠀⠀⠀⠀⠹⡆⠀⢣⡹⡄⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡟⠀⠀⠀⠀⣸⠃⠀⣸⠃⠀⠀⢠⡟⠘⢠⠏⠀⠀⠀⢰⠇⠀⣾⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⢣⠸⡄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢰⠃⠀⠀⠀⢀⡟⠀⢠⡏⠀⠀⠀⣸⠗⢠⡟⠀⠀⠀⢠⠏⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⡆⢳⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣾⠀⠀⠀⠀⣼⠁⠀⣾⠀⠀⠀⠀⣽⢀⡞⠀⠀⠀⢠⠏⠀⡀⡟⢰⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠘⡆⢸
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡇⠀⠀⠀⡼⠃⠀⠀⣿⠀⠀⠀⠀⣿⡼⠁⠀⠀⢠⠏⠀⠀⢹⠃⣸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⢇⢸
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⢀⡞⠁⠀⠀⠀⠸⣆⠀⠀⠀⢹⠃⠀⠀⢰⠏⠀⠀⠀⠜⣆⡏⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠁⢸⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠁⣠⠏⠀⠀⠀⠀⠀⢠⡞⠳⣄⡀⡟⠀⠀⢠⠏⠀⠀⠀⠀⠈⢺⠇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡴⠃⠀⠀⠀⠀⠀⡰⠋⠀⠀⠈⢹⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⢿⠿⣿⣿⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢉⣤⣴⣦⡈⠙⠻⣷⣿⣿⣿⣿⠛⠉⣡⣶⣤⣍⡙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⢭⡉⠻⣿⣿⣦⠐⠙⣿⣿⣿⠁⢀⣾⣿⡿⠛⣉⠽⢶⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠘⣧⠀⢈⠀⠈⢻⣿⡇⠀⠲⣺⡇⠀⣿⣿⠋⠀⣈⠀⢠⡞⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡏⡰⢻⡟⣆⠀⣿⡇⠀⠶⣿⣿⠀⣿⡏⠀⣾⣿⠷⠈⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢇⢻⣧⣿⠀⣿⡇⠀⣿⣿⣿⡇⢸⣧⠸⣯⣿⠃⡉⢹⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠈⠳⠆⠀⣰⣿⡇⠀⢿⣿⣿⣿⠀⣿⡎⠁⠶⠛⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⡄⠀⠰⣿⣿⠂⢀⣿⣿⣿⣿⠀⣽⣿⠘⢷⡰⠂
⠀⠀⠀⠀⠀⡀⠀⢀⠀⠐⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⢋⠀⢼⣿⣿⣿⣿⢀⣿⡟⢰⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠠⠊⣴⣾⡿⠿⠷⠦⠀⠈⠻⣆⠀⠀⠀⠀⢠⣽⠟⠡⢊⣐⣺⣿⣿⣿⠇⣹⣿⡇⢘⣿⣇⠀⠀⠀⠀⢀⠴⠊⣉⣀⣀⠀⠉⢻⣿⣶⣄
⠀⠀⠀⢡⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠚⠁⠠⣦⣼⣿⣿⣿⡟⣰⣿⣿⣧⠀⢾⣿⣦⡀⠀⡠⠋⣤⡶⠟⡉⢉⡃⠂⣌⠉⢻⣿⣷⡄
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠀⢄⠘⠀⢀⣮⣿⣿⡿⣿⠟⠋⠀⢻⣿⣿⣿⣷⣦⣤⣼⣶⣶⣶⣶⣯⣄⡷⠟⠁⠀⠀⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠈⢻⣿⣦⣀⠀⠀⠀⠀⠀⢸⠀⣼⠃⠊⢀⣤⣜⣿⡿⠟⠁⠀⠀⠀⢠⣀⠙⣋⣛⣻⣿⣿⡯⣾⡿⢿⣿⣻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⣛⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣵⣶⣿⡁⢠⡏⠀⢠⣾⣿⣿⡅⠁⠀⠀⠄⠀⣐⣄⡘⠛⠾⡿⣿⢿⡿⡿⠿⡟⠛⠿⣿⣷⠸⣿⣷⡄⠀⠀⠀⢠⢀⣬⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠙⣡⡿⠁⠁⣾⣿⣿⡟⠀⠀⢀⡄⡅⠀⣨⣿⣿⡇⠀⠀⣀⡀⠠⠄⠀⠠⣶⣶⣤⢹⡇⢡⣽⣷⠀⠀⠀⠊⣨⣿⠏
⠀⠀⠀⠠⣤⣀⣀⣀⣀⣀⣤⡤⠞⠋⠀⠀⡀⣻⣿⣿⡇⠀⣠⣾⡇⢷⠀⠉⣻⣿⣷⡀⠈⠁⢀⣀⣤⣀⠀⢰⣿⣿⡀⠇⢉⣻⣿⡆⣤⣴⣟⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣠⣤⣤⣶⣧⠰⢿⣿⣧⠸⣿⡯⠃⠈⢷⡀⠀⠱⣽⡷⢠⡞⡽⠛⠋⠩⠻⣦⠛⣿⠃⠀⢾⣿⣿⢹⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠛⠋⠉⠉⠹⡄⠹⣿⣿⣦⣉⡀⠀⠀⠀⠻⣆⠈⠛⡀⡿⢸⡅⠀⠀⠀⢀⢸⣷⠉⠀⣚⣿⣿⢏⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢄⠘⠻⠿⢿⣿⣷⣤⡀⠀⢹⡆⠐⡀⣧⢸⣷⣀⡀⠠⠄⠘⣿⠀⣿⣿⡿⠋⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠉⢻⣿⡄⡸⠃⣈⣿⣆⠊⡙⠿⠿⣿⣿⢀⣿⡾⠟⢫⡄⣠⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⠀⠙⣆⠀⢹⣿⢀⣤⣿⡟⠳⠛⠙⠀⠀⣀⣴⠞⣷⣄⡀⠀⠀⠁⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣠⠟⠀⠀⢊⡼⠃⢘⣧⣤⣶⡶⠀⠀⣺⡿⠿⢛⡭⠀⠀⠀⠚⠛⠛⢻⣧⠀⠀⠛⠛⠛⠛⠠⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⢸⣇⢀⣸⡿⠛⠁⠀⠀⢰⣿⠃⢳⣾⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣝⠷⢿⠥⣤⡄⣥⣿⡿⠁⠀⠘⣿⢰⣷⣦⣄⣤⣤⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠿⠿⠿⠛⠁⠀⣶⠀⠀⠙⢆⡉⠛⠛⠛⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣷⣤⣤⣤⣴⣦⠏⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣔⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠂⠈⠉⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⢄⡀⠤⢠⡀⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⠀⠊⠰⡁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠓⠆⠀⠒⠚⠻⡍⠂⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡁⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠒⠃⠀⠐⠠⡋⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⠤⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠣⢀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠣⡀⠂⣴⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠔⠚⠁⠠⣀⠈⢍⠀⡀⠖⠂⠈⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢇⣀⣀⣀⡀⠀⠢⠌⠔⠀⠀⡀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠒⠉⠁⠀⠀⠉⠙⢦⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⣀⣀⠀⠀⠀⠀⠙⢆⡀⠀⣀⠀⠈⠂⢦⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⠊⠁⠀⠀⠀⠈⠑⠢⡀⠀⠀⠉⠙⠓⠒⠒⠠⠈⡄⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⢀⡠⠀⠐⠒⠠⠄⠀⠀⠀⠀⢀⠞⠀⠔⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡠⠤⠊⠈⢆
⠀⠀⡰⠁⠀⠠⢲⣼⡿⡸⠀⠀⢀⡴⠋⠀⠌⠀⠀⠀⡠⠚⠄⠀⡀⠈⠑⢆⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⢇⠀⠀⠘⠦⠬⠥⠤⠴⠒⠉⠀⠀⠈⠀⠀⠀⡜⠀⠀⠀⠂⠀⠀⠀⠄⠱⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⡸⢆⠠⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⣈⢩⠭⣉⠀⠉⡠⠃⠀⠀⠀⠠⠁⠈⠑⠦⣧⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠘⠀⠳⠶⠮⠛⠉⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠸⡀⡀⠀⠀⠀⠄⢲⠤⢤⣀⣀⣀⣀⠠⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢁⠀⠈⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢄⠀⢀⠀⠊⢣⡀⠀⠀⢀⡤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢙⠢⢴⣋⣖⡰⢆⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠠⠀⠀⠀⠁⠀⣀⡴⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠄⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠈⠙⢿⣿⣷⡆⠻⠂⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣧⣄⠈⠁⠀⠀⠀⢠⣤⣿⣿⣷⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⠿⠛⠛⠛⠀⠀⠂⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⢂⣀⣤⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠰⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⣉⠀⠀⠘⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⢯⠀⠀⢀⡀⠀⠀⣶⣤⡀⠀⠈⠳⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠉⠉⢹⣿⣿⣿⣷⣄⢀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣿⣿⣿⣏⣀⢤⣸⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣴⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠎⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡯⠀⠐⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡺⠁⠀⠈⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣢⠀⠀⡹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠛⠛⠻⣷⣦⣄⠀⠀⠀⢻⡾⢗⡂⠀⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠸⣷⣻⣷⣄⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⢿⣿⡷⢾⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣧⠀⠸⣟⢒⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⠀⠀⢿⣁⣙⡖⡆⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠖⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢀⢽⣯⣉⣧⠴⠆⠀⠀⣠⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣄⣀⣀⢀⣴⡿⣯⣿⠃⢀⡈⣽⣿⡕⣺⠒⣴⡆⢸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⡁⢀⠘⠩⡧⣿⣿⠉⡱⢤⣤⡘⣿⣿⣧⡀⢀⣠⣤⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢀⣤⣿⣿⣻⣿⡟⠉⣿⣿⠞⢛⡟⢴⣿⣿⠏⡐⢧⣈⣱⡘⢿⣿⣿⣻⡿⠋⠁⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢠⠼⢏⣘⣭⣽⠏⠀⣰⣿⠿⠓⣍⣯⣼⡏⣻⣷⠞⢡⠊⠝⢇⢠⣿⣿⣿⣿⢷⣄⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣷⣶⠋⣉⣹⡏⢀⣴⣿⣿⠗⢋⠱⢠⣿⠇⢸⣤⣤⣌⡹⠒⠿⣿⣿⡆⠹⣯⡓⠒⠿⡄⠀⠀⣤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣤⡴⢗⡛⣻⣿⣿⣿⣿⡧⡤⠊⡈⢘⣿⠀⢸⣃⠀⣨⢓⣦⡴⣿⣿⣇⠀⢹⣏⠁⡴⢶⠄⣼⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠇⣏⣑⣸⣞⠹⢿⣿⡿⠁⣌⣐⣨⠆⠊⠽⡷⠀⣿⠏⠁⢁⢢⣀⣀⣿⣿⣿⡄⢸⣋⣁⡔⠲⠇⣿
⠀⠀⠀⠀⠀⠀⣼⣿⠀⣟⠁⣉⠾⡉⣟⣿⡀⢸⠋⠍⣠⠜⡒⢾⡇⢠⣿⠷⠶⠇⢊⠀⠉⢛⢿⣿⣿⣿⣙⡈⠐⠒⠆⢹⣇
⠀⠀⠀⠀⠀⢸⢕⡇⠀⣿⡋⠍⣡⢿⣉⣋⣧⡾⠙⠛⠁⠢⠠⢴⣧⣾⣧⡄⡔⠂⠘⠓⠪⡿⢸⣿⣿⣏⣁⠀⠚⠒⠆⠈⣿⣆
⠀⠀⠀⠀⠀⢓⠇⢳⡀⠸⣿⡟⠩⢉⡼⢭⣸⣷⠦⠶⣃⢇⢀⣸⣿⡏⠀⣂⡀⢰⣤⣀⢠⡆⣼⣿⣏⣀⡠⠀⠂⢸⠃⠀⢹⡙⣆
⠀⠀⠀⠀⠀⠀⢂⠀⠹⠦⣿⣿⣿⡟⢩⠙⠂⣧⢀⢀⡴⢀⢩⡿⠛⠉⠉⠉⣀⠀⠐⠀⡙⢰⣿⣁⣀⠀⠄⠚⠒⡟⠀⠀⣼⠸⣗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣤⡀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⣠⣾⠿⠋⠙⣤⣢⠞⠁⠹⢿⡄⠀⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⡇⠄⣳⣆⠀⠁⠀⣹⣶⠈⣿⣼⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠇⠀⠙⠛⠀⠀⠀⠛⠋⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⢸⣿⣦⣄⠀⠀⢀⣤⣶⣿⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⣿⢸⡟⠛⠟⠨⠁⠘⠿⠛⢿⢸⣷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢰⢈⡀⠀⠐⡀⠀⡰⠂⠀⠸⢦⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⠁⠀⠀⠑⠔⠁⠀⠀⢸⡟⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡀⠀⠘⣿⣿⢣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡵⠋⣠⠀⠀⢹⣿⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣼⣿⠇⠀⢠⣆
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣼⡟⢠⡀⠀⢻⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⡟⠀⣠⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⣼⣿⠀⣿⣷⣴⣿⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣧⣴⣿⣿⣿⣿⣳⣆
⠀⠀⠀⠀⣰⡿⠉⠀⠀⢠⣿⡇⠀⣿⣿⢿⣿⡓⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢿⣿⡏⣿⣏⠙⢿⣷⡀
⠀⠀⠀⢰⣿⠁⠀⠀⠀⣾⣻⡇⠀⣿⣿⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡇⢸⣿⡇⢸⣿⡇⠈⢿⣷⡀
⠀⠀⠀⣿⡏⠀⠀⠀⠀⢹⣿⡇⠀⢿⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⣿⡇⠀⣿⣿⠀⠘⣿⣧
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⣿⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⢹⣿⠀⠀⢸⣿
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⠀⠀⣼⣿
⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠰⣿⣿
⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡿⠇
⠀⠀⠀⠀⠈⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣿⣿⡷
⠀⠀⠀⠀⠀⠉⠛⠋⠑⠄⢠⡞⢷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⠳⣆⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠉⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠈⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣷⠀⠤⠤⠤⠤⠤⠤⠄⠐⢺⡟⢻⡄⢀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢿⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⠆⠈⠐⠒⠂⠀⠀⠀⠐⠒⠀⠀⢠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣤⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⣴⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣮⣿⣄⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡻⣟⣿⡿⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡝⣿⣿⣞⣷⡐⠄⢈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⢻⣿⣿⣌⢢⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⢿⣿⣿⣷⣷⣽⣿⣄⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡙⢿⣿⣿⣿⣿⣶⢀⠀⠀⠀⢀⡞⠁⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⢆⠻⣿⣿⣿⣿⣿⠀⠀⣠⣟⠀⣠⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⢛⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⡠⠚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⢠⣶⡒⠀⠀⠀⣼⣇⣇⠀⠀⢀⣠⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠈⠙⠦⣀⠀⣿⠃⢷⢀⣤⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡿⣿⢻⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢙⣿⣶⣾⣿⣿⣿⠟⠉⠉⠀⠩⡍⠙⢋⡀⠍⢿⣾⣽⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⣬⠋⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠄⣨⣿⣿⣿⣿⡿⠿⣄⡀⠀⠀⠀⠀⡀⠀⢷⣠⡿⠟⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⡹⠃⣠⣴⠢⠄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⡿⠉⠁⠀⣈⣑⡲⠤⢄⠘⢀⢸⣿⠃⠀⢻⣿⣿⣿⣿⡎⠉⠒⠤⠤⢤⡾⠛⠉⠀⠀⠙⠒⠢
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣿⡿⠀⠀⠀⠀⠉⠀⠠⣤⣭⡿⠟⠀⢦⣀⠀⠈⣿⣿⡙⠻⣆⠀⢀⡶⠛⠁
⠀⠀⠀⠀⠸⠟⠛⢳⣿⣿⡿⡧⠀⣀⣀⠤⠀⠀⠀⠀⠈⠀⠘⠲⠤⢥⣀⡉⣛⣻⣿⣖⡺⠿⠋
⠀⠀⠀⠀⠐⠄⢀⣠⣿⣿⡿⣿⠛⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡋⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠳⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣤⣦⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⣝⠀⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⡈⢠⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⡇⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣽⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⠀⠸⣧⢠⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣰⣙⡓⣾⢆⠀⠀⠀⠀⡀⠀⣘⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣿⣦⡆⠀⠐⢄⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⡿⠁⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣯⠻⣄⠀⠀⢀⣸⠞⠀⠀⢈⠱⠀⠀⡮⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣛⡦⡄⠈⠁⠀⠀⠀⠀⠀⠀⠂⢀⠔⠈⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠲⣿⢰⡀⠀⠀⠀⠀⠈⠳⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⡗⢀⣠⣾⡁⠀⢀⣼⣏⣆⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⣀⠀⠀⣀⢀⠀⠸⣷⣄⣀⠇⣾⠁⠈⠙⠂⠁⠀⢙⢛⡃⠀⠀⢠⢗⡾
⠀⠀⠀⠰⡆⠣⢝⠀⠀⠐⢦⠌⠋⣭⠄⣼⡀⠀⠀⠀⠀⠀⠘⣿⣇⠀⡰⠁⠘⢓⡒⠀⠀⠤⠤⢤⣤⡴
⠀⠀⠀⠀⣏⡔⠿⠺⢝⡹⠧⠶⠦⠁⠐⠂⢀⠂⠀⠀⠀⠀⠀⠘⠏⢾⣇⡴⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢃⣤⠃⠀⠀⠀⠀⠀⢀⣞⣶⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣉⡓⠠⡀⠀⠀⣠⣿⣿⣿⠃⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣷⣌⡶⣿⣴⣿⡿⠃⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⣾⣯⣾⠟⠁⠀⠀⠀⠀⠈⠓⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⣿⣿⣿⣿⡿⠋⣂⣯⣎⡌⢗⣦⡀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣿⣛⣫⣾⡿⣹⡿⠟⠀⠀⠁⠉⠛⣼⢸⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣠⣴⣦⡶⣻⣿⡿⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠴⢸⣧⡀
⠀⠀⠀⢠⣾⣿⣿⣿⡿⡑⣿⣯⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡇⠉⠰⢢⣀
⠀⠀⠀⢸⣿⣿⣿⠟⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢼⣿⠀⠀⠜⠿⠣⡀
⠀⠀⠀⢸⣿⣿⣷⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⠈⠓⠤⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢦⡙⢿⣦⡈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠙⢿⣿⣷⡅⠈⢣⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠟⠋⠉⠉⠙⠓⠦⠀⠀⠀⠙⣿⣷⡀⠀⠳⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⡀⠀⠀⠀⠐⢿⡿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⢸
⠀⠀⠀⣏⣉⡇⢸⠀⠀⠀⡞⢧⠀⡼⠉⠉⠀⣇⡜⠁⠀⠀⠀⢸⣿⣿⣧⣾⠿⠿⠿⡦⠀⠀⠀⠀⠀⢀⡴⠾⠿⢋⣻⠇⠀⠀⠀⠀⠀⠀⢿⣿⡆⡀⢸
⠀⠀⠀⣏⣈⡷⢸⣀⡀⣸⠓⠛⡆⢳⣀⣀⠀⡏⠱⡄⠀⠀⠀⢸⣿⣿⣿⡅⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠓⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⠸
⣶⣶⣶⠶⣶⢶⣶⢶⣶⢶⣶⣶⢶⣶⡶⠷⢶⡶⠶⣶⣶⣶⣶⣾⣿⣿⡿⣷⣶⡟⠻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣿⡇
⣿⣿⢇⡣⡿⡇⡟⡌⠇⣿⣙⣛⢸⣿⣿⢸⣿⢘⣛⣿⣿⣿⣿⣿⣿⣿⡇⢻⡏⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠇
⣿⣿⣮⣧⣼⣿⣼⣿⣼⣿⣿⣿⣼⣿⣿⣼⣿⣬⣭⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠀⠀⠀⢰⣄⡀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⡀⢠⡀⡀⠀⡀⣄⢀⢀⣀⢀⣀⠀⠀⠀⢸⣿⣿⣿⡀⢿⣆⠀⠀⠀⠛⢁⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠃⠘⠐⠤⠇⠱⠸⠄⠇⠆⠇⠣⠸⠠⠼⠺⠀⠂⠀⠀⢸⣿⣿⣿⡇⢸⣿⣆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⣿⣿⣆⠀⠹⢿⣿⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡟⠘⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⢿⣿⣿⣦⠀⠑⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⡽⢿⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠀⠀⢀⠎⠀⢸⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⣄⣀⣠⣤⣴⣾⣿⠿⠋⠀⠀⠀⠠⠋⠀⠀⠈⠹⣄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠾⠟⠛⠛⠛⠻⠷⠶⢶⣦⣤⣀
⠀⠀⠀⠀⢰⡶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢸⡇⠀⢀⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠘⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡀⠀⠀⠀⢀⡼⡇⠀⠀⢸⣷⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣤⡿⠁⠀⠀⣰⠟⢰⡇⠀⠀⢸⡏⣧⠀⠈⢿⣆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢠⡞⢱⠇⠀⠀⣼⠋⠀⢸⡇⠀⠀⢸⠃⠸⡆⠀⠘⡟⢧⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢠⠟⠀⣾⠀⠀⣼⠃⠀⠀⢸⠇⠀⠀⡿⠀⠀⢻⡀⠀⣿⠈⢷⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢠⡟⠐⠚⣿⠀⢸⠟⢻⣦⡀⢸⠀⠀⣸⣧⣖⣿⠿⢷⠀⢸⠶⠬⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢿⣼⠀⠀⠀⣿⠀⡿⠀⠀⠈⠁⢸⡆⢠⡟⠈⠁⠀⠀⠘⣧⣸⠀⠀⠈⣷⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠘⠋⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⠸⣧⡟⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠘⣧⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠻⡇⠀⢀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢸⣮⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣿⠘⣧⠀⠀⣀⣤⡶⠶⠟⠛⠷⢦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠞⠛⠛⠛⠛⠓⠖⢿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⢸⡇⠀⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣼⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠀⠀⡇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⣿⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠛⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⣾⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣸⡇⠈⡿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢰⣿⠀⣰⠸⠀⠈⠙⢷⣤⣀⣀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⢿⡀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢠⣿⡏⠀⣿⡀⠀⠀⠀⢰⢸⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⢿⠇⠀⣏⢣⠀⠀⠀⠈⠈⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢠⡟⢸⠀⠀⣿⢸⠀⠀⠀⠀⡆⢇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⢿⡀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠇⢿⠀⠀⢹⡘⡆⠀⠀⠀⢱⠘⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠈⢇⣹⣤⣤⠴⠶⣶⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠻⣷⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠘⣇⢀⡴⠟⠉⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣤⠶⠛⡏⠀⠀⠀⠀⠀⡾⠁⠀⠈⠁⠀⠈⠉⠀⠀⠀⣀⣤⠾⠋⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣧⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⠀⠀⠀⢻⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠸⣧⣀⣀⣀⣤⡴⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠒⠒⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠒⠅⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⢈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠁⠠⠼⡕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠄⠀⠄⠀⡐⠀⣱⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣤⠂⠀⡴⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠐⠀⠀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠥⠇⣧⡀⢘⠁⠀⠀⢘⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠐⠀⠘⠁
⠀⠀⠀⠀⣀⠄⠀⢀⠀⠳⡗⠄⡀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣻⣤⣄⡀⠀⠀⠐
⠀⠀⠀⠐⠄⠀⠁⠀⠉⠰⠗⠠⡠⢠⠤⠀⠀⠠⠀⠀⠀⠈⠉⠁⠁⠙⢿⣁⣀⡀⣀⠀⠀⠠⡀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠈⠳⡐⠄⡀⠀⠤⠘⡆⠀⠃⠀⠄⢠⠀⢠⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠖⡆⠆
⠀⠀⠀⠀⠀⠐⠀⠁⠠⣞⢄⠀⡠⠀⠠⠀⡉⢳⡂⠁⣁⣈⠀⡘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠣⠼⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠈⡇⠠⢧⡠⠐⠴⢀⡈⠁⠠⠄⠹⠂⠀⠰⠤⢍⡀⢄⡠
⠀⠀⠀⠀⠀⠀⠂⣒⢀⠀⢀⡀⠆⠈⠀⠐⠴⣄⠡⠞⢠⡄⠁⠠⡆⠀⠠⣇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠦⠈⢇⠠⡵⡀⣀⠀⠀⠂⢀⠀⠀⠉⠉⠓⠜⠘⠀⠠⠴⠘⣐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⠙⡎⢒⠆⠠⠁⠈⠀⢀⠑⠀⡀⠀⠁⠈⠙⠒⠅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠐⠲⣌⠂⢀⡠⢐⢀⡀⢁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠈⠀⠈⡉⠓⠄⠈⠤⠄⣅⣀⠆⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠠⠒⠒⠒⠂⠤⠤⠄⣀
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠤⠒⠒⠀⠉⠁⠀⠀⠀⠈⠉⠐⠒⠤⢄⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠍⠁⠈⠁⠈⠉⠐⠒⠠
⠀⠀⠀⢸

⠀⠀⠀⢰⡀
⠀⠀⡠⠊⠀⠀⠀⢀⣀⢤⠤⠐⠒⠂⠐⠀⠖⠐⠒⠒⠂⠤⠤⠄⣀⡀
⠀⢀⡠⠄⠒⠈⠁⠜⢠⠃⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠁⠀⡠⠄⣀⣸⠀⠘⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠸⠀⠀⠀⠉⠻⠃⠀⠀⢀⡤⠊⠉⠣⡀⠠⠄⠒⠉⢆⠀⠀⠀⠀⠀⡠⠊⠈⠤⢣⠀⠀⠈⠒⢄
⠀⠀⠀⢑⣤⣄⣀⡀⠈⠂⠈⠀⡇⠀⠀⢠⣶⠀⠀⠀⠀⠈⢢⡀⣀⠄⠊⢀⡀⠀⠀⢸⢇⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⡇⠀⠀⠈⡃⠀⠀⠀⠀⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⢸⠘⠀⠀⠀⡐⠀⠀⠈⢱⣄
⠀⠀⠀⠈⢁⠔⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⢀⠔⠡⡀⠀⠀⢸⠀⠑
⠀⠀⠀⠀⢸⠀⢀⡸⡀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⠀⠱⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠑⡀⠀⡰⠁⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢀⠃⠀⠈⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⣀⣴⠀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢰⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣻⡭⢭⣟⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡵⣫⢖⣻⣟⡲⣝⢮⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢳⣧⣏⡖⢲⣹⣼⡞⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡜⣏⢧⣳⡽⣫⢞⡼⣹⢣⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡭⢷⣒⡶⢭⡻⣮⡷⣫⢞⡵⣫⢞⣱⢟⡭⢷⣒⡾⢭⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⢫⢞⡭⠿⢭⡳⣝⢮⡻⣷⣫⢞⣥⡿⣝⢿⣞⡭⠿⢭⡳⡝⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢾⢸⣉⡷⣝⢮⡳⣝⢮⣿⣿⡳⣝⢮⡳⣝⢾⣉⡇⡷⣿⣹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡹⣜⢮⣓⣿⣚⡽⣷⣝⣾⢟⡵⣫⢿⣮⡳⣝⢮⣓⣶⣚⡵⣣⢏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣓⡾⠭⢷⣚⣵⢟⡵⣫⢞⡵⣫⢾⡻⣮⣓⠾⠭⢷⣚⡵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⢧⣏⡞⡵⣫⣞⢯⢳⣹⡜⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡼⡟⣇⠧⠼⣸⢻⢧⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡳⣝⠮⣽⣯⠵⣫⢞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣽⣓⣚⣯⠵⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡿⣽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢿⣿⣷⡆⠀⠀⠀⠀⠀⠀⣠⣾⠟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠠⠦⡄⣀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣹⣿⣿⣿⣷⣦⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢿⣿⢿⣿⣿⣿⣿⣵⣾⣿⠇
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣦⣀⢸⣿⣿⣿⣿⣿⣿⣯⣶⣶⣦⡀⠄⣀⠄⠄⠄⠄⠆⠆⠦⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣟⢡⡍⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠙⠛⠛⠋⠀⠙⠻⣿⣿⣿⣿⠿⣿⣿⡀⠙⣋⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠙⠿⠿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢠⣤⣤⣀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠠⡀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⡀⠄⠠⠄⢀⠀⠀⡠⠄⡀⢀⠀⠔⡄⠤⠀⡀⠀⠀⡀
⠐⡆⠀⠠⠑⠀⠀⠠⡄⠀⠀⠈⠀⢠⣾⣿⠿⢿⢿⠿⡿⠿⣿⣷⡀⠀⠎⠀⣀⢁⡤⠀⢠⠘⠆⠠⠃⠈⠀⠒⢉⣀⠀⠀⠐
⠀⠸⡀⠈⠀⠀⢉⠁⠀⠀⠀⣈⠆⣿⠿⡿⣿⣿⡿⣿⣿⡾⣿⢿⡇⠀⠄⠁⠀⠉⠀⠁⡘⠀⠀⢀⠤⡆⢡⣀⡅⠀⠔⠐⡁⣡⢠
⠀⠠⣧⡀⠀⠀⠈⠡⣘⢃⠔⠈⠄⢿⣼⣆⣯⣬⣜⣧⣤⣄⣧⣴⡇⠀⠐⠀⢀⣂⠠⠐⠀⠀⠀⠀⠀⡠⡄⠀⡆⠀⠀⠀⠀⡈
⠀⠀⠋⢧⠀⠀⠆⢲⠀⠀⡲⠠⠂⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⠠⠒⠄⡀⠀⠀⠂⠐⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠅
⠀⡖⠈⠀⠁⡄⠈⢨⠉⠉⡁⠆⢀⠀⠀⣀⡉⠉⠉⠉⠉⠉⣀⡀⣂⣀⣀⣀⣀⣀⣁⠀⣀⠀⠀⠀⠀⡀⢁⠀⡄⠀⡀⠀⠄⠄
⠀⠰⡀⡀⢄⠁⠔⠘⠀⢀⠃⠃⠀⡄⠀⠉⠁⠀⣠⡄⢨⠱⠒⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠒⠉⠐⠒⠃⠐⠒⠒⠒⠒⠐⠂⠚⠒
⠀⡠⠀⡀⠀⠀⡀⠀⠀⢨⠀⠄⠆⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄
⠀⡂⠀⠈⣀⠀⠥⠠⠀⠈⠤⠠⢲⠂⠀⠀⠀⡁⠀⠀⢸⠀⠀⠴⠀⢀⠀⠀⠀⠀⠀⣐⣀⠀⠀⠀⡇⠠⠤⠠⠠⠀⠀⠀⠀⠂
⠀⢋⠀⠀⠈⠀⠀⣠⠀⠀⠀⠀⠐⠃⠀⣤⢒⣄⠀⡀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⣍⡤⠀⠁⠠⡇⠀⠀⠀⠀⠀⠀⡄⣰⠂⢲
⠀⠀⠀⠀⠀⠄⠘⠋⠀⠀⠀⠀⡎⢁⠀⠀⠀⠀⠀⠐⠘⢠⣀⣀⠀⠀⠀⠃⣀⣀⣀⣀⣀⣀⠀⠀⡇⠈⠉⠁⢀⣀⠀⢏⡇⢰⢸
⠐⠖⡀⠀⠂⠫⠀⠀⠴⢠⡄⠀⡇⠐⠀⠀⢀⠠⠀⢰⠈⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⡁⡀⠉⠁⠉⠁⠀⠓⠃⠚⢚
⠀⠨⠀⠀⠀⠀⠀⠀⠔⡉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠸⠉⠉⠉⠅⠆⠀⠶⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸
⠀⠀⣀⣀⣀⣁⡉⢁⡉⠀⠀⠀⠐⠦⠤⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠄⠀⢀⠄
⠀⠘⠁⢀⣀⠀⠀⠀⠀⠩⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⡆⠀⡆⡆⡄⢱⣧⢠⡄⢰⡄⠀⣀⣴⣄⡇⠀⣴⣶⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡁⠁⠀⠁⠀⡇⠸⣿⡀⢻⡄⠿⠟⠛⠋⠉⠁⣸⡿⣝⠛⠿⣿⡇
⠀⠀⢀⣤⣀⣀⣀⣤⣤⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠃⠋⠉⢻⠁⠃⠀⠛⡇⠈⢿⡄⠠⡾⠇⣀⣀⠳⣿⣽⣿⣝⣯⠟
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠧⠤⠄⠀⠀⠶⠄⠀⠾⠶⠼⠇⠀⠀⠸⡿⠃⠀⠘⠗⠀⢻⣿⡆⠀⢤⠙⠋⠁⢸⠟⠿⠟⠁
⠀⠀⠇⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⣲⠀⢀⠀⠀⠀⡀⢤⢄⠀⠀⠀⠀⡡⠔⠐⠤⠷⢦⡀⢠⡳⡀⠈⠀⠄⠈⠁⠀⠀⠈⠒⢀
⠀⠀⠇⠀⢀⣀⡀⠀⠀⠼⠀⠀⠀⠀⢀⠀⠀⠁⠈⠂⠀⠐⠃⢱⠀⠌⠀⠀⠀⠀⠀⢀⢣⠀⢀⠈⠂⡌⠀⡄⠀⠀⠀⠀⢀⠀⠁
⠀⠐⠆⢀⠀⠀⠄⢀⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⠀⠀⠀⠀⠘⡜⠀⠆⠐⠄⡀⠔⡃⠀⠀⠀⠀⢸⠀⢸
⠀⠈⠁⠐⠀⠀⠀⠠⠇⠛⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⣤⡀⠠⣀⠜⠀⡸⠇⠀⠀⠠⠀⠋⠈⠀⠂⠀⢹⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠠⠀⠸⠀⠀⠀⠙⠓⢋⠁⠀⠀⠀⠈⠀⠆⠰⠀⡂⠀⠀⠀⠀⣄⠕⠎
⠀⠀⠀⠀⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠘⠀⠀⠂⠀⠄⠀⠁⠁⠀⠀⠀⠀⠀⠀⠨⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⣠⡴⢤⡀⠀⠀⠀⠀⠀⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⠲⠚⠁⠁⠀⡀⢳⡀⠘⠉⠁
⠀⠀⠀⠀⠀⢠⡟⢁⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⣇⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⡀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⣴⣾⣿⡿⠿⠋⠁⠀⢠⠀⢢⡀
⠀⠀⠀⠀⢈⣷⠀⠻⣿⢿⢥⠀⠀⠀⠀⠀⠀⠀⠁⢠⠂⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡇
⠀⠀⠀⣠⡾⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣿⣧⠀⠀⣀⣤⣶⠾⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⢤⣄⠀⠀⠀⠀⠀⠀⢀⠞⠉⠙⡆
⠀⠀⠀⠙⢿⣿⢿⣿⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠒⠀⠀⢈⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣾⣿⣽⠋⠚⣻⣷⠀⠀⠀⠀⠀⡼⢿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡖⠀⢧⢀⣼⡿⢷⡇⠀⠀⢯⣿⣆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠤⠶⠾⠋⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠈⠺⢿⣵⡶⠖⠁

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠱⡤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠐⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⡀⠂⠀⠀⠠⡄⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠆⢀⠐⠒⠂⠀⠀⡀⠀⠀⠀⠉⠒⠈⠤
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⢿⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠁⣠⣄⠀⠀⠁⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠢⠈⠀⠀⠀⠁⠀⠀⠀⡌⠁⠴⠂
⠀⠀⠀⠀⠀⠀⠰⠈⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡡⠐⠒⠉⠀⠀⡑
⠀⠀⠐⡀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠠⠤⣠⣤⡶⠒⠀⠀⠐
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠒⠀⠂⠉⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢺⣿⣶⣤⣀⠀⠀⠀⠀⠀⣄⡀⠂⣄⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣶⣦⣤⣾⠿⠟⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣠⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤⠚⠙⡰⠉⠻⠿⠯⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡿⠛⠉⠙⠟⠿⣿⠟⠚⢉⠀⠉⠈⠉⠲⠧⢄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠅⠆⠚⣿⣧⠀⠀⠾⠓⠄⠀⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⢀⡂⠀⠀⢐⣿⡇⠀⠗⠐⠀⠀⠀⠀⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⢹⠁⢸⢿⣦⡄⢈⣻⡷⠐⡆⠂⠀⠀⠀⠐⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠈⣿⣥⠸⡦⠊⠀⣹⡿⢷⣿⡇⠀⢧⡀⠄⠀⠀⠀⠈⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠥⣤⠼⢦⣶⠓⠙⢷⣮⣓⣐⣆⣷⣿⣿⣏⠀⠀⠈⢣⣀⠀⠤⠄⠊⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⠃⠀⠀⣇⠀⡀⠀⠉⠻⡿⠟⠋⠁⠸⣿⡀⠀⠀⠀⠉⠠⢬⠀⡹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⡿⠊⠁⠀⠀⠀⠯⠈⠀⠀⢉⣿⡇⠀⠀⠀⠀⢀⣔⣶⣼⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣇⠀⣰⠧⡄⠀⠀⠀⠀⣧⡀⠀⠀⠲⣿⡅⠀⠀⠀⢠⣿⠋⠀⠀⢻⣧⠄⠀⠀⠀⠀⣠⣶⠶⠶⢤⡀
⠀⠀⠀⠊⠙⢲⣄⠀⠀⠀⠀⠀⠀⡸⢶⠁⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠘⣿⡂⠀⠀⠀⢸⣟⠀⠀⠀⢸⡗⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠈⠸⠷⢄⣀⣀⡠⠞⠁⡈⠿⣄⠀⠀⠀⢀⡜⠁⠌⠀⠀⢀⣿⣇⠀⠀⠀⠘⣻⡄⠀⢀⣾⠁⠀⠀⢀⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠕⠁⠀⠃⠀⠀⠂⢈⣛⡖⠒⠛⠀⠄⠀⠀⠀⠀⢀⢿⣆⡀⠀⠀⠘⣿⡶⢟⠃⠀⣀⣤⡿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠽⠛⠟⠿⠉⠓⠻⠿⠿⠉⠂⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣶⣶⣦⡀⢠⣴⣾⣶⣦⠰⣶⣶⡆⢀⣤⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⣿⣿⣷⣿⣯⣤⣽⣿⣇⣿⣿⣷⣿⠟⠛⠋⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⡤⠠⣼⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⣿⣏⠀⢃⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⢻⣿⠀⠠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣷⣶⣶⣾⣿⣷⣶⣿⡿⢹⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠙⠛⠋⠉⠉⠉⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢢⣿⣿⣿⠟⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⠽⠏⣂⠤⣄⣂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠱⠇⣭⣭⣴⡶⣿⣾⡟⠿⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠮⠞⠍⠴⠵⡭⢒⡖⢭⠪⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠒⠂
⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣦⣀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣤⣀⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣠⣤⣿⣿⣿⣷⣿⣿⣿⣳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣾⣿⣟⣴⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡾⢰⡾⢰⡾⣶⠹⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣿⣬⣭⣭⣽⣿⣤⣿⣿⣿⣥⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠠⢤⠤⠤⠤⢤⠤⣬⣭⣭⣭⣭⣭⡭⣭⡭⣭⣤⡤⢤⡤⠤⠤⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⠿⠿⣿⣿⣿⣯⡉⢉⣽⡿⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣷⣤⣴⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠉⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣁⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢄⣀⣀⣤⡄⡀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠜⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠐⠶⠶⢶⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⣤⣤⣶⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⣰⡿⣿⣿⡿⠿⠛⠛⠋⢉⣩⣭⣽⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢼⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠹⣧⡀⠉⠀⠀⠀⠀⠂⠁⠀⠩⠿⠛⠛⠛⠛⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⡀⠀⠠⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢈⠁⠀⠀⠐⠁⠚⠁⠁⠳⠊⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠛⠛⠉⠉⠉⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣠⡤⠶⠒⠛⠋⠉⠉⠉⠙⠛⠒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⢹⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⣧⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⢀⣀⣤⡼⠇
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡕⠋⠁
⠀⡼⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣷⠀⠀⡀⠀⠀⠀⠀⠀⠐⡦⣄⢳⡀
⠼⠗⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⡜⡇⠀⠀⠀⠀⢰⠃⢧⠀⢳⠀⠀⠀⠀⠀⠀⢹⡾⠳⣷
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣴⣳⡇⠀⢀⡞⠀⢹⠀⠀⠀⣠⠟⠦⣼⡀⢸⡆⠀⠀⠀⠀⠀⢸⡟⡄⠘⠂
⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⠞⢸⢻⣇⣰⠋⡞⠀⠘⡆⢀⠔⢩⠀⠀⡞⣇⡏⢹⡀⠀⠀⠀⠀⢸⠁⠹⡄
⠀⠀⠀⠀⠘⣆⠀⠀⣰⡏⠀⢸⠀⠈⠀⠀⠁⠀⠀⠘⠁⠀⠈⠆⠡⠃⢸⠃⠀⡇⠀⠀⠀⢀⡟⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠘⣆⣰⢳⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣿⠀⠀⢀⡼⢃⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠈⠁⡞⠀⠀⡜⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⢸⠀⢀⡾⡀⠠⠳⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⠃⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⣀⡤⣶⠁⠀⠀⡟⢺⣶⡟⠶⣌⡆⠑⡑⡄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡼⠀⠀⠀⢠⠏⠀⡽⠛⠚⢛⣏⠁⣰⠃⠀⠀⣸⠀⢠⡏⠀⠀⠀⠹⡄⠈⠜⢄⠀⢸
⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⠇⠀⠀⠀⡾⠀⢰⠃⠀⠀⣼⠉⣰⠃⠀⠀⣰⠃⢠⡏⠀⠀⠀⠀⠀⢿⠀⠐⡘⡄
⠀⠀⠀⠀⠀⢀⡇⠀⠀⣸⠀⠀⠀⢠⠇⢀⡏⠀⠀⠀⡏⢠⠃⠀⠀⢠⠃⠀⡟⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⢸
⠀⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⢀⠏⠀⢸⠁⠀⠀⢠⢁⡏⠀⠀⣰⠃⠀⢰⠁⡇⠀⠀⠀⠀⢀⡏⠀⠀⠀⡀⡆
⠀⠀⠀⠀⠀⡟⠀⠀⢰⠇⠀⣠⠏⠀⠀⠘⣆⠀⠀⠈⡟⠀⠀⣰⠃⠀⠀⢸⣰⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⡴⠁⠀⠀⠀⢀⡼⠳⣄⣰⠁⠀⢰⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢄⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠌⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠴⢦⠤⡶⣀⣆⠤⠤⠴⣄⣀⡀⠀⠀⠀⠰⠄⠀⢀⠔⢡⠤⡄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⡀⢀⠀⠀⠀⠹⠿⢠⣯⣄⠀⠀⠘⠁⠀⠀⠀⠀⠀⢤⡴⠈⠀⢻⠈⢘⡤⢻⡀⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠈⠁⠀⠀⠀⠰⢇⠁⠙⢷⣄⠀⢀⣄⠀⠀⠀⢐⣻⣝⢠⠀⣴⣾⢋⠁⢰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⠊⠑⢤⢈⠛⣄⠈⠀⠘⣧⣈⢁⡠⣦⠘⣇⣀⠟⣿⡿⢷⡯⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠸⠀⠑⣀⡵⠲⡷⣶⣆⠈⢿⣿⣷⣿⢟⣯⣿⣾⡫⢷⣮⡿⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠰⠀⠠⡧⣝⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢤⣯⡙⢄⣇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡀⡀⢀⣹⣅⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣾⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⢀⢤⡐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⡉⣿⢿⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡀⠀⣼⣷⣾⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢽⢼⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠡⠋⢐⣾⡯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⣻⣝⣿⣿⣿⠝⣿⣿⣯⣘⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢺⡅⢂⣿⣡⣿⣿⣿⣣⣿⣿⣿⣿⣿⠿⣿⣿⣼⣶⣛⣿⡋⢁⣐⣿⣟⡏⣻⣾⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣿⡿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⢯⡜⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣿⣴⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⣙⣢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠚⠙⠳⠗⠓⣶⠃⠎⢛⡲⣿⣭⢻⡟⡛⠿⠻⣿⣿⣿⣿⡏⠻⢷⡂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡩⠟⠋⠁⡻⠟⠿⠟⠋⠋⠉⠉⠉⠙⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡠⠴⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢴⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠘⠛⠒⠉⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠸

⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣤⡶⡄
⠀⠀⠀⢠⠀⢿⡿⠀⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡆⣎⣀⠀⠀⠀⠀⠈⣻⣯⣽⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠘⢹⣿⢿⡋⠀⠀⠀⠀⠀⢄⢿⣿⣷⣄⣷⣼⣆⠁⠀⠀⠀⣶⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠁⡏⢲⠈⠂⠀⠀⠀⢀⠖⠻⠾⢻⡿⢿⠟⠀⠉⠀⠀⢀⡽⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠭⡳⠀⠀⠀⠀⠀⠀⣹⠋⠿⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢴⣷⣿⣿⣧⠀⠀⠀⡀⠉⡵⣠⣤⣾⣤⣀⠀⠀⠀⠀⠀⢀⣀⣣⡀⢀⣀⣀⠄⠀⠀⠀⢀⣸⣿⣿⣷⡄⡀
⠀⠰⠒⠒⣻⠟⣿⡟⠓⠇⠀⢠⠃⣠⣷⣿⣿⣿⣿⣿⡿⠀⠀⠰⠦⠮⣶⣿⣷⣯⢦⡀⢀⠀⠀⠀⢸⣿⣿⣿⡿⠃⢂
⠀⠀⠀⢸⣵⢊⡟⠙⡏⠀⠀⠈⠛⢛⣿⣿⣿⣿⣯⠉⣠⢦⠀⠠⡁⢈⣵⣿⠋⢹⣧⠉⡁⠀⠀⠀⠼⡬⢿⡿⢻⠒⠃
⠀⠀⠀⢀⠟⡟⢗⠒⠁⠀⠀⠀⠠⣬⠇⢿⣛⡯⡙⠖⠃⠁⠀⠀⠀⠀⠛⠋⠀⠘⠉⠉⠀⠀⠀⢀⡠⢣⠏⠈⢻
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠈⠃
⠀⠀⢰⣤⣀⢀⡴⡆⣠⠤⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⢀⣄
⠠⠚⠙⢻⣿⣿⣇⠀⣧⠀⠀⠀⠀⢀⡹⣄⠆⣤⣄⠀⠀⠀⠀⣀⠼⡰⡾⠿⣿⡟⠟⡦⡇⠀⠀⠀⠀⢰⣿⣿⣧
⠐⢛⣒⣢⣿⣿⡿⢷⠯⠤⡄⠀⢀⣘⣼⣯⣾⡿⠋⠀⠀⠀⠀⠐⠡⠣⢁⢺⣿⡇⡃⢃⠌⠃⠀⠀⣆⣿⣿⣿⣿⣦⡆
⠘⠁⠀⠈⢉⠉⡇⡼⠠⣀⠇⠀⠀⠈⢩⢿⠷⣶⢴⡂⠀⠀⠀⠀⠀⠀⠈⠈⣿⠇⠈⠀⠀⠀⠀⣧⣳⣿⣿⣿⣿⣾⣣
⠀⠀⠀⠀⠙⠒⠃⠘⠒⠀⠀⠀⠀⠀⢸⠈⠙⡂⠠⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⠀⠀⠀⠸⣍⡽⠛⠋⠉⠛⢿⣍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢶⠛⠿⠍⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⢄⡀⢀⣀⣀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⣠⠒⣏⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⡿⣟⠷⢾⠟⣿⣐⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠀⠀⠀⣠⡟⢀⣵⠖⠶⣿⠀⠈⠙⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠍⠐⡴⠋⠸⡄⠀⠤⠀⠴⠃⠀⠀⡰⠀⠈⠑⢄⠀⡠⢴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣰⡄⠀⠹⣄⠑⠂⣀⡤⠴⠊⠀⠀⠀⠀⢀⠿⠁⢛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠊⠀⠉⠑⠢⣹⣎⣏⡁⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⠄⠓⠂⠀⠒⠢⡈⠁⠀⠈⠑⢄⠀⢃⢰⠃⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣀⠀⠀⢺⡇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⡤⠚⠉⠉⠉⠉⠐⠢⡀⠀⠙⠉⠑⠒⠒⠀⢣⡀⠀⠀⠀⣰⠃
⠀⠀⠀⣀⠤⠤⠤⢄⠀⠀⠀⠀⡠⠋⡠⠃⠀⠀⢀⠤⠤⢄⡀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠙⠤⠞⠋⠀⠐⡄
⠀⢠⠊⠀⠠⢶⣾⣦⠀⠀⢀⠜⠁⣰⠁⠀⢀⡜⠙⢦⢲⡀⠈⣦⡀⠀⠱⡀
⠀⠸⡀⠀⠀⠢⠤⠤⠔⠚⠁⠀⣰⠃⠀⠀⡞⢀⠀⠈⠉⠀⠀⠓⢛⠀⠀⠈⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠒⠤⣀⣀⣀⣀⣀⠤⡶⠃⠀⠀⡼⠑⢌⡳⡀⣧⢦⠀⠰⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⢠⠶⣶⣶⣦⡤⠊⠀⠀⠀⡰⠁⠀⠀⠈⣇⠛⠊⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠸⡀⠈⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢸⢰⡤⡄⠀⢎⡷⠤⠤⠤⣤⠤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠈⠒⠢⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠘⡎⠷⠃⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⢠⠦⡀⠫⡷⠀⠀⣠⣾⣓⣒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣇⢀⣀⠀⠙⢷⡟⠚⠋⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠧⠤⠤⠴⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣸⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠉⠀⠀⠉⢿⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠻⠿⠃⠀⠀⠀⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢰⠟⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⣄⣀⣀⣀⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣽⡭⠝⠉⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡀⠀⢰⡟⠀⠀⠀⠀⠳⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⣤⣦⣤⠶⠞
⠀⠀⠀⠀⢠⠉⠁⠀⡿⠁⠈⣷⡄⠀⠀⠙⠲⠶⠖⠐⠛⠁⣦⡀⢀⠆⠀⠠⣾⣤⠀⠴⠒⠋⠙⢧⠙⢆
⠀⠀⠀⠀⠈⠀⢀⣤⢁⣀⣀⣼⣿⣷⣤⣤⣤⡤⠤⠤⠠⠒⠉⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠔⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣋⡠⠤⢶⣋⣁⡀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠷⠀⣀⠀⠀⠀⠀⠀⣠⡶⠘⢦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢁⣤⡄⠈⢣⡄⠀⠀⢰⠉⢀⣤⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⠸⣿⠀⠸⣿⠀⢰⣇⠀⣸⡟⡸⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣋⣻⢂⡼⠁⠀⠀⠹⣄⢻⣋⣱⡿
⠀⢀⠄⢂⡁⠈⠀⠠⡀⠀⠀⠀⢀⡜⠙⢻⣥⠀⠀⠀⠀⠀⠨⠉⠛⢿⠀⠀⠀⠀⢀⡠⠐⠂⠀⠂⠠⡀
⠰⠃⠔⡵⠚⠛⠲⣶⠀⢢⣠⠒⠁⢀⡴⠛⠃⠀⠀⠀⡀⠀⠰⣷⠀⠀⠳⣄⢀⡠⠁⣠⢴⣶⣿⣶⣄⠈⢂
⡇⠀⢸⡇⠀⠀⠀⠈⡄⡈⡇⠀⣰⠏⠀⠀⠀⠀⢀⣀⡁⠀⠀⠈⠂⠀⠈⠉⠉⠀⠐⠥⡾⠃⠀⠈⢻⡇
⢣⠀⠪⢟⣦⣀⣀⠴⠿⡇⠃⣼⠋⠀⢀⣠⣤⣾⣿⢿⣿⣤⣀⣀⣠⡤⠴⠖⠶⠤⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠣⡀⠀⠀⠀⠀⠀⡸⠁⣾⠇⠀⢀⠈⡼⢿⣿⡟⠀⠘⢻⡟⠳⠷⣵⠳⡞⠛⠢⣌⡆⠀⠀⢂⣀⠜
⠀⠀⠈⠓⠀⢠⣤⠔⡡⠊⢹⠃⠀⠀⢰⠇⢸⢻⣿⠀⠀⠀⠀⠀⠀⢀⣛⠘⠀⠀⢹⡇⠀⠀⠈
⠀⠀⠒⠒⠒⢂⠴⠚⠒⠀⠘⣆⠀⠘⣼⡴⠃⢠⠿⣳⡀⠀⠀⠁⣾⠛⠁⠩⠂⠀⣸⠂⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠴⠤⠤⠿⣄⠀⠈⠙⠚⢅⡀⡑⣷⡄⠀⠀⠙⢦⣀⣆⣴⠀⠉⠀⠀⡐⢦⡁
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⡀⠈⢣⣾⡏⠀⢀⠄⡀⠀⠀⠈⢀⣀⠄⠈⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌⠛⣿⡄⠀⡏⠀⡀⢚⢀⡁⠀⠁⢀⠈⠛⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡝⠀⢀⠤⣿⠁⢀⢶⡊⣰⠃⠁⠀⢈⡇⠀⡅⠐⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣀⣰⣡⠾⠃⢠⠦⡀⠁⢸⣶⡶⠶⠛⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣉⡀⠠⠂⠁⠀⠈⠒⠈⠠⠤⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⢀⣀⡀⠀⠀⣠⣴⣦⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠉⠻⣿⠋⠉⢻⡆⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠻⢧⣀⠀⢀⣴⠟⠀⠀⠘⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠚⠉⠉⠉⠛⠻⢿⣶⣦⣤⣤⣽⡿⢿⣁⠀⠀⠀⠀⠈⣙⣿⣿⣿⣷⣶⣶⣶⠿⠛⠋⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠉⠉⠉⠁

⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡟⠉⠉⠉⠉⠙⢛⠛⡏⠉⠙⠛⣟⣟⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⢛⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⡇⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⠀⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠈⠀⠐⠁⠁⠃⠆⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠐⣿⡷⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡞⠀⠀⠀⠄⠀⡠⠄⣠⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣿⡇⡇⠀⢀⠀⣿⡇⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢿⡇⡇⠀⠸⠀⣿⡿⠀⠀⠀⢠⠒⠁⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢀⠀⢸⣿⠀⠠⢠⠄⠀⠠⡤⠄⡤⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣸⡇⣇⠀⢰⠀⣿⣇⠉⠁⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣻⡇⣟⠀⢰⢀⠸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠎⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠕⠊⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣻⡇⣿⠀⠀⠈⠀⠁⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⢀⠀⢸⡇⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣽⡇⢷⠀⡀⠀⢠⣦⠀⠂⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣄⠘⡄⡚⢻⣤⠀⠀⠀⠀⠊⠉⠀⠃⠀⠁⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢿⡇⣿⠰⣿⣿⣿⣿⢳⠄⣸⠆⡟⢰⡀⠀⠀⣠⠞⠀⣷⠀⡈⣆⠘⡄⢸⡿⡀⠀⠀⠀⠀⠀⠀⠄⣠⠄⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢸⡇⢹⠀⠘⠉⠉⠀⢫⠀⠀⠘⠀⠀⢳⣀⠞⠁⠀⠀⠙⠀⠀⠈⠀⠀⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⡜⡇⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠈⠁⠘⡄⠀⠀⠀⠖⠀⠀⠆⢐⠄⠀⢸
⣷⡆⠀⠀⠀⠀⣿⡇⢸⠀⠀⢠⠀⣀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠀⠀⠈⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⢼⠀⠀⠀⠀⠁⢏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠰⠀⠐⡀⠀⢸⡏⠀⠠⠄⠠⠤⠀⠈⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⢸⠀⠀⠄⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⢀⣤⣶⣬⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⢸⠀⠘⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⡟⠛⠻⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡇⢸⠀⠀⠃⠤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠁⠠⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣽⣇⢼⣤⡈⠀⣶⣆⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠉⡄⠀⠒⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠿⠿⠤⠴⠤⠤⠿⠟⠻⣿⡈⠙⢲⣦⠤⠤⡤⠤⣤⠒⠋⠉⣿⠿⠃⠶⠶⠶⠶⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠓⠺⠿⢤⣄⣀⣸⡿⠧⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⣀⣶⡄⠀⠰⣿⣄⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⢿⠟⣦⣤⣄⠍⠛⠛⠋⣡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣰⣿⣿⣽⣄⡀⣀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢒⠋⠉⠉⠀⠀⠀⠉⠉⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠠⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠄⢸⠿⠾⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⢄⣈⣉⡆⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠐⢡⠀⠀⠀⠀⣸⠀⠂⠂⠀⠐⠀⡈⠄⣈⣾
⠀⠀⠀⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢃⣇⣉⣉⣉⣀⣣⡴⠏⠋⠁⠃
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠉⠂
⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠄⠤⠀⠀⡈⠙⠀⠀⠀⠀⡥⠂⠐⡤⠲⠀⠀⠀⠀⠀⠀⠠⢚⠧⠆⢀⡨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣠⠁⠂⠀⠀⠀⠀⠐⠀⣀⠄⠀⠈⠈⠀⠀⠀⠀⠀⣈⡑⠀⠈⢦⠍⠗⠀⠀⠀⠀⠀⢰⣀⡆⠀⠀⠀⠀⠀⠀⡀⠀⡈⠂⠂⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢯⠄⢄⡀⠨⣄⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡘⢈⣀⠀⠄⡀⠀⠀⠀⠀⠀⢠⠁
⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠀⠌⠄⠊⠀⠀⠀⠀⠀⠀⠀⡨⠄⠀⠀⠀⠀⠀⠉⠀⠄⢑⡠⠗⠄⠀⠀⠀⠀⣎⡀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢇⠐⢠⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠄⡈⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠤
⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠑⠄⡀⠀⠀⠈⠑⢄⠀⠀⠀⠀⡌⠀⠀⠋⠉⢃
⠀⠁⠚⠋⠀⣙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⠠⠌⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠱⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠
⠤⣀⡀⠀⠀⠈⠑⠠⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠈⠀⠀⠀⠀⢠⠔⠊⠉⠀⣰⠃⠀⠹⡄⠀⠀⠀⠀⣭⡦⠀⠀⠀⠀⠀⠜
⡀⠈⠗⠓⠦⡀⠀⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠴⠃⠀⠀⠊⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠈
⠀⠀⠀⠠⢀⠀⠍⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠐⢂⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢜⡁⡒⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠜⠝⠂⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠂
⠀⣀⠐⠀⠀⠀⠀⠀⠀⠌⡰⡆⠙⠀⡐⠀⠄⠀⠀⠀⠀⠠⣌⠔⠁⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣠⡴⠞⡋⠁⠄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠐⠠⠄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠐⡉⢸⡶⠚⠀⠀⠀⠀⠀⠇⡃⠀⠀⠄⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠃⠶⠗
⠂⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣢⣀⣈⢁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠹⡙⢄⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠲
⠀⠀⠈⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠠⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⡁⠀⠀⣈⠐⢄⠀⠀⠀⠀⠰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠠⡤⠔⠒⠊⠉⠈⠉⠀⢳⠀⠀⠀⠀⠀⠀⠠⢁⠀⣉⣁⠁⣁⣁⡀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⢀⡀⠤⡖⠈⡆⠀⠀⠀⠀⢠⠃⠀⠀⠈⠤⠃⠀⠀⣘⡄⠀⠀⠀⠀⠀⢀⠈⠈⠉⡉⣀⠉⡁⣁
⣀⠤⠀⠄⠀⠀⠀⠀⠀⣆⡀⠀⣀⠀⠀⠀⠁⢼⡇⠀⠀⠀⠀⠀⢖⡠⠤⠄⠒⠲⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⢈⣉⣉⣀⣁⠉⠔⠁
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⡀
⠀⠀⠀⢀⠐⢠⡀⢢⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠊⠉⠁⠂⢀⠀⠀⠀⠀⢀⢔⡉⠁⢐⡠⠠⡨⠀⡁⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄⠈⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢟⠻⠷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠷⣟⣃⣴⠈⣋⠀⠀⠀⠀⠀⠀⠰⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡆⠀⠀⢠⣤⠶⢤⣄⡀⢠⣼⠇⣈⡉⠿⢦⡉⠴⠆⠀⠀⠀⢀⡠⠀⠈⠒⣄⠀⣠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣨⡟⠁⠀⠛⣩⡴⡞⢠⣭⣝⠀⠀⣀⣄⠀⣘⠷⣾⡋⣀⣀⣴⣦⡀⠉⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠂⣠⠃⠀⡀⢸⡿⠉⣇⠈⠋⡷⠀⠉⢻⡎⠙⠛⠋⠁⠈⠳⣄⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠈⣿⠂⠀⢻⡜⠇⠀⢹⠀⠀⢡⠀⠀⠀⠙⠆⢠⣈⣐⠀⡀⠀⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠈⢿⣄⠀⠀⢀⣿⡁⠀⢸⣿⠀⠀⠸⣆⠀⠘⢿⣤⣀⡀⠀⠀⠉⠉⠛⠛⠃⠀⠙⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠻⠦⠤⠜⠃⠀⢀⡜⠃⠀⠀⠀⢿⣆⠀⠀⠉⠉⠉⠉⠒⢄⠀⠀⠀⢀⠀⠀⠀⠳⣄⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠔⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠈⠻⢦⠴⠟⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⡏⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣭⣟⢦⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⢿⣿⠟⠋⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣧⣀⠀⠀⠀⢀⣀⣤⣴⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠈⢹⣦⠉⠿⢿⣿⣿⣿⣿⣿⣿⡟⢹⢿⣟⠿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣧⣠⣈⡉⢛⣻⠿⠛⠋⠁⠛⠁⠢⠀⠀⠀⠀⠤⠂⠘⣿⣿⣿⣿⠿⢟⣛⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⣼⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣵⣾⢀⣾⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⢷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣿⣿⣿⣿⣿⣿⡿⢸⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠂⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣹⣾⣿⣿⣿⣿⣿⠿⠛⠛⠛⠁⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣼⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣿⣿⣿⡟⠛⠛⠻⣿⣿⣷⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⣾⣿⡟⠁⠀⠔⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢻⣿⣿⣿⣿⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣱⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⠷⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣷⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣶⣾⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣀⣤⣶⣾⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⠿⠿⠟⠋⠁⠀⣰⡿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣶⣶⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⡿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣠⠆⠀⡄⢠⣄⡀⢉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⣾⠏⢠⣴⣿⠀⣿⣿⡌⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣰⣯⣿⠀⣾⣿⡟⠇⢿⣿⣯⡘⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢔⣿⣯⢾⣷⣦⣿⣿⣷⢀⠸⣿⡏⣷⡟⢾⢿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⢋⠁⢤⣶⡟⣵⣻⣿⡟⣼⣿⣿⣿⡟⣃⠻⣷⣼⣿⡞⣯⢻⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣸⣮⡊⣙⢉⠻⠟⣫⣾⡏⣿⣿⣿⡿⣗⣶⡘⡫⠙⠻⠞⠧⡛⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣥⣾⣿⣿⣿⡿⠷⣎⠱⣿⠾⠿⣯⣿⣿⣿⡃⢶⣿⣿⣮⡢⣘⣶⣶⣷⣯⢿⣷⣟⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣾⣿⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣋⣄⣘⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠛⠛⠛⠛⠛⠒⠶⢤⣀⡀
⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠚⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢻⣴⠟⠉⠀⠀⠀⠀⢠⠎⠀⣀⠀⠀⢀⢴⠀⠀⢻⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠇⢀⢾⠃⠀⣠⠋⢸⠀⠀⡏⢣⠀⢹⣦⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡏⢠⠋⣼⠀⣰⠃⠀⣿⠀⢠⡇⠈⣇⠀⡏⢣⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠇⠈⣿⢠⡟⠳⠄⣿⠀⡼⠜⠙⠻⡄⣿⠒⢧⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠘⣇⠀⠀⠀⠀⠀⠀⣸⠁⠿⠀⠀⢹⣼⠀⠀⠀⢹⡸⠁⠀⠀⠀⠹⡇⠀⠈⢧⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠸⣆⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⢀⣻⣀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣀⣀⡘⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⣆⠀⠀⠀⢸⠁⡇⠠⠖⠛⠉⠉⠉⠓⠀⠀⠀⠀⠀⠰⠛⠉⠉⠉⠉⠉⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠈⢧⡀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠹⣤⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠈⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⡇⢸⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢸⠀⠀⠀⢸⡇⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⣳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢸⠀⣾⠀⠀⠀⠀⡇⠈⣿
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⡏⢀⠍⠓⢦⣀⠀⠀⣀⣠⠤⠖⠋⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣿⠁⠸⠀⠀⠀⠸⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇⠀⠀⠀⠀⣇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣸⢹⠀⢀⡇⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡏⣿⠀⢹⢡⠀⠀⠠⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⡿⡆⠀⢸⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⢸⠀⢈⡬⠖⠒⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡟⠀⠀⠀⠀⢸⠙⣇⠀⠀⢧
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⣇⠬⢶⠉⠀⠀⢠⠏⠀⠂⠀⠐⠀⠀⢀⣠⠖⠋⠀⠇⠀⠀⠀⠀⠘⠀⠸⡀⠀⠈⠄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁⠀⠘⡄⠀⠀⢼⠀⠀⠀⢀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣿⡏⠀⣿⣿⣿⣿⣿⣿⡿⠀⠃⠈⠂⠀⡠⠀⠀⠀⣠⠀⠀⢰⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠉⣿⡇
⠀⠀⠀⠀⢻⣷⣾⢟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⢴⣿⡄⠀⢀⣴⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣳⣴⣿⠃
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢤⣾⠦⢷⢀⡾⠩⣿⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⣹⣿⡀⣠⠞⠈⠉⠉⠀⠁⠉⠀⠢⣤⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠉⠀⠈⣏⠉⠙⠛⢁⡇⠀⠙⠛⠯⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠒⠋⠀⠀⠀⠇⠀⠀⠉⢻⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠑⠔⠀⢀⠀⡀⠄⡂⠁⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣶⡾⠃⠀⠀⠀⠀⠀⢠⣶⣶⠈⠀⢢⣄⡀⢀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠟⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢵⣿⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠞⠘⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⠛⠷⣶⡄⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⡏⠈⠉⣣⣶⠿⣿⣿⣧⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⠛⠁⢀⣴⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡖⠂⠀⠀⢀⣴⡿⣻⣿⣿⣿⣿⣿⡿⠿⣷⡌⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢳⣤⣤⡶⠟⠉⢰⣿⠋⢸⣿⠇⢹⣿⠀⢻⡇⠘⢧⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣰⣿⠏⢀⣿⠇⠀⢾⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⣾⠟⠁⠀⢸⡇⠀⠀⠘⢧⣤⣬⠇⠉⠀⠈⠀⠈⠁⢈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⣀⠀⢼⡇⠀⠠⡀⠸⣇⡀⡢⠀⠀⠀⠀⠀⠁⠠⠀⠠⠀⠀⢬⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠳⠤⠴⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⠙⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡯⣠⣀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣵⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⢷⣦⣀⠀⠀⡏⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠋⠓⢦⣀⣞⣀⠉⡻⣷⣤⡇⠀⢐⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠸⢶⡀⠀⠉⠠⣿⠄⣷⠈⠿⠀⠀⠻⠿⠋⠀⠀⢀⣴⠂
⠀⢀⢴⠂⠀⠀⠀⢠⣿⡇⠀⠛⠃⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠘⣾⣦⣄⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠐⢠⣶⣶⣦⠄⠀⠀⠀⠀⠈⠁
⠀⠀⠈⠙⠛⠋⠀⠉⠉⠙⡆⠀⠀⠀⣀⣠⡼⠿⠿⠆⠐⠒⠐⠂⢒⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠰⡛⢿⠝⠂⠀⠀⠐⢷⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⡄⠰⠀⢀⠇⠀⢣⠀⠀⠸⡇
⠀⠀⠀⠀⢀⣼⢧⣀⠔⠁⠀⠀⠈⢦⠁⠀⡄⠀⠀⠠⠤⠶⠂
⡤⠀⠀⣠⢿⣿⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⢻⣶⣄⡀
⠀⠀⣰⠏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⢀⡇
⠋⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠻⣿⢷⣄⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⡏⠘⢿⣷⡀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡟⠀⣰⢡⣿⣾⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⡄⣹⠘⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⢉⣍⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⡆⢾⠷⠿⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⡘⠉⡣⠤⠤⡎⠀⠙⢷⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠂⡀⠀⠀⠀⠰⣷⣤⡶⠃⠀⠀⣼⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠁⠀⠀⢰⣤⣶⠔⣃⣀⣠⣾⠏⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⣶⣿⣷⣶⣞⣻⣹⠛⠉⠉⠉⢁⣀⡀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⡟⣟⠫⠻⠿⣿⣿⣽⣒⢤⣶⣹⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣿⣿⣶⣷⣷⢾⡈⢿⣿⣿⣾⣿⣿⡷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣭⣿⣿⣿⣽⣟⢿⣿⣎⡿⠿⠿⢿⣿⣷⡘⣄⠀⢀⠖
⠀⠀⣠⣶⣾⢷⣶⡄⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⣆⡀⠀⠀⠘⠻⣜⣧⣴⣾⣧
⠀⣼⣿⣿⡑⠾⠟⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⡿⣿⣿⣿⣦⣤⣤⣠⢿⣿⣿⣿⣿⡆
⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣽⣿⣿⣻⠛⣋⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⢉⣙⣛⡛⠋⢉⣿⣿⣿⣿⠏⠙⠻⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢰⣿⣯⣻⣿⣶⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠉
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠛⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣭⣿⣄⠀⣤⣾⠿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁