Freak out Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠳⣇⠙⢆⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣈⡷⣄⢈⣶⡞⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⢤⡟⠋⠙⢣⠀⣰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⢀⣀⣀⣨⠷⠋⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣉⠁⠂⢉⡰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⡤⢤⢤⡴⠶⢶⡄⠘⡿⠉⠁⠀⠘⢆⠀⠀⠀⠀⢀
⠀⡀⠄⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠈⠀⠉⠀⠀⠀⠈⢻⡦⣯⡀⠀⠀⠀⠘⡇⠀⠀⠠⢁⡆
⠀⠱⡌⠀⣇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠛⠀⠀⢀⣀⣠⣠⠦⢶⡆⠀⠀⠁⠈⡹⠆⠀⠀⠀⡧⠀⠀⡀⢠⠁
⠀⠀⢹⡘⢧⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣌⠀⠀⣀⠿⣩⠀⠩⠦⠈⢹⠄⡀⠀⠀⢹⣦⠀⠀⠀⡇⢠⠒⠃⣹⠦⠄
⠀⣰⣻⠟⠲⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡻⠀⠀⣯⢈⠁⠀⣠⠂⠐⡈⠙⣿⠀⠀⣼⡁⠀⠀⢠⢃⠷⣻⡋⠹⣤⡖⢢
⠀⡜⢧⣾⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⡀⢀⣸⠇⡀⠰⢻⠜⢄⡡⠋⠐⠰⠇⠀⣹⠇⠀⠜⣳⠀⠀⡘⢠⠈⠛⠉⠲⠀⢻⡁
⠀⠈⢿⣙⣃⠀⠇⠀⠀⢀⢀⣠⣴⣿⣿⣿⣿⣿⣗⡆⠡⣷⣾⣅⠀⠀⠀⡸⠿⠗⠀⣰⣾⠟⠀⢠⠃⠀⠑⠤⡀⠠⠇⣰⠃
⠀⠀⠀⠀⠙⡀⠈⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⢨⠤⠽⢿⣿⠟⠓⠶⠶⣳⣿⣷⣤⣤⣧⣠⣤⣄⣀⠿⠒⠃⠉⠐⠲⢄
⠀⠀⠀⠀⠀⢣⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣒⡠⠄⣀⠉⠀⠀⢰⣏⠛⠋⠭⠩⠁⠐⠚⢡⣇⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠘⡆⠀⠹⣿⡿⠻⠦⠉⠱⠿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠶⢧⣶⣦⣿⣿⣧⣄⣠⣠⣄⣤⣶⣿⣿⣿⠟⠀⢀⡤⠚
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠤⠄⠀⣴⢤⠄⡁⠈⠽⣿⣿⣿⣿⣿⠟⠙⠲⠾⣿⣿⠟⠛⠯⢬⣉⡙⠛⠛⠛⠛⠉⣁⣤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⡦⠊⠁⣀⣢⣀⢠⣶⣿⣿⣿⣿⣟⠀⠀⠀⠀⠸⣁⠀⠀⠀⢀⣟⠉⠍⠋⡿⠫⢥⣟⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⣼⠋⣍⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣷⠄⠀⠙⡷⢀⡤⠚⣄⠀⠀⠉⠉⠙⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣠⣾⣝⣛⣛⣫⣾⣿⣿⣿⣿⡟⠀⠀⢀⡀⠀⠀⣰⠋⠁⠀⠀⢠⠃⠊⡴⠎⠘⣷⡀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⠃⠀⢠⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢧⣀⣠⠞⠳⣴⡞⠁⠀⠀⠀⠀⢿⡀⠟⠀⠀⠀⠙⡙⢦⡀⠄⢀⠀⢀⡟
⠀⠀⠀⠀⠀⢨⡰⠟⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠑⢄⠈⠙⠁⠀⠀⠀⠀⠀⠀⢠⣄⠈⠫⡳⣤⡀⠀⠀⠘⢄⠋⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣩⣉⣥⢠⣤⠴⡌⠀⡆⢶⣶⣲⡔⢲⠀⠀⢀⠀⢀⣴⠟⠀⠑⠒⠊⠀⠙⢦⡀⠀⢀⢣
⠀⠀⠀⠀⠀⠻⠿⢿⢀⣙⣊⣛⣉⡩⠭⠽⠓⠲⠦⣅⢨⠴⠒⠒⠛⠛⠛⢶⠚⠋⢁⡴⠒⢲⡀⢠⠤⠶⣦⢙⠦⠞⠋
⠀⠀⠀⠀⠀⠀⡟⠉⠉⣩⣄⣠⣿⡄⢰⡏⠉⣳⠀⢈⣿⠀⠀⠺⠿⡍⠛⠛⠀⣠⠎⡴⢦⠀⢧⢸⠀⣴⢫⠏⠳⣦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠴⣧⠀⡇⢠⣍⠉⢥⡶⠋⣿⠀⠀⢾⡿⠷⠒⢳⡞⠁⣤⣝⡋⠀⠘⡿⠸⣧⢎⣠⡴⠾⠃
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠰⡞⠛⠀⢷⣤⡿⠳⠴⠟⠂⠸⢤⣤⡤⠤⠶⠶⠚⠛⠲⠟⢼⣥⣀⣰⠃⠀⣀⠯⢥⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢹⡄⠀⠀⠠⢲⢉⡶⢨⠀⢱⡤⠐⣦⢠⠼⢷⢘⢵⠛⣂⢢⣤⠏⠙⣦⣸⡏⢧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⣠⡾⠁⠀⠀⠘⠠⠊⠉⡈⠄⠣⢃⠀⢸⠌⡢⣼⠀⣨⢞⡑⢫⣐⠀⡀⠈⠻⠃⠘⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠸⣶⠋⠀⠀⠀⠀⠀⣈⡦⠞⣤⠆⢠⠆⠳⠋⠴⠷⠾⠶⠯⢼⡇⢀⡇⢠⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠄⠀⠀⠀⠀⢀⣐⣮⡉⠐⣀⣀⠀⠀⠐⠀⡞⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠠⣠⡄⠠⡖⠁⢸⠀⢀⡀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢽⠋⡄⠈⣦⠸⡜⠁⠈⠻⣶⡆⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠃⠰⠳⣘⡀⢃⠀⠀⠺⣇⠀⠀⣀⡔⢁⣀⣀⡤⠄⠒⠂⠉⠉⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⠁⠒⡺⠉⠉⢉⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⡓⡲⠿⠁⠀⠀⠈⠀⠀⠀⠀⠈⠓⠲⠤⣄⣀⣀⣀⣀⣀⣀⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣉⡉⣤⠀⠀⠀⡀⠠⡤⠀⠒⠖⠐⡆⠀⢠⡌⣥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡌⢀⡔⠈⡇⠀⡇⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠊⡇⠀⡆⠀⡥⠄⠼⡀⠀⡇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠘⡄⢃⠀⠘⠉⠀⠀⠀⠘⠶⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣀⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⢊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣩⣉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⠉⠒⠤⠄⣀⠀⠀⠀⣀⠄⣀⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠂⠄⠀⠀⠀⠉⠁⡲⢧⠀⡏⠱⠾⣗⠢⢄⣀⠀⠀⠀⠀⢀⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢡⡖⠀⠀⠈⠐⠢⠼⢀⠀⢛⠳⡀⡇⢞⠦⠦⣝⠓⠢⡤⠠⡄⠼⡡⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡶⠁⢱⡀⠀⠀⠀⠐⢄⣀⡁⠘⠄⠘⢿⠀⡱⠐⢌⠑⢲⣇⢀⠃⣸⠀⠡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡔⠢⡜⢀⠌⠀⠀⢸⠆⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⢾⣿⡇⠀⠀⠑⡙⠨⢎⢡⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠷⡝⠾⡄⠃⠀⢹⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢀⣤⡊⠑⡀⠈⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠛⢚⡠⢤⡵⠠⠊⠀⠀⠀⠸⠤⣄⣀⣀⣀⣀⣀⣀⣀⣤⠤⠀⠚⠉⠁⠀⢈⡦⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠆⠧⠀⠠⠖⠀⡄⠀⠀⠑⢤⡀⠀⠀⠀⠀⠺⠠⠤⠀⣀⠀⣰⠻⠅⠀⣈⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠐⠲⠋⠙⡀⠉⠒⢢⡤⣤⢀⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⣨⠖⠂⠹⡖⠛⠃⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⠀⠤⠔⠚⣭⠞⢆⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠲⠂⠂⠀⠶⠖⠒⠚⠒⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⢰⠀⣆⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣈⢠⡆⢸⠀⣇⣿⢀⡿⢠⡿⠁⠠⠀⠀⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⢳⣶⣿⣿⣆⣷⠠⠂⣽⣿⣼⣷⣿⣾⣼⡃⢠⡟⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡼⣿⣿⣿⣿⣿⣿⣳⣞⣿⣿⣿⣿⣧⣿⣿⣡⣟⣮⣞⣡⡶⣡⣤⡞⣁⣄
⠀⠀⠀⠀⠀⠀⢀⠀⢇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡾⣛⣥⢾⣫
⠀⠀⠀⠀⠀⢀⠺⢧⣌⢶⣄⣜⢿⡿⣿⣿⣿⣟⡿⠿⠟⠙⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣻⣯⣥⣴⣴⣆⣀⡀
⠀⠀⠀⠙⢢⣝⡳⣄⡙⢷⣌⣻⢿⣿⣾⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠄
⠀⠀⠀⠈⡆⢌⡙⣻⣟⣿⣯⡻⣿⣿⠏⠀⣠⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⣿⣿⣿⣿⣵⣾⣿⡗
⠀⠀⠀⠈⠘⣿⣿⣾⣷⣶⣍⢿⣿⠋⠀⠎⠁⢀⡀⠀⢢⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡁⠸⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠐⠠⠻⣿⣿⣿⣿⣿⣿⡿⠀⠈⢀⡦⠞⣛⠃⢄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡌⠳⠀⢸⣿⣿⣿⣿⣿⣯⣽⣶⣯
⠀⠀⠀⢈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠸⣇⣾⣿⡇⠈⠀⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣹⣻⡿⣻⣿⠿⣷⣇⣀
⠀⠐⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠄⠰⢷⡆⠀⠀⠀⠀⠀⠀⠙⠿⢿⡿⣿⣿⣟⣻⣯
⠆⠀⢉⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⢂⣭⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣭⢿
⢀⠘⢿⣥⣦⣾⣟⢫⣽⣿⣿⠿⣏⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡠⠴⠦⠴⠦⣄⡀⠘⠀⠀⠀⠀⢸⣿⣷⣴⣿⣭⣟⣻
⠁⠀⠘⢿⣿⣿⣽⣿⣿⣿⣿⣾⣷⠀⣠⣄⠀⠀⠀⠂⢀⣴⣼⣤⣤⣦⣤⣶⣶⣷⠀⠆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠹⢯⠷⣿⣿⣟⣽⣿⣿⠆⠙⣿⡄⠀⠀⠀⣼⣿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠃⠀⠀⢰⣿⢷⣽⣿⣿⣿⣯⣟
⠀⠀⠀⠐⣥⠣⠾⢋⣿⣿⣿⣿⣿⣷⡄⠸⣿⡀⠀⠀⢿⣿⣬⣄⠒⣹⡟⠈⢻⡟⠀⠀⠀⢠⡟⣿⠿⣿⣿⣿⢏⣿⡁
⠀⠀⠀⠀⠊⢀⣔⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⢿⡄⠀⠈⢻⣄⠄⠀⠐⠒⣂⣼⠁⠀⠀⣰⣿⣿⣾⣿⢾⣿⣿⡄⠐
⠀⠀⠀⠀⠠⠚⠛⢻⠿⣼⣿⣿⣿⣿⣿⣿⣄⡘⢿⣄⠀⠀⣍⠻⣷⠶⠖⠪⠀⠀⠀⣰⣮⠟⢿⢿⣿⣷⣯⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠡⣾⣿⣿⣿⣿⣿⣿⣧⣄⡻⣶⡄⠙⠓⢶⠶⠆⡀⠀⠀⠀⢻⡛⣦⢼⡆⠙⠉⠫⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣧⡿⠋⢿⣿⣷⣿⣽⢦⣀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡿⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣷⣷⣿⣶⡦⠀⠀⠀⠀⣿⣿⣺⣤⣄⢁⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⣠⣶⣟⣿⣿⣿⡋⠀⠀⠀⠈⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠾⠿⠿⣿⣿⣿⣿⣻⣿⣿⣿⡁⠀⠃⢀⣴⡟⡿⣿⡿⣿⠛⠉⠀⠀⠀⣀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠠⠐⠊⠓⠀⠀⠀⠈⠁⠀⠉⠛⠿⣻⣿⣻⣿⣿⣦⣴⣿⢿⠯⣷⣿⠇⠉⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⠿⠟⠃
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⣺⡅⣻⠈
⠠⠤⠄⠤⠤⠤⠄⠄⠀⠀⠀⠀⠐⠂⠈⢉⠀⠀⠀⠀⠀⠀⡄⠞⢻⢿⡇⠶
⠀⠀⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣾⡧⠍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⡀⠄⠈⠀⠀⠄⡄⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⠄⠀⠀⠀⠉⣁⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡔⠉⠀⠀⠒⢠⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡌⠀⠀⠊⠁⠈⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⠠⠀⡠⠂⠐⠢⢀⠢⡀
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠤⠄⠀⢧⠀⠀⠣⣀⠀⣠⠃⠀⠠⢀⠀⠀⠀⠀⠀⢀⠎⣠⠒⠶⡄⠀⢹⡌⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣉⠠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠸⣄⠣⣀⡴⠃⢀⠌⠁
⠀⠀⠀⠀⣤⢄⠉⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠉⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡐⠁⠀⠀⠀⠱⠀⠀⠀⠀⡠⠀⠒⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠐⠤⠐⠊⠀⠀⠀⠀⠀⢰⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⡠⠌⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⠀⠀⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡠⠖⠋⠀⠀⡠⠂⠞⢐⡁⠀⠀⠀⠀⠠⠨⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠞⠈⠠⠊⠀⠀⠈⠀⠀⠀⠈⠠⠀⠀⣠⠀⠀⠈⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢃⠀⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠉⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣠⣿⣿⣿⣄⠀⢀⣴⡾⠋⠉⢻⣿⣦⣀⣠⡾⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣠⣤⣼⡿⠁⠀⠹⠿⡿⠟⠁⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠈⣿⡀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠉⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⠜⠋⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣦⡴⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣴⡄⠀⠀⠀⠀⢰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣴⣶⣾⣿⣷⣶⣦⡤⠶⠿⠿⠿⠿⠿⠿⣷⣿⣿⠿⠿⣿⠃⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠛⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⠀⠀⠀⠀⠀⠀⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢶⡄⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⡆⠀⢀⣤⣤⠀⠀⢰⡆⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⣶⠀⠘⠇⠀⠀⠀⠀⠀⠀⠸⡃⠀⠘⠿⠿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡄⠉⠉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⣶⡆⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣄⡀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡀⢸⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣦⡀⣤⣦⣄⠀⣴⣶⣀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⠿⢿⡿⠟⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⠀⠀⢀⣀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠉⢻⣿⡿⢳⣶⣿⡟⢱⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠋⠀⠀⠈⠉⠁⠈⠙⠋⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⣴⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡇⠀⠀⠀⣿⣿⠁⣀⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣶⣿⣇⠀⠀⠀⣿⣿⣿⡟⠛⠛⠛⠛⠛⠻⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠉⠀⠀⠙⠿⠿⢿⣿⡦⠼⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣾⠟⠛⠁⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⣠⣤⣤⣤⣤⣤⣤⡾⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⢠⣶⣶⣶⣶⣿⡿⠉⠙⢻⣿⣿⠟⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠰⣿⣯⣀⣀⠈⠙⠃⠀⠀⠀⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣠⣤⣾⠿⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣾⠟⠁
⣶⣟⠉⠉⠉⠀⠀⠀⠀⢰⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡟⠀⠀⣠⣶⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋
⣿⣿⠟⠛⠂⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠿⣿⣿⣷⣤⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠛⠷⣶⣶⡄⠀⠀⣀⣀⣶⡶⠛⠛⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠟⠋⢱⣶⣟⠉⠉⠉⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢻⣿
⠀⠀⠘⠻⣧⣤⣾⠿⠃⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⡴⠿⠿⠿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⠂⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣋⢴⣶⠄⠀⠀⠀⠀⣿⣿⣷⣄⣰⣾⠟⠉⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⡀⠀⠀⣠⣿⠟⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⣿⣁⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⠟⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⠋⠉⠛⠛⠛⢿⣿⣷⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣄⣶⣶⡶⠛⠛⠛⠻⠿⠿⢿⣿⣿⣷⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣬⣛⣻⡿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⢷⣶⣤⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣤⣤⣴⠛⠛⠛⠛⠛⠛⠛⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠂⠛⠋⠛⠉⠀⠀⠈⠙⠻⢿⣿⣿⣮⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡽⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣴⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣅⣿⣷⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⢻⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠝⣷
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐⠂⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣃
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣵⠀⠀⠠⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⣛⡀⢀⡄⠀⠀⠻⠁⠘⠀⠈⣾⣅⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⠋⣻⡯⠭⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⢹⡇⠀⠈⠀⠀⠐⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠘⣿⡟⠁⠀⣴⣿⣿⣆⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠸⠇⠀⠀⠀⠀⠀⢀⡉⠳⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣟⣛⡉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⣇⣿⣿⣿⣝⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠸⡾⠂⠰⣆⠀⠀⠒⠒⢐⣢⠔⠂⠁⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠁⢆⣀⠙⠣⢠⣴⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⡟⠉⣻⡟⠋⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⣿⣿⣴⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⣾⠃⠀⠘⣷⠧⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣬⠹⣯⣩⡴⠎⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠈⢰⡏⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⠉⢁⣴⣦⠀⠀⠀⠀⠑⠀⢄⣀⠘⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡈⠛⠁⠀⠀⠀⠀⠀⠔⠋⠁⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣤⣀⣀⡠⢴⡶⠋⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠋⠻⡿⣿⣆⠀⠀⠀⠀⣀⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠀⠀⠀⠀⠘⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠁⠀⠃⠈⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠄⠀⠀⠚⠂⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢀⠠⠤⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂⠀⠀⠀⢀⠤⠒⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⢀⠜⠁⠀⣀⣈⡑⢆⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠀⢀⣀⠀⠀⠀⠂⠁⠀⠀⠀⠀⡜⠀⠀⡎⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⠊⣠⠞⠉⠙⠢⢄⡑⣄
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠠⠤⠀⠀⢳⠀⠀⠙⢄⡀⢀⡜⠀⠀⡰⢠⠇⠀⠀⠀⠀⠀⡼⢁⡴⠲⡶⡀⠀⢹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠑⠠⠀⢀⣈⣁⡠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⢄⣠⡴⠀⢀⠜⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣀⠉⠓⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠔⠊⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠒⠃⠀⠀⠠⠴⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡜⠁⠀⠀⠉⢢⠀⠀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣀⣀⡠⠚⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡜⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠘⠦⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⡛⣡⢀⠄⠀⠀⠀⠀⠄⢀⡔⠀⠏⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠠⠔⠉⠀⠀⠀⠀⠋⠀⣡⠤⠂⣀⠄⠀⠀⠄⠁⠃⠀⡴⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠠⠊⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⡜⠁⠀⠈⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠁⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢸⣧⡀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠙⢦⣼⡆⠙⠁⠈⢷⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢛⡉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠿⠻⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠃⢀⡄⠀⢀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⢈⡿⢁⡄⠀⠀⠀⠀⣀⠀⠀⠋⣀⠐⠀⠀⠀⠈⢰⡇
⠀⠀⠀⠀⠀⠀⣰⠏⠰⠉⣤⠁⠀⠀⠀⠀⠀⠂⠀⠀⢻⡀⠃⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠤⠠⠂⠀⠀⠐⠃⠀⠀⠀⠐⢶⠇⠀⠀⠠⢿⡆
⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣼⠁
⠀⠀⠀⣀⡴⠛⠁⠀⠀⠈⠁⣀⠀⠀⠈⡁⠀⠀⠀⠀⠀⡁⠀⠀⠘⣷⡲⢤⣤⣀⣀
⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡈⠀⠀⠀⢀⣵⠀⠀⠀⠀⠙⠶⣤⣈⠉⠛⠶⣄
⡞⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠸⠀⠀⠀⠁⣀⡴⠚⠉⠉⠳⣄⠂⠄⡀⠀⠀⠉⠑⠂⢄⡈⠳⣄
⠉⠙⠓⠶⠒⠶⠚⢿⡆⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣠⡤⠦⡄⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⠟⠁⠀⠀⡇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡾⠁⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡞⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣦
⠀⠀⠀⠀⢀⡽⢂⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⢳⣆⡀
⠀⣠⠞⠉⠈⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠦⣿⣄⣀⠀⠰⣟
⠀⠛⠒⠚⠛⠛⠛⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⠈⠛⠂⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣤⣴⣶⣶⣶⣶⣶⣒⣒⣒
⣿⣿⣿⠟⠻⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡇⢀⣤⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣏⠀⠀⠀⢹⡆
⠀⠀⠀⠀⣤⠤⢤⣄⡘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠹⣆⠀⠀⠀⢻
⠀⠀⢀⡞⠁⠀⠀⣼⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢻⡄⠀⠀⠈
⠀⢀⡾⠀⠀⠀⣼⠁⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢻⡄
⠀⣼⠃⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⡀⠀⣀⣀⣠⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴
⣸⠇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠉⣹⠟⠉⣯⢁⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⢿⣀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⠞⠁⠀⠀⣿⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⣄⡴⠋
⠀⠙⠳⢦⣿⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠶⠦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠚⠋⠉⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠒⢶⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠓⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠘⣧⡤⠴⠖⠛⠉⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⡿⠀⠀⠀⠀⠀⠘⣦⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠶⣤⣤⣤⣄⣀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⣴⠄⢰⣦⡀⠰⣶⢦⣴⡶⣦⣴⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠯⠿⠤⠾⠛⠷⠴⠿⠉⠹⠿⠉⠀⠽⠇
⠀⠀⠀⠀⠀⣤⡤⣤⠀⢤⣤⠀⢤⡤⠀⢤⡄⠀⣠⣤⣄⣤⣄⣄⣤⡤⣤⣤⡤⣤⣤⡤⣤⣠⣤
⠀⠀⠀⠀⠀⣿⣛⣿⢠⣿⢻⣧⣸⣧⣦⣼⣧⣦⠿⣤⡿⠘⣿⢻⡿⠀⣿⣧⣄⣿⣧⣄⣿⠻⣿


⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠠⣄⠀⠀⠀⠀⣠⠄
⠀⠀⠀⢀⢴⣽⠧⠀⠴⢿⣴⢀⠀⠀⠁⣤⢶⢭⡁⠈⣩⡤⣤⣈⠀⠀⠀⢠⣶⣷⠀⠀⣾⣶⡆
⠀⠀⠀⠈⠛⠓⠀⣀⡀⠐⠛⠃⠀⠀⠀⠉⠛⠛⢁⢀⠓⠛⠋⠀⠀⠀⠀⠐⠽⠏⣀⢀⠙⠯⠖
⠀⠀⠀⠀⠰⣄⣀⣉⣀⣠⡴⠀⠀⠀⠀⠀⢀⣀⣌⣈⣄⣀⠀⠀⠀⠀⠐⢁⠀⠀⠈⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠏⠀⢀⡀⠈⠇⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠋⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⡤⠔⠁
⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠚⣩⣉⣍⠙⠂⠀⠀⠀⠀⣄⢉⠢⡀⢀⢔⣉⣤⠀⠀⠀⠀⢋⣝⣦⠀⠀⣰⣫⡉⠂
⠀⠀⠀⠀⠀⠀⠻⢿⠟⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠙⠛⠋⠀⠀⠀⠀⠈⠛⠹⠀⠀⠏⠛⠃
⠀⠀⠀⠀⣤⠤⣀⠀⣀⡤⣤⠀⠀⠀⠀⢀⣀⠀⠙⡟⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠛⠚⠀⠀⣀
⠀⠀⠀⠀⢿⣴⣿⣿⠿⢦⣿⠀⠀⠀⠀⠀⠹⣧⣿⣿⣶⡏⠁⠀⠀⠀⠀⠙⠿⣶⣿⣿⡶⠿⠏
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠇⣷⢰⡗⢰⡇⢿⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⡶⠿⠶⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠟⠈⠃⠘⠃⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⢻⡟⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠶⠶⠶⠶⠀⠀⠘⢷⣤⡾⠁⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⢸⡇⠀⢀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⠶⠶⠶⠶⠶⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⡿⠷⠶⠶⠿⣿⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⣀⡀⠀⠀⠀⢀⣤⡶⣿⠋⢿⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠸⠿⠟⢀⣤⠾⣯⠁⠀⠸⣧⣘⣧⠀⢀⣴⠿⠷⠶⠶⠶⠶⠶⠾⠋
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡾⠁⠀⠙⠷⣦⣄⣈⣿⣵⡾⠛⠁
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⢠⡟⠀⠀⢠⣶⣦⠀⠀⠀⠀⢹⡄
⠀⠀⣾⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠘⣷
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠃
⠀⠀⠈⠛⠻⠶⠶⠟⠛⠛⠛⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢻⡟⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣶⣯⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣲⣶⡶⠶⠶⡶⡾⠿⣿⣶⣆⣀⣀⡀
⠀⠀⠀⠁⣇⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡇⡇⠀⠨⡶⠋⠁
⠀⠀⠀⣇⡏⠉⠉⠉⠉⠉⠑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠓⠒⠒⠀⠰⣇
⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⣶⣶⣶⢶⣶⣄⠀⣶⣿⡿⣿⣷⡀⠀⠀⢀⡹⣒⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⡏⠀⠀⢹⡆⠘⣿⠀⢹⣿⣷⣿⣿⣧⠀⡰⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠣⣄⣀⡼⠃⢸⣇⡂⠀⢿⣿⣿⣿⣿⣇⢇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢽⣷⡘⣿⣿⣿⣿⣿⡞⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢻⣿⣿⣿⣿⣿⡽⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⣿⣿⣿⣿⣿⣷⢱⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠸⣿⣿⣿⣿⣿⣧⢣⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢻⣿⣷⣼⣿⣿⡎⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣬⠯⠭⠭⠗⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⠴⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡠⠞⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⠢⣈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡴⠋⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⢄⠉⠢⣀⠀⠀⢀⡴⠋⣠⠖⢁⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠙⠦⣈⣳⠞⢁⡤⠊⡡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡶⠋⣀⠔⢋⡤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⡠⠚⣡⢔⠙⢦⡈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢥⡴⢋⡠⠊⠀⠀⠙⠦⡉⠲⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡩⢊⠁⠀⡱⠃⠀⠀⠀⠀⠀⠀⠈⠲⣌⠗⠁⠬⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊⠁⠘⠒⣁⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠐⢌⡢⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⡑⢄⢀⡠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡁⠀⠀⢈⢶⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡶⣴⠋⠂⠣
⠀⠀⠀⠀⠀⠀⣀⡤⢼⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠇⠀⢀
⠀⠀⠀⠀⢀⡜⡁⡰⣡⣤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⠘⠿⡒⢦
⠀⠀⠀⣠⢊⠎⠰⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠊⠊⠢⠳⡀
⠀⢀⡴⠁⠂⠀⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠄⠑⡙⢄
⡠⠊⡜⠀⠄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠠⢨⠳⡀
⠑⢄⡁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠃⢘
⠀⠀⠈⠓⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀⡠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠚⠙⠉⠙⠙⠒⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠶⠾⠁⠀⠀⠀⢤⡠⠤⠤⡠⠄⠀⠀⠀⠹⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡄
⠀⠀⠀⠀⢠⣶⠟⠇⠀⠐⠊⠑⠒⠢⠀⠀⠀⠀⠀⠔⠒⠒⠉⠒⠀⠘⠟⢷⣄⠀⠀⠀⠀⠀⢰⢻⢸⣷
⠀⠀⢀⡤⣾⠷⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣦⡀⠀⠀⠀⢸⣾⢸⣿⡀
⠀⠀⠸⣿⣿⣄⣀⣀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢀⣾⣀⣀⣠⣾⣷⡟⠀⠀⠀⢸⢿⢸⣿⡇
⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⠋⠀⢀⣠⣶⣿⢸⣿⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠙⠻⣯⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣯⡿⠋⠛⠉⠁⠀⠀⠸⠟⠛⢻⠈⣿⠀⡟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠖⠛⠛⠛⠛⠛⠉⠉⠉⠹⠛⠛⠛⠛⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠤⠶⣷⣤⣴⣤⣤⣤⣴⡷⠦⠤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡇⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢿⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢸⡇⢀⣿⡇⢸⣇⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡏⡟⠏⠉⠉
⠀⠀⠀⠀⠀⢀⡤⠔⠉⡩⡤⠖⠂⢸⡇⢸⣿⣧⢸⣿⠀⠒⢤⢌⡉⠳⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣀⣤⣤⣿⣇⡾⣿⠿⣌⣿⣤⣤⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⢸⠀⢸⢸
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠉⠀⠈⠛⠀⠀⠀⠘⠁⠀⠉⢻⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢿⠘⣦⠏⣸
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢶⡤⢷⣤⣴⢦⡴⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣤⣺⣟⣟⣻⣿⣿⣿⣭⣭⣽⣿⣟⣋⣀⣀⣀⣀⣐⡷⠶⠿⣗⡤⠤⢴⣻
⠀⠀⠀⢀⣀⣀⣤⣴⣶⡶⠶⠛⢻⣿⡿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠉⠁
⠀⠀⢿⣿⣿⠿⠟⠋⠁⠀⠀⠀⣿⣿⠇⠀⠀⠀⠘⣿⣿⣧⡀
⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣀⣀⢀⣀⣀
⠀⠠⠀⠋⠋⠛⠚⠛⠛⠓⠠⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠒⠉⠓⠀⠉⠀⠉⠒⠘⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⣙⠇⠀⢀⠢⡤⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⢀⡀⣀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠡⠀⠀⠈⠉⠀⠁⠁⣤⠈
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⡄⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠠⠌⠀⠠⡀⠀⠀⠀⠀⠦
⠀⠀⠀⣤⣀⣤⡀⣀⣀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡹⠟⠚⠛⠛⡦⠆⠀⠀⠠⠉⠀⠀⠀⠀⣴⣼⣳⣿⡶⣤⡄⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⠂
⠀⠀⠀⠀⠘⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⡞⠀⠈⠀⠀⠀⣀⠁⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢁⠻⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⡀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠀⠀⠀⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠢⢄⠀⠀⠀⠠⣀⢀⡀⡀⠀⢂⠤⣀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠻⠟⠶⠓
⠀⠀⠀⠑⠒⠂⠀⠀⠀⠈⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢀⠠⠤⢄⣀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣀⣀⣀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢹⣂⣴⣷⢖⡟⡛⠾⣙⠲⣖⣶⡿⣛⣾⠿⠦⣼⡿⠤⠙⠋⠁⠀⠀⠈⠀⢐⡴⠒⢂⣀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣶⡿⣫⡾⠁⣾⣀⣱⡀⢉⢴⣬⡉⠉⢁⡠⠖⠒⠒⠢⠦⣤⣀⣀⣀⣀⡠⠔⠃⣴⣾⠭⠟⢉⡀
⠀⠀⠀⠀⠀⠀⢀⡛⢿⣉⠈⢦⠟⠉⠛⣧⡄⠀⠀⢱⠞⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠳⠶⠤⢤⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⢳⡆⢀⣶⡄⠈⢇⢀⡐⠁⠀⣠⣴⣿⣭⣭⣍⡙⠲⠦⣤⣤⠴⢾⠳⢓⡯⢷⣿⣭⣴⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣷⣿⣿⣻⣦⠔⠋⢀⡴⠚⣉⣥⣶⣿⢣⢒⠈⢦⣤⣤⣤⣦⣵⣾⠭⠴⣬⣿⣿⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣝⡲⣄⣝⣮⣉⣉⣁⣤⠴⣋⡴⠛⠁⠀⠀⢦⠔⢩⡵⡀⠙⠉⠉⠉⢉⣵⣞⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⠷⠶⣶⣿⣿⣿⡶⠟⠩⠴⠶⢤⣤⣴⣮⣂⣢⠜⣜⢄⠀⣀⣤⢟⡵⣫⡹⣾⣿⠏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣱⡟⠓⠆⢶⢦⣤⣄⣀⣀⣠⣴⠯⠖⢚⣽⣟⡿⢯⠭⣟⣾⣷⣟⡹⣴⣿⣛⣹⡿⠟⠁⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣟⠿⡔⠦⡀⠈⠲⢬⢉⠉⢀⣠⣔⢾⣟⢋⣭⣽⡆⣠⣾⠟⣳⠿⢛⣋⣉⣭⣥⣤⣴⣾⣻⡟⣮⣻
⠀⠀⠀⠀⠀⠀⠀⠦⠀⢵⠀⠀⣶⣴⡞⡉⠙⠛⠳⣤⡉⢿⠔⠈⠋⠙⡿⢡⣾⡷⠚⠋⠛⠙⠒⣶⣾⢟⡗⠟⣻⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠸⡄⠀⡎⢿⣿⣶⣿⣷⡾⣿⣿⣦⢫⠜⢠⢠⠀⣾⠿⡿⡓⣣⢚⡼⠞⣋⣭⢽⢿⠟⡻⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⡟⠆⡛⠛⠾⢾⣞⠽⠫⣿⡟⣰⢣⠃⣰⠏⣿⡿⡇⣰⠟⣠⡞⢻⡶⣶⣮⣔⣁⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢧⠐⣷⠤⠬⢭⣿⣦⢹⣞⡳⣼⣇⣧⡏⣰⡿⣥⢈⣶⡿⠋⣰⡿⣫⢚⠷⣾⡿⡋⢙⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢦⣜⣿⣅⣚⣟⣛⣻⡵⠜⣛⡉⠥⠬⢬⣩⡟⣛⣋⣠⡶⠋⣈⣠⣍⡛⠰⠴⡞⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠻⡙⠛⣻⠿⠶⣦⣽⣤⡶⠐⠒⠚⣼⣷⣯⣬⣥⡶⣟⠉⢺⣼⣯⣿⠻⢛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⣳⣦⣬⣮⢤⢤⣄⠈⣟⠻⠰⡥⣀⢉⣽⠟⡞⠹⢹⢟⢺⡳⢦⣭⡾⣹⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⠀⣶⣿⡄⣺⣶⠋⢀⠜⡠⠋⠨⠃⠜⡡⠁⠎⠼⠀⠛⣧⠀⡧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠼⠾⢱⣿⢁⣄⣰⣛⡋⢳⡒⣂⣋⢉⣲⣤⣾⡂⠈⠩⡆⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣮⣿⠁⣵⣬⡙⠮⣝⢀⣀⣉⡉⠍⠚⠉⣻⠽⠇⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣈⣁⣟⠀⠀⢈⡼⢉⠔⣡⠄⡠⠈⣳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⣴⠶⢋⡠⠋⡴⢁⡞⡰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠁⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣏⣑⣲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡠⠤⠤⠤⠤⢤⠤⡀⠀⠀⡗⠒⢦⡀⢀⡖⠓⢦
⢻⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠿⠀⠀⠀⠀⢸⠀⠈⠀⠀⢳⠀⠀⠉⣉⠔⠉⠙⠃
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣷⡒⠋⠁
⠀⠀⠀⠘⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢿⡀⠀⡿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠻⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⠁⠀⠀⣀⣿⠓⡄⢠⡴⠖⠒⠋⠁⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣅⡀⠀⠙⣉⡰⢃⣾⣿⡀⠀⠀⢀⠠⠒⠊⠒⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠟⠁⣸⡇⠀⠀⡀⠀⠀⠀⠀⢈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠁⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠐⠤⠤⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠛⠛⠛⠛⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠐⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⢦⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⣄⠈⠙⠳⣤⡀
⠀⠀⠀⠀⢀⣴⠟⠁⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⢳⣄
⠀⠀⠀⣠⡟⠁⢀⡴⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⢻⡑⣆⠀⠀⢻⡆
⠀⠀⣰⡟⠀⢠⡟⠁⣴⠃⠀⠀⠀⢀⠶⠶⠶⠶⠶⣶⣶⣶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠘⡇⠘⣧⠀⠀⢿⡀
⠀⢠⡿⠀⢀⡟⢀⡞⣿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣷⠀⠘⣇⠀⠸⡇
⠀⣼⡇⠀⢸⠀⡾⠀⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠋⠙⠃⠀⠀⠀⠀⠀⠀⠚⠛⠆⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣿⠀⠀⢻⠀⠀⣷
⠀⣿⠁⠀⠀⢰⡇⠀⡇⠀⠀⢠⡇⠀⠀⠀⠀⢀⡤⠶⠒⠒⠶⣄⠀⠀⠀⢀⡤⠖⠒⠲⢦⡀⠀⠀⠀⠀⢻⠀⠀⠀⡧⠀⠀⢸⡆⠀⣿
⠀⣿⠀⠀⠀⢸⠀⠀⢿⠀⠀⣸⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠘⡆⠀⡴⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⡄⠀⢠⡇⠀⠀⢸⠁⠀⣿
⠀⣿⡂⠀⠀⠈⠀⠀⠘⡆⠀⡟⠀⠀⠀⠘⠀⠀⣠⣤⣤⠄⠀⠀⠃⠘⠁⢀⣴⣶⡶⢄⠀⠈⠀⠀⠀⠀⠘⡇⠀⣸⠁⠀⠀⢸⠀⠀⣿
⠀⢻⣇⠀⠀⠀⠀⠀⢀⣹⣄⡇⠀⠀⠀⠀⠀⢸⣿⠟⠳⣴⡆⠀⠀⠀⠀⢸⡿⠋⢳⣾⠀⠀⠀⠀⠀⠀⠀⣇⣠⣇⠀⠀⠀⠈⠀⠀⡿
⠀⠘⣿⡄⠀⠀⠀⢠⠏⠁⢸⡇⠀⠀⠀⢂⠀⠀⠻⠦⠴⠟⢀⣀⣀⠀⠄⠈⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⢷⠀⠀⠀⠀⢠⡇
⠀⠀⠹⣿⡀⠀⠀⣿⠀⠉⢿⠁⠀⠀⠀⠀⠁⢄⣀⣀⣀⣴⡾⠁⠀⠉⠂⠐⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠓⡼⠀⠀⠀⠀⣼⠁
⠀⠀⠀⢹⣷⠀⠀⠸⣦⡀⢸⠀⠀⠀⠀⠀⠀⡔⡉⡁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠔⠐⠐⠀⠀⠀⠀⠀⠀⠀⣿⢀⠔⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢻⣧⠀⠀⠈⠉⢹⡄⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⣿⡄⠀⠀⣄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⠀⠀⠀⣿
⢀⣴⠂⠀⠀⣾⠁⠀⠀⢸⡇⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⡇⠀⠸⣇⠀⠀⢿⣆
⢸⣧⣀⣠⡼⠃⣠⠀⠀⣿⠃⠀⢸⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠀⢸⣧⠀⠀⠻⣷⣄⣈⠻⣷⣶⠞
⠘⢿⣿⣥⣴⣾⠏⠀⣼⠏⠀⢀⣞⡴⠁⠈⠳⣄⠀⠀⠀⠀⠀⣀⠳⠞⠁⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⢻⣧⡀⢿⣦⣀⠀⠈⠙⠛⢛⡟⠁
⢤⣤⣶⣾⣟⣁⣤⠞⢃⣀⣴⠟⠋⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠈⠓⠂⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠙⠻⠶⠽⠿⠿⠿⠶⠛⠉
⣀⣈⣁⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣶⣶⣶⣶⣟⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠖⠒⠈⠀⠒⠛⢃⡀⠀⠀⠀⠀⣠⣴⠶⠔⣇
⠀⠀⠀⢀⡶⠦⣦⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠀⠠⠄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠘⡄⢀
⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⣃⣀⣧⣤⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠖⠚⠛⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠡⠉⠠⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠘⣃⣤⣠⣤⣄⠀⠐⠲⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤
⠀⠀⠀⢀⠀⠀⠠⠠⠀⠀⠀⠀⠀⣴⢀⠖⠉⢀⠀⠀⢡⠈⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡤⣄⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠈⠈⠀⢀⠀⠀⠀⢀⡀⠀⠀⣸⢛⡁⠶⠈⠀⠰⠆⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣤⠟
⠀⠀⣤⠴⠂⠛⣡⡴⠦⣭⡁⢰⣿⠇⠀⢹⡄⠀⣠⠀⣴⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠠⣾⠏⠀⠀⠘⠿⠟⠻⣄⣀⣀⣈⠇⠀⠀⠀⡄⠀⠀⠀⢰⡞⢁⡴⢲⡄⠀⠀⠀⠺⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣤⠴⢮⣻⣼⡏
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⠃⠀⠀⠈⠁⠑⠀⣀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠀⠐⠀⠒
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⠄⠨⠀⠠⠅⠸⠀⠀⠓⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣭⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠵
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⣀⣠⡤⠠⠀⠀⠀⠆⠰⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡚⡒⠀⠀⠀⡀⠉⠵⠆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠁⣈⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⠆⠀⢨⣍⡥⠀⠁⠀⢁⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡤⠤⠀⠈⢙⠉⠀⠋⠀⠀⠤⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠻⠚⠴⢇
⠀⠀⠀⠀⠐⠶⠲⠶⠶⠶⠒⠂⠀⠀⠀⠰⠞⠀⠀⠀⠀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠓⠢⣤⠀⢰⣶⣀⠀⠉⢉⣴⠒⠀⠀⠀⠀⠀⡀⠂⡔⠀⠀⠀⠀⠀⠀⢀⠀⡔⢄⠀⠀⢤⣀⣀⠀⠀⠀⠀⢠⠾⠿⠋⠀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠁⠀⠀⠀⠀⠰⠶⠀⠐⠈⠔⠂⠀⠀⠀⢀⡀⠹⠋⠠⠄⠀⠀⠀⠀⢠⡟

⠀⣠⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡿⣤⣀
⠾⣆⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢀⡀⡀⢀⠀⡀⠳⢿⣬⣗⠲⠒⢢
⠻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡇⠁⠁⠈⣹⣿⣿⣿⣧⠀⠀⠛⠄⣟⠀⠀⠀⠀⠀⠀⠸⠸⠅⠧⠸⠀⠏⠗⠀⠀⠉⣴
⠀⢸⡛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠹⡟⠹⡿⣿⣿⡟⠛⢛⣿⡟⢋⣛⣛⣛⣛⠉⠉⠉⣿⣀
⠀⠈⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⡋⠉⠉⠉⠉⠉⢛⣿⢿⣿⣷⡀⠀⠡⠀⢰⣶⣶⣿⣿⣿⣿⣿⣧⠭⠭⠭⠵⠀⢠⣾⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣛⠿⠛⠛⠻⢿⣿⣿⣿⣿⣷⡻⡉⠋⠐⠤⠄⠤⠤⠂⠊⢏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⣆⡟⠀⠙⣿⣷⡘⡀⠄⢑⢀⠠⡠⠂⠰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⣴⠙⠁⠀⢀⣿⣿⡇⢱⠀⡀⠀⠀⠈⠂⠀⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠖⠚⠁⠈⠙⢾⡎⢊⠂⠐⠐⠄⠀⡠⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⣆⠀⡀⠠⠀⠈⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⡈⠪⠀⠀⠔⠅⠌⠠⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢡⠀⠀⡠⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⡆⠀⠂⠢⠀⠀⠕⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⠀⠀⠀⠀⡀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣨⣀⣁⣀⣀⣊⣂⣀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣽⠆⠀⡀⣀⡀⠀⠷⠶⠷⠇⣀⣠⣴⣦⡀⣀⣀⠄⣤⠀⠴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠛⠁⢀⣀⣩⣭⣤⣶⣶⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡄⢀⣼⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⣋⣉⣩⣭⡀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣶⠿⠿⣟⣚⣧⣬⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡇
⠀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣟⣛⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡿⠿⠿⠟⠚⠁
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠜⠉⠁
⠀⠀⠀⠙⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⢹⣿⠀⠀⠀⢠⣖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣯⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠻⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣤⣾⣏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠙⠛⠛⠛⠋⠉⠉⢀⡀⢀⣠⣤⣄⣰⣶⣶⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣶⣆⣼⣿⠀⣿⡇⣿⡟⢹⣿⠋⢹⣿⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⠁⠿⠇⣿⣿⣸⣿⢷⣿⡇⢸⣿⠀⣾⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠺⠿⢿⣶⡆⣿⡟⢻⣿⢸⣿⠁⣾⡿⠀⣿⡏⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣆⣸⣿⢹⣿⠇⣼⣿⠸⢿⠿⠿⠃⠀⠛⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠛⠛⠋⠈⢉⡀⢠⣤⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⠂⠸⠟⠀⠛⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣈⣀⣀⣤⣀⣤⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠬⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠈⠀⠀⠹⡀⠹⠋⣳⡍⣿⡴⢿⣟⠉⡝⠀⠜⡩⠊⠰⢁⠞⠙⠁⡠⠞⠁
⢤⣄⠀⠀⠀⠀⠀⠁⠈⢢⣴⠦⠤⣤⣄⡀⠀⠀⠀⠀⢠⢖⠛⣧⣄⢸⢱⠟⠋⠀⠀⣻⡜⣁⣤⣀⣁⣀⣀⢄⣀⣤⡈⠀⠀⠀⠀⣠⣔
⣒⠠⠀⠒⠄⠀⠀⠀⠀⣟⡀⠠⢀⠤⣼⠋⠗⠓⢀⢴⢟⡀⠀⠈⠀⠚⠓⡶⠀⠀⠈⠋⠉⠉⠀⠁⠠⠏⠀⢀⠃⠀⢻⡆⡠⠐⠉
⡒⠀⠠⠤⣀⠀⠀⠀⠀⣽⠂⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⠀⢠
⠉⠛⠂⠀⠀⠀⠀⠀⠀⠈⢲⡆⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠠⢿⠉⠉⡧⠀⠀⠀⢘⡆⠀⠀⠀⠀⠑⠉
⠤⠄⠀⠀⠀⠀⠀⢀⡠⠤⣴⢳⡤⠀⠀⠀⠀⠀⠁⠰⠐⠀⣀⠀⠀⢢⠈⡄⠊⠁⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠚⣫⠄
⠴⠒⠦⠤⠀⢀⡜⠉⠛⠁⠘⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠛⠉⠉⠷⣶⢦⡄⢀
⡒⠖⠂⠀⠀⣸⡏⠁⣀⠔⠚⠀⠈⠒⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⠟⣙
⢛⢉⡴⠎⠉⠃⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⡀⠶
⠈⣿⣀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠒⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤
⡒⡚⠻⠷⢶⣟⠀⠈⠳⢴⣎⡠⠀⠀⠀⠀⠀⠈⠀⢠⠀⠄⠆⠀⠀⠀⢀⠀⠠⠄⠈⠈⠀⠀⠀⠀⠀⠁⠀⠄⢰⡄⠀⠀⣀⣀
⢀⣀⡀⠀⠀⠘⠳⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠄⠀⠀⠀⠀⠀⢴⢼⠁⢤⠚⠋⠉⠂⢉⣉
⠿⠁⠀⠀⠀⠀⢀⠀⠍⠁⣻⠀⠀⠀⠀⠈⠙⠉⡉⠀⡀⠀⢀⣀⡁⠀⢆⠀⠀⠈⠁⠀⠈⠉⠀⡠⠶⣤⡤⠞⠋⢀⡖⠀⠈⠐⠒⠄⠠
⠈⠀⠀⠀⡠⠂⠁⠀⢀⣴⠿⣄⣄⣡⠴⡄⠀⣠⡷⢚⠂⠀⠀⣹⡍⠂⢢⣄⣀⣤⠟⠦⠴⢧⣀⣀⣶⠏⠓⠲⠞⠋⠁⠀⠈⠀⢄⠐⠠
⣖⠔⠊⠀⠀⡠⠔⠋⠙⠁⠀⠀⠀⠀⠀⠉⠋⣱⠃⠸⣏⣠⣴⠋⢷⡄⠀⠀⢡⠇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠁⠀⢀⡴⢋⡤⠊⢁⣀⣠⢂⡖⢠⢈⡠⠀⢰⢃⣴⣤⡌⢷⡱⢳⣧⣙⡃⢟⢉⠀⠀⠀⠁⠀⢰⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠢⣄⡈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⠤⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠙⠳⡂⢌⡛⢶⠤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠳⡃⠀⡤⠚⠉⠉⠲⣄⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠲⢌⠉⠓⠊⠙⠳⡴⠚⠓⠶⠉⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡇⠀⣀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡽⠄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠗⢋⣵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢿⠄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠦⡼⠘⢤⠃⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⡆⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⠀⠀⠉⢹⣃⣀⣤⣤⠶⠚⠉⠀⠀⠀⠀⠰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢈⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣁⣀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠅⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠆⠀⠀⠐⠒⠛⠻⠶⡄⠀⠀⠀⠀⠀⠀⠀⡤⢝⣷⣌⡉⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠉⠓⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠔⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⣴⣴⡀⣶⣾⡁⠚⠆⠀⠀⠀⠀⠀⠀⠀⢺⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠘⠇⢷⡏⠃⠙⠀⠀⠀⠀⡔⠢⠤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⣞⠉⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠙⠢⢤⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠰⣕⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣖⠚⠁⠀⠀⠀⠀⠀⠀⠁⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡏⠹⡄⠀⠀⠀⢀⡄⠀⠀⠀⡇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡘⠀⠀⠉⠓⠒⠚⠁⠘⠦⠤⠞⠁⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠰⣄⣀⠀⠀⢀⣠⣶⠾⠼⢶⣤⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢄⣽⣷⣶⣾⣿⣟⣥⣄⠀⠀⠈⠛⠻⢷⣄⡀⢤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣷⣽⠏⠁⡦⠊⠀⠀⠀⠀⠀⠀⠈⢲⣾⣿⣏⣴⡙⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡄⠀⠀⠀⡠⠔⠚⠓⠒⠄⠀⠈⠙⠍⠙⢿⣧⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠁⠉⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⡀⢠⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣧⡑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣾⣷⣄⢀⡀⢤⣠⢤⡀⠀⠀⠀⡠⠀⠀⠐⢺⣿⠁⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠈⢦⣙⠿⠿⣿⡛⣆⣈⣉⣙⣳⣶⣍⣂⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⢈⠛⠻⠿⠛⡋⠉⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡭⠭⠭⠭⠭⠭⠭⠭⠭⣽⢃⣀⣀⣀⣀⣀⣀⣀⣄⣏⢧⣿⣤⣤⣤⡤⠿⠛⢛⣛⡃⣀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣇⣸⣿⡆
⠀⢀⠈⠉⠁⠉⠉⠉⠁⠀⠉⠉⠈⠉⠉⠉⠉⠉⢿⠙⠉⠉⠁⠈⣹⢩⡽⢻⡟⣡⣤⣬⣭⣭⣭⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣾⣿⣿⣿⠃
⠀⠈⣳⣄⣀⣀⣴⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣾⠗⠋⣀⡾⠁⣋⣁⣠⣉⠉⢉⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣿⣿⣿⡟
⠀⠘⣷⣈⡛⢻⡿⣯⡆⣿⣦⠀⠀⠀⡆⠀⠀⠀⠀⣯⠲⠶⠶⠶⠶⣾⠟⠛⠻⣿⡿⣿⣿⣿⡶⠾⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣿⡷⣿⡍⢱⣧
⠀⠀⣧⠻⢿⣿⡿⣝⣧⢸⣿⣆⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠠⣽⣧⠀⠠⠶⠖⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡿⣧⣿⣿⣧⣿⣧⣼⣹
⠀⠀⢿⣏⡞⣾⣷⣿⡞⢆⠻⣿⡄⢸⣿⠀⠀⢀⣀⡄⡤⣞⣭⣿⡇⠀⠀⠀⠀⢘⣿⣆⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⠤⠒⢏⡁⣿⣿⣿⢸⣿⣻⣿⣿
⠀⠀⠪⣼⢸⣿⠗⣶⢭⡛⡇⢹⣿⣿⣿⣿⣿⣿⣷⡷⣿⡿⠻⣿⡇⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⢧⡀⠀⠈⣷⣿⣿⣿⢸⣿⢼⣿⣿
⠀⠀⢸⢣⣾⣿⡜⣿⣥⣽⢀⠀⣿⣿⢿⡟⠛⠁⢹⡧⢿⠃⠀⢹⡇⠀⠀⠀⠀⠀⠹⠿⣿⡶⣿⣿⣿⣿⢿⠟⠃⠀⠀⡀⠳⠦⣼⡏⣿⣿⣿⢉⢹⣺⣿⢾
⠀⠀⣿⢸⣿⣿⣿⢡⣥⣸⢸⣇⢸⣇⣘⣻⣆⢵⠌⠴⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠠⠟⠁⣿⣹⣿⣎⣘⣿⣿⢿⡀
⠀⠀⣿⡈⣿⣿⣿⡠⣿⣿⡆⣿⣿⣿⢹⠙⢻⣖⡶⠲⠒⠒⠂⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣋⣽⠶⢤⣀⠀⠀⠀⠀⠀⠈⢢⢊⢏⢩⣿⣿⡟⢩⣍⡾⠇
⠀⠀⣿⢰⣿⣿⣿⣷⣜⢶⣄⣿⣿⣿⡉⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣮⡿⡿⣎⡽⢳⡦⣤⣤⡴⣫⣤⣼⣸⣿⣽⣵⣰⡿⠃
⠀⠀⢻⡎⣿⣿⢟⣿⣿⣷⣽⣿⣿⡏⠁⠀⠀⠀⣤⠴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣵⡟⣈⠇⣼⣇⣬⠒⢛⣮⠷⣼⡿⣿⠛⣹⣿⡀
⠀⠀⠋⣿⣹⣷⣏⣴⣿⣿⡿⣿⣿⣶⠀⢠⡎⡘⠀⢛⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢋⢹⡕⢿⠓⣷⣼⢨⡇⣶⣶⡉⢯⣽⣷⠟⠀⢻
⠀⠀⠀⢸⣿⣯⣻⣿⣿⣿⣽⣿⠏⠀⠀⣿⡇⠃⢠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣿⡿⣭⠾⠶⠾⠏⠚⠛⠉⠉⠉⠛⠳⠿⠀⠀⠈
⠀⠀⠀⠀⠻⣿⣯⠙⣛⣭⣿⠏⠀⠀⠀⣿⠇⢦⡀⠉⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⢠⣿⣿⡇⢻⣷⣿⡆⠀⠀⠀⢹⡀⠀⣸⡲⡀⠀⢜⢿⡄⠀⠀⠀⠀⠀⢀⢮⠋⠀⢾⠀⠀⠀⢨⡗
⠀⠀⠀⠀⠈⢻⣿⡄⢠⣿⣿⠃⠀⠀⠀⠈⢧⡀⠸⣷⡈⠀⠀⠈⠻⣦⣀⠀⠀⠀⡨⣾⡀⣠⣎⣻⣦⣴⢟⣥⣴⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠐⢿⣿⣇⢀⣿⣯⠇⠀⠀⠀⠀⠈⠳⣦⣬⣉⠳⠀⢄⠀⠩⠝⠟⡿⢡⣤⣤⢥⡄⢤⣤⣴⡆⢸⣿⣿⣟⣘⣛⣋⣙⣟⣛⣓⣆⣐⣂⣐⣲⣰⡃
⠀⠀⠀⠀⠀⠀⣿⠃⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠰⣦⣔⡠⡄⢠⡇⠷⣿⣽⣯⡟⣾⣷⣿⡇⢿⠿⡟⣟⢹⠋⠉⠉⢉⢉⠙⠋⢉⡙⠋⠛⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠦⣀⡀⣀⠀⠤⢶⠶⣖⣶⣶⣷⣶⡶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠖⣿⡿⣫⣿⠟⠋⣠⢐⣨⣵⣾⣿⣿⣿⣟⣭⣶⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⡾⢛⡟⢡⣾⣯⣾⡟⣡⡨⣶⣵⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢿⣿⣿⣿⣿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣾⣿⠀⣾⢁⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠟⢋⣴⣿⠿⣿⣿⣿⣿⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣤⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠿⠻⠟⠻⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣄⣠⣤⣄⣀⣠⣄⡀⠀⠠⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡯⠀⠇⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡇⢠⣾⣿⠟⠋⠉⠉⠉⢉⣭⣍⡉⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠉⠉⠙⠻⣿⣿⡆⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⣾⣿⣎⡸⢏⠀⢀⣤⣴⣶⣷⣿⣿⣿⣿⣶⣦⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⠀⠙⣧⠀⣿⣿⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡾⣍⣿⡏⠁⠿⣉⣽⢻⡟⢩⣽⣭⡙⢿⣿⡿⠿⠃⠀⠠⣿⡟⣹⣿⡿⠛⣩⣭⡉⠻⣿⣿⣧⠀⠀⠀⢿⣷⠟⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣽⠿⡇⢸⠀⠉⠳⣾⠇⣼⣽⣯⣥⣤⣿⠆⠀⠀⠀⠀⣿⠘⠙⠿⢠⣜⣛⢻⠃⠀⣿⡿⠛⠃⣤⠀⡼⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢇⠀⠀⠈⠀⠀⠀⠙⠾⢷⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣉⣡⣤⠾⠏⠀⠀⠀⠘⡶⢈⡆⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⢲⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣘⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡅⠘⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡀⠀⠀⠀⢠⡀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠔⢸⣷⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢻⡟⢿⢿⣦⣤⣼⠿⣿⣼⣿⣿⠀⠀⠀⠀⠀⡀⠃⡜⠀⣽⣛⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣹⡿⣿⡿⣿⣿⣟⢿⣏⠀⠀⠀⠀⠠⠎⠀⠀⡼⠀⣤⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠻⣿⡆⠀⠀⠀⠀⢠⣾⣷⢞⣇⢼⣴⠆⣜⡷⢾⣦⡀⠀⠀⠀⠀⢿⡶⠁⣔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⢷⡄⠀⠀⣰⣿⣾⢷⣾⣿⠷⠿⢾⣿⣿⡾⣿⣷⣆⠀⠀⢊⠼⣿⢘⡐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠸⢧⡿⣶⣾⣷⣾⣿⣿⣿⣷⣤⣶⣶⣾⣿⣿⣿⣧⣺⣷⡶⣾⣾⣟⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⠛⠿⣿⣿⣿⡟⠁⠹⡿⠿⢿⣿⣿⡿⠉⢻⡿⣿⣿⠿⣻⡏⠂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢠⣽⣿⣿⣿⡄⠀⠈⠁⠉⠈⠁⠀⢀⣾⠁⠰⠂⣰⠋⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣾⣿⣿⣿⡏⠛⠦⣄⣤⣤⣤⡤⠖⠟⣁⠔⠀⠌⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⣀⣂⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡖⠲⣯⣍⣉⣩⣭⣩⣉⣨⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣸⣿⠈⠉⠓⠲⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡖⠒⠒⠒⠶⠶⠶⠦⠤⢤⠀⣀⣀⣀
⠀⠀⢀⣿⠿⣀⣛⣛⣋⣓⣒⣐⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣠⣦⡼⢧⡤⠘⢿⣛⣛⣻⣟⡷⠈⢛⣡⣶⠿⠃
⠀⢠⣿⢿⡝⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣷⣀⣸⣦⣀⣀⣀⣁⡀⡌⢿⣁
⠀⠘⣿⣌⣋⣿⣶⣶⣶⣶⣶⣶⣶⡾⠿⠿⠿⠿⠿⠟⠛⠛⠛⣛⣿⣭⢻⡯⠉⢻⣿⠿⠿⠟⢻⢿⠖⠂⠈⠉⠳⡀
⠀⠀⢨⣿⣿⣜⠛⠒⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣟⣼⠷⠶⣾⣿⣀⣠⣤⣤⡞⠀⠀⠀⣴⣷⡳⡄
⠀⠀⠘⣿⣈⢿⣴⣶⣶⣶⣶⡿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠈⣿⣧⠀⠛⠛⢛⠋⠉⠉⣠⣤⡄⣸⣿⡿⣿⣿⣆
⠀⠀⠀⠈⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣧⣶⣼⣿⣿⣧⢰⣿⠋⣷⣿⣿⣿⢿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⡌⢿⣟⣼⡇⢠⢿⣿⣿⣿⣗⡾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠭⠽⠒⠉⢸⣿⡿⣿⣷⢽⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⣿⣿⣯⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣿⣿⡿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⣄⠠⢤⣑⠢⡄⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣲⣾⡿⠿⠿⡻⢟⢿⣆⣀⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣁⣩⡽⢷⡍⠂⠐⣄⣠⣄⠛⠿⠿⡑⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣬⣕⣒⣻⣣⠔⣂⣤⣭⠶⠦⠴⠄⠠⠀⠈⠿⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⠉⠉⠀⡴⠉⠀⠀⠀⠀⠀⠀⢀⡂⠰⡀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣭⡍⣩⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⢾⣿⢾⠁⠀⠀⠀⠀⠀⠀⢦⡾⠷⠤⠀⠀⠀⠀⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠐⡤⠀⠈⢳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⠃⠀⠀⠂⠀⡀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⢻⡏⠀⢀⣇⣀⢀⠙⠒⣋⠉
⠀⠀⠀⠀⠀⣠⢔⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⠀⠈⢧⠐⠋⠈⠉⠀⠀⢠⡾
⠀⠀⠀⠀⣼⠁⣵⣠⣿⡇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⡀⠡⢀⣦⠀⠑⢊⡞
⠀⠀⠀⠀⢿⣿⣷⣿⣿⡟⠀⠸⣷⣤⣤⣤⣤⣄⣀⠀⣀⣿⡿⠋⠉⠲⢬⠀⡈⢁⠒⠳⠤⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢸⡧⣘
⠀⠀⠀⠀⠸⠋⣿⠉⣿⣿⡄⢀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⢀⡞⠙⠐⠉⢻⣿⣮⣧⠀⠉⠉⢿⣿⣿⡇⠀⠀⣠⣆⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠸⣀⠀⠀⡴⠁⣻⡟⠻⣿⠀⠀⢸⡟⢿⡇⠀⠀⠉⠙⠓⠃⠙⠊
⠀⠀⠀⠀⠀⠻⠂⣤⣧⣰⣿⣇⠀⠀⠀⠀⢸⡷⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⠛⠋⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡀⠀⠀⠀⠀⠈⠳⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠀⠀⠀⢸⣦⣄⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢀⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡈⠉⢁⠀⠏⢠⣋⣀⣀⣀⣤⣶⠊
⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⠛⢻⣕⣶⣢⣧⣶⣷⣶⣶⣿⣿⡿⠋⠉⠉⠁⡀
⠀⢨⡉⠓⠒⣲⣌⣀⣔⣄⣁⠀⡄⠀⠀⠀⣠⣬⢤⣍⣛⣃⣬⣽⣷⣿⣿⣻⣩⣙⣻⣟⣿⡿⠁⠀⠀⠈⠉
⠀⠈⣯⣫⣭⡶⠟⢓⣺⡟⣏⠀⠀⠒⠶⠾⠋⠉⠳⣬⣭⣯⡭⢴⣶⣶⣾⣿⣽⡯⢷⡿⠋⠀⠀⢀⠄⡘
⠀⠀⢛⣫⣟⣽⣟⣑⢎⣽⣮⢳⠂⠤⠤⠤⠦⣤⠀⠀⢨⣿⣿⣿⣿⢷⣶⣾⣽⣿⣋⣤⣄⣤⣶⣅⡠⠓
⠀⠀⠀⠉⠉⢙⣻⣖⣻⣯⢺⢆⠀⠀⠀⢀⣀⣌⡇⠀⢸⣿⡟⠁⣤⡀⠨⣙⣫⣽⣷⢮⡉⠍⠛⢦⣄
⠀⢰⣄⣛⣲⣤⣤⣷⠳⣗⡷⡘⣟⡝⣏⣽⣛⢟⠇⠀⠈⠛⠛⠮⣭⣤⣭⡶⣶⣄⠁⠠⠉⣰⠀⢸⡯⠛⠴⢤
⠀⠈⢮⡋⢓⡙⠘⢻⣧⠈⣿⢿⣓⣋⣩⢥⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⢷⣿⣧⡴⠮⣄⣀⣀⣤⣱⡖
⠀⢀⣄⠈⠀⠈⢻⠧⣿⣷⣌⡳⠭⡭⢶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣛⣻⡵⣋⣝⣪⣉⡉⠙⠛⣃
⠀⠘⢧⣄⠀⢊⣍⣙⣾⣿⣿⣻⣿⣿⣿⣿⣾⣶⠊⠁⠀⠀⠀⠀⠠⢀⣧⣬⣉⣫⣽⣿⣶⣿⠿⠛⠛⠿⠥⠞⠉⣀
⠀⠀⠦⠜⢉⠀⣿⣟⡭⣿⣿⡿⠿⣿⣿⣍⣿⣿⣿⣷⣦⣤⡄⣠⠀⣿⠿⠷⣷⡞⣶⣾⢷⡾⣒⣚⡳⢄⡀⠀⢸⠃
⠀⠀⠉⠙⣶⣿⣻⢏⠞⠛⢙⠯⣁⣲⣬⢭⣿⣻⡿⠛⠛⠋⠀⣿⠂⠙⡟⠷⣿⣟⠿⠿⣿⡿⠭⢍⢻⣤⣥⠄⠁
⠀⠀⠀⣨⠝⠋⠁⠀⠀⠊⠉⠳⠖⢶⣽⣷⣽⣽⡇⠀⠀⠀⠀⣾⣄⠀⣇⣤⣼⡳⣭⣽⠏⠀⠁⠀⣧⣨⣥⠛⠛⠁
⠀⠀⠀⠹⠰⠄⠈⠀⡄⠐⠀⠀⢀⣁⣉⠿⠿⠾⣧⣀⣀⣠⣴⣿⣥⣾⠿⠋⠉⠑⠦⠜⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠋⠀⣀⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⠁⢀⣠⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠟⠋⠁⣀⣤⣶⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠛⠉⢀⣠⣴⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣧⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣶⣿⣿⠃⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⣿⣿⣿⣿⣷⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠛⢿⣄⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⠷⠶⣂⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⣀⣴⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠉⠻⣿⣦⣄⣠⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠟⠛⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠻⣿⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣽⣿⣷⣄⡀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⡛⠛⠋⠉⠉⠉⠙⠻⣿⣶⣤⣀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣿⠃
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⣀⣠⣾⠟⣿⣿
⠀⠀⠀⠀⠘⣿⣧⡈⠙⠻⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⠟⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣮⢳⡐⡄⠀⠀⠀⠀⠀⠀⡄⣾⠈⢁⡀
⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⣧⢳⡀⢀⣤⣤⣤⣀⣷⡸⢀⣾⡇⠀⠀⢀⣶⣮
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣸⣿⣟⣷⣿⣿⢟⣛⣿⣿⣷⣼⣿⣷⣶⣷⣿⣿⣃⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢹⣶⣾⣿⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣭⣿⡿⣹⣿⡟⠁⠀⢀⠍⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⣤⣄⠀⠄⢘⢓⣏⠀⣠⣿⣎⣻⣿⣿⣿⣿⣯⣭⣻⡿⣿⣿⣿⡿⠉⢰⣿⣏⣤⠀⠀⠈⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢿⣷⣷⡦⣈⠁⠀⣾⡟⣛⢛⣿⡿⡿⣿⣟⣭⣽⣷⣶⣾⣿⣡⠀⠈⢿⡿⣿⣾⣶⣶⣀⣀⠈⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠺⡦⠀⠀⠀⠀⠀⠀⠉⠳⢶⣦⣝⣲⣿⣿⣁⣿⣿⣿⣿⣯⣹⣿⣿⣽⠛⠛⢿⣧⣎⣴⣿⣷⣹⣿⣟⣿⣿⣿⣿⣾⣵⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣽⣿⣿⣭⣿⠏⠀⢿⡛⠩⠀⠀⠘⠃⣸⣷⣍⢻⣟⣮⢻⣼⣿⠿⠛⢋⣉⣤⣴⠂
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣿⣿⣿⣿⣿⣿⠎⠋⢐⡂⠈⠐⢶⣶⠄⠘⣧⣽⣭⠛⢻⡟⢛⣉⠭⠔⢒⡈⠉⣉⠡⠤⠴⠶⡂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⣉⣿⣿⡿⡿⠆⣐⣿⠀⠀⠀⠀⠁⠀⢀⡿⢿⣿⠀⣠⢫⣧⣶⣾⣿⣯⣭⣶⣶⠖⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣤⣾⢠⣿⢧⢸⣿⣿⣟⢷⣿⠀⠙⠁⠀⠀⢠⣾⣧⡤⠉⣠⣾⣷⣦⣭⡾⢿⡿⣿⣟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠁⢼⣿⣿⣎⣻⣿⣿⣾⣿⣦⡀⣀⠴⠆⣼⣿⣿⡠⠐⠋⠻⠻⢿⣟⣱⡏⣶⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣽⣿⡿⠻⠛⠛⢉⣨⣿⢇⠈⠉⠁⣩⣿⣿⠿⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣦⣤⣠⣶⡿⣿⣿⣟⡷⣶⣿⣿⣏⡀⠀⠀⠓⠘⢿⣿⡿⠁⣸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠟⠉⡈⣩⣴⢿⣿⣧⣽⢷⣼⡿⣿⣿⣤⣬⣽⣻⣿⣎⡓⡄⠀⢈⡻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠹⠿⢷⣽⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡿⣆⠢⡹⣿⣧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠟⠀⠀⠀⠀⡈⠀⠀⠀⠙⣧⢻⣎⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⣆⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





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

⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢆⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠈⡶⠀⡄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣾⣿⣾⠀⠉⠃
⠀⠀⠀⠘⣦⠀⢁⡜⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣇⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⡄⠈⣀⡾⠁⠀⠀⠀⠀⠀⠛⠳⠀⠀⠠⠈⣿⣿⠞⠀⠀⠀⠀⠀⠁⠘⠂⠻
⠀⠀⠀⢄⣠⢹⣦⢹⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠂
⠀⠀⠀⠠⠇⠌⠸⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⣹⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡀⠀⠀⢀⣀⡤⠤⠤⠖⠚⠁⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢿⠏⠀⠀⠀⠀⠀⠈⢁⠀⠁⠉⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠈
⠀⠀⢀⠀⡝⠲⠀⠒⠋⠹⠈⣤⠀⠀⢀⣤⠖⡀⠀⠂⠀⠚⠠⠎⠀⠀⠀⠇⡔⠙⠂⠀⠁
⠀⠀⣆⡜⡇⡀⠀⠀⠀⠀⢧⡟⠀⠠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⢎
⠀⠀⠛⠃⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡆⢰⡆⠀⠀⠀⢠⡜⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⣷⡄⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⡀⡐⡁⠀⠀⠀⣿⣿⣦⡀⠀⠀⢸⠀⠛⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣿⡇⠙⢿⣷⣤⣬⣀⣀⣴⣿⣄⡀⢀⣀⣤⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠈⠙⠛⠛⠋⠁⠙⠛⠿⠛⠛⣿⡟⠀⢠⡤⠤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢷⣶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠿⢧⣀⢘⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⣦⣞⠁⢀⣀⣀⡀⢈⡿⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉⣀⣠⡾⠷⠤⢤⣄⣾⣻⢧⡀⠀⢠⡇⠀⠸⣧⣼⠟⣭⠿⠛⠛⠙⣿⡇⠀⢿⣀⡀
⠀⠀⣀⣀⡄⠀⠀⠀⠉⠛⣿⡟⠁⠀⣀⣀⠀⠈⠙⣿⠅⠙⣆⣸⠀⠀⠀⢹⣿⣄⢹⣤⡤⠀⠀⡿⡷⠒⠺⣄
⠀⠀⣽⣀⡡⠀⠀⠀⠀⠀⣿⣿⢴⡾⠛⠛⠳⡄⠀⠘⣷⣀⠈⠛⠀⢰⡄⠀⢻⡉⠉⠉⠀⣀⡼⣡⣿⣤⣤⡟⠛⠛⠓
⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⣻⠀⠀⣿⣿⣦⡀⠀⡾⢷⣀⣈⣿⠶⠶⠟⠋⣼⠁⠈
⠀⠀⠀⢀⣠⡤⠶⠿⠿⠿⣿⣿⣿⡳⢦⡤⠔⠃⠀⣰⣿⣿⡌⢳⡶⠇⠈⠛⠉⠁⢀⢠⣀⣀⣘⣦⡀⠀⠀⠠⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠿⢿⣿⣀⣀⣀⣠⣴⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠜⠳⡘⢦⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡴⠃⠀⠀⠟⠛⠛⠋⠉⠀⠉⢿⡄⠀⠀⣠⠖⠋⠉⠓⠦⡆⠀⠙⠦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣷⢀⡾⠁⣠⠖⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠃⠐⠆⠀⠀⠀⠀⢹⡾⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠲⡼⠀⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⣠⢤⣀⡀
⠀⠀⠀⣼⣿⣀⣀⣈⣉⣓⠒⢲⣿⡻⠭⠩⣍⣙⣓⣒⣒⣒⠲⠦⠤⠤⣀⣄⣀
⠀⠀⢸⡿⢿⣧⠀⠈⠉⠉⠉⠉⠙⣿⠀⠀⢹⡯⠭⠭⠭⢿⣿⡛⢇⠀⢰⣿⡿⠃
⠀⠀⠈⠻⣶⣿⠛⠛⠻⠿⢿⣿⣿⢿⣶⡶⣾⢿⣷⣤⣤⣤⣤⣥⣤⡄⠀⢧⡀
⠀⠀⠀⠀⣿⣻⣤⣤⣤⣤⣬⣭⣿⣀⣀⣀⣿⣶⠿⠶⠶⠶⠶⢦⣀⠀⡠⠄⠋⠷⠤⢄⡀
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠈⠹⣿⣏⠉⢹⡿⢿⣆⣀⣀⣀⣀⣈⣉⠟⠈⠁⠄⠀⢀⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠛⢻⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⣸⣿⣧⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⣤⣤⣤⣤⣤⡴⠦⠤⣶⣶⣶⣤⣴⢆⣿⣿⣿⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⠋⠉⢿⣷⠀⣴⣿⡿⣿⣿⢟⣾⣿⡿⢿⣿⣮⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⡆⠀⢸⣿⢀⣿⠿⠇⠀⣬⣾⣿⣿⣶⣶⣿⣿⣧⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠱⣄⢸⣿⣜⡝⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠬⠭⠭⠖⠒⠚⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠏⣿⣿⣿⣿⠿⢿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣾⣾⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠹⢿⣿⣿⣿⣿⠿⣟⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⡿⠿⣿⣿⣿⣿⠿⣻⣿⣯⣵⣾⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣯⣝⣻⠿⠏⠀⠀⠀⠉⠀⠈⠐⣦⠀⠹⣯⣶⠿⢟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢲⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢲⣀⣀⣀⣀⣰⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⡼⠿⢷⣶⣶⣿⣿⠛⢻⣟⣋⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⠿⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠃⠀⡀⢸⣾⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣶⣿⣿⣾⣿⣿⣷⣀⣀⣀⡀
⠤⠤⠤⢤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⡇⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠅⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⡷⣴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣀⣿⣷⠃⠸⢦⠀⠀⠀⠐⠀⠀⠀⠀⢠⡿⣀⠡⡏⠻⣷⣷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⢖⣿⠒⡒⠶⠍⠉⠀⢰⡇⠀⠀⠀⠀⢀⢰⡆⠀⠑⠺⠛⠿⠃⣰⣄⡟⠗⢿
⠀⠀⠀⠀⠀⠀⠛⠱⣄⣀⠺⠋⠂⠠⣽⡦⠸⢦⣩⠄⠀⡉⠁⠀⠀⠀⠠⡟⠘⠀⠀⠰⣿⢛⠛⠇⣽⠟⠒⠀⢸
⠀⠀⠀⠀⠀⠀⢰⠏⣹⣄⠀⣃⣠⠰⠈⠂⠓⢠⢸⠃⠰⠀⠀⠀⡤⡄⠀⠀⠀⢀⣀⠀⠈⢐⡆⣰⣯⣿⠯⠀⢸
⡄⠀⡀⣀⠀⣠⠄⢸⡏⠀⠸⣿⣿⡍⠀⠀⠀⠈⠈⠀⠀⠀⢠⠈⢀⣇⣰⣤⣠⣤⣼⡤⠈⠋⣠⠃⣘⣻⣿⡷⢸
⠁⠀⠈⠻⡧⠁⢀⣼⣰⣶⣐⣿⠏⠉⠀⡇⠘⢆⠀⠀⠀⠀⣤⠀⣸⣧⣽⣿⣿⣏⠀⡿⢷⣠⠋⢀⡛⢿⣿⣿⢿
⢀⡀⠀⠀⠁⣴⠟⢸⠃⠹⢿⡏⠂⠰⢤⡇⠀⠸⡆⢠⡄⠀⠂⠀⢋⣿⣿⣿⣹⣿⣷⡀⢀⣷⣄⠻⠁⢙⣏⠙⢸
⠃⠑⣂⠀⠰⢿⡀⡋⠀⢀⣫⣅⣀⣴⣾⡇⠀⣶⡶⠛⢳⡇⢀⣡⣾⣿⣿⣿⠉⡿⡟⣧⣾⣿⠁⢘⠃⢨⣷⡇⢸
⠀⠘⡟⡲⢤⣼⡏⣼⡖⢉⣿⠙⠻⣿⣿⠅⠀⠀⣿⡖⢸⣧⡈⠙⡷⡩⠿⠙⣿⠃⢀⣾⣽⣿⣷⣿⣾⣿⣉⣿⣸
⠀⠀⠈⠀⠀⣿⡍⢿⡇⣸⡏⠀⠀⢡⢸⠁⠀⠀⢰⠎⡉⠹⠃⠀⠀⠀⠀⠀⠋⠀⢨⡿⢿⣿⣿⣿⣿⣿⣿⡯⢽
⠀⠀⠀⠈⠚⠉⠑⠈⠓⠙⠃⠐⠀⠘⠙⠂⠒⠠⠒⠜⠳⠦⠴⠰⠆⠰⠤⠄⠠⠴⠟⠤⠎⠥⠼⠿⠿⠿⠿⠿⠿

⡀
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣫⣵⣶⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣻⢦⣄⠀⠀⣠⠊
⠀⠀⠈⠱⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢓⣽⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣗⢻⣷⠉
⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⠇⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣼⣿⣿⣿⡿⠉⢁⣀⡚⢥⣀⣀⣠⠶⠶⢶⣤⡀⠀⣿⣿⣹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢱⠀⠀⠀⢼⣿⣿⣿⣿⠃⠀⠛⠉⠛⡸⠃⢻⠁⢴⡟⢶⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣀⡀⢊⣾⣿⣿⢹⡟⠓⠦⠤⠤⠚⠁⠀⠘⢆⡀⠀⠀⣀⡴⠁⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡨⠂⢿⣿⣿⢰⡇⠀⠀⠀⠀⠀⠂⠘⠀⠀⠈⠉⠉⠁⠀⠀⣿⣿⣿⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠁⣹⣿⣧⣾⢀⡀⠀⠀⠀⣴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠈⠁⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠼⠀⠋⣿⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⠀⠀⢰⠀⠀⢸⣿⣿⣿⡟⠀⠀⢰⡀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⢿⣇⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣮⣿⡜⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⣼⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣫⡖⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣯⣻⣿⣿⣷⠃⣿⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⡿⣿⡿⣿⣿⢟⣾⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣾⡿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⠿⣿⠻⡿⠿⢿⣯⡭⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠻⠶⣿⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣮⡳⡀⠀⢸⣭⣭⣭⣭⠷⠶⠋⠁
⠀⠀⠀⠀⠀⠀⣰⣟⣿⣿⣿⠿⣦⡔⠻⡟⠋⠻⡟⠉⠁
⠀⠀⠀⠀⠀⣼⢏⣾⣿⢿⠃⠀⠈⢧⡀⠳⣄⣠⠃
⠀⠀⠀⠀⢰⡟⣾⣿⣿⣿⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⣿⣇⠿⠿⠿⣻⡇
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠒⠒⣦⣀⠀⢀⡖⠉⠉⠉⠙⢿⡻⣦⡀
⠀⠀⠀⠀⡴⠋⣠⠴⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⠉⠀⠀⠀⠀⠀⠀⡹⣆⠻⡟⢾⡛⠙⠛⠓⢦⣀⡀
⠀⠀⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣆⠹⡄⠹⡄⠀⠀⠀⣏⠙⠳⢦⡀
⠀⠀⢸⣷⠷⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⠀⠀⠀⠀⠀⢻⠀⠀⠀⠹⣦
⠀⠀⣿⠃⠀⠀⣿⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣇⠸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠳⣄
⠀⢸⠙⢄⣀⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠱⡃⠆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⠏⠀⠘⣿⠀⠀⡄⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⢹⢷⡀
⠀⡎⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⣸⠁⠠⠀⠀⢀⣎⠀⠀⠀⠀⢳⠘⠀⢻⡀
⠀⣧⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⡏⢠⣧⠤⠤⣤⠞⠉⠉⠳⣤⠤⠀⢸⠀⠃⠈⡇
⠀⢸⡀⠀⠀⠹⣿⣿⣿⣿⣧⣾⢃⣄⣄⡀⢀⡄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⣼⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⠀⠀⠀⡇
⠀⠈⢷⡀⠀⠀⡈⠛⠿⠟⠋⠁⠉⣿⠿⢣⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⢀⢠⡇
⠀⠀⠘⣷⢄⡪⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡞⠠⠃⡾
⠀⠀⠀⠈⢷⡍⠒⠦⠤⠤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠊⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠈⣠⡴⠋⢀⣤⠤⢤⣄⡀⠀⠀⠀⠀⣀⣠⡤⠚⠀⠀⢀⣠⠞
⠀⠁⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠑⠠⠀⠀⠀⠠⢀⠤⠷⠤⠒⠤⣀⣀⣤⠾⠋⢀⡔⠉⠀⡀⠀⠀⠉⠙⠛⠿⠭⠭⠀⠀⠠⣊⡵⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣀⣀⣀⣀⣠⣤⡴⠶⠛⠉⠀⠀⠀⡞⠀⣠⠿⠶⠦⢤⣔⣂⣀⡠⠤⠴⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠲⢤⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⠉⣿⣿⡝⠻⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠈⢿⣿⡆⢘⢏⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⡦⠜⠛⠁⠀⠈⠉⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣬⣽⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⢦⡀⠀⠀⠀⠴⠖⠒⢄⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡖⠦⠈⠀⠀⠀⢐⣶⣦⠀⠀⢠⠟⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡄⠀⠀⠀⠀⠀⠉⠈⠀⠀⢸⣬⣷⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠐⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠤⠤⣾⡇⠀⢸⡿⠛⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⣡⣠⣿⣟⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠂⠀⠀⢿⡀⠈⣿⣿⡿⣿⡇⠀⠀⠀⠀⢠⣤⣾⣏⣉⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠠⠀⠈⠱⠀⣿⠀⠀⣸⡇⠀⠀⣠⠔⠾⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡐⠀⠀⠀⠀⠀⠀⢆⢠⠻⣦⡴⠟⣀⡄⠀⢹⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢳⣀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⡅⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠓⢄⠀⠀⠀⠀⢹⠟⠉⢏⠀⠀⠀⠀⠀⣠⣦⣾⣿⣿⣿⣿⣿⣴⠏⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⠃⠀⠀⠀⡄⠀⠀⠈⢢⠀⠂⠈⠉⠉⢧⢈⣿⠃⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⡏⠀⠀⠀⣰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡾⠁⠀⠀⠀⢀⡤⠶⠚⠛⠛⠳⢦⡀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⡞⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⠀⠸⡄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠏
⠀⠀⠀⠀⠀⠀⢠⡟⡆⢀⠞⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠎⠀⢱⡀⠀⠀⠀⠀⠱⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢠⡏⡴⠋
⠀⠀⠀⠀⠀⠀⡼⠀⢹⠏⠀⠀⠀⠀⠀⡟⢧⠀⠀⣠⠏⠀⠀⠀⢣⠀⠀⠀⠀⠀⠱⣀⠆⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠃⡰⠃⠀⠀⠀⠀⠀⢀⡇⠈⢆⣰⠃⣀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠋⠁⠈⡇⠀⣿⠓⠶⠤⠤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢁⠀⢻⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣔⣒⣀⠒⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⣽⠟⢉⣩⣤⣤⣤⣤⣤⣬⣿⣒⠂⠀⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠯⠛⠁⠢⢴⡿⠟⠙⣓⡚⢓⠛⡛⠳⠮⢤⣀⣄⡐⠻⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⡫⠂⣰⡆⢴⣆⣤⣤⣈⠛⠿⢛⠉⠁⢀⣅⢀⡀⠀⠈⠙⠻⣦⣌⠐⠕⢄
⠀⠀⠀⠀⠀⠀⣠⣿⢿⠏⠠⣺⠟⣡⠀⠸⠟⠉⣤⢶⣳⣬⡛⢿⠿⣶⣦⣬⣉⠒⢦⡀⠈⠻⣷⣄⠲⡡⢀
⠀⠀⠀⠀⠀⣰⣳⠋⠁⢀⡼⢁⠞⡱⠃⡨⢤⣼⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣙⢾⡀⡈⢿⣷⣔⡹⣷⡀
⠀⠀⠀⠀⢰⢳⡏⢀⢠⡿⢠⢃⠠⠀⠐⣁⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣄⢩⣍⡈⠛⠻⠎⢻⢳⡀
⠀⠀⠀⠀⣿⢿⠇⠆⡟⠁⠋⢁⡄⡸⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣆⢻⡟⣦⣶⠀⠈⣏⣧
⠀⠀⠀⠀⣿⡞⢠⠁⠀⠁⠠⣿⢣⠃⣿⡇⣀⡤⡄⠀⠀⠀⠀⡠⣄⣀⣀⣃⡀⠄⠀⠀⢸⡘⡈⠗⢇⡀⣴⢻⢸⣿⡀
⠀⠀⠀⣶⣿⡇⡀⢸⣠⡆⣄⣈⠘⢢⠟⠋⠁⢀⠇⠀⠀⠀⡜⠀⢿⣿⣶⠏⡘⠀⠀⠀⠈⠓⠐⣿⢹⠆⣿⠸⢸⣿⡇
⠀⠀⠀⣿⣿⡇⣷⠈⢿⡇⡇⢻⠞⠁⠀⠀⢀⠎⠀⠀⠀⠀⣇⠀⠀⠀⣠⠜⡤⠊⠙⠀⡘⢠⠰⣿⠈⡄⡿⢀⢹⣿⡇
⠀⠀⠀⢻⢿⠀⢸⣇⠸⣟⢰⣸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⣜⣠⣄⡸⡰⢃⠃⣦⠁⠘⠄⠁⡈⣸⣻⠃
⠀⠀⠀⠸⣾⡇⠈⢏⡆⢿⣖⠗⣷⡀⠀⠀⠈⠷⢄⠀⠀⠶⠮⣥⣦⠀⠀⠈⠉⣩⡞⠁⢃⣼⣿⠃⠈⠀⢠⢡⠇⡿
⠀⠀⠀⠀⢿⣿⣆⠘⣺⡜⢿⢆⠻⡷⠀⠀⠀⠀⠀⠉⠒⠦⠤⢤⡤⠤⠤⢶⠻⠗⢀⡀⠾⠙⠁⠞⠀⠐⣿⠏⡼⠃
⠀⠀⠀⠀⠈⢻⣎⢆⠱⡹⣎⠻⣧⣿⠀⠀⠀⠀⠀⠀⢀⡠⠤⢶⡲⢤⣴⣋⣤⠴⣪⡵⡣⢦⠄⠀⠀⠠⢊⡾⠁
⠀⠀⠀⠀⠀⠀⠛⢯⣧⡙⢿⢧⡈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣤⣤⠴⠾⣋⠤⠖⢁⠔⡹⢋⡴⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠪⡻⣟⠎⠳⣝⡻⡆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠷⠾⠋⣀⠤⣚⡵⢊⠕⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣤⡀⠙⢳⠀⠀⠀⠀⢸⠍⢉⣳⣄⣀⣴⣛⡤⢄⣠⣶⠟⢉⣪⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡻⣶⣧⠀⠀⠀⠈⣗⣒⡲⠞⠒⠒⢒⣉⣉⣥⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡀⠀⠀⢸⣽⡿⠿⠟⠛⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣵⣄⡀⠀⢀⣥⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠺⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡐⠀⠀⠀⠈⠀⠀⢠⣴⠿⡿⣿⣶⣀⣀⠔⠀⡆⠀⠀⡈⢀⡇⠀⠄⠀⠀⣀⣄⡤⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠑⠀⣢⣀⢀⠀⠈⣀⣴⠉⠀⠤⠂⢢⠀⠀⢈⡇⠀⠠⠶⠛⠃⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠹⢀⡀⠀⠠⠀⠂⠠⠘⠪⠼⠁⠂⠈⠀⠐⠁⡇⠠⠀⢘⠃⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠁⣰⠟⠳⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡧⠀⠔⠉⠈⠋⠙⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⢸⡇⢠⣄⡀⠀⠀⠀⠂⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢴⣿⣿⣧⣷⡄⠀⠀⠀⠀⠀⠄⠂⠄⠈⠉⠙⠶⠤⠄⢄⠀⠀⢴⠂⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⢷⠀⣀⠀⠉⠁⠀⠀⠀⢀⣿⣿⣿⣷⡖⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠆⠊⠈⠐⠤⠢⠈⠦⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⡀⠀⠀⠨⠾⠇⠤⢳⣍⠂⠄⠀⠀⠁⠀⠉⠉⠁⠁⠀⠀⠠⠄⠈⠀⠀⢢⣾⣾⣮⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⢁⠀⠀⠀⠀⠴⠚⠟⠁⠀⠄⠀⠀⠀⠀⠠⠀⣀⠀⠀⢀⣰⠎⠀⠀⠀⣽⢿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⢀⢸⡄⠀⠀⠄⠀⠀⠀⠊⠳⣄⠀⠁⠀⠄⡄⠈⠉⠘⠀⠀⠈⠠⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣡⡤⣤⠆⠊⠃⠀⠐⠦⡄⠀⠀⠀⠀⠈⠱⠦⠐⠀⠈⠀⠀⣤⣤⣄⡀⠀⠈⢢⡄⠂⠐⠂⡐⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠻⠦⣀⠀⠀⠀⠀⠱⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠘⠀⠀⣴⠷⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠂⠀⢸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠘⠻⡿⠃⠀⠀⠈⡄⠠⠁⠀⣤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⣉⣀⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠁⠀⠀⠄⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠆⠈⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣷⣶⣶⣶⣶⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣦⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⡄⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⣿⠀⠀⢿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡟⠀⠀⠠⣤⡄⢿
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⡀⠀⣸
⠀⠀⠀⠀⠀⣾⡟⠀⣴⠶⣦⡄⠈⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢿⣧⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠿⣶⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠉⠉⢹⡟⠙⢻⣷⡀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢻⡆⠀⠘⣷⠀⠀⢿⣧⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠹⠇⠀⠈⠁⠀⢸⣿⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠿⢿⣶⣤⣤⣄⣀⣀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠈⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣷⡀⠀⠀⠀⠀⢻⣿⠀⢀⣠⣴⡿⠟⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⢿⣧⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⣿⣦⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠹⢷⡄⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡆
⢀⣴⣶⣶⣶⣶⣶⣶⣶⠿⠿⠋⠀⠀⠀⠀⠀⣠⣾⠟⠋⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⠀⣀⣠⣾⠋
⠀⠙⣿⡿⠿⠿⠿⠿⣿⣿⣆⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡟⠉
⠀⠀⠹⣿⣦⣠⣤⣶⠿⠛⢿⣧⠀⠀⠀⣸⣿⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠻⢿⣿⠿⠟⠃⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣏⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣿⠇⣿⣿⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⢙⣿⡆⢸⣿⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠚⢿⡏⠙⣿⣶⣿⣷⣾⣷⣿⣿⠀⢘⣿⣷⣿⣶⣾⣷⣾⠟⢉⣾⠗⢲⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⣽⡷⣠⣿⣦⡾⠁⠀⠀⠀⠀⢹⣿⠀⢸⣿⠀⠀⠀⠀⠀⠹⣦⣼⣷⣤⣾⡿⠛⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣁⣀⣀⣀⣨⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣀⣀⣀⣀⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇⣿⣯⣉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣿⣿⣿⠿⠿⢿⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠦⡜⢲⠀⠀⠀⢀⡀⠀⠀⠠⡄⠈⠣⡀⠘⡄⠈⠀⠓⠊⠁⡀⠠⠀⠀⠠⡀⣀⠀⠀⣼⢗⠞⢕⠟⠁⠹⣼⠀⢁⣀⢧
⠀⠁⠀⠐⢂⣀⠀⠀⠀⠰⠆⠀⠀⡀⠈⠢⡘⠀⠀⠀⠖⢨⠅⠖⠈⠁⠠⡄⠰⠶⠸⢈⣇⡸⡘⠀⠀⠁⠀⡄⠀⠁⠠
⠀⠈⢿⣿⣿⣿⠁⠀⠀⠀⠄⠁⠀⠐⠃⠀⠈⠻⠆⠀⠁⠄⠐⠀⠀⠀⠀⠁⠀⠀⠀⠙⠖⠊⠃⠀⠀⣄⡤⢀⡁⠀⡄
⠀⠀⠀⢿⣿⠃⠀⢀⣧⠀⠀⠀⢀⠠⠀⠀⠐⣀⠀⠀⠁⠀⠀⠀⢴⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣸⢋⡉⢛⣓⣓⠿
⠀⠀⢴⡎⠁⠀⠀⠘⠋⣀⣀⣀⣀⣀⡀⠃⠀⡄⠀⠀⠀⠀⠸⢄⠀⠐⠃⠀⠤⠀⣶⠄⢬⠿⢆⡹⠧⠿⠧⣬⣩⡕⠿
⠎⠀⠀⣔⢕⣚⠶⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠴⠚⢡⡆⢰⡇⢠⡀⠀⠀⠀⠐⠛⠀⠀⠀⠛⢋⠈⠛
⠀⠄⠀⢋⢜⠈⡎⡆⠘⣿⣿⣿⣿⣿⡇⠨⠂⠉⣁⡂⠀⠀⢠⠄⠀⢠⡆⢀⠈⢁⠘⠃⠀⠀⠁⠀⠰⠆⠈⠱⠓⣴⡔
⢀⡂⠛⢀⢋⠸⠳⡁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠰⡇⠈⠁⢺⠇⠙⠀⣤⠀⠀⢀⠀⣠⡀⠀⠀⠀⠁
⠘⢌⣭⠫⡆⣤⠞⠘⠀⠋⠉⠉⠙⠋⣁⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⣶⠀⠛⠀⣀⠀⠀⠈⣥⠀⠀⢂⠀⠳
⠀⠀⠁⠀⠈⢀⠀⢠⣆⡃⢠⡄⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⡀⣠⢠⠄⠀⠁⠀⠀⠀⡤⠐⠀⠆⠀⠀⠀⠀⠀⠈⠐⠂
⠀⠀⠀⢰⣆⣠⣶⣿⣿⣿⣿⣿⣾⣥⠆⠀⠀⣶⠄⠀⠀⠤⠯⠑⡖⢙⡖⠀⠀⢀⠀⠀⡀⠈⠌⠠
⠀⠀⠔⠀⣹⣿⣿⣿⣷⡿⣿⣿⣿⣿⢀⡁⠀⠘⠀⠀⠐⠑⡎⣹⣉⠍⠅⢠⣦⠀⠀⠀⠀⠀⠀⠰⠂⢱⠄⡀
⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠃⠀⠀⠀⠀⠀⠈⠨⠁⠘⠀⢀⡀⣀⡀⠠⠆⠘⢄⠐⠀⠀⠘⠒⢉⡁⠄⡀
⡀⠀⠀⣀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠀⠀⣤⡀⣤⠶⣆⠀⠀⠂⠀⢀⡮⠳⠔⠛⠺⠀⠀⠀⢀⠀⠀⣀⠀⢨⠰⠈⠁
⠀⠀⠄⠉⠀⠀⠰⠀⠀⠀⡄⠀⡆⠀⠸⡯⣚⣇⣸⢮⢞⣠⣆⠀⢀⢸⢧⢢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⢻⣿⣿⡿⠀⢀⡀⠀⢀⠀⠀⠀⠶⠀⠛⡘⠓⠀⠈⠓⠀⠀⠈⢗⢆⡩⡆⢀⡀⠀⠁⠀⠒⠀⡀⠀⠀⠀⢠⡀⠡
⠂⠀⠀⢻⡿⠙⠛⠟⠀⠀⠸⢷⣄⠀⠀⠙⠏⠁⠀⠛⠀⠀⠀⠀⠛⠈⠈⠉⠠⣿⡿⣠⣾⡧⠀⠀⡀⠀⠀⠀⠄⠃⠐
⢰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⠀⢀⡀⠀⠠⠆⠀⠜⠃⠀⣠⣄⢟⣽⣿⣧⠀⣤⠈⠁⠂⠐⡀
⡿⠧⠠⠠⠸⠂⠀⠀⠀⠀⠀⠀⠀⡌⢡⡀⠀⠀⢈⠁⠠⠁⠜⠂⢤⠀⡄⢿⢿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡂⢐⡀⠀⠀⢀⠀⠀⠦⠀⠀⠶⠂⠀⠆⠰⠈⠀⠁⠠⠁⠀⠀⠀⠀⡠⠁⠈⠿⣿⣭⡄⠀⢠⡄
⣁⡽⢼⣠⠀⠛⠃⠰⠀⠄⠀⠀⠒⠀⢈⢃⠚⠀⢠⡀⠄⠀⠠⠁⡠⢁⠠⠀⠀⡠⢉⠀⠀⠈⡃⠀⢀⠀⢀⠀⢠⠀⡳
⡼⢤⠼⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠁⠀⡘⢃⠀⡷⠀⣀⢀⡀⠀⠈⠏⠀⠀⠐⠈⠀⡴⠾⠍⡻⢏⢩⡢⠀⣀⡍⢨
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⣿⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣁⣀⢀⣤⣶⣿⣿⣿⠇⢸⠳⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⠟⣛⣥⣶⠟⣿⡟⢩⡿⣫⢀⠘⣇⠀⠀⠀⠑⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢢⡤⠖⣪⡅⣰⡿⠟⠫⢀⣠⢾⡿⠐⠛⢱⣿⠘⠄⠻⠣⡄⠀⠀⢀⣙⢮⠁⠐⠦⣄⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠘⠋⢠⠖⠀⢀⣠⢴⣿⠏⡄⠀⣀⣴⣿⣿⡆⠰⣀⡀⠀⣷⢄⡀⠹⠄⢀⡀⠀⢈⣙⠓⣿⣼
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡵⣆⣥⡶⠞⢁⣴⣿⠟⣾⠁⡼⠿⠋⢀⡝⠻⣄⠀⠁⣠⣀⠓⠈⡀⢀⡆⠙⢰⣴⡠⣃⣏⣻⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣻⠋⠸⢋⣥⡶⠾⣿⡿⠋⠰⢃⠾⠁⢷⠀⢿⠁⠑⡹⠀⠀⠀⠹⠀⠸⡇⠸⡇⡀⣿⣿⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠁⢀⣨⠉⢁⣤⡆⠉⠀⠀⣴⡟⠀⢰⡈⠀⣼⢠⠄⠃⡈⠣⠀⡇⢀⣆⣧⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠛⠛⠛⠓⠻⠛⠛⢿⣄⢠⡀⠁⠘⢠⣾⡷⢐⣿⣸⣠⡀⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⢸⡇⣰⢀⣨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⠀⣶⠀⣤⣼⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢿⣇⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠻⣿⣿⣿⣿⣾⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠹⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠁⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠁⠀⠀⣠⣶⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠄⠀⠀⡁⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣄⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⢟⣿⣿⡟⢻⣿⣿⣿⣿⣷⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠹⢿⡿⠁⢸⣿⣿⡿⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡜⡇⠀⣿⣿⣿⠁⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡀⠂
⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣾⣷⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢡⠴⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣯⣉⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁
⡀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡿⠋⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠋⠁⠉⠉⠛⠀⠀⠀⠀⡰⠛⠉⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢏⠻⡆⠀⠀⢀⣾⣿⣝⠂⠀⠀⠀⠀⠑⠺⣟⢷⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⣴⣛⣰⡏⠀⠀⠈⠁⠉⠁⠀⠀⠀⠠⠄⠀⢠⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⣼⣧⠀⠀⠘⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠈⠁⠁⠁⠀⠀⠀⠀⠀⣀⣀⣠⡿⠁⠻⢿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⣄⠀⠀⢠⣿
⠀⠀⢀⠂⠀⠀⠀⢠⠀⠚⠛⣹⣿⣷⣬⣶⣭⣽⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣉⣉⢻⣿⠀⠀⣸⣿⠷⠒⠒⠒⠂⢠⢀⠀⡀
⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡋⢉⣿⣧⣀⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⢀⣿⠠⠄⠈⠀⡤⠀⠈⡦⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀⠀⠀⠀⠀⢻⡏⠀⠀⠈⣿⠆⢀⠾⠃⠀⢀⠀⠠⣀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡈⠁⠈⡷⠂⢀⠀⠘⣿⡀⠀⠀⣿⠀⠈⡀⠀⠀⠀⠘⠀⠈⠃⠈⡖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠛⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠃⠀⠀⡁⠀⠈⡧⢤⡉⠛⠿⠟⠋⢾⣀⠎⠀⠀⠀⠀⠀⠀⠀⢈⡴⠟⠂⢀
⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⠀⠀⣼⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠂⠐⠈
⡄⠀⡀⠁⣠⡾⠛⠁⠀⠀⠀⠀⠘⣿⣈⣻⣿⣿⣿⣿⣿⣿⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⡝⠁⠀⠀⠀⠀⠀⢠⠴⢿⣷⡄⠀⠀⠈⠀⠄⠀⠀⠀⡄⠠
⡀⠠⠄⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡯⠻⣿⡿⠛⢹⡿⠶⠶⢦⣀⡀⠀⢠⡞⠀⠀⠀⠁⠀⠀⠀⠀⢀⣴⠁⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠐⡀
⠁⣤⠾⠛⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⡟⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢁
⢻⡏⠀⠀⠀⣠⡶⠛⠉⠉⠉⠙⠛⠳⢦⣀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠹⣇
⠈⢿⡄⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡼⣆⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣸⡏
⠀⠀⠻⣄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡸⠁⠘⢆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⢠⣿⡇
⠀⠀⠀⠘⢧⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⢦⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⢳⡀⡼⠈⣿
⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠃⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⢷⡄⠀⠀⣸⠃⣇⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠸⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢻⡆⢰⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠋⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣀⣠⣴⣿⡇⠀⢿⠏⠀⠒⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⠉⠁⠀⠀⠀⣿⠇⠀⡸⠀⠀⠀⠀⣧
⠀⠀⠀⡄⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⡀⡀⢀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣖⠺⣄⡙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⠓⠿⣷⣾⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣁⣀⠀⠀⠀⠀⠉⠙⠻⠿⣖⣢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⣰⠁⠉⠛⠶⢤⡀⠀⠀⠀⠀⠀⠉⠛⠶⢭⣑⠲⢤⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠷⠴⣦⣤⣀⠀⠀⠀⠀⠀⠈⠙⠚⠧⣴⣂⢄⣀
⠀⠀⠀⠀⠀⠀⠙⠓⠦⣤⣀⡾⠀⠀⠀⠉⠙⠳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢽⣍⡓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⡲⠤⣀⠀⠀⠀⠀⠀⠉⠑⠢⣄⣀⡤⣀⡀⠀⠀⠀⠈⠙⠓⡦⣭⣓⡢⢤⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣭⡓⠦⣤⡀⠀⠀⢼⡁⠀⣽⠶⡭⣕⠲⡄⠀⠀⢠⠁⡆⢈⠉⡷⢬⣝⣲⣴⣊⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⢯⣀⠀⠀⠉⠛⠻⠾⣤⣠⠟⢓⡖⠦⣼⠰⠇⢸⠆⡇⡇⢰⠉⡏⠳⠦⢭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢩⡟⠲⠦⢤⣄⣀⠀⣆⠀⠺⣄⠀⢈⡿⢲⡞⠛⡷⡷⣸⢸⡇⣇⠀⠀⣿⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣼⠁⠀⠀⠀⠀⢈⡟⠳⢦⡀⠀⢙⡶⠟⠀⠱⣄⣉⠉⣹⣮⡇⣿⠀⢠⡷⠒⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡇⠀⠀⠀⢀⣠⣞⣀⣠⠼⡇⠀⣸⠁⠀⠀⠀⠀⠀⠉⠁⠀⠙⠳⡏⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⢿⣄⠀⠀⠉⠉⠉⠉⠀⠀⣷⠀⣸⠇⢀⣤⣤⣄⠀⠀⠀⢀⣠⢶⡿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠿⣿⣶⣤⣄⡀⠀⠀⠀⣿⣠⢧⡀⠘⠿⠤⠟⠀⠀⣠⢋⡶⠲⠶⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢽⣟⣲⠾⠃⢻⠞⠁⠀⠀⠀⠀⠀⢠⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠸⣤⠀⠀⠀⠀⠀⠀⢸⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡾⠀⠀⠀⠀⠀⠀⣼⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠁⠀⠀⠀⠀⠀⠀⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⡞⣹⢷⡄⠀⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡛⠺⢧⣄⡀⠙⠷⠞⠁⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠶⢭⣽⣓⡲⣆⢀⡾⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠛

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀
⠀⡇⠤⠤⠤⠬⠭⠿⠿⠷⠞⡏⠉⠉⢉⣉⣉⣉⣉⣁⣀⣀⣈⣉⠉⠉⢦⣶⠖⠒
⠀⡷⣶⡶⠶⣶⣶⣶⣶⡶⢆⠀⠀⠀⢸⠀⠀⠒⠶⠤⡄⠀⠀⢩⠉⢆⠀⠣⣤⣄
⠀⢸⣀⣀⡗⣀⣀⣀⣀⣀⣘⡿⠿⠿⢿⠀⠀⠀⠀⠈⠁⠀⠀⢸⠀⢸⠀⠀⠀⠉⠒⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⠀⠈⠙⠛⢲⣞⣿⣿⢞⣠⡟⠠⢂⡔⢄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⠘⠒⠒⠒⠒⠒⠚⠛⠛⠚⠋⠀⠈⠉⠒⠢⢃⣠⣤⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠓⠢⡀⡠⠒⠒⠀⠸⣶⡶⠢⡄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡅⠀⠀⠀⠀⣸⠃⠀⢸⢀⣠⣾⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣒⠁⣀⣀⣼⠛⠛⠛⢻⣿⣿⣿⣿⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠐⠈⢣⢀⡨⠀⡀⠐⠈⣀⠅⠠⢇⠀⢀⡢⢸⠀⡀⠁⢀⠃⠄⢁⡊⠀⠀⢹⣿⣯⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠙⠛⠛⠛⠛⠟⠛⠛

⠱⠄⠈⢁⣀⣵⡙⠳⡿⠄⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⢀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢕⣤⠀⠀⣠⠊
⢀⣴⣕⠄⠛⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠉⠀⠛⠀⢀⡀⠀⠀⠀⡔⢠⠀⠀⠀⠘⠁⠀⠜⠁⠸⣆
⣝⠂⠙⢀⣴⠄⠓⠀⠀⠀⣠⠰⠲⠲⠆⠁⠀⠀⠴⠀⠒⠠⠀⠀⠈⠀⠀⠀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠠⠀⠀⠈
⡙⠂⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡚⠶⠄⠀⠀⢀⠥⠒⢄⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠘⠉⠁⢢⠀⠀⠀⠈⠀⠀⢸⠒⠒⢀⡀⠀⠀⠀⠁⠀⠔⠀⠀⠀⡠⠚⠁
⠀⠀⢠⠀⠤⠰⠇⠀⠀⠀⢰⠃⠚⠁⠠⡄⠀⠀⢁⠇⠰⠀⠀⠀⢰⠤⠐⣀⠸⠂⠒⢀⠰⡄⠀⢀⡀⠀⠀⠀⠠
⡰⠈⠙⠂⠀⠈⡱⠔⠶⠤⠌⢠⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠜⠀⠸⡀⠀⠉⣠
⠳⠦⠀⠀⠀⠀⣁⠀⡤⠬⠗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⠄⠀⠠⠅⠀⠠⠒
⣦⠀⠀⠀⢰⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢈⠂⠀⠀⠉⠉
⠀⠈⡁⠀⠘⠠⠂⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣤⡤⠤⠄
⣤⡦⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣴⡶⠖⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣼⡷⠖⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⢴⡶⠟⣋⠄⠀⠀⣠⠔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠢⣌⠙⠿⣿

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡟⢲⣾⣾⣶⡄⣶⣶⣶⡆⣶⣶⣶⣶⢶⣦⢰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠉⠁⢸⣿⣁⣿⢷⣿⡇⣿⣧⠁⢠⣿⠇⠸⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢸⣿⢿⡇⠀⣿⠶⢿⡇⠀⣼⠇⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣠⡇⢀⣿⣼⣿⣶⣿⣿⣿⣷⣾⣯⣀⡀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠮⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠤⠭⠭⠍⠁⠀⠀⠀⠀⠀⠀⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⢀⣠⣀⡀⠀⠀⠀⠀⣠⣶⡆⢄⠲⡄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣴⠀⠿⣿⠏⣆⠀⢀⡀⠙⠛⠁⢸⡇⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⣄⣀⣀⣠⠿⠚⠊⠳⣤⣤⣴⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢹⣿⠿⠛⠁⣴⣰⣆⡄⠈⠻⠿⠿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⡠⠀⠘⠋⠙⠃⠀⠀⣤⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢼⣧⡤⢤⣤⠄⠠⠤⠶⣿⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣶⠀⠀⠈⠀⠀⢸⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢏⠻⠶⢶⢶⢶⠞⠋⠌⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠉⠐⠀⠐⠐⠈⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠐⠂⠐⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡋⠂⡀⣠
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠠⠀⠀⢀⠀⠀⠰⢿⡀⢈⡝⠛⠁⠀⡀
⠀⠀⠀⠛⡀⠀⠀⠤⣀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⠀⠈⠁⠀⠈⠀⠀⠀⠀⠑⠊⠁⢀⠀⣰⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⢀⡠⠂⢀⠀⠀⠸⡇⣀⠀⠀⠀⢴⠋⠀⣄⣀⠀⠀⠠⢀⣠⢠⡀⣐⣦⠀⠀⠀⠰⠚⠀⠉⠉⠙⡆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠃⠈⢁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡁⠀⢂⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⠄⠀⠚⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢁⠈⢀⡀⠀⠀⠀⠈⠉⠑⠀⢹⣠⡤⣤⢴⣶⠲⢶⢲⡶⢄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠑⢦⣀⠀⠈⣷⣠⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠱⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠁
⠀⠀⠀⢀⡀⠀⢦⠀⢠⡀⠀⠈⡿⢷⠰⡆⠀⠙⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠰⢳⡄⠈⠧⠚⢣⠀⠀⠀⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠒⠚⠻⢧⠀⠄⠀⠀⠀⠀⠘⢶⢸⣠⡍
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢨⡄⠀⠁
⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠐⠈⠉⠉⠑⠢⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠙⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⠀⠀⠤⠄⠀⠀⡄⠀⠀⠀⠑⠖⠖⢀⣀⠄⠀⠀⢀⣄⣀⠄⠀⠀⠈⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠒⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⢀⡉⢣⠀⠀⠀⠀⠐⠦⠤⠄⢀⣀⡀⠀⠢⠤⠔⠊⠒⠃⠀⣠⢀⠄⠀⠀⢠⠀⠀⠀⠈⢢
⠀⠀⠀⠰⠊⠁⠀⢀⠀⠀⣈⣧⣀⠉⡉⠀⠙⠓⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡜⣠⠀⠀⠀⠀⠁⢳
⠀⢀⡤⠂⠀⠐⠊⠹⣄⡀⢀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡀⠀⢀⡜⠀⠀⡀⠈⠹⠄⠀⠀⠀⠀⠀⠒⠉⠈⠀⠀⠀⡴⠀⠀⠈⠀⢤
⠀⠊⠀⠀⠒⣆⠀⠀⣀⡍⠀⠀⠀⠑⢪⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠠⣄⡀⠐⠆⠀⠒⠁⠒⠒⠋⠀⢀⠦⠔⠄⠈⠇
⡀⠀⠀⠀⢤⡈⠁⠀⠰⡁⠀⠸⣄⠀⡀⠑⠂⢄⠀⠰⣄⡀⠄⠀⠀⣀⠀⠀⠣⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⣰⠤⠂⠈⠋⠁⢀⠄⠀⠀⡀
⢇⠱⠄⠀⠀⣉⠁⣠⠀⠉⠀⠀⢀⠉⡀⠀⠀⠀⠉⠁⠀⢀⠀⣉⡉⢀⣀⡠⢄⣈⠉⣉⣁⡀⠠⣄⣠⡄⠀⠀⢤⡀⠀⠀⠈⠉⠁⠠⠖⢊⡁
⠈⠢⠀⡄⣄⠈⠀⠻⠀⠀⠙⠤⠈⠉⣁⡜⠐⠋⠈⡐⠊⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⣀⣜⠃⠀⠀⠀⠠⠴⠒⠊⠀⠄⠈⡄⠊
⠀⠀⠀⠈⠢⡁⠀⠤⡀⠄⠐⠂⠀⠀⠀⠈⠋⠉⠉⠀⣿⠀⠀⠀⢰⠀⡇⠰⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠀⠉⠒⠂⠐⠤⡍⠉⢀⣐⡊⡐⠒⠀⠀⠖⡿⠀⠀⠀⢸⠀⢇⡇⠀⡈⠠⢸⠃⠒⠓⠒⠂⠀⠀⠉⡈⣁⣀⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠑⠄⠀⢺⡀⢈⠸⠈⡇⠸⠀⢃⠇⡆⡿⠖⠤⠒⠐⠊⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡆⡀⡇⡄⠠⣸⢰⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⡇⠁⠀⡇⡏⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡼⢇⡠⠴⢧⣇⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠌⠉⠁⠀⠀⠀⠀⠀⠁⠘⠋⠳⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢠⣴⠦⣴⠠⢤⣤⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠲⠄⠠⣿⡇⣿⠀⢸⠀⢸⢣⠔⠢⠤⠆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⡿⠀⡇⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⡇⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢳⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠴⢦⠀⠀⢈⠤⢤⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠣⠀⠀⠀⠀⠋⠑⡀⠀⠀⠉⠀⠀⠁⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠀⠀⠔⢢⡤⡈⠂⢀⡀⢩⠤⠒⢤⢤⡀⠙⠀⠐⠳⡄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠀⠠⠄⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠑⠲⠀⠈⠓⠀⠈⠈⠋⠂
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


⡿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠹⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣣⠀⠀⠀⢸⣂⣀⣀
⠀⣀⠤⠤⠀⢶⡧⡈⣻⣵⠞⠙⠉⠀⠀⣀⣭⣵⣦⣀
⢸⡱⠉⠀⠀⢹⡿⡞⡏⠀⡀⣄⠀⢤⣀⡈⠉⠉⠉⠛⠷⣦
⠀⠙⣆⠀⢀⡞⣁⣻⡷⠶⠿⠿⠾⢦⣬⣭⣥⣤⣄⡀⠀⠈⢳⡀
⠀⠀⠈⢻⡟⢤⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⢦⠀⠀⡇
⠀⠀⠀⢼⡌⢾⡏⣠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⠀⡟
⠀⠀⠀⠘⢞⣻⢀⣀⣀⣀⠉⠃⠀⠀⠐⠚⠋⠉⠙⢺⣿⣧⡞⠁
⠀⠀⠀⠀⠘⢹⠈⠛⢍⡿⠁⠀⠀⠀⠀⢐⣟⢻⡶⠀⣿⡏⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⠀⠉⠀⠀⠀⠀⣴⠟⠋⠉⠉⠓⠦
⠀⠀⠀⠀⠐⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢆⠀⢠⡴⠒⠚⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠲⣠⠉⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠠⠙⠛⢋⠀⠈⢢⠀⠐⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢀⣼⣟⣿⡇⢄⠀⠀⠀⠀⠠⡄⠘⠀⠀⡀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⣾⠸⠘⡿⣇⠀⠁⠒⠀⠒⠃⠉⠀⠀⠀⠃⠀⠀⠉⠈⠉⠉⠢⢤⣀⣀⠤⠒⠤⠤⠴⠶⠛⠁
⠀⠀⠀⠀⣿⡀⣀⠈⠚⢧⡀
⠀⠀⠀⠀⡈⢿⠂⠙⠳⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠠⠐⠂⠁⡀⠈⣷⡄⠀⣲⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠌⠂⠂⠄
⢀⠀⠀⠂⠂⢹⠟⣡⡾⠯⣀⣀⡀⠀⠀⠄⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠄
⠨⠌⠀⠐⠀⠘⠦⡽⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠁⠠⠀⠀⠈⠀⠀⠂⠈