Pineapple plant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⡀⡼⡄⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣰⠏⠀⠐⠶⢾⣯⣧⣼⣽⠶⠖⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⡜⡘⠀⠀⠈⠻⡿⣙⣯⣟⡹⡿⠋⠀⠀⠀⡿⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢡⠱⡀⢠⠃⡇⠀⠀⠐⠳⣭⣧⣧⣧⣿⡵⠓⠀⠀⠀⡇⡇⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠸⡑⣄⠀⠀⠀⠀⠈⡆⢣⣸⠀⡇⠀⠀⠠⠭⣿⣮⣿⣯⣾⡯⠥⠀⠀⢠⠃⡇⢠⢎⠎⠀⠀⠀⠀⣀⡤⠖
⠀⠀⠱⣄⠀⠀⠀⠱⡈⠳⣀⠀⠀⠀⠸⡀⠳⡀⡇⠀⠀⠀⠉⠝⢯⢻⠯⡟⠍⠁⠀⠀⡜⢰⡰⢁⠎⠀⠀⡠⠖⡩⠊
⡀⠀⠀⠘⢗⠦⡀⠀⠱⡄⠈⠢⣄⠀⠀⢣⠀⠱⣥⠀⠀⠀⣠⣼⡶⣾⡶⣼⣤⡄⢀⡜⢀⡞⢀⡎⢀⠔⠋⢀⠜⠁⠀⠀⠀⠀⠀⠀⣀
⠈⢦⣄⠀⠀⠳⣌⠲⢄⡘⢄⠀⠈⠳⣄⠀⣷⡀⠙⢦⡀⣾⢿⠿⣷⡿⢷⡿⢿⢿⡎⠀⡜⠀⣞⠔⠁⠀⡠⠋⠀⠀⠀⠀⠀⡠⢔⡺⠋
⠀⠀⠙⠭⡒⠤⣈⠳⢄⠉⠒⢧⡀⠀⠈⠑⢇⠙⣄⠀⢹⣿⢺⢻⠛⡗⡟⢻⢺⢺⣷⠞⢀⡜⠁⠀⢀⡔⠁⠀⢀⣠⠤⠒⣩⠔⠉
⠀⠀⠀⠀⠈⠒⠤⣉⠙⠓⠤⣀⡈⠢⡀⠀⠀⠑⢌⠢⣸⣿⣿⣙⣟⣏⣻⣻⣙⣟⣿⢠⠎⠀⠀⣠⣊⠤⠔⠊⢁⡠⠔⠊
⠀⠀⠀⠀⢀⣀⣀⣤⣭⣦⠤⢀⣈⠉⠛⢦⡀⠀⠀⠑⢼⣿⣽⣽⣅⣏⣯⣸⣽⣽⣿⠃⠀⢀⠔⠁⠀⣀⡤⠶⠥⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠪⢕⣒⢌⣢⡀⠀⠀⠙⢾⣤⡷⣧⡼⣮⣼⣮⢇⡠⢒⡡⠔⣒⠭⠔⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⡙⠷⢄⠀⠀⠙⡦⠻⠣⠚⠛⠫⠕⠊⡡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠢⡀⠀⠀⠈⣼⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⡀⠄⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⣉⠲⢄⡀⠀⠸⡄⢄⠈⣾⣽⣿⣹⡟⣾⣗⡤⢀⡴⣪⡴⠞⠁⣀⣤⠖⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠰⠦⢤⣤⣀⠀⠈⠑⣦⡙⢦⡀⢹⡎⣇⣸⣿⣿⠿⣷⣹⣯⣶⣿⣿⣟⣫⡴⢚⣉⡤⠤⣲⣦⢴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠈⢻⣎⠻⣆⢿⣼⣿⣿⣿⡕⢸⣿⣿⣿⣿⡿⢿⡥⣚⣭⣴⠾⠛⠉
⠀⠀⠀⠀⠈⠙⠻⠈⡙⠺⢧⣤⡽⣷⡙⣿⣟⣿⣿⡯⡪⣪⣿⣿⢟⣩⣾⡿⣟⣯⠥⠐⣀⡤⠴⠒⠀⣀⣀⣀⣠
⠀⠀⠀⠉⠉⠉⠐⠒⠾⢷⣌⣫⣿⣳⣝⠻⣿⣿⣿⢿⣶⡸⡟⣱⣿⢟⣽⠾⣫⣵⣶⡿⢽⣖⡾⠿⠋⠉⠉
⠀⠀⠀⠐⠬⢭⣘⡒⠲⢤⣌⡻⣿⣿⡿⣿⣬⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⢟⣭⠵⣚⡭⣵⡶⠞⠛⠉⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣍⡻⢄⠻⣿⣮⡛⣷⠙⣿⣿⣿⠿⣻⣿⢿⣷⣾⣿⣓⠫⢶⣯⢥⣴⣶⣶⠿⠷⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣮⡻⣮⡻⣿⣜⢧⡽⢋⣵⡿⢋⣴⡿⢛⣥⠾⣛⡿⣦⣝⢫⣿⠝⠁
⠀⠀⠀⣠⠤⠤⠤⢤⣤⣄⣀⠈⢿⣿⣽⣿⣌⢿⣎⢣⣾⢋⣴⡾⣻⡶⣋⡵⠛⠁⣠⣼⣛⣿⣷⣄⣀⣀
⠰⠞⢃⣀⣡⣍⣉⣓⣒⠨⠍⣛⢷⣽⣿⡻⣿⣆⠻⠋⣱⣿⢏⡶⣫⠞⣁⣠⣴⣾⡿⠛⠛⠛⠛⢿⣿⣙⣩⠿⠓
⠐⠛⠛⠛⠛⠛⠛⠳⠯⢽⣛⠾⣿⣮⡻⣿⣦⡹⣷⢰⣿⡿⣛⠾⢵⣞⣛⣟⣻⣯⣴⣶⣶⣶⣷⣿⣿⣿⣷⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠿⠛⠿⢌⢻⣿⡸⣿⣿⡾⣿⣿⣿⣷⣮⣿⣟⣛⢉⡉⠠⠴⡟⡃⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣩⡶⠟⠃⠉⡙⣾⣿⣇⢨⢾⣿⣿⣿⣿⠿⣖⣨⣽⣛⢿⣿⠛⠛⠓⠚⠿⠶⣤⣀⠙
⠀⠀⠀⠀⠀⣠⣴⣿⡿⢟⣩⣴⣾⡿⠟⠊⢿⣟⢯⣮⣿⣿⣿⣿⣿⣿⣿⣛⣉⣥⡀⠙⢿⣦⣀⠀⠀⠀⠀⠈⠁
⠀⣀⡤⣶⣿⡿⢟⣭⣶⣿⠿⢟⣯⣴⣶⣶⣾⣿⣷⣾⣧⣾⣯⣭⡤⠤⢤⡭⠭⡍⠉⠛⠓⠾⠭⠓⠶⠤
⠸⠿⢿⣿⣿⣿⣿⣿⡏⠉⠀⠉⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠛⠛⠋⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⣧⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⡰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⢀⠀⠀⢀⠀⡇⠀⠀⠀⣠⠄⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢢⣆⢳⣄⢀⡞⠡⠀⢀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⢀⠀⠀⢠⡑⣿⡄⠋⡟⡰⣣⣴⠟⡃⢔⡠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⢤⡀⢙⢊⢻⡜⢰⡿⢋⣴⣭⣒⡡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠦⢄⠊⠛⢿⣦⡶⠎⠰⣿⡿⠋⠉⣀⣤⠤⠄⠒⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢈⣠⣶⡿⢿⣇⣸⣶⣿⣿⣿⣟⠓⠢⠀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠉⠁⠈⠛⠟⠉⣴⣿⣿⣿⣿⢿⣿⠿⠛⠋⠀⠀⠀⠀⡀⠉⠉⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣷⣭⣍⣻⣁⣠⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⡟⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣴⣿⢿⣿⣿⣿⡿⣻⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢬⠿⣼⣿⣿⢿⣿⡿⣵⣆⣶⢆⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠷⠸⢗⡾⡳⠋⢙⡳⢿⣿⣷⢿⡬⠋⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣴⣾⠯⠕⢏⣱⢴⣾⣿⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣸⣶⣾⣿⣿⣿⣿⢩⣹⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣹⣿⠿⣷⠹⣫⡻⣿⣿⣿⣿⣿⣿⣟⢻⣿⣎⡊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣾⣿⣄⢻⣚⢡⣶⣿⣿⣿⣿⣿⣯⡽⢛⣷⣟⣛⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣏⣿⡟⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠛⡻⣧⣼⣿⣟⣀⣿⢿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢀⠀⠈⡙⢻⣿⡃⣾⣿⣽⠟⣿⣤⡿⢋⢐⡃⠻⡔⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣆⡀⢂⣼⣿⣸⣿⣧⣬⣡⣾⣟⢹⢻⣦⠀⠁⣀⡷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣏⢹⢾⣿⣿⣧⡞⠉⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣝⡞⣿⣿⣏⢹⡇⢸⣿⢙⣴⣏⠹⣿⣿⣄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⠻⢿⣷⡟⠹⣿⡇⢸⣿⣿⣿⣿⣷⡟⢛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⣿⠃⡆⡟⣿⣾⣿⡿⢯⣿⡿⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣦⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⣿⣧⡼⣿⣃⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣤⣿⣧⠿⣿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡛⠻⣎⢫⣾⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⡛⣻⣟⣧⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⢿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡍⣿⡿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠾⣝⠿⢊⡵⣪⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣿⣽⣿⣨⣶⣯⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢌⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠷⣭⣤⡻⠏⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠲⠆⢉⡁⠶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⣉⢿⠾⣙⡱⡿⣬⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠙⠁⣤⠉⠃⢴⠌⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣛⣥⣮⠙⢻⣶⣝⡫⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠃⣀⡐⠓⣀⡀⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣭⠻⢋⣥⡻⢟⣠⡟⢟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠰⠦⢈⠱⡶⠈⡁⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣉⢿⠶⣙⣷⡶⣉⣱⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢡⣤⠙⠋⣤⡌⠟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢷⣮⠛⢻⣦⡙⢿⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⠗⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠵⠻⠗⠍⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⣸⣇⣠⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣄⠀⣿⡀⣴⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢿⢿⣿⣿⣫⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠿⢷⡽⣏⣥⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣼⣝⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⢶⡑⣾⡿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣝⡿⣿⡿⣿⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣛⠻⣿⢙⣥⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⣙⢋⢻⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⢋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠛⣧⣽⡿⢳⣴⡝⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⣤⡌⠛⠠⡤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣼⡿⢟⣡⡺⠿⣪⣜⠿⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠟⢂⣀⠚⠂⣀⠘⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢛⢷⡾⢛⡡⣶⢏⡻⣶⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡁⠲⠈⡉⠰⠆⢈⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⢣⣦⡛⢿⣤⡝⠟⣴⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠋⢤⡌⠙⢡⣤⠙⠡⣤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⢿⢷⣭⡺⢷⣩⡘⢿⢮⣅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠗⢂⣀⠺⢂⣀⠚⠗⣠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣦⢝⡵⣶⣝⣹⢶⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄⠉⠶⠆⢉⠐⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡄⠈⠀⡀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣾⡇⠀⠀⠀⢠⠀⠀⠧⠘⢃⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢷⠀⠸⠈⠀⠀⠀⠑⢄⠐⠀⡀⠃⠈⢀⠎⢀⠀⢠⠎⠀⠀⠀⠀⠀⡼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣆⠐⠀⠀⠀⠀⢀⠀⠘⠂⡟⢄⠀⠀⠀⡆⣀⠈⠀⠀⠀⠀⠀⣰⢰
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠲⠇⢀⠁⠀⠶⠃⠀⠀⣈⠀⠀⠀⠀⠀⣠⠃⠌
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⣄⡀⡈⠐⣶⠀⠘⠁⠃⢀⡄⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⠖⠋
⠀⠀⠀⠀⠀⠀⠙⣎⠀⠀⠀⠀⠀⠀⠐⡀⠱⡀⡆⠀⠈⠡⡈⢁⠀⢠⠜⢩⠌⠀⠉⠤⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⢫⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢀⠀⠀⠀⠀⢳⠀⠱⣾⡄⠀⠀⣹⠂⠰⠚⡄⠃⠒⠆⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠑⠀⠀⠀⢈⢧⠀⠘⣿⣆⠎⠠⢠⠇⠘⠀⠰⡈⢠⠌⡁⣠⠋⠀⢠⠂⠀⠔⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⢸⠀⠆⠀⠸⠋⡁⢡⠃⠃⢀⠠⡄⠈⠠⢐⡄⠣⠀⡠⠁⠐⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠐⣄⡀⣄⢀⠀⢀⡞⢁⠐⠆⠒⠀⠳⠈⡑⠃⢃⡖⠁⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠈⠣⣸⡅⠀⠈⡅⠠⠀⡲⠀⠀⠄⠀⠀⠸⠁⡈⡇⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡳⡄⠀⠈⠣⡁⢠⠁⢤⠈⠗⠊⠀⠨⡀⠀⠙⠀⠀⠃⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣀⣠⠤⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠦⡀⠀⠈⠲⡀⠀⠀⠗⠀⠤⠀⡁⡄⢀⠇⠈⠀⢀⡴⠃⠀⠀⠠⢀⣲⡽⠛⠋
⠀⠀⠈⠙⠋⠁⠊⠑⠴⢖⡀⠀⠤⠄⣀⠀⠐⣄⠙⢆⠀⠀⠉⢠⠞⠀⠀⣀⠀⠀⡇⢄⠐⣦⠔⠁⠀⠀⠀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣈⠀⠘⠧⡀⠑⠄⠀⠀⠀⠐⠊⡀⠐⣾⡀⢄⣀⡵⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠢⢀⠈⠨⠢⢀⠀⠀⠐⣀⣀⠠⡍⠀⠀⠁⠠⠂⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⢦⡤⡀⠐⠒⠒⠀⡑⠀⠀⠱⣶⡄⠀⠀⣀⣀⡜⠀⡠⠊⢀⠔⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⢓⠈⠁⠀⣤⠀⠈⠐⢤⣀⠈⢏⢆⠀⠈⡋⠀⠀⠀⡠⠋⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⢀⣈⡑⠒⣄⡀
⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠄⠂⠀⠀⠁⢄⠀⠈⠑⠄⠀⠈⠉⢅⠀⢆⢧⠁⠐⡄⢀⢔⡡⠔⠂⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡔⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢤⠈⠣⡈⣮⢧⣤⠟⠋⠉⠀⡠⠔⠊⠁
⠀⠀⣼⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠙⠳⣀⠜⠋⠀⠀⡠⠀⠉
⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⣆⠀⠰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠻⠃⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠘⡦⡀⠀⠀⠀⠀⠀⣇⣾⠠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡉⡢⣸⠈⠢⣸⡄⠀⠀⣿⣟⢾⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⡇⠀⠙⡇⠀⣄⡿⠁⡿⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣌⣿⣇⠀⠀⠸⣰⡟⠀⠠⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠘⢿⠻⣄⠀⠠⠋⢸⠀⢠⠞⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⢧⡏⠳⠆⠀⠈⣇⠏⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣵⣌⣇⢠⡄⠄⠀⣿⡾⢋⠎⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⡈⣿⣿⠾⣟⣶⠈⢿⣶⣿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣶⣿⣷⣬⣻⣦⡾⢋⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢤⣿⣿⣿⣿⣿⠁⣠⣏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣿⣿⣿⣿⣿⣿⡿⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣶⡞⢹⢷⡋⢉⣻⡿⡟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⢿⣿⢎⣽⠟⠘⠳⠏⣹⠟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣩⣾⣷⣿⣆⡠⠒⠻⣿⣿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣧⣙⣽⣽⣿⡿⣧⣀⣤⠾⣇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣿⣶⣜⣿⣿⣿⢿⣷⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠟⡻⣿⡿⣿⣶⣾⡿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⣿⣎⢹⡬⣿⠒⠈⣏⣷⣛⡓⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣥⢢⢈⣳⣾⣯⣿⣇⣼⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣾⣾⠟⢿⣧⣤⣻⣯⣻⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣿⣿⣿⣶⣾⣿⣿⣅⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠈⢀⡀⢠⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢷⠀⠀⢸⠸⠀⠀⠀⢤⠀⠣⡀⠈⠁⡌⠴⠀⢰⠃⠀⠀⢀⠄⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢇⠀⠇⠀⠀⠀⠀⠀⠐⠀⡀⠰⡄⠀⠀⠠⠁⠠⠂⠀⠋⠀⠀⠀⠀⠀⢀⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠿⣄⠀⠀⠀⠀⠀⠀⡀⢀⠁⢰⠈⢀⢀⠀⠀⡂⢠⡀⠀⠀⠀⠀⠀⠀⡞⢘
⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢀⠈⠻⠀⡄⠀⠀⠛⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⢢⣠⢀⠀⠱⡶⢀⢈⠀⢋⠠⡔⠀⠀⠀⢀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢰⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⢂⠀⢠⠠⡆⠀⠀⠁⡀⠉⠀⠀⣤⠋⣡⠎⠀⠉⠠⠄⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠴⠛⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡁⠀⠀⠀⠀⠀⠈⣆⠀⠳⣱⡀⠀⠀⢈⡒⠂⠦⢧⠐⢀⠶⠆⠋⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠠⡀⠀⠀⠀⠘⡄⠀⠹⣿⡄⠰⢩⠀⣸⠀⠢⠀⢤⠐⢀⡄⠃⢀⡴⠃⠀⢠⠀⠀⠄⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠀⠀⠀⡀⠁⠄⠀⠙⠟⠃⠂⡸⠱⠀⡀⢀⠀⠓⢈⠁⢀⠺⡀⠀⡠⠁⠐⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠠⡇⣆⠠⡀⢘⠀⡓⢠⡷⠂⣤⠃⡄⠱⣆⡠⠬⡏⢤⢄⡴⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣆⠀⠀⢻⡀⣗⡜⠀⠃⡆⠐⡂⢈⣆⠁⢄⠊⠀⠓⠄⡴⠚⣄⡀⠀⠀⠀⠀⠐⡡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠳⡀⠀⠈⠺⡅⠄⠀⡰⠀⠁⢤⢁⡤⠀⢡⠄⠀⠠⠀⠀⢸⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⣀⠀⠀⠀⠂⠐⠃⠐⠂⢨⡁⠀⠀⠸⠄⠀⠀⠇⠀⠄⠀⠀⢀⡠⠋⠀⠀⠀⠀⡀⣀⣤⡴⠞⠋⠉⠁
⠀⠀⢀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠙⢦⡀⠀⡘⠀⠀⠂⠀⠄⠢⠠⡎⠀⠀⢀⡠⠊⠀⠀⠀⠀⣢⣵⠞⠋⠁
⠀⠀⠀⠀⠉⠀⠀⠌⠑⠚⠥⠄⡀⠐⠂⠤⢀⡀⠑⣄⠈⠣⠀⠀⠀⠱⠞⠁⡀⢀⡀⠀⠀⠁⠀⠈⣳⠖⠉⠀⠀⠀⠀⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⡀⠀⠘⠷⡀⠈⠂⠀⠀⠀⠀⠛⢁⠀⠑⣻⡄⠦⣀⡸⠆⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠈⠀⠀⠀⠀⠀⠀⢪⡀⣀⠠⡍⠀⠀⠉⠠⠖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⣤⠀⠀⠀⠐⠦⠀⠀⠀⠀⠠⡌⢄⠀⠀⠉⡀⢀⡼⠀⢀⠔⠁⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠈⠢⠈⠑⠂⢀⡀⠀⠉⠂⣄⠀⠈⠣⠡⡀⠀⠹⠎⠀⠀⠁⠀⡴⠁⠀⠀⢀⠠⠄⠒⠊⠉⠀⠀⠀⠀⠀⠉⠉⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠄⠀⠈⠛⠦⠀⠀⠈⠟⢀⠀⢣⢱⡀⠀⢡⡀⠀⠠⠊⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⡠⠂⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⢀⠀⠀⠢⠀⠣⡹⡀⢀⣣⡴⠐⠋⠀⢀⣠⠄⠂⠈
⠀⠀⢀⢎⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⡀⠀⠣⣤⡐⠄⣧⠼⠋⠁⠀⠀⠠⠒⠉
⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⢞⠁⠀⢀⡠⠖
⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⣨⡄⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠋⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣄⣤
⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢠⣽⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠀⣿⡇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⢰⡃⣼
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠄⢀⢀⠀⠣⡹⣿⡿⠋⡠⠎⠅⣀⠕⠀⠀⠀⠀⠀⠀⠢⠀⠀⠙⠻⠀⠠⣿⡿
⠀⠀⠀⠀⠀⠈⠀⠠⠤⠤⠤⢄⣀⠏⡰⢄⡰⣿⣷⡞⢀⠔⠁⠀⠈⠄⠀⠀⠈⠂⠀⠀⠀⠀⠘⣠⣴⣄⡃⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠬⠓⠸⠚⢱⣿⢿⣴⡄⠀⠆⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡤⠴⠂⠒⠘⢿⣿⣟⣵⠂⠈⠨⠉⠀⠒⠠⠃⠀⠀⠀⠀⠀⣾⠯⡛⣻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⡴⠒⠙⠁⣴⣿⠅⠲⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢐⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⣉⣈⣤⣿⢠⡾⠿⠟⠃⠀⠀⠁⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠙⠂⠀⠀⠀⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⣿⢀⡞⢱⠃⠀⢀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⢻⣿⡄⡎⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⡿⠃⡷⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⢸⢀⠃⣤⠁⡎⠀⢀⡤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⢦⡀⡿⠀⣿⠀⠁⢸⢀⡴⢫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠻⣇⠀⣇⠀⢀⡾⠛⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣒⠶⣄⣳⡀⠘⣷⢿⠀⡞⠀⣴⣯⠔⣨⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠙⠳⣄⣹⠀⢻⡀⣰⠟⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⢻⠃⠀⣷⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣊⡙⠓⠦⣼⠀⣠⢧⣴⠛⢉⡉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⢉⡿⠗⠂⠼⡿⣄⣠⠼⠟⠻⢭⡉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠴⡾⠋⠟⣉⣿⠁⢹⢿⣱⠦⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡧⢒⡙⣤⣰⠋⢺⡇⢸⠋⢳⡘⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣎⠹⣤⠌⢹⢻⣤⠞⢻⣼⣉⠠⣷⢋⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣤⢀⡀⢳⡸⢋⡙⣄⢹⡟⢻⡐⢸⡤⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠉⢆⡡⠎⡳⡀⣁⠞⢋⠐⢠⠿⡑⢆⡤⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢧⢉⠘⠳⡈⢃⠜⢃⠛⣨⢷⡁⢂⡷⢊⣁⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣘⢳⡘⢀⡽⣇⠘⡠⢿⡴⢂⠷⡫⢆⣤⢿⣔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠉⣠⠿⡋⠶⢘⣿⡐⢆⠿⡇⠄⠷⠚⣇⡾⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠑⢂⣷⡔⢁⡈⢻⠁⣤⢱⠚⣦⡹⢻⣦⣿⢁⣠⡤⢤⣠⣴⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠻⣉⠲⠙⣦⡔⣭⢱⠴⢻⣨⢟⡑⢾⡵⠟⢉⣠⠒⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠶⠶⠦⢤⣄⣀⠘⣗⣼⡤⠻⣏⠴⢉⣶⠁⢦⣪⣭⡤⢶⣯⣤⣖⣉⡉⠙⠲⣄
⠀⠀⢀⡠⠒⠋⠉⠈⠉⠉⠛⠳⢦⣄⡀⠈⠙⠻⣧⣹⣟⣹⣛⢹⡧⢉⠿⠻⣤⡀⠀⠹⡏⠉⠁⠀⠉⠑⠚⠷⣄
⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⠿⠛⣉⣭⡿⠷⢦⣤⠖⠳⣼⠆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡴⠞⢁⡞⠀⡴⠋⠀⠈⠐⣼⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⠟⠀⠀⣸⠀⡼⠁⠀⠀⠀⠀⢸⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⢳⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣕⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣮⣿⣴⡯⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⣷⠶⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⢹⢃⡋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣶⡤⠁⡏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣧⣎⣯⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡹⣼⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣛⣳⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣿⣿⣿⣿⣿⢏⣃⣀⣀⠀⠀⠀⢀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢹⢿⢋⣽⠇⡉⠀⠋⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⡇⣀⠀⢻⢼⣾⣿⡇⠀⠀⠄⠀⠀⢠⠃
⠀⠀⠀⠀⠋⠙⠖⠦⣀⠀⠀⠀⠀⠐⠒⡀⠈⢞⢧⡀⢀⡀⠀⠀⠀⠈⣷⡀⠀⢟⡘⠃⣾⠜⠡⠛⠀⡰⠃⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣴⠀⢀⠀⠀⠀⠀⢄⠈⢧⢻⡘⠆⠑⠀⠀⠀⢹⣧⠀⠸⣇⠀⣟⡇⣀⠀⡴⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⣠⡶⢾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⡑⠶⣄⡀⠀⠹⢦⣷⣿⡀⣄⡈⢃⠀⠈⣿⡆⠘⠻⣴⣿⣿⠏⢼⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠊⠁⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠆⢙⡲⢦⣄⢿⣿⣿⡄⠆⠀⠷⠀⢻⠗⢠⠲⣿⢹⣿⢠⠆⠀⠀⡼⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠈⠙⠒⢨⣙⢿⣿⣿⡄⢆⠐⠁⠈⣦⢸⠀⢾⡿⣿⣼⠀⠀⣸⠃⠀⠀⢠⡴⠋⠀⠀⠀⢀⡀
⠀⢀⡠⠄⠁⠀⠁⠈⠁⠀⠀⠀⠈⠒⠢⣄⠀⠀⠀⠈⠛⢮⡻⢿⣾⣆⠡⠀⢿⣼⠀⢸⣧⣿⠇⠀⣰⠇⠀⠀⡾⠋⠀⠄⠀⣠⠾⠃
⠀⠉⠀⠀⠀⠀⠈⠁⠀⠛⠉⠛⠛⠷⠶⢶⣬⣁⣠⡀⠑⢦⡙⠳⣽⣿⣆⢳⢸⣿⠀⠀⣿⣿⠀⢡⡏⠀⢠⡞⠁⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣶⣦⣬⣉⠑⠾⣕⣦⣈⠂⣌⡙⢿⣶⣧⣹⣷⣄⣿⡇⡘⣼⡁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⢾⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠈⠙⠛⠿⣶⣬⣙⠻⢦⣌⢻⣿⣿⣿⣿⣿⣿⣿⡟⢣⣿⢀⡿⠀⠀⣶⠀⠀⠀⠀⣀⠤⠖⣋⠁⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠔⠠⠦⠴⢦⣤⣤⣀⠉⠙⠿⢄⡙⢷⣽⡝⢻⣿⣿⣿⣿⣇⢸⡏⣿⠃⣠⢸⠇⠀⠀⣰⠞⣁⠴⠊⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣦⣌⡉⠛⠿⣿⣦⡙⣿⣿⣿⡿⣼⣿⡟⣰⣣⡟⢀⣰⡿⡡⠞⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣳⢆⡀⠛⢷⣾⣿⢹⣿⡟⣿⣷⣿⠟⣠⣿⣿⢏⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⣿⠷⣭⣶⣌⢻⣿⣿⣿⣵⣿⣿⢫⣾⣿⣿⡷⠋⣁⣴⠴⣴⠦⣴⣀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣄⢁⣀⣀⣩⣯⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣱⣿⣿⠟⣣⣶⣛⡁⢴⣡⢄⣀⣠⣭⣭⣙⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⠉⠀⠀⡤⠞⠛⠉⢉⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣼⣿⣷⠶⠛⠋⠉⠀⠉⠀⠀⠈⠉⠙⠙⠧
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⠀⠂⠀⠠⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⣺⡿⢓⠦⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢧⣤⡤⣤⣄⣠⡀
⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠛⠛⣧⠞⠋⠉⠹⠾⠿⢻⣿⡿⠃⠉⠁⠀⠀⠀⠀⠛⠛⠁⠙⠐⠲⠾⠓
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⢐⠶⠆⠀⠚⠋⠉⠁⠀⠀⠀⠀⠠⠴⠖⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠠⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⡀⣠⡄⡀⠀⠀⠀⠀⠄⠖⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣨⡄⣻⡶⠾⠶⠶⠾⠀⠟⠁

⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠄⢆⠀⠀⢠⡄⣱⠀⢸⣿⣿⣆⠀⠀⠀⢸⠁⠀⣠⣿⣿⡿⠋⠰⠃
⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠄⣸⣿⣿⣿⡇⠀⠀⠈⠁⠐⣿⣿⡟⠡⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢿⡿⠓⠀⠀⠀⠀⢸⡿⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠰⣄⡀⡄⠀⠀⠀⠀⠘⠀⠈⠁⠀⠀⡀⠀⠀⢠⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⢄⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣴⡆⠀⠀⠀⢀⣀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⣼⣿⡿⠿⠁⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣠⡿⠋⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠛⢿⡟⠀⠀⠀⠀⠀⠀⢠⡾⠛⢁⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢠⣰⡀⠀⠀⠀⠠⠟⢀⣴⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣠⡴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢨⡷⠆⠀⠀⠒⠋⠀⠀⠀⠀⠀⢠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣦⡀⠀⠀⠀⠀⣷⠀⠀⣀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠙⢷⡄⠀⣠⡾⠛⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠓⣄⡀⡀⠀⠀⠀⠈⢳⡀⠀⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠉⠁⢤⣀⣠⣶⠛⠋⠻⢷⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢳⣤⣤⡚⠛⠛⠓⣶⣦⣤⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣛⣻⣷⣶⣶⣷⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣴⣿⣻⣿⢟⣛⣿⣿⣻⣿⣿⣿⣽⣾⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠖⡽⢪⣿⣟⡛⠁⠈⠛⣿⣿⣿⣧⣤⣾⣿⠿⠟⠳⣬⣀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣟⣥⣴⡾⠛⠻⣷⣦⣹⣿⣿⣛⠷⠿⢻⣿⣿⣷⣘⣁⡛⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣛⡄⠸⠧⢿⣿⣿⣷⣿⣿⣦⣴⣿⣿⡋⠙⣿⣿⣿⣾⣿⣦⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣧⣤⣾⣿⣿⠛⣛⢻⣿⣿⣿⣟⣻⣧⣄⣟⣿⣿⣿⣿⡿⣾⡆
⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⡿⠻⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⢀⠰⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢁⠀⠹⠠⡆⠀⡤⠀⠐⠁⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠑⠰⢄⠀⠀⡄⠀⠀⠠⢀⠤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢡⡰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠆⠀⠀⠀⠀⢀⠐⠁⠈⠀⠔⠋⠀⡠⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠄⠈⠄⠀⠀⡠⠂⠀⠀⡀⠃⠀⠀⠀⠁⠀⠀⠐⠀⠘⠀⢀⠁
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⡀⠀⠄⠀⡄⠀⠀⠀⢰⠀⠀⠀⠄⡈
⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢂⠙⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⡀⠁⠀⢀⠤⠀⢁⠀⠠⠀⡀
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠌⠀⠀⠔⠉⠀⠁⠀⠘⠀⠀⠀⠀⠉⠀⢀⡀⠀⡈⠁⠀⠁⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠻⠀⠀⠢⠄⠀⠀⠀⠞⠀⠀⠀⠈⠁⠀⢀⠀⠀⠘⠀⡀⠃⠀⠀⠀⠠⠀⠔
⠀⠀⠐⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢀⠆⠀⠀⢀⠚⠀⠀⢀⡈⠁⠰⠀⢄⠐⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⡠⠃⠀⠀⠂⠀⢂⡀⠋⠀⠄⠄⠁⠀⠐⠃⠀⡄⢴⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠖⠀⠂⠐⠂⠀⠀⡁⢀⠶⠀⠀⠀⡐⠁⠀⠐⠀⠁⠌⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⡇⠈⠀⠂⢀⠂⡀⠃⠄⢀⠤⠀⠀⡀⡘⠁⠀⠐⠀⢀⠤⠀⠀⠁⣀⡤⠔⠂⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⣀⠘⠠⠈⠰⠀⠀⢠⠀⠀⠄⡐⠉⠀⣀⡌⠀⠊⠁⣀⠀⠀⠚⠁⠠⡴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠠⡀⠈⠀⡄⠀⠰⠀⠀⠀⣤⠞⠈⢀⠀⠀⠁⢀⠀⡀⠈⠂⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠓⡀⠒⠀⠀⠀⡂⠉⠀⠀⠀⠁⠀⠀⠀⡡⠊⡴⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠢⡄⢀⠄⠁⠀⠔⠀⠀⢀⠔⠀⡏⠀⡾⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⡘⠀⠀⢀⠀⠀⠀⠀⢢⠀⠌⠆⣾⡟⠁⡠⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⠀⠘⠦⠀⠄⠀⢀⡆⠀⠀⠀⢄⡉⡄⠘⠐⢋⡔⠀⢄⣠⡤
⠀⠀⠀⠀⠀⠠⣄⠒⠂⠄⠀⠀⠀⠀⠰⠁⠈⢠⠀⠀⣡⡔⠀⠰⠀⠀⠀⣨⢼⢰⡤⠞⢀⠁
⠀⠀⠀⠤⠀⠀⠀⠀⢤⣀⡓⠀⡀⠀⢤⢀⣜⠠⠅⠉⠀⠀⠀⠀⠀⠀⢀⡹⣎⢼⡿⣦
⠀⠀⠀⠀⠀⠤⠀⡀⠄⠐⠂⠀⢀⡀⢀⡄⢠⠋⣞⡀⠀⠀⡀⠀⠀⡀⣀⣖⣿⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠔⠰⢀⡓⢰⠇⠀⠄⠑⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠻⣯⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡶⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⣷⡂⣌⠙⢿⣿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡊⢉⡜⠀⠀⠀⢀⡠⣀⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⡇⠻⣷⣮⡑⠀⠀⠀⠀⣠⢤⡴⣟⠀⢠⡎⠀⢀⢤⢠⡽⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠙⠻⣾⣝⠉⠛⢦⣽⣦⡸⠁⠛⠄⢹⡄⡞⡀⠀⠓⡶⠊⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠭⣁⡲⠦⢄⡻⣷⡀⡀⠹⣿⠙⠁⠀⠀⠸⣶⢯⡍⢠⡿⠵⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠘⠻⢧⣀⢷⣏⣀⡀⠀⠀⢠⢿⣻⠖⠛⣀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣦⡠⠄⠀⣙⣶⣿⡿⠻⡿⣯⠙⢢⡔⣴⠞⡙⠚⣹⣯⢐⣢⡤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⣥⣭⣿⣇⡀⠀⠀⠀⠀⢻⡁⢰⣯⣴⣿⣵⣎⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣾⠁⠋⠉⠳⣤⣀⣰⣶⢋⣛⣿⣴⡿⠯⢉⣭⠽⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢾⣿⣿⡀⠘⢗⡞⠁⠈⢹⡿⠿⣿⣿⣠⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢦⣿⣦⣽⣾⣿⡷⢤⡀⠈⠀⣸⠻⠷⣾⡷⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣉⡻⣯⠉⢻⣷⢽⣯⡿⢾⣏⡻⣿⣷⡏⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣦⡤⠿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⢷⣿⣤⣶⣤⡿⣿⡿⣽⣿⣯⣽⣤⣿⣷⡂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠴⣖⢾⡟⢶⣵⣎⣟⠀⠀⠀⢻⣿⢿⣿⠿⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢲⢬⡜⠀⠀⢀⢝⣻⣟⣶⢴⠟⠛⠋⠿⢷⡤⣬⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⣛⠀⢁⣿⡷⣤⣴⠯⠼⠉⠶⠱⢿⠦⣤⣀⠀⢸⣥⣦⣿⣁⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠑⢶⣏⢲⣴⣏⣽⣦⣄⣀⠀⣠⣆⣿⣰⢏⣳⡟⠚⠙⠀⢛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠉⢠⢿⡾⢛⡻⠿⡿⣽⠘⠃⠈⢹⡟⣭⣦⣤⣫⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡴⢫⡕⠦⣀⡿⠿⠇⠘⠉⢩⣿⣒⡲⢦⣤⣿⣜⢰⠁⠸⣓⣆⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⣙⠋⠃⠼⠓⡿⡿⣶⢦⣄⠀⣡⢖⡱⠪⣌⣫⣵⣀⣀⡀⡾⣮⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠳⢆⣀⣀⣼⡏⣴⣀⠖⣈⣿⡀⠉⠁⠀⠈⣡⠾⣫⢙⢻⡟⠷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣼⣱⣎⣿⠒⠀⠉⠀⢩⢪⠶⠙⣗⢶⣾⣩⠻⠶⠋⣡⣤⣴⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠵⢄⡺⢷⣤⣔⣶⡎⢷⣚⣃⢦⣹⣿⠀⠀⢀⣴⡏⣚⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⡓⠋⢅⣿⡛⠶⣯⣗⠛⠁⠈⣨⡿⢯⣛⣛⠛⠵⠋⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠄⢴⣤⣬⣤⣄⣾⡿⢛⣛⠷⠿⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢠⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠰⠋⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠣⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣠⡶⠛⠉
⠀⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⢆⠀⠀⡇⡤⡥⣼⣶⣯⣿⣤⡀⠀⠀⠎⠀⢀⡾⠁⠀⠀⠀⢀⣠⠞⢋⣠⡶⠒
⠀⠀⠀⠀⠀⠙⢶⣄⠀⢀⡀⢀⡀⠀⠉⠻⣦⣄⡀⠈⠢⠀⣧⡉⣺⣿⣿⣿⣿⡍⠀⠀⡈⠀⢀⡞⠀⠀⠀⢀⣴⣟⣥⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣌⠳⢯⣓⢦⣄⡀⠙⢿⣶⣄⠀⢻⡝⠀⢿⣿⣿⣏⠀⠀⢐⠀⢀⡞⠀⠀⢀⡴⣻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⠳⣬⡻⢶⣤⡙⢿⣷⡘⣇⢰⡞⡽⣿⣿⣿⣄⠂⢀⡾⠁⠀⡴⣫⡾⠋⠀⠀⠀⣀⡤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣬⡛⠀⡙⢿⣦⡙⣿⣿⡾⢴⣼⣿⣿⣿⣿⠄⡾⠁⠀⢠⡾⠋⠀⢀⣀⣶⣯⠥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣤⣈⠺⡻⣿⣮⣿⣷⣾⣿⣿⣿⣿⡟⣼⠃⠁⣴⠏⣀⣴⡾⠋⠁
⠀⠠⠒⠒⠀⠐⠒⠒⠶⠶⢤⣄⣀⡀⠀⠀⠀⠉⠙⠻⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⢰⣇⠂⢊⣡⢞⡿⠋⣀⠀⣀⣀⣤⣶⠶⠛⠛⠉⠉⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢧⡢⣤⡀⠀⠈⠙⡷⣾⣿⣿⣿⡛⣻⠃⡟⢉⣴⣿⡷⠋⢔⣫⣴⠿⠿⠛⠁⣀⣤⠤⠶⢄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠒⠒⠀⣠⣤⣈⡀⠈⠀⠀⠀⠈⢺⣿⣿⣿⣧⡟⠀⢁⣾⣿⢟⣪⡶⠟⠉⠊⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢶⣤⣀⠙⠝⣿⣿⡗⢀⣾⣿⣿⠾⢋⡐⢠⡀⠀⠉⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠲⠒⠒⠲⠶⠶⠶⠤⣤⣄⣀⡀⠈⡛⣷⣬⠈⢿⣧⣺⣿⢋⣴⡾⢋⠀⠜⢁⣀⣠⣴⣦⡤⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣁⣘⡻⢜⢷⡘⣿⡿⢁⣾⣯⣶⣏⣴⡾⢿⣛⣉⣥⠶⠶⠒⠒⠛⠁⠀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠚⠛⠋⠉⠉⠙⣻⣿⣮⠻⣿⢣⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⣤⣴⣾⠟⠾⣝⣿⡁⣾⣿⣿⢋⡁⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢀⣴⣿⡿⣻⣽⡾⣷⣯⣽⣜⡿⢫⡞⢁⠈⠉⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⢛⣵⣺⣾⣫⢞⣽⣶⣾⣟⢷⣿⣿⣯⣟⢳⣦⣀⢻⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣠⣾⡭⠶⣻⣿⣿⠟⡇⠸⠛⠿⠿⠿⠿⣿⣿⣿⣿⡗⠈⠙⢷⣄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡾⠋⠀⣠⡼⠟⠉⠀⠀⠁⠀⠙⠒⠀⠂⠰⢶⣾⣿⡟⠀⠀⠀⠄⢈⢷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠐⢀⠐⡆⣠⠆⠀⢲⡀⡶⠀⠀⠐⣶⠀⢀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀⢶⠀⠹⣇⠀⠀⣀⡼⣇⠸⣤⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣄⡀⢻⠉⣉⠙⢿⡀⢹⠴⠚⠣⣄⠘⣄⣣⠀⠀⢹⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⡞⠉⠀⠀⠙⣾⠀⡀⠀⣄⠀⢸⣃⣤⠖⠋⠉⠈⠀⠀⢀⡴⠛⢫⣋⠍⠏⣏⡛⠗⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢐⡧⠚⠁⠀⠘⣦⡏⠁⠈⡆⠀⠀⠀⠀⡴⣋⣤⣤⠀⠙⣷⠶⠶⠶⠾⠾⢷⠆⡇
⠀⠀⠀⠀⠀⠀⢰⠤⠴⠖⠷⠶⠿⠷⠾⠧⢤⠤⣿⣤⣾⣀⣴⣈⣓⣾⠓⣶⠾⣇⢹⠠⢸⠀⠀⣿⣿⢻⢹⡆⠀⢸⡶⡇
⠀⠀⠀⠀⠀⠀⠘⠚⠓⠛⠛⠛⠛⠓⠒⠒⠦⠤⣤⡀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠻⠚⠶⠼⢦⣄⣾⣈⢙⠉⠁⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣄⣀⣀⣄⣀⣀⣀⡀⡀⠀⠀⠀⠈⠉⠋⠓⠒⢼⣍⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠲⠦⠤⣀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡠⢠⠴⣿⢻⡆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡀⢀⣀⢀⠉⠉⠉⠙⠒⠒⠶⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡋⢳⣯⠭⡇⠀⠀⠀⠀⠀⠀⠀⠹⣟⠿⠿⠉⠩⠉⠍⠉⠙⢛⣺⡶⠦⣤⡀⠀⡅
⠀⠀⠀⠀⠀⠀⠐⠀⢀⣤⠶⣄⠀⢹⡉⡾⠴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡒⠂⠀⠂⠀⠂⠾⣍⣽⠁⠂⡌⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⡞⢩⠷⣤⣳⢷⡊⠀⢀⣤⠞⢻⢉⣯⣿⠃⠀⠠⠀⠀⣽⢷⣮⡀⡂⠐⠀⢾⡆⢄⣅⣠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⢷⠋⣰⢻⠻⣾⢇⡴⡇⢸⣤⠞⠛⡶⠃⠀⠀⠀⠀⠀⣳⠾⠃⢹⣭⣅⣁⣹⡗⠻⣤⡿⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠼⡞⠁⡞⠀⣏⣾⣠⠷⢯⣬⠽⠋⠀⠀⠀⢀⠀⠀⠀⣇⣤⡀⠀⣿⡏⠁⢽⡏⣁⣽⡉⡒⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠦⣧⢞⡁⠘⢿⠛⠛⠉⠉⠀⠀⠀⠀⡀⣹⡛⠻⡆⢸⠿⣼⠇⠀⣿⡧⠰⢾⡇⠦⢿⠀⣤⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠶⢾⡿⠛⢷⣮⣧⣶⣤⡦⠀⠀⠸⠀⠙⡹⢿⡴⠃⢸⠀⢿⠀⠀⡟⡇⠘⣸⡗⢐⢸⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠧⠤⠤⠤⠵⠿⠩⠤⠦⠤⠾⠤⠴⠥⠤⠧⠠⠼⠦⠼⠤⠤⠧⠯⠩⠽⠍⠍⠽⠭⠭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢠⠙⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣷⣼⡄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣽⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢃⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⠄⠀⠀⠈⠩⠽⠿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣛⣛⣀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢇⣀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣔⣉⣉⣀⣀⣀⠤⠚⠉⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⢀⣤⡴⠚⠉⠁⠀⠈⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠲⢤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣾⠁⠀⠀⠀⠀⠈⢳⣰⠟⣿⠲⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⡴⠶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢀⣼⣿⠉⠳⡄⠀⠀⠀⢀⡴⠋⣸⡏⢳⡀⠀⠀⣠⠖⠶⠞⠃⠀⢿⡑⠉⠢⣄⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣦⣠⣴⠟⠀⣾⢧⣙⡢⠙⠲⢮⣁⣀⣀⠀⠀⠀⠈⢿⠂⣀⣈⡷⢾⣧⡾⠁⠀⠀⠀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⢀⡴⣾⠉⠀⠀⠀⠀⠻⣄⠀⠉⠂⠀⠀⠀⠉⠉⠑⠄⠀⠀⠈⠋⠉⠁⠀⢾⡈⠛⠶⢤⣤⣤⠞⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⣿⡄⠀⠀⠀⠀⢠⡘⣯⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡀⠀⠀⣸⠃⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⢸⣿⡇⠀⠀⠀⠀⠈⢿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⡀⢻⡄⣿⡇⠀⢠⢿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⠀⠀⡄⠘⣧⠈⠓⠦⢄⠀⣀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣿⠀⢹⣿⣿⣠⣯⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣷⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⣿⣧⠀⠀⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣏⢢⡄⣸⣿⡄⠙⢆⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⣿⣿⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠁⠀⠀⣾⣿⣿⠀⠀⢾⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡉⢻⠋⢲⠾⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⡄⠀⠃⠀⠀⡀⠀⠀⠀⠐⠐⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⡴⠋⡂⠔⠸⠀⠀⠤⠼⢦⠀⠿⠃⠀⠀⠀⠀⠈⣀⡶⠒⢡⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣤⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠰⠀⠀⠈⠃⠀⢐⠀⡸⠏⠀⠀⠀⠀⠀⠀⢠⡤⠀⣶⣶⠐⠿⠂⠀⠀⢯⡈⢇⠀⣠⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠰⠂⣤⠈⠀⣦⠀⠀⠀⠀⠙⠵⡎⡘⡳⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡄⠀⢨⠀⠀⢀⡀⠀⠀⢃⠀⠁⠀⠓⠀⡠⠀⠀⠀⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠖⠈⠀⠀⠀⠀⢠⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠇⠸⠃⠀⠀⠀⠑⠤⢀⢀⣀⣀⠤⠂⠀⠀⠀⠀⠀⡈⡠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠰⠄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣰⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠘⢰
⠀⠀⠀⠀⠠⠀⠀⠠⠐⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⡀⠀⠀⠀⢀⠃⠁⣟⡀⠈⠀⠀⠀⠀⢀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠
⠀⠀⠀⠀⠄⠠⠀⠀⡀⡄⠀⠀⠀⠀⢆⠄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠄⠀⠀⠈⠁⢸⣏⡀⠀⠀⠀⣀⠀⡀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠤⠀⢐⢤⠼⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢀⠀⠀⢀⡀⢰⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠄⠠⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠐⠈⠈⠀⠀⠈⢁⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠀⢇⢒⠆⠀⢱⠀⠀⡈
⠀⠀⠀⠁⠀⠀⠀⠀⡄⢠⡀⠃⠀⠀⠀⠀⠀⣇⠀⠀⠄⠀⠳⠀⠄⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢳⡄⠀⡠⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡀⠀⠈⠫⡀⢀⣠⡰⡶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠄⠁⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⢋⣉⠘⠑⠢⡀⠀⠀⠀⠀⠀⠤⠈⠀⡀⠄⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠛⡠⠀⢀⠜⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠦⠴⠖⠚⠁⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐
⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠞⠁⣈⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠚⠀⠄⠰⠀⠀⠄⡡⠆⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠚⠐⠂⢀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠉⠑⠲⢼⡀⠀⠀⣆⠲⠀⡠⠠⢄⠀⠀⠀⠰⠞⠀⠀⢰⣤⣼⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠘⠄⡃⠀⠚⠃⣀⠨⠵⠤⣀⠉⠀⡟⠀⢶⡸⠀⠀⠀⠀⠀⠀⠘⣿⣭⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠑⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⢇⠀⠲⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢀⠀⠱⣄⠊⠀⠘⢀⡤⠀⠀⠀⠀⠀⠀⡸⢁⣀⠀⠀⠱⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠢⣌⣁⣄⢸⣇⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠰⢈⡁⠀⠀⠀⣿⡰⠊⢁⠑⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠙⠷⢶⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⢸⡆⠀⠀⣷⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡇⠀⠀⠀⡄⢴⣯⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⢰⡇⠀⠀⠀⠀⠀⢸⣇⣿⣀⣾⣮⣇⣄⠖⣿⠀⣴⣠⣗⣷⢴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣸⣷⠸⡀⢀⣇⣿⣿⣿⣷⠂⠀⠀⠠⣄⣀⣸⡧⢸⣧⣰⣆⠀⢀⣈⣿⣿⣿⠟⠻⣿⣿⣿⠤⠿⣞⣻⣷⣹⣿⢉⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢰⣿⣿⣿⣿⡈⡒⠘⣿⣿⣟⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⠃⠀⠀⠹⢿⢛⣘⣧⣾⠛⣽⣟⠡⣛⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣆⣷⣿⣿⣿⣿⡿⢳⡏⠀⢻⣿⣿⠁⢅⢠⡀⠀⠀⡙⠈⢿⣿⣿⡿⠋⠃⠰⠴⠦⣴⡏⠀⠀⠀⠀⠼⣟⣡⡿⣟⠛⣿⠋⣸⣿⣗⣠⣿
⠀⠀⠀⠀⣠⣴⣿⣿⣻⣿⣿⣿⣻⣿⢋⣽⠀⠀⠘⣿⠟⣀⠈⣟⣰⣤⣴⡁⠈⠙⣿⣿⠀⠀⠀⠀⠗⠀⢈⡧⠀⠘⠐⠦⠀⣸⣿⠀⢸⣷⣾⠿⣗⡼⠳⣄⡀
⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⠽⢿⣼⠋⠀⠀⠀⣿⠍⠀⠀⢿⣌⣿⠇⠀⠀⢀⠻⣿⣿⣤⣤⣶⣄⡾⠁⠀⠀⠀⢀⠀⠀⢈⡿⣦⣿⢽⣿⠂⣹⣿⣤⡧⠁
⠀⠀⢠⣿⣿⠿⠟⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠐⠏⠀⠑⠒⢘⠛⠟⠀⠈⢁⡠⠄⠈⠀⠀⠀⠙⠘⠳⠀⠀⠰⠛⠻⠟⠟⢿⣤⣾⠸⠯⠐⠂⠉⢧⠀⠈⠆
⠀⠀⠈⠉⠀⠀⢺⠇⠀⠀⠐⠚⢻⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠁⠋⠛⠿⠶⠆⠊⢉⣉⡲⠏⣹⣦⡨⠷⢶⣄⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠤⠤⣄⠀⠐⠶⣦⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠛⠓⠒⠚⠛⠛⠻⠓⠒⠺⠿⠀⠀⣀⣄⣀⣀⣀⠛⣫⣉⣱⡖⠂⠉⣳⣀⣀⣸⡧⠄
⠀⢠⠀⠰⠖⠀⢀⣠⣤⣄⠄⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠙⠛⠛⠿⣷⣶⣾⣤⣼⣿⣠⡀⠰⣿⣆⢀⡄⣤⢷⣀⡄⡀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣄⣩⣿⣾⣧⣽⣧⣿⣷⣞⣻⢻⡄⣿⡆⠀⠄⠀⡀⠀⠀⠀⢰⣧⣦⡀⢂⢰⣄⠀⠀⠀⠘⣆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢿⡿⢿⣿⣟⣉⣉⣹⣿⣿⣿⡇⠀⢠⡄⣧⣶⣄⣦⢸⡿⣿⡇⠘⡞⣿⠀⠀⠀⡄⢻⢄⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠏⠛⠛⠛⠾⣓⠀⠠⠅⡽⢳⣿⣿⣼⣿⣿⣷⢀⣦⣿⠄⠀⠀⢸⢸⣿⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣉⣉⣁⣈⡁⠀⠀⢰⣉⣉⣩⡍⣻⣿⣿⣭⣄⣀⣦⠚⠀⢺⣿⢿⡟⠋⠁⢓⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠑⠈⠙⠋⠉⠍⠭⢙⣿⣦⡤⢤⣶⣾⣟⡿⣯⣭⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢶⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⡇⢿⢹⣿⠾⡵⠆⢀⣴⣶⣀⣶⣿⣿⣿⣿⣦⠀⠀⠉⠙⠋⠉⠛⠛⠛⠛⠓⠒⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠖⠮⠅⢀⠸⢾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠌⠛⢻⠛⠛⠟⠋⢩⢥⠌⠟⠗⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠚⠻⣶⣌⣁⡋⢠⠭⠬⣿⣶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠇⡉⠲⠒⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠋⣱⣾⣿⣷⣿⡟⠛⠈⡻⠋⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠛⠋⠀⣿⡀⠀⢀⠀⠀⠠⣿⣇⠀⠀⣾⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧
⣶⣶⣿⡿⠀⠀⠀⠀⢀⡄⠁⠀⣰⣿⠆⠀⠀⣼⣿⡇⠀⣼⡇⠀⣨⣿⣧⡀⢠⣿⣧⡀⠀⢸⡄⠀⠀⠀⠀⣰⣿
⣿⣿⡿⠁⣀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠇⠀⢘⣻⣿⠷⠄⣿⡷⠀⣸⣿⣷⠀⡠⣿⣿⢀⣴⣿⣷⠀⠀⠀⣴⣿⣿
⣿⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⣦⠀⣈⣿⣿⣁⠰⣿⡟⠒⢻⣿⡏⣾⣿⣿⡷⣶⣿⣿⠷⠀⠀⠀⠻⢿⣿
⣿⣿⣧⣿⡏⠀⠀⠀⠀⠀⢰⣗⢿⣷⣤⠀⢻⣿⣿⣟⣰⣿⣿⢐⣯⣿⣧⣾⣿⣿⡟⠂⢾⣿⣷⠀⠀⠀⠀⠀⣿
⠻⢿⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⠀⢾⣿⣿⢛⣇⣿⣏⣸⣿⣿⡯⣏⠹⣿⢷⣆⣹⣿⣟⠀⠀⠀⠀⠀⡟
⠀⣼⣿⡏⠀⠠⠀⠀⠀⢼⣿⣿⣿⣿⣼⡹⡒⣿⣿⠘⣿⣿⣿⡟⣿⣻⡆⣰⣶⣿⣰⣏⣽⣿⣏⠁⠀⠀⠀⠀⡇
⢰⣿⣿⠁⢀⠆⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡆⢿⣿⣿⡿⣿⣠⡮⠸⣾⣿⣽⣿⡏⣍⣽⣿⣟⠃⠀⠀⠀⠀⠃
⣾⣿⡟⠀⡼⠀⠀⠀⠀⢸⣿⡏⣼⣿⣿⣿⣿⣤⡟⣿⣾⣿⣿⣿⣷⣶⡏⡗⢸⣿⣨⣽⣿⣿⡌⠁
⣿⣿⡇⢰⠇⠀⠀⠀⠐⠻⣿⡿⡿⠛⠟⣿⢷⢿⠉⢿⣿⣿⡏⢹⣿⣿⣷⠇⢨⣿⣿⣿⣿⡇
⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⠈⠀⢿⣾⠿⡏⣵⡜⣿⣿⣿⣶⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⣿⡄⠀⠘⣿⣾⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣼
⣿⣿⡏⠀⠀⠀⠀⠀⢰⢠⠏⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣀⣼⣿⣿⣿⣿⣿⡿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢛⠿⠻⠿⠶⠶⠿⠿⠳⣤⠀⣀⣿⣿⣿⣿⣛⣋⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣰⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠐⠿⣿⣷⣲⣶⣶⣶⣷⣶⣠⣶⣶⢶⣶⣼⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⠛⡛⠿⠯⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣿
⣿⣿⣷⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⠤⠤⠀⣾⣧⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣀⠘⠒⡀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠹⣄⠀⠈⠂⠀⠀⠀⠀⢠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⠀⠀⠨⣆⠴⠁⠀⠀⠀⠀⠸⡇
⠀⣠⡠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠈⠻⣆⠀⠀⠀⠀⠀⢄⣡⠄
⠀⠀⠀⠮⠿⢦⣀⠀⠀⣀⠠⠝⠓⠦⣀⠀⠀⠀⠀⣀⣹⣆⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⣡⢘⡅⠀⠀⠀⠀⠀⠨⠟⠚⠛⠋⠉⠉⣩⠽⠒⠢⠄⣩⡆⠈⠳⣄
⠀⠀⠀⠀⠶⢦⡁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠖⠛⠛⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣨⠐⠻⠶⣦⣄⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡄⠀⠀⢀⠀⠈⠉⠛⠶⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⢬⠁⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠉⠀⠀⠀⠀⠀⠀⠲⢀⠎⠀⠂⣀⠐⠂
⠀⡀⠀⢸⡄⠀⠀⠀⠀⠐⣄⠀⠀⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠐⠲⠉
⠀⠘⢶⣄⢻⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⢸⡿⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠻⣿⣷⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⣾⣿⣿⣵⠀⣇⣴⣿⣿⣧⠀⠀⠀⠀⠀⠸⣯⠸⠇⣀⣴⣿⠁
⠀⠀⠀⠀⢀⣀⣠⣴⣿⡿⠛⠛⢋⠝⠀⠀⠀⠀⠀⠘⠛⠁⢷⡼⢁⠜⢻⡿⠋⠀⠀⠀⠀⠀⠀⠘⢆⢸⣿⡟⢃⡀
⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣶⣿⢪⣷⠟⢁⡀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠛⠛⠛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣿⣿⡿⣾⠁⠾⣿⡿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡜⢿⣿⣿⠙⣷⡴⠻⣍⡙⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⢟⠻⠛⠀⠀⠀⢠⣿⠀⢀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠙⢦⣰⣆⠀⢸⣇⠠⣶⣿⣿⣿⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣼⡟⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡟⠟⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠉⠊⠓
⠀⠀⠀⠀⠀⠸⣶⣄⠸⢆⠀⠀⠀⠈⠉⠋⠀⠀⠀⢹⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⢙⣻⣧⣼⣤⣶⣶⣦⣤⣄⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠿⠿⠖⠚⠛⠂
⠀⠀⠀⣴⣾⣿⣿⡟⠉⠙⠻⠀⠈⠉⠉⠀⠀⠀⠀⢀⣀⣻⣿⣀⣀⣀⣀⣠⢔⣒⠼⠟⠋⠁
⠀⠀⠰⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⢉⣉⣉⣉⣹⣿⣿⣯⣉⣉⣉⠉⠙⠛⠛⢷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠿⢿⠷⣶⣤⣙⡛⠿⣶⣶⢶⣦⣤⣤⣄⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣷⣶⣷⣶⣾⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⡀⠀⠀⠀⠀⢠⠖⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆⣦⢊⡯⢤⣡⠀⠘⠄⠀⠀⢠⠁⠀⠠
⠀⠀⠀⠀⠀⠀⢇⠈⠰⠄⢀⠀⠀⠀⢸⣿⣟⠔⠉⣁⠀⣚⠀⢱⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠠⡆⠐⢆⢀⠳⢀⡞⠁⠀⠉⢳⠀⣁⠀⠘⡃⠀⢃⠀⢀⠁⢐⣤⠔⣺⡟⠀⣿⠀⠀⠀⢀⡐⠁⢸⠀⢀
⠀⠀⠀⠀⡠⠶⢲⣙⡒⢮⣿⣀⢸⡇⠀⠀⢀⡟⠀⢁⠀⠐⣟⠀⠶⠔⠚⠉⣁⠠⢠⢿⣇⣠⣋⣳⣤⡤⢅⣀⡀⠲⠘⡁⡇
⠀⠀⢰⠈⡡⠏⡊⢱⡸⠒⠀⣽⢸⠃⠀⢠⣾⡿⣻⢻⣧⠀⠠⠄⠀⠀⢀⣠⣀⡴⢃⣿⠋⠋⠙⠋⢘⣷⢀⡀⣗⠀⡾⢸⠇
⠀⠀⡍⢀⡴⠲⣽⡘⠫⡷⣧⠘⡟⣀⣤⣿⡏⣸⢯⣾⡣⠤⢀⣀⣠⣴⡟⢉⢽⣷⡟⣻⣷⣀⡀⣠⡴⣷⡜⣇⣜⡟⠄⠚⠤⢀⡀
⠀⠀⢆⢇⠳⠠⡏⣮⡓⠉⢸⡀⣿⡏⡽⣿⡇⣹⣿⡟⢿⡾⢷⢟⠛⣿⠀⡾⢠⡿⢰⡿⣯⣍⣻⣧⣾⡵⢧⣷⣫⢐⡈⣨⠤⠤⡏
⠀⠀⠈⠉⠒⠘⡈⠲⢁⠀⢀⣷⣿⣷⣆⣿⣆⢸⣿⠇⣸⣁⣫⣨⣦⣵⣤⣷⣈⣷⣼⢁⡁⠚⣹⡿⠁⠀⠀⠈⠛⡇⠀⢀⢀⠐
⠀⠀⠠⣤⣤⣵⣎⠳⣄⢳⡾⢡⣶⣿⣿⣿⣿⣄⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣐⢿⣇⠀⠀⠀⠀⣰⡟⠀⣄⣾⣮⡟⣀
⠀⠀⠀⢡⢹⣗⣪⢟⣪⣻⡇⣿⠟⡭⢻⡟⢡⢦⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣿⣷⣿⣇⣀⣠⡴⣻⠖⠚⠛⣿⠅⠒⠋
⠀⠀⠀⠈⢆⢿⣪⣯⡳⣽⠻⣮⠨⣵⠏⢐⣷⣿⣿⣿⣿⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣙⠿⣅⣸⠃⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠈⢆⠑⢵⣟⣽⠆⠻⣶⠆⣰⣿⣿⣿⡿⠋⣿⣾⡡⣷⣿⣿⣿⠋⡿⠿⠟⣿⠟⣙⣿⣿⣿⣷⢹⡇⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠙⢧⣸⡟⢠⣿⣿⣨⣿⠁⣼⣿⣿⣿⣶⣿⣿⡆⢰⣶⣶⣿⡿⢠⣯⣿⢟⢻⢏⣼⣧⡴⠛⠁
⠀⠠⠖⠒⠠⠒⠂⠛⠓⠮⣼⣿⠇⣼⣿⠏⢸⠇⢼⣿⠋⣤⡏⢰⣿⣻⠀⣾⡏⣽⠁⡇⢠⡿⠉⣿⣆⣿⢛⠁⠀⠀⢦⢠⡤⠖
⠀⠀⠑⠢⡄⠰⠛⣷⣦⡤⠼⣿⣧⣽⣷⣧⣴⢀⣿⢹⣦⣽⣿⣦⡄⣻⣄⣯⣦⣭⠀⣧⠘⣇⠸⠟⣼⠇⠀⠀⠀⠐⣻⡶⠃
⠀⠀⠀⠀⠀⠂⠬⢀⠘⣇⡴⠿⠆⠉⠋⣿⡏⢸⣿⢸⡇⠈⠻⠿⠛⢋⣩⣿⣿⣯⠀⣿⣻⣻⡳⣛⣁⣀⣀⠤⠶⠻⠄⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠫⡟⠓⠀⠀⢀⡾⠻⣧⠸⣣⣿⡇⠀⠀⠈⢯⣟⣿⣿⣿⡏⣸⡏⠹⣌⠙⢯⣄⣈⠉⠦⢀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠄⠈⠀⣠⠽⣦⢀⣠⣿⠁⠀⠙⠛⢻⢣⣿⡄⠀⠀⠘⠻⣿⣿⣿⡴⢿⠀⢀⢮⡧⡎⠉⢲⢤⡈⢢⠀⠀⠋⠒⠒⠒⠂
⠀⠀⢀⠜⠁⠀⠀⠀⠉⣤⡒⡒⣒⣿⠦⠄⠠⠴⡷⣿⣺⣽⢦⡀⢀⠙⡭⡏⠉⢠⠼⣞⢮⠓⢷⣅⣨⠘⠸⠦⢀⡀
⠀⠀⠀⠀⠉⠈⠀⠀⢀⠞⡤⠛⡟⡹⠀⠀⠀⠀⠀⣿⠫⠔⠊⠉⠲⣯⣾⡁⠰⢾⠆⡉⡝⡇⠹⣈⡤⢀⣦⡌⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠐⠘⠡⡀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠈⡛⠁⠀⠑⢦⣉⡚⣃⣇⠜⠀⠀⠘⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠏
⠀⡀⣀⣰⠀⢀⡀⡀⣄⠀⢀⣰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⢠⣷⣿⣿⣾⣾⣿⣷⣿⣷⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠠⠄⠀⠀⠀⠀⠀⢬⡧
⠸⠟⠟⠿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⢍⡧⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠳⠪⣽⣷⣂
⢀⣰⣷⣠⣼⣥⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⣿⣀⠛⢭⣽⣯⠶
⠀⣿⣿⣿⣿⣿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠰⢬⣿⠔⠂⠰⣬⣷⠞
⠀⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣷⣄⠨⠽⣿⠭⠄⡼⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣴⢟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡞⠁⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⣸⢾⣿⣯
⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣆⣸⣿⣿⣿⣷⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⡏⣺⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣾⡀
⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣸⣿⡧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴
⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷
⠀⠀⠀⠀⠀⣿⡻⢿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢻⡿⠿⢟⣿⣿⣷⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⠿⣿⣦⣴⣦⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣷⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠯⠀⠀⠈⠉⠁⠉⠁⠀⠀⠁⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠠⢾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢻⠇⠀⠀⢀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣇⣸⣤⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡤⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢻⣷⠈⢿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢺⡀⠀⠀⣿⠟⠁⠘⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⢸⡇⠀⣀⠀⠀⡀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣀⠀⠀⠠⣿⣿⣿⡿⠀⠸⢇⣀⣿⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⢿⣿⣿⣧⢰⡿⠞⠛⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣶⠀⢸⣿⣿⣇⠘⠁⣠⠖⠈⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⡤⠀⠻⣿⣿⣶⣶⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣴⣿⣿⣿⣧⣿⣸⣤⣾⠿⠋⠉⠁⣾⠿⠿⠃⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣼⡟⠃⣿⠇⠐⠟⠃⠀⠀⢀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠈⢻⣿⣷⣾⣄⢁⡀⠲⠀⠿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⠀⣱⡟⠃⠉⠉⢙⣤⠜⢺⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡿⠷⠾⣷⣆⣹⣧⣼⣿⣿⣿⡿⠿⠟⠛⠃
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠘⠟⠙⢣⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⢸⡇⢠⣾⡅
⠀⠳⣄⡀⢸⣿⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⢸⣿⣾⠟⠁⢀⡄⠀⣠⡆
⠀⠀⣿⡇⠘⣿⡁⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣀⣽⣧⡴⠞⠋⢀⣶⡟
⠀⠀⠉⢁⡴⠈⠉⠀⠀⠁⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠻⣿⣿⣿⣿⡟⠉⠁⣠⠶⣠⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠑⣄⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢿⣆⠈⠻⣿⣿⣷⣮⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⠃⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⣿⡇⠀⣹⠿⠟⠋⠉⠀⠀⡀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠘⠃⠀⠀⣶⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡜⢷⢀⣿⠀⠀⢠⡤⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⢁⣴⡗⠉⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡀⠉⠀⠀⠀⠠⣤⡀⠀⢸⣿⣿⠉⢿⣿⣯⡘⠻⣧⣴⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣼⡿⣨⢻⣶⣌⣿⠃⠀⠀⠹⠁⣠⡾⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⣠⣆⠀⠀⠿⠄⢹⣿⡏⠀⠆⠀⠀⣴⣟⣵⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣆⡀⠀⣤⡀⢻⣿⠀⢺⡆⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠻⣿⠉⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⡟⠉⠉⠉⠉⠀⠹⣿⡾⣿⣇⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⢰⣦⣤⣄⠀⠈⠁⢸⣿⣤⣿⠇⠀⠀⢀⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣰⠁⣀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⢻⣿⣿⣷⣤⡀⠈⠻⣿⠇⢀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡇⢰⡿⠻⣿⣿⡿⢡⠀⣿⢠⡜⢣⣾⠏⠀⠀⠀⠀⠀⢠⣄⡀⠀⠐⠀⠀⠺⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠜⠁⠀⠘⢿⠇⢸⡄⠸⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⠈⠁⠀⣴⠁⠈⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⢠⠆⠀⢀⣤⡀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡌⠙⢧⡀⢰⣈⣷⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⣾⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣶⣼⣿⠊⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠀⠀⠀⠺⣿⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣏⠈⣿⣿⣇⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡀⠈⣤⠀⢀⣴⡀⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⡀⢃⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⢷⣄⡹⡀⢸⣿⠇⢻⣿⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠘⡷⠗⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣤⠀⠀⠀⣉⠛⣿⠈⠻⠀⢈⡟⠀⠀⠀⠀⠿⠃⢠⠀⣀⠀⠀⠾⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣘⠿⣤⡄⠀⠀⠸⠟⠀⠀⠀⠀⠀⡂⠁⢠⣿⡆⠘⣀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⣿⣷⣽⣿⣴⡀⢰⡆⠀⠀⠀⢠⣾⣿⣿⠀⢻⣿⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠈⠻⣿⣿⣿⠀⢸⡇⢠⡆⢠⡿⠋⠈⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠈⠻⣿⣤⣤⡆⢀⣶⠏⠀⣶⣾⣿⡀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠈⠙⣿⠁⠈⣡⡄⠘⣿⡇⢀⠁⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠸⡀⢀⣿⡇⢸⣿⣇⡈⣡⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⢰⣧⠘⣿⡇⠈⢻⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣄⠀⢸⣿⠀⠸⠇⠀⠏⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⢈⣿⠀⠀⠀⠀⢸⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢻⣿⣇⠈⠸⠿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⢹⣿⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣼⣿⡀⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢠⡄⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣴⣤⠀⠀⠰⠀⠀⠂⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⡇⢈⣃⠸⣿⡿⠂⠀⣤⡀
⠀⠀⠀⠀⠀⠀⢴⣀⣿⠃⠈⠛⠻⢀⣀⡀⡀⠀⡀⠀⠈⣴⣿⣿⣦⠀⠀⠀⢠⠀⠂⠀⠀⠁⢰⡿⣀⡀⠈⠀⠀⢀⠄⠹⠄
⠀⠀⠀⠀⠀⠀⢚⣯⣟⣿⠶⢠⢇⣼⣾⣧⠀⠀⠀⠔⠂⣿⣿⣿⣿⠃⠀⠀⡀⠀⣢⡈⢱⠀⠈⢀⡓⠛⠿⠠⢾⡟⠀⢠⠀⠀⣠
⠀⠀⠀⠀⠀⠘⠈⡿⠛⠉⢀⡌⠸⣿⣿⣿⠃⣌⠀⠠⠀⠈⠉⠙⡅⠇⠀⠈⠉⠣⢦⠁⠀⠀⢆⡼⠑⣧⣤⢆⣀⠦⡌⠻⠂⠈⠙⡄
⠀⠀⠀⢠⡞⢰⣿⡷⠀⣹⣿⣿⠒⠀⠁⣠⠆⠙⣦⠀⠀⠙⠀⠀⢫⣤⠴⠂⠀⠀⠀⠀⢤⣀⠈⠁⣺⣿⣿⣿⣿⣷⡄⣰⣷⣄⠀⢕
⠀⠀⠀⠈⠀⣿⡿⢱⠈⣿⣿⣿⠇⠀⠀⠛⠀⢰⡄⠀⠻⣷⣠⣶⣤⠀⠀⡤⠀⠈⠀⠀⠀⠙⠋⠀⣿⣿⣿⣿⣿⣿⣷⠘⠛⠃⡀⠈
⠀⠀⠀⠀⠸⠟⠁⢈⡁⠙⠛⠁⠀⢵⠨⡀⡖⠂⠱⠀⢾⣿⣿⣿⣿⡇⠀⠆⠀⠀⠀⠀⠀⠀⠀⡖⠘⢿⣿⣿⣿⣿⡿⠀⠀⠘⠃⠐⡄
⠀⠀⠀⢻⠀⣿⣦⠹⣷⣆⣠⡀⠘⠚⠃⠁⠀⠶⠴⠶⠈⠻⠿⠿⠋⢡⣀⣠⡀⢈⡃⠀⠀⠀⢀⣴⣶⡇⠙⠿⠛⢋⣤⠘⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠃⠚⠿⠿⢾⣿⣋⠁⡴⢋⡙⢶⠳⠄⠀⣂⠀⣀⣀⡵⠖⢈⡉⢉⣀⡈⠑⠶⠄⢀⠀⠙⠛⠁⢠⣦⠀⠋⣀⣤⣠⣄⡀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⡿⠀⣿⣿⣿⠂⠧⣌⣠⣾⣏⣀⣴⢶⣄⠺⣿⠇⠀⢘⡻⢿⠿⠁⡸⡁⢠⢺⣷⡄⢠⣶⣿⣿⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠇⢀⣠⣤⡄⠀⠀⣟⠰⠆⣻⢠⡌⣠⣾⣿⣿⣿⣷⠆⡀⠑⢌⠉⢁⡀⠘⠻⠟⠋⢀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡵⣄⠈⠛⠿⠇⣀⠀⠈⠓⠚⢁⡼⠹⣿⣿⣿⣿⣿⡟⠀⠃⣀⡀⣴⣿⣿⢀⣤⡴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣟⣲⢠⣄⣀⠀⠀⠀⢀⢠⠀⠀⠈⠙⢛⣫⣥⠀⢺⣻⣿⡷⢈⣭⣤⡄⢠⣼⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢠⡰⢢⠉⠁⣤⣤⣤⠀⠛⠿⠿⠀⠀⠙⠋⢁⡈⠻⠻⠁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢃⠀⠀⠀⠘⣿⠁⠀⠠⠑⠠⠀⠆⠀⡇⠀⠈⢰⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢠⣴⣤⣤⡀⠀⢰⡁⠇⠀⢀⢀⡀⠓⠄⠐⣡⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠻⣿⣿⣶⡄⠀⢀⣾⣿⣿⣿⣆⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⠃⠀⠰
⠀⠀⠀⠀⠀⢠⠀⣠⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢰⣿⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⢺⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡴⠊⠁
⠀⠀⠀⠀⣰⠏⠀⠆⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣤⡿⠏
⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠨⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⢡⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠰⣀⣿⠿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⣯⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⢷⣦⣄⡁
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣧
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠘⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡤⣶⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⣻⣿⣿⠟⠿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⣦⣾⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⠃⣹⠇⠀⠀⠀⣤⣴⣶⣶⣾⣿⠋⢻⣿⣿⡛⠁⠀⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠃⠰⣿⣷⠀⠀⠀⠀⠈⠉⠙⠋⠹⣷⣴⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠛⠙⠏⣻⣤⣄⣀⣀⡀
⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣧⣄⣬⣤⣆⣤⣤⣴⣿⣿⡿⠟⠋⠉⠁
⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣻⡿⣧⣤⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⡿⠛⣿⣿⠿⠿⣿⣿⣿⣧⠀⢀⣴⣶⣄⣢⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣽⣿⣿⠀⠀⠀⠀⠀⢀⣰⡄
⡟⠁⠉⠛⠀⠀⠀⠀⠀⠀⠐⣿⢿⣿⣲⣀⡀⡻⡆⣀⡼⣿⡿⢿⣿⣏⣨⣿⣩⣿⢋⣿⣿⡿⣻⣉⠀⣌⣩⠿⣜⣿⢟⠀⠀⠀⠀⠀⢨⣿⡀
⡁⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⢉⣻⣿⣿⢿⢫⣿⢷⣾⣵⢿⣩⠁⠙⠿⣿⣖⣾⣿⣿⡿⡛⢿⣷⣿⠿⣿⣧⣽⡆⠀⠀⠀⠀⠀⠈⢻⣿⡄
⡶⠂⠠⣷⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣟⣽⡿⣍⡋⠀⠈⢹⣯⣟⣷⣦⣽⣾⣿⣟⡋⣤⣴⣿⡗⣋⣁⣼⣏⣍⣽⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠓⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⠭⢩⢩⡗⣈⣻⣿⣷⣶⡿⣿⣿⣿⠿⠯⣽⣿⣾⣿⣻⣍⣥⣹⣿⠭⣿⡵⠤⣷⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣬⣨⣶⣠⣿⠾⢿⡿⠟⢛⣋⣉⠱⣿⣿⣿⣿⣿⡶⠁⠈⠛⠿⠿⣶⣾⣷⣦⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠹
⢀⣿⣿⡗⣠⣾⡀⠀⠀⠀⠉⣿⣿⣯⣉⣁⣽⣿⠁⠀⢻⡿⠀⣀⣈⣭⣿⣿⣿⣿⣿⣶⡀⣤⣀⣹⣻⡷⣿⠿⣿⣿⣿⣿⠃
⣸⣿⣿⢱⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⣯⡻⣾⣶⣿⢶⡆⢘⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠨⠭⢁⣈⣠⣨⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⢠⣶⣶⣶⣶⡿⣿⣽⡋⠋⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⠟⢀⡀⠀⢸⡟⢻⡆⣿⣿⣿⣿⡿⢿⣿⣾⡶⢾⡿⢓⢻⣿⢡⣿⣿⠟⠀⣀⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⢸⣿⠐⠙⣿⣯⣼⣿⡀⡌⢿⢻⠀⣿⣷⣿⣿⣥⣻⢿⣿⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⠸⣿⢠⣶⣿⣿⣿⣿⣿⣧⣸⠀⢂⣿⣿⣿⣿⡟⠁⢸⣿⣀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣍⠛⠟⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡿⢿⠋⠀⢸⣿⠛⣿⠿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠇⠀⠸⣿⣿⠂⠀⣿⣿⣿⡇⠹⣿⣿⣄⣿⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿
⣿⣿⣿⣿⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢁⡄⠀⢸⣿⣿⡇⠀⢻⣿⣿⡟⣧⣤⣤⡴⠂⠀⢸⠟⢀⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⡇⠀⣿⡏⠋⠀⣿⠿⣿⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠈⠙⠛⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣖⣈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣲⠄⠀⠀⢀⡀
⠀⠀⠀⠀⣿⠈⠉⠙⠛⠛⠛⠛⠛⡛⠛⠛⣛⣋⣉⠩⣿⠀⢠⠚⣁⠨⠆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⡏⢠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡀⢸⣧⢋⡈⠰⠶⠤⡔⠊⠉⠑⠚⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠶⠀⠀⠀⢀⡤⠀⠀⠀⠀⣻⣾⣏⣀⡀⠠⠤⠰⡀⠀⠀⠀⠠⣀⠀⣀⠄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢠⣚⠝⢡⠆⠰⢄⡀⠒⢄⡎⠀⠀⠀⠀⠀⢈⡝⠁⠀⠀⠀⢀⡕
⠀⠀⠀⠀⠀⢸⡀⠀⠰⠆⠀⠀⠀⠀⠀⢠⠟⢁⠔⠁⠇⠀⠃⠉⠢⢄⣗⠦⣤⠤⣢⢭⢭⢺⢳⣤⠢⠴⢊⡴
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢾⣿⠀⠀⠀⠐⠓⢪⠀⠀⠀⢰⠀⡄⠀⠀⠀⠉⠑⠒⢘⠧⣓⠵⠇⠘⡇⠈⠈⠁
⠀⠀⠀⠀⠀⠀⡕⢄⡀⠀⠀⠀⠀⠀⠀⠀⢈⣦⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠑⡄⢀⢳
⠀⠀⠀⠀⠀⠀⠈⠢⢌⣀⣁⣀⣀⣀⣀⣀⡡⠔⠓⠤⣀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⣄⡞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣮⣵⣌⡥⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡿⠀⣾⣿⣿⣍⣧⡄⠀⢠⣄⠧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠦⢀⣠⡶⢿⣜⣴⢗⠛⠋⠙⠋⠉⠟⠒⣦⡽⣶⣾⣤⣼⡝⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡶⣳⢎⣰⣟⣩⣿⠛⣴⣿⣏⣉⣹⡿⠚⣩⡑⠖⠶⠍⠛⢿⡽⠿⢣⡀⢘⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣷⣿⣿⣿⣿⡾⣿⣿⣿⢛⡟⣿⣛⠻⣿⡀⣴⡤⡎⢱⡄⠑⠉⢠⣆⡇⣨⠷
⠀⠀⠀⠀⠀⠀⣀⡖⣄⡊⢠⣥⣴⣿⢿⣿⣿⡾⣿⡟⠓⢿⠶⠿⠶⠿⡷⠿⢷⢹⣷⡞⠀⠀⠈⠉⣷⡁⠒⢒⡆
⠀⠀⠀⠀⠀⠘⠷⣾⣿⣧⣼⣿⣿⣄⣿⡟⡃⢴⣾⠖⢻⣿⠿⠷⠆⠀⣰⠆⠀⠀⢭⣳⣀⡠⣶⣴⡶⠟⢣⡟
⠀⠀⠀⠀⠀⠀⠀⣹⣹⣿⣿⡿⢷⣤⣽⣷⣿⡿⣿⣿⣷⣷⣆⣸⣆⣾⣿⣦⣴⣏⣤⡾⣻⣿⣯⣭⢈⣿⣦⠸⠆
⠀⠀⠀⠀⢀⣠⣾⣿⣏⣿⣿⣶⣆⣹⡟⣿⣯⣗⣋⣿⣟⣝⠿⢿⣿⡿⣿⠆⡼⣿⢿⣿⣻⣿⣿⠋⠀⢳⡄
⠀⠀⠀⠀⠉⠉⠽⢿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣻⣷⣺⣿⣏⣳⢾⣿⢋⣿⡤⠫⣷⣤⠤⠀⠀⠉⢦⣤⣅⡁⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣋⠀⢀⣝⢿⣿⠿⠫⠋⠉⠻⣿⣿⣄⠛⡾⠻⣿⢶⣶⣈⢘⡛⠁⠀⠠⡤⢀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠛⡿⠿⠟⠾⠃⠀⠀⢸⣿⡘⡖⢳⠀⢀⠙⠑⠿⠿⠇⠀⣠⣀⣠⣤⡂⣀⡄
⠀⠀⠐⠖⢀⣶⣞⢢⢄⡠⢀⣴⠶⣄⠙⡃⢀⡀⠐⠂⠀⣼⣿⠃⢠⢸⡄⠛⠃⠠⠂⠚⠛⠨⠉⠩⠉⠉⠉⠉⠁⠂
⠀⠀⠙⢃⢸⣿⡷⢿⢦⡇⢺⡿⣿⣼⢫⢱⣿⣬⣱⠺⣲⡿⣿⠀⣾⠴⣇⠰⡄⣰⣖⣓⠢⠀⣤⠦⡀⢀
⠀⠀⠀⠐⠡⠀⠒⠊⠃⠈⠠⠒⠃⠨⠏⠀⣨⣽⣷⣶⣿⣴⠋⣴⣿⣤⡹⠶⣴⢬⣍⣋⡛⡺⣛⡗⢺⢴⣯⣆⢠⣀⣀
⠀⠀⠀⠀⠀⠐⠒⣒⠛⣛⠻⠖⢺⠿⢻⡟⢛⡉⠀⠋⠉⠀⠀⡀⠀⠀⠉⠛⠲⠶⠚⠲⠯⠙⠋⠉⠑⠒⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠂⠲⠴⠀⠠⡬⠛⠛⠂⠂⠂⠤⠤⠌⠒⠐⠂⠀⠀⠈⠐⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣹⣿⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠾⠋⠀⢠⣄⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⠀⠀⠀⠀⢠⣤⣬
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠄⠀⣾⣿⣶⣧⣤⠀⠀⢰⣆⠀⠀⠀⠀⢌⣧⣄⣤⠤⢶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣴⣾⣿⣿⣿⡿⠟⠻⠛⠛⠛⠛⢿⡿⡿⣿⣿⣿⣿⣿⣶⣴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢾⣛⣋⠉⠉⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⠙⠙⢻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢹⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡄⣠⣐⣚⣷⣷⡦⢀⣀⡀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣤⣴⣦⣦⣽⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣶⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠉⠉⢹⣏⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⣀⣴⣿⣿⣀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣷⣾⣴⣦⣤⣤⣤⣤⣤⣶⣾⣿⡛⠭⠥⢤⠤⣴⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣽⣽⡏⣿⡿⢿⣿⣽⣿⣿⡷⠁⠀⠀⠀⠄⠘⠟⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣧⠌⣷⢻⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣦⣧⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡷⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡷⢜⠂⠀⠀⠀⣀⣴⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⣿⣀⣀⣤⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣻⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣴⡆⠀⠘⠂⠛⠃⠀⠺⠆⢴⡆⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠓⠀⠀⠀⣀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠉⠋⠰⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠁⠀⠀⠠⠄⢴⠑⣀⡰⠆⠀⠄⠇⠀⠃⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⣤⡀⠀⡀⠀⣾⡎⠛⣳⣿⣿⣆⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠼⣦
⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⢠⢠⠀⠀⠀⣿⡏⢹⣿⣿⣿⣟⡇⠀⠀⠀⠀⡀⠀⢠⣄⠀⠀⢁⣤
⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠁⠠⣄⡆⠸⠃⠸⣿⣿⣿⣿⠇⠠⠀⠀⢸⣿⣿⢈⠁⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠾⠆⠀⠀⠘⠃⠛⠁⠀⢰⣿⡆⠐⠑⠘⢿⡿⢣⣾⣦⠀⣶⡌⠉⠉⠀⡦⢰⠀⠀⠘⣁
⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡃⢠⠈⠀⠀⠸⣿⡿⢃⠈⢰⣶⠀⠀⠀⠀⠂⠀⠀⠋
⠀⠀⠀⠀⠠⣶⠀⠀⠀⠚⠓⠚⠆⠀⠀⠐⠀⣧⠀⠀⠀⠠⠀⠀⠀⠀⠰⡶⢴⣾⠀⠀⢀⣤⠀⠀⠛⠆
⠀⠀⠀⠀⠀⣥⡄⠀⠀⢁⢀⢀⠅⠀⠈⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣨⡃⠀⢰⣶
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⢀⡔⠀⣴⣤⣦⢠⣤⡴⠂⠠⠄⠘⣛⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⣻⠇⢀⠈⣀⢀⣌⠛⣃⠈⣿⣷⣶⣤⠀⣘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠟⠀⠙⠁⠛⠀⣶⣦⠉⠀⢿⣿⣿⡿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⢶⣴⠂⠀⡀⠀⠀⠀⠀⠷⠀⠀⠁⠀⠀⡦⢰⠲⣶⣷⠦⠀⠀⢀⠀⠰⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠙⠁⢠⠮⢊⠒⢀⠀⠀⠉⠀⠀⠀⠀⠀⠗⠘⠂⠀⠀⡀⣠⠠⡈⢆⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⢤⠃⠌⢀⠃⠀⢀⠄⠀⡀⢠⢠⠀⡂⠃⠀⠄⠣⠐⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠘⡅⠘⠀⠀⠀⠠⡀⡇⠡⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛
⠀⠀⠀⠀⠀⠀⢀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠴⣦⢴⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠂⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠋⠄⡿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠂⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⠎⠀⠀⠀⡇
⢰⢧⡀⠀⠀⠀⠀⡔⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠋⠀⠀⠀⣼⣁⣀⣤⣄⣀⣀⡀
⡞⠀⠙⠲⢄⡀⡜⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⠇⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠶⢖⡇
⡇⠀⠀⠀⠀⢈⠃⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣞⡎⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠂⠀⢠⠎
⡇⠀⠀⠈⢄⢘⢖⡊⠀⢱⣺⠁⢹⡠⠖⠒⠂⠃⠀⢰⠊⠉⠉⣦⠏⡏⠈⠁⢠⠤⠀⠒⠀⠒⢶⡖⠛⢛⡐⡂⠀⡵⠖⠒⠛⣀⣤⠒⠈
⢹⠀⠀⠀⠘⠻⠀⡀⠀⢸⣨⠀⢸⡏⠀⠀⣀⣠⢸⢹⠀⢀⠀⢩⢿⠇⠀⠰⢿⣰⢀⠀⠀⢀⣸⠂⠀⠀⡇⡇⠀⢀⠀⠀⠀⠹⠃⠀⠰
⠀⢧⠀⠀⠀⠘⡅⠇⠀⢸⡾⠀⢸⡆⠀⠀⠋⠁⢸⣩⠀⢸⠀⢸⣼⠁⠀⠀⠉⠓⡋⠅⠀⡏⢨⠅⠀⢰⡇⡇⠀⠉⢇⠈⡄⠀⠀⠠⠁
⠀⠈⢣⡀⠀⠈⢆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠈⢨⡂⠀⠈⠀⠀⠻⠀⠀⠀⠳⠶⣇⠅⠀⡷⢾⡆⠀⠐⠓⠃⠀⠀⠈⢆⢴⠀⠀⡇
⠀⠀⠀⠹⣆⢀⢵⠀⠀⣖⡆⠀⢸⡇⠀⠀⣴⠖⢹⡇⠀⣴⡄⠀⣶⣀⠀⠀⠀⠀⢅⡂⠀⡇⢸⡂⠀⠀⣀⡀⠀⠀⠀⢸⢨⠀⠀⡇
⠀⠀⠀⠀⠈⠙⡩⠀⠀⣿⠁⠀⢸⡗⠀⠀⠇⠠⣽⠀⠀⡇⣇⣠⠿⠶⠤⠤⠭⣉⡇⡂⠀⠁⢨⠄⠀⠀⡯⠃⠀⢰⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡺⠀⠀⣿⢀⡀⢸⡧⡀⠀⢀⢀⣿⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡶⢾⢠⠀⠐⢿⣂⠀⢸⠀⢸⡸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠶⠋⠟⠸⣷⡵⠛⠷⠭⣭⠭⠟⠋⠁⠀⠀⠀⢀⣀⡀⡤⠤⠤⠤⠤⠤⠄⣷⣼⡬⠭⠋⠸⠮⠟⠻⢄⠘⠒⠳⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠉⢉⡶⠒⠺⠍⢑⣢⠤⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⣀⡀⢤⠤⠵⠒⠛⠲⠤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠿⣁⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠉⠙⠹⡍⠉⠉⠀⢹⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠐⠋⠉⠉⠉⠓⠒⠦⢤⣀⣀⠀⠀⣀⣀⣠⠤⠞⠙⣆⠀⠀⠀⠱⡀⠀⠀⠘⡇⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠛⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⢦⡀⠀⠀⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣐⠃
⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⡿⠀⠐⢾⣿⣿⣦⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡀⠰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⢲⣼⣿⠿⠀⠀⠀⢀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢠⣇⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣸⡼⠛⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⢸⣿⣦⡙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣸⣷⠀⣼
⣿⡀⠀⣼⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⣴⣿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠈⠻⠿⠛⣿⣿⠟⠟⢛⣿⣿⣁⣼
⣿⡆⢐⣿⡆⢸⡆⠀⠀⣘⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢀⣿⣿⡂⠀⠰⣿⣿⠷⣿
⣿⣗⣸⣿⣇⣼⡧⠀⠀⢽⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⣨⣿⣿⣧⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠐⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢿⣆⠀⢸⣆⠘⠋⣀⠀⠀⠀⣷⡆⢀⠀⢠⣄⠀⠰⠀⠀⠀⢀⠘⠇⠀⠀⠀⢠⣄⠁⣀⠀⠀⠠⣤⣁⣼⠂⠀⠀⢀⠛⢀⠂
⠀⠀⠈⠻⠆⠈⡛⠀⠾⠋⠀⠀⠀⠈⠁⡿⠁⠀⠁⠲⠀⠀⠀⢀⡘⢧⡶⠂⠀⠀⠀⣉⠾⠋⠀⠀⠀⣬⡙⠁⣀⠀⠀⠈⣈⠺⠈
⠀⠀⢶⣦⡀⣰⠆⢀⣴⡶⠀⠀⠀⠀⠃⠀⠀⠀⠰⡀⢀⡀⠀⠈⣿⣆⣴⡇⠀⠀⠈⢻⣧⡶⠀⠀⠀⠉⠛⣿⡟⠀⠀⠀⠉⠲
⠀⠀⠀⠉⠀⡿⠀⠈⠁⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⡹⠈⠁⠀⠀⠈⠉⠋⠀⠀⠀⠸⣇⣡⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢈⡙⡔⠗
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⠰⣶⡄⢠⡄⠀⠰⢾⣶⢄⢿⠄⠀⠀⠸⣶⣾⣯⡔⠀⠀⢀⡀⠀⡄⣧⡀⠀⢰⣿⠀⠀⡀⠀⠀⢠⡄⠀⠀⡀
⠀⠀⢈⡄⠈⠀⠃⣀⠀⠀⢠⣌⠃⢸⠇⢀⡀⠀⠺⠃⠙⢇⣴⡆⠀⠀⠁⠀⠀⠀⠰⣌⢰⣧⡿⠆⠀⢠⣜⣡⠀⠀⠙⠳⠀⠘⠃⠀⢚⡁
⠀⠀⢀⠀⡄⠀⠀⣨⠀⢰⣬⡛⠀⡆⢰⣿⠃⠀⠀⠀⠶⢌⣾⠀⠀⠀⣠⠀⠀⠀⢳⣶⡧⠍⠀⠀⠀⢦⡟⢋⠀⠀⢠⣤⣦⣶⣤⠛⠉⠁
⠀⠀⠉⠀⠀⠐⠀⠀⠀⠘⠿⣷⠀⠄⠈⣁⣀⠀⠀⠀⠀⠀⠁⠀⠐⢶⣿⣶⠆⠀⢸⠃⠀⠀⠀⠀⠠⣤⣷⣿⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠐⠛⠛⠛⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠁

⣿⠿⢿⢿⡿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⡶⠆⠘⢛⠿⢿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠀⠈⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⣀⣸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠽⣿⠿⠛⠃⢹⣟⠿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠄⠒⠒⠀⢘⠛⠛⠛⢿⣿⡯⠛⠹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⣀⣀⣀⡀⢀⣀⣀⣿⣦⣀⣠⣤⣀⣤⡀⢀⣀⣀⣀⢀⣿⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠛⡛⠋⠉⠉⠉⠉⠉⠁⠈⠉⠉⢿⣿⡟⠉⠉⠉⠉⠁⠈⠉⣩⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣿⠶⠤⠤⠤⠀⠀⠀⠀⠀⢀⣸⣋⣤⣤⣴⣦⣶⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣯⣭⣭⣭⣿⡿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣭⠀⠀⠀⠀⠀⠀⠐⣿⠟⠀⣛⠀⠀⠀⠀⢀⢈⣛⣡⣿⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠿⠀⣬⡭⠅⠀⢠⡀⠙⠉⠉⠉⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠄⠀⣀⡀⠀⢀⠀⢀⢾⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⢻⡶⣿⣿⠟⠁⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⢿⣏⡀⠀⣿⣧⠀⢸⠀⣼⠀⢠⠅⢀⣴⣶⣶⣄⠺⠿⠿⢋⣿⡆⠀⠀⠘⠄⠀⠀⠈⠃⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡹⠧⣿⡆⠀⣿⢸⠀⢺⢀⡟⢀⡞⢰⣾⣿⣿⣿⣿⣷⣤⢠⣽⡧⣴⣷⠈⠐⠀⠈⠁⠀⢠⡸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⡁⠀⠀⣿⣼⣶⣿⣾⢃⡞⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⠈⡟⣡⡾⠃⠀⠀⠀⠀⢼⣿⠄⢸⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠂⢠⣿⣿⣽⣿⣿⡿⠀⠀⠘⢿⣿⣿⣿⡿⠟⠁⠀⠇⠀⠘⢉⣵⣿⣿⣶⣶⣦⡈⠁⢠⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣿⣿⠀⢀⠀⢀⢀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣷⠈⠉⣡⣄⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⢀⡀⠈⡉⠛⠛⠋⠀⢀⠇⠀⢀⠀⢉⢉⢀⡏⢠⠏⡜⠀⢀⢀⠋⢻⣷⡾⢛⣿⣿⣿⣆⣸⣿⠙⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣍⡈⣧⠀⡇⢠⠀⣧⠀⢸⠀⠄⠇⠀⠇⠸⠘⠀⠘⠀⠇⠇⠾⢸⠀⢸⣿⣷⠟⠉⠺⠿⠋⠋⠰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡗⠈⠿⠿⠷⠸⣆⢷⠘⣧⠸⣆⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⢀⠖⢀⡟⢠⣿⣿⠁⠀⠀⡀⠠⠀⠂⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣤⣤⠀⢠⡀⢹⣾⣧⠸⣇⢻⡄⠀⢠⡁⢠⠀⣠⠀⢀⢀⡏⠈⠀⢊⣤⣜⠛⠏⠀⠀⠄⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢋⣴⡆⠉⠚⣿⣿⣇⢻⣎⣷⡀⠸⡃⠻⠀⠓⠀⠳⠘⠀⠀⢰⣿⣿⣿⣿⣷⠀⢀⡀⠀⠀⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⡇⠀⣀⡘⣷⢻⡞⣿⡹⣧⠀⠁⢠⣷⡄⣠⣴⣷⠀⠀⢺⣿⣿⣿⣿⣿⠑⠿⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⢿⡟⢿⣞⣿⣿⣧⠹⣧⢀⣸⣿⣿⣿⣿⣿⢴⡆⣾⣿⣿⣿⠟⣁⣀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠇⠀⣶⡄⠸⠿⠻⠛⠛⠀⣀⣿⣿⣿⡿⣿⣿⣿⣾⡇⢿⣿⠟⣡⣾⣿⣿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣷⣿⣿⡿⠛⣤⣶⣦⠐⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠈⢿⡿⠛⠁⣀⣘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣦⡀⠞⢠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠄⡀⠀⠀⠀⣀⡄⠀⣤⡀
⠀⠀⠐⠒⠐⣶⠄⠈⠀⠀⠸⠀⠀⠆⠀⠀⣬⣀⣀⣸⡜⠂⠠⠈⠰⠰⡦⠄⠠⢴⠀⠀⠉⠆⢠⣉⣶⣾⡦⢰⡄
⠀⠀⠠⣤⠠⠂⠀⠊⠀⠀⢇⠐⠐⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠉⠰⠠⠀⢀⠀⠐⠀⠂⠁⠀⠘⢀⣌⠉⣱⠞⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠖⠀⠀⠀⠀⢀⢠⠴⠣⠐⠀⠋⠀⣀⡄⢠⣄
⠀⠈⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠀⠀⠀⠀⢄⠘⢋⣥⡿⠃⡄
⠀⠀⠀⠀⠈⠘⠑⠀⠀⠀⡀⠈⠐⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⣲⢢⠠⠠⠀⠀⠀⠄⠀⠀⠙⢻⣷⠖
⠀⠀⡀⠀⣤⡄⠀⠐⠀⠀⢁⠁⣉⣀⠠⢀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠈⠥⠃⠀⠀⠀⠰⠀⠀⠐⡀⠀⠀⠀⠐⡄
⠀⠀⠈⠢⠀⠀⠂⠀⣀⠔⠧⠿⠵⠂⢁⡠⠀⠀⡤⣐⣂⣤⠀⠀⠀⠒⠢⡈⠂⠀⠀⠀⠁⠀⡄⠀⠘⢄⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠰⠉⠁⠀⠁⠀⠐⢀⠀⠀⠀⢿⣿⠏⠀⠐⠀⠀⠀⡀⠀⠀⣔⠄⠄⠀⠁⠄⠔⣆⠠
⠀⠀⠐⢀⠀⠀⠀⠀⠀⠐⠠⠤⠄⠂⠄⢠⠐⠡⡀⢀⣀⠀⠀⠀⢴⣶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠃⠆⠀⠀⠂⠀⠓⠀⢁⠄⡀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠀⠀⢠⠚⠃⠀⠄⠀⠀⠀⡀⠀⠀⠠⡀⡠⢠⠄
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠂⡆⠻⠃⠀⠀⠐⠀⢀⡀⠀⠴⠑⠢⠀⠓⠀⠀⠀⠀⡀⠠⠀⠀⠐⠀⠈
⠀⠀⢀⠐⢀⠀⠀⠠⠈⠀⠀⠀⠑⠦⠤⠠⠭⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠦⠀⡜⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⢶⣒⠻⣯⡙⠻⣯⡉⠙⢯⡙⢿⠲⡖⢦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⠛⠻⠶⣬⣙⠳⠮⣝⡲⢍⡓⠤⣙⠲⣄⠑⢌⠣⡙⠸⠸⠸⢩⢟⡷⢦⣄⡀
⠀⠀⠀⠀⠀⣠⡶⠛⠲⢟⠉⠉⢓⡛⠒⠬⢝⡓⠦⢍⣓⠮⣕⡊⠑⠢⠑⠀⠀⣀⠤⠤⢄⡁⠊⠐⠩⠔⢛⣲⣄
⠀⠀⠀⡴⣛⣟⠋⢀⡤⠮⡃⠀⠺⠀⠐⠃⠀⢹⣷⢶⣮⣍⡒⠨⠁⠀⢀⣠⣴⠁⠀⠀⠀⠙⡄⠀⡴⢯⡭⠵⠒⣛⣦
⠀⢠⣾⣯⣥⣶⣿⣿⣤⡀⡬⠒⣤⡤⠶⣤⠔⠋⠀⢻⣿⠃⠙⠢⢤⣖⡛⠀⣿⣠⠴⠦⣄⣠⣿⡟⠁⣼⡿⢶⣛⣯⠽⠳⡄
⢠⣿⣿⣿⣿⣇⣨⡍⣙⠳⢾⡉⣀⣤⡚⠁⠀⠀⠀⣣⣿⡇⠀⡾⠛⠦⡉⠛⠤⣤⣶⢶⡿⢿⠍⠁⠀⢹⣇⠀⠙⣾⣵⣴⣿
⣾⣿⣿⣿⣿⣞⢿⣿⢿⡿⣶⣌⠛⠿⣿⣷⣤⠀⣼⠟⠁⣠⣾⣵⣤⣰⢃⣀⣠⣬⣽⣯⣄⠁⠀⣀⣤⣿⣷⣴⣿⣿⣻⣿⣿
⣿⣿⣹⣿⢻⣻⣞⣿⣿⣿⣿⣿⣿⠦⢤⣙⠻⢾⣷⣶⣾⣿⣯⣭⡿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣲⣿⣿⢻⣯⢿⣿⣿⣿⣷⣿
⢿⣟⣿⣿⡻⣭⡟⣿⢾⣿⢿⣿⣿⣷⣆⡉⠳⣦⣮⣉⡟⢿⡿⢿⠟⠋⣩⣭⣴⣒⡺⣿⢟⣿⣿⣛⣯⣿⣿⣽⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣦⡌⠙⠫⣽⣿⡀⠙⠶⢦⣤⣉⡭⣩⣭⣽⣯⣷⣿⣛⣯⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣟⡿⣿⣿⣿⣿⣿⣿⣷⣿⣽⢿⣿⣾⣿⣿⣵⣮⣿⣯⣳⣦⠀⠀⠉⠻⣿⣿⣿⣾⣿⣿⣿⡭⣽⣛⡳⢿⣿⣿⡿⠃
⠀⠀⠀⠻⣿⣷⣿⣻⣿⣿⣿⣿⣿⣻⢿⣶⠭⣒⢭⣻⣿⠿⠛⠉⠀⠀⠀⠀⠐⢸⣿⢿⣿⣿⣷⠾⣿⣛⣻⣯⣭⣭⠟
⠀⠀⠀⠀⠀⠙⠿⣿⣫⢯⣯⣽⣿⡿⣯⣺⣽⠾⠛⠉⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⣿⣻⠿⢟⣻⡭⢭⣖⣲⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣽⣷⣿⣻⣿⡀⠀⣀⠀⠀⠰⡀⠀⠀⠂⣠⢞⡯⣟⣭⢖⣻⣽⣒⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢭⣤⣾⣏⣈⣀⣀⣼⣿⡿⠾⠿⠞⠛⠋⠉

⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⢠⣤⣛⣷⣾⣃⠀⠺⢿⠃⢀⢮⠇⠀⢶⣦⣼⢇⡀⠀⠀⠈⠛⠁⠀⠀⠀⠊⠀⠃⠀⠀⠀⠘⡀⠘⠛⠁
⠀⠀⠙⠋⠉⣿⣿⠆⠀⣤⡮⠗⠋⠀⢠⡶⢷⣵⣿⣿⡇⠀⠀⣰⣿⣷⣦⠀⠀⠘⣁⣀⠀⠀⠃⠐⢀⣠⣄
⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠷⡀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠸⠿⣿⠟⠀⢀⡀⠀⠈⠁⢠⣶⣷⡜⠛⠋
⠀⠘⠿⠁⠀⠀⠀⢳⡐⡔⠎⠂⠉⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⣞⠩⠙⣾⠆⠠⠀⠛⠋
⠀⠀⡀⡀⢀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠈⠓⠻⢧⡤⢼⡄⠀⠀⠀⣀⣤
⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⡇⢰⡇⠀⠀⠀⠸⣔⣣⠇⠀⠀⠀⠙⠛
⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⣾⠀⣿⡆⢀⣤⣄⣴⣶⡆⣿⡄⣿⡶⢸⣿⣷⣴⣠⡆⠀⠀⠀⠀⠀⣀⣴⡖
⠀⠀⠀⠈⠛⠛⢁⠀⠀⠀⠀⢿⡟⢻⣇⠿⡯⠁⠛⠋⠁⠀⢀⣤⠀⠈⠀⠀⠈⢹⡇⠀⠐⠛⠛⠛⠛⠉
⠀⢠⠄⠀⢀⢀⣼⡀⠀⠀⢀⡘⠋⠀⠁⣰⠶⠀⠀⠀⣤⠄⢼⡿⠀⡀⢀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠻⠙⠟⠙⠁⣁⣀⠀⠀⣿⡇⠀⠖⢰⣿⢀⣶⣿⠄⣭⡷⢸⣧⠄⠷⣿⢇⣿⢠⣾⠿⠀⠀⠀⡂⠀⠁
⠀⠀⢀⠀⠀⠀⠙⠿⠁⠀⣿⣇⣠⡇⢸⡇⠀⠛⠋⠀⠀⠀⠀⠀⢠⣤⡿⢸⣯⡌⠉⠁⠀⠀⠀⠀⠀⠀⠚
⠀⠀⣸⣧⠀⡠⠐⠀⠀⠀⠛⠛⠈⠁⠀⠀⠀⠀⢀⣀⢴⣏⡂⠀⠈⠉
⠀⣶⣿⣿⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠠⠶⠚⠋⠉⠀⠀⠀⢀⣀⡤⠶⠂⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⣦⣀
⠀⠙⠛⠋⠀⠀⠈⠀⢁⠀⢠⡄⢠⣶⠀⠀⠀⠀⠀⠺⠿⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⢀⢀⠀⠀⠉⠀⣲⣟⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣶⢆⡀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⢠⠁⠀⠁⠀⠀⠀⡽⢿⠿⠟⠛⣠⣀⠀⠀⠀⣄⡖⠛⠀⠀⠀⣶⣄⠊⠀⠈⠙⢡⢂⡀
⠀⠀⠀⠀⠉⠈⠀⣠⣿⣿⠇⠀⣀⣀⣈⠁⠘⠳⡶⣠⡀⠀⠀⠀⣴⣿⣿⣧⣦⡀⠴⠀⠀⠐⠃⠀⠠⠆
⠀⠐⢿⣿⠀⠀⣼⡿⠟⠁⠀⣿⣿⣿⣿⠀⠀⠉⠁⠈⣠⣄⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠘⠀⠂
⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠙⠻⠁⠀⠀⠀⠀⠈⠛⠛⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠋⠁⠀⠀⠑⠂⠄⠀⠐⠖⠠⠀⠀⠀⠀⣠⡤⠀⠀⣠⣶⣶⡤⠖⠋⠀⠀⠠
⣆⣠⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠁⠀⠀⠘⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠤
⣿⣿⣿⣷⣶⣷⣶⢀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⣠⡶⠚⠃⠀⠀⠀⠀⠀⢀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣴⣾⣦⡆⣶⢀⠀⣿⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠟⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⢸⡇⣦⣿⣿⣷
⠟⠛⠛⠋⠋⠋⠉⠈⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⣾⡀⠀⢀⡄⢀⢠⣀⡀⣶⢀⣆⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢰⣿⣧⣆⣼⣧⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠟⠻⣿⡿⠿⢿⡿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⠉⠀⠁⠙⠙⠋⠛⠻⠻⠛
⣿⡿⣿⣿⣿⣿⣧⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⣯⠀⢻⣿⣿⣿⣿⡆⣼⣿⠀⠀⣀⠀⠀⠀⣼⡂⠀⠀⠀⠀⠀⣾⣧
⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣗⢠⣿⡀⠀⢠⣿⣧⠀⢠⡄⠀⢰⣿⣿⠆⠀⠀⣄⠀⠀⠀⢠⡄
⠆⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣯⣄⣼⣧⠀⣺⣿⣿⣶⡄⢸⣿⠀⠀⠀⣾⣷
⠀⠀⠈⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣼⣿⣿⡿⢻⣿⣿⣬⣿⣿⣿⣿⣥⣿⠿⠇⠀⢸⣿⣿⠂
⠀⠀⠀⢀⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢰⣦⣿⣿⣿⣶⠄⠀⢠⣇
⠀⠀⠐⠶⠿⣿⣿⡃⠀⢐⣿⣿⣿⡏⢹⣿⣟⠀⠐⣺⣿⣿⣿⣿⣿⣿⣿⡃⠀⢒⣿⣿⣿⣿⣿⣆⠀⣾⣿⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣛⡻⠯⠀⠀⠀⢸⣿⣿⠀⠨⣿⠥⠀⠀⠈⣿⣿⡿⢻⣿⣿⡯⠀⠀⠀⢹⣿⣿⣿⣿⣿⣼⣿⣿⣦⠀⣦⠀⢀⣿⡇
⠀⠀⠀⠀⣀⡤⠂⠀⠀⠈⠭⢿⠇⠀⠀⠘⠀⠀⠀⠉⠽⣿⠁⠸⣿⡿⠃⠀⠀⠈⠭⢿⣿⡿⠉⣿⣿⡿⢿⣿⣲⣿⡂⣸⣿⣷⠄⡄⠀⢀
⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠿⠛⠀⠀⠀⠀⠀⠤⣿⠃⠀⢹⣿⠇⠘⣿⢻⣿⣿⡿⢹⣿⣿⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢉⠉⠀⠀⠈⠋⠀⠀⠃⢘⣿⣿⠃⠈⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⢌⠎⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰
⠀⠀⠀⠀⠁⠀⢸⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣷⣣⠂
⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠄⠜⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥
⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢀⡀⠉⣀⣼⢏⡴⠒
⠀⠀⠀⠀⢡⠈⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡌⠀⠆⠀⠀⠀⠀⠀⢀⡡⣼⣿⣷⡈
⠀⠀⠀⠀⠀⢣⡉⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠐⠀⠀⠀⠀⢀⣵⡿⠉⡄
⠀⠀⠀⠀⠀⠀⠳⡀⢣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⢹⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡁⠈
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂