Freshwater bass Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⣿⢷⠲⢤⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⢻⣮⠭⠖⣚⣉⣭⣤⣤⣶⣶⣦⣤⣭⣍⣛⣛⣲⣶⣴⣒⠦⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⢀⣰⢾⡷⢚⣩⣴⣾⣿⣿⣿⣿⣿⢿⢿⡿⡿⠟⣫⡿⢻⣿⣿⣏⠾⢻⣿⠻⢡⣶⣶⡌⢂
⠀⠀⠀⠀⠀⣨⢟⣥⣾⣿⣿⠿⠟⠛⠙⠈⠁⠁⠀⠀⡴⠃⠀⠀⠔⠁⠀⠈⠛⢳⠿⠃⠀⣿⣿⣯⣿⠈
⠀⣀⡤⢒⣟⣵⣿⠿⠛⠉⠀⡀⢠⠀⣴⢠⣇⢠⡇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⠇
⢺⣿⣭⣿⡿⠛⠀⢠⡀⣶⡸⣷⢿⡇⢿⠘⡿⢸⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⢾⣿⣿⣿⡿⡰
⣸⢧⣿⠋⢡⠀⣧⢸⣿⠻⣇⠝⠚⠛⠿⢶⣶⣮⣦⣈⠀⠀⠀⢀⠐⢄⠀⢰⠀⢇⣀⡼⢸⣿⣿⣿⡁⡅
⢸⣾⠃⢠⣸⣇⢻⠀⠙⠀⠉⠢⣀⠀⠈⠉⢿⣿⡳⣤⠀⠀⠀⠀⠁⠒⠒⠰⢧⣀⣁⡼⠎⠛⠈⣉⠱⠧
⢈⡇⣸⡾⡇⠉⠀⠀⠀⠀⣀⢠⠸⠉⠒⠛⠉⠀⠀⠀⠤⢤⡄⠀⢀⠀⠀⠀⠀⠉⣙⣛⣛⣒⣒⣃⣀⣀
⠸⣷⠏⠁⠀⠀⠄⠐⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣬⣿⢷⣴⣀⢀⡠⠚⠉
⠀⡟⠀⡀⠔⠁⠀⠀⠀⢀⣀⣠⣤⣴⣶⡾⠋⢙⣿⣿⣿⣿⣶⠈
⠀⠰⡰⠁⠀⠀⣠⠶⢿⣿⣿⣿⣅⣠⢊⢠⢶⣿⡟⣿⣿⣿⣿
⠀⠀⠀⢄⣰⣿⠿⡷⣤⢀⠉⡛⠿⢿⣿⣿⣿⣿⣧⠘⣿⣿⣿
⠀⠀⠀⠀⠁⠻⢄⡀⠉⠙⠙⠓⠷⡦⣦⣤⣤⣤⣼⠀⣿⣿⣿⣧
⠀⠀⠀⠀⢢⡠⠀⠀⠉⠑⠒⠲⠤⢄⣀⠈⠉⢉⡟⢠⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣄⣾⣿⣿⣿⣿⡇
⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣴⢖⣛⡓⠶⠶⠞⣛⣛⠛⠛⢛⣛⠛⠛⠛⠶⠦⣤⣤⠶⣾⣿⣦⣤⣤⣤⡄
⠀⠀⣼⢧⡟⣫⣿⣷⣷⣾⣿⣿⣿⣧⣤⣤⢩⣝⡛⢿⣶⣶⣶⣯⣽⣛⡴⣾⣿⠿⣤⣤⣤⡀
⠀⠀⣿⣼⣾⣿⣿⣿⣿⣿⣻⣟⠛⢛⣿⣿⣼⣿⣿⣷⣜⣷⣭⣭⡹⣿⠿⣷⣮⣟⠿⣿⣿⣥⣀⡀
⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⡇⢹⣷⠰⣬⣭⣍⠙⢿⣿⡟⣿⣿⣿⣿⣧⣳⡈⠙⠟⢿⣮⡓⢿⣿⣧⡀
⠀⠀⢹⣿⣧⣿⣿⣿⣿⡿⣇⣄⣿⣧⠀⠙⢿⢷⣾⣿⣿⣿⠿⣿⣿⣿⣿⣷⣶⡀⠈⢹⢿⣦⡹⣿⣧⡀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⠞⢙⡇⢿⢿⣇⠀⠈⠀⠙⠿⢹⣿⠀⢻⣿⣿⣻⣿⣟⣷⣿⡆⡈⠘⢻⣮⢿⡀
⠀⢠⣿⡿⣿⣿⣿⣟⣡⣴⠛⠉⠁⢛⣛⣿⣦⣤⣀⣐⢭⡿⠀⠈⢈⡵⢣⡏⠟⢹⣷⢿⣿⣰⡆⢹⣿⣷
⣴⢛⣿⣷⣿⣿⣛⣭⣭⣴⣖⣒⣋⣭⣭⠤⣿⡅⠲⠶⢎⣀⣀⡴⢋⣴⣿⣶⣶⣴⣗⣾⣿⠝⣛⠶⣽⣿⣇
⠙⠿⠿⠿⢿⣯⣉⠍⠉⠁⠤⠤⣤⣤⣤⣴⠿⡿⡶⣄⣀⣠⣿⣵⣿⠁⠉⣹⣿⣿⣿⣿⣿⣿⣗⣒⠈⣿⣿
⠀⠀⠀⠀⠀⠈⠙⠛⢷⣿⣿⣶⣶⣾⣛⡤⣞⢿⣦⣤⣤⣶⣿⠟⠁⠀⢹⣿⣿⣿⣿⣿⡿⢿⣟⠊⢠⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠛⢿⣿⣿⣿⣿⣿⡉⠑⠊⠀⠀⠀⠀⠛⢿⣟⣿⣿⣟⣧⢶⣶⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣝⡪⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⣟⠁⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣷⣯⣷⣶⣤⣤⣄⣠⣔⣶⣶⣤⣙⠻⣿⣽⣧⢘⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡾⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣿⠛⣿⣿⡿⠿⠻⢿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠷⣉⠈⢀⠟⠋⠑⢲⣶⣤⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⡶⣶⣶⣶⣶⠞⢩⡏⢋⣴⣛⠀⠁⠀⠐⠁⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⠨⣷⣿⣿⣿⣿⢡⣾⡟⢿⠛⠉⠈⠀⠀⠀⠀⠀⣀⡴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣯⣽⣿⠇⠾⠁⠀⠀⢀⣠⣤⣶⣶⣶⣶⣿⣿⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡟⣿⣿⠀⢀⣠⣤⣶⣿⡿⡿⣻⣽⣯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⡟⢹⣿⠋⣻⣿⣿⣿⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢹⡿⣿⣟⣿⡿⠀⠀⢹⡆⠘⠛⠛⠋⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠿⣿⣾⡿⠁⠀⠀⠈⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣃⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣫⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠒⢂⡈⠉⠉⠉⠉⠐⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠀⠀⠀⠀⢰⣿⣷⣤⣴⣤⡄⡀⠀⣠⣤⡄⠈⠙⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣠⣾⣿⣯⣶⣶⡀⠀⠀⠙⠋⠙⠛⣫⠏⣴⣾⣿⣿⣧⠀⢠⣤⣤⡆⠈⠉⠓⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣀⣄⣴⣶⣤⠞⢡⣾⣿⣿⣿⡿⣣⣶⣿⣿⢫⣀⣿⣆⢻⣿⣶⡀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⡎⠀⣸⡿⢙⡿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠀⠀⠉⢸⡿⢿⣿⣿⡎⠻⠿⠿⠞⠛⠛⠛⠠⠴⣖⣛⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣴⣿⡿⠃⣴⣿⢃⠎⢃⠻⢹⣿⣿⣿⣿⡿⠃⡴⡸⣰⡇⠀⠀⢲⠀⠈⠀⢀⡤⠶⠶⠶⠶⠖⠀⠀⠀⠀⣴⣿⣿⣥⣶⣶⡶⠶⢾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢣⣾⣿⣿⣧⣾⣿⠟⣈⠀⠈⡄⠈⣿⣿⣿⡟⠀⢠⡇⣇⣿⣿⠀⠀⠀⠀⠀⣰⠋⠄⠂⠂⢀⠆⢠⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣸⢡⣿⣿⣿⣿⣿⡿⠠⠀⡏⠀⠀⠀⠀⠙⢻⡟⠀⡀⣾⠀⣿⣿⣿⣿⡄⠀⠀⠀⡏⠀⠀⣠⢎⠄⢀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠉⠛⠀⠀⢸
⠀⠀⠀⠀⣀⣴⢿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⡇⠀⠈⡄⢡⠀⠈⠀⢰⣷⣿⡄⠈⢿⣿⣿⣧⡰⠀⠀⠀⢀⠞⠁⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡞
⠀⠀⣠⠞⣉⠔⣫⣴⣿⣿⣿⣿⣿⡿⠀⠀⠀⣧⠀⠀⠘⢆⠳⡀⠀⢸⣿⣿⣷⣄⠀⠉⠛⠿⣿⣷⡄⠀⡎⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⠁
⢠⡞⠁⠈⠀⠚⠋⣰⣿⣿⣿⣿⣯⡴⠀⠀⣴⣿⠀⠐⡀⠈⠳⣝⢶⣌⢿⣿⣿⣿⣷⣦⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣟⠀⡜⠀⢰⠇
⢾⠀⠀⠀⠀⠀⢝⣾⠿⢟⣽⠟⠉⢀⣠⣾⡟⠀⢧⠀⠈⠢⣀⠈⢳⡌⢦⡙⠻⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⠀⠈⠘⠓⠦⢄⡈⠉⠛⢿⣿⣿⣿⣏⠞⠁⢀⡏
⠈⠳⠦⣄⣀⣀⣠⣴⡾⠋⠀⢠⣾⣿⠿⠋⠀⠀⠈⢧⡀⢄⠈⠙⠲⠭⠤⠉⠓⠦⠬⠭⠭⠍⣉⠛⠛⠁⠀⠈⠀⠒⠀⠀⠀⠈⠑⠤⣀⡀⠉⠛⠣⢄⣀⡞
⠀⠀⠀⢸⡿⡟⠋⠁⠀⢀⡀⣻⣿⣡⡂⠀⠀⠀⠀⠀⠑⢤⡑⠢⢤⣄⣘⣤⣤⡀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢤⣈⠓⡄
⠀⠀⠀⢸⠇⠀⢀⣤⣾⣿⣿⡋⢡⣿⣗⡄⢀⠀⣀⣠⣴⣤⣍⠓⠦⣄⡀⠀⠠⠚⠛⣦⣤⠀⠀⠀⠀⠀⠈⠙⠲⠶⠤⠤⢤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠈⣱⠄
⠀⠀⠀⢸⣇⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣀⣀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠀⠤⠤⠐⠚⠁
⠀⠀⣠⠞⡋⠝⣫⣿⢿⣿⣿⡆⠻⠿⣿⣯⣍⡉⠉⠹⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⠀⣤⣀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠤⠒⠂⠉⠁
⣠⣞⣁⣀⠀⠉⠉⠠⠵⢿⣿⣷⣿⣿⣶⣶⣶⣶⡶⣲⠖⠀⠀⣽⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⡟⠉⠉⡅
⠉⠉⠉⠉⠻⡄⢦⠰⣆⠘⡿⠋⠘⣿⣿⣿⢿⣯⣾⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃⢸⣿⣿⡜⢿⣟⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠹⣌⢧⡘⢷⡆⠀⠀⠽⢋⢵⣛⣛⠿⢿⣄⡀⠀⠀⠀⠈⠻⠟⠃⢠⣿⣿⣿⣷⢸⣿⣷⠢⣎⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⡤⣤⠤⢤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠈⢧⡹⣦⡇⠀⣤⣶⣤⣤⣌⣉⠛⠛⠿⣿⣄⢠⣄⡀⠀⠀⢰⣿⣿⣿⣿⠇⣼⣿⣿⡆⢠⡙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⡔⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⡙⠶⣮⣌⣙⡛⠿⢿⣷⣶⣌⢿⣦⣙⠻⣦⣄⠈⠉⠙⠛⠋⢸⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣛⣛⡃⣠⡿⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣿⣬⣥⣤⣤⣀⣀⡀⠻⣿⣷⣮⣿⣿⣦⣀⠀⠀⠘⠿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⡞⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⠿⡿⡿⣿⣿⣿⡿⡾⢿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠁⠀⠙⠛⣽⣿⣿⣿⣛⡾⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠁⠈⠌⠀⢀⡴⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⢤⣴⣿⡻⣿⣿⡟⣻⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷⣯⣇⠈⢯⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢿⣿⡛⣿⣿⣷⣽⣿⡿⢆⡈⠘⢷⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣷⣝⢿⣞⢿⣷⣝⢿⡺⣄⡈⠁⠙⣇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡻⢧⡹⠧⠙⠯⠳⣍⠀⠉⠒⢤⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠠⣀⠈⠓⢤⡀⢰⠏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡢⠌⠳⢄⣀⣽⢯⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢔⡲⠙⠳⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣟⣙⣃⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⡛⠛⣛⣉⣙⣛⠛⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠩⠵⣶⣶⣬⣭⣭⣤⣥⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⢀⠀⠀⠀⠀⣴⡾⠿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡿⢁⡄⢁⠀⠀⠞⠉⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠿⣿⣿⡿⠁⣾⣿⠈⡀⠈⠂⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣀⣿⣼⣿⡧⠀⣿⣿⣇⠣⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢿⣿⣿⣷⣾⣿⠏⣹⠄
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠟⠛⠋⠉⣠⠾⠋
⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⠒⠔⠂⠀⠀⠀⣰⠋
⠀⠀⠀⢸⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⠷⢌⡛⠿⠿⠛⠋⠀⠀⢀⡤⠂⢀⡼⠁
⠀⠀⠀⢺⣿⣿⠏⣼⣿⣿⣿⡿⠟⠋⠉⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠶⠞⠋⢀⡴⠋
⠀⠀⠀⠺⣿⢏⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢤⣄⡙⠲⢤⣄⡀⠀⢀⡀⢄⣤⡄⠀⣠⠞⠋
⠀⠀⠀⠘⡟⣼⣿⣿⠏⠀⠀⠀⠀⠀⢀⣀⣶⡾⠿⠛⠂⠀⠈⠑⠤⢄⡀⠑⠉⣠⠞⠁
⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⣈⣭⣶⣾⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⢀⣴⣿⣿⡏⠀⠀⠀⢀⡤⢖⣫⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⠞⠁
⠀⣰⣿⣿⣿⣿⠁⠀⠀⠖⣫⠔⣫⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⡚⠁
⣰⣿⣿⢹⣿⣿⠀⠀⠀⠈⡁⠾⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⣴⣿⣿⣆
⣿⣿⣿⢸⣿⡇⠀⠀⠀⢀⣹⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣷⡀
⠹⣿⢹⠸⣿⡇⠀⠀⢴⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⢀⣴⠋⠻⣿⡟⡇⡏⠁
⠀⠀⠘⠆⣿⣿⠀⠀⣠⡿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠁⠁⠃
⠀⠀⠀⠀⠸⣿⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠹⣇⠀⠈⡿⠆⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⣠⣞⣮⡄
⠀⠀⠀⠀⠀⠀⠙⣦⠸⡷⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⣀⡀⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠗⠀⠉⠙⠙⠛⠛⢿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣷⣶⣤⡤⠄⠀⢀⣘⠿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠉⠓⢦⣝⡻⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣽⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⢀⡬⠍⠉⠩⡩⠉
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡔⣿⢯⣽⣿⣿⡟⣲⣶⣶⣶⣖⡲⢲⣶⣶⣶⣶⣶⣤⣤⣖⣵⣚⣠⢤⡀
⠀⠀⠀⠀⢱⣿⣿⢿⡇⠉⠻⣿⠻⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣖⣦⡀
⡆⠀⠀⠀⣾⠟⢉⣾⡇⠀⠀⠀⠳⣄⠙⠿⣯⣿⣿⣏⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡷
⣇⣠⣶⠚⠁⠀⠛⢹⡧⠀⠀⠀⠀⠘⣷⣤⠃⡟⠃⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⡟⠛⠉⢀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⢴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣾⡿⠋⠉⠹⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠀⠀⢐⠁⠀⠓⠉⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠑⠋⠋⠻⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢀⡞⠁⠀⠀⠘⠁⠀⠀⠀⢠⣤⡀⠀⠀⢀⣀⠀⠀⠀⡠⠊⡀⢀
⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠅⠘⢠⠆⠀⠅⠀⠀⠀⢀⣠⣿⣿⣿⢷⠀⠀⠈⠟⠃⠘⠠⠎⡠⢂
⠀⠀⠀⠀⠀⡆⠘⠈⢀⠄⠀⠀⠠⠀⠐⣤⣹⣶⣶⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⣠⠄⢁⡀⠀⠀⠀⠀⠀⠄⣻⢿⣿⣿⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠠⠀⢊⠀⠋⠀⠀⠐⠀⠐⠢⠀⢀⣨⣽⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃⠁
⠀⠀⠀⠀⠀⠀⠋⠑⠄⠀⠀⠀⠀⠀⠘⠀⢨⠛⠈⢿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣶⣲⣾⣿⣭⣭⡭⠭⣭⣴⣶⡶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣤⢶⣻⣽⣶⣿⣿⣿⣿⡿⢷⣦⣬⡝⣿⢙⣽⡏⣼⡏⡇
⠀⠀⠀⠀⠀⣠⣾⣛⣷⣾⣿⣿⣿⣾⣿⣿⣿⢟⣿⠾⡟⠁⠀⢾⣿⣿⢷⣿⣿⣿⢹⡟⣿
⠀⠀⠀⣀⢼⣉⣙⣻⣷⣿⣿⣿⢿⣿⣿⣿⣵⡿⣿⡦⠀⠀⠀⠰⣾⣇⣾⣿⢹⣿⣿⡇⣿⡀
⠀⠀⠀⣸⣀⣨⣿⣿⣿⣿⡿⣸⣧⡝⠏⣼⣿⠀⣾⠀⠀⠀⠀⠀⠹⢸⣿⣿⣼⡇⣇⠃⢘⣧⡀⠀⢀⣀⣤
⠀⠀⠀⢩⣭⣿⣿⣿⡿⣟⠇⢿⣿⣿⡗⣻⡟⠀⡿⠀⠀⠀⠀⠀⠀⠸⡏⠀⣿⡇⢸⣟⣾⣟⣿⣿⣿⣟⣫
⠀⠀⠀⡸⣺⣿⣿⢿⢭⣿⢷⣿⣿⣿⡟⢸⡵⠀⣷⣄⠀⠀⠀⠀⢠⠶⠿⠀⣿⣧⣸⣿⢟⣛⣹⣷⡿⠋⠁
⠀⢠⣮⠾⣿⣿⣟⣶⣾⠻⣿⣿⣿⡟⠃⠀⢣⠳⡹⣽⣧⡀⠀⢀⡿⠀⠈⠻⠛⣉⡥⠖⠛⠋⣡⠾⠁
⢠⢳⢿⣿⣿⡿⠹⣿⣿⡧⠀⠉⠛⠃⠀⠀⠘⣷⣍⡛⠓⠛⠛⣄⠀⠘⢋⣭⣭⣥⣶⣂⠴⠚⠁
⡏⡿⣟⣽⣿⡇⠀⠘⠿⠷⠄⣠⣶⣾⣿⢿⣿⢟⣟⡹⢷⣶⣶⣷⣮⣿⣿⣿⣿⣿⠋
⡷⢋⣾⣿⣯⠁⠀⠀⠀⢰⣾⣟⠿⣯⣾⡯⢗⡿⣾⣿⠼⠀⠀⠉⠉⠉⣉⠽⠋⠁
⠁⠙⠿⣿⣟⠀⠀⠀⠀⠈⠙⢿⣷⣄⣋⣖⣣⣴⠞⠁⠀⣀⣤⣶⣶⣾⠁
⠀⠀⠈⢹⣿⣤⡀⠀⠀⠀⠀⣀⣠⣤⡿⠿⠛⠉⣠⣶⣿⣻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢻⣟⣷⣄⠀⠀⢿⠛⠉⠁⠀⠀⣀⣼⣟⠟⣷⣹⢿⣿⢿⡟⡿
⠀⠀⠀⠀⠈⢻⣯⣟⠇⢀⣼⠆⠀⠀⣴⢋⡴⠉⠘⢦⠱⠋⣿⣿⡞⠃⡇
⠀⠀⠀⠀⠀⠀⠹⣿⡃⢰⡟⠀⢀⠜⡵⣿⣷⣖⣚⣩⣵⣮⣙⢿⡗⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣇⢀⡼⠃⠀⢋⣷⣾⣯⡭⠽⠿⣾⣟⣛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡟⢰⣴⣿⣟⠙⠿⣿⣻⠿⠯⣭⣭⣭⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠛⠃⢿⣶⡬⣶⡲⠯⠭⠭⢭⠭⠥⠴⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣉⣁⡈⠙⢃⣀⣀⣀⣤⣤⠶⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠦⣶⣖⡲⢒⡶⡾⠭⣭⣽⣿⣷⣲⠤⣶⣶⣿⣿⣟⣀
⠀⠀⠀⠀⠀⠀⢰⡏⠋⢿⡌⢷⣦⢍⣷⣧⣾⡿⢮⠻⣿⣿⣿⣷⣭⡚⣩⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠈⣷⢧⠘⣿⠈⡇⠀⢘⠈⠁⠀⠔⠀⡌⠉⠃⣿⣿⣿⣶⣯⣿⣿⡄
⠀⠀⠀⠀⠀⢀⡴⢛⣛⠛⠛⠳⠤⠞⢺⣤⣄⣀⡀⠴⠋⣡⢘⠙⠿⣻⣿⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠈⢧⣭⡙⠍⠉⠐⠒⢶⣯⣅⣀⣀⣴⣋⠉⡰⢉⣷⣾⣽⣿⣿⣿⣿⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢶⣴⠶⠯⣿⣿⡿⣟⠻⠞⠉⠀⠙⢿⣿⣿⡿⣛⣥⣽⡾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⣰⣦⣤⣀⡀⠀⠉⠁⠀⠛⣛⣽⡇⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠈⢻⣿⣝⣿⠀⠀⠀⠀⠸⢿⣛⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⡿⠋⠙⠲⢿⣿⣿⠀⠀⠀⠀⠰⣿⣿⢧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⡆⣶⣦⡀⣿⣿⠟⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⠚⠁⣿⢹⣿⣶⣾⡟⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣿⣿⡀⢀⣼⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⢿⣿⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢛⣽⡿⠁⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢚⣋⣉⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⣶⠶⠶⠾⠃⢠⣿⣏⠀⠉⠝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⢉⠠⡙⠓⢁⠀⠀⢀⣿⣿⣿⣯⡓⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠠⣿⢷⠄⠀⠁⠀⠀⣼⣿⡿⠻⡏⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢫⡄⠀⠀⡾⠀⠞⠁⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⡟⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⢰⢠⣿⣿⠀⠀⢸⠀⢸⡏
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡿⢁⣰⣿⣿⠃⠀⠀⢿⡆⠀⠀⠀⢀⡾⠀⠀⡿⢸⣿⡿⠟⣛⣺⣧⣼⣷⣄⣀⣀⡀
⠀⢀⣠⣴⣞⣛⣉⣥⣿⠟⣠⣿⠛⢹⣿⠀⠀⠀⠘⢿⣤⣀⠀⣼⡇⠀⣠⢇⡾⠿⠛⠋⠉⠉⢀⣀⣉⣉⣉⣉⣽
⠈⢙⣿⣿⣿⣭⣽⣿⠏⣼⠟⠁⣄⠈⢿⣦⣀⣀⡀⠀⠉⠉⠁⠙⢷⣶⠶⠋⠀⠀⠀⠀⠲⣛⢛⡋⠉⢉⣽⠟⠁
⠀⢻⣿⣿⡷⢶⣿⢏⣾⠟⢠⣼⡟⣆⠀⣍⠉⠉⠉⠁⠀⣠⡴⠀⠀⢀⡤⠀⢀⠀⠀⠀⠘⠡⠋⢀⣴⠛⠁
⠀⢸⣿⣿⣿⣿⢏⣾⠏⢠⣼⣟⣧⣠⣤⡬⢧⡀⠒⠚⣛⣉⣀⣤⠶⠋⣀⡴⠋⣠⠆⠀⠀⠀⢠⣾⠃
⠀⣼⣿⣯⣽⠏⣼⠏⠐⣾⣿⡟⠋⠉⠀⢰⢾⣿⢓⡾⠛⠋⠩⣄⣀⡉⠩⢶⡛⠁⢀⡤⠂⣴⡿⠁
⠀⢸⣿⣿⡟⣸⡟⠀⢶⣿⡙⢿⣄⠀⠀⠀⠉⣠⡟⠁⠀⠀⠀⠀⠈⠙⠋⠉⠙⠛⢛⣵⣿⠟
⠀⠘⢿⣿⢃⣿⠁⠀⣿⡿⠀⠀⠙⠻⠶⢶⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁
⠀⠀⣾⡟⢸⡇⢰⡄⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣰⣿⠃
⠀⠀⣿⡇⣿⠁⢀⣿⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣰⠇⣰⣿⣿⣆
⠀⣸⣿⠀⣿⠀⣘⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⢡⣦⣿⣾⡿⣿⣿⣿⡀
⢀⣿⣿⠀⣿⢀⣹⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣿⣿⣿⠟⢰⣿⣿⣿⣇
⢸⣿⢿⠀⣿⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⢉⣽⣿⠋⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣴⣄
⣿⡿⢸⡇⢿⠸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠉⠻⣿⠏⠀⠀⠀⣠⠞⣡⣿⣿⣿⡆
⣿⡇⢸⣷⢸⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣡⡾⢟⣿⣿⣿⡇
⣿⡇⣾⡿⣆⠋⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠞⣩⠶⣛⣿⣿⣿⡇
⢻⣿⣽⡇⣿⣆⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⢰⡿⠀⠙⢿⣶⣤⣀⣀⣀⣀⣠⣤⣾⡅⠀⢈⠴⢞⣫⣽⣿⣿⡇
⠸⣿⣿⣿⣹⣿⣦⡙⢷⡀⠀⠀⠀⠀⠀⢠⡿⣿⣼⣧⡄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠻⣦⠀⠈⡭⠴⢾⣿⣿⣿
⠀⠹⣿⣿⣿⣿⠿⢷⣄⠉⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣾⣧⣶⣴⡀⣄⣀⣀⡀⠀⠀⠀⢹⣇⠀⢒⣩⣭⣽⣿⣿⡆
⠀⠀⠈⠉⠉⠁⠀⠀⠙⢷⣦⣀⠀⠀⠀⠈⣿⣿⣿⠈⠃⠙⠛⠛⠟⠿⠿⠿⡿⠿⣧⠀⠀⢸⣿⠀⠠⠤⢶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣀⡘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣏⠀⠈⢛⣛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⢶⣤⣤⣤⣶⡶⠶⠶⠾⠿⠛⠛⠛⠻⣧⣜⢷⣮⣝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣝⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⠌⠀⢀⣀⣌⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣄⢠⣤⣤⣄⠀⠀⡀
⠀⠀⠀⠀⢀⡤⣚⣿⣿⣛⣯⣭⣿⣯⣄⣐⣤⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⢿⣿⡆⡛⢿⡛⣻⡿⣶⣍⡻⣧⡐⢂
⠀⠀⢀⣞⣽⣿⢿⡻⣿⠋⣭⣿⣿⣿⣯⣭⡿⢙⢟⣵⡿⠀⠀⠀⠀⢀⢠⣼⣿⣿⡈⣢⠁⠉⠿⣯⠿⣻⣿⣿⣄⡆
⠀⢠⣾⣾⡏⣴⠻⠇⠛⢀⣿⡻⠋⠫⡁⠀⠰⠿⣿⣄⠀⠀⠀⠀⠀⠈⠀⢐⣛⠓⠊⠙⠓⠂⣠⣾⡟⠀⠨⣿⣿⣇
⠀⠐⣿⡇⠓⠉⠀⠁⠀⢘⡿⠉⠊⡟⢎⣿⣄⠀⠰⠭⠥⠆⠀⠀⠀⠀⠀⠀⠙⠷⢄⠒⠒⠊⠀⠉⠂⠂⠡⢡⢿⣿⠂
⠀⠀⢹⠀⠀⢀⣀⠀⣀⣀⠔⣶⣤⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣶⠆⣠⣀⠀⠀⠀⢚⣿⡆
⠀⠀⠀⠣⣰⡏⠻⣴⣿⡿⣤⠞⠻⠃⠀⠀⠀⠀⠀⡠⢤⡀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣦⣝⠿⡏⣷⣄⠀⣿⠁
⠀⠀⠀⠀⠰⣷⠠⢀⣡⠈⢢⡀⠀⠀⠀⠀⠀⢠⣾⣽⣶⣿⣾⣾⡷⣦⣀⡀⡀⠀⠀⠀⠀⠈⣿⣿⣿⠾⠟⢹⡆⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠑⠒⠻⠆⠀⠀⣠⣾⣿⣿⡿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠀⢨⢉⣿⡦⠐⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⡟⡇⣯⠛⠸⠿⠽⠯⣿⠿⣦⣭⣿⢳⡄⢀⡄⣌⠸⠋⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡥⠗⠁⠀⠀⢀⡰⠖⢂⡺⠀⠀⠊⠤⢖⡼⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡆⣴⣦⠀⠹⣷⠀⢀⠀⢩⠄⢘⣶⢶⡎⠢⠄⣌⢶⣿
⠀⠀⠀⢀⣴⣶⡾⣥⠿⢃⡜⣸⣿⣿⠀⠀⣴⣆⠤⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠷
⠀⠀⠐⢈⢉⣙⡇⠀⢀⡰⠛⣯⣽⡛⠂⠀⠸⣿⡄
⠀⠀⢰⣄⠻⢻⡏⠢⠄⠀⢱⡿⠋⠁⠀⠀⠀⠈⠻⠦⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠
⠀⠀⢸⣿⡃⠉⠀⠀⠀⡠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣿⣶⣶⣤⣄⣀⣀⢀⡀⠀⢀
⠀⠀⠈⣿⡄⠀⠀⢀⣴⣷⡌⠁⠀⠀⠀⠀⠀⠀⠲⣶⣾⡟⠿⠛⠿⢟⣛⣛⡛⠛⠻⠛⠿⠿⢿⢿⣿⢃⣴⣿
⠀⠀⠀⠈⠻⣄⣠⠘⣿⢻⣇⣠⣤⡔⠀⠀⠀⠢⠀⠩⡁⠈⠓⢘⠛⡹⢿⡸⠇⠿⡸⠃⠇⠛⠚⠚⣚⠛⣻⣿
⠀⠀⠀⠀⠀⢨⠇⠀⢨⣄⣉⡨⡟⠁⠀⠀⠀⠀⠀⠐⠋⠁⣤⡵⠚⠀⠻⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠃⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠈⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠂⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣀⠘⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⢄⣀⠈⠗⠶⣬⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣦⡀
⠀⢀⣈⠉⠛⠶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⢟⠷⣙⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣆
⠀⢀⠋⠙⢢⣼⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⢀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣷⣄⣀
⠀⡘⠛⢲⣾⣿⣿⣿⣿⣿⣿⠯⠂⠀⠁⠀⣠⡴⢆⣾⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣆
⠀⠉⢓⣿⣿⣿⣿⣿⡿⠓⣳⣀⡤⢀⡀⣐⣿⢱⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣾⣿⣧⡀
⣈⠓⣾⣿⣿⣿⣿⠛⠉⠀⢰⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⢿⣿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣵⣾⣶⣷⣶⣶⣍
⠈⢙⣿⡿⣿⣿⡯⢠⣴⣿⣶⡿⢿⣿⣷⣾⡿⡿⠘⡿⠙⢰⠁⣾⣿⡿⣿⢿⠟⠁⠛⠛⢛⠟⣳⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⣿⠃⠘⠋⠁⢀⠴⠋⠛⢟⡏⠀⠀⠣⡘⢦⣸⠸⠝⢛⠛⠌⠢⠁⠀⠀⣰⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⢼⠃⠀⠀⠀⠀⢀⣠⠌⠀⠀⠀⠀⢻⣕⡟⢦⡑⠤⠀⠀⠀⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣯⢻⣹⣿⡿
⠀⢸⣿⣿⣿⣿⣜⠷⣶⣶⣶⣿⣿⡦⠀⠀⠀⢀⡰⡌⣷⡧⣄⠉⠛⠒⣏⡚⢯⣈⠈⢸⣧⣉⠋⠛⠿⣿⣿⠆⠇⢹⠗
⠀⣾⣿⣿⠻⣿⣿⡧⠁⢙⣿⣿⣋⠀⠀⣀⠊⠉⠷⣷⣾⣷⠞⠻⢶⡿⠵⢿⡶⢭⣛⣦⣭⡛⢛⠦⣌⠒⠧⠤⠃⠘
⣸⡿⢻⣿⣿⣿⣿⡗⢰⣾⣿⣿⡿⡜⠓⢇⠀⠀⠃⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣤⣤⣄⣀⣠⣤⠞
⢸⠃⠏⣿⣾⣻⣿⣿⠂⢠⣭⣾⣿⣿⡟⠉⢻⣶⠋
⣸⢰⢰⠸⢿⣯⣿⣿⣷⣆⠉⠙⠻⣿⡷⣤⠜⣿⡀
⢸⡇⠀⡀⡈⣿⣿⣿⣿⣿⣷⣢⡰⠿⢿⣿⢀⣆⠍⠐⠤⡀
⠘⡇⡀⡇⡇⡇⠟⠿⣿⣿⣿⣿⣷⣴⣂⠻⢿⣿⣗⠢⢄⡈⡆
⠀⠸⡇⠀⠁⠇⠠⠰⣨⠟⢿⣿⣿⣿⣿⣧⣌⣻⣿⣧⣤⠝⠃
⠀⠀⠘⠢⠦⠶⠛⠚⠁⠀⠀⠈⠙⠿⣿⣿⣿⣿⣯⢿⣿⣷⠠⣄⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣾⣿⣿⣠⣿⣕⠀⠈⠀⠀⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢟⠿⢮⡑⠨⡐⠀⠄⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣏⠏⢎⠀⠱⡀⠑⠀⣁⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⡂⠀⡈⢆⠣⠐⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⢠⢀⠱⠘⡄⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡈⡄⠄⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢀⠎

⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⢀⣴⣶⣶⣦⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⣸⣿⣿⡿⣻⢦⣀⠀⠸⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣦⣤⣤⣤⣤⣀⣀
⠀⠀⠀⣾⣿⣿⣿⡇⣉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⢻⣫⣿⣿⣿⢳⣶⡆
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠈⠉⠛⠛⠛⠗⠟⠻⠋⠻⠇⠁⣻⢆⡋⠨⠛⠙⠉⢉⢺⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⡀⠀⠀⠀⠀⠉⡩⣿⣯⡃⠀⠄⠀⠀⠀⢀⡘⠀⠬⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠄⢤⣠⣼⠟⠀⠂⣤⣄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣯⡻⣦⣶⡿⣷⣶⡶⠦⣤⣮⣞⣯⠿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡏⣷⣸⣿⣿⣾⣿⣿⣦⣶⣾⣿⣿⣿⣽⢿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⣇⡇⣷⡻⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠛⢛⣊⣭⣷⣾⣫⣾⣿⣭⣽⢟⣽⣾⠛⠛⠻⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⣿⣭⡿⠟⠿⠿⠿⠛⠛⠛⣉⠭⠗⢊⣿⣦⡠⡙⢶⣬⡛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣀⠠⢤⣀⣒⣒⠒⠒⣻⣿⣿⣿⣧⡙⣷⣝⢿⣟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢲⣦⣭⣭⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣷⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠉⠛⢿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⢱⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⢫⣦⡷⠙⣯⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣦⡁⠀⠀⣼⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⡛⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠲⣴⣥⣤⣥⣴⣶⣍⢽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡷⠾⢛⣿⠻⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠉⠉⢛⠁⠚⡟⢻⠽⢛⡟⠻⠟⠟⠛⠌⠛⠩⢯⡀⣥⣀⡰⢞⣫⠿⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣦⣄⠀⠀⠈⠀⠀⠀⠞⠁⠡⢡⡀⠀⠀⠀⢠⠈⢃⡓⠽⣆⣁⣀⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣮⣿⣶⣷⣤⣀⣠⣠⣴⣿⣰⣯⣶⡶⢶⡾⣶⠾⠿⠛⠀⠉⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣦⣽⣾⣿⣶⣄⣠⣤⣤⣦⣶⣶⣾⣶⣶⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄⣀⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀
⠀⠀⠀⠀⠀⢠⠀⠀⠘⣘⣉⣉⣛⢋⠉⠉⠋⠛⠛⠉⠋⠋⠘⡉⢉⠛⣉⡛⣉⢏⡙⠛⠿⢿⡕⣿⣽⣿⣿⡷⣿⣭⣶⠂
⠀⠀⠀⠀⠐⢿⡄⠀⠀⠀⠀⠀⠉⠙⠙⠷⠿⠿⣿⢀⣹⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⣿⣎⢞⠁⣾⢞⣭⣫⠽⡛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠉⠋⠙⠋⠋⠁⣀⠀⠀⠐⡇⠀⢻⣅⠈⠓⢅⡈⠉⣀⡤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣌⣁⣀⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣀⠭⢿⣿⠻⠃⢀⣤⣬⡿⠾⠛⠛⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠉⠛⠛⠀⠀⠘⠙⠓⠂⠋⠉⡟⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⢿⡀⠀⠀⠀⠀⠀⢀⡞⢿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠙⣦⡀⠀⠀⠀⠈⣇⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢦⡈⠙⢦⣀⣀⣀⣘⡄⢦⣤⡙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢙⡲⣤⣽⣿⣿⣿⣿⣾⣿⣿⢧⡙⣿⣷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠭⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣷⣼⣿⡆⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⡵⢛⣻⣿⣷⣿⣿⠿⣿⣿⣿⣿⡿⢻⡇⢸⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠁⣴⠋⠁⠀⠀⠈⠙⢷⡈⠙⣿⠙⠍⢺⡇⣾⡇⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠟⠀⠀⠀⠀⠀⠀⠈⢻⡄⣿⢰⡘⣶⢡⣿⡇⠀⠀⠀⠀⡘⠌⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣎⡷⣣⣿⣿⠁⠀⠀⠀⠠⡜⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⣩⣾⣿⡿⠃⠀⠀⠀⠀⣄⢹⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣁⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⢰⡜⠂⠀⢠⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⣾⣿⣿⡿⠛⠁⠀⣠⣤⣄⠘⣆⠈⠃⠀⣀⣼⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⣤⣥⠄⠉⠁⠀⠀⠀⠀⠀⣴⣌⣧⢻⠀⣴⠾⣛⣯⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠋⣀⢚⣥⣤⣤⣑⢦⡰⣾⣿⡿⡿⠘⢠⡏⠀⠤⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⣀⢁⣤⠸⠽⠃⠠⢤⣤⣤⣄⠻⡌⠋⠘⣧⢠⣿⣿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣉⣉⣙⠲⢤⣠⣤⡤⠤⣄⡀⠀⠉⠛⠆⣿⠀⣼⢏⣾⠛⣱⣷⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⢿⣿⣶⣿⢦⡙⠓⢦⣝⣦⡀⣀⡴⠟⠊⢕⣻⣿⡞⣛⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡽⠛⠛⣷⣔⠦⠄⢹⣿⣉⠁⠀⠐⢚⡫⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣤⣠⢈⣡⡼⢛⣋⣩⡾⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣞⠛⠥⠚⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣴⣦⠤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡛⣯⠭⢖⣊⣩⣭⣥⣤⣤⣤⣭⣭⣙⣛⣲⣶⣤⣐⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⢓⣭⣶⣾⣿⣿⣿⢿⠿⠟⠟⡿⠛⠽⢟⡽⢿⣿⡚⣻⡟⠋⣾⣷⣦⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣫⣾⣿⡿⠟⠋⠉⠈⢀⠀⢀⠀⡜⠁⠀⠀⠁⠀⠀⠉⠹⠋⠀⢸⣿⣿⣿⡆⡄
⠀⠀⠀⠀⠀⢀⣠⡶⣩⣿⣿⠟⠋⢁⡀⣤⣰⡄⣷⢸⡇⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣻⣿⠋⠀⡄⣾⡼⣷⢛⡸⠧⢭⣘⣃⣃⠙⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⣸⣿⣿⣿⡟⠄
⠀⠀⠀⠀⠀⠀⣷⡿⢁⢸⡞⣿⠙⠇⠙⢧⡀⠀⠀⠚⣿⡿⣁⠀⠀⠀⠐⠨⠀⠀⣆⠈⠚⣡⠻⠟⠛⢣⣅⡀
⠀⠀⠀⠀⠀⠀⢹⢡⡼⡇⠃⠈⠀⠀⢀⢀⠹⠒⠒⠒⠋⠁⠈⠤⣤⡀⠀⠀⠀⠀⠈⠛⡓⠒⠂⠀⠎⠀⠀⡨⠃
⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⡀⠆⠊⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣭⡿⢤⣄⡀⡠⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠁⠀⠀⢀⣀⣤⣤⠴⣶⠟⠉⣻⣿⣿⣷⣦⠈
⠀⠀⠀⠀⠀⠀⠀⢢⠁⠀⣠⣴⠛⠿⢿⣿⣦⣴⣁⣰⣯⣿⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠼⣿⠛⠋⠧⡆⣌⣙⡛⠻⠿⠿⠿⡆⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠐⠀⠤⣀⣁⡉⠛⠛⠻⠷⢿⠇⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠉⠐⠲⢶⡏⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠶⣒⠡⣿⣯⢠⣽⣾⡟⠛⠛⢷⣶⡶⡿⣾⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣷⡘⠏⠀⢲⣿⣿⣟⡃⠀⠀⠀⠙⣿⣿⣵⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣇⠀⠀⢀⡃⠉⠛⠁⡸⣀⠤⠺⡈⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠛⠢⠴⢻⠷⠤⠔⠛⠃⠀⢀⣀⡶⢀⠙⢿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡙⠒⠀⢒⣲⣥⡀⣀⡠⠴⢋⡀⢫⠏⣽⣿⣿⣾⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣱⡦⠄⠀⠀⠀⠤⣈⠀⠘⠿⢿⡿⣿⣿⡍⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢠⣔⣖⣚⣲⣥⠓⠄⡀⠀⠠⠿⢿⣥⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⡿⢿⣿⣿⠀⠈⠑⢦⡀⠀⠿⣿⠆⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠈⠻⣿⠳⠦⣄⣀⠳⡀⢘⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⢶⣶⣦⣄⣀⣀⣿⡗⣷⠀⡿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣼⠿⣋⣿⣿⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⣿⠛⢙⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠑⠀⢰⣿⣿⣿⣷⠽⠚⠉⠟⠀⠀⠴⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡤⢅⠀⢀⠿⠛⠋⠁⠔⠀⢀⡔⠀⣠⠄⣀⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⣀⣀⣀⡔⠤⣁⠀⠀⠖⠁⠼⣋⠤⣦⣀⣀⣀⠐⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠧⠤⣤⣄⣋⣉⡁⠾⠷⠶⢈⣉⣧⣭⣤⡦⠬⣿⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣛⣿⣿⡟⢛⣏⣿⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠄⡄⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣾⣾⣿⣿⣷⣼⣕⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣴⡾⠝⠊⠁⠀⠀⠀⡘
⠀⠀⠀⠔⠚⠛⢻⣿⠋⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠀⠀⠀⠀⠀⢠⠃
⠀⢰⠐⠤⢀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⢺
⠀⠀⠑⠤⣄⡀⠄⠀⠀⠀⠀⠀⠴⢀⡴⠛⣿⡟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡓⠍⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠈⠙⠦⢤⣁⣀⣀⣤⣶⡯⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠔⠛⠁⠀⠉⠁⠐⠚⠷⣝⡂⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⠥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠀⣀⢠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠙⠋⠀⠀⠒⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢰⠀⠀⠈⠓⠤⠄⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢡⠀⣆⣰⣦⣤⣷⣴⣦⣶⣤⣽⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⢾⢿⡽⣥⣒⡂⠤⢀⠀⠀⣀⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠻⠹⡉⠆⠳⠐⠌⠂⠂⠁⠨⡙⠠⠄⠀⠊⢡⡞⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣯⡥⢶⣶⣴⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠊⣰⣿⣿⣿⣾⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⣃⣭⣶⣿⡿⡏⢉⣾⡄⢸⣇⠀⠠⠀⠀⠀⣠⠎⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣴⣿⣿⠟⠫⠛⠃⠀⢸⣿⡇⣼⢉⣷⡀⠀⢀⣼⣧⠊⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⣭⣶⣶⣾⣿⣿⣿⡳⣖⢦⣀⣾⠿⠇⠈⢹⡇⡿⢶⣿⣿⣷⠇⢀⡼⠏⢩⣿⣿⣯⣍⠙⠿⣿⣿⣿⣿⣷⣌⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢡⣾⣿⡿⢟⠋⠁⠀⠀⠀⠀⣹⣷⡌⢿⣆⢢⠀⣾⡇⣇⠈⣷⣍⣉⣴⣿⣿⣦⣤⠘⣿⣿⣿⡿⠀⠌⠋⠉⠛⣿⣿⣆⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣴⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⣸⣿⡏⣰⡿⣰⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡷⠌⠙⡌⠀⠀⠀⠀⠀⢀⠈⠿⠟⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠚⣿⠀⠀⣀⡤⢄⣀⠀⠀⠀⢰⠛⠟⣁⠔⠉⣹⢟⡿⠡⣡⡏⣰⡞⡟⠟⠉⢉⣿⡿⠏⠁⡤⠀⠂⠀⠀⠀⠉⠉⠀⠔⠀⠀⠀⡀⢧
⠀⠀⠀⠀⠀⠀⣠⠋⠛⡶⠾⢃⣀⡤⠤⠤⣄⢈⡇⠀⢀⡞⢠⡞⠁⠀⢠⠏⠞⠄⣰⠏⡰⢡⠇⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠥⠄⢸
⠀⠀⠀⠀⣠⠾⠋⠁⠀⠄⠒⠉⠀⠤⢤⡀⢸⠋⠀⠀⠉⠀⠸⡆⣀⡴⠿⠶⢶⣟⡡⠊⣠⡟⣸⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⢔⡂⠡⠒⠋⠁⠀⠀⠀⠀⠄⠀⢸
⠀⠀⣠⠞⣡⡴⠖⢚⣫⣿⣿⣿⣿⡷⠶⠼⠋⠀⠀⠀⠀⠀⠀⠋⠁⠀⢘⡛⣁⣡⣴⡿⣋⠞⡅⠀⠀⠀⣠⣶⡄⣽⡿⠻⠝⢋⡀⠀⢀⣠⣶⣿⣷⣤⣤⣾⡇⣸
⢀⣾⣵⠟⢉⣴⣾⣿⣿⣿⣿⣿⣿⡧⢂⡤⠀⠀⠀⠀⡠⠂⠀⠀⠀⠐⢿⣿⠿⠿⣓⠊⣁⣾⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢡⡏
⡾⠡⠀⠰⣿⣿⣿⣿⣿⣿⣿⡟⠁⡴⠋⠀⠀⢀⡴⠊⠀⠀⢀⣴⣷⣠⣴⡶⠛⠋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠭⢉⠓⢿⣿⣿⣿⣟⣛⣋⣉⠀⣾⣧
⠘⢶⣄⠀⠈⠛⠛⣿⣿⣿⡟⠀⡞⠁⠀⣠⠔⠋⠀⣠⣴⣶⣿⣿⣿⣿⡿⣿⣷⣿⣿⡿⢿⡿⠛⠛⠿⠿⠿⠿⢿⢿⣿⣭⡓⠢⣄⠀⢻⣿⣿⡿⠟⠁⠀⣸⣿⢿⢷
⠀⠀⠈⠙⠶⣄⠈⠻⣿⠏⢀⠜⠀⠠⠊⢁⣀⣠⣾⡿⠟⠛⠛⢛⣩⡭⠂⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈⠑⣬⣉⡙⠢⠀⠁⠀⡟⠋⠀⢀⣴⡾⢻⠓⠈
⠀⠀⠀⠀⠀⠈⢱⠊⢁⠔⠁⠀⢠⣴⣾⣛⣭⠭⠖⠒⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⠉⣿⣿⣿⡇⠀⠈⠀⢀⡴⠋⢸⡁⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠰⣄⠈⢁⣂⠭⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡌⣸⣿⣿⣿⠃⠀⠀⣠⠟⠀⠀⠀⠙⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣴⣿⣿⣿⣿⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣡⣼⣿⣿⣿⣿⠏⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣔⣺⣟⣠⣾⣿⣿⣿⣿⣿⡿⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡒⠽⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠐⠀⠠⠜⢯⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠐⠋⠡⠚⢻⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⢀⣀⠀⠀⠀⠀⠿⣿⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠱⡄⠀⠀⢠⡟⠁⣼⠋⣾⠃⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠃⣸⠃⡼⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠀⡉⢠⡇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠈⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⡠⠞

⠀⠀⠀⠀⠀⣾⣿⣷⡄⣦⡠⣶⣶⣶⣤⡤⠤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠃⠙⣿⡘⣷⡙⣿⣿⠁⢰⣿⣦⠀⠹⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢸⡇⠈⠻⠀⠑⠤⠿⢔⣴⣿⣿⣿⣿⠟⠋⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⢻⣿⣷⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⢸⡗⠀⠀⠀⣄⠀⠐⠛⠻⠿⣿⣿⣿⣇⠀⠀⠀⠀⢤⣌⠻⠿⢷⣶⣦⣄⡀⠉⠛⢿⣿⣦⣄
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠏⣸⠇⠀⣷⣤⠈⢿⣦⡀⢿⣷⣄⠙⠻⣿⣆⠀⠀⠀⠀⠙⢿⣦⡀⠈⠙⠛⢿⣷⣄⠀⠙⢿⣿⡗
⣠⣤⣶⣦⣤⣤⠤⠤⠀⠀⠏⠀⠀⣹⣿⣷⡄⢻⣷⡌⢻⣿⣷⣄⠀⠙⠆⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠈⠛⣿⣷⡀⠈⣿⣄
⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠿⠟⠛⠋⠾⢿⣿⣆⠉⠻⣿⣿⠶⢤⠀⠀⠀⢀⣴⣿⣿⠀⢠⡄⠀⠀⠈⢿⣷⠀⢹⣿
⠀⠈⠑⠢⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠃⣠⣿⣧⡀⠀⠀⠀⢻⠄⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠦⠤⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠁⠀⣀⣀⣉⣉⣛⠂⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣦⣤⣀⣀⣀⡀⠒⠛⠋⠉⠀⠀⠀⠀⠀⠰⠛⠉⠉⠩⣭⣭⣍⣻⣶⣦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⣩⣉⣁⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢳⣦⣄⡀⣶⣤⣿⣿⣿⣿⡿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆⠀⠀⠀⠙⠛⠛⠛⠋⠉⠀⣀⣀⣠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣶⣸⠉⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⡀⠀⢸⣿⣿⡀⢸⡀⢆⢠⣴⣦⡀⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⠙⠦⣄⠙⠻⢷⠘⢷⣼⣆⠉⢻⣿⡆⠀⢀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣅⠀⠀⠉⠀⠀⠀⠀⠉⠛⢓⣼⠟⠀⢠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠠⣽⠦⢸⣦⣄⡈⠙⠚⠛⢋⣁⣤⣾⣿⣿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠙⠻⣇⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠐⢊⣉⣀⣤⣴⣾⣿⣿⣿⡿⠟⣫⠅⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡈⠉⠉⠀⣀⣩⡿⠿⠛⠁⠘⠻⠿⣶⣦⡌⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠠⠖⢒⣩⣥⠶⠊⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡦⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠮⢭⣒⡿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠶⠶⠬⠝⣿⣿⡋⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢀⣥⣶⣾⣿⣿⣿⣧⡝⣦⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡾⡟⣰⣫⣾⣴⣄⠀⢀⣴⣿⣿⣿⣿⣿⠿⣛⣻⣿⡟⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢋⣾⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣬⡹⣟⣿⣿⣿⣿⣿⢟⣿⠇⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⡿⣿⣿⡿⣟⣻⣝⡗⣦⢻⣿⣿⣿⣿⣿⣶⣾⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣠⣴⣶⣟⣻⣿⣿⣿⣯⣭⣭⣤⣴⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡚
⠀⠀⠀⠀⠀⠀⢿⣷⣍⢄⠉⢿⣝⣿⠿⣿⣿⣿⡿⢷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⢆⠇⠈⠻⣬⡀⠉⠠⣄⠀⠁⠙⠙⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠻⣭⣭⣁⡁⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣿⠀⡄⢹⡷⠀⠀⠈⢻⣮⡂⢸⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠂⠀⢉⠄⢳⠿⠀⢀⡾⠻⠋
⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⡾⠀⣿⣸⠇⠀⠀⠀⠀⠙⣻⢸⠿⠋⣸⣛⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠱⡄⠦⠇⣴⣾⣿⠷⠄
⠀⠀⠀⢀⣄⡀⠀⣠⣴⣿⡿⠗⠀⢹⡏⢀⣀⣠⣤⣀⠀⠋⠃⠀⣰⡿⠻⠷⠿⠿⠿⠿⡿⠋⠁⠀⠀⠀⠀⣀⠄⠛⠉⠀⠈
⠀⠀⠀⠈⠉⠁⠶⣤⡄⠀⠀⠀⠀⠿⠷⠿⠿⠛⠋⠉⠀⠀⠀⣴⣟⠃⣠⣄⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠚⠟⠿⢷⠿⣿⣿⣿⣿⣿⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠙⠻⣷⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠐⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣿⡿⠿⣷⣦⣄
⠀⠀⠹⣿⡌⠙⠻⢿⣶⣤⡀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠉⠛⢿⣦⣄
⠀⠀⠀⠹⣿⣄⠀⠀⠈⠙⢿⣷⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⡷⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⢀⣾⡟⠁⢀⣠⣴⣾⠟⠉⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢀⣤⣾⠟⠋
⠀⠀⣾⣿⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⣴⣾⠿⠋⠁
⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⢛⣛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣤⣾⠟⠁⣰⣿⠟⠛⠻⣛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠛⣿⣿⢿⡙⠋⠉⠋⠀⣰⣿⣿⣧⣤⣄⡈⣧⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠋⠁⣄⠲⣌⠛⠋⣠⠆⠀⠀⢠⣿⣿⣿⣿⣿⣌⠳⠌⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠁⢀⠀⢀⣾⣿⣷⡄⠀⠚⠉⠀⠀⠀⣿⣿⣿⡟⢻⡇⢻⠂⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⠁⠀⠀⢀⡞⠀⢩⠟⠡⠏⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠹⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⣰⡏⠀⠀⠀⣾⠁⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣿⣿⠀⠀⠀⠀⡆⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⣠⣾⡿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢰⠇⣼⣿⣿⠀⠀⠀⠠⡇⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠁⣠⣾⣿⣿⠇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣾⠀⣿⣿⣿⣿⠿⠿⢾⣧⣀⣹⣿⣄
⠀⠀⠀⠀⣀⣤⣴⠾⠿⠛⢛⣿⣿⠏⣠⣾⣿⠟⣿⣿⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⣼⡟⠀⠀⢀⣿⢰⣿⣿⣿⡶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⢀⣠⣶⣿⣿⣿⣶⣶⡶⣿⣿⣿⠋⣴⣿⡿⠁⠀⢻⣿⡀⠀⠀⠀⠀⠙⠻⠿⣦⣤⠀⣿⣇⠀⠰⢞⣣⡾⠋⠉⠀⠀⠀⢀⣀⣤⣴⣶⡶⠶⢶⣶⣦⣾⠃
⠀⠀⣹⣿⣿⣿⣿⠶⣶⣿⣿⢃⣾⡟⠃⢀⣷⡀⠘⢿⣷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠘⠛⣫⡍⣡⠀⠀⠀⣠⣿⠟⠁
⠀⠘⣿⣿⣿⣿⣶⣾⣿⡿⢡⣿⡿⠁⣄⣼⡿⣷⡀⠀⣽⠉⠉⠉⠉⠉⠀⠀⢀⣠⠞⠀⠀⠀⢀⣤⠂⠀⣀⠀⠀⠀⢀⡼⢃⠞⠁⠀⣰⡾⠋
⠀⢀⣿⣿⣿⣿⣶⣾⡿⢡⣿⡟⠀⢀⣿⣿⣇⠈⠃⠀⣙⣳⡄⠀⣤⣤⣴⡾⠟⠁⠀⠀⣠⣴⠟⠁⣀⣼⠃⢀⣴⠀⠀⠀⠀⠀⢠⣾⡟
⠀⠀⣿⣿⣿⠿⢿⣿⢡⣿⡟⠀⠀⣿⣿⣷⣿⣶⠿⠟⠛⢉⣳⣦⣄⡤⠤⢤⡴⠶⠾⠛⣋⣡⣴⠾⠛⣁⣴⠿⠁⠀⠀⡀⠀⣠⣿⠟
⠀⢰⣿⣿⣿⣿⣿⠃⣾⡟⠀⠘⣿⣿⣿⡏⠁⠀⠀⠐⢺⡿⣿⡿⢋⣿⠟⠛⠛⠉⠳⠦⣤⣤⣀⣒⣛⣋⣁⠀⣀⣴⠟⢀⣴⣿⠏
⠀⠀⣿⣿⣿⣿⡇⣼⡟⠁⠘⣶⣿⡏⠻⣿⣄⠀⠀⠀⠀⠚⠉⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠻⠿⠟⣡⣴⣿⡿⠁
⠀⠐⢿⣿⣿⡿⢰⣿⠃⡀⠰⣿⣿⠋⠀⠈⠻⢿⣦⣤⣄⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋
⠀⠀⠀⣿⣿⠇⣾⡟⢀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉
⠀⠀⢀⣿⣿⢠⣿⠇⠘⣷⡀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⣾⣿⠃
⠀⠀⢸⣿⡇⢸⡟⠀⢀⣹⣷⣼⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⢀⣾⠃⣠⣿⣿⣿⣇
⠀⠀⣾⣿⠇⣸⡇⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⢂⡄⣼⣟⣴⣿⣿⣿⣿⣿⡄
⠀⢸⣿⣿⠀⣿⡇⠀⢷⣿⣿⡟⠧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣟⣥⣾⣣⣾⣿⣿⣿⣿⠏⣸⣿⣿⣿⣷
⠀⣿⣿⣿⠀⣿⡇⢠⣼⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⡆
⢸⣿⣿⣿⡄⢹⡇⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠛⠋⠉⠉⢉⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⡀
⣸⣿⡏⢸⡇⢸⡇⢻⣾⣿⣯⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣴⠟⣡⣿⣿⣿⣿⡀
⣿⣿⡇⢸⣷⠘⣷⣈⣿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⢀⣴⠟⣡⣾⣿⣿⣿⣿⣿⡇
⣿⣿⠁⣿⣿⡆⢿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⣾⠿⢋⣭⣿⣿⣿⣿⡇
⣿⣿⡄⣿⡿⣿⡈⠏⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⣡⡶⠟⣻⣿⣿⣿⣿⡇
⢿⣿⡇⣿⡇⢹⣷⡐⢈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣾⡟⠀⠹⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⠈⠀⠋⣡⣶⠿⢛⣻⣿⣿⣿⡇
⢸⣿⣿⣿⣿⢸⣿⣷⡀⠻⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢰⣿⠁⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⣧⡀⠀⠛⣡⠴⠾⢛⣻⣿⣿⣿⣧
⠀⢿⣿⣿⣿⣇⣿⣿⣿⣆⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣾⣷⣾⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠠⠶⢛⣛⣻⣿⣿⣿⣿
⠀⠈⢿⣿⣿⣿⣿⣿⡿⢿⣷⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣶⣿⣴⣷⣴⣄⢠⡄⢠⣀⣄⠀⠀⠀⠀⠀⢸⣿⡄⠀⢘⣉⣭⣭⣿⣿⣿⣿⣇
⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠹⡏⠻⠿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⡇⠀⢈⣉⣭⣭⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠙⠉⠀⠛⠀⠀⠀⠀⣿⠇⠀⠤⣬⣭⣭⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣀⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣼⣿⣄⠀⣀⡂⠬⣭⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠿⠛⠛⠛⠛⠛⢿⣷⣌⠻⣷⣦⣭⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⢿⣿⡿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⢁⡴⠋⢁⡤⠖⠋⢙⣻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣛⠽⠋⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡞⣁⢀⡞⢀⡴⠋⢀⡴⠚⢉⣡⠽⠿⢷⣶⡄⠀⠀⣰⡿⠋⡴⠃⠀⣠⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣴⣧⣾⣠⣞⣀⡴⠋⣠⠖⠋⣀⡤⢶⣾⠟⠁⠀⣼⡟⢀⡾⠁⠀⣼⠁⠐⣻⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠿⠛⠛⠉⠉⠉⠭⠭⣍⣙⣛⠻⢷⣾⣥⣴⠋⣁⣠⣿⡇⠀⠀⣼⡟⢀⡾⠁⠀⣼⠃⠀⡴⠃⡴⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠁⠀⠀⠀⠓⠲⣤⣀⠀⠀⠀⠀⠉⠙⠲⢤⣉⠻⢿⣧⣴⡿⠁⠀⢰⡿⢀⡾⠁⢀⣾⠃⢀⡾⠁⠈⣴⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⢿⣧⡀⠀⣿⣧⡾⠁⣠⡿⠁⣠⡿⠁⢀⣾⠏
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠙⢷⣾⣿⣋⣤⡾⢋⣤⡾⠟⣀⢀⣾⠋
⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⣼⣿⡋⣿⠀⠀⢧⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⣛⣩⡴⠞⠁⣾⠏
⠀⠀⠀⠸⣿⠹⣷⣤⡄⠀⠀⠀⠘⠻⠿⠋⠀⠀⢸⡄⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠥⠤⠤⠄⢸⡿
⠀⠀⠀⠀⠻⣷⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠬⣉⡓⠒⠒⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣾⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢿⣷⣦⣄⠙⠲⣤⡀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣤⣤⠀⠘⠁⠀⠀⣠⣾⣿⣟⢮⣙⠻⣦⡀⠀⠀⣠⣾⡟⢷⣦⡀⠀⢻⣿⣝⠻⣦⣄⠙⠦⡌⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣄⣤⣴⡾⠛⠁⠈⠻⣶⣬⣳⣾⣿⣴⣿⠛⢧⣉⠳⢬⡻⣷⡄⢻⣿⢷⣄⠙⢷⣄⠈⠂⠹⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⢿⣿⢿⣿⡿⢿⡛⠻⣟⠻⣿⠳⣤⣈⣷⣴⣿⠿⠃⠀⢿⣧⠹⣧⡀⠙⣷⡀⠀⠠⣙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⡳⣄⠙⢦⡈⠳⡙⣷⣾⠟⠋⠁⠀⠀⠀⠀⠀⢿⣆⠈⢿⡄⠈⢿⡄⠰⣌⠙⣮⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢻⡿⣷⡈⠳⣄⠙⢦⡙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⢿⡄⠀⠻⣄⢈⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠳⡜⣿⣦⡈⠳⣄⠙⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢻⣄⠀⠙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣜⢮⣿⣿⡲⣌⠳⡌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠙⢦⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠙⢿⣎⠳⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⠶⠦⠄⠉⢙⣳⣤⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡛⢛⣣⡤⠶⣚⡛⠉⢩⡄⠀⣀⠀⠶⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠞⠋⠁⠤⢀⣈⠀⠠⠄⠀⠀⠉⠀⠀⠈⠀⡴⠁⠀⡴⣢⡒⡄⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⠀⠘⠃⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⠾⠚⢁⣠⡴⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠾⣿⣿⠤⠄⣲
⠀⠀⠀⠀⠀⠀⢀⣤⣾⢃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣋⠙⠓⠒⠄⠀⠀⠙⠄⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢰⢏⢠⡇⠈⢀⣀⡤⠀⠀⠀⠀⢀⣀⣀⣼⣯⡡⠄⠀⠀⢀⣄⣀⣀⣀⣀⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⢸⣧⢸⠇⢠⡯⢒⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠙⠺⠶⠚⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠛⠗⠋⣰⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⢸⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⠏⠀⠐⣄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡶⠖⠊⠁⢀⠈⣦⠞⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠐⡄⠘⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡼⠋



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

⠀⠀⠀⠀⡔⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣤⠀⠀⢀⣀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⢁⣀⣠⣤⣤⣤⣤⣀⣁⡄⠒⠈⠛⠂⠀⠄⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠛⠉⠉⠉⠀⠀⠈⠉⠉⠛⠷⢦⣄⠀⠶⠀⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠸⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⢀⡴⠒⢤⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠓⠀⠀⠀⠀⠀⠀⣜⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡇⢩⠀⠀⠀⠗⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢥⡀⠀⠀⠀⡀⠀⠀⠈⠀⢀⠀⢠⠄⠒⠈⠁⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⡀⠠⠤⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⠀⠦⠀⠤⠀⠴⠆⠀⠀⠀⠁⠀⠀⢄⡀⠀⠀⠈⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠡⠋⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⢠⠎⠀⣠⡀⠀⠀⠀⢀⠠⠀⠀⠖⠀⠀⠀⠀⣀⡤⢒⡀⠀⠀⠀⠐⢣⡀
⠀⠀⠀⢣⠄⠀⠉⠁⠀⠀⠀⠘⠀⠀⠈⠀⢀⣠⠔⠛⠀⠀⢈⣉⡀⠀⠀⠀⠀⠈⠓⠤⣀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⠐⠚⠉⠉⠰⠊⠀⠀⠀⠈⠉⠙⠛⠶⣦⣀⠀⠀⠀⠉⠙⠒⠂⠉⠀⠐⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⡼
⠀⠀⠀⠀⢢⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⢀⣀⣄⣀⣀⣈⣀⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠛⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠉⠉⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⢊⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠒⠛⠉⠁⠉⠉⠈⠁⠐⠂⠒⠂⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠐⣤⢀⠀⠀⠈⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡀⢀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠘⠂⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⣀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⣶⣽⠀⠀⠉⠲⠄⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⢑⣆⣠⣬⣟⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠏⠑⠒⠦⢤⠉⢉⠤⢶⣶⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠘⠃
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠇
⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⡿⣛⣛⡿⠿⠿⠿⠿⠿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣽⣿⣶⣶⣾⣶⣶⣾⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠒⢶⠶⠒⠢⠤⣄⡀⠀⣀⡤⠤⠒⠒⠛⠉⠉⠉⠉⠉⣩⠗⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠲⣶⡒⠋⠀⠀⠀⣀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢠⣤⣤⡀⠉⠓⠲⠤⠤⠤⣤⣄
⠀⠀⠠⣤⡔⠃⠀⠀⢀⡴⠊⠁⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⣿⢸⣿⣷⠀⠀⠀⠀⣠⠖⠉⡟
⠀⠀⠀⠈⡇⠀⢀⡴⠋⠀⠀⠀⠈⢀⡢⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⢠⠞⠁⠀⡜
⠀⠀⢰⡛⠀⣠⠎⠀⠀⠀⠀⠀⠁⠀⠁⠘⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣞⠀⠀⠀⠃
⠀⠀⠀⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣸⣀⠀⠀⠳⢦⣀
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡀⠀⠤⠭⢽⣛⣒⣛
⠀⠀⢠⡇⠀⠀⠀⠀⣤⠞⠉⠉⠀⠀⠀⠀⠀⠀⠑⢄⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡤⠔⠊⠁
⠀⠀⣸⠀⠀⠀⠀⢸⡗⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠻⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣲⠶⠒⠚⠉⠁
⠀⠀⣯⠀⠀⠠⠈⡄⢄⠀⠉⠛⠒⠒⠒⠊⠁⠀⠀⠀⠀⢀⣤⢾⢫⠃
⠀⢰⢿⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠘⠀⠘⡆
⠀⡼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠸⡄⠀⠀⠀⢳
⢀⡇⠀⢳⠀⠀⠀⠀⠀⠀⠠⠡⠐⠀⠀⢀⡴⠋⠀⠀⠀⠙⠦⣀⡀⠈⣇
⣸⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⡏⠀⠀⠀⠸⣆⠀⠀⠀⠀⡀⠀⢠⠞
⠻⣄⠀⠀⠀⠸⣆⠀⠀⢰⠁⠀⣿⠀⠀⠀⢶⠤⢤⣀
⠀⠈⠙⠒⠶⠴⠋⢧⡀⣾⠀⠀⢹⠀⠀⠀⢸⡄⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣧⡀⠀⠣⣀⣀⣸⢃⠀⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠈⠉⠙⢮⢖⡡⢠⣼⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⢸⣿⠦⠤⠀⠀⠀⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢍⣑⠒⠀⠀⠀⠀⠀⠀⠈⢣⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⢿⣿⠷⠛⡜⠀⠈⢦⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣴⡶⠿⠛⢛⣩⡁⣽⠂⠀⠀⠀⠀⡀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡽⣷⣿⣿⠟⠛⠊⠁⠀⠺⢿⡁⠘⠀⠀⠀⠀⠀⡀⠀⠀⠈⣝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠞⢋⣼⣿⡿⠋⠀⠀⠀⠀⡄⠰⠄⠀⠈⠀⠄⠀⠀⠀⠀⠈⠉⣽⣿⣿⣷⣶⡅
⠀⠀⢠⠂⠀⠀⠀⢠⡆⢤⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠒⠢⠄⡀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠋
⠀⠀⠸⡆⠀⣴⣾⣿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⣨⣶⣶⣶⣾⣿⡿⠋⠁
⠀⠀⢸⡇⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⣿⣿⣿⣿⠟⠋
⠀⠀⠈⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠆⠀⠹⠛⠋⠁
⠀⠀⠀⠃⠀⠈⢤⡤⡶⣶⡖⠒⠂⠀⠀⠀⠲⠶⠒⠐⠾⠂⠀⠀⠈⠈⠉
⠀⠀⠀⠈⡄⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡿⠿⠿⠿⠿⠿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⢛⣉⣥⣤⣤⠶⠶⠦⠤⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⣟⣥⡶⢚⣋⣩⣥⣴⠶⠶⠦⠤⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠉⠁⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠛⠻⠿⣶⣶⣶⡒⠒⢒⣠⣾⠏⠀⠀⠀⠀⠀⠀⣠⡾⠛⣡⡴⠚⠁⣰⡿⠁
⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣭⡀⠀⠀⠀⠀⠀⣠⡾⢋⡴⠟⣁⣤⠀⣼⡟⠁
⠀⠀⠀⣠⡿⠋⣠⠤⠤⣄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣤⠾⠋⠀⣩⠶⠛⣉⣀⣼⡟
⠀⠀⣼⠟⠀⣼⣥⣈⣷⡌⡆⠀⠀⠘⣆⠀⠀⠀⣀⣴⣶⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠁⣿⡇
⣠⣾⠏⠀⠀⠹⣌⣛⣛⡴⠃⠀⠀⠀⣿⠀⣠⠾⡋⠁⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠛⠛⠓⠻⣿⡄
⢻⣷⣤⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⠘⢑⣪⠀⣾⠏⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡛⠶⢤⣰⡿⠃
⠹⢷⣬⡛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠰⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢶⣄⠀⠀⢮⣙⠦⣄⣿⡇
⠀⠀⠈⠙⠷⣦⣀⡀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⡾⠋⠁⠀⠀⠀⠙⢷⣌⠢⣍⠳⣄⠻⣧
⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡈⠳⣌⡙⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢿⣿⠿⣿⠷⠶⠶⠶⠿⠿⣿⡻⢟⡻⢟⡦⠭⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⡙⠢⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡻⣕⡘⣷⠀⠀⠀⠀⠀⠘⢿⣦⣙⠲⢭⣙⡒⠂⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣭⣸⡧⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣬⣉⣛⣓⣨⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡄⣻⣶⣤⣀⣀⡀⠀⠀⠀⣀⣤⠞⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣦⣤⡎⢀⣀⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠇
⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣻⣿⣿⣟⣻⣯⣿⣿⣟⣾⣻⡿⣻⡟⣻⡿⣻⡿⣿⡿⣿⢿⣿⣿⣿⣿⣷⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠏
⢀⣠⡴⠾⠟⠛⣿⣶⡛⠀⠙⠻⣮⣉⣠⣤⣤⣥⣿⡬⢥⣬⣧⣭⣠⣟⣘⠛⠁⠋⠘⠋⠾⠇⠸⠟⠹⡿⢻⣿⣿⣿⡿⣶⣦⣤⣤⣾⣷⣶⡟
⠀⠙⢣⡀⣀⠻⠿⠟⠀⠀⢀⠀⣻⡟⡟⠓⠉⠉⠈⠉⠉⣁⣀⣨⠭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠾⠿⢿⣿⣿⣻⡅
⠙⠻⢦⣥⣞⡃⠀⠀⠀⠀⣴⡀⣿⣓⣳⣤⣤⠖⠈⠉⠉⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠉⠁⠉⠀⠀⠀⠀⠻⣝⠛⢻⡀
⠀⠀⠀⠀⠉⠛⠻⠶⣶⣮⣿⣿⡟⣛⣛⣿⣿⣿⣭⣭⣭⣵⣶⣶⠶⠶⢷⣴⣤⣶⣴⣶⣶⣾⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣿⣯⣭⣭⣭⡭⠽⠿⠿⠿⠟⠛⠛⠛⠻⣿⡻⠏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣷⣦⡀

⠀⠀⠀⠀⣠⣶⣿⢶⡦⣄⠀⠀⠀⠀⠀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠷⠾⠁
⠀⣀⠀⡀⢻⠸⣿⢸⠃⠘⠓⠒⠄⢀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⠀⠈⠁⢸⠀⡇⠘⢸⡇⠀⠀⠀⠘⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⣶⠀⣆⢸⡧⠀⠊⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣠⡄⠰⠘⣿⣁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠙⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢩⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣉⣀⡤
⠀⠀⠀⠀⠀⠀⢠⣶⠤⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⣠⣤⠴⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠿⠛⠻⠿⢶⡆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠆⠀⠀⠠⣶⣛⠉⠠⠄⠐⠒⠒⠛⢛⣫⣇⠘⠀⠀⠀⠀⠀⢰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣛⡛⠿⠿⠿⢛⡛⠉⠁⠀⠀⠀⠀⣠⣦⠈⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢠⠘⣿⡷⠂⢤⡆⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠄⠁⠀⢹⣇
⠀⡤⠤⢤⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢰⠀⠞⠆⢰⠀⡆⢸⠋⢠⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢃⢴⣿⣶⠀⠹
⠸⠁⢠⣶⣿⣯⠈⠉⠀⠀⡀⠈⠁⠀⠀⠀⠒⠤⢄⡀⠀⠀⢸⡀⢸⠀⢆⠀⢸⠀⡇⢸⠄⠘⣄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣾⣿⠑⣠⣦⡀
⠈⠰⣿⣷⣿⣿⠀⠀⠀⠀⠡⠈⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⢸⠀⢸⠀⠀⢣⢸⡤⡇⢸⠀⠀⠈⠆⠀⠀⠈⠁⣀⠄⠀⠀⠀⠀⠀⢀⣉⣼⣿⣿⠏
⠀⠀⠈⠛⠿⠃⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⠀⢸⠀⠀⠈⢸⠀⡇⢸⠀⠀⠀⢸⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠸⠀⠦⠜⠸⠀⠇⠸⠄⠘⠤⠎
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣦⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣄
⠀⠀⠀⠀⠀⡀⠘⢿⣿⡌⠙⢿⣿⡄⠐⣦⣤⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣤⠀⠀⣠⠄⢸⡿⠁⣼⠋⢈⡷⠂
⠀⠀⠀⠀⠈⠋⠀⢸⣿⡿⠀⢸⣿⡇⠀⣼⣿⡧⠙⠿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡷⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠐
⠀⠀⠀⠀⠀⠀⠰⠿⣿⣁⣴⣿⡟⠁⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢠⡾⠟⠀⠀⠻⠀⢸⣧⠀⢿⡄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠛⠁⠀⠀⠀⠀⠀⢀⡀⠆⠠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢀⣴⣇⠀⠀⢻⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⠀⠀⠸⡟⢂⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⠻⢉⣾⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡆⠀⠰⣷⢼⣷⡀
⠀⠀⠀⠀⠚⢿⣷⡄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⢿⡶⠖⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⣧⢼⡿⠁
⠀⠀⠀⠀⢤⠄⢹⡇⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢁⣴⣦⠉⠝⠃⣄⡀⠀⣠⣶⠇⠀⠀⠀⠀⠛⠃⠤⠐⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⢁⠆⠿⢟⣻⠡⣾⣿⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⡿⠶⡗⠘⣿⠇⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣠⣤⣬⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠐⠋⠙⠓⠶⣤⠀⣠⠆⠀⠀⠀⠀⢀⣺⣼⣶⣶⣶⣄⢰⠂⠀⠀⠀⠀⠀⣤⡤⢴⣦⣤⡀⣠⡄
⠀⠀⢀⠀⠂⠀⣀⡠⠒⣀⠀⣿⡀⠀⠀⠀⢴⣿⡿⣿⠟⠽⠋⠀⠛⠀⠀⠀⠀⡄⠄⠀⣤⠴⢒⣲⠄⠹⠇
⠀⠀⠈⠀⠀⢤⣌⠁⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠦⠤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⢈⣀⠀⠻⢠⣆⠀⠀⠀⠀⠀⡊⠁⠹⣿⣿⢿⣿⠉⠻⠇⠀⠀⠀⠀⠀⠄⠀⠿⣿⣿⣯⣤⣦
⠀⠀⠀⠀⠀⠈⠉⡠⠆⠘⠇⠀⠀⠀⠀⠀⠉⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣘⠓⠿⠇⠈⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⣠⣶⣤⡄⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢶⣴⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣄⢹⡄⡇⡇⡧⠠⣼⠀⠀⠀⠀⠀⠰⣟⢰⢷⣼⢱⠶⣇⠀⠀⠀⠀⠀⠀⢤⠀⣸⡷⢮⣵⣦⣀⣤
⠀⠀⠤⣾⡘⣧⠗⣧⣏⠈⠻⠀⠀⠀⠀⠀⠙⠿⢿⡟⠛⠻⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠥⠇⠰⠗⠂⠈⠋
⠀⠀⠀⠀⠈⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣄⡀
⠀⠀⠀⠀⢨⣿⣿⠿⠿⠓⢺⡇⠀⠀⠀⠀⢀⠠⠃⢀⠩⠙⠦⠀⡀⠀⠀⠀⠀⢀⣴⡟⢻⢻⣿⣿⣧⣶⣦
⠀⠀⠄⠈⠀⣙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡴⠀⠀⠉⠀⠀⠀⠀⠸⠆⠀⡀⣸⠯⠿⠆⠈⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⣿⠀⡝⠣⣴⡆⠀⠀⠀⠀⠀⠀⠀⡩⡮⣿⣿⠂⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡉⠺⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠈⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠄⠀⠀⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠐⠀⢠⠁⣔⠀⠀⠀⠁⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢠⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢟⢾⣿⣟⠟⠳⣾⣷⣶⣿⡀⠠⠀⡀⠀⠈⠁⡀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡞⢏⣌⠀⠀⠀⠄⢃⠴⠒⠝⢍⠱⠈⠭⠻⣟⢤⣀⣀⡄⠀⠀⠀⣠⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢀⣤⠄⠀⠀⣼⡿⣝⢛⣭⠎⣀⣀⠈⢄⠀⠀⠈⠀⡳⡞⠀⠠⠃⡈⠯⠃⢀⠀⢀⣰⣯⣾⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⢀⢀⠀⠀⢀⣴⣿⣿⢽⣾⣶⡁⢀⡿⣧⡀⠈⠀⠀⠀⢀⠄⠆⡠⢀⠔⠈⠐⠀⠀⣽⠿⣿⣿⣧⠊⠀⠀⠀⠀⠀⣀⠔⠁
⠀⡾⠋⢀⢔⡫⢭⡛⢽⡆⠀⢈⡉⠉⠠⠘⠁⠀⠠⠧⠶⢫⠀⠘⢤⡏⠀⠀⠀⠀⡀⡉⢂⣿⣿⠷⠂⠀⠀⠀⢠⠋
⡴⣅⠀⠀⡏⣶⡂⢸⡌⠠⠀⠚⠁⠀⠀⡀⠀⠈⠁⠠⠅⠎⠠⠀⡩⠁⠀⢀⣀⣀⣁⣁⣾⣿⠿⠂⠀⠀⠀⠀⠘⡄
⢆⠘⣆⠀⠳⢭⡥⠞⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠈⢈⡀⠤⣴⢁⠶⣵⢾⡁⠀⠘⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠘⡀
⠀⠂⣈⠀⠐⠂⠒⠈⠀⠀⠀⠀⣠⠆⣠⡎⠀⠀⠐⠂⠘⢰⣷⣼⣶⣿⠇⠀⠣⠀⠀⣸⣿⡟⠂⠈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⠁⢤⣔⡃⠀⠀⠀⠂⡁⠀⣰⣿⠉⢠⠘⠀⠈⣀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠈⠑⠠⢤⣶⣷⣶⣮⡻⣿⣷⣤⣤⡤⣴⣏⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⠟⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠻⡻⣿⣿⣿⣿⣽⣿⣿⠟⠉⠀⠀⠀⡠⠁⠀⡞⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠙⠿⣭⣉⠉⠉⠑⠈⠛⠆⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠠⣀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠢⠀⠈⠀⡀⠈⠓⠲⠄⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠀⠀⠀⠀⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⣄⡀⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠍⠁⠀⢀⣀⣬⣿⣿⢦⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⡿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠃⢤⣀⣤⣾⣟⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⢟⠟⣴⣾⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠟⠉⠻⡻⣙⣸⡿⣿⢃⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⠀⠀⠀⠀⠈⠉⠉⡰⢁⣾⠿⠿⠿⣿⡦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠭⠒⣒⠢⢀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢸⣻⡄⠀⠀⠀⠀⠢⠄⠀⠀⠨⠔⠁⠀⠚⢁⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣷⡙⢦⣀⣄⠓⠦⡤⠄⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⡟⠁⠀⠀⣤⣶⡿⢟⡛⠋⢉⣿⡿⠛⠲⠤⣭⣍⣃⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠻⢿⣿⣷⣶⣿⠾⠁⠀⠀⣀⣤⣾⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣤⠶⠚⠙⣿⠿⠟⠟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⠀⠘⣿⡄⡀⣘⣧
⠀⠀⠀⡀⠀⠀⢠⣾⠖⠶⠦⡤⠘⣿⣷⣄⠀⠀⠀⠀⢠⡟⠁⢀⣠⣤⣤⣶⣶⣶⡎⠻⣿⣿⣿⠠⠶⢄⡀
⠀⠀⣾⠀⣀⢠⣮⠓⢶⣂⠀⢀⣉⣉⠛⢿⣶⣀⠀⠀⠘⢷⣶⣿⣿⣿⡭⣭⣽⣏⣀⣠⣶⣿⠶⠒⠉⢁⢣⢀⠇⢠⠷
⠀⠀⠘⢇⢽⡾⣟⡳⣶⣿⣟⠲⠾⢭⣉⡉⢙⣿⣿⣷⣤⣾⣿⣿⣿⣶⣾⣿⠟⣿⣥⡶⠾⠋⢅⠤⢒⣫⢏⡞⠜⠁
⠀⠀⠀⠀⠙⠟⣾⣿⣿⢿⣿⣷⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣟⣭⣵⣶⣶⣶⣶⣾⠻⣵⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠛⠻⠟⠛⠻⠿⢿⣿⣟⣛⣛⣛⣻⣿⣿⡿⣿⣿⣟⣿⡿⠛⠿⠛⠙⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠤⣟⡯⡙⣝⣦⠴⠒⠋⠉⠉⡅⠀⠀⣡⣤⣄⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⡙⠒⠆⠙⢋⢝⠀⣰⣧⠀⠀⠀⠁⠀⠸⡟⢏⣹⠂⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⣤⣛⣒⠒⣬⠶⠤⠔⢉⣡⠞⠁⠸⡆⠀⢠⣄⡀⠀⠈⠉⠁⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⡺⠵⠒⢢⡽⠁⠠⣴⣿⡍⠀⠀⠀⢸⣇⡰⠁⢈⠛⢆⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⢨⡟⠩⢭⣟⣀⠀⠈⠁⠈⠙⣦⠀⣠⢛⠟⠛⡄⠀⠀⠈⣆⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠉⠙⢳⣤⣀⠈⣖⠁⠁⠀⠀⣫⠞⠁⢰⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣀⣀⣀⡀⠹⡌⢣⣸⠀⣠⠔⠋⡝⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠸⡋⠋⠙⢯⡁⠀⠑⢧⠀⣿⠞⠁⠀⠀⠸⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣀⢱⠀⠀⢸⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⢉⣽⣏⠢⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡿⣿⣿⣽⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡏⣇⢣⠙⢿⢿⠩⣑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠈⢧⠑⢄⠑⠌⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠃⠐⢠⠋⠙⠣⢄⣉⡐⠚⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣧⠃⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣤⣤⣠⣀⣀⠀⢣⠀⠀⣀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢿⠿⡿⠳⡿⣿⠛⠛⣿⣿⡳⣾⣷⣶⣶⣿⣿⠂⠀⠀⠀⢀⡠⠔⣲⡇
⠀⠀⠀⠰⢾⠟⠿⠛⠟⣽⡿⣆⣻⣤⣴⠿⣿⠀⢩⢿⡏⠀⢻⣿⡿⣿⡿⠝⢿⠟⠿⣿⣶⣦⡋
⠀⠀⠀⠙⠪⢍⠐⠚⢥⡍⠞⠠⠬⠛⠿⠒⠛⠀⠈⠿⠄⠀⠑⠋⠀⣈⡀⠀⠀⠀⠀⠛⢺⣄⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠄⢀⣀⣄⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠨⠄⠈⠄⠀⠀⠀⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣖⣒⣛⣿⣭⣭⢭⣭⣽⣓⣲⣦⣤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣤⣄⣀⣀⣤⠶⣚⣯⣽⣶⣿⣿⣿⣿⣿⣫⣍⢝⣛⢶⣞⢟⣱⣿⢡⣾⢻
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣭⣛⣿⣿⣿⢟⣯⣶⣿⣿⣿⣿⣿⣹⣿⠟⠉⢡⣿⣿⢿⡽⣸⣇⣿⣿⢣⣿⢿⣸
⠀⠀⠀⠀⠀⢠⠶⣿⣶⣞⡿⣿⣿⣯⣾⣿⣿⣿⣿⡿⣫⣶⣿⠘⠇⠀⠀⠀⣛⢿⡿⢫⣿⡇⣿⣿⣸⡿⢼⣇
⠀⠀⠀⠀⡔⠛⣶⣒⣾⣿⣿⣿⣿⣿⣛⢿⣿⣿⢟⣾⡟⠻⣿⠇⠀⠀⠀⠀⠩⣿⠇⣿⣿⡇⣿⡿⡟⣧⠸⣻
⠀⠀⠀⢀⣇⣤⣤⢽⣿⣻⣿⣿⣿⢰⣿⣶⠙⠃⣾⣿⡇⢰⡟⠀⠀⠀⠀⠀⠀⠻⢸⣿⣿⡧⣿⡇⣇⡙⠀⢻⢧⠀⠀⢀⣀⣤⣴
⠀⠀⠀⠀⣏⣭⣽⣿⣿⣿⢿⣜⠟⢺⣿⣿⣿⡇⢻⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣟⠁⢰⣿⠁⢸⡿⠷⠿⢟⣿⣿⣿⡿⢟⣫
⠀⠀⠀⠀⢻⠽⣿⣿⣿⣿⢃⣿⣧⣼⣿⣿⣿⡷⢸⡼⡀⢸⣧⡀⠀⠀⠀⠀⠀⢀⣤⣿⡄⠸⣿⣇⠸⣿⣿⡿⠟⢩⣯⣿⡿⠛⠉
⠀⠀⢠⢞⣵⣿⣿⣿⢈⣋⣾⢿⣼⣿⣿⣿⣿⡇⠀⢷⢣⡈⣯⢷⣄⠀⠀⠀⠀⣿⠀⠀⢶⣾⣿⠿⠛⣉⣱⡿⠿⠛⣹⡟
⠀⣰⢣⣯⣽⣿⣿⢿⣼⣿⣯⡘⠻⠿⣿⣿⠁⠀⠀⠸⣇⠱⣜⣿⡿⢧⣤⡤⠴⠛⢠⣤⣬⣥⡤⠶⠛⣉⠀⢀⣤⠞⠋
⢰⢣⣛⣽⣿⣿⡟⠈⠻⣿⣿⡗⠀⠀⠀⠉⠀⠀⢀⣀⣹⣷⣤⣈⠉⠉⠉⠙⡆⣀⣀⣀⣴⣶⣶⣶⣿⠥⠖⠋
⡏⣼⢟⣭⣾⣿⡇⠀⠀⠙⠿⠷⠄⣠⣾⣿⣿⡿⢟⣻⠿⣻⢏⡸⢿⣶⣶⣿⣾⣵⣿⣿⣿⣿⣷⡿⠃
⡧⠗⣡⣿⣿⣏⠀⠀⠀⠀⠀⢠⣾⣿⠻⢟⣥⡾⣻⠵⣫⣵⣿⣿⡼⠃⠀⠈⠉⠉⠉⠉⣩⠟⠋
⠃⠘⢿⣿⣿⡿⠀⠀⠀⠀⠀⠘⠻⢿⣷⣄⠫⠞⣡⠞⣡⢤⡿⠁⠀⠀⢀⣀⣤⣤⣴⠊⠁
⠀⠂⠠⠼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢛⣛⣷⣿⡷⠋⢀⣠⣴⣾⣟⣿⣿⡿⣟⢧
⠀⠀⠀⠀⠸⣿⣿⣗⡀⠀⠀⠀⣠⣴⣶⣿⠿⠋⠉⠀⠀⣰⣿⣿⣿⠰⣽⣿⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣷⣹⣷⣄⠀⠀⢹⡌⠁⠀⠀⠀⢀⡤⢖⡿⣏⠋⡿⣱⢏⣿⣿⣸⡏⣿
⠀⠀⠀⠀⠀⠀⠻⣷⣭⡛⠀⢠⣤⠇⠀⠀⢀⡴⢋⣾⠋⠀⠘⢦⡰⠏⣸⣿⢧⡏⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠀⢰⡿⠀⠀⢠⢊⡴⣿⣿⣶⣒⣚⣋⡵⢦⣁⣫⣿⠖⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡇⠀⢀⡽⠀⠀⠟⣿⣭⣭⣍⣉⣻⣭⣽⣷⡾⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡏⣄⣠⣤⣶⠿⣿⣿⣶⣶⣶⣶⠶⠶⠶⠛⣛⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢿⣿⡟⣿⡀⠈⣍⣓⠪⠭⠭⠽⠿⠿⠿⠿⠟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠉⠀⠹⣿⣿⠳⣯⣍⡛⠛⠓⠒⠒⠒⠒⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣉⣉⣀⣀⣀⣤⣤⡶⠶⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣯⣿⣿⣿⣦⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠟⠿⠟⠋⠛⠋⠉⠉⠈⠉⠁⠉⣁⣈⣉⡈⠉⢡⡾⠉⠉⠙⠛⠿⣷
⠰⣶⣶⣶⣿⠿⣿⡟⠉⢉⣉⣁⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠉⠙⠛⠉⠁⢸⣇⣀⣠⣶⣿⡿⠟
⠀⠈⠻⣿⣿⣷⣹⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⣩⣽⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉
⠀⠀⠀⠀⣿⠏



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣖⣂⡤⢤⣀⣠⣤⣤⣤⣤⡦⠤⠀⣠⣀⣀⣠⠴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣸⢿⣿⣿⡟⣁⣀⣄⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣶⣾⣿⣿⡛⠉⠉⢻⣿⡟⢹⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠴⣴⣿⣿⣿⣿⣿⠿⠋⡀⠠⣧⡀⠋⡏⠘⣿⣿⣿⣿⣿⡿⠃⣾⣿⣿⡙⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡟⠁⠀⠘⠚⠱⡙⢿⣦⡈⠂⠈⠛⣿⣿⣿⡇⣴⣿⣿⣿⣃⣿⣿⠗
⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⢫⢋⠊⢶⣶⣿⣿⣿⣿⠳⣾⣷⣄⠀⠀⠀⠸⠇⣰⡿⠀⠉⢛⣛⣉⠥⠚
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⢡⣎⠔⣿⣿⣿⣿⢿⣿⠗⠘⢿⡋⠁⡀⠀⠈⠊⢙⣡⣴⠟⠉
⠀⠀⠀⠀⠀⣸⣿⣿⣿⠄⢾⣿⣮⣽⠝⠓⠂⠉⣡⣴⢊⠀⣉⡿⠟⠓⠚⠛⠋⠉
⠀⠀⠀⠀⠀⣿⣿⢹⡻⣦⠈⠛⠁⣄⠈⠀⢠⣾⣿⣿⣷⣫⠏
⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠘⠘⠀⢀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⠁⠀⢀⡘⢂⠀⢀⠔⠁⠹⡻⡿⣿⣳⠃
⠀⠀⠀⠀⠀⣿⠟⠀⡀⠐⠳⠀⡠⠋⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⣿⣆⠀⣵⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣿⡆⢿⡆⠀⠀⣿⣶⣖⣶⣶⣶⣿⣿⡿⢟⡷⠆
⠀⠀⠀⠀⠀⢻⣿⡃⠹⣿⣜⣄⢊⠙⣿⣿⣿⠿⠿⢋⠔⠁
⠀⠀⠀⠀⠀⠂⠉⠀⠀⠙⢿⣮⣦⣹⣾⣿⣿⡗⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡦⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⢿⡌⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠿⠓⠋⣰⣿⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⢠⠟⠀⠀⢀⣿⠛⠛⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡎⠀⡇⠀⠀⠀⠀⢸⣿⣀⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣫⡞⢻⡁⠀⠷⣄⢰⡇⣨⡼⠛⠚⣉⣉⣛⣒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣳⢋⡼⠌⠓⠒⠀⣀⠄⠉⡁⠀⠀⠈⠛⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣳⢃⣾⡿⠒⢪⣦⣭⠥⢖⢋⢖⡵⢂⡀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢧⠇⢸⡏⠳⣄⣀⡴⠁⠀⠀⠈⠉⠉⣽⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⢰⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡆⢸⡿⠓⠀⠀⠀⠀⣀⣴⣤⣼⡾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⢇⣾⡏⠀⠀⠀⠀⠐⠛⠛⣻⡟⠑⢿⣿⡇⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢠⣿⠇⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠙⠀⣠⣮⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢹⣄⠀⠀⠀⠀⡄⣼⠻⣦⣀⣀⣀⣀⡞⠋⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡙⠀⠀⠀⢸⣷⣷⣄⣀⡉⠉⠉⠁⠙⣦⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠶⣄⡀⠘⣿⡏⠉⠛⠛⠛⠛⠳⠀⣸⠀⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠤⠤⠶⠖⠒⠛⠛⢦⡲⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣞⣛⣛⣿⣿⣿⣓⣲⣤⣀⣤⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠁
⠀⠀⠀⠀⢀⣠⡴⣟⡛⠛⠛⠛⠋⠉⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠄⠀⠈⠉⠉⠙⠛⠛⠿⠷⠷⣯⣤⣄⣀⡀⠀⠀⠀⢀⡼⠁⢸⠃
⠀⠀⠀⠀⢫⡀⠘⣼⡿⠂⠀⠀⠀⠀⡀⠀⠈⠉⠉⢉⣽⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠲⠾⠤⡄⣾
⠀⠀⠀⠰⣖⠛⠂⠀⠀⠀⠀⢰⠀⢀⡇⠀⠀⠀⢀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠋⢿⠉⠀⣧
⠀⠀⠀⠀⠈⠑⠶⢴⡲⠤⠴⠃⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠎⠋⠀⠀⠀⠀⠀⠀⠈⢧⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⢯⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡻⣿⣿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠁⠙⠾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆⠀⠙⠀⠶⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⢠⡄⠀⠀⠀⣿⢻⢻⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⢿⠀⠀⢀⠹⣟⠻⣡⣾⣿⣿⣾⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⣿⡄⠄⠸⠀⠙⠛⢻⡿⢻⢿⣿⣿⣿⣩⣍⡙⢻⢷⣦⣄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠁⠀⠀⡆⠀⣿⣦⠀⠀⠛⠻⣿⡅⢻⣫⠛⣦⡸⣾⣩⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣒⠋⠀⠀⠁⠀⠀⠔⠀⠀⠀⠀⠙⠄⠀⢓⠀⠀⢹⠓⠋⢱⣶⠟⣷⠙⣏⡳⠾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⣿⠛⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠈⣄⠉⣨⣿⣇⣼⣿⡜⢻⢛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⣀⠤⢀⣸⣿⠿⠃⠀⣿⢾⣿⡞⡻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠏⣰⠟⠋⣡⠀⢀⠘⠃⢈⣻⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢠⠰⡀⠢⡀⠀⠀⠀⠀⠀⠀⠊⡡⠴⠈⠁⢠⣄⣀⠀⠈⠻⠉⠿⣧⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠊⠳⠈⠂⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⣸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⢿⣦⣄⡸⡟⠴⠛⠀⠀⠀⢀⠀⠀⠀⠀⠉⢀⠀⠤⠙⠷⠀⠐⠂⠈⠙⠋⢛⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢧⡀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠄⣾⠃⠄⡀⠀⠀⠀⠨⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⢀⠛⠄⠀⡒⠀⠀⠠⠼⢃⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠈⠃⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⠃⣀⠀⠀⠀⠁⢀⠀⢢⠄⡠⠈⠻⣦⡀⠛⠀⠀⠀⠀⠐⢷⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠘⣪⠄⠁⠈⡁⠂⢀⠀⣹⠀⠀⠐⠃⠀⠀⠀⣶⣀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠀⠈⢱⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣦⠄⠈⠃⢾⣿⠂⢠⠀⢀⡀⠀⠀⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⣿⣧⠀⠀⠻⠉⠀⣾⠋⠉⠀⠀⢀⡄⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⢾⡟⠛⠿⢃⣸⣧⣿⡆⠀⠀⡀⠈⢰⠀⠀⠀⠋⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⡀⠀⠀⠀⠀⠄⠀⡴⠃⠀⣤⢀⡠⣤⣼⢢⡙⢿⡱⣿⡷⣤⡈⠀⠀⠀⠀⢀⡬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⡟⢫⠾⠹⡏⠀⠃⠙⠈⠁⠙⠁⠈⠻⠛⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡀⠠⠞⠛⡻⠓⠀⢀⣀⣀⣀⠀⢀⢤⡤⠀⠀⡑⠂⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡰⠎⠁⠀⣴⠿⠛⠉⠀⠀⠀⠀⠁⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣀⣀⠀⠀⠐⠒⠀⠉⠉⠉⠉⠉⠉⠒⣢
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠻⢿⣆⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡍⠒⠤⠌⠧⣀⠀⡔⣩⣭⣭⡙⢶⣤⣤⣴⠶⢦⣤⡤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢸⠀⣿⣿⣿⣷⡀⣿⣿⣟⣻⣿⣿⣦⡶⣦⣬⣉⠛⠿⣯⣭⣖⡂⠰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠟⣿⣿⣿⣇⢸⡄⠟⣷⣄⠉⡜⣿⡎⢿⣿⣿⣦⣄⠙⢿⣭⣍⣀⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⢀⡾⣹⣿⣿⡄⠛⢆⣈⠉⣡⠾⢹⣴⢸⣏⢹⣿⣿⣷⣵⣮⡻⣧⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠤⣽⣾⣡⣯⣯⣿⣷⡈⣠⣿⡆⠀⠶⢸⣘⠁⡿⢃⣛⢠⣿⣿⣿⣿⣜⢷⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⠶⠶⠶⠶⠦⠝⠛⠻⢿⡶⠖⢁⠄⢠⣼⣿⣿⠂⠀⠀⢩⣿⣿⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣦⣐⠢⣄⠠⡐⢤⡐⠒⠤⢄⡶⢻⣿⠟⠋⠀⠀⣤⠋⣿⠿⣿⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡿⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡑⠺⠶⠬⠶⠒⠉⠀⠀⠈⠳⠦⠖⢋⡍⢠⡁⣸⡟⣿⣿⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣛⢡⡿⣿⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣶⠶⡀⢠⣄⣀⠀⠀⠀⠀⠀⠁⢘⢣⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⡄⠘⢮⡹⣿⣽⠒⣦⣄⠀⠀⠉⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⣦⣄⡀⢻⢁⣽⣶⣤⡙⢦⣽⡄⡸⣿⣷⡄⠀⠣⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠞⠛⣻⣿⣾⣿⣿⣿⣿⣽⣷⣬⣿⣾⢿⠿⣿⡀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⣍⠙⣿⣿⡹⣿⣿⣿⠛⠏⠿⠎⢑⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣴⡄⣦⠀⠀⢠⣼⣷⣾⣿⡟⠸⠿⣿⣮⣀⣀⡠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⡆⣀⣸⣿⣿⣿⣿⡷⢀⣴⡷⣿⠟⠁⠠⡍⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢳⣦⣴⣿⣿⢃⣼⣿⢿⣿⡟⣿⠁⠹⣫⣿⣯⣶⣶⣾⣿⣿⣿⡟⠧⣄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠏⣸⣿⡟⣼⡿⣱⡧⠔⢊⡵⣻⣽⣿⣿⣿⣍⡻⣿⣤⡀⠈⠃
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⢀⣶⣿⣿⢿⣿⡿⠁⣴⡿⢋⣼⠟⡱⠃⠀⠀⣩⡾⣻⣿⣿⠟⠋⠈⠁⠉⡽⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣰⣿⢟⣭⣶⣿⣿⣀⡀⠁⣰⡿⠋⠀⠀⠀⢀⡾⢋⣾⠟⠋⠀⠀⠀⠀⠀⠀⠁⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠵⣿⡿⠟⠉⠙⠋⠀⠀⠋⠀⠀⠀⠀⠀⠉⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠒⠀⠉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠦⠤⠤⠤⠔⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡄⡰⢀⡜⢁⡴⠁⠀⠂⡂⠀⠀⠀⠀⠀⢀⠀⠄⠀⠢⠂⠁⠀⠈⠀⠀⠀⡀⢀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡵⠿⢒⠋⡒⠍⡀⠠⠉⠀⡒⠲⠆⢦⣤⡆⣀⠔⠂⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⣀⠜⢁⡀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠕⠒⠢⠀⠀⠀⠀⠀⠀⠀⡠⠔⡰⠃
⠀⠀⠀⢀⠄⠀⠀⢠⣮⠎⡠⢊⣁⢀⡤⠜⣦⣴⠦⠦⠤⠤⣤⣄⣀⣀⡀⠀⠉⠘⠙⠋⠋⠂⣀⠴⠊⠁
⠀⠀⠠⠁⠀⠀⠀⢟⠳⢿⣊⣅⣸⡧⡞⢉⠀⠀⠀⠀⠀⠀⠀⠈⢋⡍⢉⡇⠀⠀⠀⠈⠀⠉
⠀⠠⠀⠀⠀⠁⠑⠢⡀⠸⡅⣾⣿⣗⣚⠲⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠃⣀⣀⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠐⢀⠆
⡐⠈⠣⠈⠁⠀⠀⠄⣸⠟⢁⡠
⡇⠀⠀⣠⣤⡬⡶⠚⠁⠠⠁
⠳⠴⠋⠀⣬⠝⠦⠂