Crocodile Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣾⠈⢂⠀⡀⣤⡵⠄⢄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠻⠿⡿⢷⣖⣋⠘⢓⡃⠀⠙⠓⢬⣋⠑⠁
⠀⠀⠀⠀⠀⢀⡄⢰⣦⠀⢢⡯⣻⢻⣭⣷⣄⠙⠷⣶⣤⣤⡀⠁⠀⢈⢄⡀⡂⠀⠀⡀
⠀⠀⢀⣀⡀⠂⣵⠛⠙⢷⡯⠀⣷⢈⠢⣿⣿⣧⣤⣠⣠⡋⡛⠻⠿⢿⠋⢰⠿⢿⣷⣶⣶⢷⣧⡀
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠸⠦⠝⢦⣁⠾⠻⠭⠟⡿⢿⡁⠞⡃⢼⠶⡶⡘⠓⡐⡞⢿⢋⢯⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠊⠙⠓⠓⠂⠴⠤⠥⠔⠁⠀⠀⠀⠈⠆⠏⠠⠐⠺



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⠎⣂⣠⣤⣦⣴⣭⣦⣤⣶⣄⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣷⣧⠼⠛⠛⢋⢉⣥⣍⣭⣩⣿⣽⡿⢿⣻⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠿⢋⣀⣤⣶⡀⢿⣅⣷⣯⣿⣴⠿⠷⠿⠶⠿⠗⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠟⣡⣤⢸⣿⣬⣿⠷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⣿⣠⣬⢿⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠘⣿⣭⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠒⠀⠙⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠆⠀⠘⢿⣾⣦⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠰⠆⠀⠸⣿⣿⠳⣿⣦⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠂⠟⠀⠀⠙⣷⣎⠉⠳⢿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⠀⠐⠃⠀⠈⠙⢷⡦⠚⠉⠳⢿⣿⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡆⠀⠘⠃⠀⠀⠾⢶⣤⡄⠶⠏⠢⢽⡟⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡔⠄⠀⠠⠗⠀⠀⡙⣦⣤⣀⠰⣦⠛⢄⣿⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡶⠳⣤⠀⠦⠉⠙⠻⣄⣀⡀⠀⣤⡽⢟⣹⡿⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⣿⡇⠀⠈⢷⣆⢠⡄⠀⠿⣏⠁⠀⠆⠀⣈⠙⣷⣼⣻⣿⣿⠿⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢰⡟⡇⠀⠀⠘⢿⣤⡀⢀⠀⠈⢷⡿⠆⠀⠉⠗⠙⢷⣿⢺⣿⣿⡿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢰⣘⣇⡏⠀⠀⠀⠈⣿⡄⠉⠀⠀⠛⢷⣘⣄⡑⠀⣠⡀⢻⣌⢻⣿⣷⡶⣎⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣦⠘⣧⠸⣧⡀⠀⠀⠀⢈⣷⠀⠰⠀⠀⣸⣿⠛⡏⠁⠙⠏⠉⢯⣿⣿⣿⣿⣜⣧⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⣆⣹⡄⢹⣆⠀⠀⠀⣀⣆⠀⠀⠀⠀⠈⢻⡐⢰⣄⠂⢠⡀⠘⣿⣄⣻⣿⣿⣀⡰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⢷⣄⡙⠀⠀⠀⢺⣿⠀⠀⠋⠀⠀⢸⡟⠉⠋⢠⠉⠉⠈⣹⠟⣝⣿⢿⣿⣿⣿⣷⡀
⠀⢀⢤⡖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣤⠿⣿⠀⠀⡀⠀⠀⢹⣷⣤⣦⠀⣰⡄⠀⢻⣶⡯⣿⣿⣿⢻⣼⣿⣟⠢⡀
⠀⢹⣶⢾⠁⠛⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠃⠀⠀⣸⡟⢩⠉⡄⢹⠉⠀⢿⣁⣅⣾⣿⣿⢿⡙⣧⠙⢷⣷
⠀⠠⠿⣾⣰⣦⡤⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⡴⠀⠀⠀⣿⣧⣾⡀⣡⡆⠀⢸⡞⢙⣧⣼⣿⣿⣽⣧⣽⢷⡆
⠀⠀⠘⢩⠻⢿⣷⣦⣿⣯⣟⠲⠶⣄⣂⡤⢀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠁⠀⣄⣴⠋⡠⣉⠀⡙⠁⢲⣿⠂⡿⣈⣿⣿⣿⠻⠈⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣱⣿⣙⣛⡷⣮⣭⣽⡿⢶⣿⣭⣽⡎⡩⣯⡳⣆⠀⢀⣠⡞⠀⠞⣠⣠⣼⢿⣧⡄⢀⣠⠎⠀⣠⡟⢁⣿⡟⢻⠿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠿⡹⢦⣿⡨⣿⣤⡈⢿⣴⣆⡀⠁⢹⣷⣦⣿⣿⣾⠻⣿⣍⠙⠳⠾⠿⢯⣤⣘⣉⡱⠟⢧⣤⠞⠃⠀⠊⠀⠀⠀⠘⠁⠋⠹⢙⡟⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⠉⠉⢦⡙⢯⡎⠹⢿⣧⣿⣼⡿⣿⡙⢉⣿⣿⣶⣿⣄⢾⣮⣲⣦⡀⠙⣿⣤⠶⠊⠃⠀⣤⡴⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠘⣹⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣷⣤⡋⣛⡻⠷⡿⠷⣞⠛⢛⠷⣾⣽⣫⡛⠹⡟⣽⣆⠘⣷⢀⢀⠠⣼⢟⢀⡶⢈⡄⣸⠀⡖⢠⠆⠀⠀⠀⠀⠈⢛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡿⠿⢿⣷⣶⣤⣴⣾⡿⢟⢻⣷⣾⣈⣙⠿⣬⢫⣿⡄⢛⣿⡞⠛⠃⢻⡌⣷⢹⡆⢻⠙⣿⢺⡿⠻⠀⠀⠀⠄⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡀⣀⣤⠖⠁⠛⠉⠀⢸⣿⣁⣠⣜⣛⣻⣿⣿⣿⣷⣌⢻⣏⢘⡏⠁⢀⣰⣼⢷⣿⣿⣷⣿⣼⣿⣿⣷⠃⠀⠀⢀⠀⠰⢾
⠀⣀⢤⣱⣃⡀⣀⢠⣤⣴⣶⣶⡶⣾⣿⣿⣛⣁⠀⣁⠠⣄⡴⠟⢃⣉⣩⣭⣭⣭⣭⣍⣉⣍⣩⣾⡥⣿⡷⠞⠻⣙⣦⠛⣡⣿⣿⠃⠀⠀⢸⣟⠁⠀⢀⡈⣠⣛⣿
⣆⠛⣼⣯⠿⠿⢿⡿⣿⣯⣿⡞⢷⣛⣉⣙⣛⣛⣉⣙⣛⣯⣴⡞⠿⣋⡉⢉⡉⣻⣏⣽⠿⣭⣬⣉⣿⣿⣧⡼⠶⣋⣤⡟⣿⡿⠃⠀⠀⠀⢸⡇⠀⠐⠆⢡⣬⣿⡏
⠙⠷⠿⠾⠿⠿⣿⣴⣶⡶⠾⠿⠟⡛⣏⡛⡙⢿⠛⡟⢻⣟⠰⢛⣤⢉⣧⡸⠟⣫⢾⡧⣴⣦⣶⣿⣧⣴⢼⡶⣟⣯⣵⡿⠋⠀⠀⠀⠀⠀⡸⠃⢠⠋⣀⢶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠛⠛⠻⡿⣷⣿⣦⣿⣿⣨⣷⣺⣭⣶⣿⣷⢾⣷⣷⣾⣿⣶⣷⡾⠿⠿⠿⠚⠉⠀⠀⠀⢀⣠⣖⣿⠶⢋⣹⡿⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢄⣘⡟⠳⣿⣿⣵⣫⣿⣿⠟⠛⠿⠿⠿⠿⠿⠛⠋⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣀⡞⢋⣵⠉⢃⡾⢟⣡⣶⡟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢵⣾⣋⣥⣤⡞⢉⣌⣛⠿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢫⣴⣾⢁⣴⡟⢁⣤⡆⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⡞⠛⣩⠟⠛⠁⡟⠋
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠀⠉⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣔⣩⣁⠠⠅⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣭⣯⣤⣾⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡀⠀⣠⢜⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠧⣾⣥⣤⣼⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠠⠀⠄⣀⣁⠜⣁⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠧⣶⡏⣤⣤⡟⠛⠻⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡓⣿⣒⠭⢄⣊⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢑⣶⠧⢤⣄⡽⠛⠳⣾⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠮⣥⣽⡟⠓⢦⣴⠟⠛⢷⣦⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢟⣉⣭⡗⠚⠛⣤⣬⠿⠯⡉⠙⣶⡶⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⣤⡤⢖⡋⣁⣨⡿⢯⣁⡈⢙⣦⠼⠟⠉⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡤⠀⠀⠀⠀⠀⠒⠊⢠⣤⡄⠈⠛⠛⢤⣄⣀⡼⠿⡍⠀⠁⠀⠀⠤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠉⠀⠀⠀⠞⠀⠠⣤⠔⠋⠁⠀⠀⣤⠄⠚⠙⠅⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠐⠁⠀⠠⣄⠈⠑⠀⡤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⢀⣴⠾⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢤⣀
⠀⠀⣞⠈⠁⠀⠠⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣔⠂⠤⠀⠀⠀⠋⠙⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣀⡀⣠⢄⡀⠀⢢⣿⣷⡖
⠀⠀⢫⠟⢶⣦⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠿⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠈⠛⡙⢿⡁⠀⠀⠉⠀⠀⠈⠑⠒⠚⠃
⠀⠀⠈⠀⠈⠾⠀⠿⠀⠈⠟⠉⠳⣶⣶⣶⣿⣶⣦⣤⣠⣤⣤⣴⣤⡀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡹⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠃⠀⢈⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⢠⣤⠀⡰⠀⢠⠷⣴⣧⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡠⠘⣧⠄⠀⠽⠛⠉⠁⢀⣈⡹⢫⠇⠀⠀⠀⠀⠀⡻⠿⠷⠂⠚⠋⠉⢻⠁⠀⠀⢐⠃⠁⠀⠁
⠀⠀⠀⠀⠀⢀⠀⡟⣤⠟⣣⠀⢨⠔⠂⠀⠀⣶⠀⠰⣚⠯⠅⠀⠀⠀⠀⠀⢀⡸⠁⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠺⠏⠉⠁⠉⣀⠀⢐⡶⠂⠀⠒⠋⠀⠈⢀⣀⣀⣀⣤⣤⣠⡶⠟⠁⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⣄⠀⠲⠴⠴⠿⠂⢀⣤⣦⠀⣉⠥⠀⠚⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠘⠀⢰⡀⠀⣀⣤⡀⠀⣦⣙⡄
⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢣⡀⡸⠁⠙⠲⣼⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣔⠀⣿⣿⢈⣿⣿⠄⣤⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⣿⣎⣻⣟⣦⣿⣧⣿⠿⢦⣶⣿⣿⣿⣿⣽⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⡀⣀⣠⣤⡾⣿⣻⣜⡷⢻⣃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣄⣴⢦⣤⣶⣶⣶⡶⢶⣿⣶⣿⣿⣟⣻⣽⣦⣿⢮⡻⢿⣋⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⢒⡿⢯⠽⢛⣒⣋⣉⣾⡉⠽⢷⠛⣙⠫⢿⣲⠟⠁⣟⡕⣷⣿⢻⣾⣷⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢼⣛⣹⣯⣭⠿⠦⠛⠋⣐⡉⣍⡿⢠⣥⠴⡶⣭⣿⣿⣿⣽⣿⣿⣿⣿⣾⣿⣾⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⠷⣿⡉⢓⡶⣄⠿⢲⣟⣿⣉⣼⢩⡝⢷⣾⣶⣹⠿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡿⢿⡳⣷⣼⢉⣭⣿⣶⣿⣷⣻⣿⡟⣿⣿⣽⣿⣿⣟⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⠤⠶⣟⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡫⣧⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⡆⠘⠛⠁⣀⣀⣠⣿⣴⣿⣿⣿⣿⢷⣯⣿⣩⣿⣿⡻⡿⠛⠛⠋⠉⠁⠀⠀⠈⠙⠛⠙⠋
⠀⠀⠀⠀⠀⠀⢠⣴⣿⠟⠁⢠⣥⡤⠊⣛⣽⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣃⣀⣘⣧⣤⣶⡿⠷⠿⠛⠛⠛⠛⠉⠉⠀⠀⠀⢀⣤⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⣿⡿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋






⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠠⠤⠀⠦⠤⠴⠔⠤⠀⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠄⢀⠀⠅⠠⠈⠀⠃⠘⠒⠐⠘⠛⠛
⠀⠀⠀⠀⠀⢠⠏⠸⢐⡴⡨⠂⠁
⠀⠀⠀⠀⠀⡾⠈⠂⡈⠊⠩⠐⠶⠒⡦⠐⢦⠤⠄⠠⢤⣀
⠀⠀⠀⠀⠀⣇⠀⡀⡐⠁⠈⠄⠁⢃⠐⠒⠀⠢⠠⠭⡀⢘⠙⢲⢤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⡗⠐⠤⠐⠐⠄⢀⠀⠀⠀⠘⠀⠓⠀⠀⠀⡁⠁⢐⣄⠀⠉⠀⠒⡀⠂⠐⠢⠀⠴⠊⠀⠈⠀⡂
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠠⠂⡀⠀⠀⣈⠄⠃⠀⠀⠢⠀⠀⠠⠀⠐⠀⠖⠀⠈⠋⠀⠀⣀⣤⣤⣤⡶⠻⠛⠙⠁
⠀⠀⠀⠀⡴⠒⠾⡄⠀⠀⠐⣻⡀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠔⠋⢉⠛⠛⢿⣍⢌⠆
⠀⠀⠀⢠⠀⡜⢦⣀⣀⣀⡿⠃⠉⠓⠶⢤⣄⣀⣠⠐⠊⠳⣄⠈⠀⠁⠢⡀⠳⢄⠂⣈⠀⠛⠓⠽⢲⡦⣀⡀⠠
⠀⠀⠀⢀⡃⣠⡰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣤⠦⠗⠦⣀⣀⢘⣦⣄⠁⠺⠿⣖⡤⢄⣀⠈⡙⡿⣷⡄
⠀⠀⠐⠛⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠁⡩⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠋⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠀⠀⠀⠪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑

⠀⠀⠀⢀⢐⣦
⠀⠀⠀⠀⠂⢕⠀⠁⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠑⠤⣂⣐⠀⡄⠘⠿⢶⣔⢂⢦⠲⠄⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⡀⣄⠤⠄⠄⠄⠤⠄⣄⣀⡀⡀
⠀⠀⠀⢀⠀⣀⢀⠀⠄⣀⢱⢌⡀⠐⠠⡨⣽⠌⠦⠀⢈⠈⡀⠀⠀⠀⠀⠒⠀⠀⠀⠠⠀⠀⠀⣤⠤⠀⠠⠀⠀⠁⡄⠀⠛⡈⠉⡙⠑⠈⠁⠂⢒⣤⡀
⠀⠀⠀⠁⠓⠲⠤⠭⠿⠯⡍⠿⠾⠷⢦⡈⠷⠀⠀⠀⠉⠰⢆⡀⠂⢀⡀⠀⠀⠀⠀⠀⠈⣃⡾⠁⠠⣤⣄⠰⠀⠰⠇⠀⣼⣇⠀⣃⠀⠠⠆⠀⣼⠇⡤⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⣀⣀⣀⣀⣴⠀⠀⠀⠀⢀⣀⣈⡁⢠⡀⠑⠂⡀⠀⠀⠲⢄⡝⣧⠠⣿⣿⡿⣇⡤⠿⠒⠉⠈⠁⠀⠉⠀⠈⠐⠚⠇⣠⣄⢘⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠧⢤⣤⣀⣋⣅⣼⡿⢿⡐⠶⠀⠉⣦⠈⠀⣤⠄⣼⣦⢛⣻⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠝⣹⣍⣤⣮⠏⠁⠐⠘⠐⠓⠒⠊⠻⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠜⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠛⣉⠄⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠙⢀⡴⠋
⠀⠀⠀⠀⠀⢠⣾⣿⢟⡁⠀⡰⠋
⠀⠀⠀⠀⣰⠿⣿⠟⠘⠁⢰⠁
⠀⠀⠀⠀⠏⢾⣿⣏⡀⠀⢢
⠀⠀⠀⠀⡄⣙⢿⣿⣑⣄⡐⢦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⣿⠃⠐⢾⣿⣿⣕⣳⢦⣽⡀⠗⢲⡆⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⢁⡾⠁
⠀⠀⠀⠀⠸⣦⣀⣀⠠⠙⣿⣿⣻⣶⣭⣟⠳⠶⢤⣜⣋⠷⢤⡄⠀⠀⠀⠀⠀⠀⣀⠰⠾⠟⠛⣡⣴⣶⠟⠁⠈
⠀⠀⠀⠀⠀⠈⠉⠀⠄⣦⡾⠙⠉⠛⢯⢯⣾⠿⣶⣨⣽⣛⡺⢧⣛⡶⢂⣠⣠⣼⣁⠎⠽⣦⠟⢊⠑⠂⠈
⠀⠀⠀⠀⠀⢀⣮⠷⠚⠿⣄⡠⡀⠀⠀⠀⠋⠘⠛⠱⠽⠿⠟⢓⠋⠙⠋⠛⠉⣠⡶⢶⣦⣤⣦⣵⡶⢶⣖⡲⠶⢟⡶
⠀⠀⠀⠀⠻⠛⢂⣀⡀⠀⠈⠻⢧⣄⡰⢀⠀⠀⠀⣀⠄⠉⠀⠀⠀⠀⢀⣆⠈⠀⠀⠀⢀⣉⠩⠤⠲⠖⠶⠒⠋
⠀⠀⠀⠀⠀⠐⡶⠿⠁⠀⠀⠀⠀⠈⠙⠺⠶⡶⠋⠁⠀⠀⢀⣀⠀⠀⠀⠘⠷⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠱⡤⠴⠚⠛⠓⠂⠴⠶⠶⣾⡇⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠇⡶⢽⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠄⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠄⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠐⠂⣀⣈⣀⣢⣀⡀⠀⠔⠒⠂⠀⠀⠚⠀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢠⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⠤⡖⠢⠤⠒⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠐⠦⠤⠤⠴⠖⠛⡷⡈⠉⠉⠉⣀⠤⠂⠀⠂⠤⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠈⠢⢄⡀⠀⢘⣪⡦⠔⢊⠤⠀⠈⠒⠤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⠀⠀⠀⠠⠾⡀⠀⠀⠀⠀⠋⠉⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠁⠀⠀⠀⠀⠀⠀⢳⢤⡀⡠⠔⢄⣀⡜
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢉⠐⠠⡀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠆⠈⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠰⠕⠊⠉⠀⠀⠀⠈⢢⠀⠀⠀⠀⢸⠀⠀⢀⡤⠚⠚⠀⠀⠀⠀⠀⢸⠠⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⡆⠀⠀⢠⠀⠣⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢸⠀⠀⢠⠁⠀⠀⢈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⡇⠀⠀⣹⠀⠀⠀⠳⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⢽⠀⠀⠀⠀⠐⠉⠉⠉⠉⠑⡄⠀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠣⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡸⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⡠⠀⠀⠀⠸⢀⠔⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣔⣊⡚⠒⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠤⠤⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢠⠛⠪⣶⠥⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠚⠂⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣤⣶⣶⣿⣶⣾⣷⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣦
⠀⠀⠀⢸⣿⡄⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄
⢀⣀⢀⣀⠉⠻⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⢿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠿⢿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣶⣤⣤⣦⣤⣠⣤⣤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⠙⠃
⠀⠀⠈⠘⠻⢿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⢿⣿⣟⣿⣿⣽⣿⣿⣯⣽⡷⣦⡀
⠀⠀⠀⠀⠀⠁⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡟⣙⣫⣥⣿⢿⣿⣿⣿⣿⡿⠃
⠀⢰⣀⣀⣦⣬⣦⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡋⠿⢻⣤⣀⣿⣿⠟⠛⠁⣰⣿⣿⣿⡿⠁
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⠿⠿⠿⠿⠟⠛⠛⠛⠿⢿⣛⣟⣙⣿⣷⣴⣾⡿⠾⠛⠉⠀⠀⠀⢠⣾⣿⣿⣿⣿⢷⡄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠉⠉⠉⠙⠋⠙⠋⠙⠚⠛⠚⠛⠛⠛⠛⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠟⠀⠛⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠴⠐⠂⠂⠚⠋⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣀⠀⠄⠠⠤⠦⠄⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡆⡀⠀⠂
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡤⠜⠁⠀⠀⠀⠈⢁⣀⣤⡤⡤⠤⣠⣠⡄⠘⠉⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡒
⠀⠀⠀⢀⠈⠀⠀⠀⢀⡀⠄⠐⠀⠁⠂⣁⠤⠒⢊⣛⡩⠤⠤⠴⠶⠶⠴⡎⠀⠀⠀⢈⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠈
⠀⠀⠀⠐⣄⡀⠈⠀⠀⠀⠐⡀⠔⣚⠭⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⡄
⡀⢀⡀⢀⡈⠐⠲⠒⠶⠒⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠄⠀⠀⢠
⢣⣤⣤⡀⠈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⣉⠑⢦⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢻⡄⣧⡀⢦
⠈⠟⣻⢿⣦⣄⡐⠈⠉⠐⠒⠊⠸⠖⣀⢷⡶⠄⠰⠢⠄⠤⠖⠾⠟⠙⠋⢨⠁⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⠤⠤⣠⣿⠀⠁⠈⠁
⠀⠀⠀⠈⠹⡿⣿⣦⣀⠁⠂⢤⣀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣄⡈⠑⠂⠒⠀⠄⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠤⡀⠈⣁⠀⠀⠐⠂⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠻⠿⣿⣷⣷⣷⣶⣶⣿⣿⣆⡀⠀⠸⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠤⠘⠡⢀⡰⢒⢴⠇⢀⠀⠨⡐⣸⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⣠⢞⠋⣉⣽⣿⡿⠿⠟⠟⠋⣀⠐⢀⠀⠀⡀⢀⡀⠤⠀⠐⠂⠀⣠⠐⠂⢅⡀⣁⣦⡾⠿⡃⠀⠀⢀⡜⠃
⠀⢰⣤⣄⣶⣶⣶⣾⣿⡿⠟⠁⠊⢛⢉⡅⠠⠄⠔⠒⠚⢂⣭⠀⢉⠀⡀⣤⡀⢄⡀⠀⠲⠀⠒⠩⣔⣠⠭⠶⠟⠉⠀⠰⢧⠀⠀⠞
⠀⠢⠉⠉⢉⣩⣩⣄⣀⣐⣄⣠⣄⣈⣏⡔⢒⣚⠓⠚⠓⣋⡁⣀⡁⠂⣙⣓⣄⣀⡴⠷⠶⠿⠗⠚⠁⠀⠀⠀⠀⠠⣶⢢⣄⠤⠐⠢⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠰⣧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠁⣠⢎⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠓⠊⠛⠩⠏⠉⠚⠓⢓⡒⣒⣒⡢⠤⠤⠤⠴⠚⠉⠁⣠⣤⡶⠟⠷⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠙⠈⠡⠀⠈⠀⣀⣸⣦⣶⢶⣿⣻⣿⠿⠛⣻⣿⣿⣶⠶⣾⡿⠛⢙⡅⠆⢊⣴⠏
⠀⠀⠀⡐⠂⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⡠⠀⠠⢀⣤⣼⣟⣿⣿⠿⣿⣿⣿⣿⡃⡬⢀⣙⣿⣯⣉⣀⢭⣵⢤⠽⠗⢸⡷⠃
⠀⠀⠀⠹⠿⣷⡄⣀⠈⠒⠂⠐⠒⠢⠤⢤⣤⣀⡀⣠⡴⠋⠀⠂⠀⣠⣶⣿⣿⣻⣿⣽⡚⣏⡹⣿⣇⣻⡿⠣⠀⢲⡿⣿⡶⢻⡔⣿⠸⣜⡼⠚⠁
⠀⠀⠀⠀⠀⡛⠛⢿⣿⣦⢤⣤⣄⠀⠈⠙⠚⠚⠉⠁⠉⠳⣦⣨⣞⣿⣁⢌⢿⣇⠄⣿⣟⢚⠅⡸⣿⢽⣿⣎⠒⡌⠥⢻⣟⣼⡧⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣿⣷⣦⣄⢀⣠⣌⡀⠀⠐⠙⢿⣿⡗⣍⣞⢋⢻⣿⡸⢿⣽⠪⢻⡿⣹⠿⠿⠗⢾⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⣛⣿⣿⣿⣟⡩⠍⠻⢦⡀⢀⣈⡔⣜⠜⣶⢿⣿⣿⠧⢬⣿⣯⣽⣷⠶⠶⠒⣶⠾⠿⠿⠃
⠀⠀⣤⣦⣤⣴⣷⣿⣿⣿⣿⡻⠿⠿⠿⠟⠉⠀⠀⠀⠀⠈⢹⡚⡗⣐⣷⢛⣻⣳⣿⣦⣦⣭⣿⣏⠁⠛⠋⠟⠛⠟⠁
⠀⠰⣆⣉⣉⠛⠛⠛⠉⠁⠁⠀⠀⠀⠀⣀⣀⣀⣀⣤⣠⢔⣣⠵⣿⣿⣻⣿⠿⣿⢯⣅⢵⡁⣈⣿
⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠯⠭⢭⠭⠶⠿⠓⠚⠋⠀⠀⠀⢠⡇⡓⠻⣾⣩⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣺⣅⣷⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⢶⠤⠖⠶⣪⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡛⠛⠋⣀⣴⡾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢄⣠⡖⣶⣖⣶⣶⣶⣤⢤⡶⠻⣻⡷⠛⠛⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⢷⣰⣿⡅⢾⣮⣿⣿⣾⣿⣿⣿⣅⠸⣟⡒⠀⢀⣼⣿⣿⣻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⣤⣴⡸⣿⡿⠋⠚⢏⡟⢻⣫⡵⣿⡟⣿⡇⠘⢿⡆⠀⠙⠿⡛⢿⠁⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠏⣿⣿⣛⣿⣥⣧⠷⢽⡴⣿⣄⣉⣽⣿⣟⠨⢘⣷⣆⣤⣝⣲⢤⣄⡈⠙⠒⠤⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡟⢸⡿⣿⡁⢹⢶⢢⠟⣹⣷⣿⡟⣯⣿⠍⠟⠀⠀⢹⣀⣿⣿⣿⣿⣷⡿⠛⠓⠒⠂⠤⠉⠀⡄⠀⢆
⠀⢠⡠⣄⣦⣴⣿⣯⣿⢫⣿⠈⠱⣿⡗⢦⡋⢠⣾⣿⣿⣿⣿⣿⣛⣃⠀⠐⣂⣸⣿⡿⢿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚
⣰⣎⣧⢿⣽⡟⢸⡄⠜⣨⢙⣈⣳⣾⣇⢸⣷⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣯⣁⡀⢸⣿⣧⣴⡶
⠸⣯⣿⣸⠈⡇⢸⠆⣷⣭⣿⣯⣿⣿⡀⣼⡄⢼⣿⣿⣷⠐⠂⠀⠀⠈⠈⠙⠻⠿⠿⠿⠿⠿⠿⢇⡰⠂⠁⡀
⠀⠀⠙⠛⠛⠻⠛⠛⠛⣉⠉⠁⠈⣿⣿⣾⣧⣸⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠠⠄⠀⠦⠤⠴⠔⠤⠀⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠈⠀⠀⠀⠀⠠⠈⠀⠃⠈⠂⠀⠘⠛⠙
⠀⠀⠀⠀⠀⢠⠎⠸⡔⡔⡨⠂⠁
⠀⠀⠀⠀⠀⡞⠈⡆⡀⠈⠁⠑⠶⠒⡤⠀⢠⠠⠆⠀⢤⣀
⠀⠀⠀⠀⠀⣇⠂⠀⡐⠁⠈⠄⠀⠁⠐⠒⠀⠀⠠⠬⡀⢈⠙⢢⢤⠄⣀⡀
⠀⠀⠀⠀⠀⠹⡶⠒⠤⠐⠀⠄⢠⠀⠀⠀⠘⠀⠒⠀⠀⠀⣁⠁⠀⣄⠀⠉⠀⠒⡀⠂⠀⠠⠀⠴⠊⠀⠈⠀⡂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠂⡐⠀⠀⢈⠄⠀⠘⠀⠂⠀⠀⠀⠀⠈⠀⠖⠀⠈⠋⠀⠀⣀⣠⣤⣤⡶⠻⠛⠙⠁
⠀⠀⠀⠀⡐⠒⢾⡄⠀⠀⠐⣻⡀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠔⠛⠉⠛⠛⠻⣅⢀⠂
⠀⠀⠀⢀⠀⡘⢦⣀⣀⣀⡽⠁⠉⠳⠶⢤⣄⣀⣀⠐⠊⠱⣄⠈⠀⠁⠢⡀⠳⢄⠀⣈⠄⠛⠓⠝⢲⡤⣀⠀⢠
⠀⠀⠀⢀⡂⣀⠰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢂⣤⠤⠷⠤⣄⠀⢘⣦⣄⠁⠺⢶⣒⡤⢄⣀⠈⡉⡿⣶⡄
⠀⠀⠐⠛⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠁⡨⠲⢄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠛⠻⠿⠯⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⣫⣝⣻⣿⡏⠀⠉⠓⢛⡾⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣫⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠀⠉
⠀⠀⠀⠀⠀⢀⣞⡾⣿⣧⣻⣋
⠀⠀⠀⠀⠀⠈⣏⢿⣟⢿⡿⣿⣿⣲⡶⢶⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠪⡟⡄⢈⣉⣙⣛⣿⣛⠿⠻⢟⣶⣬⣭⣉⢛⠓⢲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣇⣿⣇⣿⡭⣿⣛⣻⠗⠶⢶⠤⣍⠪⣳⡛⡄⣤⠙⡏⠋⣳⣶⣦⣤⣤⣤⣤⣀⣀⢀⣀⣠⣄⡠⣤⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣾⣾⣤⡺⠛⢶⣯⣿⣿⣟⡿⢷⣾⡿⣴⣌⢮⣋⠀⣻⣶⢳⣭⢽⣿⣉⣻⣿⣟⣻⣛⣛⠭⠱⠾⠿⠟
⠀⠀⠀⠀⠀⠉⠻⠛⠋⠀⠉⠀⠀⠀⠈⠙⠛⠩⠟⠻⣿⡷⣶⡿⠛⠛⠀⡳⣽⣾⡲⣯⣏⢫⡟⠋⠝⢿⣷⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣶⣿⣿⣿⠷⠴⠺⠿⠿⠿⠿⠯⣟⣿⣦⣦⣤⣈⣉⡛⣛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠉⢐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣤⣤⣴⣶⣿⠛⣭⡉⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⠛⠛⠉⢁⣴⠲⣶⣤⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⡇⠘⠷⣶⡄⢸⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⢸⣧⣈⡉⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⢷⢻⣿⣿⣿⣿⣦⣈⣙⣤⡿⠿⠛⠛⠛⠛⠀⠀⠀⢸⣿⣿⣿⡘⡄⠀⠀⠀⠈⠻⠷⠶⠛⢀⣀⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠈⣧⠻⠿⠿⠿⠿⠛⣋⣡⣴⣶⣿⠿⠿⠿⠀⠀⠀⢸⣿⣿⣿⣷⡹⣄⣀⡀⣀⣠⣤⡶⠿⠛⠉⣁⣀⣀⣈⣿⣿⣿
⠀⠀⠀⠀⠘⣷⣶⣶⣶⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠐⠀⠉⠉⣁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣈⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣠⣤⣶⣾⠿⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⣁⣤⣴⣶⠿⠟⠛⠉⠁⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⣁⣠⣤⣶⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠂⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⣀⣠⣤⣶⣾⡿⢛⠩⣀⠀⠀⠐⢨⠙⠿⠖⠐⠀⣀⣀⣠⣤⣴⣶⣶⠿⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⣀⣤⣶⣾⠿⠛⠛⢉⡼⠿⠴⠀⠀⠉⣀⣀⣤⣤⣴⣶⣶⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠉⠀⢴⣶⣿⠿⠟⠉⠁⠀⢀⣈⣀⣤⣤⣶⣶⣾⣿⠿⠛⠉⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣶⣶⣾⡿⠟⠛⠛⠉⠉⢀⣰⡟⣁⠊⢀⣨⣧⣤⣄⠀⠈⢂⣻⣷⡀⠀⣀⢊⣠⣤⡈⣀⢸⣿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠈⡏⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⠟⠋⠩⢉⠭⠙⠛⢿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢋⠀⠁⢀⣤⣿⣤⡀⠀⠐⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⠀⠀⢀⣀⠀⠄⠀⠀⣿⠇⠀⠀⠀⣾⡁⣿⠸⠿⠀⠀⠈⠈⣿⡄⠀⢀⠐⣀⡀⠢⠀⢸⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣿⣿⢰⠀⣿⣿⡧⢈⠀⢸⣿⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⠀⠀⣿⡇⠀⠆⢸⣿⣿⠆⡁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⠀⠀⠈⠉⠠⠂⠀⠀⣿⡄⠀⠀⠀⣾⡆⣿⠈⣿⠀⠀⢀⢀⣿⠃⠀⠈⠀⠉⠁⠔⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠀⡀⠈⠛⣿⠛⠁⠀⠠⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣷⣦⣄⣒⣈⣐⣀⣤⣾⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠷⠖⠛⠷⠲⢶⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠛⠛⠋⠉⠉⠉⠉⠛⠒⠒⠬⢽⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣦⠾⠫⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⣲⣖⣤⣤⣤⠤⢶⣖⠛⠩⠅⢠⠁⠐⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠶⠾⢛⠛⣉⠉⠵⠀⢒⡞⠉⠉⠉⠳⣄⣂⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠞⢋⡅⠀⠒⢀⠉⢠⠄⠀⠒⢀⣾⠀⠀⠀⠀⠀⠉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠔⡏⠐⢃⡀⠀⠒⠀⢩⠄⠀⠚⡠⠖⠉⢙⡶⠒⠒⠒⡟⠁⠀⡀⢬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠟⠱⠀⢡⠄⠈⡁⠀⠚⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⣤⠦⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣥⡶⠯⢀⡃⠠⠂⢠⠀⠈⠁⠀⠀⠀⠀⢢⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠀⠉⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣧⠤⠋
⡒⠒⠐⢶⠀⠉⠉⠀⠀⠉⠀⠈⠉⠁⣈⠠⣄⡀⠀⠀⠠⣄⠀⣾⠀⠀⠀⠀⠀⠙⣦
⠘⠛⠦⡤⠶⡶⠦⠤⡴⠖⢻⠿⠿⣯⠄⠊⠉⠀⠀⠀⣠⠟⢀⡼⠛⢓⡶⠂⠀⠠⠋⡆
⠀⠀⠀⠀⠀⠀⢀⢠⡴⢺⢁⡤⠊⠀⣀⡠⠤⠶⠒⠛⠉⠉⠉⠀⡤⠥⣀⡄⣀⡄⣠⠇
⠀⠀⠀⣄⡴⠖⢊⣥⠔⠋⢉⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠺⠁⠑⠃
⠀⢞⠛⠳⠒⠛⣉⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣀⡤⠶⡻⢶⢤⢄⣤⡖⢟⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠶⠷⣷⣮⣳⡗⡐⡱⠡⢪⣞⢕⢹⡳⠲⢖⢶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣍⣿⠛⠽⣻⣴⣿⢵⡫⠉⠉⠉⢳⣛⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣌⣿⡄⢸⣺⠀⠀⣷⣥⡤⠔⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣎⣙⠷⢴⡿⣏⣰⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠽⣿⣶⣶⢭⡶⢻⣋⣭⣤⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣧⣼⣥⣮⣾⢿⣟⣿⡍⠝⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠝⣿⠛⠁⠁⠃⠀⠘⠆⠱⣄⠀⠁⠊⡜⡹⢲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠔⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠊⡰⠉⡹⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⡠⠰⠊⠀⠀⠀⢀⣀⣀⣸⣿⠝⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⢊⠜⢑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⡆⡇⠃⠀⠀⠀⡰⡫⢋⢅⣵⢵⠕⡫⣻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠔⡡⢎⡝⣦
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠣⠉⠀⠀⠀⠀⢸⠋⣈⡵⠝⢳⡧⡪⣮⣏⣕⢉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⡴⢋⠔⣡⢷⡀
⠀⠀⠀⢠⠞⠁⠆⠢⠘⠀⠀⠀⠀⠀⠀⢿⡼⣿⣇⠀⢸⡪⡮⡟⠀⠙⢷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣡⠞⣡⢊⠝⡄
⠀⠀⡴⠁⢠⠺⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣕⢟⢷⠿⡪⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠞⡡⢋⠜⡼⡄
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣕⡩⡪⣞⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠊⡠⢂⠞⡰⣳
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣪⣾⣵⠟⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⢁⢞⣔⣽⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡄⠀⠀⡼⣊⣼⡇⠈⢿⣮⡪⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⡫⢪⢾⡅
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡱⡻⣦⡀⣿⣿⣿⠁⠀⣸⣯⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⡡⢊⠔⡵⡱⣻⠇
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣊⡿⢻⡿⣯⢞⢟⢟⣽⡻⣮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⢊⠔⡡⢪⢎⡔⣩
⠸⡆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣏⢔⢵⠵⠦⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡫⢖⡡⢊⠔⡡⢊⠴⡏
⠀⠱⡀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⢋⠴⣋⠔⡡⢊⠔⣩⡾
⠀⠀⠱⡀⠰⢘⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⢀⠀⠀⠀⢀⠀⡀⢀⠀⡰⢃⠄⣁⡴⢩⠞⡡⢊⡴⣡⢞⣽⢭⠉⢩⠉⠉⣠⣤⡄
⠀⠀⠀⠘⢦⠈⠸⢈⢠⠠⢀⠀⡀⢀⢀⢀⠜⡰⢃⠜⡡⢊⠤⢊⠴⢊⠴⢁⠔⡠⢂⠞⡱⢡⢮⠎⡰⢁⠞⡰⢋⢜⡵⠟⠛⠒⠒⠒⠒⠒⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢙⣦⣈⠘⠸⠸⠄⠃⠂⠂⠘⠐⠀⠃⠚⠐⠃⠐⠁⢘⣁⠚⠁⠊⠐⠡⢊⡔⡱⢃⠞⡰⢃⣎⣴⠷⠋⠉⠉⠉⠉⠉⠉⠩⠭⠭⠭⠭⠭⠉
⠀⠀⠀⠀⠀⠀⠁⠉⠉⢲⠦⣤⣤⡄⠒⣶⣶⣲⣶⡶⠾⢿⣿⣭⣤⣬⠭⢭⣉⣁⣰⣋⣞⣰⣧⠾⠶⠿⠭⠤⠤⠤⠤⠤⠬⠥⠤⠭⠭⠭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣒⣀⣀⣀⡭⠭⠍⠉⠭⠭⠍⠉⠉⠀⠂⠘⠉⠩⠿⠿⠿⣭⣭⣭⣽⠉⠉⠩⠭⠭⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡄⠒⠒⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣿⠋⠀⠀⣷⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠀⠘⠀⠀⠀⢸⡄⠀⠂⠀⠀⠀⢻⠘⠳⣤⣶⠶⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠀⠀⠀⣀⡈⢢⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣼⠇⠀⠲⠒⠠⣤⣀⢀⣀⡤⠴⠦⠴⠼⢏⡁⡀⠘⣿⣿⡄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡿⠄⢠⡤⠖⠋⠙⠉⠉⠁⠀⠀⠀⠐⠀⠀⠈⠱⢶⡙⣿⠃⠖⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⢿⡿⢾⣇⡰⠊⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠈⢻⣄⠠⡃⡀⠒⠐
⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠴⠁⠀⠀⡾⢻⡏⠻⣦⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢻⣿⣯⡐⡀⠀⠄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡀⠸⣇⣸⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠿⢿⡁⠒⢀⠅
⠀⠀⢨⠀⠀⠀⠁⠉⠀⠀⣈⡩⠁⠀⠙⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣾⠟⠂⠉
⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⠂⠀⠄⢀⡀⢹⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠠⠘⠋⣠⣷⣦⣄⡀
⠀⠀⠀⠀⠐⢀⣐⠀⠀⠀⠀⠀⠀⠀⡳⣤⣇⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢀⡆⢀⣴⡏⡁⠒⠍⣿⣷⠆
⠀⠀⠀⠀⠰⠀⣒⡎⠄⣀⡀⠀⠀⠀⢳⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣠⣾⣿⣿⣿⣕⡬⣭⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠯⢀⠒⠒⠀⣨⣄⣈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠢⣿⡿⠋⣨⡿⠿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⡇⠀⠀⠀⠀⠀⠞⢁⣾⡯⢇⡀⠀⠉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⢰⣿⡏⢄⣛⣮⢶⣿⡟⠁⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣭⣵⣿⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿
⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⣼⠁
⠀⠹⣟⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣠⡾⢻⠇
⠀⠀⢘⣦⡀⠉⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠁⠀⣀⡤⠞⠉⣰⣯⡦
⠀⠀⠘⢯⡙⠲⢤⣀⠀⠀⠈⠉⠉⠛⠒⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⠶⠚⢛⡖⢀⡤⠞⠉⠀⢀⣀⡤⠴⣒⣋⣭⠀⣠⡾⢋⡼⠁
⠀⠀⠀⢶⡿⣦⡀⠉⠉⣛⣒⡒⠶⠦⠤⣤⣤⣀⡀⠉⠓⢦⡀⠀⢠⣶⡿⠟⢋⣵⣿⣿⣾⣿⠿⠟⣿⣼⡵⠋⠀⣠⠴⠚⠉⠀⠀⠀⣀⠴⠋⠀⠁⣠⣞
⠀⠀⠀⠀⠻⣤⡉⠓⠀⠛⠬⣅⣀⡀⠀⠀⠀⠈⠉⠓⢦⡀⠙⢦⡻⣭⡀⢀⡙⣏⠋⠉⠁⠀⠀⠀⣿⡟⠀⣠⠟⠁⠀⠀⠀⠀⢈⣉⡭⠞⢀⡤⠞⣫⠟
⠀⠀⠀⠀⠀⢰⣿⢦⣄⡀⠐⠮⠭⣉⣀⣀⡀⠀⠀⠀⠀⠉⠢⡀⠹⣄⠙⠳⣝⣪⣳⣴⡄⢰⠀⢸⣿⠀⠞⠁⠀⠀⢀⣀⣉⡭⠽⠂⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣭⣁⣀⠀⠘⠓⠒⠒⠒⠲⠆⣠⡶⢦⣌⣀⠙⡆⠀⠈⠙⣿⣿⣿⣄⣇⣠⣿⣿⡄⠀⠤⠔⠋⠀⠀⠀⣀⣺⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣭⣤⣄⣀⣀⡀⠈⠛⠻⠿⠿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⠿⣧⡀⠀⢀⣠⣶⣾⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⢲⣶⣤⠶⠟⠛⠩⢛⣿⣿⢿⡟⢹⣧⠹⣆⠈⠻⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⣠⡶⢶⡶⣻⡿⠟⢡⠟⠀⠈⡟⢧⠙⢦⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠘⠛⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠁⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢿⠿⠏⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⢒⡾⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⣻⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣃⣾⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠄⠢⠀⣀⣤⣾⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⢂⡃⢌⢒⡘⣈⣠⣤⣆⣷⣽⣾⣿⡿⢿⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠐⠚⣃⠱⠜⢪⡱⠖⣾⠿⣩⢽⡻⣧⣿⣯⣿⢿⡟⢀⣭⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢩⣤⠖⢛⣤⠶⠟⣁⠰⠎⠀⣾⣿⣿⣿⣿⣿⣯⣥⡾⡂⠉⡉
⠀⠀⠀⡐⡶⡄⢀⣀⠀⠰⣷⣚⠿⣛⢶⣾⣶⣼⣟⣿⢿⣏⣡⣴⣾⣿⣿⣝⣷⠼⣿⣔⣼⣿⣿⣿⣿⡏⠿⠛⠟⠛⠋⠋
⠀⠀⠀⠛⠛⠞⠳⣤⣤⣶⣌⣉⣤⣴⣤⣬⣿⣿⣷⢻⣯⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢀⣤⣾⣷⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⡿⠟⢹⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣛⡽⠛⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡛⣉⣽⣿⣛⣟⣃⡤⠈⠉⠋⣀⡀
⠀⠀⠀⠀⣶⣏⣽⣿⡛⣋⡭⠴⢶⣿⣿⣿⣿⡿⠿⠿⠟⢻⣿⣿⡿⠿⠛⠉⠈⠁⠀⠀⠂⠀⠈⠉
⠀⠀⠀⠀⠈⠉⠉⠉⢀⣤⣴⣶⠿⠛⣉⢁⡀⢠⡂⠠⠞⠹⡿⢿⡗⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⣀⣀⣀⣀⡀⢀⣀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢷⣤⣤⣖⠊⠁⠀⠀⠈⠛⣔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠋⠀⠀⢄⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡤⠒⠊⠉⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠑⠄⠀⡀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠈⠢⣀⡠⠒⠁⠀⣡⣀⠙⢿⣿⣷⣄⠀⢀⣴⣦⡈⠳⣄⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡠⠖⠁⠀⣣⣀⠙⢿⣿⣷⣌⠻⡿⠋⠀⠈⢳⠊
⠀⠀⠀⠀⠀⠀⠀⢆⠀⡠⠊⠀⠀⡠⠊⠀⠀⡧⢄⠙⢿⣿⣷⣄⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡠⠊⠀⢀⡤⠋⠀⢀⠇⠀⠙⢿⣿⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⣀⡴⠋⠀⢀⠔⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠔⠉⠢⣀⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⠦⢤⡀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠳⣄⠀⢀⠜⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⠤⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡱⡄⠀⠀⠄⠀⠀⢀⠀⢀⡜⠁⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣦⠤⠬⠷⠶⠥⣤⣿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⣀⣀⣀⠀⠀⠈⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⠋⠉⠀⠟⡏⠉⠙⠒⢤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠀⠱⡀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⣿⠉⣟⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⣿⢠⡇⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢻⡷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠃⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠇⣿⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢻⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠲⠤⣤⣤⣠⣤⡤⠴⠚⠧⠤⠤⠔⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠖⠸⣀⠀⠰⣠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠄⠂⡀⠀⡀⣉⠠⠖⠃⠀⢈⠢⠄⠂⠢⡀⢠⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⣀⢄⠋⠀⠀⠀⠀⣀⠀⠀⡀⣀⠀⠀⠀⠀⠉⠁⢊⠀⡀⠂⠐⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠠⡉⠀⠊⠁⡀⠀⠀⢀⣴⡾⠂⡀⠉⠂⠀⠀⠀⠀⠈⠂⠄⠀⠀⠈⡄
⠀⠀⠀⠀⢀⠀⣿⠴⠻⢙⠈⢹⡆⡇⠀⠀⠀⠀⠔⠤⠉⠨⣯⣀⡀⠰⣄⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢀⢠⠠⡘⣄⠀⠀⠁⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠘⠲⠙⠀⠀⠀⠤⠋⠡⢄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⣀⣬⣶⣬⠨⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠐⠁⠛⠉⠈⡡⠁⡠⢂⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠤⠠⣀
⠀⠀⠀⠀⢠⠀⢀⠔⣥⣶⣭⡊⠑⠀⢰⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⢦⠸⣿⣿⠿⢽⢠⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠻⣅⣠⡟⠰⢃⣾⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠛⣶⢄⡄⣀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠀⠀⠈⠛⡛⠴⠟⠋⠀⣀⣼⡗⠁⡀⢰⠤⠶⢇⣄⠀⠅⠀⠀⠀⠀⠁⠉⠀⠀⠀⠋⠀⠲⠀⠀⠂⠐⠀⡈⢬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⡧⡀⠳⠈⠃⠛⠈⢨⠀⠀⢐⠠⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⡷⡀⠐⢦⡑⠀⠀⠛⠀⠀⠸⠳⠤⠠⠀⠀⠀⠀⠈⠉⠁⠈⠃⠀⠈⠑⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡭⠋⠉⠉⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠦⢤⣤⣀⠀⠀⠀⣿⢮⣅⣀⣀⣀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡫⡞⠉⠀⠀⠀⠀⢙⡇⠀⢠⡿⣦⣄⣉⣉⣉⣁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡛⠶⢤⣤⣤⡤⢶⣿⡇⠀⢸⡟⠶⣬⣭⣭⣭⡭⣾⣿⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠟⠶⣤⣤⣤⣤⣾⡟⠁⠀⠀⠛⠦⣤⣤⣤⣤⡤⠿⠋⢀⣀⣤⠴⠞⠋⡡⠴⠞⠛⠦⣉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠓⠶⠶⠶⠖⢻⣿⠇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⣛⣉⣤⣤⠶⠶⠚⠛⠋⠉⢀⡙⢿⣿⣿⣿⣷⣄⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⢿⣿⣿⣿⣷⣄⠈⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣟⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠙⢿⣿⣿⣿⣷⣬⡃⠀⠀⠀⣀⡤⠞⣋⣥⠶⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡛⠷⣄⠀⠙⢷⣄⠠⢄⡀⠀⠀⠀⠈⠛⠿⠶⠤⠌⠻⣿⣿⣿⣿⣦⢖⣛⣭⢶⣛⣭⠶⢚⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣛⢦⣌⠳⣄⠀⠉⠳⣄⠙⢶⣤⡤⠤⠤⠀⢀⣀⣤⡴⣾⣿⣿⣿⣿⡿⠿⣛⣩⡥⠶⣛⣻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢷⣝⢷⣌⠳⣦⡀⠈⠻⠦⠶⠶⢖⣛⣻⡭⢿⣞⣿⠿⣿⣿⣿⡷⠖⣛⣭⡵⠖⠛⢉⡴⢖⡛⠛⠛⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⣝⠷⣌⠻⣦⠴⠶⠚⣛⣩⡭⠶⠚⣋⣥⠴⢾⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⣾⣄⠋⠀⠀⠀⠀⢀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⣌⠳⣤⡴⠖⢛⣉⣥⠶⢚⣋⣭⠶⠚⠋⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⢿⣍⠙⠛⠒⠒⠛⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⣤⠶⢛⣫⡥⠶⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣿⣬⣉⡙⠛⠒⣚⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠶⣻⠝⠉⠉⠉⠛⢶⡄⠀⠻⣄⣉⠉⠉⠉⢉⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣁⣀⠀⠀⣀⣀⣴⡇⠀⠀⠈⠉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⡉⠉⠉⢉⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠠⢄⣀⠀⠀⢀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣓⠄⠰⡱⠙⠦⠠⢀⣩⠤⢀⠝⡦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠁⠀⠀⠉⠛⠒⠀⠒⠛⠋⠉⠁
⠀⠀⠀⣀⠤⣆⡒⠺⡺⢻⡅⡀⠲⣦⠴⠀⠀⠁⢐⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠰⢤⣀⡀⠀⢀
⠀⠠⠎⠘⠒⠛⠒⠬⠠⣈⠽⠛⠚⠁⠀⠀⠀⠀⠀⠈⢡⠄⠀⠀⠀⠀⢀⠖⠀⠀⠠⠂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠠⠔⢠⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠿⣥⠭⡅⠂⠀⢀⢄⠞⠁⠀⠀⢀⠀⡂⠤⣀⠠⡀⢀⣼⠇⠒⠒⠀⣲⣤⣤⢀⣀⣠⡷⢶⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⠲⡀⠀⢀⠄⠠⠂⠁⠀⠀⠀⠐⠃⢈⡠⠤⢍⡿⢀⠾⢇⡀⠀⠀⠈⢚⣈⣡⠁⡠⢄⡀⠹⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠒⣩⠔⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠉⠁⠀⠀⠀⠢⠀⠀⠀⠉⠀⠀⡀⠞⠩⠝⡟⡳⠁⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠰⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢆⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⠀⠸⠀⠀⠀⠀⠀⠊⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠢⢧⣀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠲⠥⠠⠄⠀⠀⠀⠐⠒⠦⠒⠂⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠕⣒⠀⠀⢰⠽⠒⠰⡦⠤⣔⢃⢷⣮⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠖⠒⠒⠒⢀⣢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢝⠚⠉⠁⠊⠀⠑⠫⣢⡰⠂
⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⣀⡠⣄⠀⠺⠄⢲⣆⣀⠨⣟⠐⠯⠕⠶⠤⠤⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢥⣀⠐⣀⠀⠀⠈⠑
⠀⠀⠀⠠⡊⠁⠀⠏⠃⠁⢠⣄⡜⢢⠀⠈⠀⠀⠀⠈⠁⠛⠬⠤⠤⣥⡤⠤⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠉⠀⠉⠐
⠀⠀⠀⢠⡁⠂⢅⠱⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⡖⠚⠒⠲⠄⡀⠄
⠀⠀⠀⠈⢏⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠯⠷⡷⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠉⠊⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠆⢁⣠⠬⡈⠦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⡀⠀⢀⠀⡀⢠⢀⢀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢴⣶⣤⢞⣶⣤⣴⣺⡷⣬⣭⡭⣶⣢⣚⣳⡥⢰⠙⡔⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠊⣥⠶⢋⠘⢿⣿⠿⠚⠁⠀⠂⠀⡜⠿⣛⣀⡎⢶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢓⣫⠖⠊⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠠⠭⠕⡋⠡⠒⣲⡙⣷⡄⣲⣦⣤⠤⠓⡄
⠀⠀⠀⠀⡰⠦⡆⢶⣺⡤⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⠤⠒⠀⠀⠀⢸⡷⠞⣠⠄⣾⣿⣿⠋⠀⠀⠠⣿
⠀⠀⠁⠨⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢠⣞⣧⣾⣥⣦⣿⣿⠫⠀⡴⣄⣽⡟
⠀⢲⠶⠗⠢⡄⠀⣀⡀⣀⢀⣀⣠⣴⠾⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣴⣿⣍⣿⣿⣶⣿⣿⡇⠖⠀⣼⣿⡏
⠀⠀⠀⠀⢀⣶⣼⣿⣷⢻⣿⠟⠋⠁⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⢿⣿⣿⡟⠻⠿⠛⠛⠛⠿⣼⣺⣇⣿⣇⡀
⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠛⠛⠋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠈⠁
⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⡿⠏⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢒⣊⣉⣍⣍⣭⣭⣙⣒⡰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡛⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢨⣀⣸⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠽⠋⠋⠀⠀⠀⠀⠀⠀⠀⢀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⡈⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠒⠐⠀⡀⢀⠀⠀⠂⢀⠔⠂⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠈⠀⠀⠠⠁⠀⢹⣿⣟⣽⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠰⠁⠀⠀⠔⠁⠄⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢼⢃⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠂⠀⠘⡀⠀⢰⣽⠘⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢐⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠠⠀⠸⠀⠀⢸⣿⢈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠄⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⡷⠊
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⡇⢪⡀
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣟⠃⡏⢩
⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⡶⠶⠲⠲⠶⠖⠖⠖⢿⠄⠀⢿⡶⡲⠆⠆⠠⠄⠦⠄⠄⠦⠦⠤⠤⢤⡴⢿⠭⠀⡇⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⠈⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⡀⣸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⢁⢸⡋⠀⣗⠗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣆⠀⡇⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⣀⠄⠀⠠⢸⡵⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⢸⠖⠀⡇⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠨⠈⡧⠀⡇⡔⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠟⠙⠛⠛⠃⠀⠀⠸⡧⠀⣿⢸⣿⡄⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢍⡀⠀⠀⡁⠠⣿⢸⣿⠅⣿⣿⣿⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⠀⣿⣃⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠀⠈⠉⠁⠀⠒⠂⠠⠤⠤⠄⣀⡀⣀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⣻⡦⢯⠿⠙⣀
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡁⠐⠒⠠⠆⠀⠤⠀⡤⡤⠄⠀⠄⠈⠅⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠔⠒⠊⠉⠀⢀⣀⡨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠒⠒⠉⠁⠀⣀⣀⠤⠔⠒⠂⠉⠁⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⣀⡠⠤⠒⠒⠊⠉⠀⠀⠀⠀⠀⢀⠤⠤⠒⠒⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒⠉⢡⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠰⠠⠀⠆⠀⠀⠀⠰⠀⠀⠀⠀⠰⠰⠰⠰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠠⠤⠤⠒⠶⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣠⠤⠤⠤⠤⠤⠤⣄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠀⠀⠀⠀⠒⠒⠒⠛⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠚⠒⠒⠒⠀⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇
⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠀⠀⡔⠐⠒⠀⠒⠒⠒⠒⡄⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⡇⠀⠀⠀⠀⠀⠀⠀⡱⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠰⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⣛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣻⣧⣼⠿⠿⠿⠾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣨⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣸⡿⢉⡛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡈⣤⠻⣁⠈⠻⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣮⡵⣿⠃⣽⢾⠛⠋⢻⣿⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣤⣿⣾⠿⣹⣷⢖⠒⢿⣿⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢿⣿⣏⣿⣿⣾⠏⣹⣾⡶⠴⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣶⣒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⢻⣿⡦⣿⣷⣧⣤⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣝⠲⡤⢀⣠⣤⢀⡀⠀⠀⠀⣼⣏⣴⣿⠻⢹⣿⣿⣾⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣦⣑⢦⡱⠾⣿⣷⣶⠾⢷⢠⣾⣇⣔⣴⠟⡝⡉⠉⢻⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣶⣍⡒⣟⠿⠾⠿⠍⢌⠁⢳⣿⣭⣹⣽⣷⣾⠏⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⢠⡼⡿⠿⣿⣿⣿⣿⣿⣶⢺⣿⣿⣿⣿⣿⡿⢿⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠠⣛⣛⣛⣛⣋⣹⢯⣾⡟⣫⣭⣭⣤⣦⣤⣴⣿⣿⣿⣿⣿⠋⠀⣸⠆⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠁⠠⠂⠅⣠⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⡿⠟⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾⡔⣴⣳⠏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠋⠘⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⢀⣀⠀⠈⢻⣿⣾⡿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⠟⠳⠶⠶⠛⢉⣷⣾⡿⠟⠉⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⣠⠞⠁⠀⠀⢀⣠⣶⣿⠟⠉⠀⡀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢠⡾⠋⠀⠀⣠⣶⣿⠟⠋⠀⣠⡴⠟⠙⠶⣤⣤⠶⣦⠀⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠴⠏⠀⣠⣴⣿⠿⠋⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢰⣶⣾⡿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⣾⡿⠟⠁⢀⣀⠀⠈⢿⣦⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢋⣠⣾⡿⠟⠉⢀⣠⡶⠋⠁⠀⠀⣾⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣿⠟⠉⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⢻⣷⣤⣴⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⢀⣴⣾⡿⠋⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⣿⣧⠀⠀⠀⠀⣠⡴⠟⠁⢀⣤⣾⡿⠛⠁
⠀⠀⠀⢀⣾⡿⠋⣿⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣤⣿⠇⠀⠀⠰⠞⠉⢀⣠⣾⡿⠟⠉
⠀⠀⠀⢸⣿⡁⠀⠙⣿⣦⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢿⡆⠀⠀⢀⣠⣶⣿⠟⠉
⠀⠀⠀⠈⢿⣷⣦⡀⠈⢿⣷⡄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠻⣿⣆⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣜⣿⣷⡀⠈⢻⣤⣤⣤⣤⣀⢀⣠⡶⠋⠁⣀⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣄⠀⠁⠀⠀⠀⠙⠛⠁⢀⣴⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⢀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⣻⣿⢿⡿⠷⠖⠒⠐⠶⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣎⠻⡀⠀⢀⣴⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠻⣿⣿⡄⣷⠀⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣍⣭⣿⣿⣿⠿⠿⠆⡉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢡⣾⣿⣿⣿⢿⠋⢿⣧⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⡿⠃⠞⣀⢈⡉⠃⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢀⣤⣿⣾⣧⣄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⡇⠀⣾⣿⣻⢸⡟⠛⠃⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠙⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠿⠄⠀⢀⢸⡟⣿⣿⣆⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠐⣷⣶⣶⣦⡤⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣇⣧⣿⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⠉⠛⠿⣿⣷⣴⣭⣿⣿⣿⣿⣷⣆⣠⠤⢲⣿⡏⢻⡿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡽⢛⣫⢤⣤⣼⣿⣷⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆
⠀⠀⠀⠀⢈⣿⣷⣶⣶⡦⣤⣤⣉⡙⠃⠀⠀⣀⠤⠊⣹⣿⣦⠀⣸⣦⣤⡄⠀⢀⣀⣤⠖⠋
⠀⠀⠀⢠⣤⣀⣉⢉⠉⠛⠛⠻⠿⢿⣿⣟⣉⡤⠔⣲⣿⣿⣿⣿⣶⣺⣾⡆⣲⠿⠉
⠀⠀⠀⠘⠿⠿⢯⣿⣿⣶⣶⣤⣤⣀⡤⠟⠓⢊⡉⠭⠃⠀⠈⡉⠉⠉⢹⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠒⠉⠁⠀⠀⠀⠀⠀⣓⡿⠀⣚⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣯⡀⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⣀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⡴⠦⠌⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⠐⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⢻⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢡⣤⣴⡞⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⢒⡀⠀⠁⠉⠀⠀⠈⠁⠀⠁⠀⠀⠐⡤⠀⢸⣿⣿⣫⡭⣿⣿⣷⣶⣿⣿⣷⣾⣿⣾⣿⣿⣍⢻⣿
⠀⠀⠀⠈⣧⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣿⢸⣷⢸⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⡤⠄⠹⣄⠀⢠⡄⠀⠀⠢⡖⠀⠀⢸⣿⣿⢸⣿⣾⣿⣛⣿⣜⢿⣿⣿⣿⣿⣯⡟⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠀⠀⢸⡇⠀⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣷⢰⡶⠀⠒⠀⢀⣶⡤⠤⠤⠀⣿
⠀⠀⠀⠀⢸⣇⣀⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠛⣿⣿⣿⠯⠭⠉⣿
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠛⠉⠛⠤⠤⠠⣿
⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡿⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⢸⡟⢉⣉⡉⣉⠉⡉⠉⠉⢉⣩⠿⣷
⠀⠀⠀⠀⢸⡇⢠⣿⡦⠀⠀⡁⡀⠀⡀⡀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠐⠒⠀⠒⠒⢂⡤⠖⣉⣤⣾⣿
⠀⠀⠀⠀⢸⡇⢀⣀⣀⠀⣀⣀⣀⡀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⡴⠚⣡⣴⣾⠛⠛⣿⣿
⠀⠀⠀⠀⢸⣇⠐⠀⠂⠐⠀⠀⠂⠂⠘⠟⠀⣿⠀⠀⠀⠀⠀⠀⢸⣧⣴⣋⣡⣶⣿⣿⣿⣿⣤⣤⣿⣿
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠂⢈⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣂⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣠⣼⣿⣿⡯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⢦⠂⠁⠁⣠⡄⣖⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡂⣅⠤⡒⣩⣬⠦⢶⣾⡟⣷⣿⣿⣿⡟⠫⢧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢙⡠⢄⢓⣩⠦⢛⡩⠜⢩⣾⣿⣯⣿⣿⡿⣋⣟⠡⠞⠟⠁
⢀⣀⡀⠀⠀⠀⣠⣤⢤⣤⢤⣤⣄⣠⡶⣶⣿⡴⠞⣋⣴⣞⡿⢭⣔⢶⣅⣠⣿⣿⣿⣿⡟⣿⣿⣿⠷⠶⠔
⠷⠯⡵⣬⣁⣀⣭⠛⠋⣀⣁⣈⣻⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠉⠉⢉⣿⣿⣿⡏⢉⣩⣿⣽⣷⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⠿⠃
⠀⠀⠀⠀⣠⣴⣿⢛⡿⠛⠀⢩⣾⣿⣿⣿⣿⣿⣶⣿⠟⢲⣽⡿⣿⡟⢀⡀⠋⠟⢁⡀
⠀⣴⣞⣻⢿⠟⣛⣩⠤⢴⣾⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠛⠉⠉⠁⠁⠀⠀⠈⠉⠁
⠀⠈⠉⠉⠉⢡⣤⣴⡾⠟⢛⡉⣁⠀⡄⢀⠞⠻⡿⢿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠛⠛⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⢠⡞⠛⠉⠉⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣷⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⣿⠀⠀⢐⣁⣸⠆⠀⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠀⢸⠄⢼⠤⠤⠭⠭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⠀⠑⠚⠒⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⠆⠰⠀⠆⠰⠀⠀⠢⠘⠄⠐⠐⠂⠀⠐⠆⠶⠐⠀⠆⠀⠰⠀⠶⠐⠔⠒⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⣀⣤⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⢀⣀⠀⠀⠉⠉⠀⣀⣀⣀⠀⠈⠙⠛⠒⠲⠶⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⣠⡾⠛⠉⠉⠛⢶⣶⠾⣭⣉⡉⠻⢦⣴⣤⣤⣤⣤⣀⣀⡀⠈⠉⠙⠓⢶⣤⡴⠶⠶⠶⣾⡛⠉⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⢀⠀⣿⠀⠠⢶⣶⣄⠀⠙⢦⣄⠈⠙⠛⠛⠛⠛⠛⠿⠿⢯⣽⣿⣿⡷⢤⣶⠟⠁⢀⣠⣄⡀⠈⠛⠦⣤⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣠⢔⣴⠞⢻⡿⠆⠀⠸⡇⠸⠷⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠛⠉⠀⠉⠂⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢀⡴⠋⠀⣠⣾⣿⢸⣇⢀⣿⠀⠀⠀⢀⣉⣷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢶⡶⠶⣶⠾⢻⠇
⠀⠀⠀⢀⡾⠁⢀⣾⣿⣱⠞⢛⡿⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠺⣶⡶⢦⣤⣀⣀⣀⣤⣶⣿⡏⠁⠀⣸⠃⣠⠏⣠⠏
⠀⠀⠀⣼⠁⠀⣾⣿⣿⢻⣤⡟⠁⠀⠀⠀⢀⡤⠴⠦⣤⣤⣀⡀⠀⠀⠀⢀⣠⠴⢻⣿⣇⠀⣼⣿⡇⠀⣠⣿⣿⠉⠀⣼⣿⠇⠀⣰⢏⣴⡧⠞⢻⡄
⠀⠀⠀⡇⠀⢸⣿⢟⡵⠛⡿⠀⠀⣴⠃⣰⠋⠱⣄⡸⠁⣸⢋⣩⢟⡟⢋⡟⢳⣀⠞⡤⣝⠋⠉⠙⠓⠾⣿⣿⣿⣤⣾⣿⣿⣤⣾⣿⣿⣿⠀⠀⠈⣧
⠀⠀⠀⣷⠀⠈⣿⡸⣇⢸⡇⠀⢸⡇⠀⣿⢠⠞⢧⣠⢲⡈⠉⣀⠘⠖⢻⠲⣌⣁⣴⣃⣈⢣⠀⣠⠏⢷⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿
⠀⠀⠀⠸⡆⠀⠹⣷⣝⢿⡇⠀⠘⣧⣠⡿⠾⠒⠺⠧⣌⣧⡼⠈⣧⢀⣾⡴⠞⠉⠉⠉⠉⠙⠻⢧⣄⣸⣀⣤⠶⠋⢸⣀⡼⠃⢸⠋⡿⠋⣆⠀⣸⠇
⠀⠀⠀⠀⠹⣆⠀⠙⢿⣯⢿⡄⠀⠙⠉⠀⠀⠀⠀⠀⠈⠙⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠾⠷⠶⠶⠾⠶⠛⠛⠉⣹⠏
⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⢧⣹⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠉⠓⢭⣛⠶⣤⣤⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⠀⣀⣀⣀⣀⣀⣀⡴⢶⡶⣶⣶⣖⣺⣵⠶⠂⠈⠉⣩⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠉⠑⠲⠶⢿⣭⣓⣲⣶⣶⣶⣶⣖⣒⣯⣾⣿⣿⣷⣶⣾⣿⣿⠿⠟⠛⠉⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣄⣀⡀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⢀⣀⣠⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠉⠉


⣿⣿⡿⠿⣿⠿⢿⢿⢿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣶⣶⣷⣶⣷⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣶⣶⣶⣶⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⢸⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿
⠀⠀⠀⢰⣶⣦⣬⣍⣉⣛⠛⠛⠃⣿⣿⡟⠛⠛⣛⣉⣉⣥⣤⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⠉⠙⠛⠶⠶⠦⣤⣤⣼⠀⠀⢸⣤⣤⡤⠶⠶⠞⠛⠋⠉⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣛⣱⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⢸⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⣀⣀⣼⣷⣤⣤⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣾⢿⣿⣿⡷⢾⣿⣿⣿⣶⣿⣏⡿⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿⣿⣾⣉⣻⣿⢿⠛⣛⣿⣏⠛⢦⣭⠿⣯⡉⠻⢶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣟⠫⡿⢿⣍⣉⣭⣻⣶⣌⡻⢮⣭⡻⣟⣭⣽⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣱⢿⣫⣞⣿⣴⣶⣦⣬⣉⡁⠈⢩⣙⠻⣷⣍⠻⣮⡓⣤⣰⠀⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣵⣿⣋⣼⣿⣿⠞⠛⢿⣿⣿⣿⣷⣝⢿⡏⣿⣧⠈⠿⣞⢻⣆⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⣯⣿⣿⡟⠀⠤⠒⠻⡿⢿⣽⣿⡷⣿⣿⡿⣿⣿⠃⠀⠹⣮⡿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⠟⠻⠿⠯⣿⢿⣿⡁⢀⠀⠙⠿⣮⡛⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣦⣤⣤⣶⣧⣤⣀⠀⠀⠀⠀⠀⠉⢅⣁⠀⠀⠚⠿⣦⡈⣻⢿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣿⣿⣿⢛⣻⣿⣿⣻⠿⠿⠿⠿⠿⠛⠛⡛⠒⠂⠀⠀⠙⢃⣠⣤⣈⣛⣻⣿⣿⣿⠿⣿⠛⢶⣶⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣏⡻⣷⣤⣀⣀⣀⣤⣤⣶⣿⣿⣇⡀⡀⠀⠀⠈⠀⠛⠋⢩⣽⣯⣴⣶⡈⣧⠀⣿⠺⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣌⣣⣉⢹⡯⢭⡟⠛⠿⣿⣿⣿⣿⣿⣷⣷⣤⡁⢀⠄⠀⠀⠉⠃⠉⢉⡵⡏⣬⣿⣷⣿⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣃⣅⡀⠀⠛⢿⣽⢿⣿⣾⣿⣿⣿⣷⣶⣾⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⣿⣹⣿⣿⣿⣿⡇⣸⣿⣷⣿⣿⢷⠀⠀⠀⠉⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠁⠿⢾⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣞⡇⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠚⠉⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠨⢿⣩⣿⣿⡿⣿⣿⣿⣿⣿⣩⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⢷⣌⠋⣩⢿⣀⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠙⢧⡹⣤⣭⣭⣽⣍⣉⣧⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⣀⣠⠤⠒⣦⣀⣀⣀⡤⠖⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠈⠻⣯⠥⠀⠀⠀⢿⠉⣽⠉⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⢳⡀⠀⠀⢸⣠⠇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⢀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢴⣶⡷⠞⠛⠛⠉⠉⠉⠉⢉⣩⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣛⣿⣯⡤⣤⡤⠤⢴⡶⠶⠛⠉⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⣭⡽⠋⡽⠀⢀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡟⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡸⠓⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠰⠃⢀⡄⡦⡀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠰⡀⠀⠓⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡄⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⡉⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠱⠼⠘⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣋⣥⠴⠶⠶⠦⣬⡛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣿⣿⣷⣞⣉⣀⣀⣀⣀⣀⣀⣙⣶⣾⣿⣇⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡴⠋⠳⡄⠀⠀⠀⢸⠀⡇⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣧⣼⣤⣤⣤⣤⣇⣠⣀⣧⣤⣤⣤⣼⣤⣧⣤⣤⣴⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠁⠀⢹⣻⣟⡏⠁⠈⠹⣏⣉⣉⡿⠁⠀⠙⣟⣟⣻⠉⠀⢹⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⡟⢻⡇⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠛⣿⠀⠀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠸⡇⢸⡇⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⢿⠀⣿⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠘⢦⣤⣤⣽⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣤⣤⠞⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠶⠾⠛⠋⠉⠉⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠛⠛⠉⠉⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣀⡀⢠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⡀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠉⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⡇⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⣤⢤⡀⣤⠤⢠⡤⣄⢠⡄⣤⡤⠀⢀⡤⡄⢠⣄⢀⡤⣤⢠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡄⣿⢺⡁⣿⣃⢸⣧⡿⢸⡇⢸⡇⠀⠸⣄⣄⡿⢿⡬⡟⢿⢸⣧⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣦⣀⣄⣠⣀⣄⣠⣀⡠⢦⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣾⠟⣿⣿⣿⣟⣩⣉⣩⣙⠛⠻⠞⠻⣏⣹⣴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣼⣿⣿⣧⣽⣿⣹⣟⣻⡿⣽⣷⢤⣴⡄⠉⠻⣿⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢷⣴⣟⢋⣿⡆⢀⡙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣡⣿⣧⠈⣿⡏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣴⡿⣿⡇⢈⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⢠⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⡿⠇⢀⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣉⣾⣿⡟⠁⢀⠈⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣗⣸⡿⠟⣉⡿⠗⠁⣀⡈⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⣻⣿⡏⢁⣀⣾⠿⠂⢀⠀⠉⢀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣫⡟⠋⠁⠀⢉⡻⠏⠁⢀⡀⢈⠁⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡞⢫⡿⠛⠁⠛⠁⢶⡾⠛⠛⣀⠀⠈⠀⠉⢸⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣯⣿⠗⠋⠸⠟⠂⢤⣶⣮⡅⠀⠀⠙⠀⠀⢸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣿⡿⠻⣯⡼⠛⠶⠆⠠⣤⣤⡾⠉⠀⠀⠂⣠⡾⠛⢣⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢻⠟⣧⣿⣏⠷⣾⢋⣠⡀⠰⢂⠀⣩⠟⠛⠀⠶⢀⣶⡟⠀⠀⢹⣿⡉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠙⣿⣿⣿⡗⣿⡟⠃⡘⢉⠀⠘⠛⣿⠃⠀⢀⠀⢠⣾⠏⠁⠀⠀⢸⢿⡃⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣾⢋⡜⣰⣿⣿⣟⣱⡟⢀⣤⠀⢈⣠⣿⣼⠛⠁⠀⠈⠁⣼⣏⠀⠀⠀⠀⣹⡾⣡⡆⠀⡿
⠀⠀⠀⠀⢀⣿⢣⣿⣼⣿⣿⠷⣿⡞⠁⠹⠃⡀⠸⠛⣻⣿⠀⠀⠤⠀⢺⣯⠀⠀⠀⠀⢀⣽⠇⣿⠁⣤⣘⡀
⠀⠀⠀⠀⢸⡿⣤⣸⣿⣿⡿⣤⣿⠁⢀⣄⢀⣀⣆⢁⡿⠁⠀⠀⠀⡆⢸⣇⡠⠀⠀⠀⣸⠇⢸⣇⣰⠃⠘⠇
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡶⢿⡟⠀⠉⠃⡀⠙⠋⢻⣿⠀⠀⠸⠃⠀⢸⣯⠄⠀⠀⠸⢋⣠⡿⣇⠃
⠀⡠⠚⣿⣿⣼⣿⣿⢻⡟⣷⣼⠃⠀⢠⣆⠀⣰⣀⣾⡟⠀⠀⢠⠀⠀⢸⣿⣆⣄⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣀
⣸⣷⡟⢡⡟⢹⢿⣿⢻⣧⣹⢙⣷⠀⠙⡏⢉⠙⡉⢻⣇⠀⠀⠈⠁⠀⢸⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⡆⠐⣨⣭⡆
⠈⠀⣶⢿⣁⣿⣻⣿⣹⣇⣻⠛⢿⡄⠀⢰⡈⠀⣿⣼⣿⠀⠀⠀⢤⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢈⠁⣼⢻⣿⣟
⠀⠀⠋⠠⡟⢩⢿⣿⣿⣿⠱⡗⢸⣷⡄⠙⡿⠈⠛⢉⠻⣆⣀⠀⠀⠁⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠄⣀⣠⡤⣜⣿⣷⣩⣿⣿⠿⠻⠄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⢾⣦⠙⣷⡀⠈⢢⡘⠀⢢⣹⣿⣇⡀⢀⢦⡀⠱⡀⠀⠀⠀⣠⡴⣟⡛⣻⣟⠻⣿⣍⣳⣶⠛⢛⣭⡴⠶⢻⣍⢿⣿⡟⠁⠈⠁
⠀⠀⠀⠀⠀⠀⣴⣿⠇⢠⠌⠀⠙⣤⠘⠻⣦⡀⣹⣶⡞⠛⠋⢉⣻⣷⣦⣤⡤⠟⢒⣦⡞⣣⣾⣏⣐⣰⡟⠛⠛⢉⡉⣻⠿⡉⣭⡖⢿⡏⣿⢾⡃
⠀⠀⠀⠀⠀⣸⡿⠋⢠⡙⠀⠀⠀⠜⣦⢀⠈⠻⣧⣄⣀⣺⡿⠛⣉⣩⢍⣀⡀⣘⣛⣿⣼⡟⣽⠿⣿⣿⣇⣄⢰⣿⣿⠋⢴⣵⢟⣥⠾⢷⡉⠈⠁
⠀⠀⠀⠀⣰⣿⡟⠀⡸⠀⠀⠀⠀⠄⣹⣯⡀⠀⠀⠈⣹⡿⠁⣤⠟⣿⢻⡿⡽⢿⢿⣽⣿⣷⣆⣼⣯⣿⣿⣿⠟⠛⣴⣾⣛⡴⠋⠀⠀⠘⠁
⠀⠀⠀⢀⣿⣿⠀⣠⠃⠀⠀⠀⠀⠀⣸⠏⢻⣾⣤⣰⣯⠀⣾⡿⡜⣧⡦⠿⠞⣛⣿⣭⣭⣄⣛⡉⢉⡍⣹⣤⣶⣯⣿⢿⠏
⠀⠀⠀⢸⣿⢮⠀⢉⠀⠀⠀⠀⠀⢨⣿⡀⠀⠀⠘⣿⣧⢼⣿⡿⢿⣭⣽⣶⣿⣿⣵⠛⠋⢻⣟⠛⠻⢿⡿⠎⡉⠉⠉
⠀⠀⠀⣿⣻⣇⢀⡆⠀⠀⠀⠀⠁⣾⣯⢛⣷⣤⣠⢿⣧⠼⣇⠱⠿⡿⢿⡽⢯⣶⡤⣤⢤⡜⣿⡇⢀⠀⠈⠠⠙⢷⣾⣖⣤⣀⣀⠐⠂⢶⠀⠀⠀⠀⠀⡀⢀⢀
⠀⠀⠀⣿⡵⣇⠈⣗⠀⠀⠀⠀⣸⢯⣤⢛⣴⡉⡍⢻⣿⣶⠿⠷⣶⣦⡶⣿⣾⡷⠾⣷⣶⣬⣍⢟⠣⣶⣠⣤⣠⣤⣬⣿⣿⣿⣏⡿⣿⣾⣷⣶⣤⣤⣴⣼⣤⢣⣴
⠀⠀⠀⣿⣟⡇⠀⠷⠀⠀⠖⢙⡿⣷⣝⣳⣬⣩⢛⠟⠛⢿⣶⡶⠶⠟⢻⣎⠻⣤⣤⠀⣴⠿⢋⣿⠷⣮⣭⣬⣤⣽⣽⣧⣧⣼⣭⣛⣛⠼⠿⡟⣿⣛⣻⣿⣿⡜⢡
⠀⠀⠀⣿⣯⡄⠀⢹⡅⠀⠀⠸⡇⠈⠻⣷⣯⣽⣹⣧⡷⣾⠿⣿⣶⢷⠾⣟⢳⣏⣛⣶⣇⠰⣦⠟⣀⡿⢉⡽⢨⣏⣉⣉⣌⣫⣜⣛⡙⢿⠶⣿⣿⠿⠛⠛⠛⠻⠋
⠀⠀⠀⠸⣿⣺⡷⠀⢗⠂⠀⠐⢷⠀⠀⠈⠉⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣷⣼⣯⣷⣾⣿⣿⣿⢏⡉⠉⠉⠁
⠀⠀⠀⠀⠹⣿⡷⡄⢈⣥⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠛⠛⠛⠛⠛⠛⠉⢻⣿⣿⣽⣷⣿⣿⠛⠻⣆⣒⠢⣤⡀
⠀⠀⠀⠀⠀⠹⣿⡵⣀⠘⢤⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢿⣿⣤⡈⢻⣶⣼⣽⣿⠾⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣯⣴⣿⣟⢋⡀⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡈⢿⣥⠻⣦⠀⠀⠹⠂⣀⣠⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⢤⠿⠖⡈⠃⣀⡀⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢾⣶⡀⠻⣧⣌⠻⣷⣄⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⠀⠈⠳⣼⠃⠙⠲⢥⠈⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠁⠀⠀⠈⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡴⠒⠋⠙⠛⠒⠲⢤⣠⠇
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣔⡴⠶⣶⠴⢦⣠⣴⣲⠶⠤⡤⣿⣦⡤⠤⠤⢤⣤⣤⣴⣧⣤⣤⡴⣆⣀⣀⢶⣶⡤⠤⢤⣤⣤⡤⠤⣄
⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⣠⠞⠛⠁⠠⠾⠋⠉⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠙⠉⠁⢠⡾⠋⠡⡄⠀⠉⠁⠐⠢⡀⡆⢸⡆
⠀⠀⠀⠀⠀⢸⠑⢊⠔⠋⠁⠀⣇⠀⣀⣧⠀⠀⠀⠠⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⠀⢸⡇⠀⠀⠙⢦⡀⣈⡦⠀⣧⡇⢸⡇
⠀⠀⠀⠀⠀⢸⣀⠏⠀⠀⠀⠀⢧⠤⠤⣤⠀⠀⠁⠀⠓⢄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⢤⡇⠀⠀⠀⠀⠙⢦⡀⠀⡿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⢀⠠⠀⠀⠀⣿⠀⠀⠀⠑⢀⠈⠐⠉⠀⠀⠂⠂⠀⠀⠀⠀⡃⠀⠀⡼⠇⠀⠀⠀⠀⢀⢠⣙⠐⡇⡇⠀⡇
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡃⠀⠀⠑⠔⠉⠀⠀⠀⠀⠀⠐⣠⢦⠀⠀⡇⡇⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠠⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠰⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢀⠀⠈⠁⠀⢿⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢀⢀⡀⡀⠀⠸⠀⠀⠀⠀⡀⠀⠀⠀⠄⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠘⠀⢫⡀⠀⢀⠀⠀⠅⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡄⠀⢀⠀⡈⠃⠀⠀⠀⢰⠀⠈⠁⠂⠀⠤⠤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠚⡳⠠⠀⠀⠤⣤⠆⠀⡆⢀⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢡⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡆⠀⠀⡆⡀⠈⠑⠪⡥⢤⡌⠀⠀⠃⢸⠃
⠀⠀⠀⠀⠀⢠⠋⢢⠀⠀⠀⣡⡠⠀⠀⢸⠀⠀⠐⠀⠀⠀⠉⡀⠀⠀⠀⠈⠉⠀⠀⠀⡁⠁⠀⠀⠀⠈⢆⠀⠀⠀⠉⠀⠀⠀⠀⠼⡄
⠀⠀⠀⠀⠀⢸⡀⢀⠑⣄⠉⠀⢸⠀⠀⢸⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⢀⠀⠂⡘⡄⡀⠑⡇⠀⠀⡆⠀⡘⠀⠀⠀⠀⠂⠈⢶⡄⢸⡇
⠀⠀⠀⠀⠀⠸⣅⣨⣤⣈⣷⠤⢬⣀⡀⣸⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠁⠁⠀⠀⡇⠀⠀⡗⠈⠀⠀⢀⠀⠁⡀⠀⢟⣧⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠧⠤⠀⠷⠦⠠⠴⣁⣀⣐⣁⣠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⢒⣉⠉⣶⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠔⠒⣂⡉⠤⠄⠒⠂⠉⠀⠈⢄⡚⢃⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠐⢂⣉⣡⠤⠒⠂⠉⠉⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢱⡀
⠀⠀⠀⠀⡀⠤⠐⠒⣈⡁⠤⠐⠒⠈⠁⢀⠔⠁⠀⣠⣿⣶⣦⡀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⡈⡇
⠀⠀⠀⠀⢡⠀⢣⠀⡃⠀⠀⠀⠀⠀⢀⠂⠀⠀⢸⣏⠸⣷⠈⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢣⢹
⠀⠀⠀⠀⠘⡄⡤⠒⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠷⣿⣶⣤⣄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡈⣆⡀
⠀⠀⠀⠀⠀⢡⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿⠈⢻⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⡔⢩⠁⢠⡄
⠀⠀⠀⠀⠀⠈⡄⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢰⣦⣤⣿⣷⡿⠃⠀⢠⠃⠀⠀⠀⠀⢀⣀⠇⠀⠇⢀⡇
⠀⠀⠀⠀⠀⠀⢣⠰⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠉⠉⠙⠛⠀⣀⣔⡁⠤⠄⠒⣊⡉⠥⠄⠒⠊⢹⠉⡇
⠀⠀⠀⠀⠀⠀⠸⡆⢇⠤⢀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠲⠶⠒⢒⣉⣥⠄⠒⢒⠏⠁⠀⠀⠀⠀⢠⠊⡤⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠲⡀⢡⠠⠤⠐⠂⣈⢩⡤⠀⠒⠚⠛⣿⠟⠁⠀⡠⠊⠀⠀⠀⣀⡀⠠⠼⠀⠘⠂⣸
⠀⠀⠀⠀⠀⠀⠀⣿⣄⣈⠡⡄⠒⠂⠉⠁⠀⠀⠈⠐⣀⣤⡤⠤⠤⠖⠛⢒⣈⣉⠡⠤⠀⠒⠒⠂⠉⠉⡇⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢘⡄⠸⠤⠤⠐⠒⢀⣈⢉⡤⠤⠀⠒⣶⠞⠋⠉⢀⠔⠁⠀⠀⠀⠀⠀⢀⠖⣀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⡏⠦⠤⠄⠶⠦⠭⠭⠭⠤⠤⠤⠬⠴⠦⠤⠤⠤⠴⠮⠥⠤⠤⠤⠤⠤⠤⠤⠼⠀⠵⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠃⠀⠒⠒⠒⠂⢬⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠔⣠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⡠⠒⠒⠂⠉⠁⠀⠀⣠⣾⣿⡿⠋⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠐⠤⣀⣴⣁⣀⣀⣀⣀⠀⣠⣾⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠒⣩⣾⣿⡿⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠉⠀⠀⠈⠺⣿⡿⠋⡠⠎
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠊
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠑⢄⠀⠀⡠⠊
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠑⢎
⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠐⠋





⣏⠉⣹⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣛⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠈⠁⠈⠙⠳⠾⠛⢓⡶⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣄⣀⣀⣀⣞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠲⠦⠤⠶⢦⠀⠀⠀⠀⠀⢀⣠⠼⠿⠿⠿⠿⠿⡿⠿⢤⡀⠀⠀⠀⠀⠐⣏⠉⠓⠚⠉⠙⢲⠆⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⣳⣤⣦⣤⣴⠃⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⢈⣦⣤⣤⣴⣴⡏⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠻⠛⠿⠛⠦⣀⡴⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢀⠜⠛⠻⠛⠛⠛⠻⣄
⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡴⠒⠛⠓⠲⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⡴⠃⠀⠀⠀⢀⡤⠶⠄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡴⠦⠄⠀⠀⠀⠀⠹⣄
⠀⠀⢰⠇⠀⠀⠀⠀⠸⣄⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⣸
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⠞⠁⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠓⠞⠁⠀⠀⠀⠀⣰⠃
⠀⠀⠚⡼⢦⣄⡀⠀⡀⠀⠀⠀⠀⠀⣀⣨⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣁⠀⠀⠀⠀⠀⠀⠀⣀⡤⢚⢁⢀
⠀⠀⠀⠀⠁⣠⠟⢉⡽⢋⡽⢛⡽⢛⡥⠋⡠⠋⣹⠗⡶⢲⡶⠒⡶⠒⢲⠖⢲⠖⢲⠿⢲⠟⡵⠋⡼⢫⠟⠲⢒⠖⡲⠋⡽⠣⠛⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠀⠈⠀⠈⠀⠀⠁⠞⠴⠋⠀⠚⠀⠐⠃⠐⠋⠐⠋⠐⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠚⠀⠀⠀⢉⣁⠄⠀⠀⠀⠀⣀⣦⣶⡶⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠲⣶⠖⡠⠶⠛⠀⠀⠀⠀⠐⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⠠
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⠀⡀⠀⠈⠉⠄⠀⠀⠀⠈⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⢘⣿⡗⠤⣤⡠⠀⠀⠀⠀⠀⢉⣡⠼⠗⠂⠨⣴⡄⠀⡀⡀⢠⠀⠀⠀⢠⣆⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⡏⠁⠀⠀⠉⠒⠢⢄⠀⣤⣦⣤⡀⠐⡒⠋⠘⢁⣋⣀⠀⠚⡋⠐⠃⣀⡈⠈⠀⠂⠠⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣶⣿⡗⠸⠮⢤⣦⣦⡂⠒⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⠁⠀⠀⠀⠀⢀⢀⠀⣀⡀⠀⠉⠛⠆⠀⠀⢀⡙⢿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢒⠛⠀⠀⠀⠀⠐⠂⠂⠀⠀⠢⠀⠀⠤⠀⠤⠀⠙⠛⠋⡌⠻⠛⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⢴⠉⠥⠂⢡⠀⢠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣣⣿⡽⣍⣀⠀⢁⠀⢠⡤⣴⣦⠼⡇⠘⡦⡂⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣿⣿⣿⣿⣳⢢⡶⠽⠁⣴⢏⡶⠂⠐⠎⠡⠿⣄⡙⠳⢙⣳⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣫⢁⠰⣣⣃⢼⣏⣿⣿⡿⠼⢶⣯⠙⣿⣧⣶⣰⣀⢼⠀⡛⡓⠶⣽⠛⡶⠶⡀⢀⠀⢀⢠⣐⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⣷⡴⠤⢻⢿⠖⢻⡏⢿⡿⢶⢿⣦⡳⡀⠻⠿⢿⠿⣷⣤⣼⡆⢙⡒⠁⢤⠶⣬⠖⡇⡒⣬⠲⠄⡄⠀⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠠⠐⠃⡱⣼⠿⠓⢿⣵⣟⡘⠀⢿⡔⣎⢧⢸⣿⡿⣿⣇⠀⠠⠀⠀⡪⠘⠟⠟⣷⣷⣾⣾⡟⠋⣤⣿⣿⣿⣷⣤⣼⣴⣥⣷⣸⣆
⠀⠀⠠⠐⠲⢮⡦⠴⠀⠚⠁⠀⠀⠀⠉⠻⢄⠈⢼⣆⠳⣆⢙⠻⢿⣿⢿⣿⡿⣿⣿⣷⠃⠖⣦⠐⠘⣭⢹⢀⡀⣼⡍⣉⢙⣋⣿⣿⣻⢦⣹⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡁⠞⢻⣳⣄⡀⠛⠛⢟⡠⠋⠱⡷⠿⣻⡀⠞⣿⡋⠐⡟⠊⠿⢋⣀⡅⢃⣀⢿⡹⢹⣅⣼⢱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⠙⡣⠛⠹⠶⠶⠥⠶⢤⣭⣤⣬⣥⣥⠚⠀⠄⣀⣠⣀⠒⠉⢭⢨⡗⢀⣖⣠⠤⡏⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣿⣿⡿⠿⠿⠛⠛⠛⠛⠻⠿⠿⣿⣿⢷⣶
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣶⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾
⠀⠀⠀⠀⠀⣿⣿⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣉⣉⣉⣉⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⣿⣿⣿⣿⡇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣡⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠛⠛⠛⠛⠃⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠛⠉⠙⠛⠓⠶⢤⡀
⠀⠀⠀⠀⢀⡴⠋⠁⣀⣤⠴⠖⠒⠒⠶⢤⣀⠀⠙⢦⡀
⠀⠀⠀⣠⠏⠀⣠⠞⠉⠀⠀⣠⡤⢴⣇⠀⠉⢳⡀⠀⢹⡄
⠀⠀⢠⡏⠀⢰⠏⠀⠀⠀⠀⢯⡀⠀⠙⠂⠀⠀⣷⠀⠀⣷
⠀⠀⢸⠀⠀⢾⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⡿⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⣋⣉⣉⣉⣉⣙⠛⠒⠶⢤⣀
⠀⠀⠸⡆⠀⠸⣆⠀⠀⠳⣤⣤⡴⠃⠀⠀⢀⡼⠃⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣤⠖⠛⣩⠉⠉⢉⡭⠿⠯⣍⣛⡲⣄⠈⢳
⠀⠀⠀⢻⣄⠀⠈⠳⣄⣐⠋⠀⠀⣀⣠⠴⠋⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠳⢬⣉⣛⡲⠚⠋⠀⠀⢀⣋⣠⡤⠞⠀⣰
⠀⠀⠀⠀⠻⣷⣤⣀⠀⠉⠉⠉⠉⠉⠀⣀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⣦⣤⣀⣉⡉⠉⠉⠉⠉⢉⣁⣀⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣶⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣽⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣽⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⡀⠀⢸⣷⣽⣻⠿⣿⣿⣶⣾⣿⣿⣷⣶⣿⣿⢿⣟⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣉⣩⣤⠤⠤⠤⠤⠤⢤⣬⣉⡙⠻⢷⣽⣻⠿⣿⣷⣾⣿⣿⣿⣿⣷⣾⣿⠿⣟⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠠⡞⢩⣤⣖⣀⣀⡴⠛⠉⢛⡶⠾⠙⣦⠀⢹⡿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⢿⣻⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠉⠓⠶⠭⣭⣭⣤⣤⣤⡤⠤⠖⠛⠁⣠⣾⡿⣷⣾⣿⣭⣭⣭⣭⣭⣭⣿⣷⣾⠿⣻⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⡿⣻⡿⣷⣾⣿⣭⣽⣿⣿⣯⣭⣿⣿⣾⠿⣛⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣷⣯⣿⣛⣿⣿⡿⠿⠿⣿⣿⣟⣻⣯⣷⡿⣻⣿⣷⠾⠛⠉⠉⠉⠙⠛⠿⣽⣿⣾⡿⣟⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣷⣯⣿⣻⣿⡿⠿⢿⠿⠿⣿⣿⣻⣯⣷⣾⣿⠏⠀⢀⣠⠴⠶⠶⠦⢤⣀⠀⠙⢷⣿⢟⣿
⠀⢀⣠⠴⠖⠛⣋⣉⣉⣉⣉⣉⡙⠛⠲⠦⣿⣿⣶⣭⣟⣻⣿⠿⠿⠿⠿⠿⠿⣿⣛⣯⣽⣿⠃⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⣿⣿
⣴⠋⢠⠴⠛⣉⡍⠉⠀⣠⠶⠿⢭⣍⣟⢦⡀⠙⢯⣟⣻⡿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣿⡟⠀⢠⡇⠀⢠⡄⠀⠀⠀⣀⣀⠀⠘⣦⠀⠹⡿
⣷⡀⠘⠲⢭⣙⣓⡒⠛⠁⠀⣀⣘⣁⡤⠞⠃⢀⣾⣟⣻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⠀⢸⡇⠓⢿⡀⠀⢀⡞⠁⠈⣧⣀⢸⡄⠀⣷
⣿⣿⣷⣦⣤⣀⣉⡉⠉⠉⠉⢉⣉⣀⣠⣴⣾⣿⢿⣟⣿⠿⣿⣿⣷⣶⣶⣿⣿⡿⢿⣟⣿⣿⡄⠀⢷⡀⠀⠙⠶⠋⠀⠀⠰⠏⠈⢸⠃⠀⣿
⣿⣿⣽⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⣷⣿⠿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡿⠿⣿⣷⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⡇
⢿⣾⣽⣻⠿⣿⣿⣶⣶⣶⣶⣶⣿⣿⠿⣟⣫⣷⡿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠙⢿⣿⣦⡀⠈⠓⠶⢤⣤⣤⠴⠚⠁⠀⣠⠞
⠀⠙⠿⣿⣿⣿⣶⣾⣾⣿⣷⣷⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⣀⠀⠀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣤⣴⡾⣿⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣍⣀⣀⡄⢀⡄
⠀⠀⣀⣤⣶⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠁
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠉⠉⠉⠛⠛⠻⠿⣿⣿⣟⠋⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠻⠒





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣤⣤⣤⣀⣤⣶⣦⣦⣴⣤⡿⢦⣴⣿⣧⣀⣴⣦⣴⣿⣿⣿⣿⣻⣛⣛⣯⣷⣾
⠀⠀⣀⣀⣀⡀⢀⣀⡀⠀⢀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣛⣿⣿⣯⣿⣿⣛⣻⣯⣿⣿⣛⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣾⣿⣿⡿⢿⣿⣿
⠀⢸⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠛⠻⣋⣿⡛⠛⠻⠶⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠛⠿⡷⣾⣯⣍⣛⣻⣯⣬⣮⣵⣋⣿⣿⣷⣿⣭⠶⠟⢛⡛⣿⡿⣾⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠟⠋⠁⠀⠉⠙⣻⣿⣿⣿⠿⢦⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣶⢴⡾⠉⠁⠀⢀⣦⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣠⠦⠤⠔⣩⠴⠿⣤⣤⣤⣤⠴⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⡧⠤⢳⡮⡤⡤⢞⣻⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣻⣭⣾⣾⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠶⠿⠶⠶⠶⠾⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⣉⣉⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠿⠾⠿⣿⡿⠛⠉⠙⠻⠿⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠛⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⣀⣀⣀⣀⣀⠀⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣠⣶⣟⣉⣉⣉⠉⠉⠛⠳⣤⡀⠙⢧⡀
⠀⠀⠀⠀⠀⢀⣴⡏⢿⡉⠉⠉⠉⠉⠉⠛⠛⠶⢶⣬⣿⣆⣀⣻⣤⣤⠶⠻⣦
⠀⠀⠀⠀⠀⣾⢿⡅⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⢉⠠⠐⠂⠙⣧⡀
⠀⠀⠀⠀⢀⣿⢿⣇⠀⠹⣆⢀⣀⣀⣤⣤⠶⠞⠛⣉⠡⠔⠂⠁⠀⢀⡠⠔⠂⠈⢳⣄
⠀⠀⠀⠀⠈⣇⠀⢿⡄⢀⡙⣿⡉⡉⠠⠀⠂⠈⠁⠀⢀⠀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢻⡕⢜⣧⣿⣿⡎⣧⢀⣀⠠⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⠈⠛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⢻⣄⠹⣿⣿⣵⠟⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠫⠷⠀⠘⠿⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠁⡀⠑⢄⠈⠢⡀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⢔⣒⠄⠀⢀⠤⡀⠀⢖⡲⠄⠙⣋⣛⠛⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢦⣄⡀⠀⠈⠐⢄⠀⠀⠀⠘⠒⠁⠀⣀⢄⠀⠀⠀⠀⠈⠒⠁⢀⣀⡀⠀⠀⠓⠊⠀⠀⢀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡄⠀⠀⠁⠠⢀⠀⠀⠀⠀⠃⠚⠀⠀⠰⣍⡵⠀⠀⠈⠓⠁⠀⠀⠀⡀⠤⠂⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡐⣄⢮⡑⡆⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠐⠂⢁⠔⠒⢆⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⡳⢌⠃⠀⠀⢀⠤⠤⣉⠀⠈⠀⠉⢩⠤⠴⢄⠀⠀⠀⠀⠨⠤⢒⠡⢂⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣁⠢⢀⠈⠓⠦⠬⠀⠀⠀⠀⢦⠤⠠⠔⠀⠀⠀⠀⢐⣨⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⣐⡂⠀⠀⠤⠀⠀⣀⣀⣀⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣼⣿⠇


⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⢀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⣤⣰⠉⠲⡆⣀⡀⠆⡤⠀⠀⢂⠄⡀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⡄⠀⡀⢸⡤⠣⢽⠄⣶⡿⣠⣖⢋⣬⣩⡨⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣟⡛⠛⠛⠛⠛⠛⠻⠤⠒⠚⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⢴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⠻⢻⡟⠉⠉⠉⢹⠟⠉⠁⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠶⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠚⠛⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠋⢹⡄⠀⣀⡤⠖⠋⠉⣉⠛⠷⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢀⣀⣀⠀⢷⣉⠀⣀⠴⠉⠊⠍⠀⠁⠀⠀⢀⣠⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣰⠞⠉⠀⢘⣧⠤⠾⠋⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠇⠀⢹⡠⠴⠚⠉⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⣸⠤⠴⠒⠋⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⣉⡤⠒⠺⢉⡍⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣰⣶⣏⣁⣀⡀⠼⠂⠡⠐⠊⠁⣀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠉⣟⠙⠛⠓⠶⢤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣇⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠲⢿⣄⣀⠀⠀⣼⠀⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣤⡴⠞⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⢿⣟⡿⠻⢋⣴⣺⣦⡙⢮⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⠋⠀⢉⠽⠅⡶⠚⠉⢉⣩⣭⣆⡉⠛⠲⠶⡴⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⢶⣛⠉⣡⣤⠶⣢⣴⡏⡄⠲⠀⣠⣚⣝⠳⣞⣦⣿⣦⣶⡆⠈⠃⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣫⣶⠆⠀⠀⠀⠀⡤⠹⣤⡞⠻⡙⣷⣳⠄⠀⠋⣁⣠⣥⣤⣤⣤⣌⡙⣦⣔⡀⠀⣸⡇
⠀⠀⠀⠀⣠⠶⠛⠿⣿⣿⣶⣾⡇⡀⠀⠀⣰⠉⠙⠂⠈⠙⠻⣿⣿⣿⡿⠟⠋⠁⠀⠈⠛⠶⣤⣤⠿⠛⠉
⠀⠀⠀⣼⣧⠀⢀⡀⠉⠉⠹⢯⡴⣷⣀⡴⠁⠀⠀⠀⢀⡀⠀⢿⡀⠙⣇
⠀⠀⣰⣿⢯⣼⣿⣆⣀⣠⣶⣿⣿⢻⣧⡀⠀⠀⠀⠀⢰⠇⠀⢸⢸⡟⠻⢦⡀
⢠⣿⡙⢿⡄⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⡴⢾⡀⣀⣸⣾⡇⠀⠀⢹⣶⣦⡀
⢸⡿⢧⡀⠀⠠⢊⣉⣥⣶⣿⣿⠿⢋⣤⣴⠞⣉⡝⢛⣆⣻⡿⢿⣿⣯⣻⣶⣿⣿⣻⣷⣤⡴⢶⡄
⠸⣿⣦⡛⠀⡰⢟⣣⣨⣷⣷⢧⡾⣥⠾⢤⣴⣋⡽⠛⠉⠉⠀⠀⠉⢻⣟⣏⣱⡹⡏⢸⣻⣔⣿⠟
⠀⠀⠙⣷⢠⣶⣿⣿⣾⣅⣿⣜⣄⢣⡀⠀⣠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⡁⠀⣖⣻⣛⣿⡄
⠀⠀⢠⣿⣾⣫⣾⣿⣿⣾⣿⣿⣿⣿⣻⣿⣿⣿⣧⣴⣦⣤⣀⠀⠀⠀⠀⠈⢻⣓⡦⣿⡷⠿⠿⠃
⠀⣸⣟⣿⠛⠟⣷⣿⣿⣿⣻⢿⣵⠿⡟⠿⠟⠛⠛⠛⠛⠛⠋⠙⠛⠲⢦⣄⡘⢿⣿⣿⠇
⢰⣿⣽⡷⣄⢀⣿⣝⣻⡼⠛⠉⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠒⠒⠶⠶⠮⣽⣶⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣷⢮⣻⣿⣯⠞⠋⠁⠀⠀⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⠾⠟⣡⣌⠛⣦
⠀⢻⡛⠛⠛⠉⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⠾⠟⠁⢈⠈⠐⠈⡁⡽⣷⢌⠑⠲⠖⢤
⠀⠈⠻⣤⣀⡀⢀⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠉⠉⠙⢀⢘⣩⠞⢿⣤⠀⠞⢉⣚⣂⣉⡛⢧⣀
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠹⡿⣶⠇⡀⢀⠜⠉⠀⠈⠹⡿⢿⠛⠉⠁⠈⠛⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣴⡀⢀⣠⣿⣿⡈⠀⠀⠀⣄⠈⣧⠸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠀⠙⡿⢿⣿⣿⡷⠿⢶⡶⣖⢦⣤⣿⡇⣀⣹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡳⠀⡠⠖⣺⣿⣫⣀⣟⣱⢾⠾⠟⠋⠙⢿⣿⢛⣷⢻⣏⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣰⣾⣿⡅⡷⣤⣡⣀⣼⡇⠀⠀⠀⠀⠈⠻⣿⡀⣰⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠷⢿⣿⣿⢿⣿⣿⠿⠛⠛⠛⠛⠖⠤⢄⣀⠸⣯⣽⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣄⢸⣿⠓⠋⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠊⠷⢮⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠟⠈⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⣟⢿⣿⡿⡷⣶⡤⠤⠄⠤⣤⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣿⣷⡽⢷⡄⠀⠀⠀⡠⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⣷⡀⠀⣼⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢦⣼⣿⣿⣧⣿⣇⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣾⣿⣿⣿⣛⣛⣙⣠⢄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⢀⣴⣿⣿⣿⣿⢻⡏⠘⣿⣦⠐⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⠃⠾⢁⡀⣈⠊⠃⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⣠⣼⣷⣿⣤⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣟⣿⡁⠀⣼⣿⡿⡏⣿⠿⠿⠆⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⢀⠀⢻⣿⣿⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⠀⠀⠙⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠀⠠⣤⣷⢸⡟⣿⣷⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⠓⢶⣦⣤⣤⣀⣀⡀⠀⠀⠄⠀⠀⣀⣠⣿⣿⣾⣷⣿⡿⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣀⣙⣛⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣤⠴⠚⢻⣿⣧⢙⣿⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣷⡾⢟⣫⣥⡤⣴⣾⣿⣿⡗⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⣹⣿⣶⣶⣤⣦⣤⣄⣀⡉⠙⠓⠁⠀⠀⣀⠤⠈⣹⣿⣷⡄⢢⣽⣤⣤⡄⠐⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⣀⣈⠉⠉⠛⠛⠻⠾⠾⣿⣿⣿⣷⣶⠖⢀⣀⡤⢴⣾⣿⣿⣿⣯⣬⣭⣽⡭⢠⣾⡟⠉
⠀⠀⠀⠀⣿⣿⣟⣓⣾⣶⣤⣄⣀⣀⠀⠈⠉⣻⡛⠭⠖⠒⢛⡏⠉⠙⠛⠛⠛⠛⢻⡆⣘⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣏⣁⡤⠔⠚⠉⠁⠀⠀⠀⣳⣢⡄⠀⣸⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣑⢼⠇⠠⡾⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣏⡬⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡀⠀⢠⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠓⠚⠉⠀⢀⡎⠙⢀⡼⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠺⠷⠤⣤⣤⣀⠀⠀⠀⠉⣨⣦⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⠀⠈⠀⠀⠀⠀⠈⠉⠓⠲⠤⣾⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡢⠌⠋⢸⠈⠙⠛⡲⠦⢤⣄⣀⠀⠀⡀⠀⣿⣿⣿⣿⢿⠉⣩⣳
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢒⠭⣦⠉⠀⠀⠀⠈⠳⢄⣠⣌⠦⠅⣺⣫⣽⠐⡕⡰⣿⡿⠿⢉⣼⣾⣿⡿⡄
⠀⠀⠀⠀⠀⢰⣎⡀⠰⠚⣡⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⣀⢔⣩⣾⣿⣿⠄⣼⣿⠿⠭⠴⣿⡷⣝⣟⡼⠃
⠀⠀⠀⠀⠀⢸⠚⢭⣙⡓⠮⣭⣒⠠⣠⠄⢒⣲⡖⣐⡬⣖⣿⣿⣿⣿⣟⡤⠿⠉⠀⠀⢠⢸⣯⣫⡞⠢⣄⣀
⠀⠀⠀⠀⠀⣸⠂⠀⠙⠪⢕⡒⣉⢿⣷⡲⢭⡴⣾⣶⢿⣿⣿⣿⣿⡛⠫⠥⣤⣀⣠⣼⢏⣸⣿⠟⠓⣤⠀⢘⠏⢒⡢⢄
⠀⠀⠀⠀⠀⠈⠑⠒⠠⢍⣒⠦⢭⣈⡈⠍⣛⣚⣯⣽⣿⣝⡋⠃⣀⠤⠤⢲⣫⣿⠗⡟⢊⡿⠟⠛⢉⠹⢖⠦⣐⣉⣵⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠲⠮⢍⡓⢃⣾⢿⡟⠩⠬⠀⠀⠀⢀⢔⣵⢿⣿⠙⢈⡞⠁⠀⡠⠂⠀⠀⠉⣋⠛⠿⣿⠿⣂
⠀⠀⠀⠀⠀⠀⢀⡔⠊⡡⠉⢠⡀⠐⠠⢍⣙⡉⠈⠀⢀⣀⣀⣀⢔⣩⣿⣷⣿⣿⣼⠯⠀⠐⠊⠀⠀⠀⠀⠤⠀⠀⠀⡃⠀⣆⡍⢁⣶
⠀⠀⠀⠀⠀⠀⣺⠦⠥⠌⠉⣀⢒⣂⠉⠱⠖⠦⠤⠂⣁⣰⣋⣴⡟⣫⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⢂⡱⣀⠤⢚⡭⢞⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠍⠭⠄⠒⣒⣀⡀⠤⠍⠡⣤⠆⢤⣄⣐⣩⣮⣿⣿⣧⣀⣀⠠⣤⡀⣀⠀⠀⠀⢀⠀⠀⡐⡨⢔⣫⣴⣮⣵⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢋⣭⠩⣤⣔⣒⣒⣒⣒⣉⡩⣥⢭⣈⣭⡹⢫⣿⠟⠏⠉⠛⠷⡦⢌⡑⠎⣑⣲⣭⣐⠾⣽⣶⣿⣿⡿⠿⢛⡩⢔⡎
⠀⠀⠀⠀⠀⠀⠀⢸⡓⠑⠪⠢⢌⠐⠁⠩⠊⢔⡅⡩⢈⠑⡡⡩⠛⢶⣵⠀⠀⠀⠙⢳⠪⢹⣿⣧⣽⣷⡿⠿⢛⡋⠥⣒⣮⡾⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠼⡃⠀⠀⠀⠀⠉⠒⢷⡤⠄⠒⢒⣤⢄⣤⣶⣷⣿⣽⣷⣄⡀⠀⠈⠀⢽⢿⣟⠯⣭⣖⡾⡅⠯⠑⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠈⢮⢷⠬⣩⣴⣾⣻⣿⡿⣿⡻⠕⠁⠈⠐⠤⣀⠽⠟⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠈⢶⠀⣩⣷⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⢄⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠄⡠⢀⠄⡀⠐⡀⡠⠐⠠⢊⠄⡨⠀⠔⡡⢂⠄⠠⢂⠄⠀⡀⡀⢂⠔⠡⢂⠔⡡⢊⢄⠄⡠⢊⢔⠕⡵⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠊⠐⠁⠂⠁⠀⠂⠐⠨⢀⠄⠀⠔⠁⠪⢊⠀⠐⠡⠂⠔⠁⠊⠐⠁⠂⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣒⠐⠒⠺⠿⣿⣓⠢⣼⣷⣷⣦⣄⡠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠲⠦⣄⡀⠉⠓⢬⣙⢟⠛⠿⣟⢿⡷⠉⠒⣤⣀⣠⠒⡶⠒⡄
⠀⠀⠀⠀⠀⠀⣰⣿⠟⠿⣿⡏⠀⠐⠒⠶⢤⣝⣷⣦⣤⣿⠗⢷⡄⠘⣦⣱⣄⠀⢈⣿⣯⠀⠀⡰⢣
⠀⠀⠀⠀⠀⣰⡿⢁⣠⣾⣿⣧⣄⣀⣀⣠⣤⣽⣿⣿⣛⠿⣴⣃⢻⣾⡌⢹⣧⣴⣄⢾⣼⣦⣷⠉⣶⡆
⠀⠀⠀⠀⠠⢟⡰⠟⠉⠉⠛⠿⣟⡿⠛⠛⠟⠻⢷⣟⠉⣉⣒⣊⣉⣉⣹⣼⣯⣭⣴⡶⢶⣬⡛⣷⣿⢟⣢
⠀⠀⠀⢀⣴⣏⣀⣠⣤⣶⣾⠿⢿⡿⠾⢷⣦⣤⠈⠉⠣⠀⠬⣉⣉⣹⡿⠟⣈⣍⢴⢖⡒⠘⠿⠄⣙⠋⠙⢦⡀
⠀⠀⠀⣸⣿⣿⣭⣩⣉⣉⣿⣗⣶⣖⣲⣢⣺⣿⣷⣦⡀⠀⠀⠋⢉⣠⣶⠾⠿⠟⢈⣉⣉⣶⣆⠈⠹⠷⠶⠛⠿⢶⣄⣠⣴⣖⣲⣶⣶⡦⢄⡀
⠀⠀⠀⣿⠻⣟⠿⢟⣻⡻⠿⢿⣿⣿⣿⣿⣿⣟⣽⣿⣷⣾⣀⠀⠋⢩⠴⠖⠻⠿⠋⠛⣉⢀⣤⡴⠒⠐⠒⣩⠽⢿⣿⣿⣍⣿⣿⠛⠛⠁⠀⠙⢦⡀
⠀⠀⠀⡿⣷⣜⢷⣄⣠⣉⠉⠒⣾⣥⣻⡻⠟⣿⣿⢃⣾⠛⣿⣾⣄⣠⠀⠀⠀⣄⠀⠀⣩⣷⠹⠟⠀⣀⣈⣴⣾⣿⠛⠓⠯⠛⠛⠛⠛⠛⠛⠛⠛⠷⣄
⠀⠀⠀⣿⢽⣿⣧⠙⠻⣿⣿⣦⣄⠀⠉⠙⠻⣿⣿⠖⣛⡚⢻⢫⣿⠿⣿⢶⣶⣿⣿⢿⣿⣧⣄⠀⠀⠉⢀⣾⣿⣿⣀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⣸
⠀⠀⠀⢳⠀⠙⢿⣇⠀⡜⣿⣿⣿⣦⠀⠀⠀⠘⠟⢻⣇⣦⠄⠀⠣⠾⠟⣰⣟⣸⣹⡸⢻⠛⣿⣷⣾⣷⣿⣿⣿⢿⣿⣿⣶⣶⣶⣿⣿⣶⣾⣿⣿⡿⠃
⠀⠀⠀⠘⡆⢈⢮⣹⡆⠘⣾⣿⣿⣿⡄⠀⠀⠀⠀⢊⡏⢿⡼⣷⠁⣤⡞⡌⣠⡀⠋⠳⣌⠞⠙⡿⡹⣿⡇⣸⣟⣰⢀⢹⠏⠋⢿⠇⠋⠈⣿⡏⠘
⠀⠀⠀⠀⠸⣾⣦⡻⣿⣆⠘⣞⢿⣿⡅⠀⠀⣠⠀⠘⠀⠋⠀⢸⠛⠻⣇⣼⡇⢀⡐⠂⣁⠑⣤⣟⣠⠈⠓⢿⣿⣵⡇⠌⡆⠀⠘⠌⠀⠀⠸⡃⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢷⣌⡳⣿⣿⣦⣲⣿⣦⣀⠀⠀⠀⢰⠀⢸⠃⠘⡧⠿⣇⣴⠋⠀⡄⠀⠈⠳⣦⡀⠛⢿⣷⣟⣠⠖⠀⣠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠬⣿⣿⡿⣿⣯⣒⠀⠀⠀⢀⢠⠀⠀⡀⠀⣿⠦⣿⠀⢀⢤⠀⠉⠙⢦⡀⢻⣿⣿⣰⣄⡇⡇⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠭⣿⣶⣤⣿⣾⣄⢀⡇⠀⠃⢰⡿⢊⣿⡀⣀⡞⠁⢠⠻⠶⡈⠛⠛⢿⣧⣷⣾⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠽⢿⣿⣶⣧⡈⠀⠸⠿⠟⣿⣇⡴⣿⣠⣄⡼⢳⠀⢰⠌⢫⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣦⣼⣧⣋⡁⠋⠉⢹⣇⣼⣶⣯⣸⣾⡶⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠺⢷⣮⣌⣩⣀⡉⣁⣘⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣄⣠⣤⣶⣶⣿⢿⣷⡄⠀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣛⣻⣿⣿⣶⣶⣾⣿⣍⠉⠁⠀⣴⣿⠵⠞⠛⠉⠁⢀⣠⣬⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡉⠉⠉⣴⣿⡛⠋⣹⣦⣤⣾⡿⢿⣿⣶⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⠘⢿⣿⠿⠿⠛⠋⠁⣰⠏⠀⠀⠀⣠⡿⠋⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣬⣿⣦⣀⡀⠀⠰⠏⠀⣀⣠⣾⣯⣴⠶⠛⢛⣛⣩⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠿⣯⣭⣭⣉⣉⣙⣛⡛⠛⣛⣭⣿⣿⠟⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠋⠉⠀⠘⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣀⣬⣷⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠛⠋⠙⣧⠀⠀⠙⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢻⡄⠀⠀⢸⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠿⠟⢿⡛⠉⠙⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠘⣷⠀⢀⣴⡟⠁
⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣤⡀⠀⣷⣀⣀⣠⣼⣷⠿⠋
⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⣿⠟⠛⠛⣿⡀
⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠹⡇
⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⡾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⢀⣀⣀⠀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣾⣿⣿⣆⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⢀⡀⠀⡀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⡇⢸⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⠇⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⢠⣤⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⡇⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙⠃⠘⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⢰⣿⠋⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣇⡀
⠀⠀⠀⠀⢸⣿⠀⢠⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠛⠁⠀⣶⡄⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⢿⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⣿⡇
⠀⠀⠀⠀⠈⢿⣷⣼⣿⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣂⣀⣙⣁⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣀⣀⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⡴⠊⠉⠉⠙⠓⠒⠂⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠒⢤⡀
⡇⠀⠀⠀⠤⢄⠄⠒⠄⡠⠄⡄⠤⢄⡠⠤⢤⠀⠀⢄⠀⠀⠤⡀⣀⣀⠀⢀⡀⡀⢀⠀⠀⢱
⡇⠀⠀⡇⠀⢏⠀⡁⠆⡁⠸⡅⠀⠀⡭⠀⢇⠁⠀⠊⠀⠀⠰⣁⢐⠂⢄⢈⣼⡀⠆⡁⠀⢸
⡇⠀⠀⠈⠐⠊⠑⠋⠊⠙⠒⠂⠒⠈⠑⠒⠂⠀⠊⠀⠀⠈⠐⠉⠀⠈⠉⠉⠈⠁⠉⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⣶⠀⠉⠟⠃⡆⠀⠀⠀⠄⡄⠀⠠⡄⢠⡀⡀⠀⡄⠀⡀⠀⢄⢀⡀⢀⠀⠀⠀⠀⢸
⡇⠀⠀⣧⠀⠀⡀⠀⡇⠀⠀⠀⠁⠁⠀⠈⠁⠀⠁⠈⠀⠀⠈⠓⠀⠃⠘⠃⠉⠃⠀⠀⠀⠸⣄⡀
⡇⠀⠀⠋⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⢀⠒⠀⠠⠀⢄⠄⢄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⡀⠀⠉⠒⠤⣄⡀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⣅⣈⠁⣀⡁⠅⢸⠸⠈⣄⠑⠁⡔⣔⣢⣒⡄⠀⠈⠚⠧⣨⠒⠂⠀⠀⠀⠈⠑
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠓⠀⠐⠓⠀⠚⠀⠂⠀⠈⠀⠉⠉⠁⠉⠁⡀⠀⠀⠀⠀⠉⠚⠌⠘⠀⠀⢀
⠀⠓⠦⠤⠤⠤⠤⠤⠤⠤⠤⡄⠠⠤⢤⠤⠤⠤⠤⢠⠀⡤⠤⡤⠀⠤⠤⠤⠤⠄⠠⠀⠊⢐⡐⠠⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣀⠈⠉⠙⠃⠢⡘⡐⠐⢂⡄⠀⠀⠔⠢⡀⠀⠀⠀⠀⠀⠀⠓⠐⡟⢠⠄⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⡀⠈⠉⠁⠀⠀⡄⠘⢀⠴⢈⡵⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣄⡀⠈⠉⠀⢄⣛⠀⡀⢠⢀⠂⠠⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⡀⠀⠙⠒⠂⢀⠁⠤⠈⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠈⠉⠀⠀⢠⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀⠠⣀⣠⡄⢤⡠⣤⠄⡤⠄⠄⠠⠀⠤⠀⠄⠒⢐⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡔⠀⠐⠊⠀⣀⠕⠠⠈⠑⠀⠀⠀⠈⠀⠀⠄⢀⢀⡂⣠⡀⠤⠴⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡈⠅⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⣀⣠⡠⠤⠴⠖⠒⠚⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡠⠃⢈⡰⠀⠀⠀⠀⠀⢄⠀⢄⡤⠴⠚⠉⠉
⠀⠀⠀⠀⠀⢸⡧⠡⠄⡠⠀⠀⠀⠀⠀⠺⠷⠋
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⢢⢆⠀⠀⠀⠀⠒⠀⣀⣀⡀
⠀⠀⠀⠀⢿⡍⠀⠀⠀⠀⡙⠀⢀⠂⠄⠀⠀⠀⠀⠀⠀⠓⠂⠠⠄⠀⠀⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠀⣀⡤⠀⠀⠀⡀⠀⠀⠓⠀⣤⠀⠀⢀⠀⠀⣀⠀⠠⠀⠀⠐⠀⠀⠀⠀⢀⣠⣧
⠀⠀⠀⠀⠰⡂⠀⠀⠀⣜⠀⠈⠀⠁⣀⡠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠠⠀⢀⠉⠰⠂⠂⠀⠀⣀⣀⣀⢀⣤⠒⠁⠉⠉⠁
⠀⠀⠀⠀⠀⡇⢀⡄⢀⠳⣄⡀⠀⠀⠀⠀⡒⠀⠢⠀⢀⣈⠀⠀⠬⡀⠀⡖⠀⠀⠀⠀⠀⠀⠤⣀⣠⣠⣤⠾⠀⠈⡝⠂
⠀⠀⠀⠀⣜⡀⢘⡄⠈⠣⣄⠝⠲⠀⠢⣀⡀⠀⢠⠀⠉⢀⣀⡠⣀⢼⣎⢷⠀⠀⠐⢆⠀⠀⠀⠀⠈⠃⢈⣙⠒⠤⣧⣀
⠀⠀⠀⠀⠀⠀⠿⢰⠂⠉⠪⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠻⣿⣫⣅⡁⠽⢦⣦⣦⣽⣖⣦⢤⣤⡀⠀⠈⠉⠣⢄⡙⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠭⠈⠤⠐⡴⠤⠭⠒⠷⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢪⠗⠀⢦⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠘⠏⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⣀⣤⠀⢀⠔⠚⢩⠂⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠈⠁⠀⡁⠁⠀⠀⠀⢩⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣁⣀⡏⣠⣡⣴⡖⣓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠘⡄⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⣤⣬⣿⣛⣛⣉⣭⠽⠿⣕⠤⣀⠀⠀⠀⠀⠀⡠⠰⡄⠀⠀⠀⠰⠁⠀⠀⢀⠛⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠛⠀⠒⠐⠒⠖⢺⠒⠳⣟⠷⠀⠅⣈⠀⠀⠀⠀⡎⠀⠀⢡⠀⠀⠀⠆⢀⠀⠀⠌⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢐⡇⠘⣀⡀⠀⠈⠈⢣⢱⡀⠀⠱⠀⠀⢰⠀⠠⠀⢸⡀⠀⢀⡀⠐⡂⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡔⢉⣀⡀⠀⠀⠈⠳⡄⠐⠈⢣⡵⠀⠀⠑⢄⠘⡄⢔⠀⠀⡇⠀⠸⠀⠅⠒⠠⠀⠥⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢪⡀⡃⢸⠉⠑⣀⣁⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⢐⠀⠀⢰⠀⡠⠀⠭⠰⠆⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠘⠢⡈⠁⠘⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⣯⣄⠢⠀⢸⠰⢁⡒⡨⠋⡒⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⡄⠀⠀⡜⠒⢄⠙⡆⠀⠀⢀⡡⢂⠔⠠⠂⣀⠄⢹⣎⣀⣶⠥⠂⣔⡁⠤⠖⠂⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠘⢄⠘⠒⠀⠀⠀⠊⠀⡘⠀⠀⡠⠒⠡⢊⢔⠞⡡⠖⠉⠀⢀⠤⠒⠒⠒⢤⡎⠀⠀⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡂⠀⠀⠀⠈⠑⠒⡄⡐⠒⠀⠂⠁⠀⠀⣀⠄⡂⢑⠔⠋⠀⠀⠀⠀⠘⢔⠢⣀⡠⠾⠁⠂⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠡⠂⢀⠀⠀⠀⠉⠁⠀⠀⠀⡀⠔⡈⠔⣈⠔⠁⠀⠀⠀⠀⢀⠀⠑⠀⣽⠫⠭⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⣰⡥⠞⠚⠛⠛⠉⠁⠀⠋⠓⠒⠂⠈⠁⠀⠀⠀⠀⢠⠒⠀⣀⠴⣙⠲⠈⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⣠⠺⢅⡒⠠⠈⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⢀⡜⠭⣑⠂⠈⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⢀⣤⠪⠌⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⠀⠀⢀⡀⡀⠐⠁⠔⡡⠞⠁⠔⡀⠀⠠⠔⠺⠉⠂⠁⣀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⠄⣀⡀⠀⠨⠊⡠⠊⣠⠊⡀⠊⢡⠊⠐⡡⠀⢀⣀⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠉⠐⠒⠠⠾⣡⣊⣀⠔⡡⠊⢔⠐⠊⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠉⠐⠂⠤⠄⣀⡀⠀⠀⠀⠈⠈⠁⠐⠒⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡁⠄⠂⢀⡀⠀⠉⠑⠒⠠⠄⢄⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢁⠠⠐⠀⣀⠤⠒⢉⡠⠔⢀⡠⠄⢀⠉⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠤⠂⢁⠄⠂⣁⠄⢊⡡⠐⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠐⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⢀⡠⠀⢂⡀⠄⠒⡀⠄⢒⡀⠤⠐⣈⠠⠐⣀⠡⠐⢈⠡⠐⢂⠡⠀⢂⠨⠐⠂⠡⠄⠂⠀⠀⠂⠁⠐⠀⠡⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠂⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀⠀⠀⠉⠉⠑⠐⠂⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⣖⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠴⣏⣀⡀
⠀⠀⠀⠀⣄⣀⣀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠚⠻⢥⣀⠀⠀⠀⠀⠉⠒⠩⠽⣳⡆⠀⠀⠀⢀⣠⣴⢯⣥⣶⣶⣛⣫⡀
⠀⠀⠀⠀⢠⣌⣙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠿⣾⣯⠓⠦⢄⡀⠂⢤⣀⡠⠬⠉⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣧⣈⠙⠒⠦⣍⡙⠲⢤⣤⡤⠤⠤⣶⣶⣶⣶⣶⣾⣿⣿⡇⠀⠀⠀⢀⠀⣷⣿⣿⣿⣿⣿⣟⣛⣛⣉⠁
⠀⠀⠀⠀⠀⢹⣌⠉⠂⠀⠀⠉⠙⠲⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣤⠼⠶⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⣱⠦⢄⡀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣝⠲⢬⣑⠒⠤⢀⣉⠻⣛⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠉⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢍⣙⡒⠲⠤⠴⠚⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠚⣏⡉⠀⠉⠐⠲⠶⡄⠀⠀⠀⢀⣀⣤⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠾⠁⠀⠀⠀⠀⠀⠀⢘⠣⠤⣀⠀⠀⠀⠀⠀⠙⠛⢋⣀⡄⣦⠄⠒⠀⢸⣿⣿⣿⡿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣤⣤⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠂⠀⠉⠒⠴⢶⣾⣿⣿⣿⣿⡇⣯⣀⣀⣤⣾⣿⣯⣷⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢩⣑⣲⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠤⢀⡀⠈⣿⣿⣿⡿⠟⢛⣹⣾⡞⠉⢀⣼⣿⣿⠗
⠀⠀⠀⠀⠀⢭⣐⣒⣶⣾⣓⠲⠬⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣔⠚⠣⢤⣀⠉⠈⠉⠀⣤⣾⣿⣿⣿⠓⠛⠛⠋⠉
⠀⠀⠀⠀⠀⢐⠂⠭⢽⣯⠤⢍⣛⣿⣿⣿⢄⣒⣶⣾⣿⠀⠀⠀⠀⠈⣇⠉⠉⠒⠢⠤⣀⡀⢐⣻⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠠⢌⣙⣻⣿⣑⡒⠶⣿⡿⣿⡀⠬⢿⣭⣽⡗⠀⠀⠀⠀⠉⠒⠠⠀⢀⡀⠀⠀⠽⣺⠟⠋
⠀⠀⠀⠀⠀⢘⠒⠲⣿⣿⠦⢈⣉⣛⣛⣿⠍⣙⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣓⣒⣺⣿⣿⣿⠃⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣫⣴⠾⠛⠛⠻⣿⣿⣤⠤⠴⠶⠤⢃⠈⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠟⠁⠀⠀⠀⠀⠈⣏⢹⠦⣀⢀⠀⠠⠀⢙⣢⠀⠰⠊⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠋⠀⠀⠀⠀⠀⠀⠠⢈⣁⡠⢤⠳⠒⠃⠉⠻⣿⠠⠰⠰⠿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠤⠈⠁⠀⠀⠀⠀⣀⠁⠀⢐⣀⣠⣱⡶⢻⠛⢹⠸⠃⠀⠀⠀⠀⢀⠴⣿⠀⠀⢀⠴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⠀⠀⢀⠀⠄⢐⣢⣄⠀⢱⣶⢿⡛⠋⠉⣈⠡⠀⠀⠘⠀⠀⠀⣤⠀⠀⠈⢦⣻⢀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⢀⠔⢈⣥⣶⣿⣿⡿⡿⠐⠸⣏⠐⠁⠄⢈⣴⡶⠈⠀⠀⠀⠀⠀⠂⠑⠄⠀⠀⢹⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽⠀⠀⠀⠎⢠⣿⣿⡿⣯⣿⣧⣿⠠⠀⡏⢀⠀⣰⣾⡿⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠸⢸⣿⣿⣟⡿⠋⢿⣷⠶⠚⡇⠀⠀⠟⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠸⠀⣿⡿⡿⠇⠀⠈⢿⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣴⠖⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⣇⣟⡠⠒⠦⢼⠆⠰⠃⠀⠀⣟⣃⡒⠤⢀⠀⠀⠀⠉⡅⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⣿⣿⡜⢱⡁⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠑⠃⠀⠀⠓⠀⠢⢄⠘⠆⢸⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⣿⢻⡆⠮⡁⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⢸⠀⠀⠀⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⢻⣨⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⢈⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡁⢸⡇⡀⡀⠀⠀⠠⠀⠀⢄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣤⣴⣿⣿⣟⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⢸⣿⢁⡇⠀⠀⣰⡆⠀⢺⠉⠢⡄⠠⠐⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠿⠟⠏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⡀⠀⠀⢸⠈⣿⣿⣿⡶⠀⡿⡇⠀⢸⡄⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⡿⠛⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣶⣤⣀⠸⠅⣿⣻⣿⣇⡆⡇⣿⠀⢸⣷⣀⣠⣴⣶⣿⣿⣯⡛⠲⢭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡉⠛⠿⢿⣦⣿⣿⣿⣩⣛⣧⣽⣤⣾⣿⣿⢿⣿⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠓⠦⢶⠝⠻⠿⣿⣿⣿⣿⣿⣿⡿⢿⡻⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⢁⠀⠀⠀⠉⠋⠛⠙⠢⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⢀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠞⠛⠉⠁⠀⠀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⣀⣠⣼⣇
⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠁⠀⠀⣀⣠⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⢻⡄
⠀⠀⠀⣴⠟⠋⠉⠀⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⢻⣄⣤⡴⠖⠛⠉⠁⠀⠀⠀⠀⢀⣀⣤⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠸⣧⡤⠶⠚⠋⠉⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡴⠚⢛⣷⠞⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⣾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣿⠀⠀⠀⢳⣄⠀⠹⣆⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣀⣿⠀⠀⠀⠀⠉⠛⠛⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠋



⠀⡁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠖⠶⠲⠖⠲⠖⠶⠲⠖⠶⠒⠶⠲⠖⠶⠲⠖⠲⠖⠶⠲⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠤⠥⠤⠤⠬⠤⠥⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠲⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⣢⢴⠀⣦⡆⠐⢰⠀⡦⠐⢐⢀⡄⢴⠰⣴⠀⠂⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣧⣀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡗⡀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⣄⠀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⢠⡀⠸⠀⠀⠀⠀⢀⣸⠀⣀⠔⠋⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⢇⠦⠀⠀⠀⠳⡀⡇⠀⠀⢀⡄⠈⠛⠭⣀⢄⠀⠀⠐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢆⣰⠎⠍⠀⠙⣿⣟⣁⠈⠀⠀⠠⠓⡼⠦⠑⠎⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⣄⠉⢀⣤⣤⡶⣶⡁⠈⠙⠪⢲⡀⡀⡐⣰⣇⣠⣿⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⢷⣤⠃⣤⣄⠎⠀⠫⣄⣠⡀⠀⠑⣷⡼⠟⣫⡴⠞⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠢⢌⡓⠿⠵⣦⣤⣄⣀⠤⠼⠧⠤⠚⠛⠋⣁⣠⠖⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠂⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠴⠖⠋⠉⠉⠁⢠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠃⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⢀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠤⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⠡⣄⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠒⠒⠀⠀⠐⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣶⡚⠓⠒⠒⢶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠔⢺⠍⠽⢽⣻⣶⣦⠀⠘⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⡣⠉⠀⠀⠀⠀⠈⢻⣿⣧⠘⠆⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣴⣯⢯⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠛⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⣀⡠⢞⡛⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡔⠂⡘⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⣿⣛⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⡈⠂⡰⢁⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⢊⣴⠋⣠⡔⢣⢮⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢛⡻⠤⣹⠉⠒⡰⡞⢁⡔⢡⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⢿⣠⠞⠉⠐⠂⠰⠑⠉⠀⣠⠿⢡⡿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⣼⠚⠋⠈⡉⠡⠶⠧⠀⠀⣀⠄⠁⡀⡼⠁⠈⠛⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⢁⠛⢁⢉⣴⣊⡵⠆⣈⣠⠄⠾⣁⠀⣦⠞⢁⣀⡆⡀⠠⡻⡆
⠀⠀⠀⠀⠀⡀⠈⠉⠀⢀⡤⣤⣀⡀⠀⠐⡡⠬⠉⣁⡁⠈⡀⠸⠑⠀⢩⠖⠉⠙⡆⢠⡤⠿⠋⣡⠴⣶⣿⠿⢿⣶⠿⠟⠤⢀⡀
⠀⠀⠀⠀⢺⡘⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠈⠛⠓⠈⠀⠀⣀⡀⠘⠀⢋⠙⡁⠐⣛⢈⣠⣿⡿⠟⠀⠐⠷⠐⠲⠉⣶⠿
⠀⠀⠀⠀⠈⠙⠶⣤⢠⢤⠤⡶⢤⣀⣀⣠⣄⠐⢀⣀⣀⢀⡀⠀⠀⠀⢻⣷⠀⠃⠀⠁⠈⠁⠻⠟⠋⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⣰⠿⢿⠟⣻⣿⠿⠿⣿⠎⢃⡴⠀⢠⡈⣽⣿⣿⣷⣷⡶⢊⣠⣠⡤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢷⡷⢊⠌⠁⠠⢂⡰⠋⢀⡠⠃⠀⠰⡘⠛⠛⠛⠋⢨⠇⠀⠀⠉⣵⡟⠁
⠀⠀⠀⠀⠀⠀⢀⡇⠔⢊⡣⠊⠩⣀⣅⢠⡴⠂⠉⠀⠀⣋⣤⣶⠈⠈⠀⠀⠀⠀⠀⣸⠀⢀⣐⠾⡏
⠀⠀⠀⠀⠀⠀⠿⣤⣀⢈⣩⡖⢓⣫⣥⡤⣒⠶⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡞⠁⡀⠈⠁⡙⢈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠈⢧⣠⠊⠱⢼⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁