Rhino Emojis & Symbols

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢄⣠⠤⣤⣄⡀
⠀⠀⠀⡰⢁⠂⠀⠀⠀⠀⢠⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣿⣆⠳⡀⠀⠈⠙⢦⡀
⠀⠀⢰⠁⡌⠀⠀⠀⠀⠀⡏⣸⣿⣦⡀⠀⠀⠀⠀⣠⣴⡛⠀⣾⣡⣿⣿⡆⢳⠀⠀⠈⠆⠻⣦⡀
⠀⢀⠇⢰⠁⠀⠀⠀⠀⠸⣤⣿⣿⠘⠉⠳⣦⣴⠚⢓⠦⡀⢀⣿⣿⣿⣿⠇⣸⠀⠀⠀⠀⠘⢿⣿⣶⢤⡀
⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⣨⣿⠑⠙⠂⣁⣤⣾⡟⠛⢿⣇⣰⠟⠀⠀⠀⠀⠀⠈⠘⠿⣄⠙⠢
⠀⡏⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⡟⣁⠠⠀⠀⢻⣿⡟⠂⠠⠼⢋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠳⣄
⠀⡇⡆⠘⡆⠀⠀⠀⠀⡆⡇⠀⠀⢈⡇⠀⠀⠀⠀⢀⣢⡡⣽⣎⣒⠀⣋⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣆
⠀⡇⡇⠀⢳⡀⠀⠀⠀⡇⠠⠀⠀⣼⠀⠀⠀⠀⠀⣴⠛⠈⠀⠈⠀⠁⣻⣏⢳⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣧⠀⠀⠀⠳⡀⠀⠀⣷⡀⠑⢄⣿⣄⠀⠀⠀⠀⠀⠀⠄⠀⢠⡰⠋⠛⠃⠃⡷
⠀⢻⡀⠀⠀⠀⠙⢆⠀⣿⣷⡀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⡀⠨⠃⠀⠀⠚⡄⣷
⠀⠘⣧⢀⠀⠀⠀⠀⠙⠿⣿⣅⡀⢀⡞⡟⠀⠄⠆⢁⠐⢰⡇⠈⠀⠀⠀⠀⣀⣼⡆⠀⡤
⠀⠀⠸⣎⢆⠀⠀⠀⠀⠀⠀⠉⠻⣿⡾⠃⠀⠀⢇⣿⣷⣾⠀⠀⠀⠀⠀⠀⡿⡿⠁⢸⠃
⠀⠀⠀⠹⣮⠢⠀⠀⠀⠀⠀⠀⠀⡻⡃⠀⠀⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢠⠃
⠀⠀⠀⠀⠘⢷⣕⢄⢀⠀⠀⠀⢠⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡽⡤⠀⣶⠏
⠀⠀⠀⠀⠀⠀⠻⣷⣷⣍⣉⣠⠟⠉⠘⠄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣼⠔⠱⠃⡼⢋⡤⠁
⠀⠀⠀⠀⠀⠀⢸⠟⠿⠟⠋⠑⣠⡌⡆⠀⢀⢄⠀⠐⠀⠁⠀⢀⣠⠞⠉⠁⠰⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠱⡆⢲⠂⠀⠾⢋⡅⢇⡘⢁⡩⠀⡠⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣔⠀⣀⣀⣡⡴⢩⡏⣺⣄⠤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠉⠻⡯⠴⠷⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⡤⠤⢤⣄
⠀⠀⢀⠄⠈⠀⠀⠀⠀⢠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⣦⠱⡀⠀⠈⠛⣦
⠀⠀⡈⢀⠀⠀⠀⠀⠀⡎⣰⣿⣷⣀⠀⠀⠀⣠⡴⠎⠁⣾⣥⣿⣿⡆⢳⠀⠈⠂⡈⠳⣄
⠀⢰⠀⡈⠀⠀⠀⠀⠀⢦⣿⣿⡘⠀⢹⣶⠞⠉⢙⠂⠀⣿⣻⣿⣿⠃⣾⠀⠀⠀⠘⠆⠹⣿⡶⢄⣀⠀⢀⣀
⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠛⠿⣿⣄⣼⠇⠀⠈⢠⣴⣾⡟⠉⢹⣧⣼⠃⠀⠀⠀⠀⠀⠀⠙⠳⣄⠉⠉⠁⠀⠉⠲⣄⣀⣀
⢰⣇⠀⢣⠀⠀⠀⠀⠀⠄⠀⠀⢹⡿⠣⠆⠃⠀⢨⠿⢯⣄⠀⠘⡴⣿⡀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢳⡀⠀⠀⠀⠀⠀⠙⠢⡑⣄
⢸⡇⠀⢸⡄⠀⠀⠀⡌⢀⠀⠀⢰⠁⠀⠀⠀⠀⣰⠃⠓⠫⠔⠄⣤⡿⣇⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠑⠌⠟⢧⡀
⢸⡇⠇⠀⢳⡀⠀⠀⣿⠀⢄⠀⣯⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⡤⠾⡷⡝⡾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠦⡀
⠀⣇⠀⠀⠀⠱⣄⠀⢻⣆⠀⠙⠛⣷⡀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⢀⠁⡇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⢹
⠀⢹⡄⠀⠀⠀⠈⠳⣼⣿⡇⠀⠀⡽⡟⠀⣠⠀⠀⠄⣀⠀⠀⠀⠀⠈⠀⣻⠀⠸⣸⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸
⠀⠀⢷⠡⠀⠀⠀⠀⠀⠉⠛⢷⣾⣵⠃⠀⢸⢠⣦⣼⡏⠀⠀⠀⠀⠀⣷⣿⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠈⢧⡱⡀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠘⠉⠿⠁⠀⠀⠀⠀⢠⣼⡇⠀⢐⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠹
⠀⠀⠀⠈⠳⣄⢀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣀⡾⠋⢀⠄⠀⠈⠑⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡼⢸
⠀⠀⠀⠀⠀⠙⣷⣕⣗⣊⣠⠟⡉⠚⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⣰⣿⡏⢠⡿⢁⡔⠁⠀⠀⢀⡀⢤⠠⠀⠀⠀⠈⡆⠀⠀⠀⠀⣠⠀⠁⢺
⠀⠀⠀⠀⠀⠀⡿⠿⠿⠛⠁⣠⡌⡆⠀⠠⣀⠀⠀⠈⠀⢀⣠⣾⣿⣿⣷⣿⢁⡎⢀⠄⠠⢂⠥⠤⠀⢳⣇⠀⠀⣰⠃⠀⠄⢆⣴⣏⡏⠀⢸
⠀⠀⠀⠀⠀⠈⢦⠰⠆⠀⠸⢫⠄⣃⡚⣨⠍⣠⠄⣠⣾⣿⣿⣿⣿⣿⣿⢹⡾⠀⡌⣰⠟⠁⠀⠀⠀⠢⢻⠀⢀⡏⢀⠜⣴⣿⣿⠛⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠈⢦⠀⣠⣤⣤⠞⡹⣋⣥⡤⢴⣿⣿⣿⣿⣿⣿⢿⠛⠛⢾⣷⣾⠟⢁⡴⠂⠀⠀⠀⢦⣟⣶⣾⣿⣯⣾⢟⣿⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠷⠞⠛⠃⠀⠀⠘⣿⣿⣿⠿⢿⣿⢧⣕⣀⣀⣽⣿⣴⢏⠀⠀⠀⠀⠀⣇⣿⣿⣿⣟⣯⣷⣿⡏⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀⠘⢿⣾⣿⣿⣽⠿⢿⣷⡀⠀⠀⠀⠁⣸⣿⣿⡟⠉⠉⠙⣿⠆⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣼⣯⠃⠀⠀⠀⠀⣿⠀⠀⡀⢠⣧⣿⣿⣿⣿⡄⠀⠀⣿⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⣏⠀⠀⠀⠀⠀⡟⠁⠀⠘⠈⣿⣿⠁⠈⣿⠃⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⢡⢡⠀⠀⠀⠀⠀⣿⠄⠀⠀⢷⣿⡟⠀⢺⠇⠀⠀⠀⣿⡎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡺⣿⠁⠀⠀⠀⠀⣿⡁⠀⠀⠸⡏⠄⠀⢹⡄⠀⠀⣰⡿⠁⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠳⠖⠘⡟⢿⡀⠀⠀⠀⢀⠻⠁⠀⠘⠀⢷⠚⠓⠛⠀⠀⠸⠧⣶⠀⢀⣶⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⠀⣠⡆⢠⡀⢸⠇⠀⠀⢠⠎⣴⣂⣀⢀⣦⠌⠇⠀⠀⠀⠀⠑⠒⠣⠤⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠼⠅⠀⠼⠛⠀⠀⠀⠈⠤⢜⣀⢀⣈⠯⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡔⣾⠀⠀⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠉⠃⠰⠋⠁⠀⠙⣿⡏⠒⠀⢴⡿⠏⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠚⠉⠀⢀⠀⠀⠀⠀⠀⡄⢀⡔⠀⠙⠃⠀⠀⠆⠆⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⡤⠚⣡⠄⡠⠊⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣿⡞⣡⠀⠀⢀⠀⠀⠀⢝⡤⠄⣸⠏
⠀⠀⠀⠀⠀⣠⠊⠀⣾⡏⡾⠀⠀⠀⠀⠀⣼⡜⠀⠀⠀⠀⢠⣇⢣⡸⡜⠀⡀⠀⢰⠄⠰⢶⣾⡏
⠀⠀⠀⡴⠀⡇⢄⠀⢿⣇⣇⠢⠀⠀⠀⣰⢻⠃⡠⣤⠶⢶⣾⣿⣿⣿⣷⣶⣷⣄⡙⢀⣂⣤⣿⡆
⠀⠀⠀⠁⠀⢿⣎⠻⢎⣿⣾⣷⣄⠀⠀⢫⠿⣶⣾⣿⡛⠩⡻⣿⣿⣿⣿⣿⡏⠛⠷⠶⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⢻⣷⣌⠘⣿⣾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣖⠉⢻⣿⣿⣿⣿⡵
⠀⠀⠀⠀⠀⢰⣊⣿⣿⣦⣼⣿⣿⠏⠙⠛⠛⠛⠛⠙⠛⢿⣿⣴⣦⠙⢿⣿⣷⡇
⠀⠀⠀⠀⠀⢸⣿⡟⠉⠙⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣿⣶⣿⣿⢏⣀⣸⣿⠟
⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠉⠻⣿⡓⠄⠀⠀⠀⠈⠻⠛⠉⠉⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠀⠀⠀⠼⠷⠻⠦⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⣸⠉⢿⠋⠉⠳⠦⢤⣤⣤⣄⣀⡀⠀⢀⣀⠤⠖⠊⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣶⣿⣿⠀⣸⠀⠀⠀⠀⢘⠿⠛⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡀⠲⣶⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠀⠛⢰⠀⠆⠀⡖⡈⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡈⠓⡝⣆⢈⣿⣄⠀⠀⠙⣄
⠀⡶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⡀⠄⠀⠀⢠⠁⡥⠀⠀⠀⠀⢸⣿⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠘⢮⠂⢸⡈⣿⣿⡆⠀⠀⠸⣦
⠀⣧⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠈⠑⠔⢰⣦⠸⢸⠀⠀⠀⠀⠀⠀⢿⣿⡸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠆⢈⣿⣿⣿⡇⠀⠀⢀⣿⡇
⠀⣿⡘⣄⠀⢸⡍⠒⠚⢻⡿⠋⠀⠀⠀⠀⠀⣿⣆⣸⣦⡀⠀⠀⠀⣀⠸⣿⡇⢿⣿⣄⠀⠀⠀⠀⠀⢀⣠⣾⣾⣿⡿⣿⣇⢀⣠⣿⣿⡇
⠀⠹⣷⡌⠑⠲⢿⣦⣤⣾⠇⠠⡶⠀⠧⠀⠀⢹⣿⣿⡿⣿⣷⣶⣿⣿⣷⣿⣿⢸⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⢸⣇
⠀⠀⠙⣿⣦⡀⠈⣷⣿⣯⠀⠀⠠⠄⠀⠀⠀⣾⣿⣿⣷⣬⣛⣻⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣈⣿⣿⣿⠈⢿⣆
⠀⠀⠀⠙⢿⣿⣞⣽⡿⠛⠀⠀⠀⠀⠀⣀⣾⣿⣿⡹⣿⣶⣾⣿⣶⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⣹⣿⣿⢁⡴⠁⠄⣦⠼⠛⠉⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⢸⣿⣿⣿⡇⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⢿⣿⣦⠥⠔⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠹⠿⠿⠿⠁⢞⡛⡟⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠥⠼⠭⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠐⠤⠀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠂⠀⠀⠀⠈⠉⠈⠀⢀⠙⣾⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠹⣷⣦⣂⠀⠀⠀⠀⠀⠀⠈⠁⢹⣿⠈⡀
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠓⠀⠁⠀⠀⠀⠀⠀⢉⣯⡼⣧⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⢿⣿⣿
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠋⠀⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢘⡇⠀⢠⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⡀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢸⡇⠀⠀⡂⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣬⢁⠛⢀⠀⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⢈⣷⠀⠀⠀⡀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡎⢠⣏⣀⡀⠀⠀⠀⠀⠞⡿
⠀⠀⠀⠈⢽⢅⠀⠀⠹⢄⠀⠀⠀⢸⡄⠀⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣷⡟⡚⢻⡇⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠷⣄⠀⠘⣧⣆⡀⠀⢘⡆⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣰⠀⠁⠈⠀⠈⣧⠀⠀⣠⣤⡜⠄
⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠙⢷⣦⣅⠛⠛⠛⠋⠀⠀⠀⠀⠀⢀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⠀⠸⣙⣿⠁
⠀⠀⠀⠀⠀⠀⠹⣦⡦⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠴⣁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡀⢑⣿⡟⠀⣄⠒
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡊⠒⢶⣴⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣿⣿⠏⢁⣾⣿⣤⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣶⣽⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⣴⣾⣿⣯⡤⣰⣿⡿⣷⡃⠴⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡓⠒⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡄⠀⢠⣼⣿⣶⣿⣿⣿⣿⣯⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠘⠛⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⣼⠁⢀⢀⣾⣥⠖⠉⠻⣿⣿⣷⣿⣿⣿⣿⣧⣶⣷⢋
⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡿⢀⡐⢃⡾⠋⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠙⢿⣿⡎⡁⡀
⠀⠀⠀⠀⠀⠀⠰⣶⣤⣴⣤⣤⣀⣠⣀⡀⠀⠀⢀⣴⠂⠀⠀⣿⣴⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⢿⣷⣿⣵⡤⣌⠉⠠⠂⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⡿⠿⠟⠓⠲⠖⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣶⣦⣶⡿⠋⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣅⠀⣠⡾⡀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣷⣤⣄⣀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢠⡀⣬⣸⣆⣀⠀⠀⠀⢰⠆⠀⠀⣻⣹⡇⠀⢐⠠⣤⣤⢿⣷⣿⣿⣿⣄⠁⣹⣦⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠁⠛⣀⠻⣽⠀⠰⠀⠀⠈⠀⣸⢃⣿⣿⣄⣤⣶⠒⠻⣾⠟⠉⠁⠀⠉⠛⠉⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣧⡿⠇⠰⣦⣀⣀⣰⣿⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢨⣿⠆⢸⡇⠀⠀⠀⠉⠛⠛⠋⠉⠉⠁⣸⡟⠻⠋⠙⢻⣿⡇
⠀⠀⠀⠀⠀⣤⠀⡿⢃⣠⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⡁⠀⢴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡄⠀⢠⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⢧⠀⢸⡇⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡵⠴⠟⠓⢼⣦⡞⢷⣴⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣼⢹⠀⠀⠀⠀⣠⠖⠛⠁⠀⠴⠦⡄⠀⠈⠀⢸⠻⣎⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣴⣿⠁
⠀⠀⡇⡄⠣⡀⢀⣸⠇⠀⡀⠀⡀⠴⡟⠄⠀⠀⠀⣭⡀⠸⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⣦⣀⣀⣠⡿⠏
⠀⠀⣇⢷⡄⠈⣯⠙⡆⠈⠁⢸⠠⣾⡟⠀⠀⠀⠀⢹⣷⠀⣷⠀⢹⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣿⠛⠛⠉
⠀⢀⣿⣎⣡⠴⠃⠀⠀⠀⠀⢴⡿⠏⠀⠀⠀⠀⠀⢸⣿⠀⠇⠀⠈⡇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠾⣇⡺⠆⠆⢀⣦⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢀⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢠⡇⢀⡏
⠀⠰⣽⡯⠙⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡼⢁⡞
⠀⠀⠀⠉⠛⠛⠳⠦⢤⣤⣤⣤⣤⠴⠶⠾⠿⣿⣿⣷⣦⣀⣤⣾⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⡼⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠛⠿⣿⠁⠀⠀⠀⠀⠈⢶⣧⣤⣤⣴⠞⠋⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⣦⠶⠚⠓⠶⣄⣸⣿⣿⣿⡄⠀⠀⠀⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠀⣤⡀⢾⠀⠀⠀⠀⠀⣾⣿⣿⣏⡗⠉⠓⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢶⣤⠀⣠⡞⣀⡘⠓⠀⠀⣿⣿⣿⣞⣁⣀⣀⣀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⢿⣿⣽⣿⣞⣿⣧⡼⠛⠻⡿⢿⣿⢿⣿⠷⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠄⠀⠀⠀⢀⡀⢀⣤⡿⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⢀⢊⠀⠀⠀⠀⠀⣷⣦⣝⢶⡀⠈⣷⡀⠄⢀⠂⠀⠀⠀⠀⢁⡀⠠⠀⠀⠀⢴⢠⡄⣿⢀⣶⡶⢠⡄
⠀⠀⢘⠁⠀⠀⢀⣠⡀⡬⠛⣹⣦⢿⣦⣸⣿⣶⡃⠀⠤⣁⣀⣀⣠⠆⢀⣴⢀⣤⣿⣾⣱⣿⣾⣿⣿⣿⣷⠀⠐⠀⠂
⠀⠀⢏⣀⠀⣅⢑⠿⠿⣿⣿⣿⣿⣣⣿⣿⡟⣿⣷⣼⡀⠀⣤⠐⣇⡤⣳⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡤⡲⠄
⠀⠀⠈⠻⣿⣾⣿⣦⣬⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣷⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠈⢹⣿⡏⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠙⢿⣿⣿⣿⣿⡷⠋⠉⠁⠀⠀⠈⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⡃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣿⢿⡿⣿⢁⣀⣤⣄⡀⠀⣠⣿⣿⣁⣀⣤⣤⣤⣄⣀⣸⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠃⡌⠁⠰⡿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠛⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠁⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠢⡤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣧⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⢿⣷⠑⡄⠀⡈⠳⣄
⠀⢀⠁⡌⠀⠀⠀⠀⠘⢰⣿⢳⢤⣀⠀⣀⣴⡚⠁⢸⣷⣿⣿⡇⢱⠀⠈⠀⡌⢳⣄⡀
⠀⡜⠀⡃⠀⠀⠀⠀⠐⣿⣿⣄⠀⢹⡿⠡⠀⠎⠀⣼⣿⢿⡿⢁⡿⠀⠀⠀⠈⠀⠻⣏⠓⢤⣤⠤⠤⣄
⢀⡇⠀⡇⠀⠀⠀⠀⠀⠈⠉⢿⣶⡟⠁⠀⠀⢶⣿⡟⠀⢈⠟⣾⠁⠀⠀⠀⠀⠀⢀⠈⠳⣄⠀⠀⠀⠀⠙⠶⣴⠢⡀
⢸⢁⠀⣇⠀⠀⠀⢠⠁⠀⠀⢘⡏⠀⠁⠀⠀⢊⢩⣷⠀⠀⠈⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠨⡑⢽⣄
⢸⠈⠀⠸⡄⠀⠀⢸⠀⡄⠀⣼⠀⠀⠀⠀⢰⠋⠁⠀⠁⠉⣺⣏⢧⣱⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠀⠈⢳⣄
⠸⡇⠀⠀⠙⣄⠀⢸⣇⠈⠢⣿⣄⠀⠀⠀⠀⠀⠂⠀⣤⠈⠈⠃⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣦⣍⢳
⠀⢷⠀⠀⠀⠈⠢⣘⣿⡆⠀⠀⣿⡇⠀⢀⠀⠀⠠⡀⠃⠀⠀⠸⠐⢇⠀⢧⣰⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸
⠀⠘⣆⠄⠀⠀⠀⠈⠙⠳⣦⣴⣣⠇⠀⢣⣠⣄⣿⠁⠀⠀⠀⠀⣤⣾⠀⢸⡿⢀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠹⣎⢄⠀⠀⠀⠀⠀⠀⢽⠃⠀⠀⠀⠛⠻⠏⠀⠀⠀⠀⢠⣽⡇⠀⢸⣧⠎⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠘⢦⡀⡀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣠⡞⠁⡀⠀⠀⠓⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⢱
⠀⠀⠀⠀⠈⢻⣮⣦⣂⣠⡞⡋⠚⠀⠀⠀⠀⠀⡄⠀⠀⠀⣰⣿⡏⣰⡟⢠⠀⠀⠀⠀⡀⢦⡀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣄⠁⢸
⠀⠀⠀⠀⠀⠸⠛⠟⠛⠁⣴⡌⡆⢀⢤⡀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⢰⠃⡠⢀⢀⠅⠒⠀⠹⣧⠀⠀⡼⠀⠀⢘⣰⣿⡜⠀⢸
⠀⠀⠀⠀⠀⠘⡆⠋⠀⠘⠣⠆⣣⣍⡤⠂⠄⣠⣾⣿⣿⣿⣿⣿⣯⢹⡏⢠⢁⡾⠁⠀⠀⠀⡐⣹⠀⢸⣇⡠⣠⣿⣿⠟⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠘⣆⡰⣶⡶⢏⣜⡴⠷⠒⣿⣿⣿⣿⣿⣿⡻⡍⠉⠻⣷⡿⢋⡴⠋⠀⠀⠀⡓⣯⣿⣿⣿⣵⢟⣿⠟⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠸⣿⣿⠟⠙⢿⣿⣶⣤⣴⢿⣿⣮⡀⠀⠀⠀⠀⢦⣿⣿⣯⣽⡾⣿⣿⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⢹⡿⡟⠛⠛⠉⢻⡗⠀⠀⠀⡄⣸⣿⣿⣇⠀⠀⢹⣯⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠐⢼⡿⠀⠀⠀⠀⢸⡇⠀⠐⡄⣿⣿⠟⠻⣿⡇⠀⢸⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠌⢗⠀⠀⠀⠀⢸⣆⠀⠀⢠⣽⣿⠀⣰⡏⠀⠀⢸⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠀⢸⣾⠆⠀⠀⠀⢸⡗⠀⠀⠉⣿⠃⠀⢾⡀⠀⠀⣸⡟⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠥⠀⡿⣻⠀⠀⠀⠀⢘⡟⠀⠀⠂⣧⠤⠦⠾⠁⠀⣴⢯⡄⠀⣠⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠃⢀⡤⢀⠀⢸⡇⠀⠀⣠⢇⡄⣀⠀⣤⡈⣣⠀⠀⠀⠀⠂⠼⠅⡀⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠬⠇⠀⠰⠟⠀⠀⠀⠃⠠⣏⡀⣀⡿⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠸⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠈⠉⠀⠘⣿⣷⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣄⣤⡀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⢠⣔⣬⣭⣤⣴⣯⣽⠶⣄⢿⣿⣿⡟⠁⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⢻⠛⠋⠉⠉⠀⠐⠛⠛⠛⠛⠟⠿⣿⠁⣴⣿⣿⣿⣿⡷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢣⣯⢠⣀⣀⠈⠙⠛⢿⡟⠃⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣷⣾⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣿⣯⣤⣤⣶⣿⣥⣦⣤⠀⠀⠀⢸⡏⠀⢻⣿⣿⣿⣿⣿⣿⣿⣝⢿⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢻⣿⣿⣿⣧⣸⣿⣿⣿⡿⠋⠀⠀⠀⡜⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠿⣿⣿⣿⣿⡟⠉⣉⣉⠉⠀⠀⠀⠀⢰⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣆
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠀⠛⠃⠘⢻⣯⣀⣀⠀⠀⡀⠈⠀⠀⠀⣸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⢘⣿⡇⢻⣦⡀⢀⡼⡟⠉⠀⠀⠀⠀⠀⠀⠙⠛⠿⡿⠟⠀⠀⠀⡀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⢻⠇⠈⣻⡇⠈⠁⠰⠶⢤⣾⣤⣷⣤⣄⡀⠀⢠⠀⠀⠀⠀⠀⠀⢠⣿⡆⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡜⢺⣇⣠⡣⡀⠀⠀⠀⢺⣿⣿⣿⣿⢫⣽⠇⠀⢸⣧⠀⠀⠀⠀⠀⢸⣿⣷⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⢰⣿⣿⣿⣧⣄⠀⠀⡄⢹⣿⣿⠟⠐⠋⣀⣠⣾⣿⣿⣦⣤⣤⣀⣼⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣧⣴⣿⡈⠛⡏⢄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣏⣵⣤⣶⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣹⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⠃⠀⠀⠀⠀⢿⣯⣽⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣻⣿⡇⠀⢰⣿⣻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠉⠉⠉⠁⠀⠀⠘⠛⠛⠛⠛⠿⠿⠻⠿⠛⠃⠀⠀⠀⠀⠙⠟⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⣤⣶⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡏⠀⠀⣸⣿⣿⣿⣿⣿⣧⣿⣯⣽⣿⣶⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠁⠠⣿⣤⣆⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⡇⠀⠀⠀⠀⠀⠀⢰⠀⣿
⠀⠀⠀⠀⠀⢀⠎⣴⣿⣿⣿⡷⠀⠀⠀⠘⣭⣿⣿⣿⣿⣿⣿⡏⣰⣏⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⠏⣴⣿⣷⠀⠀⠀⠀⠀⢠⡇⠀⣿
⠀⠀⠀⠀⠀⣼⢀⣿⣿⡿⠀⢁⠂⣸⠂⠀⢹⡧⣩⣽⣿⡿⠋⣴⣿⣿⡿⠛⠛⢨⣽⠟⣘⣿⡿⢥⣡⣾⠳⣿⣿⡆⠀⠀⠀⢀⣾⠁⢸⣿
⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⣰⣿⣿⣶⣀⠻⣿⡿⠿⠋⢰⣾⣿⣿⡟⠁⠀⠾⢿⢷⣶⣿⣟⣤⣾⣿⠇⠀⢈⣿⣿⡄⠀⣠⣾⠏⠀⣾⡿
⠀⠀⠀⠀⠈⠃⣸⣿⠏⢀⣼⢇⣿⣿⡟⠉⠀⠁⢠⣶⠞⢻⣿⠟⠁⠀⠀⠀⠀⢠⣬⣿⣿⣟⡛⠋⠀⠀⢀⣾⣿⣿⢿⣶⣿⠏⢀⡟⣿⡇
⠀⠀⠀⠀⠀⠀⢹⡿⠋⣠⣿⣿⣿⡿⠁⠀⣠⣀⣿⣧⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣷⣶⣿⠏⢸⣿⠟⠛⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣷⢀⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⠁⠀⠀⢒⠶⣶⠀⠻⣶⣶⣴⣶⡄⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣰⣿⣿⣿⡛⣿⣿⡇⠀⢠⣾⣿⣿⣿⣶⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠃⣿⣿⣧⣀⢠⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣇⣠⣾⣯⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣏⣿⣿⣿⣿⣿⣿⠘⠿⠿⣿⢁⡏⠿⣿⣿⡏⠻⣿⣿⣯⣿⣿⣿⣿⣿⠿⡏⢁⣼⣿⣿⣿⣿⠉⠛⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣦⠀⢠⠛⣿⣿⡄⢸⣿⣿⣄⡿⣿⣿⣿⣿⣟⣿⡿⢁⠔⠛⠋⣿⣿⣿⣿⠃⣀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡆⣿⣿⣿⣿⣿⣿⣿⣧⡘⣷⣿⣿⣷⣾⣷⣜⢿⡷⣞⣿⣿⡿⠛⠏⣰⣇⣤⠒⠀⣉⠉⢸⣿⣼⣿⣯⢹⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣶⣿⡟⣁⣦⡀⠁⠛⢣⠀⠛⠁⢀⣤⣿⣿⣿⣿⡞⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡋⠁⠀⣡⣸⣶⢀⣾⣿⣿⣿⣿⢻⣿⣿⢙⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣼⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣯⣿⣿⣿⢿⣿⢲⣆⣼⣿⣿⣿⣿⣉⡹⠿⡿⠟⠘⣿⡟⣘⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠙⢺⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣷⣯⡿⠿⠿⣿⣿⣿⡿⣿⣿⣶⣦⣆⣼⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⢠⡼⢤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣤⣬⣽⣯⣿⠿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠛⠛⠛⠻⠟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡄⠀⠀⠀⠔⠀⠒⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠼⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸
⠀⠀⠂⠀⠠⡀⠀⢠⠀⠀⠐⠀⠀⡀⢘⠆⠀⠀⠀⠀⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢸
⠀⠀⠘⡄⠀⠀⠁⠠⠓⠐⠁⠀⠈⢴⡾⠀⠀⠃⠀⠀⡇⠘⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠐⡄⠀⠀⠀⡇⠀⠀⠀⠈⠉⠀⠀⠀⡇⢠⠜⠁⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠈⠦⠤⠔⡰⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠃⠀⠀⠀⠀⠀⠀⣀⣠⡔⠋⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠀⠀⢀⣄⣴⡣⢀⠎⠀⠑⠢⣀⠀⢉⣠⠀⠀⠀⠀⠀⠀⢀⣆⣀⣀⣀⣀⡤⢴⠚⠉⠁⠈⠀⢱⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠰⣀⠐⠀⠀⠀⠁⢀⠴⠛⠂⠀⠒⠁⠀⠈⠂⠀⠀⠉⠉⠀⠁⢧⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣸⠀⢸⠆⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡇⠀⠈⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⡀⠂⢄⡄⠀⠀⡄⠀⠐⠀⠘⠄⠀⠀⠀⠀⠀⠀⠐⠀⠨⠀⠼⠲⠂⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠒⠊⠀⠀⠀⠠⠂⠀⠢⡄⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢦
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠒⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⣰⡿⠓⠄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⠀⠀⠀⠀⠉⠀⠂⠀⠋⠈⠉⠀⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢘⣄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠸⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣊⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡆
⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠉⠻⠿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣉⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢻⡄
⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⣿⡀
⠀⠀⢸⡇⢠⡀⠀⠀⣧⠀⣼⣿⡇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢹⡇
⠀⠀⢸⠁⣿⡇⠀⠀⢻⡆⢿⠏⠀⣿⣇⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⢠⡇⠀⣼⣿⡇⠀⠀⠀⢸⡇
⠀⠀⢸⢸⣿⣇⠀⠀⢸⣿⡈⠇⠀⣿⣿⣦⡴⠀⠀⠀⢰⣤⡴⠀⠀⠀⠀⣸⠁⢠⣿⣿⣧⡀⠀⠀⢸⡇
⠀⠀⠸⣞⣿⣿⡀⠀⠀⢿⣷⡀⡀⠀⠉⠁⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⢠⡏⠀⣾⣿⣿⣿⣿⠀⠀⣸⡇
⠀⠀⠀⢻⣿⣿⣇⠀⠀⠘⣿⣿⣿⣦⣀⣷⠀⠀⠀⠀⠀⠈⢉⣤⣦⠀⣾⣤⣰⣿⣿⣿⣿⣿⣷⣴⣿
⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⢻⣿⣿⣿⣿⠏⢀⠀⠀⠀⠀⠀⠈⢻⣿⣴⣿⣿⣿⣿⣟⣛⣛⣛⣋⣁⣽
⠀⠀⠀⠀⠈⢿⣿⣿⣦⣾⠐⢿⣿⣯⣵⠖⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠐⠒⠖⠒⠀⠀⠀⠐⢋⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣤⣤⣤⣴⣾⣤⠴⠛⢁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣆
⡦⡀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠟⠛⠛⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣷⡈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛
⣿⣿⣦⣴⣣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣻⣟⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢹⢿⣷⡄⢀⣄⠀⢈⣢⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢀⠸⣿⣿⣯⣉⣥⡤⠄⠀⠀⣀⣾⡿
⠀⠀⠑⠀⠀⠀⠀⠀⡟⠀⢰⣧⣿⣿⣀⠏⠀⢰⢺⣷⣚⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⠋⣾⣿⡟⢀⡔⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠞⠳⡿⣧⣿⣤⣾⣿⡷⠋⣁⠹⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣴⡏⢣⠠⡀⢴⣿⡟⠉⠙⢛⣅⡀⠀⠀⢨⡇⠀⠀⠀⠀⣴⠏⠁⢀⡖⢩⣾⡟
⠀⠀⠀⠀⠀⠀⢸⣿⣷⠈⣇⠛⣾⣿⣧⣠⣇⡀⠀⠐⠂⠀⠿⣀⠀⠀⣀⣴⣃⣰⠀⠊⣰⣿⡿
⢠⠀⠀⠀⠀⠀⢹⣿⣿⣦⣼⡆⠘⣿⣿⡿⠃⠀⢀⢻⣧⠈⠰⣝⡛⡿⠋⠙⠁⡀⢠⣤⣿⡿⠁
⢘⠀⠀⠀⠀⠀⢿⣿⣿⣿⣻⣿⣤⢸⣿⣷⠀⠀⢞⡋⠉⢥⡂⠀⢹⡄⠀⠀⡦⣾⣾⣿⠟
⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡍⠋⢀⠈⠀⠀⠙⣴⣿⣿⣿⠟⠁
⠛⠋⠉⠉⠁⣉⣹⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠿⣿⣧⣶⣀⣰⡆⠀⠲⣾⣿⣿⣧
⣶⣶⣶⣾⣬⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠿⡙⢿⢇⣴⣤⣿⣿⠁
⡯⠀⡉⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠁
⣿⡟⡱⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⣼⠙⣿⠟⠛⠳⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠛⠉⠉⠉⠛⠛⠒⠒⠒⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣀⣠⣴⣾⡇⠀⢸⠀⡀⠀⠀⠀⢶⣶⠶⠋⠉⠓⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⣤⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠹⡴⢋⠀⡀⠀⢠⡀⡇⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠳⣄⢢⡀⠙⢿⡄⠀⠀⠙⢦
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠇⠀⠀⠘⠀⠀⠀⠸⠰⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠨⡣⢱⡀⣿⣿⣆⠀⠀⠈⢳⡀
⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠈⢂⡈⠐⠀⡀⢀⡇⡰⠁⠀⠀⠀⠀⠀⣿⣷⡀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠑⠠⣇⣿⣿⣿⠀⠀⠀⠈⣿⡄
⠀⣿⢰⡀⠀⠀⢠⣀⠀⠀⣼⣿⣿⡟⠀⠀⠈⠢⠸⣿⡘⠀⡇⠀⠀⠀⠀⠀⠀⠸⣿⣧⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿
⠀⢻⣇⠳⡀⠀⢸⡌⠙⠛⢙⣿⠋⠀⠀⠀⠀⠀⠀⢻⣷⣤⣿⣦⣀⠀⠀⢀⣤⡀⢿⣿⡆⣿⣿⣆⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⢻⣿⣄⣠⣴⣿⡇⡿
⠀⠘⣿⣦⠈⠓⠺⢿⣦⣤⣾⡇⠀⢾⠆⠀⠃⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⢸⣧
⠀⠀⠈⢿⣷⣄⠀⢈⡷⣿⣿⠀⠠⠠⠠⠂⠀⠀⠀⣼⣿⣿⣿⣦⣍⣛⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣄⣨⣿⣿⣿⠈⢿⣧
⠀⠀⠀⠈⢿⣿⣷⢞⣽⣷⠛⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⢿⣯⣶⣭⣭⣽⣿⣿⣽⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙
⠀⠀⠀⠀⠀⠙⣿⢿⣿⠃⣀⠀⣀⠠⢀⣰⠖⠛⠛⠋⠙⢿⣿⣝⣿⣿⣿⣿⣿⡿⣿⢣⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⢻⣿⣿⣿⡿⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠛⢀⠵⠚⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢻⣿⣿⣿⣷⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⣿⢿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠼⠿⠟⠛⠁⠲⢅⡨⣏⡹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠚⠦⠞⠛

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢠⡀⠀⢀⣀⡤⠶⠖⠓⠂⠀⠴⠖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⣾⣧⠘⢷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠤⠄⠀⡰⠅⠀⠈⠉⠁
⠀⠈⣇⠀⠀⠀⠀⠆⠀⠀⠀⡀⠊⠀⠧⠶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⢧⠄⠀⢀⠶⠀⠀⠈⠀⠀⠀⠀⠀⠁⠰
⠀⠀⠀⠀⢲⣷⣏⠀⠀⢤⣴⡷⠀⠀⠀⠀⠀⢐⡦⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢸⣿⣿⢙⣇⡀⠀⠁⠀⠀⠀⠀⢀⣼⣿⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠘⠿⠿⣿⣿⣷⣆⣴⣶⣾⡶⠖⠿⣿⣵⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⡀⠀⠀⠂⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠀⠀⠀⠈⢿⣿⡿⣆⠈⣀⠀⠃⠀⠀⠀⠀⠈⡆⣿⡄⡆⠅⠇⡀⠀⠀⠁⠀⢀⣾⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣌⢢⡀⠙⠓⠄⠀⠀⠀⣴⣷⣿⣿⣏⣡⣈⠁⠀⢀⣤⣼⣿⡟⡼⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⢧⣸⡀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣔⣶⣿⣿⣿⣿⣀⠂⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡋⢹⣷⡀⠀⠀⠙⠛⠛⠛⠛⠉⠁⢸⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⡩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⡙⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣶⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⡵⡎⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣇⠀⠀⠀⢰⠆⠀⢾⣿⣿⡇⣹⣟⠀⠀⠀⠀⠀⠖⠀⠀⠀⢀⣼⣿⡿⣅⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⠟⠲⣾⣄⡄⠀⠀⠀⠀⠀⠀⠿⠿⠧⠤⠘⠻⠇⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠛⠋⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⣀⣠⣤⣀⡀
⠀⠀⠀⠀⡠⢃⠇⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⡌⢫⡀⠀⠈⠙⠳⣄
⠀⠀⠀⡰⠁⡘⠀⠀⠀⠀⠀⠀⡜⠀⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⢡⡿⢛⣿⣿⡀⢣⡀⠀⠀⠢⡘⢷⣄
⠀⠀⢠⠁⢰⠃⠀⠀⠀⠀⠀⢰⠃⣼⣿⡏⣷⣤⣀⠀⠀⢀⣴⣞⠛⠂⠀⢸⣷⣿⣿⣿⡇⠈⡇⠀⠀⠀⠈⠀⡹⣷⣄
⠀⠀⡏⠀⣼⠀⠀⠀⠀⠀⠀⠘⣤⣿⣿⣇⠉⠀⢙⣷⣾⠏⠀⠬⡳⠄⠀⣼⣜⣿⣿⣿⠇⢰⡇⠀⠀⠀⠀⠀⠙⣞⣿⣿⠲⣄⡀
⠀⢸⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⡠⣠⣿⠑⠉⠙⠢⣘⣤⣾⣿⠛⠞⣿⣧⢰⡿⠁⠀⠀⠀⠀⠀⠀⠈⠈⠻⣦⡈⠙⠦
⠀⣾⢰⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⣿⣿⡿⣹⢠⠀⠀⠐⢿⣿⣿⠛⠀⡀⣼⢋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠻⣆
⠀⡿⢸⠀⢸⠀⠀⠀⠀⠀⠀⡉⠁⠀⠀⠀⢸⠏⠘⠉⠁⠀⠀⠀⢊⠃⡑⣦⠠⠤⠄⡟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣧⢸⠀⠈⣇⠀⠀⠀⠀⢰⡇⢇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣐⡮⠒⠉⠀⠪⠳⢐⣶⣿⢻⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⣿⢸⠀⠀⠸⣆⠀⠀⠀⢸⣇⠘⢆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢀⡤⣾⣧⢮⢻⣸
⠀⢻⡀⠀⠀⠀⠘⣆⠀⠀⢸⣿⡄⠈⠳⢼⣷⣄⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⣾⠸⠀⠀⠉⠸⠈⡇
⠀⢸⡇⠀⠀⠀⠀⠈⠳⣄⠈⣿⡷⡀⠀⠀⠈⣏⣶⠄⠀⠀⠀⠀⠀⠁⡆⠀⠜⠀⠀⠀⠰⣃⢸⡇
⠀⠀⢳⡐⡀⠀⠀⠀⠀⠈⠳⢿⣿⣕⡀⠀⢀⠏⡟⠀⢠⢰⠈⠀⠺⢠⡧⠀⠁⠀⠀⠀⠀⢀⢀⣸⠀⠀⣠
⠀⠀⠈⣧⠱⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣯⣴⠃⠀⠠⢸⢰⣿⣴⣼⡇⠀⠀⠀⠀⠀⠀⢸⣾⡿⠀⢰⡏
⠀⠀⠀⠘⣧⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⠃⠀⠀⠀⠔⠹⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⡾⣼⠁⠀⠈⠀⡜
⠀⠀⠀⠀⠘⢷⡌⢆⠀⠀⠀⠀⠀⠀⠀⢸⠏⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡏⠀⠀⢨⣰⠃
⠀⠀⠀⠀⠀⠈⠻⣦⡑⣕⢄⠀⣀⠈⢂⣿⡢⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⢱⠇⢠⣿⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣳⣬⣁⣠⠟⣓⡈⠉⠆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣼⠔⡡⠛⢠⡿⢁⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠿⠿⠋⠑⢈⣤⢹⡆⠀⠀⡄⠀⠠⠆⠀⠁⠀⠀⢐⣠⠞⠉⠉⠀⠔⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠐⣤⠆⠀⣰⡿⢝⢸⡃⢰⡋⠒⡣⠀⡀⠀⣀⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⣁⠀⠀⠁⠴⠋⣠⢖⣖⡼⠏⠠⠊⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⡶⣷⣾⠿⢣⣞⣥⠾⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠙⠒⠚⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣰⣏⣭⣾⣿⣿⣉⡻⣿⣿⣿⣿⣿⡿⠘⣿⣿⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠸⣿⣿⣿⣿⣿⣿⣿⡯⠘⠛⠿⠛⠁⠀⠉⠉⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠙⠿⣿⣿⣿⡿⠟⠁⢀⣴⣶⣶⣿⠀⢠⣴⣇⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⠟⠀⠀⠿⠟⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⡀⢢⣄⣀⣀⣘⠻⠿⠿⠿⢛⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣄⣠⣄⠙⢻⣿⠿⠏⠁⠀⠀⠩⠞⠀⠀⠀⢈⡇⠒⣲⠂
⠀⠀⠀⠀⠀⠀⢀⣼⡌⠛⠃⠘⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⡲⠇
⠀⠀⠀⠀⠠⣶⠟⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰⠟⢰⠉⢆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠤⢤⣤⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⡩⠭⠿⠖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠠⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣠⠖⠁⢐⠁⠀⠀⠣⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠠⢊⡠⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠱⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠒⠤⠀⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣷⡀⢂⠀⠀⠀⠈⠀⠀⠀⢀⠘⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣷⣱⡀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠀⡁
⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠇⠀⠉⠈⠀⠀⠀⠀⢉⣽⡸⣧⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⢿⣺⣟
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠋
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⠇⠃⠈⠑⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡍⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⢸⡇⠀⠀⡄⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣜⢁⠛⢀⠀⠀⠀⠀⠀⠀⢺⡆
⠀⠀⠀⢘⣷⠀⠀⠐⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡎⢁⢞⣀⡀⠀⠀⠀⠀⠞⡯
⠀⠀⠀⠀⣽⠄⠀⠀⠹⣄⠀⠀⠀⢸⡄⠀⠀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣷⡝⡚⢯⡇⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠷⡄⠀⠈⣯⣄⠀⠀⢨⡆⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠠⠁⠘⣧⠀⠀⣀⣤⡼⠂
⠀⠀⠀⠀⠀⠻⣆⢀⠀⠀⠀⠈⢳⣶⣁⠛⠛⠞⠋⠀⠀⠀⠀⠈⠀⣤⣤⣠⡀⠀⠀⠀⠁⠀⠀⠀⠀⣶⣿⠀⠰⡝⣿⠁
⠀⠀⠀⠀⠀⠀⠻⣇⡤⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⡃⠀⠀⠀⠀⠀⠀⠐⢠⣿⣏⢀⢁⣿⡿⠀⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠹⣷⠞⠶⢶⣴⣆⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⣿⣿⡟⠁⣾⣿⣡⠊⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⠁⠀⠀⠀⢀⣡⣾⣿⣯⣠⢰⣿⣿⣧⡇⠴⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡐⠖⠚⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⡄⠀⢠⣠⣿⣷⢟⠁⢉⣱⣬⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⠄⣾⣦⠔⠛⠿⣿⣷⣿⣾⣿⣿⣿⣧⣴⣧⢞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢁⡐⢠⡼⠋⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠙⢿⣿⡎⠁⡀
⠀⠀⠀⠀⠀⠀⠠⣴⣄⣤⣤⣤⣄⣠⣀⠀⠀⠀⠀⣴⠂⠀⠈⢳⣴⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠻⠿⠿⠿⢿⣿⣿⣤⣴⣈⠋⠠⠄⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠓⠶⠖⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⣦⡀⠀⠀⠀⠀⠀⣠⣿⢠⣿⣇⠹⣿⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣾⣿⣷⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠙⢿⣿⣿⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣌⡙⠛⢛⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠰⠁⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠙⠀⠻⣿⡷⢶⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⣈⡰⠀⠀⠎⣹⡀⠟⠹⠄⠨⠛⠁⠀⡴⠁
⠀⠀⠀⠀⢠⠇⠀⡜⢋⠈⢉⡻⣿⡇⠀⠀⠀⠀⣤⣶⣾⣿⣷⡇⠀⠀⢀⣠⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠁⢀⣼⣿⣿⠀⠀⣨⣿⣀⣀⣐⣀⡼⢿⣿⣿⣿⣿⣷⣤⣄⣼⠟⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡖⠒⠐⠂⠐⠂⠐⠒⠀⠉
⠀⠀⠀⠄⠀⣼⣿⣿⣿⠀⡞⣹⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢤⣀⠀⣿⠀⠠⡀⠀⣠⠔⢊⣁⣠⠔⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣮⣙⣩⣤⣼⣿⠋⠉⢁⣤⣮⣙⣿⣿⣿⡟⠀⠀⠀⠀⠀⣏⠀⠑⢄⠁⠛⠀⢻
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⠿⣯⡀⠀⣴⣿⣿⣿⣻⣿⣿⢿⣿⡀⢠⠀⠀⠀⡇⠀⠀⠀⠑⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⣀⠀⠀⠐⢣⢰⣿⣿⣿⣯⠗⠘⢿⣿⣸⣷⡈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⣿⣿⣯⠏⠀⠀⠨⣿⣷⣿⣷⣤⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣸⣿⣿⣿⣧⣁⣀⣀⢿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣀⠆⠈⠙⠛⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠘⠊⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢀⠁⠀⠀⠀⠀⠀⢀⣰⣤⣭⣭⣿⣿⣿⣷⣄⣀⠀⠀⠀⠰⣿⣿⣦⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⡘⠀⠀⠀⠒⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⢠⡀⠙⠃⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢲⠃⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠂⠢⠂⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠠⠀⠀⠀⠄⠃
⠀⠀⠀⠀⠂⠀⠀⡀⠀⠤⠰⢠⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡏⢥⡉⠻⠀⠀⠀⠀⠀⠀⠈⢁⣠⠆⠛⠀⠀⠒⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠺⠞⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣷⠘⠷⣶⣾⠀⠋⠿⢿⠀⠀⣼⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡌⠈⣿⠿⣿⣿⣌⢢⡌⡙⠛⠆⠀⡀⣠⢾⢛⣿⣿⠿⠃⠀⠀⠀⠀⠀⢀⠀⠈⠂
⠀⠠⠀⠀⠀⠀⠀⡄⠀⡐⢲⠃⡄⠀⠀⠀⠈⢀⣴⣶⠀⢈⣿⣏⡀⠃⠉⢮⣄⠬⠯⣕⣺⣿⣿⠂⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢂⡄⠀⠀⠀⠀⣸⣿⣿⠀⣏⡗⣿⣿⣿⣿⢿⣿⣧⡀⠈⠓⠓⠁⠀⡅⠀⠀⢀⠀⠀⠄⠀⢀⠀⠀⠠⢤⡀⠀⢀
⠀⠀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠈⠀⡄⠀⠀⠀⠹⣿⣿⣷⣿⣶⡾⠟⢉⣤⣶⣾⣧⣴⣷⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠇⠐⠋⠀⠐⠂
⠀⠀⢀⠀⠁⣾⣿⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠻⠀⣾⣿⣿⣯⠹⣿⣿⣆⠀⠀⢸⡇
⠠⢊⠀⠀⠀⠀⠈⠙⠻⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⢹⣷⣿⣧⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠴⠀⠀⠀⠀⠀⢐⡲⢄⡈⠣⡀⠈⠙⠋⠂⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⣤⣤⣜⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡔⠂
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘

⠀⡄⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠾⠁⠀⢨⠇⣄⠀⠐⠿⠃⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠒⠀⠀⠈⠩⢉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣰⢳⣶⠾⡏⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠁⠀⠓⠤⠔⠁
⠀⢀⠀⠀⠀⠀⠀⢹⣟⠸⠄⠁⠋⠹⠀⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠈⠆
⠀⠀⠵⢤⣀⣀⣀⣈⣉⠀⢈⡀⠀⠁⢀⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠘⠻⣾⣷⣴⡁⠂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠐⠎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠶⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠻⠷⠾⠓⠶⣌⣻⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⡄⠀⠀⣀⠀⢠⠀⠀⢀⠀⢰⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢰⣆⣾⠁⠊⢀⠙⠂⠀⠴⠷⢯⠐⠃⠀⣸⠟⠀⠀⢀⡀⢋⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠐⠀⠳⡀⠀⠈⠿⣿⡄⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠛⠀⠀⣴⠟⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⣿⣧⣀⠀⠘⣇⠀⠀⣾⣿⣿⣿⠀⢀⡰⠀⠯⠀⢀⣼⣿⠂⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠙⢿⣿⡶⠚⡉⢱⢦⣈⣁⠀⣠⣴⣎⠁⠀⠀⠰⣾⡿⠈⢀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠀⢨⣅⣸⣿⣧⢈⣁⣀⢶⣆⣹⣿⣀⣠⣦⣶⡁⠐⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣾⣿⣿⢿⣿⣻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠓⠒⠀⠀⠀⡛⠛⢾⣿⡏⢸⣿⣹⣿⠷⠍⠈⠉⠓⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡂⠀⠀⠀⢠⣿⣷⣶⣿⣾⣿⣦⣤⣉⠲⢄⡀⣀⣀⣤⡤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⣦⣤⣀⣀⣠⡼⠟⠛⠋⠉⠀⠀⢀⣾⣿⣿⣿⣿⣾⡻⣯⣽⡏⣾⣿⢻⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠠⣀⠀⠀⢼⠿⠛⠋⠉⠉⢻⣿⣦⣉⣴⡿⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠗⠀⠈⠉⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣦⡀⠀⠀⠀⠀⠘⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠟⠓⠦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠙⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠑⠂⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣁⠤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣙⣇⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⣯⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠒⠚⠓⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠳⢀⣀⠀⣀⢀⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⠤⠵⣿⠤⠠⣼⣓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⡠⠖⠛⠊⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡄⢠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⢇⡌⢧⠀⠀⠀⠀⠀⡸⣳⠆⢰⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠸⠷⢄
⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⢠⠁⠸⠃⠸⡄⠀⠀⠀⡰⠁⠛⠀⠀⢆⡱⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣷⠛⠀⠀⢠⡏⠀⠀⣠⡄⠘⢄⢀⡼⠁⠀⠀⣀⠀⠘⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠈⢦⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠘⡅⢠⠏⠀⠀⠀⣿⡇⠀⠈⠉⠀⠀⠀⠀⣿⠇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠁⢀⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠙⠏⠀⠆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢀⣤⠤⢠⡇⢀⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣥⠂⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢣⠀⠀⠳⣈⠃⣾⠀⠙⢢⡀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⡐⢀⠀⠀⠀⠀⣰⣠⡇⢀⠞⠀⠒⠢⣶
⠀⠀⠀⠀⠳⣄⠀⠈⠀⠈⠐⣄⠼⣡⢏⠁⣶⡤⠢⣤⢀⡤⠢⡔⢶⡶⣟⣻⠯⡾⢣⡴⠊⠸⠋⠖⠁⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠈⠒⠤⢀⡀⠀⠀⠀⠈⠀⣙⠹⣧⢾⣌⣻⣶⠂⠛⢢⠵⠯⠐⠢⣀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⢀⣀⡤⠶⠦⠈⠙⠛⣉⡰⠖⠋⠁⡴⢡⠶⡼⠃⢹⠣⣤⣿⢸⠀⠀⠀⠈⠉⠶⢦⠴⠆⠀⣀
⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡰⠃⠈⡾⠃⠠⠼⣧⠘⠃⠈⠂⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠈⠉⠒⠦⣄⣀
⠀⠀⠀⠀⠈⠙⠂⠤⢀⣠⡏⠣⣀⠀⢠⠇⢀⡜⠁⠀⠀⠀⢹⡄⠀⠀⢰⠀⠀⠀⢀⡠⠞⣡⣏⠀⣀⣀⣀⠠⠤⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣢⡬⣭⡇⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⠒⠶⢉⠴⢎⠛⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠖⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣌⠳⡄
⠀⠀⠀⠀⠀⠀⢰⡅⠚⠁⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠓⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⣠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠳⠶⣄⣀
⠀⠀⠀⣠⠶⠛⠉⠀⢻⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡷
⠀⣤⠋⠀⠀⠀⠀⠀⢸⡄⠀⡠⠚⠁⠈⢆⠀⠀⠀⠀⣠⠎⠱⣄⠀⠀⠀⣈⠃⠀⠀⠈⠙⠒⠶⠀⠀⠀⢀⡴⠋
⠀⠛⠦⣄⠀⠀⠀⠀⠈⠷⠋⠀⠀⠀⠀⠘⢧⠀⢠⠜⠁⠀⠀⠈⠳⣄⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⡦⠤⣤⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⣤⠒⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣹⠀⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡤⠤⢤⣀
⠀⠀⢀⠂⠄⠀⠀⠀⠀⡐⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣾⣿⣧⠱⡀⠀⠈⠳⣄
⠀⠀⠄⠰⠀⠀⠀⠀⢰⠁⣾⡿⣦⣀⠀⠀⣀⡴⠊⠁⢸⣧⣿⣿⡇⢱⠀⠈⠀⡈⢳⣄
⠀⣘⠀⡇⠀⠀⠀⠀⠘⢼⣿⣇⠁⠈⣷⠞⣁⠨⠁⠀⣼⣿⣿⡿⢃⡾⠀⠀⠀⠙⠀⢻⣿⠲⢄⣀⣀⣀⣀
⢀⡇⠀⡇⠀⠀⠀⠀⠀⠈⠛⢿⣷⣴⠟⠀⠀⠀⣴⣾⡟⠁⢹⡷⣾⠁⠀⠀⠀⠀⠀⠀⠙⠷⣄⠁⠀⠀⠀⠙⠦⣤⡤⡀
⢸⡇⠀⢇⠀⠀⠀⠀⡰⠀⠀⠀⢿⠋⠚⠀⠀⠀⠛⠱⣧⠀⠈⠔⣿⡀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢦⠀⠀⠀⠀⠀⠈⡑⢎⢢⡀
⢸⡿⠀⠸⡀⠀⠀⠀⡇⠄⠀⠀⡇⠀⠀⠀⠀⣰⠏⠚⠉⠒⠒⢴⡟⣇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠈⠂⠉⠻⣄
⢸⡇⠀⠀⠳⡀⠀⠀⣇⠈⢀⣸⣇⠀⠀⠀⠀⠋⠀⠀⠀⡀⠐⠛⠗⠎⡟⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠓⣄
⠀⣧⠀⠀⠀⠙⢄⠀⣿⣆⠀⠉⢹⣦⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⠠⡇⠈⠆⢠⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢸
⠀⢹⡄⠀⠀⠀⠈⠑⠿⣿⣀⠀⣸⢿⠁⠀⠂⢀⠂⣼⠀⠀⠀⠀⠀⠁⣽⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸
⠀⠀⢳⡀⡀⠀⠀⠀⠀⠀⠙⢿⣷⠋⠀⠀⢴⣿⣷⡇⠀⠀⠀⠀⠀⣾⡟⠀⢸⡿⣠⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢳⡔⢄⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢰⣿⡇⠀⣸⡿⠃⠀⠀⢠⡀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠙⣦⡠⡀⣀⡀⢀⣾⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⣶⠏⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠎⢸
⠀⠀⠀⠀⠀⠈⣿⣾⣶⡴⠞⠁⣀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢀⣾⣿⣇⣼⠏⡴⠁⠀⠀⡀⠄⠘⢧⣁⠀⠀⠀⡼⠀⠀⠰⠀⣴⣡⠀⢸
⠀⠀⠀⠀⠀⠠⡋⣉⡉⠀⣴⠿⣸⢀⡄⠣⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⢿⣸⠁⡴⢠⡮⠂⠉⠁⠀⢻⡆⠀⣰⠃⢀⢀⣬⣾⣷⠇⠀⠸
⠀⠀⠀⠀⠀⠀⢷⡨⠀⠀⠉⢊⡠⣶⢰⠋⢐⣨⣾⣿⣿⣿⣿⣿⣿⣿⣸⣇⣰⣣⠞⣁⠀⠀⠀⢀⢠⣇⣄⣿⣤⢎⣾⣿⡟⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡴⠻⣿⣟⣤⡷⠚⠋⠙⣿⣿⣿⣿⣿⣿⣝⠆⠀⠙⣿⣿⢡⡾⠃⠀⠀⠀⢈⢻⣿⣿⣿⣿⢟⣿⣿⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠉⠻⣿⣳⣶⣶⣿⣿⣿⣄⠀⠀⠀⢰⠘⣿⣿⣿⡶⠾⠿⣿⡇⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢹⣟⡏⠛⠋⠁⠹⣿⠀⠀⠀⢰⢰⣿⣿⣿⡄⠀⠀⢿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⣻⡟⠀⠀⠀⠀⢀⡏⠀⠀⢢⢿⣿⡟⠙⢿⣿⠀⠀⣿⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠆⢣⠀⠀⠀⠀⢸⣧⠀⠀⢀⣾⣿⠇⢠⣿⠁⠀⠀⢻⡄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢾⣿⠀⠀⠀⠀⠈⡟⠈⠀⠊⣿⡋⠀⠰⣇⠀⠀⠀⣼⠇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠤⠀⡿⣿⠀⠀⠀⠀⠘⡿⠀⠀⠀⢸⡤⣤⣴⠏⠀⢀⣾⣡⠄⠀⣄⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁⢀⡤⢀⠀⢸⡆⠀⠀⢠⠎⣠⣀⠀⢠⣄⢳⠀⠀⠀⠀⠐⠤⠎⣀⣀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠍⣀⣸⡇⠀⣰⠿⠀⠀⠀⠏⣀⡟⠁⠀⢻⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣀⡤⠴⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⢤⡾⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠎⣠⠀⢰⠉⣆⠐⣆⠀⢠⣀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢺⠇⠀⠇⡀⠘⣆⢸⣷⣀⣿⣦⡀⠀⠀⠀⠀⢸⣇⡧
⠀⠀⠀⠀⠀⠸⡂⠄⣰⢤⡀⠀⠀⠀⠀⠀⠀⢀⡷⢻⠀⢸⡀⠈⠓⠈⠊⠃⠩⢿⣯⢻⡆⠘⢇⠀⢸⣿⡅
⠀⠀⠀⠀⠰⣂⠨⠒⠈⢢⠉⢦⣄⣀⠀⠀⠀⡼⠁⠘⡄⢯⡗⠒⠓⠀⠀⠀⠀⢠⣿⠇⡝⠂⢠⠆⣿⢧⠃
⠀⠀⠀⠀⠠⠎⢉⡅⠀⠈⠂⠀⠀⠈⠉⠑⠚⠷⢶⣮⣥⣈⣥⡀⠀⠀⠀⠀⣀⠈⠉⡐⠀⠀⠀⢠⣿⠘⡇
⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠓⠒⠦⠤⣄⣀⡆⠀⠉⠙⠛⢷⣼⣧⣾⣭⠴⡾⣋⡴⣠⡶⣾⠿⠄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠠⢾⡉⠲⡀⢀⡞⡺⢹⡾⣟⠴⠧⠔⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣰⣗⠉⠁⠀⢑⡊⣰⢣⡟⠀⠘⢦⣰⣿⣋⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠴⠚⢩⡏⠈⠓⠶⢤⠼⠉⠁⣾⠀⠀⠀⠀⠙⢿⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⣠⡡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣆⣀⣠⠾⠋⠳⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠀⠀⠹⣄⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⣤⣮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠎⣿⣿⠿⠤⠤⠤⠖⠚⠛⠙⠓⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢁⡾⠁⠀⣨⣅⡀
⠀⠀⠀⠀⠀⡰⢫⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠸⣻⣄⠴⢿⣿⣿⣿⢿⣦
⠀⠀⠀⠀⡼⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠘⠁⠺⠋
⠀⠀⠀⢰⠃⢸⣿⡄⠀⠀⢀⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢰⣿⡛⠀⡀⣴⡀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⣼⠀⠸⣿⣇⠀⢀⡏⢿⣆⣰⣧⡤⠀⢠⡀⠀⠀⠹⠟⠀⣰⣵⣽⠆⠀⠀⢀⠀⣀⠔⠋
⠀⠀⠀⡇⠀⠀⢻⣿⣆⣸⣇⣿⠟⠘⠿⠧⠴⣿⣗⠰⠀⠀⠄⢴⣿⣿⣿⠀⣠⢞⡵⠊⠁⠀⠀⠀⡀
⠀⠀⠀⢿⠀⠀⠀⢿⣿⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⢃⣾⡵⠃⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠘⣦⡀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⣴⣿⣿⣿⣡⣿⡟⠀⣀⣤⠴⠞⠋
⠀⠀⠀⠀⠘⢿⣦⣴⡾⠃⠐⠂⠀⠀⠀⣀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⣿⣴⠟⠉
⠀⠀⠀⠀⠀⢸⣧⡁⣤⣀⣶⣿⠟⠿⠟⣛⣦⣶⣿⣿⠿⠋⠹⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⠳⠾⣿⣼⣯⣾⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠈⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⢿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠒⠒⠒⠚⠛⣄⢀⣧⣆⡀
⠀⠀⠀⠀⣠⣤⡤⠤⠶⠒⠉⠉⠉⠑⠒⠒⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⢿⠃
⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⣧
⢀⡎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠓⢖⡏⠀⢀⢼
⣼⡀⠀⠀⠰⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠈⠃⠀⠹⣏⣁⠎
⣿⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠀⠀⠀⣠⣄⠀⣀⡼⠻⣿⡆⠀⠀⠀⠀⠀⢨⠇
⢹⣇⠀⠀⠀⠀⣿⣦⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠏⠉⠉⢸⣿⠚⠉⠀⠀⠈⠙⠦⣤⣠⣀⣱⠎
⢸⡜⣆⠀⢀⡴⠿⢿⡟⠻⠿⣶⣶⣶⣤⣤⣤⣄⡤⠾⡄⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠈⠃⣿⠀⢸⣷⠀⠘⡇⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣾⡀⠀⡏
⠀⠀⠸⡇⢸⣿⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⡇
⠀⠀⠀⡝⠀⢣⣙⣄⡈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣁⡤⡬⠦
⣤⣤⣤⣿⣷⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⣠⣤⣠⣠⢰⡄⡤⡄⢠⡄
⠀⠀⠀⠀⢽⠟⢽⠟⠈⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⢟⣿⢟⡾⢒⣛⡟⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠙⣿⡏⢉⠘⠋⢿⣟⣂⣚⣵⠠⠀⠈⣇⠀⠀⠀⠀⠀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠚⡁⢋⣿⡉⠚⠁⠶⠶⣿⣏⣩⠋⠀⠀⠀⠘⢦⡀⠀⢰⡾⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡜⠁⣠⡔⠈⠀⠉⣢⣐⣴⠾⢿⣿⡷⠁⠀⠀⠀⠀⠸⣇⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢧⡘⣏⠀⣠⣀⣶⣿⣿⠋⢠⠞⢉⡔⠀⠀⠀⠀⠀⠀⢏⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣟⢉⡟⠛⠁⣼⠛⡱⡽⠂⠀⣴⡿⠃⠀⠀⠀⠠⣤⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⣼⡏⠈⢥⡴⡾⠉⠖⢁⣶⠇⢰⡿⣿⠇⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠹⢍⢣⣤⣤⣼⡂⢣⣤⠋⠘⢧⠞⢀⡟⠀⠀⢠⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠿⣿⠛⡟⠋⣼⠀⢀⣿⣰⠞⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⠴⠺⢭⡨⠟⠒⠏⢠⢎⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠈⠀⠈⠀⠀⠠⢚⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁


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

⠀⠀⢠⡶⡶⠿⠿⠿⠛⠛⠉⠉⠙⠛⠛⠛⣳⣶⣴⣶⣛⣛⣶⣦⡶⡛⠛⠉⠉⠉⠉⠉⠙⠛⠋⢹⣿⡇
⠀⠀⠈⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠿⠿⠛⣛⡻⣛⠭⠿⠟⠛⠻⢿⡂⠀⠀⠀⠀⠀⠀⠀⠘⣽⠁
⠀⠀⠀⢻⡀⠀⠀⠀⠀⣀⣄⣤⠖⠋⠐⠒⠒⠒⣂⠀⠀⢘⡛⠛⠒⠠⠀⠈⠳⣦⣤⣤⡀⠀⠀⠀⡟
⠀⠀⠀⠈⢧⠀⠀⢠⠾⣿⡿⠃⠀⠀⠀⠠⠂⠀⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠙⣿⣿⣛⡆⠀⢸⠃
⠀⠀⠀⠀⠈⢷⣶⣿⣿⡿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⢻⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⡏
⠀⠀⠀⠀⠀⡠⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠀⠀⠀⠀⢢⠀⠈⠢⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⡎⠀⡀⠐⠀⠀⢠⠀⠘⢡⠀⠀⠀⠀⡌⠡⠀⡀⠀⠀⢁⠀⠀⢠⠈⣷⣤⣀⣀⡄⠀⠀⢀⠼⠁
⠀⠀⠀⠘⢿⣶⣿⣿⠇⠀⡇⠀⠀⡆⠈⢦⠤⢼⣆⡀⠀⢀⢱⡄⠒⠛⢢⡀⢸⠀⠀⢀⠀⢹⣿⣿⠟⠀⢀⡔⠁⣄⠔
⠲⠤⡀⠀⠀⠉⠛⠿⠀⠀⠃⠀⠀⣿⣠⡼⠶⣄⡀⢋⠢⠀⣠⢀⣴⣿⡛⠻⡿⠀⠀⠀⠀⠀⣋⣀⠀⣠⠋⢀⠼⠛⢠
⣴⡀⠀⢀⠀⠀⢚⠟⠀⠆⠀⠀⠀⢉⢿⠀⣾⣿⣿⠀⠀⠀⠀⠸⣿⣿⢟⣰⠃⠀⠀⠦⠈⠂⠈⠂⡴⣡⠄⠁⠀⠀⠊
⣀⠙⠢⣀⠱⣤⠁⠈⢀⠀⠈⠁⠀⠀⡀⠓⠮⠟⠋⠀⠀⠀⠀⠀⠈⠉⠉⢠⠀⠀⡀⠀⠀⠐⡀⣱⣘⡥⠖⠉
⠈⠙⠒⠬⠵⣼⡆⢠⠂⠀⠀⠀⠲⠄⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢘⠀⠀⡀⠀⠈⢋
⠀⠀⠀⠀⠀⠀⠠⠁⡄⠀⠸⡀⠀⣦⠀⢨⣳⣦⣄⠀⠀⠉⠀⠀⣠⣴⣯⡄⠀⡼⠂⡀⠁⠀⢸⠂⠡
⠀⠀⠀⠀⠀⠀⢁⠆⠐⡄⠘⠈⠢⡩⡓⠤⠹⣿⣿⣿⣷⣶⣶⣿⠛⣿⢿⠒⠪⠇⠊⠀⠀⠐⠁⠀⢰
⠒⠲⠤⢤⣀⡀⠘⠀⠀⠀⠀⢁⡀⢠⣭⣤⣶⠃⠈⠻⢿⠿⠛⡁⠀⠀⠀⡿⠳⣦⡄⠀⣀⠀⠀⢀⣀⠤⠴⠒⠚⠉⠉
⠒⢒⣒⣒⣶⡾⠟⠀⠀⠀⠘⠉⠀⠀⡇⠀⠹⡄⠀⠀⣠⣷⣾⣷⡄⠀⢠⠇⠀⠀⡇⠀⠀⠉⢀⠻⢭⣉⡉⠉⠛⢟⠛
⠉⠉⠉⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⠀⠀⡿⣄⣾⠿⣿⢩⣟⢷⣰⠋⠀⠀⠀⡇⠀⠀⠀⠈⡆⠀⠀⠉⠑⠲⠞⠓
⡀⣀⣤⣴⣶⣧⡀⣀⣼⡅⢰⣤⣷⣦⣿⣄⡀⣿⣈⢀⡾⣹⡿⣯⣦⣁⣼⣦⠀⣀⣿⣾⣴⡆⡀⡷⣄⣀⠀⡀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢣⠀⢀⠇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⡄⠀⡜⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠑⠄⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⣶⣶⣶⣶⣶⡄⠛⢿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠛⢠⣶⣶⣶⣶⣦⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠙⠋⠉⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⠉⠙⠋⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣶⣶⣾⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣷⣶⣶⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⣀⣀⣀⣸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⣀⣀⣀⣀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠟⠿⠟⠿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠒⠒⠒⠒⠸⠿⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠿⠇⠒⠒⠒⠒⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠈⠉⠑⠦⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠬⠤⣄⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⣰⡟⠁⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠈⢛⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣼⠟⠀⠀⠀⠀⠀⣅⠀⢀⡐⠁⠀⠀⢀⡌⢇⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡇⣼⠀⠀⣶⠞⢒⡚⠆⡸⠗⣘⡳⢾⡇⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⡶⠑⡏⠰⠛⠛⠀⠀⠚⠉⠃⣸⠗⢄⢹⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠇⡄⠑⠄⠿⡀⢀⠀⠀⠀⠀⢠⢀⡯⠠⠚⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠸⠂⠣⡀⢠⠀⠘⠢⣙⡀⠀⣀⠔⠋⣀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣸⡏⢿⣦⡞⣸⠿⠿⡟⢲⣴⡿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡿⠛⠁⠜⠋⠀⢈⠦⣼⡯⠟⢿⠀⠻⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⡶⠀⠀⠀⣼⠃⠀⢈⣷⡀⠐⠀⣾⠅⠀⠀⢣⡉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣴⠟⠉⢷⡄⣀⣴⠟⢻⡦⡄⣻⠸⠓⢄⣤⡟⢶⣄⡀⠀⣪⡞⠳⣄⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠑⢦⡶⠯⠹⠿⠤⢀⠀⣧⠀⢩⡀⠃⠀⣌⡀⠀⠙⠳⢶⣛⣦⣀⠌⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠙⠳⣄⡀⠀⠀⢰⠏⠐⠲⠀⠀⠀⢸⣇⠀⠀⠀⠀⣠⡶⠋⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡈⠙⢶⣤⡟⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⡴⠞⠁⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣤⣼⢿⣀⠀⠀⠀⠀⠀⠀⣹⠿⠉⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠈⠁⠀⠐⠒⠛⠛⢹⠶⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠚⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⢦⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⢡⡄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠦⡀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣇⠀⠀⠀⠀⠀⢸⠏⠈⣧⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⣠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠢⣀⠀⠀⠀⡜⠀⠀⢹⣧⡂⠀⠠⠄⠀⠀⠀⢀⡠⠴⠖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢰⠃⠀⠀⣾⣿⣬⣷⡶⠤⠀⠀⠀⠘⣧⣆⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠁
⠀⠀⠠⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀
⠀⠂⠀⠀⠀⠨⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣅⡀
⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡠⠀⠀⠀⠆
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡅⠀⠀⠀⠀⠀⣇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠄⡀
⠀⠄⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⢣⡖⠀⠀⠀⠀⠀⠸⡄⠀⡇⡀⠀⠀⠑⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠒
⠀⠀⠁⡄⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠹⡄⢀⣘⣦⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⠀⠀⠆⠀⡔
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⢠⠞⠑⢎⢢⡀⠀⠀⡀⡠⢋⠀⠀⠈⢳⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠀⣟⠀⢀⡈⠀⠁⠀⠀⠆⠀⡗⡤⠀⠀⠈⡇⣔⠀⠀⠀⠀⠀⠀⢠⠀⢠⠜⠀⠓
⠀⠀⡀⠀⠀⠀⠀⡗⠀⢰⠀⡦⣽⠀⠃⣌⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠼⠸⠀⠀⠀⡀⠀⣂
⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠄⡟⣯⠂⠀⠛⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢑⡄⢘⡠⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠴⠀⡰⠂⠀⠀⢽⣧⡄⠀⠀⠀⢠⠄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠐⠂⠀⡠
⠀⠀⠀⠀⢀⡄⠀⠃⠀⠀⠀⠀⠹⡜⠉⢲⢤⢸⡀⠀⠀⣀⣠⣄⠂⣇⠀⠀⠀⠠⣿⠀⢀⣆⠀⡴⠁⠀⠊
⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠐⠀⠀⠂⠀⠭⠈⠋⠙⠏⠀⠀⠘⠃⠒⠚⠁⠀⠀⠁⠂⠉⠀⠐⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠐⠂⢀⡀⠐⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣀⠴⣊⡥
⠀⠀⠰⠀⠀⠀⢠⡔⠀⠀⢀⠀⠀⠀⠀⠐⠀⡀⠀⠙⠸⠸⣣⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠾⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠤⠄⠐⠀⠉⠀⠀⠀⠀⢀⡀⠐⠀⠀⡄⠀⢻⡃⠀⠀⠀⠀⠀⢠
⠀⠀⡄⠀⠀⠀⠠⠀⡢⢄⡀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠈⢯⠂⠁⠂⠀⠀⠁
⠀⠂⢀⠊⠀⠀⠀⢸⣧⠢⢬⣁⣀⢀⣀⡘⢉⣀⠱⠀⠀⠀⠀⠘⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠐⠒⠂⠩⠩⠩⠈⠂⠂⠳⢀⠀⠀⠀⠈⠻⢵⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠫⠯⣌

⠀⠀⠀⣠⠔⠉⠀⠀⠀⣞⣷⣰⡾⢃⣤⡴⠀⠺⢿⡅⣸⠃⣠⣿⢟⣘⡽⠉⠻⣦⡀⠹⣌⠠⡈⠺⣧⢄
⢀⡴⠚⠁⠀⠀⠀⠀⠀⣽⡼⣏⣰⠏⠈⠀⣨⣟⠚⠋⠋⠉⠉⠉⠉⠉⠒⠲⣖⣄⡙⢦⡌⠣⡘⢶⡈⠳⡱⣄⠀⠀⢀
⠟⠀⠀⠀⠀⠀⠀⠀⢠⠙⣿⣿⡃⠀⣠⣾⡿⠟⠁⠀⠀⢀⣀⣠⡴⠿⠿⠷⠶⠝⢻⣮⣿⡧⣈⣤⢽⣄⠈⠪⡁⠀⡿
⣴⣴⠀⠀⠀⠀⠀⢠⣿⣷⣼⡟⢠⣾⡿⠋⠀⣀⡴⠶⣛⣭⠗⠀⡠⣐⣢⣬⣿⣿⣶⣿⠿⡛⠈⡿⣧⠻⣗⠠⠀⠘⠛
⡿⠃⠀⠀⣀⡄⣠⢾⡃⣿⡿⢠⡿⠋⢀⡴⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⡞⠉⠛⠶⣄⣣⣿⡇⢻⡆⠀⢀⣴
⢀⣠⡴⢞⣥⣾⣿⡌⠃⣿⢁⡟⢁⣴⣿⠾⣛⡭⣿⣿⠦⠤⠤⠌⣿⣭⢥⣤⣶⠾⠷⢠⣤⢒⣹⣯⣛⠥⠼⠷⠶⠿⠛
⠯⠷⠾⢯⣷⣾⣿⣿⢦⡹⣜⣠⣿⣛⣥⢶⣾⣟⣻⣷⢶⣶⣶⣿⢿⣷⣶⣶⣖⣢⣿⠘⣡⣿⣿⡿⡋⣿⠷⣶⣶⣶⣶
⢋⣛⣛⣥⣴⣾⠯⢽⣫⣿⣿⠏⢠⠇⣿⠀⠙⣷⣶⡿⢟⣩⠷⠚⠉⢉⣀⣤⣤⣭⢙⣾⢿⡿⢛⡴⠧⣹⣤⣤⣤⢤⠼
⣷⣶⣶⣶⣾⣿⡾⠟⣫⠞⠁⣰⡟⣰⣿⠀⣷⡼⡫⠞⠋⠀⠀⣠⣾⣿⠟⠉⠈⣏⢰⣮⢝⠻⢇⡀⠀⢘⡏⠀⣠⣶⣾
⠛⢣⠿⢟⣛⣥⠶⠋⠁⣠⣾⡟⢠⣿⣿⣼⡏⠀⠀⠀⠀⠀⣾⣿⣟⣁⠀⠠⢄⠻⣆⢿⢸⠀⢸⣿⣿⣿⣶⣾⣿⠿⢟
⠤⠖⠛⠋⠉⠀⢀⣤⣾⡿⠋⠀⣿⣳⡈⡿⠀⠀⠀⠀⠀⠀⠁⢀⡼⣻⠃⠀⢄⠈⢻⣮⠛⡇⢸⡿⢿⣇⡉⣉⣁⣉⣀
⠀⠀⠀⠀⠀⣘⢿⡿⠋⠀⢄⣼⣻⡟⣿⠀⠀⠀⠀⠀⠀⢀⣴⠿⡹⠋⠀⠈⠢⡑⢄⠙⢷⣳⠈⣿⣦⣌⡙⠲⢍⣉⠋
⠀⠈⠋⢍⡒⢤⠀⠀⣠⡄⠀⡐⠛⠛⠛⠀⠀⢀⠀⣀⢴⠛⠀⠀⠀⠀⠀⠀⠀⠈⠪⢷⡈⢳⡵⣿⡄⠙⢿⣦⡂⠀⠉
⠀⣀⣀⠴⢷⣿⠖⠸⣭⣥⣤⣄⡠⠔⣒⡭⠭⠚⢊⡵⠛⠁⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⣿⡄⢳⡈⠙⣆⢀⠙⢿⣀⠂
⠉⠁⠀⠀⢸⠀⠀⠀⠀⡈⣻⡟⠂⣀⡤⠀⠀⠔⠋⠤⠛⠛⠑⢲⡒⠶⠀⢿⣏⠂⠀⠀⠀⠈⣆⢷⠀⠿⢮⣧⡀⠉⠁
⣒⣒⣀⣠⣟⣠⡴⣶⡽⡺⣁⣶⡿⠋⠀⠀⡀⠈⢳⣦⠤⠤⢴⡄⢷⣀⣀⠈⢻⡲⣶⠂⢄⠀⠘⣾⡇⠀⠠⢹⣧⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠠⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀⢀⣦⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⣿⣧⣾⢽⣶⣶⢀⣀⠀⢀⣤⣼⣤⣄⢰⠂⠁⢠⣼⣿⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠋⠀⠀⣀⠘⠛⣯⣿⣿⣿⣟⠛⠛⣿⡿⣿⣿⣿⣿⣟⠔⠉⠈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⡀⢁⡀⠀⠀⡄⢀⡸⠁⠀⠀⠘⣿⣿⡞⠊⣸⣷⠘⠛⠛⠛⢻⣿⣿⡄⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠻⠿⣿⠏⠋⠀⠉⠀⠀⠀⠀⠀⠈⣿⠃⠀⢻⠏⠀⠀⠀⠀⠀⠉⢿⠃⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣦⣯⣄⡀⠀⠀⠀⠀⡀⡂⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣿⠇⠀⠀⠀⢶⣷⠊⠀⠠⣐⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⠝⠄⠀⠀⢀⠄⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⡴⠾⠛⠛⠛⠒⠻⠤⣸⡦⣴⠋⠀⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣥⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡰⠋⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠘⠁
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣇⡆⠀⡆⡟⣄⣆⠀⡀⠀⢄⠀⠀⠀⠀⠀⢸⣿⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⣇⠀⣗⢠⣾⣾⡷⣼⡄⠀⠐⡄⢀⡐⡄⢸⣿⡞⣀⡀⢀⡠⠤⠤⠶⠒⠒⠛⠛⠉⠉⠉⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣛⡿⠀⢿⣸⡇⠀⣿⠠⡆⢸⣰⠁⢹⣼⢫⣋⣾⠖⠋⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⡀⠀⠀⠉⠀⠀⡏⢰⠇⢸⡇⠀⣾⠇⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⡶⠋⠀⠀⢎⠤⠗⡠⠏⣄⢘⡷⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⡦⢶⣶⡿⣻⣟⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⣿⣽⠟⠀⢁⠜⠛⠒⢦⣴⡞⣳⠦⠤⣒⡂⠐⠉⠉⠉⠁⠀⠁⢈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⣴⣿⣿⡁⢠⡟⠀⠀⠀⠐⠧⠭⢥⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣃⡾⣿⣷⣧⡷⣽⡁⠀⠀⠀⠀⣟⣬⡆⠀⠀⠉⠉⠙⠒⠶⣤⢤⣄⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⡸⢱⠃⡿⣿⢡⣏⡝⠻⠖⣶⡁⠘⠀⠉⠛⠲⣄⡀⢀⣀⡡⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⢀⡇⣸⠀⠀⣽⢸⠟⢧⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠉⠻⣧⠠⡤⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⠃⡇⠀⠀⣿⣸⣤⠟⢷⡀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢹⣄⠈⠋⠉
⠀⠀⠀⣀⣀⣤⣤⣿⣤⣀⣀⣠⣿⢙⣇⣀⣀⢿⣸⣇⡴⠚⠉⠉⠙⠛⢷⡀⠀⠀⠀⠀⠀⠸⣯⣄
⠀⢀⡞⠉⠈⢀⡠⠴⠶⠂⠀⠉⠳⣍⡀⠉⢁⣠⠞⠁⠀⠀⠀⠀⠒⠤⣀⠙⠛⢲⡷⣄⢀⡼⠉⢨⣭⡿⠇
⠀⢸⡇⣠⣾⣋⠀⠀⠀⠀⡄⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢄⡀⠀⠘⠛⣆⡟⣷⠊⠛
⠀⢸⣧⠏⠀⠹⡇⠀⢀⠞⠀⠀⢠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⠉⠢⡀⠀⠉⢸⡇
⠀⠀⣿⠀⢀⡤⢿⠀⡞⠀⠀⠀⡜⠀⠀⡀⠸⡀⠄⠀⠀⢀⠀⠀⠱⡀⠀⠀⢀⣴⠶⠺⢦⣄⣼⠃
⠀⠀⠸⣴⠏⠀⠘⣿⠃⠀⠀⢸⠃⠀⠀⠁⠀⣇⠀⠈⠀⠀⠀⠀⠀⢹⡀⢀⡾⠛⠓⠶⣤⣿⡏
⠀⠀⠀⠉⠀⠀⠀⠹⣆⠀⠀⣾⢀⣤⣤⣀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣷⣼⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣸⣯⠞⠋⠉⠙⠲⣽⣄⠀⠀⠀⠀⢀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠸⣿⣿⣿⣿⣿⣷⣦⣄⣤⣄⣤⣶⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠃⠀⠀⢿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⢲⣀⢸⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⢻⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢀⣠⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠈⠋⣀⣴⡶⠾⠛⢿⣿⠟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢦⢀⣀⣤⠴⠶⠛⠉⠁⠀⠀⠀⠀⠘⠃⠀⠈⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠀⠀⠀⠘⢻⣿⣷⠆⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⢇⡤⠀⠀⠀⠈⠑⠋⠀⠀⠀⠐⣿⠟⠃⠀⣠⠂
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢦⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠦⠦⣄⣀⣘⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠶⠻⣿⣎⣷⡄⠹⠷⣤⡀⢀⡄⠴⠋⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣿⡝⢧⠀⠀⢽⣅⣸⣇⠀⠋⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⢷⣶⣾⠛⣿⡏⠀⠈⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡘⣿⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⣉⣠⣽⡿⠏⠀⠀⠀⠀⢠⣀⠀⣠⡄⢀⣴⣿⣿⠃⠈⢰⡿⢿⡀⠈⢠⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⣸⣿⠌⠀⢠⣿⣿⣿⣿⡄⠀⠀⠁⠈⠃⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢰⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⡿⠀⢃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣴⣶⣤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠋⠀⢘⣿⣿⣿⠀⠀⠀⣿⣿⠿⠛⠀⢠⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠁⢀⣴⣿⡿⢟⢻⠀⠀⠀⠀⠀⠀⠀⠾⣆⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣏⡄⠀⠀⠀⠀⠀⠀⣸⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⠄⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⠀⣨⣤⡀⠀⢸⠉⣿⡿⢿⣿⡃⠀⠛⢋⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢫⠀⡀⠉⠻⠶⠀⠰⣿⠄⠀⠈⠙⠿⣦⣽⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⢦⣶⣦⡀⠀⢠⣼⠃⠀⠀⠘⠆⠠⠀⠀⠀⠀⠀⠈⠀⠀⠰⣾⠿⠿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠉⠀⠀⠁⠠⣍⣶⣿⠃⣀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠙⠛⠋⠉⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣡⣴⠍⢿⣶⣶⣄⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡅⠈⠁⠀⠓⠈⠁⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠗⠿⠋⠐⠈⠉⢱⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠿⠋⠉⠻⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠲⠄⠁
⠀⠀⠀⢀⣴⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠑⠒⠛⠛⠁⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢠⣿⣿⡟⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣀⠀⠀⢀⣠⣤⡀⠀⠀⣀⣴⣾⣿⠀⣠⡶⠿⣷⣦⣤⣦⡀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢺⣭⣿⣿⣶⣟⣻⣿⣿⡏⢩⡔⡤⢦⣿⠟⠉⠉⠉⠁⣠⣀⣀⣹⣿⣿⣿⣷⡀⢿⡄
⠀⠀⠀⢠⣶⠟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⡄⣾⣿⣶⣶⣿⣿⣷⣟⣯⣍⡉⣻⣿⣿⣿⣷⣾⣿⡄
⠀⠀⠐⡟⠛⣤⣤⣶⣦⠞⣡⣤⣿⣿⣿⣿⣿⣯⣿⣦⡘⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⢠⣿⣧⣶⣿⡀⢠⣷⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣿⣿⡇⢀
⠀⠀⠙⣿⣿⣿⠁⣼⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧
⠀⠀⠀⠀⠃⣵⢤⡟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⣸
⠀⠀⠀⠀⣶⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⠏⢀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣳⡞
⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇
⣸⣿⣿⡿⣿⣿⣿⣿⠟⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⠏⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢄
⣿⣿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣶⢶⣤⣄⠑
⠹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢹⠆⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡏
⠀⠀⠀⢸⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠁⠀⠉⠉⠙⠏⠻⢿⣿⡛⠿⠿⣿⣿⣿⣷⠟⣯⣻⣿⣿⣿⣿⣿⡿⠿⣿⣇
⠀⠀⠀⢸⡇⠀⠀⠙⠻⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀⢀⣽⣿⣿⡆⣿⢀⡿⠛⠛⠋⠁⠀⠀⠉⠻⣆
⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣸⣿⠁⣿⢣⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⢣
⠀⠀⠀⠈⢿⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠋⠉⢀⣤⠀⠀⠀⠀⠀⠸⠻⢿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⠀⠀⡀
⠀⠀⠀⠀⠀⠑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡶⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠇⠀⠀⣶⣄⠀⠀⠀⢀⣴⣿⣷⣶⣄⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠘⣇⠀⢀⣿⣿⡆⠀⠀⣸⣿⣿⣿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠢⠄⡀⠠⠔⠁⠀⠀⠀⢸⠀⠈⠙⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⠀⠈⣿⡄⢸⣿⣿⣿⡿⢿⣿⣿⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡸⠁⠀⠀⠀⠀⠈⠛⢿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⢀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣾⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⡀⠀⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠴⠊⠀⠀⣤⣶⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠛⠛⠁⠀⢸⡀
⠀⠀⠀⠀⠠⣤⣤⣄⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡂⠤⡀
⠀⠀⠉⠀⠙⠑⠒⠂⠀⠘⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠘⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠑⢄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⢀⡠⠔⠈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠛⠒⠳⠄⠀⠀⠀⠀⡀⠐⠁⠀⠀⠄⠂⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⡠⢶⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠀⠀⢀⠂⠴⠀⢹⠀⠀⠀⠀⡴⢃⡅⢠⠿⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⢠⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡌⠀⡤⢇⢴⠚⢳⠹⠀⠀⣀⠘⠛⢳⣤⡁⠰⠠⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢱⠇⡟⠰⢦⠀⠷⠄⠟⢀⢂⣌⠂⢷⡄⠇⠀⠀⠀⠀⠀⠀⢰⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠈⠋⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠄
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠸⠈⢆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠱⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠆
⠀⠀⠁⠂⠀⠁⣤⠈⠈⣦⠒⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⡁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠁⠐⠙⠀⠂⠈⢧⠀⠀⠀⠀⠀⠀⠀⠣⡀⢸⡄⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠁⠀⠀⠄⠀⠀⠀⠀⠺⠄⠀⠈⢂⠀⢀⡠⠔⠋
⠀⠀⡀⠐⠃⠀⠁⠘⠆⠀⠈⢣⠀⠀⠀⠀⡀⠀⠀⢩⠈⠁⠀⡔⠃⠑⠠⠀⢀⣀⣀⣀⠀⠀⠀⡄⠀⡀⠀⠓⢀⠞⡀⠀⠀⢀⡠⠴⠛⠁
⢒⠰⡀⠠⠀⠀⠀⠀⠂⠀⠀⠀⢳⡀⠀⠊⠀⠀⠀⢸⠀⠀⠀⡅⢀⢀⠔⠈⡍⠉⠀⢀⠀⠠⠸⠛⣸⠇⠻⢀⠁⠞⢠⠴⠚⠉
⢻⡂⠇⠀⠐⠀⠤⠐⠛⠚⠓⠢⠀⠓⠢⠤⣀⣀⡀⢸⠆⠂⢉⠝⠁⡾⠀⠀⡨⠶⡈⠀⠀⠀⠀⢀⠞⠂⠢⠇⡀⡰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠓⠚⠒⠂⠀⠤⠄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡩⠁⠀⢀⠂⠀⠀⢠⣠⢊⣅⠀⠹⡄⠀⢀⡴⠁⢀⠌⠀⠀⣨⢧⡄⠀⠀⠂⠀⠀⠀⢀⡤⠚⠁
⠉⠉⠁⠒⠒⠒⠒⠒⠰⠇⠀⠀⠈⡀⠀⠀⠀⢀⠃⠀⢀⠆⠀⢀⠃⠀⠉⠀⠙⠁⠀⠥⠀⡚⠁⢀⠎⡀⢶⠿⠚⠋⠉⠒⠢⢄⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠒⢤⣀⠊⠀⠀⡌⠀⠀⠸⠀⠀⢠⠀⠀⠀⠀⠀⠰⠀⠀⠎⢠⣷⠋⠀⠀⠈⠀⠠⠀⠀⢣⠀⠀⢀⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢰⣡⠀⠀⢸⠀⠀⠀⠀⠤⢀⣘⡄⠀⠀⡀⢀⠃⠀⠜⠧⣤⡇⠀⠀⠀⢀⢀⠰⠂⠀⠀⡗⠸⠇
⠑⠒⠂⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⢻⠋⠈⠻⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣡⠀⠀⢀⠀⠀⣰⠀⠀⢠⠁⠀⠀⠀⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠀⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠘⡉⠁⠢⣀⠉⠈⡁⣠⡔⣁⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠆⠀⠘⢿⣀⠀⠀⠉⠀⠀⢀
⠀⠀⢀⣀⡤⠴⠒⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⢀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠣⠀⠀⠀⠑⠀⡀⠀⢀⠦⠤⠤⣄⣀
⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢀⡴⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡞⠓⠲⢄⣈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡤⠔⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠔⠒⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⢀⡠⠐⠁⠀⠈⢢⡀
⠤⠤⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠳⡄

⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⢀⣬⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿
⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⣰⣿⣿⠟⠁⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⢰⣿⡿⠃⣠⣾⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁
⣷⡄⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣦⣄⠀⠀⠀⠀⠻⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣷⣤⡀⠀⠀⠙⢿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠈⠛⠿⢷⣿⣿⣿⠿⠟⣫⡿⠋⣰⣿⡇
⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣶⠶⠟⠋⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⣀⣠⣤⣶⣿⣿⠟⠁
⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠑⠆⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠃⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⣰⡟⠀⠀⠀⠀⠆⠀⠀⢠⠀⠀⠀⠈⢏⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠾⠋⡄⠀⣀⣀⣀⣲⡀⢠⣄⣠⣀⣠⢴⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣇⠄⣼⢁⠴⣦⠁⠊⡤⠶⠏⣿⡈⠻⡅⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⡀⢻⠀⠀⠀⠀⠀⠁⠀⢠⡏⢈⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡦⠺⡀⢀⠀⠑⢌⠦⠀⠀⢀⡡⠊⠈⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⢳⣄⡴⢹⣶⣶⡯⣤⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡾⠋⢸⠟⠁⠉⠄⣴⣣⠿⣟⠸⢷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⠎⠀⠀⣰⠇⠐⢘⣶⠈⠀⠀⣾⠀⠀⠑⣍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣴⠋⠹⣦⢀⣠⡞⠻⣦⡄⢺⠹⠳⣀⣴⠿⢦⣀⠀⢘⣴⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠐⣶⡞⠍⠻⠧⠄⠀⣿⠀⠨⡀⠃⠀⣍⠀⠀⠙⠶⠟⡷⣄⡬⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠙⠶⣄⠀⠀⢠⡏⠀⠒⠀⠀⠀⢹⡆⠀⠀⠀⣠⠶⠋⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡈⠛⢶⣟⠀⠀⠀⠀⠀⠀⠘⣷⣤⡴⠟⢁⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣶⣾⠽⢦⡀⠀⠀⣀⣀⣀⣿⢋⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠁⠙⠉⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⡄⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠀⠀⠲⠾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢺⣦⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠐⢠⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡞⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠢⡀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⠀⠀⠀⠀⡿⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣁⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⢦⡀⠀⠀⢠⠃⠀⠘⣯⣆⠀⠠⠄⠀⠀⠀⣀⠤⠶⠚⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⡜⠀⠀⣸⡿⣤⣷⡶⠤⠀⠀⠀⠹⣿⡄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰