Autumn pumpkin Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣴⣧⣶⣶⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⢤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⢿⣿⠿⠋⠀⠀⠀⠀⠘⡗
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠚⠓⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⠄⠂⠀⠀⠀⣴⣿⣿⣧⣿⣿⣿⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢁⡀⠆⠀⠠⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠼⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⡀
⠀⠀⠀⠀⣠⣴⣾⣷⣦⣄⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠛⠛⠉⠉⠃⠀⢀⣴⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠛⠻⠿⠿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢋⠭⠙⣹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠔⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠶⠶⠶⠦⣄⣿⡄⡇⢸⢸⡇⢀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠿⠥⣤⣄⣀⠀⠀⡈⠑⢄⣿⠇⡇⠀⠀⢿⡋⢁⠔⡀⠄⠀⣀⣠⡤⠬⠿⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⡀⠠⠄⠀⠀⣠⣭⣛⣶⣌⠢⣼⠛⢀⠁⠀⠀⢈⠳⣦⠊⣠⣴⣛⣉⣀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⣰⠟⠁⠀⡠⠒⠁⢂⣠⡴⠞⠛⠋⢙⣛⣻⣿⣿⣧⠀⢀⣀⣤⣤⣤⣥⣼⠟⠛⠉⢉⡉⠉⠙⠳⢦⣄⠀⠀⠀⠀⠐⠄⠙⢷⡄
⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⣰⠟⠁⢀⡤⠒⠉⠀⠀⠠⠀⠙⠻⣶⠛⠁⠔⠋⠀⢀⠙⣦⠀⠀⢄⠀⠈⠀⠠⡀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⢸⠃⠀⠀⠀⠀⢀⡾⠁⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⣼⠁⠀⠌⠈⠀⠀⠀⢆⠘⢧⠀⠀⠡⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⡿⠀⠀⠀⠀⠀⣾⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢻
⠀⢰⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⢸⡇
⠀⠸⡇⢠⠀⢠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠡⠀⠀⡆⣼⠁
⠀⠀⣷⠸⡆⠘⡄⢻⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢀⠰⢠⡏
⠀⠀⠸⣆⢷⠀⡌⠜⣇⢠⠀⠈⡄⢀⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⣼⠀⠀⠀⠀⠀⢀⠀⡀⠁⡀⣿⠁⠇⠌⢄⡾
⠀⠀⠀⠹⣾⣇⠘⡐⠹⣆⢂⢂⢱⠀⠆⠀⡄⢀⠀⠁⠀⢿⡀⠆⠂⠃⡇⠀⠀⢠⠀⠀⠸⠀⣿⠀⠀⡄⠀⢨⠆⢠⡀⢠⣿⡏⠘⢠⣨⡾⠁
⠀⠀⠀⠀⠘⢿⣦⡑⡌⢻⣮⢆⢂⠣⠈⢄⠐⡈⠆⠘⠄⠜⣧⠰⢰⢠⡇⠀⠀⠈⠀⠁⡀⢠⡏⡘⡰⠠⢀⡞⠀⡼⢁⣾⡟⡠⣡⣿⠟
⠀⠀⠀⠀⠀⠀⠙⠷⣌⣢⡙⢿⣦⡑⡱⡈⢢⠐⡈⢆⠈⢾⣹⣆⠂⡆⣇⢰⠀⡀⠀⢀⠃⡼⠑⢀⠠⢁⡼⠁⣸⢣⣾⠏⣔⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢿⣿⣬⡛⡦⡑⠌⣂⠱⢄⠙⠿⣮⣜⣹⡈⠀⡅⠰⢌⣼⠇⣡⠕⣡⠞⢀⣼⣷⣿⡵⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣮⣽⡶⠾⠛⠉⠻⢷⣷⣤⣣⣷⠿⠿⢾⣥⣾⠧⠶⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠋⠉⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡒⠚⠋⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢳⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢛⣩⠭⠿⢿⣷⠤⠤⢤⣿⡿⠯⢭⣍⡓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢦⡀⠈⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣰⠋⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠹⣄⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡆⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⡏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢹⡀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣼⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⣇⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣼⠀⠀⣸
⠀⠀⠀⠀⠀⣠⠤⠿⢤⢤⠿⢤⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠓⢲⣤⣀⡏⠀⣤⡿⠤⣄
⠀⠀⠀⢀⣞⣀⣀⣟⠛⡴⠚⢷⣇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣻⠳⣄⡏⠷⠋⠹⠟⣇⡀⠀⢺⡀
⠀⠀⠰⡏⢀⡼⠿⠿⢼⠀⠀⠈⣯⣤⠶⣛⠓⣦⠤⢤⣤⢤⣀⣄⢐⡏⠛⠀⢀⠀⢹⢠⡤⢤⣀⠀⡤⡵⠶⣟⠉⠓⢦
⠀⢠⣴⠿⡮⠔⠒⠒⠚⣆⢸⠙⠃⠀⠀⣼⡴⠃⠀⢸⠇⠀⠀⠿⢻⣀⣤⢤⣿⠱⣎⣿⡀⠀⠀⠙⡇⠀⠀⢺⣄⣠⠔
⠛⠿⠧⣤⣷⡀⠀⠀⠀⢯⡉⠀⠀⠀⢶⡚⠛⣶⠶⠿⣶⠀⠀⠀⢺⠏⠋⠀⠀⠀⠸⡏⠑⠦⣄⣀⣇⣠⠞⠋⠉⠙⢦
⠀⠀⠲⢾⣇⣙⣒⣦⣶⣶⠛⢦⣐⣯⠉⢀⡴⠃⠀⠀⢀⡿⢂⣠⣧⣀⡀⣠⣀⡖⣦⡷⡤⢤⡽⣶⢤⣹⣄⣀⣀⡠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣙⣿⣦⣴⣰⣋⠁⠐⠒⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣿⣿⣿⣟⢿⣻⣿⣷⣯⣉⣉⠉⠙⠛⠢⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠶⠛⣻⣿⣿⣿⠟⢻⡻⢿⣷⢄⡀⠙⠢⢄⠀⠀⠠⣀⢀⠀⠀⠀⣠⡔⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⠋⠀⢀⡶⠛⡻⠃⠀⠀⠀⠀⠀⢳⡀⠙⠂⠀⠀⠣⡀⠀⢹⣄⣤⣴⣾⣟⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠇⠀⠀⠊⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠁⠀⢸⣿⣿⣿⣿⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠫⡀⠀⠀⠀⣼⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⣹⣼⠞⣋⣩⢭⣿⣟⣿⣧⣄⣀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠘⢿⡆⠀⠆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢠⡿⠟⠉⣀⡤⠶⢿⣿⣿⣿⣿⣿⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠘⣷⡀⠰⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⢠⡾⠁⢠⠞⠁⡠⠚⠋⠉⠛⢿⢿⣿⣿⣮⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⣶⣽⣷⡀⠱⣄⠀⠀⢆⠀⠀⠀⠀⠀⠀⣸⠀⣀⢣⡾⠇⢰⠃⢀⡞⠀⠀⠀⠀⠀⠀⣼⢉⡟⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠈⠛⢻⣿⣿⣷⣜⣷⣄⣈⣷⣤⣀⠀⣀⣴⣿⣴⠿⠋⠀⣆⢨⠀⡜⠀⠀⠀⠀⠀⠀⠠⠋⢠⡇⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⣄⡇⠀⠀⠀⠀⢀⠀⠀⢀⡜⠀⣼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣹⣿⣿⣿⠛⢿⠿⣿⠿⣿⠛⠛⠫⠍⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⣠⣴⠞⢁⣤⠴⠋⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠾⠛⠋⠐⠛⠢⡀⠀⢂⠅⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠯⠭⠤⠶⠞⠋⠁


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣿⣀⣀⣷⠀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⣻⡿⠟⠋⠉⢉⡿⠋⠉⠉⠙⢿⡉⠉⠙⠻⢿⣛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡼⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠙⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡾⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⢷⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⣧⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣼⠃⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⡄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡟⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡹⣦⡀⠀⠈⢷⡀⠀⠀⠀⠀⢠⡿⠀⠀⢀⣴⢏⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⠾⠿⢦⣤⣤⡴⠿⠶⠶⠞⠛⠛⠋⠁



⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⢀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠘⠄⠀⡀⠀⠀⠀⠊⠁⠀⠀⠀⢠⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⡰⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠂⠈⠀⠈
⠀⠀⠀⠀⣠⠀⠈⠀⠀⠁⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠃⠉⠀⠀⠀⠀⠀⡠⠄⠒⠲⢄
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⢀⡀⠠⠀⠀⣀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠜⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠒⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠤⠒⠐⠣⠄⣀⣀⣀⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠐⠀⠒⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣦⠆
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠄⠀⠐⠁
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠧⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠀⠀⡀⠀⠉⠐⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠑⠒⠂⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠒⠀⢄⡀⠀⡰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠈⠖⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡐⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠐⠚⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠐⠠⠖⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢀⡀⡀⢀⡴⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠢⠊⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⠀⠀⠆⠘⠊⢡⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠉⠁⠀⠀⠣⡀⠡⠀⠐⢸⠀⠀⢠⠊⢀⠎⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠈⠉⠒⠌⣢⣥⠂⡸⠀⡰⠁⢠⠗⠈⠉⠀⠀⠀⠉⠒⣤⠄⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠀⠤⠄⠊⢉⢎⠀⡰⠁⢀⠏⠀⠀⠀⠀⠀⠀⠀⠎⠈⡆⠀⠀⠀⣱⡤⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠄⠐⠚⠁⠀⢱⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⠦⠔⠁⠀⠀⠎⠀⡇⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⠒⠒⠠⠤⣀⡇⠀⠀⡧⠴⠖⠪⠭⠥⢄⣈⠉⠑⠒⠢⢄⠀⢄⠴⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⡹⠒⠒⠣⢄⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠉⠢⡄⠀⠀⢠⠒⠉⠒⣜
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠈⠢⡀⠈⠒⠒⠉⠈
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠱⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢱⠀⠀⠈
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠜⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡠⠊⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠵⠄⠒⠒⠂⠉⠉⠉⠉⠉⠁⠒⠂⠴⠁⢠⠴⠭⠐⠒⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣵⣶⣴⣶⣴⣯⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣼⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣬⣛⡹⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡂⢑⡀⠈⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣘⢥⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢃⠀⡃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠘⡄⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⢤⡷⢶⣇⣀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠁⡠⠞⠉⣿⠉⠁⢠⡋⡉⠛⡶⢧⣤⣾⣗⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡅⢰⠁⠀⣼⠁⠁⠀⠃⠈⠇⢰⠐⠀⠈⢷⡬⢷⡌⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢷⠀⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢈⣾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⢷⠀⠸⠀⡄⠀⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣻⠯⢟⣿⣦⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡀⠑⢠⡤⠷⢾⣶⡗⠄⣿⠀⠀⠀⠀⡗⠀⠀⡀⠈⠉⢉⡷⠞⣷⠟⠮⡩⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠙⠢⠜⠳⠦⠵⠚⠤⠤⠾⡇⠀⠀⡈⠀⠀⠘⠃⠀⠐⠆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠲⣉⡙⢎⡀⠀⠀⠀⢀⠀⠤⠀⠀⠐⠄⢸⡇⠀⠀⠀⡆⠀⡀⣱⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⠴⢽⣆⠈⠙⢦⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⠒⠷⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠶⠶⠒⣠⡟⠁⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢀⡔⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠢⢤⡤⠖⠒⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⡴⠁⠈⢢⡀⠀⠀⠀⠈⠑⣤⠔⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢳⠀⠀⠀⠀⡎⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠙⢧⡀⠘⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⠴⠏⠀⠀⠀⠀⠘⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⡆⢹⣷⠀⠀⢤⣄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⢦⣄⠀⠀⠀⡇⢸⡟⣧⠀⢀⡟⠀⣀⣴⣿⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢐⣲⡶⠶⠔⢻⠿⠟⠂⠀⠁⢸⣿⢻⣷⣌⣴⠞⠛⠉⢀⣀⣤⣤⣈⡉⠻⢦⣄
⠀⢀⡄⠀⢀⡴⠚⠉⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⣯⠸⠛⠋⠁⠀⠒⢤⣄⠀⠀⠀⠀⠉⠳⣄⠹⣷⡀
⢠⠎⢀⡴⠁⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠹⣦⢿⣿⡀
⡎⢀⡞⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⣿⣿⣿⡇
⣇⣸⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⣿⣿⡟
⢿⣿⡆⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⢰⣿⣿⡇
⠘⣿⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣰⣿⣿⣿⠃
⠀⠈⢿⣧⡀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡯⣿⣿⠏
⠀⠀⠈⢿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠻⠟⠋
⠀⠀⠀⠀⠙⠻⢿⣿⣿⡘⣦⣄⡀⠀⠀⢀⣠⣾⣿⣿⡟⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠐⢶⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠋⠙⠛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣤⣤⠴⠞⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⣧⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⣉⣭⡭⡽⣿⣧⣠⣤⣤⣄⣼⣶⣯⣭⣍⣉⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⠶⠋⠁⠀⣠⠶⠋⠉⠀⠀⠀⠀⠉⠛⢦⡀⠀⠉⠛⢦⣄⠈⠳⣄
⠀⠀⠀⠀⠀⣠⠟⠁⢠⡞⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢷⡀⠈⠳⣄
⠀⠀⠀⠀⡼⠃⠀⣰⠏⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠹⣄⠀⠙⣦
⠀⠀⠀⡼⠁⠀⣰⠃⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠹⣆⠀⠈⢧
⠀⠀⣼⠁⠀⢰⠏⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢹⡄⠀⠘⣧
⠀⢰⠃⠀⠀⡿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢷⠀⠀⠸⡆
⢀⡟⠀⠀⢸⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢻
⢸⠃⠀⠀⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠀⠀⠸
⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⡿⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⣇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿
⣿⠀⠀⠀⢿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡿
⢹⡀⠀⠀⢸⡆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⡇⠀⠀⢀
⠘⣇⠀⠀⠀⣷⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡾⠀⠀⠀⣸
⠀⠹⣆⠀⠀⠘⣆⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣸⠃⠀⠀⣰⠏
⠀⠀⠹⣆⠀⠀⠹⣆⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣰⠇⠀⠀⣰⠋
⠀⠀⠀⠈⠳⣤⣀⠘⢧⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⡼⠃⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠶⣄⡀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⢀⣠⠴⠛⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠚⡦⣄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠙⠅⠆⠁⠈⠸⡄⢠⡔⢲⠖⡚⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⡑⠚⠃⣰⠂⢀⣇⡇⠀⠀⣎⠀⠊⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡊⣑⣒⠤⣀⠀⠀⠀⣤⣴⣶⠀⠀⠀⠀⠳⣤⠬⠒⠄⢉⠠⠢⠩⠁⢃⣠⠃⣤⢒⣡⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⣧⡤⣀⠀⠙⠢⢝⠢⡀⠘⣿⣼⡄⠀⠀⠀⠀⠈⠑⣄⣰⣃⣀⣘⣁⡠⠚⠁⡠⠊⠉⡸⠐⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠇⠇⠀⠈⠻⡳⡀⠀⠀⠙⠮⡳⣼⡷⣧⢀⣠⡴⠖⠛⠉⣹⠁⢷⠠⡉⢂⠈⠏⠛⠐⠶⠶⡴⢀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠨⡜⡀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠈⠪⣧⡹⣏⠀⠀⠀⡰⠋⠀⡠⠋⡀⠈⡦⢆⠀⠘⠆⠰⡗⢴⣄⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠳⡳⢄⣀⠴⡣⠃⠀⠀⠀⠀⠀⠀⣽⡽⡺⣆⠀⠀⣇⡄⠊⢀⠊⠋⠐⢧⢸⡠⠊⣃⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣏⡳⡛⢿⣆⠀⠈⢣⡀⣆⢠⢛⢢⡀⡇⢣⡴⣍⣍⣫⠁
⢠⠖⠓⠦⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠫⣝⠫⠩⣣⢝⢦⡀⠀⠉⠉⠣⣴⡏⠉⠁⠀⠀⠀⠈⠁
⡏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⠀⣠⣴⣿⣦⣅⣈⣸⣷⣶⣦⣾⣷⣄⠀⣀⣀⣈⡀
⢻⡄⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣠⡴⠿⣉⠣⡀⠡⠉⡟⢹⠡⣿⣝⡏⢹⠋⡠⢊⣀⣐⠈⡙⣟⠛⠟⢉⡟⠳⢦⣄
⠀⠉⠓⠶⠚⠋⠁⠀⠀⠀⠀⣠⢾⡭⣤⣄⠈⣆⢰⣠⣏⠳⣌⠲⠔⠊⡀⣮⣼⢰⠋⡖⣮⡧⠠⣿⠈⢮⣹⠀⣴⡭⣝⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢸⡸⢽⠟⢁⡏⣸⣟⡓⢔⣁⠮⠥⠥⠤⡬⣿⢘⢦⣉⣩⣀⠶⢅⢁⠘⣿⣄⠘⠛⣃⡜⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠐⢄⠑⠒⠛⠋⣰⡟⢢⠒⡡⠔⠂⣒⣀⣐⠂⣿⠐⠑⠈⡅⠀⢩⢋⣉⡉⢻⡎⠙⡉⠃⢸⢀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠑⢠⠬⢉⡉⣿⣿⠑⡄⢋⢀⡴⠋⠡⠀⠌⡉⣿⡠⢀⢁⠐⠿⠻⡘⠿⡻⠈⣷⡠⢓⢩⡉⡺⡔⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠕⡈⣐⣠⣐⡀⣿⡿⠇⠇⡀⢸⠠⢵⣫⢭⡑⡄⣿⡢⡕⠣⠐⠀⣐⢍⠋⢍⠐⣿⠡⢰⢻⢻⡇⣿⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⢠⠎⢁⣤⢤⡙⣿⣴⣈⣼⣤⣈⢧⣀⠛⠚⣠⠇⣿⢐⠴⠛⠓⠲⢬⠂⠯⠠⠑⣿⠀⢊⢦⣥⡞⢁⡽⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠀⠸⣜⣚⡡⣿⢀⣀⡀⠑⣌⠢⡉⢍⣩⡣⢵⣿⡏⢀⡔⡿⣦⠘⡎⠡⡱⢈⣿⡤⡢⢲⣾⠲⢳⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢈⠳⣌⡀⢂⠌⣿⠡⣞⡿⠀⡼⠀⡇⠈⠟⠗⣈⣿⠐⡈⢧⣓⣃⣼⠖⠚⠙⢻⡿⢈⢔⠒⡐⢤⡽⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⡂⠩⠉⠩⢹⡗⢦⠴⣎⣠⢴⣁⡰⠸⡀⢴⡟⢈⢌⢄⣼⡆⣏⢰⣿⡟⣾⡧⠟⠓⢤⡈⡆⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⣡⠜⡓⢌⢷⣠⠟⠡⢀⣂⡀⠹⣖⠱⣸⠇⡤⣆⣈⠄⡰⢸⠳⠬⢶⢿⠡⣾⣷⡄⢹⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣼⣨⡏⣤⢰⢱⡒⡿⠠⡇⠡⠈⢠⢎⣥⣌⠻⣆⣡⠂⠀⡋⠈⠓⠮⣾⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⣼⣦⣍⣤⣞⣀⣤⡴⠿⢮⣿⣿⣀⣯⣬⡴⠷⠷⠾⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣠⠊⠠⠀⢉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠉⠻⡀⠀⠀⢠⠃⠀⠀⢠⠋⠉⠉⠉⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠛⠒⠒⠤⢄⡀⠀⠱⡀⡰⠁⠀⠀⠀⡌⠀⠀⣀⠤⠒⠂⠉⠉⠉⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡻⠁⠂⠀⠀⠀⢇⡠⠊⣀⠤⠄⠐⠒⠢⠤⢄⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣀⠤⠖⠒⠂⠉⠉⠀⠒⠒⠤⡁⠀⠀⠀⠀⠀⠘⣖⣊⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⡴⠊⠀⠀⠀⠀⠀⠀⡠⠤⠒⠊⠉⠉⣲⠖⠒⠈⠁⠚⠣⣄⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠈⢺⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠱⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⢀⢎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠱⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢝⢦⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠄⣀⣈⣦⣀⠀⠀⠀⢀⡀⠴⠓⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⡾⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠀⠤⢀⡁⠠⠀⢹⡇⢠⣿⡀⡾⠀⢀⠴⠒⢂⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠤⠤⠩⠝⢻⣶⣶⣞⣁⢈⢛⢳⣧⣤⣥⡖⠉⠭⠤⠄⣀⠀⠈⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⠈⠠⠆⠀⠀⠀⢀⡛⠋⠉⠙⠻⠙⠋⠙⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠁⠀⠀⠑⠄⠀⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢐⠀⠀⢐⢸
⠀⠀⠀⠀⠀⡃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⢸⠬
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠀⠀⢸⡼
⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⡄⠐⠀⢎⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡀⠀⠣⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⠂⠀⠀⢐⠃⠀⣰⡾
⠀⠀⠀⠀⠀⠀⠡⡀⠆⠀⢡⠀⠰⠀⠀⠁⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⡘⠀⠀⢀⠌⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢌⡄⠀⢧⠀⢂⠀⠈⡄⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠀⠠⠀⠀⢀⡌⣰⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⢣⠘⢁⠀⠀⠀⠀⠁⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡴⠁⡀⣠⣾⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢬⡀⠀⠸⣄⠀⠆⠀⢸⡀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠊⠀⣀⣾⣡⣾⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠼⠷⢬⣀⡈⣷⣄⠀⠀⢀⢀⣼⣿⡤⣁⣤⣾⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣎⠻⣿⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⠙⠸⠿⢋⣠⣴⣶⣶⣄⠀⢠⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠐⠚⠉⠁⠀⠀⠙⣿⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣶⣾⣿⣿⡶⢩⣾⣿⣿⣿⣧⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⢀⣀⣀⣘⣛⡛⠻⠿⠟⣡⣿⣿⣿⣿⣿⣿⡄⢿⣿⠟⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠿⠿⠿⢂⣾⣿⠿⠛⠛⠛⠛⢿⣷⡈⠁⠾⠿⢿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⣉⣤⣶⣶⣶⣦⡉⠁⢠⣴⣿⣿⣿⣿⣶⣬⡁⢠⣴⣤⣤⣤⣈⠙⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⣿⣿⣿⣿⣷⣦⡙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣷⣄⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣇⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⡟⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠻⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣤⣴⣶⣿⣋⣀⣤⣄⣀⣨⣿⣷⣶⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⢠⣴⠟⠋⠉⠀⣠⣾⠟⠋⠉⠉⠛⢿⣦⡀⠈⠉⠛⢷⣤⠈⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⣴⡟⠁⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠙⣷⡄⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣼⠏⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠈⢿⡄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⡟⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⣿⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢹⣇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀⣿⠁⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⢿⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣼⡏⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠘⢿⣄⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⢀⣼⠟⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣌⣻⣷⣄⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⣴⣿⣋⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠷⣶⣾⠿⣶⣤⣄⣤⣴⡾⢿⣶⡶⠿⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠂⠀⢰⡆⢠⠀⢂⠀⡂⠀⢀⠀⢲⠀⠀⠀⠐⢎⠀⡔⠀⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢊⡀⡘⠀⠀⠀⠈⠀⢸⠃⠐⠂⠀⠀⠀⢀⡁⠄⢹⠀⢈⠠⠈⠀⠂⠀⠀⠀⠐⣁⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠈⠀⠸⠆⠠⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠸⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠂⠈⠀⠀⠀⠀⠀⠀⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⡀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⠀⡈⠀⢈⠒⢄⣀⡄⠀⠀⠀⠀⡀⠈⠁⠉⡂⠀⠀⢀⠀⢈⠂⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠉⠉⠦⣾⣷⡌⠐⠂⠈⠀⠲⠀⡀⢈⡆⠀⠈⠸⠁⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠀⢠⡘⠐⠠⠀⠂⠙⠁⠀⡀⠁⢂⢀⡴⠃⠀⠀⠀⢀⠀⣀⠠⠄⡀⡀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠉⠂⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⣀⠀⠔⠀⠠⠁⠀⢀⡄⠀⢺⠁⠀⠈⠁⠀⠀⠈⠁⠀⠈⠠⣀⠐⠁⠀⠀⠑⢀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⠠⢆⠄⠀⠈⠀⠀⢰⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠊⠁⠀⠐⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⡔⠀⠀⠀⠐⢄⠉⢢⡔⠂⢶⡁⢉⠀⠘⠁⠱⠂⠄⠀⠐⠀⠀⠀⠀⠀⠀⠈⡀⡀⠠⠘⠃⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠔⠀⠈⠁⠈⠐⠀⠀⠀⠀⠀⠃⣤⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⠠⡄⠂⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢌⠋⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠁⠀⠀⠂⠀⠀⠀⡈⠉⡡
⠀⠀⠀⠀⠀⠉⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡀⠐⠒⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠈⠡⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢬⠆⠀⣀⡀⠱⠂⠄⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠀⠀⠀⠀⠀⢂⠀⠀⢄⠀⠀⡀⠐⠦⠔⠀⠀⠈⠀⠀⠀⠀⠁⠐⠒⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠑⠠⠈⠣⠀⠐⠀⠙⠂⡐⠣⡀⠀⠀⠀⠀⢀⠔⠉⠀⠆⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠣⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠄⠀⠀⠈⠂⡄⡀⠀⠈⠓⠀⢤⡀⠈⢂⠈⠖⢐⠐⠈⠀⠀⡀⠈⠀⠀⠀⠀⠲⠀⠀⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠈⠉⠢⡄⡠⠐⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣀⣀⠘⠀⠀⠰⠀⠐⠀⠀⠀⢐⠶⠒⠀⠀⢀⣈⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⡆⠀⠈⢁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠴⠆⠀⠀⠀⠱⠁⠂⠈⡸⢗⡂⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠶⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠆⠔⠂⡌⢀⠀⠂⠀⠀⠠⢀⠤⢤⠒⢂⡄⢀⠖⠀⠀⠤⠴⠀⠊⢀⠀⠀⠀⠀⢲⡄⠂⢸⠉⣤⠐⢂⠠⢄⠠⠤⣀⠈⢀⡘
⠀⠀⠀⠉⠁⠀⡇⠀⠀⠀⠓⠀⢸⠃⠀⠀⠀⠀⠀⢀⠸⠀⢸⠀⠀⠠⠁⠀⠀⠠⠈⠂⡄⠀⠀⢀⠀⢰⡄⠀⠇⠀⡄⠀⠏⠀⢸⠀⠀⠳⠀⣏⠐⠀⢄
⠀⠀⠀⠀⢀⠀⡇⠀⠀⠐⢐⠀⠘⠀⢐⠘⠀⢀⡄⢈⢃⠀⢸⠁⠘⠂⠀⠐⠘⡀⠁⠠⠙⠄⠀⠀⠠⠂⢀⠀⠀⠀⠁⠠⠀⡄⠈⠀⢸⠄⠀⠉⢄⠀⠀⡀⠂
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉
⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣴⣶⠙⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣈⡍⢷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠖⠒⠾⢿⣍⣎⣻⣿⠧⣴⣭⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⡝⢷⣤⣄⣀⣀
⠀⠀⠀⣠⢞⣉⣉⣿⡿⠾⠿⢿⣿⣛⡻⢦⡄⠀⠀⠀⠀⠀⡼⡀⠁⠄⠀⠀⠋⡉⣿⠀⠘⢦⠈⢹⢿⡷⠀⠀⠀⠀⠀⢀⣠⣞⠉⢙⣿⡷⢼⠿⣿⣿⣋⣳⣦⡀
⠀⠀⡼⠱⠋⠠⠊⢋⢙⡿⡟⠻⣤⡉⢷⡾⣿⡄⠀⠀⠀⠀⣅⠃⣼⠀⢠⠋⠀⢁⡭⢰⠁⠹⡖⣾⠜⣧⠀⠀⠀⠀⢀⡎⠘⢉⠄⠈⠉⢻⠿⠟⠻⣆⡉⢿⡧⣷
⠀⠰⢷⠁⣞⠀⢰⠃⠀⠀⡇⠀⠘⢿⡠⣿⢻⡇⠀⠀⠀⠀⠸⡄⡟⡀⢸⠀⠀⠈⣧⠀⠚⢀⠟⢹⣶⡇⠀⠀⠀⠀⢈⠈⢰⠆⠀⢰⠁⢸⠀⠇⠑⠙⢣⣤⡁⢿⡅
⠀⠀⣯⢸⡇⠀⠙⠀⢰⠖⡇⠀⠀⣸⡑⣿⣸⠇⠀⠀⠀⠀⠀⠑⠿⡀⣠⡆⠀⡏⣋⠈⣷⢨⣇⣻⠟⠁⠀⠀⠀⠀⠈⡆⢸⠁⠀⠃⠀⢈⣲⠀⠁⡣⢄⢸⣷⣾⠁
⠀⠀⠙⢼⡇⠀⣯⠀⢸⠁⡇⠀⠀⣷⢐⣏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢷⣶⣴⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⢸⡆⠀⡄⠀⢈⠿⠄⠂⢐⣼⠸⣫⡟
⠀⠀⠀⠀⠉⠲⣿⣄⣨⣌⣁⢘⣀⣿⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢼⣿⣄⣹⣈⡄⢐⣠⣿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣀⣀⢨⣭⢿⢦⣤⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢤⣟⣷⣦⣤⡤⣤⡀
⠀⠀⠀⡀⣚⡯⠈⣿⣟⢸⠻⣻⣿⣉⡛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡡⠤⣬⣿⣃⢻⢻⣻⣿⣍⣙⣶⡄
⠀⠀⠖⡘⢁⠀⠛⣡⠻⠛⡏⠹⣇⢉⠻⣷⣿⡄⠀⠀⠀⠀⠀⠀⡠⠖⡋⢳⣿⣌⣿⣿⣿⠟⠳⣦⡀⠀⠀⠀⠀⠀⠀⠂⠘⡰⠀⠈⠁⢻⠛⠻⢹⣦⡌⢷⣷⣿
⠀⠀⣰⢀⡟⠀⣐⠁⠀⠀⡄⠀⡀⣿⢿⣧⢿⡇⠀⠀⠀⠀⢠⠎⠐⢉⠡⠛⠻⣦⣷⠶⣯⡙⠳⣶⣽⡄⠀⠀⠀⠀⠈⡖⢀⠁⠀⡘⠀⠏⠠⠀⠨⡼⢷⢨⣿⣷⡀
⠀⠀⣧⢸⡇⠀⣉⠀⠀⠻⡄⠀⠀⣘⡎⣿⣼⠃⠀⠀⠀⠀⡌⡌⢰⠃⠀⡜⠀⠅⢙⠀⠘⢿⣄⣽⢹⣟⠀⠀⠀⠀⠘⡇⣸⠀⠀⠇⠀⠐⢡⠀⠀⡇⢸⢚⣿⣾⠁
⠀⠀⠈⢦⣦⠀⣿⡀⢰⠚⡇⠀⡃⣿⣸⣧⡟⠀⠀⠀⠀⠀⢢⠀⡟⠀⠸⠁⠀⡰⣞⠀⢐⠀⡏⢿⣈⡟⠀⠀⠀⠀⠀⠱⣻⡄⠀⠆⠀⣝⢸⠂⢛⡈⡞⣸⣳⠟
⠀⠀⠀⠀⠈⠻⠿⣤⣨⣤⣄⣤⣥⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢇⣯⠀⢰⠀⠀⣤⣿⠀⡌⢠⡇⣾⣹⠇⠀⠀⠀⠀⠀⠀⠈⠙⠶⢿⣄⣻⣸⣀⣿⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢢⣾⣇⠀⡇⠂⠀⡇⣸⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠊⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢉⣈⣁⡴⠀⠐⠩⠐⠓⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠔⠁⠀⡠⠂⠉⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⡠⠋⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⢒⣠⠠⠔⠂⣢⠀⢃⠶⣚⡢⠄⡀⠀⠀⢀⠀⠤⠤⣐⠒⣌⠁⢐⠀⠐⠧⠖⣉⠁⠀⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⣒⠠⠒⢺⣅⠀⢀⣨⠄⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⣅⠀⠀⣨⣗⠲⠌⠤⣘⠳⢦⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡰⠊⠀⡠⠒⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠑⢦⡀⠀⠙⢆⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢤⣀⢀⠁⠌⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡠⢠⠇⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⢠⠃⠠⡦⠐⢚⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⡃⢀
⠀⠀⠀⠀⠀⢠⠖⢂⠄⠀⡆⢀⡌⠀⢠⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡰⠒⠉⠛⢦⡀⠀⠀⠀⢡⡀⠀⠀⠀⠀⣠⢁⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡜⠀⠀⠁⠀⡀⠀⠀⠠⠄⠀⠀⠠⠀⠠⠚⠑⠒⠒⠒⠈⠀⠀⠀⠀⠀⠉⠒⠒⠀⠀⠑⠤⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠃⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣍⣛⣋⣙⣛⣟⣋⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⣿⣿⡷⣶⣿⣷⢶⣾⣿⠿⢶⣦⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢉⣀⡀⠀⢈⡩⠁⠨⣍⠉⠀⢈⣉⠙⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣾⡿⢩⣶⣿⣿⠋⣾⣿⣿⣿⣷⠙⣿⣿⣶⣍⢿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⢀⡴⠋⠀⠀⣰⠏⠀⠀⠀⠈⢳⡀⠀⠈⠳⣄⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⢡⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡄⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⣼⠁⠀⠀⢀⡿⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢹⡆⠀⢻⣿⣿⣿
⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⡇⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠈⣿⣷⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⡇⣼⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⣿⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢠⡇⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣦⠻⣿⣿⣷⠸⣿⣿⣿⣿⣿⠇⣼⣿⣿⠟⣰⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⣤⡀⠀⠀⣿⡀⠀⠀⠀⠀⣸⡟⠀⠀⣠⡟⠁⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⢷⣬⣿⣿⣧⡹⣿⣿⣿⢏⣼⣿⣿⣭⣾⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣀⠰⠤⠀⠀⢦⡀⠀⠀⢠⠟⠀⠠⠴⠋⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠃
⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠊⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠞⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡅⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⢙⠀⠀⠑⠄⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠰⡀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠐⡄⠐⠁⡀⠀⠃⠀⠁⠈⠀⠀⠂⠀⠀⠁⣠⠃
⠀⠀⠀⠀⠑⢄⣂⠑⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠁⠀⠀⠀⠀⠈⠦⣡⡀⠈⠢⡀⠀⠀⢀⡄⠀⢀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠷⠤⠤⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠵⠤⠤⠚⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⢀⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒⠀⠟⠀⠀⠒
⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠐⠀⢀
⠀⠀⠀⡇⠀⡈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐
⠀⠀⠀⢃⠀⢂⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠀⠈⠀⠀⠂⠀⠀⠈⠀⠀⠀⠐⠀⠀⡀⢀⡆
⠀⠀⠀⠈⢆⠘⡈⠄⠡⠀⠰⠀⠀⠀⠀⠀⠀⠘⣠⠋⠀⠀⠀⠀⠣⡀⠄⠢⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⢁⠞
⠀⠀⠀⠀⠀⠑⠲⠄⣀⣐⣄⠀⢀⡐⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠦⣀⣀⣆⡀⠀⣠⠂⡀⠔⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢾⠀⣻⠌⢳⢲⡜⠀⢰⠃⠀⠀⢦⡠⠞⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠈⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⣌⡀⡏⢸⠃⠀⡇⠀⠘⢦⣀⣀⣀⣀⣤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠘⠀⠃⠃⠘⠀⠀⠃⠀⢲⠀⠀⠉⠀⠀⢀⡀⠀⠼⠃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣧⡇⠰⢳⡄⣾⢹⡇⡇⡾⢠⢤⡌⡄⢀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡸⣦⠀⠀⠀⠀⡀⡐⣦⠿⣯⣿⠣⠐⠼⠋⠙⢸⠇⠉⠳⠋⠺⠾⠛⡽⣡⢖⣆⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣷⡽⣧⡸⣧⣸⣧⡿⠏⠁⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠉⢛⣾⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠋⠳⣌⢳⣏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⡆⠀⡇⢳⡞⠰⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠒⠒⢄⠀⠈⠋⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢰⣰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡒⠤⠚⠀⠀⢀⡠⠒⠉⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠛⠁⠃⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⣐⣮⣤⣶⣶⣶⣶⣤⣤⣀⠀⠘⣾⡟⢁⣠⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢀⣉⣥⣭⣭⣭⣭⣝⣛⡿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⢏⣴⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣶⡝⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡹⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⢇⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣝⢿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⢏⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠝⢿⣿⣿⣿⣿⣿⡿⢣⣿⣿⡿⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⣂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⡠⠊⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⣴⣈⣁⣀⡀⠀⠀⠀⠙⠂⠤⢽⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠄⠀⢠⣮⡤⠤⠤⢖⠦⠭⢷⣄⠀⠀⠀⠀⠂⠀⠀⠈⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠵⠶⠤⡀⠲⡓⠤⡀⠀⠀⠀⠀⠀⠑⢢⡀⢰⣇⠀⠀⠀⣆⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠀⢰⠁⠀⣙⡧⠃⠀⣀⡀⠀⠉⠳⣮⡻⣾⡏⠠⠀⠀⣿⡀⠈⣧⠰
⠀⠀⠀⠀⠀⠀⡔⡡⠀⠀⠀⠀⠈⠉⠁⠐⢤⡀⠀⠀⠹⣷⣌⠢⡈⢿⡜⡇⡀⠀⢠⣿⡇⠀⣿⡀⠃
⠀⠀⠀⠀⠀⢘⡐⠀⠀⠄⠀⠀⠆⠀⠀⠀⠈⣷⡄⢀⠀⠘⣿⣷⡐⠈⣿⣱⠂⠀⣾⣿⠃⠀⣿⠇
⠀⠀⠀⠀⠀⢸⢠⠀⠰⠀⠀⢈⡁⠀⠀⠀⠀⠾⣿⡄⠄⠀⢹⣿⣧⠁⢸⡏⠀⢼⣿⣿⠐⢰⣿⠀⠇
⠀⠀⠀⠀⠀⢸⢸⠀⢀⠀⠀⢨⡇⠆⠀⠀⠀⠰⣿⣷⡘⡀⠈⢿⣿⡌⠈⣧⣀⣿⣿⢃⢂⣾⠇⡜
⠀⠀⠀⠀⠀⠀⣾⡀⠈⠀⠀⠠⣿⠰⠀⠀⠀⠀⢿⣿⡇⢀⠀⠸⣿⣧⠖⠻⠾⢿⠏⢀⣼⠃⡔⢀⠄
⠀⠀⠀⠀⠀⠀⠸⡡⠀⠁⠀⠀⠸⠆⢃⠀⠀⠀⠰⢿⣿⠀⠀⠀⣟⠁⠀⠀⠀⠚⢦⡞⣡⣾⣷⡧⠒
⠀⠀⠀⠀⠀⠉⢉⠑⣅⠀⠂⠀⠈⢹⡄⠀⠀⠀⠀⣹⣿⠖⠉⠉⢿⣷⠀⠀⠀⠀⢀⡹⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⣄⣪⣷⡈⠑⢄⡀⠀⠀⢒⠀⠀⠀⠀⠐⣿⠀⠀⠀⠂⠀⡡⠀⠀⠙⠣⡀⠀⡠⡄
⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠁⠒⠐⠒⠀⠀⠀⠒⠙⠒⡇⠀⠀⣠⠀⠀⠄⠀⠀⠗⠒⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣰⣰⣤⣀⡀⠀⠀⠀⠉⢦⡰⠋⠦⢄⣀⣀⡸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠰⠀⠀⠆⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣟⢹⡇⡸⢄⠠⡿⠧⠀⠀⠁⠀⠀⠀⠀⡀⠀⢠⠀⡷⠲⣄
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠂⠀⠈⠫⠟⠉⠁⠀⠘⡒⠠⠀⠀⡄⠬⠂⠀⠄⠀⠐⠐⠀⠀⠙⠿⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠀⠀⠆
⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠠⢤⡀⠁⠙⠰
⠀⠀⠀⠄⠀⠂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⡁⠀⡘
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⢈⡄⡀⠀⠀⠀⠀⡔⠃⠐⠊⠀⠀⡀⠱
⠀⠀⣀⡄⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢘⡔⠀⠀⠀⠁⠀⠂⠀⢁⡄⠐⡐⢠⠘
⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠢⠠⠤⠀⠀⣠⢀⠊⠂⠀⠀⠀⠘⠳⡄⣀⠀⠀⠀⠉⠠⠈⣇⠉⠀⠁
⣴⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠍⢀⠀⠠⠸⡷⠔⠁⢚⡐⠡⠀⠀⠈⠈⠐⠄⠀⠻⣀⢀⠄⡞⣠⠊
⠙⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠉⠻⡦⠥⠏
⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠂⠱⡿⢀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣷⡀⠸⡹⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡻⠿⣿⣿⣧⠈⢿⡄⠃⠘⣿⣿⣿⣿⣶⣾⣿⡛⣳⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢮⣛⣩⡬⣟⣻⣿⣿⣿⣿⣿⡄⢾⣿⣄⠰⣿⣿⣿⣿⡿⠾⢿⣿⡲⠶⠬⣝⡿⢦⣀
⠀⠀⠀⠀⠀⢀⡴⣿⠗⠚⣫⠵⣛⢩⣴⣯⣿⠿⣋⡟⣓⢰⣯⣿⠶⣿⣍⡿⠛⡿⠄⡀⠀⠉⠓⠤⣄⠙⠢⣍⠳⣄
⠀⠀⠀⠀⣠⣿⠟⠡⣠⠞⢁⣄⡾⡿⢩⡏⢡⢰⠏⣈⠇⢸⡏⢻⣆⠙⡿⡻⣄⠘⠒⢌⠱⢦⡀⠀⠘⢴⣄⠈⡳⣬⣦
⠀⠀⠀⣰⡏⠁⢀⠞⡡⠰⢢⢋⠎⣰⠟⡑⢁⡞⢀⡟⠀⢸⠀⠸⡏⠁⡁⠑⢌⣦⠀⠀⠀⢃⠙⣦⠀⠀⠈⢧⡀⠸⣿⡆
⠀⠀⢰⡿⠁⣠⠂⢘⢠⣳⢋⡎⢠⠋⠄⣴⠘⠀⠘⡇⠀⢸⠀⠀⣧⠀⠠⡀⠈⠊⣇⠀⠀⠀⠑⡈⢧⡀⠀⠀⢷⡔⠆⢷
⠀⢠⡿⠀⢰⠇⡰⠋⣼⠇⠞⠀⠋⢈⠜⣸⠁⠀⢠⠃⠀⢸⠀⢀⣟⠀⠀⡌⠄⠀⠹⡄⠀⠀⠀⡀⠠⢳⠀⠹⡄⠻⡄⡬⡇
⠀⣾⠀⢠⡏⠀⢡⢀⣇⠀⠁⣠⠁⡈⢠⡿⠀⠀⡼⠀⠀⢸⢰⠻⣿⠀⠀⢱⡀⢸⡀⢳⠀⠀⠈⠇⠀⠈⢣⠀⢹⡀⣿⡟⣇
⢰⡇⠀⣼⠁⠀⠸⣾⢨⠀⠰⠁⠀⠇⣾⠃⠀⠀⡁⠀⠀⢰⡜⡆⣿⠀⠀⢸⡇⠀⡇⠘⡆⠀⠀⠀⢀⠀⠈⣇⠈⣷⣀⣻⡏
⢸⡇⡄⣏⡀⠀⣦⣿⠘⠀⠀⢀⠀⢀⣿⠀⠀⠀⠃⢀⠀⠊⡇⣇⣿⠀⠀⠀⠓⠀⢳⠀⢣⠀⠘⠀⡀⣇⠀⢹⡀⡘⣿⢾⡇
⠘⣷⣰⡇⡇⢰⣿⠋⠀⢠⠁⠎⠀⠘⡇⠀⠀⠀⠀⢸⠁⠀⠀⣯⣿⠀⠀⠀⠄⠀⠘⠀⢸⠀⠀⠀⢣⠙⠀⠨⠇⠸⣿⣻⡇
⠀⢹⣿⣿⡇⠎⣾⡀⠁⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠄⢻⢸⠀⠀⠀⢀⠀⢸⡀⢼⡎⠀⠀⢾⣤⣤⡄⣆⢀⣿⡿
⠀⠀⠻⣿⣿⡀⣿⠀⡂⣸⡆⠀⠀⣾⣷⠀⠀⡆⠀⠃⠀⠸⡇⠸⣸⠀⠀⠀⣾⠀⠈⢃⠀⣇⠀⡀⠸⣧⠋⣇⡟⣼⣿⠃
⠀⠀⠀⠘⢾⣇⢻⡇⢷⣿⢇⠀⣠⢹⣿⠀⠀⡇⠀⠰⠀⠀⡇⢰⣿⢰⠀⠀⣿⡀⠀⡿⠀⣿⢸⠑⡀⣿⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠙⢿⣿⣅⢻⣿⣆⠇⢸⣷⡄⢀⡇⠀⠸⠀⢠⡆⠈⣿⣼⡀⠀⡟⠰⠀⣿⢇⣿⢸⡌⢃⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣿⣼⣏⢀⣿⡇⢸⣿⠀⢀⢸⡾⠁⠀⣿⣯⡇⠸⣇⡸⢸⡟⠸⣾⢸⣇⣸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣇⣿⣽⣼⢼⠀⣸⣼⣿⣦⠎⣿⣿⡗⡞⣿⣷⣿⣿⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣼⣇⡱⣷⣿⣿⣾⣿⣿⣸⣿⣯⣿⣿⣯⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢻⢿⣿⣖⣤⡠⢠⣴⢀⡀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣶⣦⣀⣹⣇⣸⠿⢨⣿⠿⣯⣿⡻⣿⠁⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠟⢿⢟⣦⠁⡙⣏⠙⠜⠃⣙⣛⡡⠏⢩⢣⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡈⠒⢤⣰⡀⠘⠷⢬⣙⢇⣤⣄⣩⣀⡾⣷⣬⣽⠿⠓⠉⢰⠀⠦
⠀⠀⠀⠀⡀⢨⠟⣀⣤⣤⣤⣤⣶⣾⢋⣷⣶⣾⡟⠱⠛⠛⠋⠀⠀⠀⠈
⠀⠀⠀⠠⠀⣐⠀⠸⣿⣿⣿⠿⠄⣟⢾⣿⣿⣿⡿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠋⠁⢰⠀⡁
⠀⠀⠀⠀⠀⠙⠄⢀⠁⣀⣈⣱⣤⠝⢮⣙⣫⣵⡤⠾⣿⣄⡆⠀⠀⠀⠀⠀⣠⣶⡾⠁⢀⡴⠂⠉⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⢹⣦⠐⣠⠌⠉⠐⠗⠀⠀⠉⠻⡀⠀⠀⣾⠋⠭⠁⠸⠂⠬⠁⠀⠀⡦⠀⠘
⠀⠀⠀⠠⣤⠀⢀⠀⠀⠀⣄⠀⠙⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠊⣉⡄⠀⠀⢀⠀⠀⠾⠁
⠀⠀⠀⠀⠓⢴⣿⣄⠀⠀⢸⡆⠀⠀⢦⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⢠⠀⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣆⣠⡀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣦⣦⣤⣴⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠟⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⡄⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⡏⢿⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣰⡟⢀⡿⠮⢿⣿⣿⢿⣿⠿⢿⣿⣦⠋⣼⡟⢹⣿⣿⣿⣿⡷⢟⣿⣷⡼⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣿⢻⣾⣿⣦⣬⡃⢿⡄⢹⣧⡀⢿⣿⣰⣿⡇⣸⡟⢁⣿⢈⣴⣿⣿⣿⣟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢚⣽⣟⠛⠻⣷⣾⣟⢺⣿⠿⢮⢿⣿⣏⢹⣿⣷⢚⣿⣾⣟⣡⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⠿⠛⣻⠷⣰⣷⣶⣶⡟⠟⣉⣽⣎⠟⣟⣙⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠛⠛⠛⠀⠛⠉⠋⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⡇⡁⠀⠄⢐⢈⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠄⠀⠀⣁⢀⡀⠀⠀⠃⠉⠉⠉⠁⢘⣀⣀⢀⡀⡀⠀⠀⠤⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠆⠈⡐⡡⠄⠙⠝⡀⠀⠡⢉⠤⡈⢂⠁⠰⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠁⠤⠄⢲⣁⢤⠞⡐⠁⠂⠾⡔⡀⠬⠤⠈⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠔⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠂⢠⠂⠀⢀⠁⠀⠀⠀⠀⠀⡀⠀⠐⠀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠁⠀⠀⠰⢄⠀⠀⡠⠂⣀⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡐⠠⢑⡈⠄⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠂⠐⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠔⠁⠀⠀⠈⠢⠀⠀⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⠆⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣼⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡷⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⡁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣹⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⣀⡀⠤⠤⡾⠀⠀⣟⠀⠷⠤⠄⢀⡀⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠂⠉⠉⠀⠀⡀⠀⠀⠀⣵⣳⠀⡴⠀⡜⠠⡿⡄⣤⢀⡄⢀⣤⡤⠀⠀⢀⠠⠞⠯⢉⡁⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠔⠊⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⡀⣤⣜⠇⠀⠀⠈⠉⠁⠐⠲⡞⠉⠁⠀⠀⠀⠈⢳⡠⡀⠈⠉⠙⠒⢾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠈⣽⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠛⠾⣆⠀⠀⠀⠈⠹⣷⡟⣦
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⡀⠀⠀⢀⣜⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣱⡀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⣿⣧⢸⣧
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠁⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣷⠀⠀⠀⠀⠀⠀⠀⠊⣷⣂⠀⠀⠀⠾⡻⠀⢿⢇
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⠀⠀⠀⠀⠐⠀⠀⠀⢿⣇⠀⠀⠀⠀⢡⢣⡜⢾⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠁⠀⢀⢈⡟⠀⠀⠀⠀⠀⡚⡄⢸⣇
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡇⠀⠀⠀⠀⠀⠀⠀⢘⡇⡆⠀⠀⠀⠀⢡⡇⢺⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣍⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⢸⡇⡾⣿
⠀⠀⠀⠀⢱⠀⢂⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠨⡇⠀⠀⠀⢀⠰⠀⠠⢸⡏⠃⠀⠀⠀⢸⣆⣿⣷⡇
⠀⠀⠀⠀⠈⡆⢸⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⠀⠀⠀⠈⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⢸⠀⠀⠀⢦⡸⡀⠀⠀⢂⣼⣟⣿⣻⠁
⠀⠀⠀⠀⠀⠘⢆⢥⡀⠀⠀⠀⠈⡓⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢆⣿⠈⠀⠀⠀⠀⠃⠀⠐⡼⠣⡘⠄⠠⣼⣿⡾⡱⠃
⠀⠀⠀⠀⠀⠀⠈⢦⡓⡀⠀⠀⠀⣶⡂⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠦⢸⣇⠀⠀⠀⠀⠀⠐⡈⢴⠏⢠⠄⣖⣽⣿⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠶⣄⠀⠜⣧⡀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⢠⣿⡌⢁⠀⠀⣄⢠⠡⣼⢏⣴⣠⣾⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣘⣧⠄⡀⠀⠀⠀⠀⣶⡿⣦⠀⠀⠀⠀⠀⠀⣆⡠⡆⣾⢷⡟⣄⠃⠀⡜⣧⢟⣵⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠢⠄⣐⣤⠶⠾⣿⣧⣳⡆⠀⣨⣿⣿⣟⡻⢏⣹⣷⣶⣶⣿⡿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠈⠉⠉⠁⠀⠀⠀⠉⠉⠁


⠀⠈⠉⠁
⠀⠐⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⠊⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠁⢀⣠⣶⠿⠿⢿⣿⣶⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⠟⠋⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡐⠲⣶⣶⠘⡟⣿⡆⢀⣴⣶⠖⢂⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣛⠻⢿⣿⣷⣌⠻⠀⣿⣿⣇⠸⠟⣡⣾⣿⣿⡿⠿⠿⠿⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢛⣩⣭⣤⣭⣅⣀⠙⢿⡿⠃⣼⣿⣿⣿⣆⠸⣿⠟⠉⠀⠒⠒⠲⠶⣶⣦⣌⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⣡⣾⣿⣿⣿⣿⣿⠟⣩⣴⣶⣶⣶⣦⣍⠛⣩⣭⣤⣤⣤⣌⠛⢿⣿⣿⣷⣦⣍⠻⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⣴⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣷⡌⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⣿⣿⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⡄⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣷⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠃⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠁⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⠀⢠⠀⢑⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐⡡⠤⠒⠈⠉⠀⠀⠀⠀⠘⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠀⠀⡴⠚⢘⢓⣒⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣸⠀⠀⠀⢆⠌⠁⢀⣀⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠌⠁⠀⠀⠀⠈⠑⠀⠠⠁⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⡈⠤⠤⠄⢄⣀
⠀⠀⠀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠑⠒⠢⢄⡀⠀⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢦⡀⠀⠀⠀⠀⠙⢆
⠀⢀⡞⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⢦
⠀⡼⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠘⡆
⢰⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢹
⣾⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠸
⡏⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⢿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸
⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠇
⠀⢧⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡞
⠀⠈⢧⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡜
⠀⠀⠀⠳⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢠⠞
⠀⠀⠀⠀⠈⠢⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⣷⣶⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠀⠤⠄⡀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣤⣠⣴⣶⣶⣤⣾⠷⠆⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣿⣯⣤⣈⠉⠛⠿⣿⣆⠲⢼⣿⡇⠀⠀⢀⣰⡿⢿⣛⣛⣛⡿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠏⠁⣀⣤⠦⠌⠉⠛⠻⢷⣤⡈⠻⣆⠠⠟⠁⢀⡼⠋⠁⣚⣉⣥⣤⣤⣤⣤⣬⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡵⠁⠀⠞⠉⠀⣀⣠⣤⣤⣤⣤⣬⣙⣷⡿⠁⠀⠀⢈⣤⠖⠛⠉⢁⣠⣤⣄⠀⠀⠀⠉⡙⠻⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⡞⠀⠀⢀⣠⢶⠛⠉⢉⣀⠀⠀⣀⣤⣭⠿⢢⡤⠤⣤⠾⣷⡶⠶⠦⢤⣤⣀⡀⠀⠀⠀⠀⠈⠑⢮⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠘⠀⢀⡴⣫⠗⠁⠀⠖⠋⣠⣴⠟⠋⠁⠀⣴⠏⠀⠀⢹⡆⠈⠙⢷⣄⠀⠀⠉⠙⠳⣦⣄⠀⠀⠀⠀⢳⠹⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⢋⡞⠁⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⣼⠏⠀⠀⠀⠀⢿⠀⠀⠀⠙⣧⡙⢦⡀⠀⠢⡙⢿⣆⠀⠀⠸⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⢣⠏⠀⠀⠀⠀⣼⣟⠝⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣷⠀⠉⠀⠀⠘⢦⠙⣷⡀⠀⢁⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⠀⠀⠀⢀⣾⣿⠋⢠⠎⠀⠀⢰⡟⠀⢠⡟⠀⠀⠀⠈⣇⠀⠀⠀⠀⣹⣧⠀⠀⠀⠀⠈⢳⡘⣷⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⣼⣿⠃⠀⠏⠀⠀⢀⣿⠁⠀⠀⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⢻⡆⠀⠀⠀⠀⠀⣧⢸⣧⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠰⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢦⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⣯⣿⡀⠀⠀⠀⠀⣽⠈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡆⠀⠀⠀⠀⢸⣼⡇⠀⠀⠀⢀⡏⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠈⣿⡇⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠈⡇⣿⠀⠀⢀⠎⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣄⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⢸⢣⡿⠀⠀⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀⠀⠀⢻⡌⣇⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⢀⡠⠃⣾⣧⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⢿⣬⡳⢤⣄⣀⣤⣴⣫⣿⣀⣀⣀⣡⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠋⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢫⡇⢸⠀⣄⠀⣄⣰⣿⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣇⣼⣄⣿⣤⣿⠙⣷⣤⣠⣤⡴⠞⠋⠁⠀⠀⣠⣄⠀⠀⠉⢀⣀⣤⠤⠶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠻⢾⣿⠁⠉⠈⠙⠁⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿⢘⠀⠀⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣾⣿⠀⢀⣿⣤⣼⠉⠀⠀⢀⣤⣄⠀⢀⣴⡄⢸⣿⣼⡀⠰⣿⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⠶⠚⠛⠛⠀⠀⣼⢣⡿⠀⢩⣿⠀⢸⡔⣀⠀⣸⡇⣿⠀⢸⡏⢸⠀⣿⣷⡃⢀⢿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠹⠟⠁⠀⢸⣿⠀⡸⣟⢹⡆⣹⣧⠞⣧⠿⡷⠈⠒⠹⠋⠙⢡⣿⡇⠀⠀⢀⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠁⠻⠀⠹⠅⠀⠀⠀⠤⢄⣀⠀⠀⠀⠀⠀⠉⠀⠀⠰⡇⠀⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣤⣈⢂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢲⠀⠀⠀⠀⠀⠀⣀⣀⡙⢦⣀⣠⠴⠒⠒⠚⢛⡛⠛⠛⠓⠲⢤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠈⠁⠀⠀⣠⠴⠚⠉⠁⠀⣀⠄⠁⠒⢤⡀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⣶⣄⠀⠒⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⢼⢳⠚⠩⣝⢦⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠾⠥⠤⢤⣄⠓⠄⠐⠁
⠀⠀⡔⢰⠃⠀⣧⠀⠈⣆⠇⡞⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⢀⠔⡉⠠⣄⠀⠑⠢⡈⢳⣄
⠀⠿⠀⢸⡄⠀⠇⣀⡠⠋⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⢀⡾⠁⠀⡏⢸⡇⠀⢹⡆⠀⠀⠱⠀⣿⡄
⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⣇⠸⣧⠀⣼⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠹⣆⠹⢰⣿⢇⣀⣀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⣠⠴⠶⢤⣀⣀⡀⠀⣀⣠⣟⣁⣀⣤⡶⠛⠁⠀⠀⠀⣀⠤⠴⠖⠚⠓⠘⠡⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠉⠹⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⢮⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⢀⠄⠀⠰⡀⠀⢀⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠐⠐⠀⢄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⡀⠁⠀⠀⠤⠖⠁⠀⢀⠀⣱⠂⢨⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⢰⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠐⢄⠀⠀⠀⠀⢲⡌⠀⠁⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠉⠉⠁⠀⠀⠂⠐⣋⠀⢀⣈⢥⡍⠤⠓⠉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⠀⠀⠀⠀⠈⠒⠤⢀⢀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⢀⡠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡤⠞⠁⠀⠀⠀⠀⠀⠊⢢⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠚⠃⠘⠛⠛⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⣀⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠑⠒⠊⠉⠁⠀⠀⠀⠀⠀⢀⡤⠒⠈⡁⠀⠁⠀⠠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠠⢼⡄⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠔⠀⢁⠠⠀⠀⠃⠠⠀⠀⡀⠂⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢸⠓
⠀⠀⠀⠠⠀⠀⠈⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣾⠔⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⡄⢡⠀⠀⠀⠀⠠⠁⠰⠀⠀⠀⡸⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡜⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠
⠀⠀⠀⠀⠠⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢰⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠎⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠀⣌⠀⠀⠀⡄⠀⠠⠆⡘⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢰⠐⠂⢲⡁⣀⡐⠀⠀⠀⡂⠀⠀⠀⠀⠳⣄⠀⣇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⢀⡼⠃⠀⠀⠐⢁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⡷⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠳⢌⣦⡀⠀⠀⢳⡀⠀⠀⠀⠀⢀⠎⠀⠀⣀⣌⠴⠋⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠈⠒⠖⠃
⠀⠀⠀⠀⠀⠱⣌⠑⠀⠀⣀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠵⢤⣀⣀⠴⠏⠤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠈⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠤⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⡨⠊⡑⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠉⠤⠉⡑⢂⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠑⠄⣀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠀⠉⠑⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⣀⡀⠀⠀⠀⢀⣀⣠⣐⣀⣀⣀⣁⣂⣤⣤⡤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢉⠄⡑⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⣄⠰⢇⡀⠅⠖⣀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢐⠠⠐⠀⠀⠉⠀⣓⣉⣁⣀⠐⠂⢬⡂⢰⡖⢶⠂⠈⠤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠔⣡⠮⠐⠈⠄⠒⠲⠿⠽⠌⠦⠓⠛⠁⠀⠀⠙⠆⠀⠑⠀⠁⠢⡀
⠀⠀⠀⠀⢀⠀⠁⡄⠀⡯⠊⡁⠄⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢠⡀⠀⠀⠈⢂
⠀⠀⠀⠠⠀⣄⠐⢀⠊⠀⡌⠠⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⣂⠀⠄⠄
⠀⠀⠀⠀⠀⠈⠀⠈⠠⠊⠁⠀⠀⠀⠐⠤⠤⡧⠚⢀⡀⣀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠑⡐⡆⠀⡆⢢⡄
⠀⠀⠀⢀⠐⠰⠀⡠⣁⠀⡀⠀⠀⠀⣀⠠⠠⠖⠨⡉⠓⡏⠃⠘⠓⠄⠀⠀⠀⠀⠀⠀⠐⠼⠀⠉⠨⡅
⠀⠀⠰⢹⠀⠀⠠⠁⡣⢪⠀⠀⠀⢏⣀⠀⢸⢄⠀⠀⠀⠐⠣⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⡄⢊⠂⠅
⠀⠀⠀⠈⡀⡆⠀⢸⠇⠀⠀⠀⠀⠀⠀⠄⠐⢾⢶⢀⣄⢀⣀⣸⡆⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠰⡄⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢜⠈⠋⠉⠈⠙⠼⠙⠉⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠄⢀⢀⢀⣀⢠⣠⠀⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⢑⣚⡂⠈⠁⠑⡀⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡀⠰⠄⠠
⠀⠀⠀⠀⠀⠀⢠⣌⠀⠀⠀⠀⣆⠀⠀⠀⠀⠸⡀⠀⠈⠳⡄⠀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥
⠀⠀⠀⠀⠤⠀⣧⠙⠀⣍⠈⣛⠂⢡⠀⠀⠀⠀⠈⠉⠀⠀⠙⠮⣀⢁⠜⠀⠀⠀⠀⠀⢠⢀⡀⢀⠸⠀⠰
⠀⠀⠀⠀⠀⢋⢉⠀⣀⡀⠢⢈⢳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠃⠉⠠⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠈⠐⢠⡌⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⢀⠅⢁⡄⣫⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢀⡁⠐⠀⠀⠀⠄⣄⢙⡋⠙⠃⠁⢀⠞⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠢⢍⡴⠦⣒⡚⠀⡀⠠⠀⠄⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡀⠀⠀⠀⠀⡰⠂⠉⠙⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣴⠀⢙⠏⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠡⡈⠀⠀⢀⠠⢺⢣⢀⡀⠀⠘⠀⠀⠀⠤⢒⣤⠄⢤⡀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⣩⢷⡿⣿⡄⠑⢠⢂⡴⣞⣳
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠥⠈⠀⠱⣄⣚⣁⣀⣘⠀⣇⠀⢀⡆⣠⢉⢽⡀⠰⠇⢌⡲⢟⣂⠁⠀⠀⠀⠀⠒⠙⢃⠘⡧⣿⣿⣽⠉⣂⡾⣟⣽⣲⠅⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⡦⢠⠄⠀⠈⠢⡀⠀⢸⢀⢿⠀⢸⢹⡝⡇⢸⠀⠂⢀⠈⣈⢊⣻⣅⣀⣀⠀⢀⣀⣀⢈⡤⠞⠓⡯⠇⠄⣯⡛⢞⣿⠏⣐⡏
⠀⠀⠀⠀⠀⠀⠀⢘⢀⣸⡄⠷⠔⠒⠉⣋⣑⠤⣁⣈⣆⠀⡟⠛⠂⠘⡖⠊⠙⠆⠸⠁⢹⠇⠀⢸⡠⠃⢀⠌⣍⠀⢰⠋⡡⡳⢂⣿⣪⣷⠇⢜⠏
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⣀⣀⠉⢸⠀⡄⠀⠀⢰⠁⢘⣹⠀⡄⠀⠀⠸⣤⠀⢸⡖⠀⠈⠀⠰⡃⠀⠈⢢⠀⠙⠻⣠⠞⠉⠤⡴⣡⡊⣀⡀
⠀⠀⠀⠀⢠⡀⠀⣤⠀⠒⠂⠀⢸⠀⠁⠀⠘⠋⠁⠀⢀⡄⠀⣈⣁⠀⢠⠀⢺⡀⠀⠀⢸⠉⠀⠸⠦⡀⠈⢙⡏⠉⠀⠀⣠⠏⡴⠶⠭⢄⡥⠤⠤⡌⢆
⠀⠀⠀⣓⢤⡉⢂⡎⢣⡀⠄⠀⢸⠀⡀⠀⠰⠚⢳⠀⢸⠀⢠⠁⠘⣇⣸⣄⠼⠘⠦⠔⠚⠛⠒⠚⠀⣈⣲⣧⠓⢲⠚⢻⡭⠋⢀⡀⢤⢾⠀⠀⠀⠀⠘
⠀⢰⠠⠽⡄⠉⢤⠸⠦⡘⡴⢶⡚⢦⠳⠦⠾⣀⠼⠶⠮⢍⡉⠀⣠⠔⢦⡔⠚⢃⠀⢀⠋⠉⡧⠒⢦⡇⠀⠈⢆⢸⠀⢸⠁⢰⢡⡤⠶⠚⠃⠙⡃⢈⡇
⠀⠀⡷⣅⠘⢆⡀⠳⡀⠃⠳⣈⢥⡀⡣⢤⠞⠁⠀⣀⣄⡠⠋⠀⢱⠀⠈⡱⡀⠘⡆⠸⠀⢸⡇⠀⢸⡇⠀⠀⠈⢾⠀⢸⡀⠘⣄⣧⡶⠀⠐⡋⠁⠘
⠀⠀⠣⡙⢬⣆⠱⣆⢠⣼⣼⠁⡐⠉⢇⡈⠀⠀⠚⣤⠤⠓⠒⠉⠉⡃⠀⢧⠱⡀⠈⠆⠀⢈⠁⠀⠈⡇⠀⠻⡄⠀⠀⠈⠳⣄⠀⠀⠀⡀⢀⠧⣀
⠀⠀⠀⠈⠦⣈⣰⡚⢿⠍⣸⣭⠙⠃⠦⣥⠀⠀⢆⢰⣤⡄⠀⠰⠂⢇⠀⠸⡀⠱⡀⠀⣠⢦⠛⠊⡤⢿⣀⡼⠘⣦⠖⣾⢳⣎⣟⢻⣍⡙⠀⠀⠀⢃
⠀⠀⠀⠀⡠⠊⡥⠒⠙⡾⠌⠧⡈⠉⠢⡈⢧⡀⠀⠉⠉⠀⣀⠀⢆⢸⠆⣉⠉⠛⠻⣉⣜⠠⢄⠒⡤⣈⠈⢡⠴⢉⡟⠯⣹⠾⡠⠄⣰⠃⠀⠀⠀⣼
⠀⠀⠀⢀⠁⡀⡈⠀⠈⠶⠀⠀⠸⠀⠀⢡⠈⣏⠁⣖⠚⠉⢉⢉⡽⡇⠀⢋⡀⠤⢀⣟⠀⢞⡊⣁⠀⢁⡔⡉⢑⠋⠍⠑⢺⣂⠬⠛⢁⠂⠀⠀⡰⡎
⠀⠀⠀⠸⠀⡇⠃⠀⠀⣧⠀⠀⠀⡇⠀⢸⠀⡹⣰⠗⠊⣱⢤⡸⢶⣿⣁⠍⡢⢄⠀⢹⠋⣥⠀⠀⠙⠙⢅⠀⠄⠀⡀⢀⠊⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠃⢁⠀⢸⡄⠀⠀⠀⡆⠇⠀⢪⡞⣰⡘⠂⠸⠁⠀⢱⣠⠽⡡⠀⠉⠢⡑⠾⡈⠋⠀⠀⢇⣀⠘⠂⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⡔⡰⠁
⠀⠀⠀⠀⠈⠺⢦⡀⠛⡄⠀⢠⠃⠀⢃⣈⢇⠈⠀⠀⠀⣀⢤⡆⠘⠀⠈⠒⠬⡀⠉⠳⢞⠓⠂⠀⢈⡘⠚⠂⠀⢀⡀⠾⣜⠢⠤⠤⢔⡩⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠋⠊⠉⠀⠀⠑⠢⠤⠤⠒⠁⠈⠑⠋⠑⠊⠤⣀⡙⠒⠠⢵⠒⠒⠉⠈⠂⣂⠀⠥⠄⠚⠁⠉⠑⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣀⠀⢀⣀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠸⣄⣀⡧⢤⣀⡼⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⡀⠀⠀⠀⠀⣀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⢀⠀⠐⠐⢉⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠘⠛⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⡀⠀⠀⢠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣬⣥⣭⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⠉⠉⠉⠉⠉⠒⢤⣸⡇
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⣾⡏⡙⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⢶⡆⢠⠄⢀⡤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡀⠀⠀⢀⡀⠀⠤⠤⠤⠤⣤⣄⠀⣿⠀⢸⣿⠘⣰⡏⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠸⣿⣷⠘⢡⠀⠀⠀⢀⠀⠀⠀⢀⡀⢠⣿⡏⠀⣿⠀⠀⣿⠇⢿⣇⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⢻⣿⣆⠈⠒⠀⠠⡠⣄⠀⡀⡞⠀⣿⡟⠀⠐⠿⠀⠀⠹⠀⠈⠛⠷⠤⠤⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠙⠿⣷⣤⣀⢱⡽⠎⡁⢹⢥⡞⠋⠀⠀⣀⢀⣀⣀⡀⣀
⠀⠀⠀⢱⠀⠀⠀⢂⠀⠈⠉⠙⡛⡠⠧⠄⠄⢠⠀⠀⠈⠀⡇⠀⣿⣿⠀⢸
⠀⠀⠀⠈⠁⠀⠀⠤⡴⢳⡜⠒⢳⣠⠊⢦⣐⠀⠄⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠈⠐⠢⡠⠇⡠⠶⠹⠀⠀⠀⢢⠠⣔⡀⢙⡀⠀⣀⠀⠀⠀⣿⣿⠀⠀⢸⣇⣠⡀⠀⠀⣀⠠⢤⣀⠀⣀⣀⣠⡀⢸⣿⠀⢀⠀⠀⣀
⠀⠀⠀⠀⡔⠀⠊⠀⠃⠀⠀⠀⠀⠑⠛⠀⢵⣾⣃⠖⠲⣠⠀⠀⣿⣿⠀⠀⢸⡏⢸⡿⠀⣀⡥⠤⠄⣿⡆⣿⡏⢸⡇⢸⣿⣤⡀⠀⢸⣧⠈
⠀⠀⠦⠀⠟⠶⡀⡀⠆⠀⠀⠀⠀⠄⠀⠀⠟⠉⠻⠀⠀⠁⠀⠀⣿⣿⠀⠀⢸⡇⢸⡟⣼⡏⠀⠀⠀⣿⡇⣿⡇⢸⡇⢸⣿⠹⣷⠀⠀⠙⣷
⣀⣀⢄⠀⠀⡀⠂⢸⡠⡀⠀⠀⡀⠱⡞⠁⠀⠈⠀⠠⠼⠂⠠⣀⣿⣿⠀⠀⢸⡇⢸⣷⠘⢷⣄⣀⡠⣿⡇⣿⡇⢸⡇⢸⣿⠀⢹⣧⠰⡀⡸
⠀⠀⢠⡀⠁⠁⠆⡶⠁⠀⠀⠀⠀⢢⠄⠀⠀⠈⠀⠀⠒⠀⢀⠄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠸⡾⣑⠀⠲⠇⠀⠄⢒⡀⣠⠋⠉⠰⡜⢤⠀⣄⠀⢈⣀⡈⡉⣭⣅⣀⠀⢀⣀⠀⠀⣀⠀⠀⢀⡀⠠⢀⣾⣿⣟⣀⣀⢤⣤⣤⢤⠤
⠀⠀⠀⠳⠀⠠⡦⠤⠖⡊⠀⠉⠁⠀⠀⠀⡏⢡⠘⢉⣿⠋⠀⠀⢰⠃⠈⠊⠱⣶⣶⡶⠶⢤⣬⡭⢛⡛⠿⢛⣉⣉⡛⠋⠉⡩⠕⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠄⠀⠀⠀⢀⠼⢃⣹⡃⣉⠉⣨⡗⠀⢳⣀⢀⢰⣰⡏⠛⠶⣬⡛⠞⠻⠿⣟⣵⣏⡏⣽⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠦⡉⣶⡉⠟⠛⠀⠉⠛⠋⠉⠉⠈⠁⠘⣽⣦⣤⡎⠁⠀⠀⡹⠓⠒⠿⠓⠺⠳⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⢎⠀⠀⢀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠁
⠀⠀⠀⠀⠀⣀⡤⠴⠋⢩⡉⠀⠀⠈⢫⡝⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⡆
⠀⠀⠀⢠⠞⠁⠀⡀⠀⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⠂⠀⣠⡛⠒⠒⠀⠤⠤⠤⢄⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠄⠒⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⠖⣞⣹⡖⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢲⣎⣸⣅⡿⠀⠀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣨⣧⠴⢧⡨⣿⡗⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠣⠀⠀⠁⠘⢳⣿⣤⡟⠀⠀⠮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠱⠀⢀⠀⠉⠁⠀⢉⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠈⢳⡤⠊⠉⠀⠉⠃⡀⠜⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢸⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠘⡄⠀⠀⠰⠄⠀⣤⣄⢠⣎⣹⣯⣠⠖⠒⠒⠳⣄⠀⠀⠀⠘⡄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠈
⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠚⠻⣠⢯⡬⠷⠼⠁⠀⠀⠀⠀⠀⠉⠒⠒⢾⠀⣠⡌⠁⢠⣀⡀⢀⡀⠤⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠎⠁⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣦⡀⢀⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⣍⠐⠁⠉⠉⠉⠋⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠁⠀⠀⢀⠛⠘⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⠐⢀⠀⢸
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⢀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡀⠤⠤⣅⠀⠈⠪⣀⠈⠐⡀⠀⠀⠀⠀⠠⠀⡇⡇⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠐⠀⠠
⢀⢣⣀⣀⠈⠙⠦⡀⠘⢧⠀⢡⡖⢂⠀⠀⠀⠀⡇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠒⠂⠤⡀
⢇⠀⠀⠉⠙⠒⠄⡈⠢⡈⢇⠀⣇⢀⡄⠀⠀⢰⡇⠘⣄⠀⠀⠀⢤⡀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠔⠀⠈⠁⠀⡀
⠰⠁⠉⠉⠐⠒⠠⠌⡑⢌⢎⠀⢿⢸⠁⢀⣢⠞⠃⠀⠱⡡⣎⢎⠄⠉⣺⡂⠐⠒⠒⠒⠂⠒⠒⠂⠐⠊⢜⣀⠤
⠀⠑⡶⠒⠒⠂⠠⠤⠤⣑⣻⠧⠼⠚⠊⠉⠂⠒⣆⢤⣐⠐⠙⡊⠀⠈⠟⠒⠒⠚⠂⠀⠀⠀⠠⠀⢐⡒⠚⠡⠒
⠀⠀⠑⠤⠤⠶⠒⠒⠒⣲⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣑⠰⠀⠱⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠂⠤⠒⠉⠈⢣⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡔⠁⠱⠀⠐⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢐⢄⠀⠀⠀⠀⠒⠀⠀⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠄⢺⡶⠂⠀⠤⠄⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠢⢔⣶⡒⢆