Hang loose Emojis & Symbols

⡴⠋⠙⠲⡀
⢳⢆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛
⠈⢦⡀⠀⡀⠘⢦⡀⠀⠀⠀⠀⢀⣀⣤⡤⣤⡀⠀⡴⠛⡭⠭⠍⠳⣄⢠⠏⠘⠛⠋⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣰
⠀⠀⢻⣀⠀⠀⠀⠱⣄⠀⠀⡴⠫⠕⠒⠂⠀⠉⢺⠃⠀⠁⠀⠀⢀⠘⡟⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠳⣄⠠⠒⠀⠘⢦⡀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢴⡇⠀⠀⠀⠀⠀⣷⠀⢸⡀⠀⠀⠀⠀⣼⣥⣤⡄⠀⠀⢠⠏
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⢠⢸⡀⠀⢄⠀⠀⠀⣾⡇⠀⠒⠲⠄⠀⢹⡇⠈⡇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠹⡄⠄⠀⠀⡀⠹⣇⠀⠒⠃⠀⢸⣾⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⣼⠃⠀⣷⠀⢠⠞⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠹⣦⡴⠊⠀⠀⢹⡄⠀⠀⠀⠈⢷⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⡀⠀⠀⣿⠀⠙⢻⣀⡞⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⡄⠀⠀⢀⠈⢿⠀⢀⡤⠒⠀⢸⡆⠀⠀⠀⠀⢠⣿⠀⠀⢼⡿⠓⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠀⠀⢻⣄⠀⠁⠀⠘⣧⠀⠀⠀⠒⠘⣇⠂⠀⠀⠁⣸⣿⠋⠒⠛⠛⠲⠄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⠀⠀⠤⢿⣆⣆⠀⠀⢸⣧⡄⠀⠀⠀⣿⡀⠀⠀⣸⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡴⠀⠀⠀⢉⡿⣿⣦⣶⣿⣿⣿⣄⣤⡾⢿⣿⠿⠿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠀⠀⠀⠈⠙⠛⠋⠙⠉⠩⠔⠒⠊⠥⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡰⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡤⠔⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⡙⠒⠀⢀⣀⣀⠀⠀⠀⠰⢤⣀⣀⣀⣀⣀⣴⡞⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠉⠉⠉⠁⠀⠀⠀⠀⣧⠀⠀⠉⠉⠉⠀⠈⠃⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⣇⠀⣇⠀⠀⠀⠀⢀⣀⣠⡴⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣳⣶⣶⣤⣤⣾⣿⣶⣛⣒⣛⣛⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⠀⠀⠀⠀⠀⠀⣀⡴⠂⠰⣴⠏⠀⠀⣄⠈⢳⡄⠀⠀⠀⠀⠀⢀⡴⠚⠉⢁⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠠⡈⢧⠀⢀⡴⠊⠁⢿⠀⠀⠀⢹⡄⠀⠀⢹⡄⠀⠙⣦⡀⠀⢀⡴⠋⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠈⢧⠸⡇⠀⠀⠸⡆⠀⠀⠘⣇⠀⠀⠈⣷⠋⠀⠈⠳⢠⠞⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⢧⢿⡀⠀⠀⣿⡀⠀⠀⣿⣆⡠⠤⣿⠔⠀⠀⣰⠏⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⢧⠀⠀⣸⣧⡔⠲⣼⠘⣧⠀⢻⠀⣠⠞⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⢿⡅⠈⣿⢧⠀⠻⠀⠈⣁⡵⠞⠁⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙⠆⠘⢀⡄⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣞⠋⠙
⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀
⣞⠁⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⡾
⠹⡄⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡒⠒⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⣸⠃
⠀⠹⣄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣛⠛⠳⢾⠁⠈⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢀⡟
⠀⠀⠘⢦⢀⣠⠀⠂⠙⣦⠀⠀⠀⠀⣠⣤⣄⣰⠇⠀⠁⠀⠈⢾⡇⠀⠀⠀⠀⢰⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢿⡁⠀⠀⠀⠈⢷⡄⢠⠞⡵⠒⠀⠈⣧⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⡇⠀⠈⢷⡀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠳⡄⠀⠰⠀⠀⠙⢿⡄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠹⣆⠀⠈⠀⠀⣷⠀⠀⠈⢧⠀⠀⠀⢀⡿⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣇⠃⠀⠀⠀⠈⢳⡀⠀⠀⠀⠠⢿⡄⠀⠀⢀⣀⢹⡄⠀⠔⠀⠸⣄⠰⠄⠈⢷⡀⢀⡞⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠊⢳⡄⠀⠀⠀⠈⣿⡄⠀⠉⠀⠀⢿⣀⠄⠀⠐⣽⡦⠀⠔⠛⠛⠻⢦⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠀⠀⠀⢹⡄⠀⠊⠁⠘⣿⡀⠀⠐⠂⢸⣿⣆⠀⠀⣸⠗⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠙⢆⠀⡀⠀⠻⣷⡇⠀⠀⢈⣿⡿⠿⠟⢫⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣠⠄⠀⠀⠈⢷⣇⠀⠀⣹⣿⣶⢶⠟⠉⢉⡀⠀⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠠⠞⠁⠈⠙⠓⠻⣛⣭⠄⠀⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢄⠳⡀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢷⣍⠂⠉⠐⠀⢀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠑⠀⠒⠛⡉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣕⣦⡤⣤⠀⠀⠀⠀⣠⡶⠂⡀⠀⠀⢀⣀⣠⠌⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠨⠍⡀⠐⠒⣩⠵⠞⠛⠛⠛⠒⠒⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⢠⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠈⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣶⣶⣶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⠟⠛⠳⣦
⣿⠀⠀⠀⠘⣧
⠸⣆⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣤⣤⣤⣄
⠀⠹⣦⠴⠚⠀⠈⠻⣄⠀⢀⣤⣤⣀⣴⠟⠉⠉⠙⢷⡟⠁⠀⠀⠉⠻⣆
⠀⠀⠹⣆⠀⠀⣀⠀⠹⣶⠋⠁⠀⠉⣯⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢹⡆
⠀⠀⠀⠙⢧⡰⠛⠁⠀⡏⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⢷⠀⠀⠀⠀⠸⡆⠀⢀⠀⠀⣧⠀⠄⠀⠈⣏⡀⠹⣆⠀⠀⠀⢀⡴⢾⡋⠁⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠘⡆⠀⠠⠄⠀⢻⠈⠁⣂⠀⠸⡄⠀⠀⠀⡟⠒⠀⠹⣆⢀⡴⠋⠀⠀⠙⠀⠀⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠤⠼⣆⠀⠥⠀⠈⢧⡀⠀⠀⢀⣷⣄⣀⡤⠛⠒⠂⠠⠛⠋⠓⠀⠀⠀⠀⠀⣀⡴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠼⠧⣄⣀⣵⠿⠿⣷⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⠉⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣤⡶⠂⠈⠉⠀⠉⠁⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣤⣄
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣦⣤⡤⠲⢖⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐
⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⣋⢀⣠⣀⢈⣉⡉⢉⠛⠛⠷⠖⠐⠄⣩⠙⠀⠀⠀⠀⠀⠀⠘⠃⢘
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣾⣿⣟⣿⣧⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡀⢀⡃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣀⣘⣲⡄⠀⠈⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⣄⠘⡇⣸⣶⣠⢼
⠀⠀⠀⠀⠑⢤⡌⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣶⣶⣬⡇⢶⡇⠀⠀⠁⠀⠀⠀⡀⡻⣿⣶⣿⣿⣿⣟⣾⣴⣦⣖
⠀⠀⢀⣀⣸⣾⣿⣦⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠆⠀⠔⠀⠝⠳⣼⣿⣿⣿⣿⡿⠟⣛⠏
⠀⢠⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣰⣄⣤⣴⣿⠟⠀⢉⣿⡁⠀⠘⡇
⠀⠀⠚⠉⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠛⠻⠟⠟⠛⠻⣿⡟⠛⠛⠻⢿⠟⢿⠿⠿⢛⡿⠻⢿⡿⢿⠿⠿⡿⠿⢿⢿⣿⣶⣾⣿⣿⡿⣿⠶⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠚⠿⠙⠓⠆⠀⠀⠀⠀⡀⣀⣤⣄⣀⠀⠀⠈⠀⠁⠂⠉⠀⠉⠉⠉⠀⠀⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠡⠀⠐⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠀⡄⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢇⠀⠤⠖⠒⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠆⡠⡅⣸⠀⠀⠀⠀⠀⠀⢈⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⣟⡄⠀⢀⡔⢹⣷⣿⣇⠢⠀⢦⠔⠀⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠆⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢲⣎⠀⢸⣿⠘⣰⢎⢀⣿⣿⣿⣿⠀⠀⡟⢠⢻⣾⠁⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠸⣿⣿⠦⢀⣾⣿⣿⣿⣿⣧⣀⠀⡿⣾⣏⣳⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⢰⣿⣿⡀⠈⣿⢿⣟⣉⡽⠿⠛⠚⠛⠛⠻⠖⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⣿⣿⣧⡀⠘⢿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⢁⠀⡀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣇⣿⣿⣿⣿⡖⠋⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠈⡴⠤⢤⣶⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⢘⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠐⠐⠲⢄⡀⠀⠀⠀⠀⠀⣼⣀⣠⠾⠟⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠠⠴⠾⠋⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠖⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠄⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢷⣄⠀⢀⡀⢠⡟⠀⠀⠀⠀⠀⠹⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢺⣌⣶⣻⣀⡟⠀⠀⠀⠀⠀⠀⠆⢱⡈⠢⡀⠀⠀⠀⠀⠀⡞⠙⠋⠉⠉⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⠛⠛⠋⠛⡉⠍⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⡀⠀⠀⠀⠀⢤⡿⠼⠳⡄⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⣠⢴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⣰⠟⠁⠀⠀⠀⢧⠀⡤⠀⣠⠟⠀⠀⠠⠈⡆⢀⣀⣀⣀⠀⠀⢀⣇⠀⠀⢀⠀⣿⢶⠶⠶⠶⠶⠶⠦⣼⣷⠋⣴⣩⠄
⠀⠀⠀⠀⠤⣄⡀⢷⣌⢿⡏⠑⠢⢤⣈⣀⣀⣱⣤⣴⣋⠀⠀⠀⣀⣴⠟⠉⠁⣨⢟⣷⣠⠋⢈⣢⣀⣠⠟⠁⠈⠳⡁⠀⠂⠀⠀⠀⠉⠻⣿⣡⡆
⠀⠀⠀⠀⠀⠈⠻⡲⣏⣾⡇⠀⠀⠀⠀⠀⣴⠯⢽⡉⠉⢙⣶⠞⠉⠀⠙⡞⢉⡾⠋⠉⠙⢶⠋⡟⣹⡏⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠈⢻⡅
⠀⠀⠀⠀⠐⠶⣲⡿⠋⢫⡉⠛⠓⠶⣤⣀⣿⡀⠀⢱⢀⠎⠘⢧⠀⠀⣀⣈⣾⣏⠉⠉⣉⣽⠧⣧⡟⠹⡀⠀⠀⠀⠀⡰⠋⠳⢄⡀⠠⠄⠀⠈⣧
⠀⠀⠀⠀⠀⣼⣋⣀⣀⣠⠵⢄⣀⣠⡟⢻⠈⠛⠛⢻⡏⠀⣴⠿⣛⡉⠉⠁⣈⣉⣻⣾⣏⠀⠀⠘⣧⠀⠙⣄⣤⢶⣶⣥⢶⠶⢦⣌⠙⢢⣤⣤⢼⡆
⠀⠀⠀⠀⠀⠙⣦⣀⡀⠀⠀⣠⣤⣼⣇⣀⠇⠀⠀⢘⣧⣼⠃⠀⠀⠬⢹⠏⢯⠀⠀⣽⣈⣦⣀⣀⡼⠷⣴⠏⠀⢸⡘⣳⣾⣠⠞⣉⣧⣸⣄⣠⡞
⠀⠀⠀⠀⠆⠀⠀⠈⠉⢻⡟⠃⠀⠀⢈⠹⣷⠒⡒⠛⠁⢯⣤⣤⣄⣀⣸⠀⢸⣀⡴⣿⠧⠤⠭⠟⢷⣼⡇⠀⠀⢠⠋⠀⢸⠷⣾⣩⠋⠈⣿⠡⢄⣀
⠀⠀⠀⠀⣾⣟⡛⢻⡆⠈⠳⠦⣤⣤⣤⡶⠋⠀⠉⠀⠀⠀⠂⠀⠀⠤⠉⠛⠛⣉⣀⣈⠛⠒⠒⠶⠚⠁⠙⠶⠶⠾⠚⠛⠋⠄⠘⠷⠶⠟⠁⠀⠀⠈
⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡍⢉⡩⠟⢳⡆⠉⠀⠀⠀⠀⠈⠛⠀⠀⣴⣚⣳⡄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣮⣿⡷⠶⠤⣤⣤⣠⣴⣶⠧⠚⠛⠉⠀⠀⠈⡀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⢿⣉⡉⣉⠙⠟⣳⡮⣗⠒⠖⠻⠿⠳⣦⣤⣤⣄⡤⢀⣀⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠉⠉⠁⣠⠏⠀⠀⢹⡆⣌⡀⠀⠿⠛⠉⠉⠉⡠⠜⠛⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠉⠀⠀⣰⣿⣗⣻⡿⠇⠀⠄⠒⠛⢁⠀⠀⠀⠒⢛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠂⠄⠒⠀⠀⠄⠐⣦⣬⠟⠋⠁⠀⠀⠀⠀⠀⠖⢀⢴⡾⠃⢺⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠷⢿⠟⢁⣀⡀⢀⡀⣠⣤⠄⣽⠇⠴⠟⠲⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⡤⠶⠛⠂⠈⠴⣉⣀⠻⠜⠓⠒⠠⠄⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢀⣦⣶⣤⣤⠙⠀⠀⠤⠄⠀⠬⢁⣀⡐⠠⠀⠀⢄⠉⠀⠀⠀⠀⠀⢀⣼⡷⠋⠁
⠀⠀⠀⠀⠀⠀⡀⣬⡆⠀⠀⠀⠒⠀⠀⠀⢶⡶⠟⠁⣠⠆⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⢀⠀⠉⠉⠀⠦⠀⠐⣾⡆⣠⠿⣁⣤⠀⠈⠉⠁
⠀⠀⠀⠀⢀⡶⠈⠀⠀⠀⠀⠀⠠⣀⠀⡀⠈⠙⣄⠠⠬⠀⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⡷⠦⠀⠀⠀⠀⠀⠀⢀⡀⢀⠈⡀⠀⠀⠀⠀⢠⣄⣤⣰⡄
⠀⠀⠀⠈⠙⠁⠀⠀⠀⠠⣀⣀⠴⠟⠐⠚⠂⠚⠃⣀⠀⠀⠀⠀⠐⠒⠚⠃⠀⠀⢤⣶⢾⡁⣀⣀⠀⢀⣨⣧⠀⠀⢻⡥⠘⠃⠀⠀⢠⡀⠀⠾⠛⠛⠋⠁⠁
⠂⠀⠀⣀⢠⣴⣶⠀⠀⣰⣟⣀⠀⠤⡀⣤⣤⣤⣤⠽⠆⢄⠀⠀⠐⠦⣤⣤⣤⠄⢀⣄⡀⢀⣀⠈⠀⠘⠁⠀⠀⠀⠀⠀⠐⠀⠐⢨⣸⣿⡆⠀⠀⠀⠄⡀
⠀⠀⠀⠛⠛⠉⡁⠀⣴⡟⢈⡀⣠⠔⢛⣻⡏⠀⣀⣀⠠⠴⠃⠤⣀⢴⠄⠉⠁⠀⢸⡿⠀⠀⠉⠀⠀⣴⣿⣦⠀⡀⣀⣀⣀⣤⣤⣾⠋⠀⠀⠀⠀⣀⣴⣷⡀
⠀⠀⠀⠀⠀⠀⠁⠚⠋⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠈⠉⢻⠛⠂⠀⠀⢙⡟⠉⠙⠛⠀⣡⡈⣶⣶⣿⣿⣿⣟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣠⣿⣟⠃⢀⣴⣶⡆⠀⠀⢙⣶⣶⣽⣌⢩⡌⠛⠻⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢾⡛⠉⠁⠀⠀⢠⡓⣚⣁⣠⣾⢾⠿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣀⠀⡀⠀⢁⠍⠉⢉⣷⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡄⣀⣠⣾⡿⢀⠔⠁⠀⢠⣿⡿⠟⠉⠀⠀⠀⠀⠀⣆⢀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣤⣶⣾⣿⣟⠟⠋⠚⠁⠀⢀⡴⠋⠁⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⣡⠇⡀⠀⠀⣤⡴⠋⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⡿⢿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠀⢀⣼⠃⠀⠀⠀⠀⠀⠶⢤⣶⣿⣿⠿⠟⠟⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢴⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⠃⠀⠰⠤⣤⣄⣰⣄⣤⣠⣴⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠓⠶⢤⡄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⣾⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣽⣿⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣠⣤⣤
⠀⠀⠀⠀⣄⠀⠀⣀⠀⠀⣠⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⣀⠀⠀⠀⠀⠠⡀⡀⢸⠐⠂⠐⠒⠒⠊⠀⠀⠀⠀⢠⣶⡀⠘⣿⡷⠋⢠⠊⠀⡇
⠀⠀⠀⢀⣿⠆⠀⡇⠀⠸⠟⠋⠁⠀⠀⠙⢏⠀⠀⠀⠀⠐⢿⠄⠀⠀⠀⠐⠟⢻⣾⡿⠷⠀⠀⠒⠢⠤⣤⠔⠀⠀⠉⠁⠀⠀⠀⠀⠉⠂⣴⣧⡀
⠀⠀⠀⠰⠿⢿⣿⢁⠀⠀⠀⠀⠀⠈⠀⣀⣦⣷⣄⡀⠀⢠⠈⠵⠆⠀⠀⠀⠀⠀⠿⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢲⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣶⣿⣿⣷⣿⠿⠿⠟⠙⠛⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⢀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⡄⠆⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣏⠀⢖⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣸⠀⢻⣷⠈⠀⢨⡄⠈⡅⠀⠀⠀⠀⠀⠀⠀⡆⢘⣿⣿⠀⠹⠛⠃
⠀⠀⠀⠁⠂⠠⡄⣤⠀⠀⠀⠀⡤⡤⠀⢠⣶⣶⣾⡟⠁⠀⠀⠀⠀⠀⡏⠘⠙⣿⣷⣦⣌⡁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠷⠀⠁⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠼⢧⡄⠀⢀⣿⠇⢀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠠⣿⣿⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠙⠻⠂⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠆⠀⢀⡀⠀⢠⢄⣴⣾⠀⠀⠀⠀⠀⢠⣿⣮⢻⣗⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⣀⠀⢠⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠈⠘⠟⣿⠀⠀⠀⠀⢀⠘⣿⡇⢣⡻⡇⠀⠀⠀⠀⠀⠀⢸⢸⣿⡿⣇⠀⠘⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠲⣤⡀⡄⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⡟⠀⠀⠀⠀⢸⣦⠈⣧⠀⢹⠁⠀⠀⠀⠀⠀⠀⠘⠈⢛⡵⣹⠀⢰⠛⠀⠀⠀⠀⠀⢸⣿⣲⣦⣤⣄⡀⠀⠘⣧⣡⣇⡴
⠀⠀⠀⠀⠠⣤⣄⣄⣠⣴⠞⠀⠀⠀⠀⠀⢸⣿⣷⠬⢠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣻⡇⢀⠀⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠛⠛⠛⠓⠛⠓⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠉⠙⠻⡛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠐⠀⢳⡎⠀⠀⠀⠀⠙⣄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠫⢤⣀⣀⡤⠾⠷⠒⠶⣄⠀⠀⠈⢆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⠶⠷⢦⡔⣉⣀⠀⢀⡤⢒⣽⠶⠶⠶⠦⣦⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢹⡄⠈⡟⠛⡶⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣤⡤⠿⠴⠷⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠉⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⢹⣠⡤⠴⠶⠚⠛⠛⠺⣧⡟⢄⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⢧⣀⣀⣀⢸⡀⠀⠀⠀⠀⣠⠴⠶⠶⠶⠶⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠳⣄⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⠀⠀⠀⡏⠉⠉⠉⠳⣄⠀⠀⢾⠁⠀⠀⣀⣀⣀⣸⡟⠛⣦⡴⠖⠒⠲⠶⢤⣀⢸⠇⠀⠈⢛⠓⢚⡿⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠓⢒⣺⣤⣄⣀⠀⢨⡟⠓⣺⠶⠚⠛⠉⠉⠁⠈⠙⢶⡏⠀⠀⠀⠀⠀⠀⠉⠻⣶⠉⠙⣶⠓⢾⠁⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠀⣠⠞⠉⠀⠀⠀⠉⠙⢻⡄⢸⡧⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠛⠛⠛⢧⡀⠀⣸⣌⣳⡀
⠀⠀⠀⠀⠀⠀⠀⡋⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⡧⣼⠃⠀⠉⠓⣤⢤⡴⠚⠒⠶⠷⠶⣄⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠹⣶⠁⠀⠈⡇
⠀⠀⣠⠞⢻⡓⠒⠓⠺⠭⡟⠀⠀⡠⠤⢤⡀⠀⠀⠀⠃⠘⢦⡀⠀⣾⠀⣾⠀⠀⠀⠀⠠⠀⠙⢧⠀⠀⢀⣀⣠⣼⠋⠀⠀⠀⠀⠀⣿⠈⠉⠉⠳⣄
⠀⣰⠋⠀⠀⠉⠢⣄⡀⠸⣇⣠⠤⠷⠶⠶⠓⠒⣳⠾⠿⠛⠿⣏⣉⠉⠉⠛⠦⣄⠀⠀⠀⠀⣠⡾⠛⠋⠉⠉⠉⠉⠙⣦⠀⠀⢀⡴⠃⠀⡠⠀⠀⢸⡆
⠀⡟⠀⠀⠀⠀⠐⠉⠙⣢⣬⣧⣤⣤⣀⣀⣀⣌⡀⠀⠀⠀⠀⠀⠉⢻⠖⠒⠒⠛⠻⣶⢾⡋⠉⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠛⢿⡀⠀⠀⠀⠀⠀⢸⣇
⢸⡇⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⣃⣀⣀⢀⣠⠴⢋⣈⡽
⢸⡇⠀⠀⠀⠀⢰⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠤⢤⣤⣤⣾⡀⠀⠀⠀⠀⡿⠀⠀⣷⠀⠀⢀⣀⣀⠀⠀⣿⢹⠟⠋⠉⠉⠉⠙⠻⣶⠊⠉
⠀⠻⠦⣄⣀⣀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⣴⣇⣀⣼⣋⢒⣒⣧⡤⠾⠶⣴⢁⡏⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⡤⠶
⠀⠀⠀⠀⠈⠁⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⢸⡧⠚⠉⣠⠞⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⠾⣆⠀⠀⠀⠀⠀⣀⣴⡿⠶⡖⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⢤⣤⣤⣤⠶⠶⢯⣁⠀⠀⠀⠀⢀⣀⣠⠞⠀⠀⠀⣇⠀⠀⣀⣤⣤⣤⠤⠤⢤⣴⡛⠀⠈⣛⢷⡛⠛⠛⠉⠸⡀⠀⠈⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣽⣟⣛⣛⠋⠉⣡⡤⠤⠤⣄⠈⠑⡞⠣⣀⡀⠀⠀⠀⠀⠀⠉⠳⣜⠧⠤⠟⠀⠀⠀⠀⠙⠒⠛⠋⠁
⢠⠞⠛⠛⠛⠛⠛⠲⣤⡀⠀⠀⠀⠀⢾⣍⡀⠀⠀⠀⠀⠈⢹⠀⢸⣅⣀⣀⣠⡾⠀⢸⡇⠀⠈⠉⠉⠛⠛⠛⠓⠛⠓⢹⡇
⡟⠀⠀⠀⠤⠤⠤⠀⢈⡇⠀⠀⠀⠀⠀⠣⣌⣉⣉⣩⣤⡴⠋⠀⠀⠉⠉⠉⠁⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠈⠓⠦⣤⣀⣤⣤⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠛⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡄⠀⠀⢹⣆
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢹⣆
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢻⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣠⣤⠶⠿⠖⠛⠛⠛⢶⣄
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣤⡀
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢹
⠀⠹⣆⣤⣤⣤⠤⠤⠤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠀⠀⢸
⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠔⠒⠛⠋⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢳⡄⢄⣀⣀⣀⠀⠀⠀⠀⢀⡀⠀⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣧⠒⠒⠀⠀⠀⠀⠀⠀⠀⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠸⣆⠸⡇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣹⠟⠉⠉⠛⠛⠛⠒⢓⣒⣒⣶⣶⣿⣿⣍⠉⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁
⠀⠙⠲⣷⣀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠁⠀⢀⣤⠖⠛⠛⠉⠉⠉⠉⠁⠀⠀⡴⠉⢳⡄⠀⠙⢷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⡟⠈⠓⠦⢤⣄⣀⣀⣀⣀⣀⣼⠃⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉⠛⠲⠶⠶⠖⠛⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠉⠉⠉⠁⡇⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⢀⣠⣠⣷⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠂⠀⠀⢀⠀⠸⡁⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠘⠢⡀⠀⠀⠀⡀⠀⠄⠁⠠⡀⠀⠀⠀⠠⠀⢆⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⡓⠈⠀⠀⠀⠀⠄⠈⠁⢀⠈⢂⢀⢀⠐⠀⠌⠂⠀⠀⠀⠠⡄⠀⠀⠁⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢄⠀⠀⡠⠀⠀⢆⠠⠀⠀⠂⠈⠣⠁⠀⠀⠀⠀⠆⢀⡈⠂⠀⠀⠀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⠀⠬⠂⠀⢢⢂⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢄⠂⠀⠐⠀⠀⡈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠀⠀⣧⠀⡀⢀⠀⠀⠀⠱⡀⠐⠀⠂⡑⢄⠀⢠⠆⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⡀⠁⠀⠈⢢⠀⠠⢠⢠⢧⣀⠀⡴⠀⠀⠀⢹⠀⢀⠂⠐⡺⡄⠀⠠⠀⠀⣌⠄⠀⠑⠀⠘⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠠⠂⠱⡇⠈⡍⠀⠑⢮⠇⠀⠀⠀⢸⠀⠘⠀⢺⠃⢹⠀⢠⠀⢄⠋⢄⠀⠀⠇⠑⢀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢂⠀⠂⠀⡅⠀⠀⠈⡇⠀⠀⠀⢸⡀⠀⢠⠃⠀⢸⠅⠀⢚⠋⠀⢸⡆⠀⠁⡀⢰⠀⡄⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠠⢼⠑⢤⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠍⠀⠀⢸⠔⠁⠂⠀⠀⡸⠀⢀⠔⣀⢀⣀⠃⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠸⡀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠘⡂⠁⠀⠀⡼⢡⠅⡁⢬⡄⠂⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠄⢀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⢸⠅⢘⣨⠜⢡⡏⠘⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠈⠀⠥⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡤⠋⠀⢠⠎⢠⡆⡁⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⢀⠂⠈⠀⡀⠀⢘⠢⣠⠁⢄⠀⣀⠀⠀⠠⠊⡥⠘⠀⡀⠀⠁⠀⠀⢉⡠⢪⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣁⣀⣐⣒⢶⣦⠥⠀⠀⠀⠀⠀⠒⠀⢐⡂⡈⠋⠂⠠⠀⢄⠀⠘⠉⠁⠀⠀⠀⠒⢋⣁⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣭⢹⣧⣤⠄⠀⣠⢲⠞⠫⡉⠀⢀⣀⣠⢶⠶⠦⣤⡆⡾⠠⠠⡒⣦⠁⠒⢲⠦⣌⠁⠚⠛⠛⢻⠯⢭⡠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠾⠶⠾⠶⠖⠛⢣⣚⠀⣶⣷⣿⣋⡻⣧⣸⡕⣤⡼⠁⣟⠃⡇⠀⢹⣧⡃⠘⡓⣿⣨⣈⡀⡶⡾⢺⣭⣥⠴⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠛⠷⠚⠀⠀⠹⢦⡶⠶⠯⠍⠙⠷⠥⠯⠭⠈⠛⠛⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⣀⠀⢸⡌⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠛⢦⡹⣦⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠘⣇⠀⠀⠀⠈⣷⠈⠙⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣏⠙⢦⡀⠹⣦⠀⠀⠀⣿⠀⠀⠈⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡟⠀⠀⢳⡀⠈⢷⡀⢠⡏⠀⠀⠀⠀⠀⠀⡾⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⡄⣠⠟⠀⠀⠀⠈⠳⢤⣼⠇⠀⢿⡄⠀⠀⠀⠀⠸⣇⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠘⢷⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠙⠳⠶⣤⣄⠀⠀⠀⢠⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠙⢦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⡇⠀⠀⠀⠀⣰⣧⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠠⠀⠈⢷⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡠⠞⠀⠀⣠⡴⠞⠁⣸⠃⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠄⠀⢸⡇⣴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⢾⠀⣠⡴⠋⠁⠀⠀⠼⠃⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⡇⣿⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⢹⡏⠀⠀⠀⠀⠀⠀⠄⠀⡠⠖⠁⠀⠀⠀⠀⢀⠀⣰⠃⠀⢀⡞⠀⣾⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢶⠀⠀⡀⠀⢀⣄⠀⠀⠀⠀⡸⠐⠁⠀⠀⡿⠔⠚⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⣤⣄⡠⠄⠀⠛⣡⡾⣿⣵⣶⡆⠀⠀⠀⠀⣤⠀⠀⠁⠀⠀⠀⠀⠀⢰⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠻⣷⣄⠀⠀⠀⠀⠄⠉⠻⢿⣶⠶⣶⣿⣿⣿⠟⠋⠀⠐⣀⣈⣀⣠⣶⠿⠂⠀⠀⠀⢀⣴⣟⣉⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣩⣽⠿⣦⣌⣃⠈⠚⢀⣴⣾⣿⣛⣉⡉⠰⢿⣶⣤⣝⡛⠉⢿⣯⣤⣤⡄⣀⣤⣶⣿⣥⣤⣤⣀⣠⣤⢤⡄
⠀⠀⠀⠀⠀⠀⣶⠉⠉⢀⣀⣀⣤⣤⠤⠾⠛⠛⠛⠛⠛⠉⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣤⢤⣤⣶⣾⣛⣉⣛⣛⠻⠿⠿⢥⣄⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠛⢽⣿⠿⠟⠋⢈⠉⠙⠛⠒⠚⠓⠲⠯⢭⣟⡂⠉⠉⢉⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⡚⣉⣁⡤⠴⠒⠚⠉⠀⡤⠶⠊⠉⠹⠖⠒⠶⠦⠤⢤⣀⣀⣠⡬⠭⣞⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠩⢽⠈⠢⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡰⠈⢧⡀⠄⠀⠍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢰⠄⡤⢇⢀⡂⠁⠌⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⡀⠠⠃⡀⠄⠈⣇⡂⠀⣰⠄⢀⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⡏⠀⡂⠈⠉⠈⠟⢐⡃⠄⣀⠠⠍⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⠠⠄⢠⢄⡀⡎⡂⠅⠂⠀⡇⢀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⢰⠣⠌⢂⠀⠀⢰⢑⠢⠁⠐⠨⠅⠅⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠰⡕⠂⠀⢐⣀⠀⢸⠃⠁⠀⡀⢸⢐⠠⢀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢄⡀⠀⠐⢏⡚⡎⠀⡴⠀⣜⠄⡊⠔⠠⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠐⠈⠸⡀⠄⢀⠘⠁⠣⢠⠏⠀⢗⠨⢂⠁⢂⠅⣂⢣
⠀⠀⠀⠀⠀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠉⡯⠂⠠⠀⠀⠐⠀⠸⡄⠀⠸⣂⠕⢊⠄⣊⠔⠀⣀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠹⡂⠄⢐⠀⠂⢀⠌⣮⠀⠼⡅⢊⠔⡨⠐⡈⠀⣆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡎⡂⠡⠐⠒⠀⢈⠰⠓⠀⣄⢨⠔⡩⢐⠡⠀⠔⢉⠘⣄
⠀⠀⠀⠀⢀⠂⢀⡜⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠔⠇⡇⣒⡨⠅⠀⠀⠬⠂⠀⠰⠊⣀⣡⣂⣕⡈⡐⣀⣄⡠⠈⢢
⠀⠀⠀⠀⢠⠀⣸⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⢠⠭⠀⡂⠅⠀⢸⠍⡢⠅⠀⠈⠁⠠⣠⠅⠀⠠⢘⠵⣪⠅⢸⡆
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⣠⠆⠀⠀⠘⡎⠅⣂⠈⠀⣘⠡⢂⠁⢀⠇⠀⠀⠲⠒⠖⢢⢒⠠⢒⠤⠀⢿⡲⠄
⠀⠀⠀⠀⢰⡀⣷⡄⠀⠀⠂⠀⠀⠀⡔⠣⠀⠀⠀⢠⡃⠅⠐⠀⡄⠳⡌⠂⣠⠎⠀⠈⠀⠀⠀⠀⢸⠅⢂⠅⢂⠀⠿⡧⡀⠈
⠀⠀⠀⠀⠀⠙⠢⡁⠠⠀⠀⠀⠄⢰⠁⠠⠀⠀⢀⡖⠀⠁⠐⠀⠀⠀⢂⠎⢑⠀⢐⠨⠀⠈⡥⠤⠸⣊⠄⡈⠄⠀⣠⠇⢀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠴⠢⠸⠤⠉⠀⣰⠃⠀⠄⠀⠀⠃⠈⢰⠑⡈⠅⠀⠁⡀⠕⡠⢀⠀⠀⢷⡠⢂⣤⠎⣁⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⡄⣀⣁⠒⠨⠀⠀⠲⠴⡀⢞⠄⠀⠅⠂⠡⠂⠅⠪⠀⠅⢀⡄⠒⠉⡀⠄⢀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠈⠉⠒⠒⠲⠤⠀⠲⠚⠒⠒⠒⠒⠀⠖⠃⠀⠀⠀⠀⠐⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣖⠚⠋⠉⠉⠉⠁⠀⠀⠉⠉⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢳
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣼⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠈⢧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠚⠛⠒⠦⣄⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠬⡗⠶⢤⣄⣀⠀⠀⠀⠀⣀⣀⡀⢸⡇⠀⠈⠓⢦⡀⢀⣀⡀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠸⣅⣂⣀⠟⠀⠀⠈⠉⠉⠛⢻⠋⡁⠈⠹⡾⣇⠀⠀⠀⠀⡷⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⠛⠲⣜⢄⣈⢀⣀⠗⠙⢦⣄⣀⢀⡇⠀⠀⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠳⢄⠀⠈⢧⠈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠠⠄⠄⠄⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⠋⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⢠⣿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⡇⠀⣿⡟⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢰⠀⠀⠀⠀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⡜⠀⠀⣿⡇⠀⠀⠀⢀⠎⠀⠀⣀⡀⠀⠀⢀⣿⣿⠀⠀⠀⡆⠀⠀⣠⣾⡿⠋⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⡠⠊⠀⠀⠀⣿⣇⠀⠀⡠⠊⠀⠀⠸⣿⡿⠀⠀⢸⣿⡏⠀⠀⡜⠀⠀⢰⣿⡿⠁⠀⡔⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⣿⣿⡠⠞⠀⠀⠀⠀⠀⣿⣿⣀⠔⠁⢀⠀⠀⠀⢀⣀⠀⠀⢸⣿⡇⠀⡜⠀⠀⢠⣿⡿⠁⡠⠊
⠀⠀⠀⠀⠀⢇⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠠⠊⠀⣿⠀⠰⣿⣿⠀⠀⠀⣿⣇⠜⠀⠀⠀⣼⣿⡧⠊
⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⠜⣿⣿⡃⢀⣾⡿⠀⠀⢿⣿⠀⠀⠀⣿⡏⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⠎⠀⠙⠿⠃⣾⣿⠃⠀⠀⠀⠻⢧⠠⠚⠹⣿⠀⠀⡰⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⠎⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠊⠀⢸⣿⠀⠀⠀⠀⠐⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠤⠔⠁⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢀⣴⠾⠛⠳⠀⠀⠀⠀⠀⣠⣼⣿⣶⣶⣶⣤⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⢠⣤⠀⢻⣆⠀⢀⣿⡏⠀⠀⢀⠀⠀⠀⠠⠋⠁⠀⠀⢀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢢⠀⠀⢡⠀⠘⡄⠀⠀⣠⣤⡅⠀⠀⠈⠉⣼⣿⠀⠀⠀⡌⠀⠀⣀⣤⣄⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠆⠀⠀⠀⠑⠲⡦⠒⢸⣿⣿⠃⠀⠀⠀⠀⣿⣿⠀⠀⡘⠀⠀⣴⣿⠋⢨⠀⠀⠀⢿⣷⡀⡌
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡏⠀⠀⠀⠀⠀⣿⣿⢀⠜⠀⠀⠀⣿⣏⠤⠃⠀⠀⠀⠈⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⡔⠹⣿⣇⠀⠀⠀⠀⠀⢀⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠊⠠⢤⡤⠔⠻⣿⡀⠀⠀⢀⡠⠂⠁⠙⢿⣷⡀
⠀⠀⠀⠀⠀⢸⠀⠀⢻⣿⡄⠀⠀⠀⠀⡌⠀⠀⠈⢿⡇⠀⠀⠀⠀⡠⢿⣿⡆⠀⠀⠃⠀⠀⠈⠉⠀⠉⠁⢀⠔⠂⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠠⠁⠀⠀⠀⠈⠻⠤⠤⠔⠉⠀⠈⢿⣧⠀⢀⠇⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⡠⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠿⢋⢀⠀⠀⢀⣀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣦⠀⣸⣶⢸⣀⣴⡆⣁⣴⠟⢩⣿⡇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠉⣿⣿⢴⣿⠁⡘⢸⣿⣀⢸⣏⡀⠉⣿⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢠⢾⣿⡟⠈⠿⠞⠀⠈⠙⣥⠘⢋⡴⢲⠈⠛⠁⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⢡⢾⣿⠇⣰⣿⣶⢲⠀⣴⡆⢀⣾⠐⡁⠀⢀⣴⠒⠘⢶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣾⡟⠀⣿⣿⠀⢹⢹⣿⠁⢸⣧⠊⢹⣷⣸⣧⠀⢀⢢⠚⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⠟⠀⠀⢻⣿⡠⠃⠘⠿⠤⢻⣿⣜⣸⠟⠈⠛⠒⠁⠘⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡔⠲⣄⠀⠀⡀⠀⣠⣤⡀⠉⠀⣰⢎⠕⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡆⢸⣀⣾⣿⡜⠀⣿⡇⠀⣸⡟⠀⣠⣿⠂⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠉⢸⠁⢿⣿⡇⢸⣿⠁⣼⣿⠁⢠⢹⣿⠀⡜⣿⡷⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢠⠎⠀⠸⣿⠇⠘⠿⠞⠘⣿⣤⠏⠀⠛⠛⡴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢄⠀⠀⠀⠀⠀⡄⠀⡇⢀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⢷⠀⠀⠀⢰⡿⣄⠐⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠜⠀⠀⠀⠈⡧⢈⠑⢄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣧⠀⠀⠀⠀⠀⠘⢖⠁⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠈⢸⠀⡼⠀⠀⠀⠀⠀⠑⣤⠂⢀⠙⣆⠀⠀⠀⢀⠞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⢀⠨⣸⠀⢇⠳⡀⢤⣀⠀⠀⠈⢢⠀⢐⡘⡆⠀⢠⢁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⡂⠑⠄⢳⠀⠀⠁⠺⠌⡮⠳⡄⠀⢸⠂⡁⠁⢵⠀⠘⣡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡇⠀⠘⢄⠈⠢⡀⠀⠀⢠⠇⠂⣻⢠⠏⠀⠇⠠⡍⠀⢰⢻⡀
⠀⠀⠀⠀⠀⢯⠢⣄⡀⠀⠀⢳⠅⠘⡀⠑⢄⠙⣆⣠⠋⣠⠀⠿⠉⡠⠁⠂⢠⠃⠀⡼⠐⣇
⠀⠀⠀⠀⠀⠈⠢⡀⠙⡄⠀⠀⠱⡄⠑⡀⠀⠳⡈⠃⡐⠀⡄⢀⠎⠀⡐⢠⠏⢀⣴⠇⠀⢻⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠰⣤⣅⡚⠀⠀⠀⠘⣦⠐⡀⠀⠱⡐⠀⠀⡖⠁⠀⡐⢠⣮⡴⠛⢁⡀⠀⣼⠀⠀⢀⠜⣹
⠀⠀⠀⠀⠀⠀⠀⠈⠑⡌⠓⢤⠀⠀⢸⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠛⣀⠄⠒⡉⠀⣴⠏⠀⢐⡡⠞⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⡀⢳⡀⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠊⠀⢀⠎⢀⡤⠁⠀⠀⢈⠔⢫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⡄⢷⠟⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘⠀⡜⢁⣴⠏⡴⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠐⠀⢠⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠘⣵⠯⢹⢰⠃⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⠃⢦⢘⠟⡌⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠈⢦⡰⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⠀⠀⠀⣀⣀⠀⠠⠌⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠡⠐⠈⠐⠠⠀⠠⠀⠤⠂⠄⠂⠀⠠⠀⠠⠤⠆⠑⠀⠀⠁⠒⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡄⠀⠀⢀⣀⣀⠄⠀⢀⣀⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⣿⢀⣾⣿⡿⣿⡆⢠⣿⡿⢻⡇⠀⢸⣿⡿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⣼⣿⡿⠁⣿⠁⣼⣿⠃⢸⣿⠀⢸⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⣿⣿⠃⢠⣿⠀⣿⣿⠀⣼⡇⠀⣿⣿⠇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠐⢶⡞⠀⣿⣿⠀⣼⡏⠘⣿⣏⢠⣿⠃⠀⣿⣿⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⠾⠁⠀⠙⠿⡿⠛⠁⠀⠻⠿⠾⠋⠀⠀⠿⡿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢰⡆⢠⣶⣤⠀⢰⣶⢤⡄⠀⣴⣶⣦⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣾⠁⢸⣿⡟⠀⣿⣿⢸⠇⠀⣿⡇⠀⠀⢸⣿⡏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠇⠀⢸⣿⡇⠀⣿⣿⣇⡀⢠⣿⣇⡀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣸⣿⠇⠀⣿⣿⣸⡇⢸⣿⡏⠁⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠹⠿⠀⠀⢿⡿⠟⠀⠸⣿⣅⡀⠀⢷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⡀⠀⣠⡀⠀⠀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠙⡆⠀⣿⣿⡆⢸⡇⠀⣿⣿⠀⠀⣿⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠀⣿⡿⣿⢸⡇⠀⣿⣿⠀⠀⣿⣿⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⡏⢀⣿⡇⢸⣿⡇⢀⣿⡏⠀⠀⠈⠛⠷⢾⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡿⠁⢸⣿⠇⠀⠻⠀⠸⣿⣧⡀⠀⠀⢠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⢸⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⣼⡿⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⣼⡿⠁⡀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⣠⡞⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⢀⠀⣸⣿⡃⣸⠁⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀⢀⣴⣿⠁⠀⠀⣠⣾⣿⣿⡿⠁⠀⢠⡄⢰⣿⣿⠃⡿⢰⠋
⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⣰⣿⣿⠃⠀⣠⣾⣿⣿⣿⡿⢁⠀⠀⣸⡇⢸⣿⡿⢀⠳
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⢀⣼⣿⣿⠃⣠⣾⣿⣿⣿⣿⠋⢀⠂⠀⢠⣿⠁⢨⡿⢁⡿⣈
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣼⣿⡿⠙⡿⣿⠇⣼⢡⣿⢇⣴⣿⡿⣿⣿⠟⠁⣰⢋⡞⣠⣾⠋⠀⠈⣠⣟⣼⠃
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⣿⠏⠀⢰⡇⣿⢸⠇⣸⣿⣾⣿⠋⣴⣿⠏⡌⣰⣧⣞⣴⡿⠁⠀⣠⣾⣿⡞⠁
⠀⠀⠀⡄⠀⣿⣆⠀⠀⠀⣿⡏⠀⠀⢸⠃⠋⢸⠀⣿⣿⣿⠁⣸⣿⡏⣼⢠⣿⣿⣿⡿⠁⣠⣾⣿⡟⠉⠀⢀⣤⡾
⠀⠀⠀⡇⠀⢿⣿⡄⠀⠀⣿⠁⢠⡇⣾⠀⠀⠈⢀⣿⡟⠀⢠⣿⣿⢰⡏⢸⣿⣿⣿⠁⣼⣿⡿⠋⢀⣠⣶⣿⡟⠁⠠
⠀⠀⠀⣧⠀⡘⣿⣷⠀⠀⡿⠀⣸⣿⡟⠀⠀⠀⢸⣿⠀⠀⣼⣿⡇⣾⣇⢸⣿⣿⡿⣸⣿⡿⠁⢀⣾⣿⠟⠋⣠⠶⣡⠔⠁
⠀⠀⠀⣿⡄⠱⣍⢿⡆⠀⡇⢀⣿⣿⠇⠀⠀⠀⢸⡇⠀⠀⣿⢩⢣⣿⣿⢸⣿⡟⣿⣿⣿⠁⢠⡿⠋⣠⣴⣿⡷⠞⠁
⠀⠀⠀⢿⣿⡄⣿⣿⣷⠀⠃⣸⣿⡿⠀⡀⠀⠀⢸⠀⠀⢸⡇⡾⣸⣿⣿⢸⣿⣧⢹⣿⣿⠀⣿⢀⣼⣿⢟⠁
⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⢠⣿⡿⠁⠀⡇⠀⠀⠸⠀⢸⣼⣸⢣⣿⣿⢇⣾⣿⡇⣼⣿⣿⠀⠁⣼⣿⡿⠋
⠀⠀⠀⠀⠘⣿⢿⣿⡇⢠⣿⡿⠁⠀⢀⡇⠀⠀⠀⠀⣾⣿⢇⡞⢹⢟⣾⣿⣟⣴⣿⣿⠟⢀⣴⣿⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⣿⣿⢁⣿⠟⢀⡞⢀⣼⡇⠀⠀⠀⣸⣿⠏⢌⢀⢫⣾⣿⣿⣿⢿⠿⠋⣠⠞⠋⠀⠀⠀⠀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠘⠇⣼⠏⢀⡞⢀⣼⣿⠁⠀⠀⣰⣿⠋⠀⣼⣠⣟⣵⣿⠿⠋⠀⢀⣈⠄⠀⢀⣤⣴⠾⠛⣩⡟
⠀⠀⠀⠀⠀⠀⡈⣾⠃⢀⡾⣠⣾⣿⠇⠀⠀⣼⡿⠁⠀⣼⡇⣏⣿⡟⠁⢀⣠⠞⠋⠀⣠⡾⠋⠉⢠⣴⣾⡟
⠀⠀⠀⠀⠀⠠⢰⠏⠀⣼⣿⣿⣿⠋⠀⠀⣼⠟⠀⠀⣼⣿⣇⢻⡟⠀⣠⣾⡏⠀⣠⠞⠉⠀⣠⣶⣿⣿⡿⠀⣾
⠀⠀⠀⠀⠀⠀⡎⠀⢠⣿⣿⡟⠁⠀⠀⢼⠋⠀⠀⣰⣿⡿⢻⢸⠃⣰⣿⡿⠀⠀⠀⠀⢀⣼⣿⣟⣾⡿⠁⢠⢻
⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢀⡼⠋⣾⡷⣄⣾⣰⣿⣿⠃⠀⠀⠀⢠⣿⣿⢻⣾⡿⠁⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢠⠏⣰⣿⡟⢇⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⢠⠊⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠰⢣⣾⣿⣿⣿⣾⡿⠟⠋⠀⠀⠀⢀⣾⣿⣽⡿⠛⠁⢀⡴⠁⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣶⠀⠀⠀⡴⢋⣽⣿⠿⠋⠁⠀⠀⠀⠀⢀⣴⣿⠿⠟⠉⢀⣠⣶⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠠⢸⣇⢰⡇⠀⢀⠞⣰⠟⠋⠀⢀⣀⣤⡶⣮⡤⠞⠋⣁⣀⣤⣴⣾⣿⣿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⡟⠀⠀⢀⠞⠁⠀⣠⡶⠟⠋⠁⠀⣀⡴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⢠⣡⣿⡟⠀⠐⠀⣠⠄⢀⡾⢋⡠⠆⠀⠀⢊⣥⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⢀⣠⡾⠁⠐⣡⡴⠋⠀⠀⣠⣴⠿⠛⠋⠉⠉⠁
⠀⠀⠀⠀⢰⡿⠋⢀⣤⣶⣿⠋⠀⣠⣾⠟⠁⠀⣠⠾⠋⠁
⠀⠀⠀⢀⠟⢠⣾⠿⠟⠋⠀⠐⠚⠋⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠠⠀⠀⠀⣠⠄⣸⡇⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⡇⣶⠇⠠⣶⡆⢀⢴⡏⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⣿⠇⣿⠀⠀⢿⠀⠀⠸⡇⠘⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠀⢀⣤⠦⠀⠀⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢾⠀⠀⢀⣾⠁⠀⠀⠀⠈⠀⢰⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⡖⠀⢡⠀⢸⡏⢀⡀⠀⢀⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣧⢠⡿⠀⣿⡅⠁⣿⣰⡏⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠸⡇⠀⣿⠁⢰⡿⠸⡇⠰⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠑⠀⠙⠀⠚⢁⡤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢲⡄⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠠⠀⣼⠇⢸⡇⠀⢠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢰⡇⠀⠎⢹⡇⠀⣿⠀⢸⡇⠀⣿⠀⣾⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⡠⠀⠸⠇⠀⣿⠀⢸⡇⡸⠻⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⠀⡀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠁⠀⠀⢀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢿⣷⣔⣦⣀⡀⠀⠀⠀⠀⣠⣶⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⢷⣀⠘⡿⠷⠋⠉⠙⢣⣠⡀⠛⠛⠛⢛⣿⠀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣄⣈⡀⠀⠙⠣⢬⡗⢒⡒⠐⣶⠛⣦⣄⡀⠀⢀⠸⠒⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠓⣦⣤⣀⣀⣀⣁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣻⠁
⠀⠀⠀⠀⡀⠀⠀⠑⠒⠚⠛⠛⠛⠛⠻⢛⣟⣛⢛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠿⠷⠶⠶⠤⠤⠆⠀⢠
⠀⠀⠀⠈⠁⠀⠀⠀⠊⠀⠀⠉⢀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⢰⣷⣿⠇⠀⢻⣷⡆⠀⠀⢰⣷⣿⠿⣿⣿⣆⡄⠀⠀⠀⠀⢻⣿⣿⣿⣶⣇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣶⠀⠀⠀⠀⡄⣿⣿⠏⢿⣿⡆
⠀⠀⠸⣿⠁⣰⣦⠈⣿⡇⠀⠀⢸⣿⠿⠀⠘⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣶⡿⠁⡀⠛⣿⠀⠀⠀⠀⣿⡿⠁⠀⢸⢿⡿
⠀⠀⠀⠙⠦⡙⢛⠴⠋⠀⠀⠀⠀⠻⠄⠀⠀⠠⠟⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠹⠄⢾⡿⠀⠋⠀⠀⠀⠀⠙⠧⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣆⢸⣿⡄⡄⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⢠⡄⣾⣿⢿⣿⣀⡄⠀⠀⠀⠀⣶⣻⣿⣷⢀⡄
⠀⠀⠀⢸⣿⣿⣿⣇⣷⠀⠀⠀⢈⣿⣿⠏⠻⣿⣿⣶⠀⠀⠀⣼⣿⣿⠋⢻⣿⣧⠀⠀⠀⣿⣿⣿⠟⠈⣿⣿⣿⠀⠀⢰⣦⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇⢀⣦⠀⣿⠇⠀⠀⠀⢻⣿⠁⠀⣼⢿⡟⠀⠀⠀⠸⣿⠉⢀⣆⠉⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠈⠁⠘⠟⠁⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠛⠟⠀⠉⠀⠀⠀⠀⠈⠙⠚⠛⠛⠋

⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⢀⢀⣼⣿⣷⡄⠀⠀⠀⠀⡀⠈⣿⣧⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠀⡀
⠀⠀⢀⣿⣿⣿⢿⣿⣿⡄⠀⠀⢀⣿⣄⣽⣿⡟⢀⡀⠀⠀⠀⡀⢻⣿⠛⢿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⣿⣿⣿⣾⣿
⠀⠀⠸⣿⡟⠉⠀⠹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⣿⣾⠋⢠⡀⢻⣿⠀⠀⠀⢠⣸⣿⡏⠿⣷⣾⡆⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿
⠀⠀⠀⠻⣧⡀⠀⣰⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⢿⣄⣿⣧⡼⠃⠀⠀⠀⠀⠻⡏⠁⠐⢻⡟⠀⠀⠀⠈⢿⡿⠷⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⣼⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢳⣶⡆⠀⢰⡏⠀⠘⡇⠀⢠⡏⠀⠈⡇⠀⠀⣴⡟⠑⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⡞⢹⡇⢀⣾⣿⠀⠀⡇⢀⣾⣿⠀⠀⡏⢀⣼⡿⠀⠀⣿⠏⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢀⡞⠁⢸⣿⠾⣿⡏⠁⣾⠟⠋⣿⡏⠑⢶⠟⠋⢿⡇⢀⡴⣿⡄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣠⣾⣿⠀⠻⢧⡴⠋⠀⠀⠹⢧⡴⠏⠀⠀⠈⠛⠛⠀⠙⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣸⡇⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⣿⠃⠀⢠⡄⠀⠀⣼⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠀⠾⠁⠀⢰⣿⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⣰⡆⠀⠀⣼⡿⠀⠀⢸⣿⡞⢀⡴⣦⡀⠀⠀⢠⣾⢟⡦⠀⣾⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡿⠳⠤⢴⣿⡇⠀⠀⣼⣿⢀⡏⠀⣸⡇⠀⢠⣿⠗⠚⠁⠀⣸⣿⡀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠇⠀⠀⢸⣿⠁⠀⣰⢿⣿⡼⢀⣤⣿⡧⠖⠛⣿⠀⠀⠀⣼⡧⢽⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠴⠏⠀⠀⠀⠀⠻⣦⡴⠃⠈⠿⠇⢯⣼⠟⠀⠀⠀⠙⠦⡤⠞⠙⠧⠼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⢷⠀⠀⣶⣦⠀⢠⣶⣦⠀⠀⣿⣇⡾⠁⠀⣶⡄⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⢸⡇⢀⣿⡯⢀⡏⣽⣿⠀⢀⣿⡟⠁⠀⢸⣿⡇⠀⡼⢻⣧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠓⢤⣾⠶⠛⣿⡇⣼⠀⣿⡇⢀⡾⣿⡇⠀⢀⣾⣿⠁⢰⠃⣿⣿⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣴⠃⠀⠀⢿⣿⠇⠀⢿⣧⡾⠁⠙⢿⣴⠟⠘⣿⣤⡏⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡉⠓⢄⠀⠑⠀⢠⠀⠆⠀⡆⠸⠀⡄⢀⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠖⠛⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⠀⠀⠱⡄⢡⠈⡇⠀⡠⠴⠦⣄⠀⠌⢠⠂⢀⠂⠀⠀⠀⠀⠀⡴⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢹⠁⠀⠀⢳⠀⠣⢁⣾⠁⠈⠁⢸⠖⠒⠲⡄⠁⡴⠃⢀⠔⢠⠞⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢸⡇⠀⠀⢸⠀⢠⢞⠇⠀⠀⠀⡏⠀⠀⠀⡼⠒⡒⢤⠀⡰⠃⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠄⢸⡇⠀⠀⠈⢷⠋⣨⡴⢒⠒⣒⠲⣤⣀⠸⠁⠀⠀⢨⠟⠀⠈⢂⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⠀⠀⠉⠀⢠⠞⡥⣤⡏⣿⡏⣷⡖⡌⣧⡀⠀⡰⠋⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⡀⠀⠀⠀⡸⡀⣷⡾⣧⠟⢷⡋⠏⣥⠬⡁⠼⠁⠀⢲⡼⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⣇⠀⠀⠀⡗⢨⣓⣒⣒⡬⡅⣞⠙⢯⠀⣿⠀⠀⢀⠞⠠⠤⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠔⠒⡀⢸⡄⠀⠀⠹⡌⢿⢹⣿⡿⣧⡟⠸⠾⣡⠃⠀⢠⠏⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⢁⠄⡞⠈⠂⠀⠀⠙⠲⣜⡛⠷⠛⣛⡡⠟⠁⢀⡴⠃⠤⡈⠑⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠄⢧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⡴⠋⢄⠀⠢⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠂⠙⢦⡀⠀⠀⠀⠀⠀⠀⠒⣲⠞⠉⢄⠈⢀⠑⠄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⠉⠲⠤⣄⣀⣀⣠⠔⠁⡀⠡⠀⠣⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡄⠀⠀⢰⠀⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠉⡰⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠛⠲⢤⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠜⢁⡀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠱⡄
⠀⠀⠀⠀⡞⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⣠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢻⠀⠀⠀⠀⢤⡀⠀⢦⡀⠀⢀⣼⠃⠀⠹⣦⡀⢀⣼⠏⡴⠏⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢸⠰⢦⣄⠠⢤⡛⡷⡄⠻⣤⠻⠹⠀⠀⠀⠘⢝⡎⡞⡜⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢸⠀⣤⣙⢿⢦⣿⣶⡼⠖⠓⠓⠚⡱⠻⣷⣦⡸⢰⡿⢀⠏⣾⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠘⡆⠀⣙⣷⣱⡹⡟⠀⠀⠀⠀⠐⠁⠀⠈⢿⡇⢸⡇⡞⣸⣿⣘⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠉⡏⠁⠀⢘⡷⢧⡀⠀⠀⢀⣀⣀⣀⡠⠾⣇⣸⣷⡉⠉⠁⢹⠇⠀⣇⣀⣸⣀⣀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠚⠋⠉⠈⠉⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣴⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⣿⣹⣄⠀⠀⠀⠀⠀⣎⣿⡀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⣰⣿⣷⡇⡀⠀⠀⠀⣠⣻⣿⣇⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⢾⠆⠀⠀⠀⠀⢸
⠀⠀⠈⢏⠙⠙⠳⠃⠀⠀⠐⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡧⡰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣸⣿⣯⣿⠃⠀⠀⠀⠀⣴⢢⠀⡀⠀⠀⠀⠀⠀⣤⣵⢡⡀
⠀⠀⠀⣀⣤⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⢠⣶⣧⣦⡾⠵⠀⠀⠀⠀⣤⣿⣿⣧⣿⡄
⠀⠀⠀⠹⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠕⠚⠎⠉⠁⠀⠀⠀⠐⠿⠿⠿⠿⠋⠀⠀⠀⠰⠿⠿⠿⠿⠿⠟⠿⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⠸⣄⡄⠂⠀⠀⠀⠀⠀⠀⡾⡇⢠⠇⠀⠀⠀⠀⠀⠀⠈⣉⣰⠀⠀⠀⠀⠀⠀⣴⡴⡀
⠀⠀⢠⡘⡰⢪⡕⠚⢀⠀⠀⠀⠀⣄⡇⢷⡾⣴⠀⠀⠀⠀⠀⣄⣠⣏⡍⠀⠀⠀⠀⠀⠐⠛⠛⣥
⠀⠀⠀⣷⢃⣾⠳⣉⠛⠀⠀⠀⠀⠻⠃⣰⣄⠹⠀⠀⠀⠀⠀⠈⢢⡻⣧⠔⠀⠀⠀⢰⣟⡆⣳⠛⠟
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠈⠋⠠⠈⠂

⠀⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⢾⣿⢊⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⡀⠀⠀⠀⠀⠀⠠⢂⣿⡄⡄⠀⠀⠀⠀⢀⢠⣆⡿⡸
⠀⠀⠀⠀⢾⡘⢶⠀⠀⠀⠀⠀⠘⠹⡶⢆⠛⠓⡃⠀⠀⠀⠀⣦⣺⠙⣷⣷⡀⠀⠀⠀⠀⠹⡉⢘⠃⡆
⠀⠀⠀⢲⣸⡷⣾⡇⠀⠀⠀⠀⠀⣟⠃⣼⢆⡙⡇⠀⠀⠀⠀⢻⡏⢣⡅⠻⠁⠀⠀⠀⢠⣷⠿⡏⠲⡄
⠀⠀⠀⠀⠀⠾⠙⠀⠀⠀⠀⠀⠀⠉⠘⠋⠈⠋⠀⠀⠀⠀⠀⠀⠁⠋⠉⠀⠀⠀⠀⠀⠀⠘⠰⠙⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣀⣀⣀⣀⡄⠀⣠⣤⢴⣦⡀⢀⡖⡫⠻⣶⡄⠀⢀⡴⢿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠰⣿⡟⠁⢉⣿⣁⣴⠟⣏⠀⣿⡇⡞⠀⢧⣠⣿⣇⣴⡟⠀⠀⡿⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠈⠉⠉⣿⠏⠀⣯⠀⠈⣹⡿⠋⡇⠀⢀⣽⠟⠁⢾⣇⢀⣼⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠞⠁⠀⠀⠙⠤⠾⠋⠀⠀⠙⠶⠛⠉⠀⠀⠘⠿⠟⠁⠳⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢸⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢸⣿⡆⠀⣴⡿⠀⠀⠀⣿⡡⠋⠀⠀⠀⣠⡤⡄⠀⠀⣿⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⠀⠀⠀⡿⠖⢪⣿⠁⠀⠀⣸⣿⠒⣷⣄⢀⣾⣟⡴⠃⠀⠀⡹⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⣿⣄⣀⡼⠁⠀⠸⣯⠀⢀⡴⢻⡇⠀⣼⡇⣸⣿⡏⠀⢀⠀⠊⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠙⠓⠛⠁⠟⠻⠶⠟⠒⠁⠉⠛⠛⠁⠀⢰⣷⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⢤⣄⢀⣀⡀⠀⠀⠀⠀⠈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠊⠀⠀⠀⠀⠀⠀⠁⠠⣷⡄⢀⡀⠀⠈
⠀⠀⠀⣠⣾⠙⡉⠉⠉⠉⠑⠀⠃⠠⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠁
⠀⠀⠀⠹⢿⣦⡦⡀⠀⠀⠀⠀⠒⠗⠀⠈⠐⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠉⢣⠰⣄⡰⣄⣀⢠⠀⠀⡀⠬⣤⣘⠀⢤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠪⣍⠳⢷⡀⢁⡑⠰⠡⡥⠚⢰⡊⢳⣶⡆⠠⢀⣠⠞⠀⣀⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠥⣤⣿⣥⣏⣽⣿⣟⣿⣧⣥⡼⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣾⣿⠿⠲⣄⠠⠀⠀⠀⠉⢻⠉⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣴⣿⣿⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⠇⠀⠀⠀⠋⠀⠀⣀⡀⠀⠀⠀⢀⣀⠠⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢈⣴⣶⡶⣄⠀⢁⣴⣶⡶⡄⠀⠀⣀⣤⣤⣿⣿⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⠀⠀⠀⣹⣧⠀⢰⣿⣿⡏⠀⡟⢰⣿⣿⡏⠀⡿⢀⣾⡿⠁⢸⣿⣿⡟⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⣿⡇⠀⢀⣴⣿⣿⡇⢸⣿⡏⠈⢳⠷⢾⣿⡇⠈⢳⠷⣾⣿⠁⣰⠻⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⣿⣿⣶⠟⠩⣿⣿⡇⠀⠙⠳⠒⠁⠀⠈⠙⠳⠒⣁⠄⠘⠛⠛⠁⠀⠙⠛⠓⣋⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⢀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣿⠋⣱⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⣸⣿⣟⣠⠏⠀⠀⠀⠀⠀⠉⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⡙⠿⠆⠀⣀⣿⣿⡟⠁⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⢇⢸⠀⢀⣿⣷⠀⠀⢀⣿⣿⣃⡤⣤⡀⠀⣠⡶⠓⣦⠀⣴⣾⡇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢈⡟⠒⢺⣿⣿⠀⠀⢸⣿⣿⠏⠀⣸⡷⢸⣿⣇⡼⠋⢀⢿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣇⠞⠀⢀⠸⣿⣿⣄⠴⠻⣿⡿⢀⣴⠟⠁⠘⢿⣯⣀⡴⠋⡜⢻⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⣦⡄⠀⠀⠀⠀⠧⡼⠿⠛⠊
⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣾⣿⠛⢧⠀⠀⣿⣿⡆⣠⠶⣶⠀⠀⣿⣿⡏⠀⠀⢲⣶⠀⠀⣶⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⢧⣀⣸⣀⣰⣿⣿⣿⠃⢸⣿⠀⠀⣿⣿⡇⠀⠀⣿⣿⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣿⣿⠀⢈⡟⠉⠙⣿⣿⡇⠀⣼⡿⠀⠀⣿⣿⡇⢀⡴⢿⣿⣠⢾⣿⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡛⠓⠉⠀⠀⠑⠄⠉⠀⠀⠸⢧⡠⠞⠀⠉⠉⠁⠀⠀⠉⣀⣼⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣿⣿⢇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡄⢀⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠁⠘⢾⣿⠇⠆



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢻⣿⣦⡹⣿⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠂⡀⠀⠀⠀⢿⣿⣷⢹⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠐⢦⣄⠀⠀⠀⠸⠃⣼⣇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠋⠇⠀⠀⠀⢸⣿⣿⣦⣤⣴⣿⣿⡏⠀⠸⣷⣄⠀⠈⢿⡷⠈⢷⡄
⠀⠀⠀⠀⠀⢀⣦⠀⠀⢸⣿⡇⠀⠀⠀⠘⣦⣸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣧⠀⠸⡇⠀⣼⡗
⠀⠀⠀⠀⠀⢸⣿⣶⣴⣾⣿⠁⠸⣦⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡄⣼⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣧⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⡋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠰⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⢀⡇⠀⠀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠉⠳⡀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢀⣙⡲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠐⢤⡀⠀⠀⠀⠀⠀⣷⠋⠁
⠀⠀⠀⠀⠀⠀⢞⠩⠄⢈⠆⠈⠙⠓⠒⠶⠶⡶⠚⠙⢲⣼⡃⠀⠀⠀⠙⡆⠈⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⣠⠶⠖⠲⠤⣜⢀⠀⠀⢀⡏⠳⣄⠀⠀⢀⠃⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠒⢄⠀⠈⢧⠉⠛⠉⠀⠀⠈⠉⠙⠛⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠁⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡆⣴⠀⢸⡆⠀⣰⡏⢐⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⠚⡇⠀⠸⠇⠀⠸⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⡁⠀⠀⢀⡴⠒⠀⠘⠇⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠣⠀⠀⣼⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⡇⢠⡇⢰⡏⠐⢦⢀⡴⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠃⢸⠃⢸⡇⢀⣾⢻⡇⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃⠘⠃⠰⢃⣀⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠐⡆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠄⢰⡇⢸⡇⠀⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠃⣿⠀⢸⡇⢸⡇⢀⡏⠰⣧⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⠀⢸⡇⠸⠧⠈⠑⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⢀⢴⠖⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣾⢸⠀⠀⠀⠈⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢸⣿⠎⠠⠀⠀⠐⠒⠺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⢀⣼⣿⣠⣤⣤⣴⣾⣶⣾⣧⣌⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⣧⣷⣀⣤⠶⠚⢤⡀
⠀⠀⠀⠀⠀⠚⠛⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠷⠶⠽⠷⢶⠤⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣤⠤⠶⠒⠒⠲⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣦⣾⣷⣶⣆⣄⠀⠀⠀⡀⢹⡧⣭⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠿⠶⠟⠛⠋⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣄⠙⣿⡆⠟⢁⣴⣾⣿⠿⢿⣿⣶⣤⣀⠀⠀⠀⣤⣶⡿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⢸⣿⡇⠘⠃⠰⣿⠟⣉⣀⣀⠀⠈⠙⠛⢿⣿⣶⣴⣿⣯⣤⣴⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⣿⠇⢀⣀⣀⣀⠀⣡⣶⣿⣷⣆⢠⣼⡿⠛⣿⣧⠀⠀⢀⣠⣈⣽⡿⠛⠛⠛⠋⠁⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡀⠹⢻⣿⠟⠁⢿⣿⣀⣿⡿⠀⣿⡇⢠⣿⡟⢀⣾⡿⠛⣿⣿⠃⢠⣴⡆⢠⣿⡄⠈⢀⣴⠆
⠀⠀⠀⠀⠀⠀⣶⣱⡀⢻⡇⠀⠘⣿⣧⠀⣾⡿⠀⠀⠘⠻⠟⠛⠁⠐⠻⣷⣾⡿⠁⣾⣿⣠⣾⡿⣿⣦⣾⡟⠁⢸⡟⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠉⠀⠀⠘⣿⣷⣿⠃⠀⣠⣄⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠉⠋⠋⠀⠀⠚⠤⠞⠛⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣙⣛⠋⢀⣄⡀⠈⠙⠁⣰⣿⡿⠋⠀⢸⣿⠛⠿⣿⣆⠀⠀⠀⣀⣀⡀⠀⠀⣀⣶⡿⣿⣦⠀⠲⢦⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠘⢻⣷⡀⠀⢰⣿⠏⢴⡶⠀⣸⣿⠀⠀⢸⣿⡆⢰⣾⡟⢻⣿⡄⠀⣿⡟⠀⠘⣿⡇⠀⡀⢻⣷⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣤⣼⣦⡀⠈⢿⣷⢠⣿⡟⠀⣴⣦⠀⣹⣿⠀⣠⣾⡿⠁⣾⣿⣶⣾⣿⠃⠀⣿⣇⠀⠀⠛⠁⣾⣿⠈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⢿⣷⡀⠘⣿⣿⣿⠁⠀⣿⣿⠀⢸⣿⣿⣿⣿⡄⠀⣿⣿⢉⣽⡁⠀⠀⢿⣿⡄⠀⠀⣼⡿⠃⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠈⠁⠀⠹⣿⡇⠀⠀⣿⣿⠀⢸⣿⣤⣴⣿⡇⠀⠸⣿⣿⡿⠁⢠⣾⡞⣿⣧⠀⠠⣤⣦⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⣠⣦⠀⠀⠁⠀⠀⠀⠙⠁⠀⠀⠛⠋⠙⠁⠀⠀⢀⠈⠉⠀⠀⠸⢿⣧⣿⡟⠀⢰⣦⡙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⣿⠀⢠⣾⡿⢿⣷⡄⠀⣴⣆⠀⣀⣀⠀⠀⢰⣿⡇⠀⢠⣴⡄⠉⠉⠉⠀⠀⠀⣿⡌⡄⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠘⣿⣦⣿⣟⣀⣼⣿⣿⠀⢹⣿⣴⣿⢿⣿⠀⢸⣿⠇⠀⣿⣿⠀⠀⠀⠀⣠⣤⡄⣿⣷⡇⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣞⡢⡀⠀⠈⠛⣿⡿⠿⠻⣽⣿⠀⠹⣿⡿⠁⣼⣿⠀⢸⣿⠀⠀⣿⡇⠀⣠⣴⣿⣿⡿⠀⣿⣿⠇⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠐⢿⣷⡀⣰⣿⠇⠀⠀⠛⠁⢀⣿⡟⠀⢸⣿⠀⠀⠻⣿⣿⠟⢫⣼⣿⠃⠀⠻⠋⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣦⣄⠈⢿⠿⠿⠋⢰⣦⠀⠀⠀⠸⠿⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⣾⣿⠃⢀⣴⣶⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⢀⣠⣴⢀⡄⠰⠂⣀⣤⣶⣶⣶⣤⣄⣀⠈⠉⠀⣤⡀⠀⣠⣿⡿⠁⠀⠉⠀⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡿⠃⣾⡇⠀⢲⣿⠋⠉⠉⠉⠛⠻⢿⣿⣶⣤⣉⣠⣾⣿⠟⠀⣰⣶⡆⢹⣦⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠔⠁⠀⣿⣧⠀⠸⣿⣦⣀⠀⠀⠀⠀⠀⠀⣹⣻⣿⣿⣿⣷⣶⣾⡿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠈⠙⠿⣿⣷⣶⣶⣶⣿⠿⠛⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⠭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢰⣿⡇
⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣮⣿⣷⡄
⠀⠀⠀⠀⠈⠻⣧⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠙⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣾⠇⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣰⣿⠃⠀⠀⣧⣀⢀⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣰⣧⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢹⣿⣿⠙⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⢰⡄⠹⣿⣿⣿⣧⠀⠀⠀⣄⠀⢠⣿⣆⠀⠀⣸⣿⣿⠀⢄⡀⠀⠈⢻⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⠁⠀⠀⣦
⠀⠀⠰⣄⣠⣾⠃⢠⠘⣿⣿⣿⡇⠀⢀⣿⠆⢸⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣦⠀⠀⠙⠿⣿⠟⡁⣿⣿⣿⣿⣿⣷⣤⣴⣿
⢀⡀⠀⢻⣿⠃⠀⢸⣿⣿⣿⣿⢇⣴⣿⠟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⣼⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣷⣤⣿⡟⠐⣦⡀⠙⢿⣿⢫⣿⣿⣿⣄⣸⡆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⣦⡹⣿⣦⣿⣿⣿⣿⣿⣿⡟⠁
⠹⣿⣿⣿⣿⣾⣿⡇⠀⢀⢸⣏⣿⣿⣿⣿⣿⢣⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⣠⠈⠻⣿⣿⣿⡿⠃⠀⢈⣿⣿⣿⣿⣿⣿⠁⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⠃⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢿⣷⣿⣿⣿⣿⢁⣴⣶⣿⣿⣿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⢹⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠙⠒⠤⣀⠈⡆⠀⠀⠀⢠⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣀⣠⣤⣤⣄⡀⠉⢣⠀⠀⣰⠃⠀⠀⠙⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠋⠉⠉⠀⠀⡇⠀⠙⠲⡄⠳⡰⠁⠀⠀⠀⠀⠘⣏⢉⠟⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⠛⠦⣀⠀⠀⠀⣠⡃⠀⠀⠀⢻⠀⣷⡀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢳⡔⠋⠀⠉⠢⠤⢤⣸⣶⠀⢳⡀⠀⢀⣠⠴⠟⠒⠾⣍⠉⠉⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠚⠛⠻⡆⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣸⠿⠶⠶⠛⠋⣹⠉⠳⣄⠀⠀⠈⠳⣄⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠦⣇⠀⢀⣀⣀⣀⡟⠲⣤⣀⡀⠀⠙⣄⣀⣠⡤⠞⠛⠶⣤⣠⠒⠉⠉⠉⠉⠉⢷⠀⠀⠀⠘⢧⡇⠈⢷
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⣶⣋⣉⡽⣿⠀⠀⠀⠉⠻⢍⣉⡉⠉⣀⣀⣀⡤⠤⡔⠻⡆⠀⠀⠀⠀⢀⡼⠧⣀⠀⠀⠈⡹⣶⠺⡇
⠀⠀⠀⠀⣀⣤⣿⣀⡀⠀⠀⣸⣤⠤⠶⠿⠿⣤⡀⠀⠀⠀⠈⢣⢨⠋⠀⠀⠀⠀⠀⠈⢆⢻⠀⠄⢀⡴⠋⠀⠀⠀⠉⡖⢺⠓⣿⣠⣇
⠀⠀⠀⣾⣋⣼⣿⠭⣿⡶⠚⠉⠀⠙⠢⣀⣀⣀⡙⢧⡀⠀⠀⢀⡿⠞⠓⢦⡀⠀⠀⢀⣼⠟⠛⠛⠛⠓⠶⠤⣄⣁⣸⠀⣾⡴⠯⣄⣈⣙⣦
⠀⠀⠘⠷⠴⢾⡿⣏⣁⠀⠀⠀⠀⡠⠊⠹⡄⠀⠀⠉⢳⠀⡼⠛⢄⣀⣀⠀⠙⣦⢀⡞⡹⠦⣄⣀⣀⣀⠀⠀⠀⠉⢻⢒⡿⠶⣴⣧⣤⣤⡼⠃
⠀⠀⠀⠀⠀⢸⡏⠁⠀⠉⠉⠉⠙⡄⠀⠀⠘⡄⠀⣠⣼⢶⡇⠀⡼⠁⠈⠉⠉⠙⣿⣷⠁⠀⡼⠁⠉⠉⠉⢉⣩⠿⢋⠸⠯⠭⠿⠁⠠
⠀⠀⠀⣠⡶⣦⠓⢦⣤⣤⣤⣀⣀⣸⣤⣤⠶⠾⠛⠛⠶⠭⠽⠿⣤⣀⣤⣤⡤⠞⠁⠈⠙⠺⠷⠶⠒⠒⠛⢩⣵⢶⡄
⠀⡀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠰⣾⣭⠿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠃
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⣤⠞⢋⣤⠞⠃
⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠠⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣶⣏⣥⣾⣏⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⡛⢦⣌⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠈⠛⠆⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡄⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⢀⣤⣶⣄⠀⢀⣴⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠙⠁⠀⠀⣰⣾⠿⠛⢿⡇⠀⢀⣴⡿⠟⠛⣿⡆⠸⠟⢻⡏⠉⠉⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢀⣀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣿⠀⣼⡿⠀⠀⠀⢹⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⣿⣿⣿⡄⠀⣿⡇⠀⠀⠀⢸⡟⠀⣿⠇⠀⠀⠀⣾⡇⠀⠀⢸⣿⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⣸⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠘⣿⡄⠀⠀⢠⣿⠃⠀⠀⠈⣿⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣰⡿⢿⡇⠀⢹⣿⡀⠀⣼⣿⠀⠀⢿⣧⠀⢀⣾⡟⠀⠀⠀⠀⣿⠆⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⠁⢸⡇⠀⠀⠻⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⠟⠁⠀⠀⠀⢰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣤⡄⠀⠀⣀⣤⣤⣤⣤⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢸⣿⠀⠐⠿⠿⣿⡟⠃⠀⠘⢿⣿⠉⠉⣿⠀⠀⣼⡿⠛⠋⠉⠀⠀⢀⣾⡿⠛⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⢀⣼⡏⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣿⡿⣿⡆⠀⢸⣧⣤⣴⣶⠀⠀⠙⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣿⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⢸⣿⠛⠋⠁⠀⠀⠀⠈⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⣿⡄⠀⣸⡏⠀⢸⣯⠀⠀⣀⣄⠀⢸⡷⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⣶⣾⣿⡿⠃⠀⠀⠀⢿⣷⣾⠟⠀⠀⠸⣿⣶⣿⡿⠋⠀⠸⣿⣶⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣿⡀⢐⣿⣿⡄⠀⠀⠀⢰⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⢿⡇⢸⣿⡿⣷⡀⠀⠀⢸⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣿⡇⢸⣿⠁⢻⣷⠀⠀⢸⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣿⠃⢸⣿⠀⠈⣿⣧⠀⣸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟
⠀⠐⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⣼⡟⠀⢸⣿⡇⠀⠘⣿⣆⣿⡇⠀⢸⣿⠀⠀⢀⣠⣤⡀⠀⠀⠀⢰⣿⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠸⣿⣦⣾⡿⠁⠀⠘⠿⠀⠀⠀⠹⣿⣿⠇⠀⠈⣿⣷⣿⣿⠿⠛⠁⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣄⡀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣌⡙⠶⣌⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠳⣦⣀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⢈⡿⠖⣺⡿⠖⣻⡿⠖⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠒⠲⠲⣷⠀⠀⣉⡿⠆
⠀⢀⠀⠀⠀⠀⢀⣴⠞⣋⣴⠞⣩⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⡀⡄⣀⣀⣀⠀⣀⠀⢀⡀⡀
⠀⠀⢠⡇⠀⠀⠀⠀⣠⣾⣷⣷⠀⢰⣿⣿⡄⠀⠀⢠⡀⡀⡀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⠂⣨⡽⣠⡷⢫⡀
⠀⣰⣾⣿⣴⡄⠀⢀⣿⣿⣿⣿⣇⠈⠈⠏⠁⡄⣌⣬⣖⣿⣷⣤⡀⠉⠙⢙⣙⣛⣛⣛⣉⡁⢈⣿⣬⡿⢻⣞⣖
⢠⣿⠏⠘⣿⣧⠀⠈⠿⠿⠻⠿⠟⠀⠀⣠⣾⣷⣿⣿⣿⣿⣷⣿⣿⣶⡔⣿⣯⣑⣾⢭⠉⠁⠈⠛⠚⣷⡿⠛⠉
⠀⠙⠂⠀⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢉⠀⢀⠀⠀⠀⠀⢀⠀⠀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣆⣥⡗⡧⡣⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠋⠡⣈⢂⠀⣐⣧⡠⣂⠀⠀⢀
⠀⠀⢸⡆⠀⢾⣷⣿⣿⣿⣷⣷⣿⣿⡇⠀⠀⠀⢀⣴⣷⣶⣦⡀⠀⠀⠀⣁⢀⡀⠛⠃⠰⣾⣿⣿⠟⠀⢀⠤⣗
⢠⡇⣿⢰⠀⠀⠀⢠⡄⠀⠀⠀⢈⣠⡀⠄⠀⠰⣿⣿⣿⣿⣿⣷⠀⢠⣾⣩⣿⣀⠀⠀⡤⠾⠿⠿⠤⠄⠳⣷⡿
⠀⣻⢸⣿⡷⠀⣰⡿⣿⣿⡄⠀⢮⣿⣧⣌⢳⠀⠉⣿⣿⣿⣿⠏⢸⣽⣾⣽⣿⣿⡀⠀⠀⢀⠀⠀⠀⠀⣾⡟⠃
⠰⣿⣾⣿⡇⠀⢿⡀⠉⣽⠇⠈⣷⣿⣿⣾⣯⣶⠀⠻⡏⢻⡯⠀⢠⣿⣿⣿⣿⣿⡇⢀⣠⣤⣶⣄⣀⠀⢈⣽⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⢤⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡭⠄⠤⠶⠀⠀⠊⠉⢉⡉⠒⠉⠛⠒⠶⠶⠒⠒⠂⠀⠄⣤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣒⣀⣉⠉⠉⠁⢈⣗⡂⠒⠒⠂⠀⠉⠩⣤⣄⡀⠈⣿⣃⣠⢷⠀⠀⣤⣵⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣀⠀⠰⠾⠽⠟⠀⠀⠀⠀⠬⠥⡄⠒⠒⠞⠃⠀⠀⡠⠄⣀⠀⠀⢠⣶⡗⠉⢉⣹⣶⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣤⠴⣴⡶⢶⡿⣷⠶⢶⣶⣶⢦⣾⡒⡒⠺⣗⣿⣶⡇⢺⠋⣁⣹⣷⠾⢛⡥⣾⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⣿⣶⣿⣧⣦⡾⢶⡷⠷⠿⠿⠟⠿⢿⠿⠿⠿⠿⠿⠿⣾⣿⠛⢹⣿⢒⣁⠠⠘⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣶⣶⣿⠶⡾⠷⠾⣿⠟⡟⠛⢿⠿⠻⠻⠿⢿⣿⣿⣿⣷⢈⠈⣿⢋⣡⣶⠟⠛⣡⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣿⣿⣷⣶⣟⣒⣶⣓⣛⣛⣛⣻⣻⣿⣿⣿⣿⣭⣭⣶⣷⣿⣿⣿⣿⣶⠞⢛⣿⣽⣾⣿⡟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⠟⠻⠛⠛⣛⣛⣫⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣷⣼⣿⠟⣿⣙⣆⡁⣠⠼⠋⣹⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⢿⠿⣿⡿⠿⠛⣛⠛⣻⡛⠛⣛⣛⣉⣙⣉⣻⣿⣛⣿⣿⣿⣿⡖⠝⣩⢭⣁⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠒⠶⣶⡿⠶⡿⢿⣟⣛⣛⣛⣛⣏⣉⣉⣙⣛⣻⣏⣉⣽⣭⣶⣿⣾⣿⣷⣾⣿⡿⠟⠟⢻⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⠿⢿⠿⢿⠿⠿⢿⠿⢿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⡟⠹⣿⣟⣀⣠⡔⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣸⣐⣀⣠⣤⣾⣐⣀⣠⣄⣺⣆⣀⣖⣤⣤⣀⣤⣴⡼⣿⣿⣿⣗⠛⡛⠛⣉⣸⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣭⣉⣭⣍⣉⣉⣉⣁⣁⣜⡉⣄⣭⣍⣉⣐⣂⣀⣀⣀⣀⣽⣾⣽⣿⣴⠿⣿⠿⢟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⠿⠿⣿⢿⣿⡿⠫⠤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠋⠉⠉⠉⠛⠛⠛⠛⠛⠗⠛⠘⠉⠒⠒⠚⠂⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠓⢞⣖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⠂⠀⠀⠥⠀⣰⠋⠰⠀⠀⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢀⣉⡐⠉⠀⣀⡀⠀⠉⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⣰⡿⠯⢽⣶⡾⠯⣽⣶⡟⣿⠁⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣠⣴⣿⠹⣇⢀⡞⢻⣇⣠⠏⣿⣠⢧⢀⡻⠖⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣿⣀⣬⣭⣄⣀⣉⣁⣀⣈⣀⣤⣭⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠋⣿⢉⠉⠉⡉⠙⢛⣋⠉⢉⡉⢉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢹⠘⡇⢰⠃⡇⢸⣠⠇⣿⡀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⣸⠀⢳⡏⠀⣷⢸⠀⣱⣿⠀⢀⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁⠀⠈⠃⠀⠛⣨⢭⡁⠈⠉⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⢢⡀⣀⠀⣀⠀⢸⣇⡼⢡⣤⠀⢰⡄⠺⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠓⠴⠖⣿⢿⣿⠋⢷⢸⣿⠁⣼⣿⠀⢿⠁⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⡿⢹⡏⠀⢸⡞⣿⣸⠹⣿⠀⣼⡇⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⡼⠃⠈⠃⠀⠀⠀⠈⠁⠀⠈⣩⡼⡏⠉⠺⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡉⠉⠀⣄⠶⠠⠚⠓⠄⠀⠀⢠⡾⠋⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠀⣹⠬⠥⢤⣀⣈⣁⠔⢁⣿⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠆⠀⠈⠉⠀⠀⠀⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⠤⠂⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⢻⣿⣿⣇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⢻⣿⣿⣦⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⣠⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⢹⣿⣿⣷⣤⣀⣠⣾⣿⡟⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠀⠀⢀⣼⣿⣿⡟⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠁⠀⢠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣄⢀⣠⣿⡿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠻⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡇⠀⠀⠰⣿⡟⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⠇⠀⠀⠀⠙⠃⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣉⠉⠉⠉⠙⠊⠁⠀⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡥⠿⠂⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⣀⣤⠀⠐⡾⠟⣯⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⢀⠀⢀⣠⠤⠤⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⡴⠂⠠⠐⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠋⢁⣽⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⣤⣉⣄⣀⡀⢴⣿⣿⣿⣿⡟⡽⣼⢯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠓⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⣠⣾⠿⢿⢿⡟⢡⣿⣿⡿⣯⠁⣠⣼⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠠⣴⣿⡿⠷⣄⠀⠀⠈⠋⠉⠈⠈⢉⣼⡿⣫⣾⣡⡾⣫⣹⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣤⣼⣧⣠⣤⣤⣤⢄⠤⠤⠤⢤⣼⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⢳⣆⢀⡇⡄⣌⠛⡹⣻⣿⡟⡿⣫⣾⠟⣩⡿⣿⣿⣿⣆
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣠⣤⣼⣿⣾⡟⢠⡿⡄⣷⠟⣫⡮⣨⠟⣡⢞⢟⣕⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣸⣾⡄⠐⢀⣀⢠⡤⣼⣻⣟⢿⣿⡿⣿⣿⣿⠁⠸⡇⣀⣸⣞⣅⠻⠁⠘⠓⠉⠉⠉⣩⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠠⠀⢠⣥⣾⣿⣿⣿⣤⡿⢃⣿⡼⠡⠝⠊⡞⡙⣨⣿⣿⣿⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⣠⡾⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⡀⠀⠈⣠⣤⡼⢹⣿⣿⡟⠀⠠⠻⠁⠁⠀⠀⠐⠛⢿⣿⣭⣿⣿⣿⣿⠃⠀⠀⠀⡀⠀⢀⢠⣛⢉⡶⠋⠪⢾⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⢻⡷⣆⣸⣶⣿⣟⣯⣴⣾⣿⣿⣷⡴⠷⢶⠂⠶⣶⣷⣿⣿⣟⡿⠿⠿⣿⣿⣿⣷⣧⡄⠈⣸⡷⣿⣿⣾⣏⠀⠈⢁⣻⡛⠁
⠀⠀⠀⠀⠉⡉⠀⠠⠠⣶⠾⣿⠧⠀⠈⠘⠛⠉⠉⠀⡀⠐⣲⠶⢶⣤⣬⣭⣍⣉⣉⢠⣄⣤⠄⢀⡿⠿⠿⠷⠶⢛⣋⠉⠀⢀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠄⠈⠀⠠⠄⠂⠈⠉⠁⠀⠈⠉⠉⠉⠉⣋⠀⠀⠠⠄⠈⠻⠶⠶⠶⠀⢀⣠⣤⡤⠖⠉⠛⠛⠒⠳⠆

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⢀
⠀⠀⡜⠀⠀⠢⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡢⠜⠀⠈⣆
⠀⣸⠀⠀⠀⢰⠏⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⢳⡀⠀⠀⢸⡆
⠀⣿⠀⠀⠀⠘⠛⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⠛⠁⠀⠀⢸⡇
⠀⠘⢦⣀⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣠⡾⠁
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⠀⣴⣿⠟⠁⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢀⣾⡿⠁⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠘⢮⢻⣷⡀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢸⣿⡀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠘⡇⣿⣧⠀⠀⢀⣠⣾⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣧⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⡿⠀⣠⣿⠟⠁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⡇⠀⠨⣿⣿⡿⠂⠀⠀⠀⢠⡆⠀⠀⠀⢠⣿⠇⣰⣿⠃⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⠋⡇⠀⠀⠀⢸⣿⣰⣿⠃⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⡼⠁⠀⢹⡀⠀⠀⠘⠿⠟⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣿⡀⠀⠀⢹⣧⠀⠀⠀⠀⡼⠁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢸⢰⡏⠀⠀⠀⢀⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⢿⣄⡀⣸⡿⠀⠀⠀⢰⠁⠀⠀⠀⠀⠘⡆⠀⠀⡲⠀⠀⠀⠸⡈⣧⡀⢀⡴⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠢⣝⣛⡛⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⠀⡜⠀⠀⠀⠀⠀⠙⠈⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣾⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠙⢄⢱⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠱⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⣷⢄⠄⠀⢰⡀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠠⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠰⠄⣿
⠀⢤⣤⡘⣆⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣼⢃⣴⡶
⠀⠈⣿⠳⠟⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠛⠋⣿
⠀⠀⠘⣦⡀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⡼⠃
⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⢠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⣠⣿⣿⣿⠁⠀⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠻⠀⢠⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⢿⡇⢸⡟⠁⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠘⡇⠈⠀⠀⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⡇⠙⣿⡄⠈⣿⣿⣿⣿⣿⣿⣦⠀⠀⠃⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠈⠛⠀⠘⣧⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠐⢶⣤⡀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣧⠀⠀⠀⠀⢀⡿⢋⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠈⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣧⡀⣼⣿⣿⣧⠀⠀⠀⠈⢃⡾⠋⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⡦⠈⠃⠀⢀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⡀⢸⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⡏⠀⣼⣿⠁⠀⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⢿⣿⣿⣿⣅⣰⣿⣿⡆⢠⠟⢋⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⢻⣆⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⠀⢠⠞⣻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠠⢞⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⣿⣿⣿⡇⠙⢿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠙⠻⠦⠀⠀⠀⠀⢸⣿⣿⠃⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⣀⣀⣀⣤⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⠻⠿⠿⢟⡫⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢡⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣾⣟⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠻⠿⣯⠻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠤⡔⠠⠂⠘⢁⠆⢀⢺⣿⣗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⣠⡀⠀⠉⢿⣏⢿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠻⢅⠁⠀⠈⠉⠙⠓⠐⠈⠀⠀⠀⠀⠀⠀⣀⣴⠟⢋⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣫⢽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠈⠀⠀⠄⠀⠀⢤⠀⠀⠀⠐⡌⠀⠀⠀⠀⠀⠚⢻⣿⢿⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠰⡄⢀⣼⣯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⣙⠀⠀⠀⠀⢳⠙⢄⣀⣠⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣠⡄⠹⠄⠤⠤⠀⠂⠀⢀⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠁⠀⠀⠀⠀⠀⢀⠠⠆⠉⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣠⡤⠤⣴⠀⣴⡖⢷⡄⡜⡉⢹⣇⢀⡴⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⠃⢰⠟⢸⠁⠑⣾⠷⠁⠈⣾⠟⢻⡁⣰⡇⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠖⠋⠀⠀⠲⠚⠁⠀⠑⠚⠁⠀⠘⠛⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡞⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢴⡄⠀⣤⠀⠀⢸⡣⠃⠀⠀⣀⡀⠀⣼⢻⠃
⠀⠀⠀⠀⠀⠀⣀⢼⡇⠀⢸⠗⢸⡏⠀⢀⣿⠓⣦⢀⣾⡵⠃⠀⠹⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡴⠃⠀⠸⣧⡴⢫⣧⣠⡟⠜⠿⡤⠔⠀⣀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⠀⣀⡀⠀⣰⡧⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⡀⣿⡆⢼⡾⣿⠃⢠⡟⠀⢰⠃⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣸⠟⠀⣾⠁⠯⠀⣿⢀⡠⢻⣶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠛⠉⠀⣠⡤⣾⠗⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠦⡀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡀⣁⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢠⣿⡇⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣼⣿⣿⣄⠀⢠⡆⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢻⣧⠈⢡⣿⣿⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢹⣿⣿⠀⣿⣇⢸⣿⣿⣷⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠏⢸⡇⢻⣿⢸⡟⢿⡿⣷⠀⠀⠀⣾⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⣼⣱⡟⢀⠘⠁⢸⣿⣸⠇⣸⡇⣿⠂⡴⢰⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠏⠀⣰⣿⠟⢀⠎⡀⡀⣸⣿⠋⠀⠸⣱⣿⣾⣷⡿⢹⣧⠀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⣧⠀⢠⣾⡿⠋⡀⠀⣼⠑⢡⡟⣡⠎⢀⣾⡿⠋⠉⠉⡰⢸⡟⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⣴⡿⣋⠀⠘⢡⣾⠃⢀⡞⢠⠏⠀⣿⣿⣧⠖⣀⣀⣴⠟⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⣿⣿⣾⣿⠞⠁⠀⢰⣿⠃⡰⠘⠁⡾⢰⠘⣿⣿⡇⣾⠟⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣿⣿⣿⠋⠀⠀⠀⣿⡇⠀⣧⠀⠄⠁⠀⢆⢻⣿⣷⡏⣼⠃⣠⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⣿⣿⠇⠀⡄⡀⡀⣿⣇⠀⠻⠄⡄⢠⡀⠂⠀⠻⣿⣿⣿⢰⡟⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⣿⣿⠀⠀⠁⡇⢧⠸⣿⡆⠀⣄⢷⠀⠹⡄⠀⡆⢹⣿⣿⠀⡄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣿⣿⣇⠀⠀⢷⡘⠀⠙⢿⡄⠞⣿⡇⠂⣿⡀⣿⢸⢹⣿⢀⣼⣿⠃⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⣿⣦⠀⠈⣷⡀⠰⣌⢻⠀⢸⣿⠀⣼⡇⣿⡾⢸⣿⣾⣿⣿⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⠹⣿⡄⢀⡑⠀⠈⢿⣦⡙⠈⢁⢸⣿⢠⣿⠃⠟⣡⡿⠟⠹⢣⣿⡇⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢧⡀⢩⠀⠻⠄⢦⡈⢻⡿⣦⠘⣸⣏⣾⠏⠀⠴⠋⠀⠴⣋⣾⡿⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⡢⠝⢾⣷⢾⣿⣹⣧⣿⡿⢋⡴⠚⣡⣤⣶⡿⠿⠋⠠⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣶⡌⣿⣼⣿⣿⣿⠟⣵⡿⣱⣿⠟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣸⣿⣷⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠁⠀⠉⠉⠉