Watering plants Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⢿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣠⡅⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⣿⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠋⠐⢉⠉⠉⠀⠀⠈⠻⣿⠉⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡇⠹⣄⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⡹⢻⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠉⠀⠀⠈⠓⣤⣀⣀⠀⠀⣀⣀⣴⡚⠁⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⣠⠴⠒⠉⠁⣸⣭⠽⠛⠉⠁⠀⠈⢦⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣾⡉⠀⣀⣀⡤⢯⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⣴⣏⢷⡫⠵⠚⠛⠉⢁⣀⣀⣸⣆⣀⣠⠤⠶⠒⠚⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⡽⣭⡽⣀⣴⣶⣒⣿⡉⠉⡽⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⡿⠧⠋⠉⠁⢀⡿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠉⠉⠙⠓⣲⠶⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣳⡤⠴⠒⠋⠁⠀⠀⠀⠀⠹⣖⠒⠒⠒⢒⣖⡒⠒⢖⣒⠖⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⣄⠀⠀⠀⠀⠈⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠘⠴⠃⠀⠀⣀⣄⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⢶⣄⣠⣴⣿⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⡔⢦⠀⠀⠀⠳⠜⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⣇⣸⠟⠛⠒⠲⠤⢭⣍⣙⡛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡙⠉⠀⠀⣏⣳⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⠀⠀⠀⠀⠀⣀⡴⠯⢤⡯⠼⠦⢤⠤⠬⢤⠴⠿⠦⠿
⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠖⠋⠁⡇⠀⢸⠃⠀⠀⢸⡆⠀⢸
⠀⠀⠀⠀⠀⠐⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣾⠀⠀⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⡴⠒⢶⣋⣉⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠁⠀⡇⢀⣀⣀⣀⡏⠉⢹
⠀⠀⠀⠀⣨⠤⢤⡖⠒⣲⣵⠒⠙⣒⠋⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢀⣀⣠⠤⠴⢺⡟⠉⠉⢀⣀⣀⡤⠼⠃
⠀⠀⠀⠀⢱⠦⠘⠭⠜⠩⡭⠟⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠈⠓⠚⠉⠉⠁
⠀⠀⠀⠀⠈⠒⠒⠉⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠈⠻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡿⣛⣿⠏⠀⠀⠂⠀⠀⠈⠉⢸⣿⠁
⠀⠀⠀⠀⠀⠀⢧⠉⠈⠀⠀⠐⠇⠀⠀⣀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠜⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⢀⣀⡴⠖⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠘⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⣿⣿⣿⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣶⣶⣤⡂
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⢸⣿⣿⣿⣿⡯⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠈⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣾⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⢰⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋
⠀⣾⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⣿⠻⡿⠿⠿⠟⠁
⢠⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏
⣼⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣦⡀⠘⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠂⠀⠌⠙⠻⠿⠿⠿⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⣍⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠸⢄⢢⡅⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠙⠿⣿⣇⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⢞⢚⠿⡻⢆⠂⡀⠀⠀⠀⠀⠀⢀⠀⢀⢶⣀⠀⠐⠠⡀⠀⠀⠀⠀⠘⠂⠘⠀⢈⣻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠏⢘⢣⣧⡡⢾⡈⠓⠌⠤⡚⠀⠀⠎⡊⣀⣀⢤⡈⡉⡁⠠⡀⠁⠂⣄⠀⠰⢤⡀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⣟⠽⣀⠿⡗⡇⠀⡰⢆⠀⠀⡠⠚⠉⠀⠀⠀⢱⡛⠋⠂⠌⡐⠄⣼⠀⠀⠿⠀⠀⣩⡄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⢸⠅⠀⠪⠿⢦⡀⠉⠉⠢⢉⠁⠀⠀⠀⠀⠀⠀⡗⠂⠄⡀⠀⠀⠐⠀⠯⡧⠙⠉⠀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⠀⣀⠀⠔⠊⠀⠀⠀⠀⠈⠐⠠⢀⠀⡆⠀⠀⠀⣀⠄⠀⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⢀⡀⢙⠁⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠈⠁⢀⠀⠙⠀⢰⡞⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠘⠃⡠⠈⠀⢘⠃⠸⡗⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠰⠂⠀⡌⠀⢿⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠉⠀⠀⠆⠀⠀⠀⠸⣆
⠀⠀⠐⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⢀⡄⠀⢺⠀⠀⠒⠉
⠀⠀⠀⣉⣻⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣦⡤⣴⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢠⠗⠀⠘⠀⠀⠀⠀⡆⠀⠀⠐
⠀⠀⢀⡀⢛⢽⡆⠈⣸⡆⠀⢰⡦⣠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠈⠄⢉⣱⡵⡆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⠀⠖⠀⢘⠂
⠀⢀⡈⠱⠸⢟⡿⣏⢺⡔⢀⣏⡼⢋⠈⣰⣴⡖⠘⠂⠈⠷⠈⢀⢤⢄⢼⡿⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂
⠀⢀⡹⣦⣀⣿⣿⣃⠰⢶⣼⣾⡟⢃⣴⠟⠡⣐⠖⠀⠆⢈⠴⠄⡀⠋⣻⠹⠿⠁⠡⠀⠈⠁⠀⠀⠀⠀⠀⠣⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠴⠋⠈⢪⢿⣿⣿⣿⣶⣿⣿⣿⡾⣯⣶⣔⢾⣄⠠⣀⡷⠀⠰⠈⠉⠀⢹⠰⠆⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣀⣹⡉⠉⠉⠉⣯⣴⣾⣷⡄
⠀⠀⠠⢡⠋⠛⣻⣷⣷⡻⠛⠻⡗⡞⡿⣯⣟⠃⣀⡨⣮⢊⠐⠷⢀⣧⣞⣤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⡴⠀⠀⠀⢻⠏⠈⠺⠿⠷⠳⠘⣰⠌⠀⠀⠈⠀⣻⡌⠃⠀⠀⢡⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣽⣿⣿⡿
⠀⠀⠃⠀⠘⡄⠋⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⡠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢶⡶⠶⣶⣶⣦⡤⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣁⣤⡁⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠈⢿⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡒⠀⠋⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠁⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡄⠀⡠⠎⠹⣷⣦⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠓⡒⣾⡅⠤⠄⠒⣨⢋⠳⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢚⠋⠀⠀⠀⠀⠶⣀⡎⠸⠀⠀⠀⢀⡜⠃⠀⠀⠀⢷⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠞⠐⠒⠒⠒⠊⠉⢙⢁⡀⠆⠀⣠⠏⠸⠂⠀⠀⠀⢸⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠤⠚⠁⢠⠃⠀⠀⠀⢠⡟⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢀⡌⠀⠀⠀⠀⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡖⠉⢛⣦⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠤⠁⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⢣⡤⠈⠀⠘⠀⠒⠲⠖⠒⠛⠛⠛⠛⠃⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠤⠴⢶⡉⠉⠙⠒⠶⢤⣄⣀⡀⠀⠀⠀⢀⠀⠀⢸⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠁⠿⠀⠀⢸⠆⠀⠀⠀⠀⢰⠆⠉⠉⠛⠛⠛⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠂⠚⠁⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⢸⡀⡠⠞⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⠙⠳⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⢷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⢩⡅⠀⠀⠀⠀⠀⠀⣸
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠒
⠈⠓⠀⢀⡀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⡼⠁
⢀⠈⠀⠸⠈⢆⠀⢸⠃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠓⠚⢅⠸⠂⠀⣇⢀⠠⠐⠀⠂⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡀⠀⠀⡇⠀⣀⠤⢤⡀⠀⠀⣠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠾⠀⠀⠀⠀⢧
⠀⠀⠐⠉⠈⠉⠉⠰⠋⠀⠀⠀⣹⠪⡁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⡀⠀⠀⠀⢸
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⢸⠆
⠀⠈⠀⠀⢃⠀⢀⠃⠀⡜⠃⠀⠀⠀⠀⠀⣠⡴⠛⠙⢳⠄⢠⠀⠀⠀⢠⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠂⠈⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠒⣤⡄⠀⠉⠉⠉⠉⠈⠁⣼⠃⠀⢀⡰⠏⠀⠘⠀⠀⠀⡎⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⠀⠠⡎
⣀⠀⠀⢀⡀⠘⠀⠈⣂⠀⠀⠠⠀⠀⢰⠇⣠⠖⠋⠀⠠⠀⠛⠛⠓⣤⠁⠋⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠰⠁⠀⠈⠁⠀⠛⠊⠀⠀⠐⠃⠜⠁⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⠠⡤⠴⠊⠁⠀⢀⣠⡤⠞⠁⠀⠀⠀⡇⠀⠀⡝
⠀⠀⢤⡠⠔⠂⢀⠔⠓⡀⠤⠀⠀⠁⠀⠀⢀⠤⠒⠛⠓⠈⠁⠀⡄⢀⠔⠋⠉⡢⢀⣠⠖⠈⣷⣉⣁⣀⣀⠠⣴⡶⣾⠁⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⡁⠀⡠⠖⠒⠲⠦⢠⡀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠉⠀⢾⠁⢀⡴⠛⢦⣤⠀⠌⠉⠀⣰⠏⠀⠀⠈⣿⠀⠀⠀⠀⠀⢀⠴⢄
⠤⠤⢄⣀⠀⠀⡄⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠔⠁⠀⢱⠀⠀⡰⠋⠀⠀⢀⡾⠟⣀⠤⣄⠀⢰⡏⠀⢸
⠀⠀⠀⠉⠙⠂⠶⡀⠀⠀⠈⠳⠤⢄⡀⠤⠶⠚⠀⡔⠀⠀⠠⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠜⠀⢀⡴⠃⠀⢸⢆⡠⠦⣰⠞⡡⠊⠁⢀⣼⠃⠀⠀⢀⡞
⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣭⣴⣤⣤⣤⣭⣭⣭⣤⣮⣤⣴⣶⣿⣮⣥⣤⣴⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢛⣛⣛⣛⣛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣥⠶⠛⠉⠉⠉⠉⠉⠛⠶⣮⣙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⣇⢀⠀⠀⠀⠘⢷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⢋⡿⢿⣤⠀⠀⠀⠈⢻⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡶⢋⡴⢋⡴⠋⠙⢶⣄⠀⠀⠈⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⣠⠞⢡⡼⢋⡴⢋⡴⠛⠀⠀⠀⠀⠙⢧⣀⠀⠸⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣠⠞⣁⡶⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢹⡄⣠⠞⢁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⠟⢁⡴⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⣯⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣗⠲⠶⠶⢦⣤⣤⣤⣀⣀⣈⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠞⠉⠉⠛⠳⠶⢤⣄⣀⡀⠈⠉⠉⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⡀⠀⠙⣦⡀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣿⣦⡀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⢰⣿⣯⡉⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⢿⡉⠙⢿⡀⣿⠀⠀⢀⣤⠶⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⣡⡾⠋
⠀⠀⠀⠀⠻⢦⣤⠿⢧⣾⢠⡟⣿⣴⠿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣷⣟⣁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠈⠉
⣴⠞⠓⠚⠛⠛⠛⠓⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⢶⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠙⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠟⠁
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠄⡈⠓⢄⠀⠀⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣇⠀⠈⠢⣠⠇⠀⠀⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⡤⣑⢦⣸⣷⣦⣀⣀⣦⠎⢻⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠇⠘⠛⢬⣯⠈⢿⣿⠇⠘⢿⡟⠁⠀⢠⢀⣤⠌⠀⠀⠀⠀⠀⠀⢠⣀⠀⠴⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠘⠀⠀⣹⠀⠀⠘⠀⠀⢠⣾⠟⠃⠀⠀⠀⠀⠀⢀⡖⢸⢃⠀⠀⠴⠛
⠀⠀⠀⣀⣀⣀⢡⡀⠈⠀⠁⠀⠠⣧⣃⡟⠀⢀⣄⣠⡶⠏⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠏⠰⠀⠐⣯
⠀⠠⠟⡉⠉⠉⠉⠉⠓⠐⠢⠤⣤⣤⣼⠷⠶⣿⠷⠤⠤⡀⠀⠠⠴⠂⠀⠀⠀⠀⣻⣴⢣⡆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠂⠄⢂⡤⢦⡴⠎⠁⠀⠀⠐⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢾⣷⣶⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⡀⠂⠀⠀⠀⠀⠄⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣴⠃⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠚⠀⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠀⠀⠀⠃⠀⠀⠀⢀⠀⢢⠀⡀⠂⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⠀⠀⠀⠀⠀⠀⠀⠐⠩⡶⢿⣷⣱⣶⣴⠦⠀⠀⠚⠂⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⡄⠂⠀⠀⠀⠘⠁⠶⠺⢧⠩⡭⣝⠀⠠⠀⠐⠖⠶⠤⢄⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠃⠃⠀⠐⢤⠀⠀⢀⣒⠐⠂⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠀⠀⠀⠻⣟⠣⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠄⠀⠀⠀⠈⠙⠲⢴⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢁⠀⠀⠰⢂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠉⠉⠋⠚⠛⠲⠤⠬⠦⠤⠵⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⡇⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡘⠃⠀⠀⠀⣰⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣠⣆⣀⣀⣀⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡠⠤⠠⠤⠤⣂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠶⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣠⡾⠿⠠⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⢄⠈⢀⠀⠂⠀⠀⠡⠄⠤⠌⢤⣈⣀⠄⡀⠀⠀⠀⢇⠀⣀⣰⣽⡿⠞⠡⠰⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡂⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣢⠽⢟⠋⠄⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡴⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡜⠀⠀⠁⠒⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠀⠄⡀⠀⠀⠀⠀⠔⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⣂⣀⡠⠤⠖⢒⡋⠉⠉⠈⠂⢄⠀⠀⣂⡠⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⢁⣀⣁⡀⠔⠁⠀⠀⠁⠀⠀⠀⠴⡈⢋⠢⣤⣺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠄⡄⠀⠠⠀⠁⠀⠀⠀⠀⠀⠆⣠⠑⢢⢁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠄⠃⡄⡈⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠐⠒
⠀⠀⠀⠀⠠⠒⠠⣀⢁⡒⡐⠒⣂⡂⡄⣀⢢⠀⠀⠀⠀⡄⢁⣤⣷⠚⢠⢠⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⢾⠃⠋⣄⣶⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⢁⡼⣗⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠿⢼⠷⠋⢠⠁⡀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠠⡂⢧⠰⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⣀⡃⣸⢀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠠⠤⠠⠄⠰⠆⠴⠀⠀⠙⠋⠠⠇⡈⢼⠏⠁⠀⣠⡀⣠⠀⠀⡀⠀⠀⢂⡠⠀⠤⡈⠉⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠉⡱⠀⢡⣤⠀⠀⠶⠀⠁⢠⡅⠀⢄⣄⠁⠘⡋⠌⣛⣁⠀⠂⠁⠀⠁⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢚⣉⣉⣩⣉⣹⣖⣒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣡⠶⠓⠉⠉⠀⠀⠀⠀⠈⠉⠙⠓⠶⣝⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣤⠋⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡼⠁⠀⠀⠀⡴⣫⣴⣦⡹⡉⠒⠦⢄⣀⠀⠀⠀⠀⠸⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣺⠁⠀⠀⢀⣞⡾⣿⣿⣻⣧⠃⠀⠀⠁⠘⠹⢳⡶⢤⣀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣿⠀⠀⠀⡞⣾⡽⣟⡿⡝⡜⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠷⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠸⡄⠀⢸⠁⠈⠙⠻⠿⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⢦⡏⠀⠀⠀⠀⡼⢁⠎⠔⡄⡄⡄⡀⡀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡉⣦⠆⣢⢞⡵⡣⣪⢮⢊⠜⡔⡱⢁⠃⠄⡴⠠⢀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠴⢮⣕⣍⡊⢔⣕⠵⡣⢊⠜⡵⢣⢎⠜⡰⢁⢮⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡟⠙⠓⠺⢾⣵⣪⣖⡵⣫⢎⣔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⠀⣀⠴⢚⣡⠵⠋⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣼⡧⠊⣁⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⢣⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⠖⠒⢒⢒⠒⢏⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠈⣷⠈⢣⠹⣯⢆⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡎⠠⠀⠐⠀⠚⣧⠡⢳⢸⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⠀⠆⠀⠉⠰⠋⠆⡀⢳⠦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⡱⠰⠀⠐⠁⠰⠂⡰⠀⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⢠⠠⠀⠀⠂⠀⡄⠀⡄⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⡠⠀⠰⠀⢀⠀⠀⠄⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠁⡁⠀⠆⡀⢈⠀⠀⢀⢁⠀⣄
⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠘⠀⠁⠀⠀⡀⠈⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⣤
⠀⠀⢀⡀⢰⢧⢀⠐⠀⠀⠘⠈⠁⠀⠀⡁⠈⠁⣶⣄⡜⠀⠈⡀⠀⠀⡶⣿⣤
⠀⠀⠈⠻⣾⠶⢀⠔⠒⠤⠴⠘⡥⣤⠤⡔⠒⡐⢻⣧⡛⠦⠤⢠⠤⣀⣷⡯⠜
⣠⢔⡉⠙⢡⣴⡦⣤⡤⠶⠦⣂⡴⠦⢳⢇⢦⠥⢶⢶⡅⡀⣤⣀⣦⣀⣀⢉⣑⡎⣍⡒⠦⠠⠄⡠⣠⢔⡤⣢⢔⠥⣊⢔⡠⢒⠠⡢⢀⢄⡀

⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⣍⢢⡀⢀⡤⢒⡦⣄
⠀⠀⠀⣠⢴⣶⢤⠸⡄⠸⠤⠴⠃⢸⠀⠻⣍⡼⣀⠤⣄
⠀⠀⢰⡃⠸⠬⠼⠀⡨⠗⠒⠋⠉⠙⠓⠢⢄⣸⠁⡴⢦⢳
⠀⠀⠀⠳⠤⡤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⠂⠋
⢀⡔⡺⢲⠀⢰⠁⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠈⢄⠔⢒⡲⡄
⠸⡀⠑⠋⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡇⠟⣹
⠀⠉⠓⠊⠁⠘⡀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡤⠞⢀⡞⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠉⠉⠉⠉⠉⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡶⠶⠶⠖⠒⠚⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⡠⡖⠉⣀⣉⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣽⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⠒⠤⠄⠊⠁⠈⠖⠛⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡠⠊⠑⠒⠂⠄⣸⠀⠀⢀⣄⡄⠠⠆⠀⠦⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⢢⠤⠜⠹⠄⠀⠐⠀⠠⠀⠀⢀
⠀⠀⠀⢀⡴⠒⠻⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠤⠚⠤⠆⠀⠠⠀⠀⠀⠂⠀⡀
⠀⠀⠀⢯⡠⠾⠴⢣⣧⡄⠀⣤⣄⠀⣠⠀⠰⠆⠀⠉⠘⡆⠀⠙⠲⠤⠤⣀⣀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠉
⠀⠀⠀⠀⠀⠀⠰⣇⠤⠤⠄⠐⡶⠒⠊⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠉⢳⠀⠀⢠⠖⢢⡤⠠⣡⡖⠲⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⡜⢲⡏⠉⡞⠙⢣⠚⢄⢤⣧⠗⡔⢢⠴⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⡍⠈⣻⠑⡖⠈⣠⣁⡴⠻⣄⡽⠋⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡄⠀⠀⢀⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡟⠋⠁⠀⠙⠚⣷⠀⠀⠀⠀⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⢆⠀⠘⢆⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠈⠁⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⠤⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢠⠀⠋⢐⡀⠁⠀⠀⠀⠘⡄⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⡀⠀⠙⣄⠲⡆⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⠀⠁⠀⠀⠈⠳⢄⣀⣀⣀⠠⠊⠀⣀⠄⠸⡀⠀⢛
⠀⠀⠀⠀⠀⢔⠢⠀⢒⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⢬⡉⠁⠀⠈⠉⠈⡄⠀⢧⠀⢸⡄
⠀⠀⠀⠀⢀⠈⠠⠐⠀⠀⠀⢠⣐⠀⠀⠒⠀⠀⠀⠀⠀⡀⠠⡈⠁⠑⠀⡀⠀⠸⢻⡀⠸⡄⠈⡇
⠀⠀⠀⠀⠀⠘⠀⠀⢡⡠⠂⠰⠇⠔⠁⠀⠤⠀⢀⠞⠀⠁⠀⠹⡟⠀⠀⠁⢠⡏⠀⢧⠀⢳⡀⢹⡀
⠀⠀⠀⠐⠀⠑⠀⠀⣄⡃⡆⢠⡤⠃⠴⠂⠀⠀⣊⠉⠀⠀⠀⠀⠑⠌⠄⠀⠊⠐⠀⠈⢂⠀⢷⡀⢇
⠀⠀⠀⠀⠐⠁⠀⢦⠈⠁⠛⠀⠀⠀⢠⠠⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠘⠄⠀⢀⠀⢠⠘⡤⢄⠳⣌⢆
⠀⠀⠀⠀⢀⠔⠀⠈⠥⠴⠤⠠⠤⠤⡄⠀⠢⡃⠀⠀⠈⠢⡀⡠⠀⠀⠀⠘⠉⠸⠀⠈⠉⢡⠀⠉⠀⠈
⠀⠀⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⣠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠠⠤⠀⠀⠀⠒⢒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣬⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⣛⣛⣛⣛⡓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡵⠞⠋⠉⠉⠉⠉⠙⠛⠶⣭⡛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣻⡆⡀⠀⠀⠀⠹⣦⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣡⠞⣩⠿⣧⡆⠀⠀⠀⠘⣧⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡏⠀⠀⠀⠀⠀⠀⢀⣴⠏⣡⠞⣡⠞⣡⡾⠋⠻⣦⡀⠀⠀⠸⣇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢀⡴⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠈⠻⢦⡀⠀⢿⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣇⠀⠀⢀⣴⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡸⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⣀⣴⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠟⣡⠞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⡞⣡⠞⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣩⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⣛⡛⠶⠶⠶⢦⣤⣤⣤⣀⣈⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡴⠟⠁⠉⠙⠛⠶⢦⣤⣀⡀⠀⠀⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢦⣤⣀⡀⠈⠻⣦⡀⠀⠀⠀⢀⣴⢏⣴⠟⣡⡾⢋⡴⠋
⠀⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠾⣿⣦⣀⣴⢟⣵⠟⣡⡾⢋⡴⠋
⠀⠀⢸⣟⣯⡉⣿⢶⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⡟⣡⡾⢋⡴⠋
⠀⠀⠀⢻⡍⠙⢿⣀⣿⠀⠀⣀⣴⠞⣋⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣋⡴⠋
⠀⠀⠀⠀⠙⠶⠶⠟⢧⣿⢰⡏⣿⡾⠛⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⡿⣯⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⣴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠙⠳⣶⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠞⠋
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣤⣬⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠤⢿⣋⣛⣛⣛⣙⣋⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠈⠠⠀⠂⣀⣀⡀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠁⠀⠀⠀⠀⡀⠀⢴⣤⣠⣴
⠀⠠⠀⠀⠀⠀⡴⣻⣿⣿⣿⣶⣶⣤⡧⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣧⠀⠈⠀⠉⢠
⠀⠀⠆⢸⣄⣼⢷⣿⣾⣿⣿⡿⡿⣿⣿⣿⡀⠀⠐⠀⠀⠀⣠⠀⠀⠀⢸⢸⡇⠀⠀⣰⣤⣾⠿⣧⡄⠈⠐
⠀⠀⠼⣆⣿⣷⣾⣿⣷⣤⣿⠟⠛⣿⣿⣿⣷⠀⠀⠠⠁⢀⣸⠀⣠⠀⣇⣾⠀⠀⣺⣟⡅⢇⣠⢈⢙⠀⠻⢈
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣂⠠⣴⣿⣿⣷⣦⣤⣀⣸⣮⣡⣸⣼⣷⣿⣛⣻⠋⠙⡿⣿⣾⣿⡆⠂
⠀⠀⠀⣿⣿⡟⢿⣿⡿⣴⣿⡿⣻⣿⣀⣹⣿⣿⡿⣿⣿⢿⣿⢿⣿⠿⣿⣻⣿⡿⣿⣧⣾⣟⡿⢟⣿⣿⣾
⢀⠀⠙⢿⡿⣿⣿⣿⣘⣧⣤⣿⣿⣦⡶⡛⢛⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣯⢹⣛⣾⡏⠽⢿⡿⣿⣿⣿⣿⢀⣀
⠙⠀⡀⢀⡿⡿⢂⣿⡻⡿⡛⠋⣩⢎⣙⣛⣇⡻⣿⡇⣘⣿⣿⣿⣿⣿⣿⣿⡳⣿⢻⣇⠀⣸⣿⣟⣻⣯⣿⠀⠁
⠀⠙⡅⠃⢀⣤⣿⡞⢝⣯⣼⠻⣴⣠⠟⡸⣶⢃⣿⣿⣿⣻⣿⣿⡿⡿⣿⣿⣧⣿⡿⡽⣿⣿⡟⣯⣟⡻⢟⡇
⠀⠀⠰⡛⣏⣹⣷⣃⣅⣯⠿⣹⣾⣭⣴⣿⣸⡿⠿⢿⣿⣿⣿⣿⣷⣿⣿⡏⣈⡙⣽⣿⣿⣷⢻⡟⣿⣷⣿⡇⠂
⠀⣀⣀⢰⣿⢿⣯⣭⣙⣿⣿⣿⣿⣿⣿⣿⡏⣠⣷⣗⣿⠿⡇⢉⡉⢘⠛⣓⠾⣷⡏⣿⣿⣟⡟⣋⢿⣾⣉⠁⢁
⠰⠐⠢⢼⡗⢼⣿⣿⣿⣿⣙⣿⣿⣿⣿⣯⣿⣩⣿⣿⣿⣷⣥⣮⣤⠒⣷⣿⣴⣾⣿⣿⡟⠛⠢⡐⠖⣿⣼⡋⠁
⠀⠀⠀⠈⣿⣻⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⡟⢿⣧⢴⡿⠟⡛⣿⣃⣸⣇⣴⣾⣷⢴⡏⣹⠋
⠀⠀⠀⠀⢿⡿⣽⡵⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣧⣰⣤⣾⣿⣿⣿⣀⣋⣥⣀⣽⣿⠏
⠀⠀⠀⠀⠘⠀⠻⠐⠁⠀⠀⠁⠙⠋⠁⠈⠙⠁⠀⠉⠉⠙⠛⠙⠛⠛⠛⠛⠙⠋⠉⠙⠋⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣤⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢾⣟⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⣿⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣭⣅⠀⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⢀⣀⣤⡿⠀⠀⠀⠀⣾⡛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢷⣄⠸⢯⣤⠀⠀⠀⠀⠀⣸⠇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠈⣷⠀⠀⠀⣀⣽⠇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⣷⣺⡏⠀⢠⡾⠋⢀⣠⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣬⡷⠶⠶⢦⣼⣿⣁⠀⠈⠷⡴⠾⠁⣼⣏⣤⠶⠳⣦
⠀⠀⠀⠀⠀⠀⢸⡏⣩⣭⡉⣿⠉⠁⠀⠠⣤⣀⠀⠉⠉⠛⢷⠀⢀⣠⣾⠟⠋⠁⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠻⠾⠃⣿⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⠿⠛⠋⠉⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣴⠿⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠏⢁⠌⡁⠀⠀⠀⠀⡠⠂⢁⡤⠔⠒⠒⠢⠤⣉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡂⢉⢸⠀⠀⣀⠠⣁⠔⠀⠀⠀⢀⠊⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠤⢀⠦⣼⠻⠇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡀⣄⢀⠀⠀⠀⠀⠀⠂⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠄⢀⠑⢿⠍⠐⠋⣷⢯⠀⠀⠀⠀⠐⠀⠈⡄⢀⢴⢿⡿⠀⠀⠈⠉⠐⠢⢄⣀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠫⡁⠫⣔⣵⣞⠿⣯⠆⠀⠱⠭⠢⡀⠀⠀⢟⢆⠛⡛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣄⠀⡀
⠀⠀⠀⡠⠐⣄⠀⠄⡀⠙⢻⢩⢹⠞⡿⠀⠀⣅⣠⣤⡇⠀⢠⢤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⠁
⠀⠀⢊⡀⢺⠗⠃⣂⠁⠀⠸⣌⣣⢀⠂⠀⢻⣔⣿⠙⠂⠀⠈⠓⢦⡀⠀⠀⠂⠂⠀⠄⡀⡀⠀⠀⠀⡀⠈
⠀⠨⡞⠀⢠⢷⡾⡟⢻⢂⡌⠀⠙⣧⠀⣶⣼⣛⡟⠋⠀⠀⠀⠀⠀⠈⡿⢧⡀⢀⣀⡀⠊⠀⠀⠀⡹⡝
⠀⠀⠀⠀⠈⠈⠹⣥⢾⣷⡿⠀⠀⠙⡾⠁⠀⣂⣼⡄⣶⠆⠀⠀⠀⢰⠃⠀⡙⠁⠀⢈⣵⣔⣡⡺⠊
⠀⠀⠀⠀⠀⠀⠀⠘⣉⣉⣻⡄⠀⢼⠀⠀⠰⣯⣟⣿⠃⠸⠍⠁⢀⡏⡠⠊⢀⡠⠖⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⡄⣠⠾⠥⠚⠉⠘⠒⠀⠀⣼⠋⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⢠⣧⠏⠀⠀⠀⠀⠀⠀⠀⢊⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣳⢰⡗⠃⠀⣠⡤⠤⢔⣣⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠊⠀⠀⠀⢄⠀⠑⢆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡰⠈⠒⠤⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣸⣋⣥
⠀⠀⠀⠀⠀⠀⠀⠠⡔⠐⠀⠀⢠⡄⣹⢛⡼⡁⠇⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠈⠉⡭⠹⠃⠒⠀⡩⠉⠿⠛⢑⠀⢠⠙⠋⠃⠊⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠗⠀⠀⠀⠀⠀⠡⡐⠆⡄⡰⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣊⣲⣿⡇⠀⣉
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠍⠹⡑⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⢸⣑⣿⠄⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠁⢰⣶⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠒⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠰⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻⠀⠀⠸⡇
⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠙⠃⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠉⢀⠀⠀⠀⠀⣤⣟⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠐⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⠀⠛⠃⠀⠀⠀⠋⠿⠀⠐⠈⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠱⡆⣾⠀⡠⠀⠺
⠀⠀⠀⠀⠀⠰⠂⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠹⣿⣠⠁

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⣃⣤⣶⣶⡿⠿⠿⠿⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠀⣴⣾⠟⣋⣥⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀⠉⠁⣠⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣉⡙⠻⢿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣷⣌⠻⣿⣿⡷⠂⣡⣴⢶⣿⡟⢛⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣷⣿⠟⣠⣾⣿⣿⠘⢁⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⡟⢠⣿⣿⠟⢁⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣇⢸⡟⢁⣤⣬⣭⣽⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡀⠛⠛⠛⠉⠀⠀⠀⠀⣠⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⢸⡃⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠦⢉⣡⣰⣆⡔⣄⣆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣼⣿⣾⠃
⠀⠀⠀⠀⢀⣤⡸⠇⡐⠀⠀⠂⠲⠀⠀⠀⠀⠠⣀⣸⠆⣘⢶⢿⠿⡦⡖⠞⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⢊⣡⣤
⠀⠀⠀⣰⠞⢉⡔⠊⣩⢀⠀⠠⠈⠀⠀⢀⣻⠧⣄⣸⠇⣼⣷⣿⡟⠁⣉⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠘⠿⠟⠁
⠀⠀⢰⠏⠀⢼⠀⣼⠦⠦⢤⠀⠀⡆⠀⠀⣿⡖⣳⡀⢐⢛⣻⣿⣿⣿⠛⠿⠘⠄⠀⠀⠀⠀⠀⣰⣾⣅⣦⣶⣤⡀
⠀⢀⡞⢀⡿⢁⣿⢋⣩⠂⠀⠂⠄⠀⠀⠀⠸⠿⣿⣤⣁⣨⢉⣩⠇⡛⠄⠀⠀⠀⠀⡤⠀⠀⣤⣿⣿⣿⣿⣿⣿⡏⡿⢰⡄
⠀⠀⣿⣿⣽⡟⣱⣟⠉⠀⠀⠰⠷⣄⠀⠀⠀⠈⠛⢿⣷⣾⣉⣵⣤⠣⣀⣴⣤⠎⠈⠀⠀⣶⣿⣿⣿⣿⣻⡏⡝⠁⠀⠘⣱⡆
⠀⠈⣿⣯⣾⣿⣻⣄⡄⢡⡄⠁⠀⠀⠑⠀⠀⢀⠤⠀⠁⠛⠩⠿⣧⠀⣧⢉⠂⢀⣦⣼⣿⣿⣿⣿⣿⡿⢿⣿⣀⠀⠀⠈⠉⠰
⠀⠀⠸⣿⣿⣿⠛⠝⠁⠀⠀⠀⠀⠀⠀⢠⣆⣈⡠⢀⣮⠆⠀⣠⠀⠈⣿⠀⢠⠀⢻⣿⣿⣿⣿⣿⣋⣘⠐⣿⡯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠠⣤⣀⡀⠀⢠⡀⠀⠿⣿⣿⣾⡏⡀⠀⣿⡇⠀⢸⢠⠏⣀⠈⣿⣿⣿⣽⣿⣿⣿⣿⡟⠃⢢⣔⠒⠦⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣷⣿⣶⠢⠄⠱⡀⢱⢰⣾⣿⣿⣶⢰⡏⠀⠈⣆⠜⢻⢟⣽⡿⠉⢏⡋⡄⠀⠀⢉⣳⣦⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⣦⡘⢳⠸⣾⣿⣿⣿⣿⣸⠀⢀⡾⠁⠀⡜⠻⣯⣴⠄⣸⢣⣇⢴⡳⡼⠞⠁
⠀⠀⠀⠘⣿⣇⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡍⢻⣿⣿⡇⣿⢠⡞⠀⠀⣼⢁⡤⡄⠁⠈⠉⠋⠙
⠀⠀⠀⠀⣉⣉⣳⣞⡠⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⣸⣿⣿⣥⣻⠟⠀⡄⠀⠇⢸⠿⠃⠀⣠⠁
⠀⠀⠀⠐⠻⠟⢁⣜⠁⠠⣀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠞⣿⣀⣃⣿⠀⣶⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢳⣴⡷⠒⠒⠂⣉⣀⡐⢀⣨⣿⣿⣿⣿⣿⣟⠠⠀⣀⣴⣿⢿⣿⣿⣿⣿⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠦⠾⠁⠾⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠏⢰⣿⣿⣿⢿⡜⣸⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⡿⠟⣿⣦⡿⠋⢀⣴⣦⣜⠷⣿⡟⣸⣃⣴⣾⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⢀⣴⣿⣿⠧⠂⢈⣉⣛⡿⡆⢿⢹⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠹⢿⣿⣿⢰⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠡⡯⣞
⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡤⢸⣷⡿⣣⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡛⡉⠉⠀⠸⣿⣿⣿⣟⣰⢚⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣶⣯⣿⣿⣷⣯⣬⣽⣿⣿⣿⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣟⢿⡛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣁⢶⠊⠜⠉⡉⢹⠽⣯⠻⣽⣳⣿⣿⣿⣿⡅⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠙⢦⡀⠀⠀⠀⠀⠀⠀⣿⠿⣼⣥⣬⣥⣬⣉⣌⣩⣭⣬⣿⣿⣷⢿⣟⣿⡇⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢦⡀⠀⠀⠀⠀⣿⣿⣛⠷⠶⠶⢶⠿⠶⢶⠶⡶⢾⣿⣿⣯⣿⣿⣧⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠙⢷⡀⠀⠀⣿⣿⣽⣛⣛⠓⠾⡟⡿⣟⢛⣻⣻⣯⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢦⡀⢿⡷⢯⣭⣍⣙⣛⣛⣛⣛⣿⣯⣿⣿⡿⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠙⢿⣿⠶⠶⢬⣭⣭⣭⣽⣽⣯⣿⣶⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⣿⣿⣟⣛⡶⠶⠶⠶⠶⠶⣾⣟⣻⣽⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣿⡶⢿⣭⣽⣛⣛⣛⣛⣛⣯⣯⡿⣶⣟⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣝⣓⣒⣶⠾⠯⣭⡽⠷⠶⡷⣟⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠩⠟⠻⠛⢛⣻⢛⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠦⠤⢼⣭⣤⣾⡿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⣦⠙⢿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣄⠀⠙⠿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣆⠀⠈⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠤⡀⠉⠉⣉⠀⠀⠁⠀⠀⡉⠉⠩⢿⣿⣿⣿⣿⣿⣿⡟⠻⠟⠻⣿⣿⣿⣿⣿⣿
⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣟⣛⡛⠛⠿⣷⣶⣾⣿⣿⣿⣟⣷⣶⣦⣽⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣷⣶⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣙⡛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣃⡀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣿⣿⣭⣥⣶⣦⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠸⠇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠸⡁⠀⣁⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠁⢠⣼⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣤⣛⣴⣿⣿⠁⠀⠀⠀⣿⣿⣷⡀⠀⠀⡀⠐⠂⠈⡐⠀⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠉⠙⢦⠀⠠⠀⢰⡟⡛⢻⣧⠀⣠⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠛⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⣄⠸⠿⠿⡟⠃⢠⡾⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠾⠃⠀⢠⣶⣦⡠⠀⣀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣾⣷⣦⡄⠀⠀⡾⠛⠉⠀⠀⠀⠰⠠⣾
⢀⣤⣤⣠⠀⢀⡀⠀⠴⡒⢄⠀⡇⢀⡴⣲⡘⠻⢿⣿⡼⠛⠃⠀⠀⠀⠀⣯⠀⠀⠀⠀⢘⡝⡿⠃⠀⠀⠁⠀⠀⢀⣤⣠⠀⠃⠊⠀⠀⢀
⠈⠿⢿⣿⣰⠿⠋⠀⠂⡈⠊⣳⣷⡫⠊⢀⠆⢰⣦⣹⠁⠀⠂⠀⠀⠀⠀⣿⠀⡞⡽⡆⢸⠋⣀⣤⡄⠀⡇⠀⠀⠹⣿⣽⣿⣼⣇
⠀⢠⣤⣹⡇⠀⠀⠀⠀⠈⠑⢺⡗⠐⠊⠀⠀⠀⠉⠻⡆⠀⠀⠀⠀⠀⠀⣿⠀⠙⠚⠻⡾⠶⣏⣪⠏⠀⣇⣶⣶⠀⠈⠀⠙⢺⣿
⠀⠀⠉⠻⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⡇⠀⣀⣠⣤⠀⡟⠁⠀⠀⠀⠀⠀⠀⡿⠀⠀⠰⡶
⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⣿⣿⣾⢀⣴⣦⠀⠀⠀⠀⡿⠀⠀⡤⢸⠁⣄⠿⠟⡏⠀⡇⢀⢀⣤⡄⠐⡓⠀⢰⠰⡶⠀⠁
⠀⣾⣷⣮⠀⣠⣤⠀⠀⢀⣀⡸⡧⡶⠆⠠⠄⠉⠛⢿⡞⠉⠀⠀⠀⠀⠀⡇⠀⠀⠉⢹⠉⠉⠀⠙⠇⠀⡿⣙⣻⡽⠀⠊⠱⡄⢸⠀⠁⣀⣦
⠀⠉⠛⢿⡼⠋⠁⠀⠂⠈⠯⠁⣷⠘⠀⠂⠀⠸⠿⣾⡇⠀⠀⠈⠀⠀⢀⡇⠀⠀⠀⠸⡆⠀⠂⠀⠀⠀⡇⠀⠀⠉⠦⠈⣉⣠⣼⣶⣿⣿⣿
⠀⠐⢿⣦⡇⠀⠀⠀⠀⠀⢀⠀⢸⣄⣁⣀⣀⣀⣀⣈⣇⣀⣀⣀⡀⠀⢸⠇⠀⠀⠀⠀⢷⠀⠀⠀⡄⣀⣇⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣗⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣦⡀⣰⣿⠏⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠛⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣶⣶⢠⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⢎⣻⣿⡈⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⣿⢟⣵⣾⣿⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠃⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠿⣿⣿⣿⣿⡿⠿⢃⣀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶⣦⣤⣀⡀⣠⣶⣿⠟⠁⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣯⣭⣶⣭⣭⣵⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠛⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢋⣟⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⠟⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⢛⣷⠛⣻⡚⢻⡟⢠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⡛⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⣿⠀⣿⡇⢸⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⢿⠇⢸⡇⢻⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠿⠟⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠋⢀⣀⡄⢿⣿⠟⣄⣀
⠀⢀⣠⣴⣿⣿⣿⣿⣿⣶⣦⣤⣄⢠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⣿⢠⣿⣿⣿
⠺⣿⣿⣿⣿⢿⣿⣿⣶⣶⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣼⣿⣿⣿
⠀⠀⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣶⣤⣤⣤⣤⣤⣤⣶⡶⠾⠟⠛⠉⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠂⠀⢴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠂⠀⠀⠀⠀⠉⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢿⠋⠀⠈⡤⠀⠄⠀⠀⡄
⠀⠀⠀⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠂⠂⠀⠀⠀⠀⠀⢀⣤
⠰⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⢀⠂⠀⠀⠀⠿⣿⣿⢇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢠⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡂⠆⢒⡄⠀⠀⠐⠀⠀⠀⠀⠀⠡⠀⠉
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠤⡧⢈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠎⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣄
⠀⠀⡀⠋⠀⣤⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠛⠛⠉⠃⠘⡀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣬⠉⠉⣷⣦⢶⣄⢊⡀⢳⡀⠀⠘⢿⣷⢀⣴⣿⣿⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⣀⣰⣧⠛⠃⠀⠹⠛⠻⠛⢁⡶⠆⠹⡷⡞⠋⢁⠿⢁⣨⡄⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠒⠛⠛⠁⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠘⢰⣤⣤⣷⣿⣿⡇⠀⣺⣤⣤⡀⠀⡄⡀⠀⠀⡠⡀
⠀⠀⠀⠀⠄⠀⢀⠢⠷⣦⣀⠀⠉⠙⢶⣤⣿⢃⡁⣩⣏⣿⣿⢿⣿⣅⣈⣿⢉⣐⢾⢟⡄⡀⣀⠁⠠⣄⠀⠈⢀
⠀⠀⠀⢄⠠⠴⠎⠃⠀⣽⣈⣄⣀⠀⠀⢍⡉⣲⣿⣿⡿⣷⣿⣿⣿⣿⣷⣿⠁⢸⡃⣤⣹⣿⣿⡴⣶⢋⢀⣀⡆
⠀⠀⠀⢸⠇⡄⠙⠃⠀⢹⡟⢻⣿⣷⠰⢾⣴⣿⣿⢻⣷⣿⣿⣿⣿⢿⣿⣿⣧⢘⣿⢙⣩⣿⣿⣿⣿⣷⣔⠸⠓
⠀⢰⠀⠰⠀⡇⠀⠀⠀⣾⡆⢸⡟⢙⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣍⣸⡿⠀⢀⣿⣿⣇⣼⣶⣛⡑⠓
⠀⢸⠀⣂⢸⣇⣀⣴⣴⣿⡇⢹⣴⣿⣟⣻⣖⣿⣿⣿⣿⢯⣽⣿⣿⣷⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘
⠀⢸⣁⠈⢘⡏⠛⠡⣭⢹⣏⢹⣯⣿⣿⣍⣫⢿⣿⣿⣿⢿⣿⠏⠉⠹⣿⣿⣿⣿⣿⣇⣿⣿⢋⣏⡴⠠⠆
⠀⠺⣿⢇⡐⡇⠀⠀⠠⣼⣟⣸⡏⣉⣽⠛⠉⠛⣻⣿⣿⣛⣿⣷⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠄
⠘⠲⡽⠊⠈⠃⠀⠐⠂⠙⣿⣿⡇⠀⢹⠀⠤⠶⠀⠰⠼⠿⣷⣤⡤⠄⢻⣿⣿⣿⣿⣿⣿⣿⠏
⢀⣠⣽⠏⠀⠀⠀⠀⠤⣿⣟⠋⠀⠀⢹⡀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠠
⢀⠽⡯⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⢀⣈⡄⠀⠀⠀⠶⠿⠉⠉⠛⠛⠛⠟⠛⠻⠿⡋⠙⠻⠿⣧⠠⠀⠀⠀⠒⠲⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⣤⣀
⠀⡸⠀⠈⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣡⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢤⣄⠈⠙⢷⡀
⠀⡇⠀⠀⢀⣀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣵⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣷
⠀⡇⠀⣤⣿⠿⠛⠢⠙⢗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣳⣿⠇⠀⠄⠐⠂⠀⠈⠀⣀⣤⣤⣤⣦⡔⢢⣤⠉⠒⢄⠀⠀⠘⣧⠀⣿
⠀⣿⣴⡇⡩⠒⠋⠓⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠿⢧⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠁⠀⠀⠈⠁⠀⣸⠇⠀⣿
⠀⠸⠟⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠈⠑⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⢤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠀⠂⠀⠀⠀⠀⠀⣰⠃⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠔⠂⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠶⠖⠒⠒⠚⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠐⠢⠤⠤⣀⣀⣀⣀⣀⠀⠠⠤⠤⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣤⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢱⣿⣿⣿⡏⢘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡼⢿⣿⣿⡟⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡦⠀⠀⠀⠀⢀⣿⣿⡇⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⡟
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣴⡆⠀⠀⢻⡿⢻⣦⠀⠘⠃⡄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠛⢠⡀⠀⠀⠀⠀⢨⠢⠀⠀⠀⠀⠀⢄⠑⠶⠀⣰⣦⡀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣦⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣼⣿⣿⣧⠀⡇⠀⠀⠿
⠀⠔⡀⣿⣿⣿⣻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢧⢹⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡖⡋⠿⣿⠏⠀⡇
⠀⠀⠀⢿⣿⡟⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠈⣎⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡆⠁⠀⢸⠀⠀⡇
⠀⠀⠀⢸⠁⠁⠀⠀⠀⢀⡘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢹⡄⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⢀⡄⢰⣿⡄
⠀⢰⠀⢸⡄⢠⣤⠀⠀⠘⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣤⡌⣧⠀⠀⣮⠛⢀⠀⡀⠀⠀⠉⠀⠀⢹⡌⢆⢠⡄⠈⡗⢤⡀⠀⠀⠀⠈⠀⠾⠛⠏
⠀⢸⡇⢸⣷⣿⣿⠀⠀⠄⠀⣶⠈⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⣄⢹⡄⠔⠉⠀⡏⠀⠛⠀⢀⣀⡤⠀⢸⡇⠘⡎⡇⢈⡇⡀⠳⡄⠀⠀⠀⠀⠂
⠀⠀⢻⣿⠊⢻⣿⣶⣿⢟⣿⠃⠀⠀⢀⠀⠈⠙⢿⡉⠉⠟⣇⠀⢹⡎⣿⡆⠀⣸⡇⠀⠀⠀⠐⠻⠆⠀⠀⣷⠀⢻⣷⢰⡇⢡⠀⢹⡄⠀⠀⠀⠀⠀⢀⡔
⠀⠀⢸⠸⡁⢹⡟⠉⣙⣯⣿⣀⡀⢀⣸⠀⠀⠀⠀⡿⣄⠀⣿⠀⠀⣷⢹⡁⠀⡿⠀⠀⢠⠀⠀⢀⠄⠀⢀⣿⣀⢈⣿⣾⡇⢸⣤⠀⢻⡀⠀⠀⠀⣠⡾
⠀⠀⣼⠀⣇⣹⣿⣿⢿⣿⣿⣯⠛⢉⣿⣶⣾⣷⡄⢹⣿⣷⣼⡆⠀⢸⣾⡇⢰⡇⠀⠀⣴⠀⠀⣼⠀⠀⠈⢻⡙⠛⢿⣿⡇⢸⡿⠀⠈⣧⠀⠀⠾⣿⠃
⠀⠀⣿⡄⠹⡇⢸⢹⡀⢟⠛⢿⣿⠾⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⣷⣿⢸⡇⠀⣀⠃⢀⣼⣃⣴⠏⠀⣿⡿⡄⣸⣿⡇⢸⡇⢡⠀⢹⡇⠀⢠⡟
⠀⢠⣇⡇⣦⣇⢸⡇⣷⠈⢳⡀⣷⠀⢸⣿⣿⣿⡿⠀⣿⣿⣿⡇⢠⠀⢹⣹⣼⠀⠀⢹⢰⣠⡿⠻⣇⠀⡜⢹⡇⢳⡏⢹⡷⣾⣇⠈⡆⠘⡇⣧⣾⠇⢰
⠀⢸⠉⡟⣿⣿⢻⣷⢸⣵⣾⣷⢸⣆⣼⣷⣽⢻⡇⠀⣟⡏⠈⣇⢸⠀⢸⣿⣿⣶⣿⡿⣿⣿⠿⣷⠿⣸⠁⢸⡇⢸⣇⢸⡇⣿⢹⠓⢷⠀⡇⣿⣹⡀⠀⡇
⠀⣿⠀⣿⡇⢿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⢸⡇⠀⣿⡇⠀⣿⢘⡇⢘⣿⣿⣿⠙⣇⢻⡏⣰⠋⢀⡏⠀⢸⣁⣸⣿⢸⣇⣏⢸⠀⢸⠷⣟⡿⡿⠃⠀⢱
⠀⣿⠀⣽⣧⣼⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⡇⠀⣿⣧⠀⣿⠸⡇⢸⡿⣿⣯⣠⡏⣼⣡⠏⠀⢸⠃⡤⢾⠏⢸⣿⣿⣿⣿⣸⠀⠈⡇⣿⣇⡿⣼⠀⢸⡀
⠀⣿⢠⣿⣏⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⡇⢠⣿⣿⡀⢿⣐⣇⢸⡇⣿⣿⣿⢻⣿⣾⣦⣦⣿⠟⠀⢸⠇⢸⣿⣿⣿⣿⣿⣢⠖⡏⣿⣿⡇⢹⡀⠀⡇
⠀⣿⣤⣿⣿⢸⡇⣿⡏⣿⣿⣿⠛⣿⣿⣿⣼⣿⣿⣾⣿⣿⣧⣿⣿⣿⢸⡆⣿⢻⣿⢸⣿⣿⣿⣹⣿⣄⠀⡾⠀⠘⢿⣿⣿⣿⣿⡅⠀⡇⣿⣿⣇⠸⡇⠀⡇
⠀⣿⡟⣻⣿⣸⡇⣿⣷⣽⣿⣿⣠⣿⣸⡟⠈⡿⡿⡟⢻⠃⣟⢻⠛⡋⣾⡄⡇⠀⣿⣼⣿⣿⣿⣿⡇⠀⢀⡇⠀⡇⢸⣿⣿⣿⠘⣧⠀⡇⢹⣿⣿⠀⣧⠀⣷
⠀⣿⠁⢹⣿⣿⣷⣿⣿⠿⣿⢻⠿⣿⢹⡇⠀⡇⣿⡇⢸⢰⢸⣸⠀⡃⣿⡇⡇⠀⣿⣿⣿⢏⡟⣼⠁⡀⢸⡇⢠⣧⠿⣿⣿⣿⠀⠀⠀⣧⢸⣿⣿⠀⣿⠀⣿
⠀⣿⠀⢸⣿⡿⡃⢹⡿⣆⣿⢸⠀⢿⢸⡇⠀⡇⣿⠃⢸⠸⢸⣿⠀⠁⢸⡇⡇⠀⢻⠃⡇⣾⣷⣿⣟⡉⢹⡇⢸⣿⠀⣿⣿⠉⠀⠀⠀⣿⡿⣿⢻⠀⣿⠀⣿
⠀⣿⠀⢸⢹⡇⠀⣿⡇⠀⣿⢸⠀⢸⢸⡇⠀⡇⣿⠀⢸⡇⢸⣿⠀⠀⣿⣷⡇⠀⢸⠀⡇⡿⠋⣼⠈⠃⢸⡇⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⠇⣿⢸⠀⢻⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠿⣿⡿⠿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢋⣽⡿⠋⠀⠀⣿⡇⠀⠀⠙⢿⣏⠛⢿⣦⣀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢀⣾⠏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⣧⡀⠈⠻⣷⣄
⠀⠀⠀⠀⣠⣿⠛⠿⢶⣦⣾⣧⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣽⣷⣴⡾⠿⢿⣦
⠀⠀⠀⢰⡿⠁⠀⠀⠀⣼⡏⠉⠉⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠉⠉⢿⡇⠀⠀⠀⢻⣧
⠀⠀⢠⣿⠃⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢻⣇
⠀⠀⣼⡏⠀⠀⠀⠀⢰⣶⡶⠶⠶⠶⠀⣠⣶⠿⢷⣦⡀⢀⣴⡶⠿⣶⣦⠀⠀⠀⠀⠘⣿
⠀⠀⣿⣧⣤⣤⣤⡀⢸⣿⣤⣤⣤⡀⠀⣿⡇⠀⠀⠉⠁⢸⣿⠀⠀⢸⣿⡇⢠⣤⣤⣤⣿⡇
⠀⠀⣿⡏⠉⠉⠉⠀⢸⣿⡉⠉⠉⠀⠀⣿⣇⠀⢀⣴⡄⢸⣿⣄⠀⣸⣿⠃⠀⠉⠉⠉⣿⠇
⠀⠀⢸⣇⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⢰⣿
⠀⠀⠈⢿⡆⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠘⢿⣄⠀⠀⣀⣸⣷⣤⣶⣶⡶⠶⠶⣿⡿⠶⠶⠶⣶⣦⣤⣿⣇⣀⠀⢀⣾⠏
⠀⠀⠀⠀⠈⢻⣿⡟⠛⠉⢻⣯⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⠏⠙⠛⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠻⣧⡀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣾⠏⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣽⣿⣦⣀⠀⣿⡇⢀⣠⣴⣿⣷⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠛⠛⠉⠁

⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠿⠿⢿⣷⣦⣄⣀
⣾⡿⠛⠻⠿⢿⣶⣶⣤⣤⣀⡀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣶⣶⣤⣀
⠻⣿⣶⣤⣀⠀⠀⠉⠉⠛⠛⠿⢿⣷⣶⣾⣟⠉⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠈⢹⣿
⠀⠀⠉⠛⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣰⣿⠏⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⡀⢀⣀⣠⣤⣶⣶⡿⠿⠛⠛⠉⠙⠻⣿⣯⣀⢀⣾⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣿⣿⣟⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣟⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡛⠉⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠋⠀⠙⢿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠉⠁⠀⠈⢿⡀⠀⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣸⡧⠀⠀⠀⠀⢀⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣠⠞⠛⠉⠉⠀⠀⠀⠀⢀⡿⠁⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣷⠀⠀⠀⣴⠟⠉⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⡀⠀⢰⡏⠀⠀⠀⠀⢸⡏⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠳⣄⣿⠀⠀⠀⠀⠀⢸⡇⠘⢧⣠⡴⢦⣄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠀⢠⣟⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠉⠙⠓⢦⡀⣰⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⠠⣾⣵⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⣹⣷⣄⡀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⢀⣴⡟⣻⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠛⠇⠙⠻⢶⣤⣀⣀⣉⣀⣀⣀⣠⣤⣶⡾⠋⢰⣿⠏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠙⢯⠉⠉⠉⠉⠉⠉⢡⡏⠀⠀⠈⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠁⠀⠐⠇
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⠀⠀⠀⠀⡴⠺⠓⠆
⠀⠠⡇⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠺⣀⡁
⠀⠀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⢱⣶⣶⡾⢿⠷⢶⣶⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠐⠀⠐
⣆⠠⠤⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠋⢀⣄⣀⠀⠈⠛⠁⠀⠀⠐
⣯⠙⠲⡄⡈⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⢀⡄⡀⢀⠀⠀⠉⠀⠀⠀⠸⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡔
⠙⡤⠀⠀⠀⠀⠀⡇⠰⠄⠀⠀⠀⠀⠀⠘⢿⡿⡇⠀⢀⠀⢀⢠⠂⠀⠀⠀⠘⠀⣠⠀⠀⠀⠂⠀⠈⡚⠀⠀⡄
⠄⠗⠓⡄⢀⡄⠈⡗⢠⡌⠂⠀⠀⠀⠀⠀⠀⢿⠁⢂⠏⢠⠀⠈⠀⣠⠄⢃⠄⠳⠟⠂⠀⠀⠀⠑⣌⠱⠚⠂⢀
⠀⣰⠲⡄⠀⡅⢀⡟⢾⣇⠀⠀⠀⠀⠀⠈⠒⠠⠃⠤⠆⢰⠂⣤⡰⠇⢸⠀⡄⣸⡞⠀⡀⠀⠀⠀⠀⠙⠖⠀⠈
⠀⠁⠀⢱⢀⣤⢨⡇⢸⢻⣎⠁⠀⠀⡄⣼⠆⡷⠀⠀⢌⢙⠂⠃⢍⡁⠻⣤⠳⠝⠃⠀⠑⣤⢀⠀⢀⠀⡀⠁⠆
⠔⠄⠈⠒⠋⢗⣠⡇⢂⠉⣿⠳⠀⠄⠀⡏⠀⠈⠳⣔⡀⢈⣀⡀⠀⠀⢾⣾⡧⢤⠀⠐⣤⠒⡖⣆⡓⠀⠈
⠀⢾⠾⠔⣶⣟⢙⡟⠋⡐⠿⠀⠇⢐⢟⡟⢠⣄⡒⠊⠭⣹⠀⠀⡴⢀⠈⣽⣦⡔⡀⢠⣤⢰⡿⣄⡁⡀⠀⠘⢣
⣥⢰⣿⡦⡰⠿⢾⣷⠄⠀⢣⠐⣌⣩⣿⣤⣜⣀⠀⠀⣀⡽⢒⣟⢠⣽⠈⡄⠤⢼⠃⠆⠀⠀⠀⠀⢳⠏⣔⣿⣠
⡤⢺⢿⣷⠟⠻⡖⠃⠀⢀⡈⢸⣫⣿⣿⣿⡿⠉⢄⡀⠹⡳⡷⠆⠻⣿⣿⠗⠂⡬⠜⢓⠠⢀⣯⣾⣁⣴⣣⣄⠈
⠁⢼⣗⣤⣄⢀⣥⣺⣶⡦⣦⣻⣉⢡⣶⠚⣗⣀⡴⠀⣤⣟⣆⡁⡘⠻⡞⠂⠀⢃⠰⢺⠐⠿⡝⣜⣧⢿⢷⠻⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⢻⣿⣿⣿⣿⢟⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠚⠛⠛⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣛⣵⣿⣿⣿⣿⡿⣢⣿⡿⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠿⠟⡀⣤⣤⣤⣤⢀⡀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠃⠿⠿⣿⣿⣿⣿⣧⠻⣿⢸⡿⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠠⠞⣣⣾⣿⣿⢇⣹⣿⣆⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⣿⣿⣎⣛⢿⣿⣿⣷⣶⢸⡿⠇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣌⢈⣛⠻⣿⣿⣜⠿⢿⣿⡆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡙⣿⣿⠿⢳⣿⣿⣿⣿⢸⡿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⡸⣿⣷⡎⣿⣿⣿⡇⣿⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢸⡏⣾⣿⣿⣿⣿⡿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢷⠸⢇⣶⣿⣿⣿⣇⠛⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣿⣿⣿⣿⣿⠱⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠁⠸⠿⠿⠟⠛⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣤⣀⣀⣠⡤⠴⠊⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣛⣯⣭⡟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣱⠿⢿⣿⣿⢢⣿⣦⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠍⡏⠭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⣏⢾⣦⣝⢻⣎⣛⢿⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣤⢸⡟⡻⡟⡛⡇⣤⡤⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⡎⣿⢫⣾⣿⠟⣼⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣣⣿⠸⣧⣵⣷⣥⡇⢿⣇⣃⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠻⣦⣿⣿⣿⡶⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡐⢶⣶⣶⡶⢆⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣥⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢸⣿⢇⣾⣿⣿⢫⣵⣶⣮⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⣛⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡛⣺⣿⣿⣧⣝⣛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⣤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢈⡁⠀⠠⡀⡀⠁⠈⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣲⠮⠃⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠉⠁⠱⣄⠀⠀⠐⠀⠀⠔⡤⡀
⠀⠀⣀⠀⢁⡀⢀⠚⠀⢀⡀⠀⠂⠐⠀⠠⠀⠀⠂⢀⠀⠁⠀⠀⠀⠀⠂⠀⡀⠀⠀⠰⠋⡁⠈⠉⠘⠤⠀⠀⠀⠀⠐⠉⠇
⠀⡐⠀⠀⠈⡬⠀⠀⠈⣈⠁⠐⠂⠂⡀⠀⠀⢀⠀⡀⠂⠀⣄⣀⠀⠀⠀⣀⡈⢀⢘⡀⠀⠐⡄⠁⠁⢀⣂⠀⣀⠀⡀⠀⠈⢀⣀
⢸⢡⡀⡼⠀⠀⠀⠀⠈⠀⠉⠚⠇⣀⡀⠈⡀⢀⠁⡀⠠⠈⠉⠛⠓⢀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠂⢀⠀⢀⠀⠀⢀⣀⠐⠋⠉⠁
⡄⠈⠱⠃⠀⡀⠀⠀⠀⢀⠄⠀⢀⠀⠠⣠⠀⢈⠀⠃⡒⠀⠐⠛⠠⠈⠀⠀⢙⠀⠂⠉⣍⠀⠀⠀⠈⠀⠀⡈⠘⠀⠀⠀⠀⠉⢲⢨⠧
⠷⡀⢂⠁⣀⠐⢌⠁⠐⡀⢪⢄⠔⢀⣠⡀⠀⠄⠀⢂⡥⡤⢀⠀⠃⠀⠀⠠⡀⠀⠆⠄⠐⠀⠁⠀⡀⠐⠀⠁⠈⠂⠀⠼⠰⠃⠬⠀⠉
⠀⠀⢸⡀⠈⠀⠈⠀⢀⡐⠈⠀⢀⠙⠟⠓⠀⠀⠀⢵⠣⠀⠀⢀⣀⠂⠀⠀⠈⠀⢀⠚⠀⠀⣅⠀⠈⠃⠀⠀⠁⠀⠀⠀⠠⠀⠂⠁⠸
⡀⠀⢻⠁⠉⢠⣦⡆⠀⠀⠄⡀⢊⣱⠂⠠⠂⠀⢀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢻⡄⠃⠐⠀⠄⠀⠀⠀⡀⡀⠊⠀⠀⠀⠀⢀
⠀⠀⢀⣠⠄⠈⠉⠀⡂⠀⠀⣀⠀⢻⣤⡠⠄⠀⢄⠀⠀⠐⠀⠀⠀⣠⠶⠞⠀⠠⢀⡅⠀⠁⠀⠆⠁⢀⣁⠄⠈⡙⠛⠄⢀⡉
⠈⠀⠂⢲⣀⠀⠄⠋⣴⡀⠃⠠⢀⠀⢪⢂⠀⠈⣀⠐⠠⠀⠔⠀⡂⠀⠰⠁⠄⠀⡄⠻⢦⣅⢠⠀⢁⡌⢰⠂⠃⣰⡔⠀⠀⠀⠗⣂
⠁⠀⠄⠠⡌⡈⢀⠀⠈⢇⠀⠀⠀⠀⠈⡅⣇⠀⠀⠑⢄⡔⠂⡀⠀⠜⡓⠀⣈⠀⡤⠀⡀⠚⠉⡦⠀⢠⠉⡄⠒⠈⢹⡿⠤⠄⠀⢧⡤
⢕⣦⣠⠰⠂⠐⠏⢱⡀⠾⡀⣅⠘⡍⡄⠰⠵⠿⢠⣄⣲⠵⠧⠤⣦⡀⠋⡀⠈⡾⠻⠧⣤⠺⢄⣁⡄⢈⣄⢠⡀⢅⠽⠈⣔⠴⠤⢾⣶
⠐⠈⠈⠑⣿⢦⣆⠀⠁⠐⠀⠘⢊⡀⡁⠀⠀⢚⣻⡹⠃⠀⠃⠂⠈⠓⠀⠑⠾⠁⠀⠀⠉⡾⢫⠉⢤⠘⠛⣆⠀⠘⠈⠒⠋⢒⢸⠃⠂
⠀⠐⠐⠀⠁⡀⠁⠑⠀⢀⣀⢠⠀⢃⠀⢀⠀⠀⢹⠢⠀⠀⠰⠊⠀⠀⡴⠂⠀⠀⠊⠄⠠⠁⠠⠀⠈⡀⠀⠈⠙⠎⣔⠤⡅⢠⠉

⢀⡚⠀⠀⠄⠀⡀⠈⠌⣽⠁⠀⢀⣈⡻⢀⡀⠀⡍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⢀⣀⡀⠀⠀⠰⠇⢰⣧⢠⣶⡄⠀⢘
⢉⠁⣷⠀⠀⠀⡿⠀⠀⠉⠀⠀⠚⠿⠀⡈⠁⠀⠁⠀⠀⠀⢲⡼⣦⣄⡠⠀⠀⠀⠀⠀⠀⢋⣾⡿⠃⠀⠀⠈⢾⢋⣦⣉⡀⠐⠟
⠀⣾⣙⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠆⠀⢀⣤⣤⡀⠀⠀⠸⣿⣧⣿⣿⣖⠀⠀⠰⠾⠂⠀⠈⠁⠀⠀⠀⠀⢉⣈⣧⣽⡋
⣎⠢⠔⠀⠀⠠⠀⠀⠀⢰⣥⣟⡧⠀⠀⠘⠙⣿⡃⠀⠀⢀⣹⡉⠙⣯⢷⠀⠀⠠⣄⠊⠀⠀⡀⠀⡀⠀⠀⠘⠟⠓⠀⠀⠀⠀⠸
⠀⣶⠶⠀⠀⢠⡀⠃⠰⠿⡽⢿⡇⠀⠀⢀⣤⣤⠀⠀⠀⠈⠉⠘⡏⠁⠀⠀⠀⣠⠄⠙⠀⢀⢈⣠⠀⠀⠀⢀⠀⠀⠀⣴⣦⣤
⠀⠦⠀⠀⠀⠀⠉⠐⢦⠀⠇⢀⠀⡄⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⢙⣇⣤⠔⠁⢀⠀⠘⠛⢻⠟
⠀⠀⠀⠀⠀⠄⠀⠀⠈⢳⡀⠌⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠠⣾⣿⣷⠀⠀⠘⡄
⠀⢀⠀⠀⣤⠀⠈⠛⠀⠀⢷⡘⠀⠀⠀⡀⢀⢀⡀⣀⣀⢀⡀⢀⡀⡀⣀⣀⣀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠈
⠀⢸⠀⠀⠀⠐⠿⠀⠛⠀⠘⡇⠀⠀⠈⠃⠈⠈⠁⠉⠉⠈⠉⠈⠀⠁⠁⠁⠋⠈⠀⠉⠈⠁⠀⠐⠲⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣬⠀⠸⠿⠀⣠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠑⣄⡇
⢠⠋⠀⠀⠀⡴⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠆⠀⢠⠀⠘⢿⣼
⡏⠀⠀⠀⠀⢠⡗⠀⠀⠂⠀⠎⠀⠀⠀⣄⠀⣠⡀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠾⢃⡈⠇⠀⠀⠀⠀⠈⠂⠀⠀⠀⢸⠀⠀⠀⣿
⠀⢀⠀⠀⠀⠰⡟⠀⠀⠀⠀⡀⠀⠀⠀⣤⢠⠨⢀⠀⠀⢀⣥⡤⢐⣂⠀⠀⠀⠐⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⢿
⠰⢜⣑⠏⠀⠀⠠⡀⠀⠀⠘⠤⠀⠀⠛⢾⠎⠾⡭⠀⠀⠸⠿⠷⣿⠟⠃⠀⠀⠀⠀⠉⠑⠀⠀⣴⣿⣿⣿⡄⠀⠈⠿⠟⠀⢀⣈
⡇⠈⠈⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡟⣉⠋⠀⢀⣔⡓⠀⢾⣿
⢣⣄⠰⠁⣠⡀⠁⠛⠀⠀⢰⣿⣿⣿⠆⠀⢒⡀⢦⣠⠄⠀⣈⡿⢃⡀⠰⣞⣷⣷⠆⠀⢾⡿⠀⠀⠤⣥⠉⠀⠀⢰⢚⣂⠀⠈⢩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠃⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣙⠖⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠠⠀⠈⢢⠀⣀⠔⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠙⡀⠚⠀⠀⠈⠽⠍⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠇⠀⠀⠀⠀⠀⠀⠛⠄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢀⣤⡶⢈⡦⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠄⠀⠀⢀⠀⠀⠈⠀⠰⢆⢭⣦⢤⣄⣨⣑⣄
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠘⠻⠷⠚⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⢀⡓⠲⡤⠤⠼⢥⣴⣾⣀⣆
⠀⠀⣾⣿⡟⠀⠀⠀⢀⣤⠂⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠠⠄⠀⠀⠄⠀⠀⢀⠀⡉⠹⢯⡽⠒⠒⠏⠀⠀⢁⡠⠷⡀
⠀⠀⢿⣿⡇⠀⢀⣴⣿⡿⠋⠀⠀⠛⠄⠀⠂⡀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠐⠀⠀⠂⠀⠐⠐⠠⣀⠈⠂⠌⠀⠛⣋⠛⢀⠀⢃⣀⡤⢞
⠀⠀⠈⠿⣿⡄⠉⠛⠻⠷⠀⠒⠋⠑⠊⠂⠀⠲⠆⡤⠀⠀⠀⠀⠀⠁⠀⠔⠄⠀⠀⠘⡇⠀⠆⠀⠹⡔⠀⣀⡀⠂⣠⠖⠀⠀⠰⣯⣭⣭⣴⣾⡿⠀⢀
⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠔⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠅⠀⠀⣆⠀⠇⠠⠀⢀⠞⣁⠀⠀⣴⣾⣿⣿⣿⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠒⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠤⠒⠂⠖⠁⠁⢉⣥⠾⢴⣥⣩⠖⠡⢦⣾⣿⣿⣿⣿⣿⠀⡀⣀
⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠿⣯⣖⠤⠋⠀⠉⠂⢄⠉⠉⠉⠉⠉⠀⠀⠐⠅⠠⠔
⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣽⣽⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣷⣿⣷⣶⣿⣷⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀
⠀⠀⠀⠖⠆⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠤⣠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠐⠒⠒⠀⠂⠐⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠡⣅⠉⠉⠁⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠓⠶⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠣⣀⠂⣤⠂⢠⠂⡆⠂⡆⢠⠂⣆⠠⢰⠂⡂⡇⡆⠢⠂⡆⢰⠒⡄⠂⡆⢠⠂⡇⠀⡤⠂⣤⠂⡇⢠⠐⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠑⢄⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠴⠤⠖⠒
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⡀⠀⠀⡤⠤⠀⠀⠀⠀⢀⠀⠀⠀⢄
⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⡥⠠⠀⠀⠀⠒⠒⠒⠞⠂⠠⠐⢃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠠⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⡆⠉⠁⠰⠤⠀⠙⠊⡤⢉⠉⠒⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⢀⠝⠉⠀⠀⠴⠀⠃⠊⡀⡀⠠⠊⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡏⠀⠀⠀⠀⠀⢇⣀⡠⠀⠐⠊⠉⠓⠘⠐⠋⡄⠠⠀⠂⣀⠄⠒⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⢐⡫⠇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠢⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡿⢂⠖⠢⠤⡀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⢀⠜⢂
⠀⠀⠀⠀⠀⠀⠦⢄⡀⠀⠀⢀⣠⠁⢨⣀⣀⠀⠈⡑⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠃⢀⢀⢀⣑⣲⠽⠦⠤⠤⠄⠀⠒⡘⠁
⠀⠀⠀⠀⠀⠀⠘⠀⢌⠉⠚⠲⠾⠄⣀⠙⠓⢎⡀⠑⠈⡀⠀⠄⢀⠔⡀⠄⡠⢀⢄⠠⠂⢀⠔⠀⢔⡵⠛⠈⠁⠀⠀⠀⠀⠀⢀⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠉⠒⠢⢵⡎⡜⢷⠆⡊⢔⠨⢒⠡⠢⢑⠠⠂⢔⡡⢾⠔⠁⠀⢰⠀⠀⠀⠀⠀⠀⡰⠁⠈⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠉⠲⣕⠪⢐⠅⡂⢐⠡⡂⣥⢨⡴⢫⠕⠁⠀⠀⡜⠀⠐⠄⠀⠀⢀⠊⠠⠀⢱⢸
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠒⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠨⣂⠕⡨⡰⢒⠨⡶⠃⡀⠀⠀⠰⠃⠀⡸⢈⠀⠔⠁⡀⠀⡆⢈⣸
⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⣀⡀⠀⠢⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⠚⠨⡐⢅⠟⠰⠀⠈⡆⠀⠀⠣⣤⣴⡿⠋⠀⠀⡅⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⠒⠤⠀⠁⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠘⣖⠈⣰⠋⠀⠘⢤⡼⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠁⠀⣇⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⢒⠀⠬⠉⠁⠀⢓⢄⠀⠀⠠⠄⠀⠀⢸⡷⠁⠀⠀⠀⠠⠀⢀⠤⠊⠁⠀⠐⠀⢠⠀⣀⡤⠊⠁⡐⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢔⠂⠀⢉⣀⣀⣞⣓⣦⡀⠁⠐⠀⠘⠃⠀⠀⠀⢀⠠⣔⣁⡀⠀⠀⡀⠄⣀⣰⠚⠁⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠁⠀⠀⠀⠉⠉⠐⠚⠒⠀⠶⠄⠴⠞⠛⠉⡁⠈⢉⢢⣀⠥⠚⠉⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠀⡰⡘⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠄⠀⠀⢀⡨⠵⠊⠀⠀⠀⠆⠈⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⠉⠁⠀⠀⠀⢠⠀⠈⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠤⠀⠈⣀⣀⣀⠀⠀⠀⠀⣈⡈⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⠀⠀⡈⠅⢀⠉⢐⠀⢀⠈⠐⠈⠀⡈⠀⡈⢀⠀⡀⠀⠠⢈⠄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠈⠀⠂⠀⠈⠀⠀⠁⠀⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠈⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢶⡀⠀⠀⠀⢸⠟⠀⠀⢳⣿⣿⣿⣦⡀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣾⣿⣦⠊⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⡀⠀⢶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠠⣤⣹⣿⣿⡆⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣶⠖⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠁⢀⠀⠠⢈⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣇⠀⠐⣿
⣸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠞⠃⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡧⠀⠀⠀⢀⣼⣿⣿⣷⣄⡈⠙⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⠄⢻⣿
⣿⡆⠀⢠⣧⠀⠀⡀⠀⠀⠀⢨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢠⣿⠿⠛⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠈⠛⠉⠙⣿⣿⠉⠉⠉⣽⣿⣿⡤⣾⣿
⣿⡗⠀⣸⣿⡀⢰⡇⠀⠀⢀⣸⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⢾⣿⣿⠶⣿⣿
⣿⣿⡀⣻⣿⡃⣼⣧⠀⠀⠠⣽⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⠀⠘⢿⣿⣿⡿⣿⣿
⣿⣿⣽⣿⣿⣿⣿⣿⠄⠀⠴⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣭⣿⣿⣿⣿⣿⡃⢀⣤⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠴⠶⠒⠒⠒⣲⣶⡄⠀⢀⣠⣾⣛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠀⣀⣀⣤⣤⠶⠾⠿⣯⣤⠿⣶⣿⡿⠋⠉⢳⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣴⡶⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢹⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠦⣤⣤⣄⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠘⣿⠃⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠈⠉⠉⠙⠛⠛⠶⣿⠀⠀⠀⠀⠀⠀⠀⣀⣄⣈⡙⠁⢀⡀⠀⣤⣶⣾⣿⡆⠀⠀⠀⠀⢀⡿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢛⠁⠈⠃⢀⣀⠉⠙⠉⠁⠀⠀⠀⠀⠸⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⢰⣶⡌⠻⠃⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⣠⡄⠀⠸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⢠⡿⣷⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⣦⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⣼⠇
⠀⠀⣀⣤⣤⣄⣀⣸⡏⠀⢀⣾⠏
⣠⡾⠋⠉⠀⠉⣻⣿⣷⡾⠟⠁
⠙⠛⠷⠶⠶⠿⠛⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟
⣀⣀⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⠀⠀⠀⠀⠄⣘⠁⠀⠀⠀⠀⠀⢲⣶⣟⣿⣿⡯⠟⠻⡅⣀⠘⢿⡟⢿⠃⣶⣶⣉⡀⠀⠄⠀⠀⡠⠀⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠋⠠⢐⡄⠀⠀⠀⠈⠉⠀⠈⠶⢀⣀⠀⢰⣭⠀⠈⠉⢠⣎⡿⠛⠋⠀⠰⠂⢠⠂⠀⠀⣀⡀⢁⠀⠂⠐
⠀⠀⣀⠀⠀⢠⢒⡐⠰⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⣾⣷⠀⠀⠀⠃⢾⡇⠀⢀⠔⡈⠀⠀⠞⣉⠁⠀⢄⠀⠰⢄⡀
⠀⣀⣴⣆⠖⣾⢟⡅⠀⣨⣴⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⡬⠳⡟⢂⣠⣀⣼⣯⡕⢠⡅⠀⣅⠐⠘⠁⢠⠀⠅⠨⠁⢰⠀⠁
⠀⢯⣶⣏⣢⣿⣿⣊⣡⣤⢅⠀⡀⠈⠃⢀⣠⣤⡠⢤⣰⠦⢧⢸⠪⣿⣿⡿⠟⠐⠀⠀⣄⠊⠐⠀⠇⠀⣀⠄⠁⢂⠈⢁⠂
⠤⢈⠙⣿⣿⣿⡙⢯⣬⡽⣟⢥⣠⣴⣿⣿⣷⣾⡿⣿⣿⡶⢺⠟⣏⣉⠙⡷⣉⢀⠀⠀⠈⡅⠐⡘⠒⠌⠉⠜⠁⠘⠀⠘⢀
⡆⡿⠿⠛⢿⠁⠍⢲⣽⣾⣟⣿⡟⢛⡝⠉⠉⠙⠅⣾⣿⣿⡿⣾⢿⣟⢿⣿⣟⡹⣇⠀⡀⠀⠐⠠⠤⠀⠓⠂⠂⡉⠀⡀⡁
⠃⢰⢰⡆⢸⣄⢰⣤⣏⡙⢿⠿⣇⡞⠀⠀⠀⠀⣴⣼⠋⠉⢧⣽⣄⠙⢷⣿⣻⠀⣾⣇⣴⣈⠁⠤⠀⢄⡁⠐⡊⠀⠺⠁⣸
⢦⣬⣿⢃⠁⠀⠈⢻⣿⠿⠈⠀⠈⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⡷⠾⣿⣾⣿⣦⢸⡿⢣⣶⣶⢦⡀⢀⡠⣾⡖⠿⣿
⠻⣿⣿⣿⠃⠱⡀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⠀⠀⢱⡈⢿⣇⡌⠈⠾⠃⡞⣻⣬⣾⡷⠼⠄⠀⠀⠀⠹
⣽⢸⣿⣿⣄⠀⠁⢴⣶⡄⠀⢢⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⢨⠅⠋⠠⠛⢻⣷⡄⡈⠦⢀⡔
⣿⣾⣽⠹⣿⣷⣦⣈⡿⣅⡞⠻⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⡤⡄⠀⠂⢠⣠⣶⣥⣦⠄⠀⠐⡄⠀⠀⢀⡤⢻⣿⣷⣿⣿⣷
⣏⡻⠋⠀⣭⣿⣭⣶⣁⣈⣁⠀⠀⠁⠀⠀⢄⣄⠀⠀⠘⠻⢇⡀⠀⠀⠀⣦⠙⢀⡴⠞⠃⠀⠀⠀⠷⢿⡿⣷⣾⢯⢻⡿⣿
⡈⠀⠀⠃⣌⢻⠿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢿⡉⢿⡆⠀⠀⠀⠀⡀⠀⠀⠋⠀⠀⠀⣴⢆⣀⣠⠀⡀⠐⠋⠘⣏⢁⣿⣥⣿
⡁⠀⠀⠀⢩⡏⠀⠐⠃⢀⣦⡀⠀⢰⣿⣧⠄⣋⡛⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣾⢱⡽⣀⠁⠀⠊⠀⠷⢼⡽⣿⡿
⣿⣦⣀⠢⢘⡇⠠⠀⣀⢾⣿⡏⢲⣿⣿⡷⢯⣽⠻⠆⠀⠀⠁⢀⠄⠀⠀⠀⠈⠁⠼⠟⠓⠛⠁⠘⠀⠀⠋⠀⠀⣼⣿⣿⠏
⠈⣙⣻⣷⠖⠒⠊⠀⠀⠀⠀⠁⢄⢀⡉⠻⣿⣿⠏⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢡⠖⠀⠀⠂⠀⠀⠐⠻⣀⠻⣿⡆
⣷⡍⠉⠉⠈⠑⠈⢁⡉⠲⠄⠛⠀⠠⡀⠀⠨⠁⠀⠐⠁⠀⠀⠀⠀⢀⡆⠈⠴⢶⣅⢾⡟⣧⢰⢸⡀⠀⠀⠀⠀⠙⠀⠿⣧
⡟⠀⠀⠀⡌⢠⠖⠁⢀⠀⢘⣉⡑⢂⠱⠰⠀⢠⠀⠀⠀⠀⠠⣷⣤⢎⠀⠹⣕⣏⡟⣿⡇⣧⣿⣿⠄⠡⠸⠃⠉
⡇⠀⠀⠞⢡⠄⠂⢀⡘⠋⢠⣀⠱⢀⠀⠁⠈⠀⠑⠀⠀⠀⠀⠈⣱⣌⠫⣙⣼⣝⣿⣿⣷⣿⡿⣫⠾⠓⠁⠿⠉
⢠⠆⠠⠀⠁⠲⢀⠋⠀⠑⢀⢤⠈⡀⠳⢀⠃⠀⠀⠀⣤⢀⠀⢠⣟⠦⣝⣾⣿⣿⠟⣉⣤⠈⢻⣿⠗⣊⣵⣚⡀⠊⡀⢈⡀
⠐⡄⠀⠢⢀⡘⠀⠳⠠⠄⠭⠐⠚⠀⢀⠁⠐⠄⠀⢂⢠⠈⣶⣦⣬⣏⢿⢿⣿⣿⣤⣉⣀⣤⣿⣿⣷⡤⠿⢿⣿⣿⡛⣟⠤
⣦⢠⠆⢁⠀⠧⡀⠒⠓⢀⣒⣃⡰⠄⢸⠀⠠⠰⡇⣮⠻⣽⡾⣈⣇⡃⡍⡼⣫⠟⢻⣏⡹⢶⡾⣬⠷⠛⠙⠙⠛⠻⠻⣿⣾
⣇⠀⠣⡈⠦⠀⠈⡀⠈⣉⣀⡄⠁⢰⣯⠶⣜⣢⣜⠻⣷⣿⣧⣿⣿⣿⣾⣷⢃⣴⣯⠽⡀⢺⡁⠁⠀⠀⠀⠀⠀⢠⣄⠂⠹
⠛⠃⠀⢁⠀⣤⣤⠀⠠⣀⡁⢀⡄⣈⠉⢻⣿⣿⣿⣧⡽⠟⠛⠛⠻⣿⣟⣿⣿⣻⣷⢎⡁⢀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌
⣳⡄⠀⢸⣦⣀⣀⣡⠠⢄⡈⠠⢃⠤⠒⣴⣴⣭⣽⣿⠀⠲⠞⠃⣰⣿⡿⠿⢟⣿⣿⣿⣡⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢈⡩
⠩⠃⠀⣸⣿⣿⡿⠏⢀⠀⣶⣶⣶⣦⣍⠉⣤⡾⠟⡿⣷⣶⡴⢺⡏⢳⣄⡙⣿⣶⣿⣿⣏⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣙
⠚⠖⡴⠁⠁⢩⡆⠈⣻⣛⣽⣄⠻⣯⣴⣞⣵⣞⣩⢼⣿⡋⡶⣿⣌⡿⠑⢟⣿⣿⣟⢻⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⣠⡞⢳⡾⣤⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣴⣾⠿⠛⠛⠻⣿⣶⡀
⠀⠀⠀⠀⣼⣙⣿⣿⡋⣻⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡻⠭⢭⣛⣛⣛⣛⣛⣛⣫⣭⢷⣿⡟⠁⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⣼⣏⣿⣧⣼⡟⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠚⠿⠁⠒⠒⠒⠒⠒⠒⠊⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⣿⣹⠷⣾⣛⣿⣟⡭⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠘⠻⠷⠟⠋⠀⠳⣄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠈⡇⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢸⠀⠀⠸⣦⣀⠀⠀⠀⠀⣠⡶⠋⡇⠀⠀⢷⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⢿⣦⡀⠀⠀⡼⠀⠀⠰⡜⠮⣑⢆⠀⣜⡟⠀⢠⠃⠀⠀⢸⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠉⠪⡷⣄⡇⠀⠀⠀⠙⢦⣈⠻⣾⡟⣀⠴⠃⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠙⢻⡏⠁⠀⠀⠀⠀⠀⠀⢿⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡟⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡣⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣣⢏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⣤⣤⣤⣀⣀⣠⣤⣤⡤⠤⠶⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⢃⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⣶⣻⣿⠀⠀⠀⣠⣀⡙⣾⡀⠋⠀⠀⠀⠀⠀⠀⠞⠋⣉⣽⣤⣠⣤⡄⠀⢠⣶⣿⠟⠇⣄⣾⣷⣄⣀
⠀⠀⠀⠀⢀⡀⣀⣈⠻⠋⡟⠛⠀⠀⣲⣿⣿⢿⣷⣿⡿⠂⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣀⡿⣭⣷⣿⡗⠀⠁⠀⢀⣤⣿⣿⣿⣿⣿⣧⣿⣿⠂⠀⠀⠀⠀⣴⣷⣿⡟⣿⣿⣿⣿⣿⡟⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⢘⣿⣿⣿⣿⣿⣿⠂⡀⠀⢣⣿⣿⣇⠘⠿⡾⢿⣿⣿⠇⠀⠀⠀⠀⠛⢿⠟⠛⡷⠋⢻⣿⡆⠀⠀⢘⠗⢻⡿⣿⠛⠿⢿⡿⡟
⠀⠀⠸⣽⣿⢺⠚⠛⣫⣤⣦⡀⠀⠀⠿⠂⡆⡾⣿⡟⠉⠁⠀⠀⠀⠀⠀⢰⢶⣶⡄⡇⠀⠈⠛⠁⠀⠀⢀⠀⠀⠀⡏
⠀⠀⠀⠈⠁⢸⠀⠀⠘⢙⢻⡇⠀⠀⠀⠀⡇⠣⠾⠧⢠⣴⣶⣶⣷⣦⡄⠰⠸⢿⠀⣧⣀⠀⠀⠀⠀⡛⣿⣿⠆⠀⡃
⠀⠀⠀⠀⠀⢸⠀⠀⠘⠺⠿⠷⣶⣷⣶⣴⣧⣀⡀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⣷⣶⣶⣶⡄⠀⣦⣿⣿⣀⣀⣇⣀⣀
⠀⠀⠀⢀⣀⣼⣄⣠⣀⣀⣀⣀⡙⠻⢿⣿⣿⣿⣿⡷⠶⢿⣿⣿⣿⡿⢱⣶⣿⣿⣿⣿⣽⡻⠕⠁⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢜⡸⢿⡿⡿⠿⠶⢿⢿⣦⣾⣿⣿⣶⣾⣿⣿⣿⣻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⢹⡿⣿⣿⣿⣽⣿⣿⠿⠿⣿⣟⣿⣿⣿⣮⣷⣤⣴⣎⣶⣎⣭⣤⣪⣾⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⡿⣿⣿⣿⡟
⠀⠀⠀⠸⣿⣿⣿⣇⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣭⣉⠓⠛⢿⡏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⢺⣿⣿⣿⣿⣾⣽⣿⡿⣿⣿⣿⣿⣿⡏⣹⣿⣿⡗⣿⣿⣿⣇⠀⠈⠃⠛⠛⠛⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣇⣼⣿⣿⡗⠾⠿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠿⠛⠛⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉