Angel dog Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠻⣦⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣏⠁⠈⡉⣋⡍⠉⠙⣳⣶⣦⣄⡙⣇⡡⠐⠄⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠐⠦⣰⡵⠶⠒⠐⢾⣿⣿⣿⣿⡷⡷⢆⡴⣓⣚⣷⡿⣿⣟⣛⡿⢷⣏⣽⡋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢁⣀⡐⢀⠙⠃⠀⠀⠄⡈⣿⣿⣿⣿⣿⣷⢡⣾⣟⣿⢯⡭⠿⣭⣽⣛⡿⢍⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠋⢩⣿⣶⣷⣤⣿⣿⣷⣤⣴⣭⣭⡸⣿⣿⣿⡿⣿⢲⣷⠻⣮⢿⣽⣿⣿⣿⣟⣛⣿⢋⡛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠁⢻⣿⣿⣿⣿⣽⢾⡛⣽⣳⣹⣿⢿⣳⣿⣷⣬⣍⣽⣈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⢋⡏⡟⡅⡻⣯⣽⡶⣯⣷⡟⠖⠋⠁⠉⠉⠁⠀⡮⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⣿⣿⣿⣿⣿⡿⠃⠈⠋⡼⠠⠇⠉⠓⠛⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣬⠍⠉⠉⠉⠀⢸⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⢆⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡗⠂⡴⠖⢠⠖⠾⠀⠀⠀⢀⢀⡇⠀⠀⠀⠀⠀⠀⢼⣃⡄⠦⠀⠀⠀⠀⠀⠸⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣤⡘⠠⣆⢀⡀⠀⠀⠘⠺⡿⠁⠀⠀⠀⠀⠀⠈⠶⣿⣿⣄⡀⢠⡀⠀⠀⠀⠉⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⡿⣶⣽⡬⠉⠀⠀⠠⢁⣷⠦⢀⢀⣀⡀⣠⣶⣷⣾⣿⣿⣵⣮⣌⠀⢀⡀⠀⢠⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⣿⣾⣿⣿⣷⣿⣿⣿⠿⢾⣿⣿⣿⣿⣟⣦⣤⡩⡤⠀⠠⣙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⣏⡄⠀⢸⡴⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠹⣿⣿⣿⣿⡟⠳⣿⡀⡀⠀⢹⢻
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⠁⠀⠈⢻⡄⠀⣰⣾
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢛⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⢀⣠⡼⠃⠀⣳⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠛⠚⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⣯⣦⣤⡤⠞⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡔⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢂⣀⢠⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⡿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡙⢄⠐⢄⠸⣿⣿⡟⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⠾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢌⠂⠑⠀⠁⢹⣿⣇⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⢈⣿⠀⢠⠄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠏⠀⡀⢈⣿⣷⣿⣿⣧⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣴⣿⣿⠁⠄⡉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣀⣤⡇⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⣴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⣂⣼⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⡿⠃⢹⣿⣿⣿⣿⡁⠠⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣇⢉⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⠀⠀⠈⢿⣿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠰⠀⣠⣴⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⠟⠁⠀⠙⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠻⣍⣀⠈⠉⠉⠙⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄
⠀⠻⣄⡀⠈⠉⠓⠦⣄⡀⠀⣀⣀⠀⠉⠉⢓⣒⡲⠶⠶⠞⠛⠀⣤⠦⡀⠀⠀⠠⣔⡳⡆⠀⢀⣤⠖⠋⠉⠀⢀⡼⠃
⠀⢀⠌⠙⠲⢤⡀⠀⠈⠙⢿⡁⠹⣷⠀⣴⠋⠙⣿⡆⠀⠀⠀⠀⠳⠷⠇⠀⠀⠀⠛⠋⣡⠞⠉⠀⠀⣀⠤⠞⠋⢄
⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠹⡄⣿⣿⠃⠀⠀⣿⣿⠀⣰⡏⠙⡆⠀⣴⡖⢆⣤⡄⡼⠁⠀⠀⠀⠀⠀⠀⣀⡤⠋
⠀⠀⠀⡄⠉⠉⠀⠀⠀⠀⠀⠀⡇⣿⡏⠀⠀⠀⣿⡟⣰⣿⣧⣀⣇⣼⣿⢀⣿⣿⠃⡇⠀⠀⠀⠀⠀⠈⠉⠁⡄
⠀⠀⠀⠙⠲⠦⠴⠒⠀⠀⣀⡼⠀⣿⠃⠀⠀⣰⣿⠛⠹⣿⡀⣸⠃⠘⣿⡼⢸⣿⠀⠸⣄⡀⠀⠐⠢⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠿⣠⠖⣻⡿⠃⠀⠀⠉⠛⠁⣠⢤⡀⠀⢸⣿⠀⠀⠈⠉⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⠾⠋⠀⢰⢞⣢⠄⡤⡾⠓⠲⣿⣄⣼⣿⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡲⣆⣀⡈⠛⠋⠸⡅⢳⠀⣰⠏⢠⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠵⠒⠂⠭⣝⢛⡷⠈⡉⠫⣥⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⣮⣝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⡚⠉⠙⠋⠙⠒⢦⣤⣄⢻⣘⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⠐⢰⠀⠀⠀⢾⣿⣿⣷⣾⡢⣾⣥⣿⢿⣿⣿⣿⣯⣿⡁
⠀⠀⠀⠀⠀⠰⠿⣿⢀⣀⢠⣤⣄⠀⢀⡈⢿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣷⡮⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠾⢻⣿⣿⣿⠙⢿⡛⠸⣿⣿⣾⣾⣽⣾⣾⣿⣿⣿⣿⣉⣂⣆⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠹⡀⢐⣩⣿⠃⠀⠈⡁⢠⢃⢩⠠⣽⣯⣷⡿⠿⠛⠁⠀⠉⠁⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠓⠐⠿⠓⠚⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢧⡠⠀⢠⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠑⣦⡀⢇⠀⠀⠀⠀⡅⠀⠀⠀⡀⢀⣀⡿⠗⣄⡀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣠⠞⠁⠉⠹⡀⠀⠀⢸⠓⠒⠒⠚⠋⠉⠈⢻⡇⠀⢹⡶⢤⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠈⠓⠓⠒⠉⠀⠀⠀⠀⢀⡇⠀⠀⡞⠀⠀⠀⠀⠀⠀⡠⠴⠃⠀⡿⠀⠀⢹⡀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣄⣤⠼⠁⠀⠀⠀⠀⠀⠘⠷⠒⠒⠚⠁⠀⣶⡋⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⡄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⡐⠀⢀
⠀⠀⠀⠀⠠⡈⠀⠈⠢⡀⠀⠀⠀⠀⠀⣀⠠⠠⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠠⠊⠀⢀⠔
⠀⠀⠀⠀⠠⠉⠂⠄⠀⠉⠂⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣄⠘⣷⡠⠀⠀⢀⠂⢀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠐⢆⡰⠁⠀⠀⠀⡇⠀⠀⢾⣿⡇⡠⠤⠄⠿⣿⠃⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡜⡀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠋⠀⠰⣿⡗⠈⢢⠻⡀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠛⠠⠀⠀⠀⠀⢰⣁⠀⠀⠀⠀⢰⠀⠀⠀⢂⠀⠀⢀⡈⠀⠀⢸⠇⢁⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⠎⠑⠤⢀⣀⠀⠀⠀⠀⣀⠠⢆⠀⡌⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠀⡀⠀⠀⠑⠊⡱⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣺⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢄⠉⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠊⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⡏
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡄⠀⠀⢣⡀⠀⠀⠀⠀⢸⠀⠰⠊⠀⢡
⠀⠀⠀⠀⠀⠀⢔⡸⠂⠀⠀⠀⠀⢠⠧⠤⢀⡀⢣⠀⠀⠀⠀⠀⢾⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠂⠀⢀⠜⠉⢟⢆⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⠉⠑⢒⠣⢀⣀⡠⠛⢢⠀⠀⠀⠀⠁⠓⠄⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡠⠖⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⠤⠤⠤⠤⠶⣦⣤⣄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠠⣿⡛⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢩⣾⣿⣷⣜⠛⠛⣱⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠛⢛⣿
⠀⠙⣿⣦⣀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⣀⣴⣿⠋
⠀⢸⡁⠀⠉⠛⠲⠦⠄⠀⠈⢻⣦⣀⠀⠙⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⠏⣀⣤⣴⡟⠁⠀⠠⠴⠖⠛⠉⠀⢈⡇
⠀⠀⠛⡶⣤⣀⣀⠀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠉⣉⣤⣤⣤⣄⡈⠉⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⣀⣀⣤⢶⠛
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⣠⣾⣿⠿⣿⣿⠿⢿⣶⡀⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠈⠛⠶⢶⠚⠉⠀⣀⣤⠟⠛⠉⢰⣿⣿⡇⠀⠈⠃⠀⢠⣿⣿⡄⠉⠉⠳⣤⣀⠀⠙⠓⡶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⢀⣿⣿⣿⣿⣦⣀⢀⣴⣿⣿⣿⣿⡄⠀⠀⠈⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢸⣧⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣷⣄⢿⣧⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⢿⣦⡻⣧⡹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣌⡻⢷⣝⣷⣝⢿⣌⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⡿⣷⣝⡻⣎⢥⡉⢧⣭⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⢿⣾⣽⣻⠷⣬⠻⢦⡍⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢷⣾⣭⣟⡻⠶⡜⢿⣶⣦⣤⣝⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠶⠖⢒⣊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣶⣯⣭⣝⣃⠳⣶⣽⣻⢾⣯⠗⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣷⣤⣤⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡶⢶⣭⣭⣟⣓⡈⠻⠏⠝⠀⢶⣶⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡛⠿⠿⢶⣶⣯⣭⡱⣦⠻⣿⣷⣶⣈⠙⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣟⣓⣲⣶⠶⠦⠴⠈⣥⣤⣭⠟⠋⢴⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣭⣭⣭⣭⣭⣭⣥⢀⣭⣝⠊⢴⣶⣾⡤⢍⣉⣇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠙⠻⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣛⣛⣛⣛⣯⡤⣙⡛⢁⣴⣶⢖⣢⣈⡉⢛⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣆⠺⠿⠿⣛⣛⣯⡭⣗⣧⢛⡛⠉⣩⣭⠉⠸⢟⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠠⣿⣿⡿⢿⣻⡽⣞⡭⣢⠘⠿⢟⡛⡁⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣶⡆⣾⣿⠿⢛⣵⣾⡿⢋⣞⡾⣱⢣⡎⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠸⠿⣋⢰⣿⠟⣰⡷⢋⡀⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣌⣡⣶⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠈⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⣶⡟⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⢰⢫⠾⣹⣏⢀⡴⢩⣮⡀
⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣶⣦⢤⣀⡀⠀⠀⣀⣀⣴⣿⡿⠟⠁⠀⠀⠀⣟⡰⢋⡾⠟⣵⣊⣴⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞
⠙⢽⣮⣉⡛⠿⡦⡀⠀⠀⠻⣄⣲⣾⣭⣿⣿⣽⣿⣿⣆⣤⣶⣶⣿⣿⣿⣿⣿⠏⢰⢘⡓⠶⣶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⠏
⠀⠀⠈⠙⠛⠻⠯⠟⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⣿⣿⡟⠛⠛⠛⠛⢉⢇⡿⠘⢠⡟⠓⢶⡏⠀⠀⠀⠀⠀⠀⢀⣴⣯⡼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠦⠴⢾⠾⣧⣤⣾⣿⣿⣋⣀⣀⣀⣀⣀⣀⣴⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⡉⠉⠀⢀⣴⠀⠀⠀⢀⣥⡤⠤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡴⠚⠋⡠⣿⣿⡿⣦⣾⣾⠃⠀⠀⢴⣾⣿⣧⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣆⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠛⣷⣾⠿⠛⠉⠀⠀⡽⠁⠀⢤⣧⣿⣿⣿⣶⣶⣶⣶⣦⣬⣍⡙⣐⢒⣀⣀⢤⣀⣹⠛⠛⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡤⠊⣀⠀⣮⣿⠿⣿⣯⣟⣿⣶⡮⠭⠉⠉⠛⠛⠛⠛⠛⠛⠛⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⡿⣾⣾⣾⡟⠁⠀⠀⠉⠛⠷⣾⣿⣿⣏⣁⣠⣀⣀⣀⢀⣀⠀⢨⡿⠶⣾⣷⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣃⣀⣙⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣙⣛⣋⣀⣀⣀⣈⣁
⣿⣿⣫⣛⣭⣛⣻⣫⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣀⣀⣤⡿⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣈⣉⣉⣁⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⣏⠳⣄⠀⢀⣠⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⠞⣹⠃
⠀⠀⠀⠀⠀⠙⢆⠈⠓⢼⡇⠹⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⠏⢸⡧⠞⠁⣰⠋
⠀⠀⠀⠀⠀⢻⡛⠷⣄⡈⢇⠀⠈⠳⢄⣀⠀⢻⣿⢻⣿⣿⣿⣿⣿⣿⡟⣿⡟⠀⢀⡠⠖⠁⠀⡸⢁⣠⠾⢛⡟
⠀⠀⠀⠀⠀⠀⣙⣦⣀⠹⡟⠷⠤⠀⠀⠉⠙⠢⡉⠀⣻⣿⣿⣿⣿⣟⠀⢉⡔⠋⠁⠀⠀⠤⠾⢻⠏⣀⣴⣋
⠀⠀⠀⠀⠀⠀⠻⣌⠉⠙⢻⠶⠤⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠤⠶⡟⠋⠉⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢦⡷⠤⠤⠄⢀⡠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢄⡀⠠⠤⠤⢾⡴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⢲⡫⠍⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠩⢝⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣄⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣀⣀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠦⣤⣤⢠⡄⢠⡄⢤⣴⠦⠀⢠⡄⣠⢠⣤⣤⣤⣤⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣀⠀⢻⣾⠀⠀⣿⠀⠀⢸⣥⣿⢸⣄⡀⣇⣴⠇⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⣤⠠⠟⠹⡆⠀⠿⠀⠀⢸⠀⠿⢸⣥⡄⠏⢹⡄⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⣿⣿⡿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉


⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠻⣦⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠋⠁⠀⠈⠋⠈⠉⠙⢳⣶⣤⣄⡙⣆⡁⠀⠔⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠄⢰⡄⠄⠀⠀⢼⢿⣿⣿⣷⡶⡧⢆⡴⣓⣒⣶⠿⣿⣿⣛⡿⢿⣟⡽⡋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢁⡀⠀⠀⠘⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣷⢡⣾⣿⣿⢯⣭⣿⣯⣽⣛⣻⢍⡫⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢩⡇⣴⣦⣤⣾⣷⣦⣤⡀⣡⣥⡈⣿⣿⣿⡿⣿⢬⣷⠻⣭⢿⣟⣟⣿⣿⣿⣻⣿⠛⠛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠶⠋⣿⣿⣿⣿⡦⡙⢎⣛⠁⢻⣿⣿⣷⣿⣸⢿⡓⣽⢷⣻⡿⢿⣳⣿⡣⠌⢉⣽⡈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠁⠜⣹⣯⠣⠑⠀⠈⠉⠀⣠⠃⡏⡅⣏⣻⣮⣽⡦⣯⣷⡿⠾⠉⠀⠉⠉⠁⠀⠈⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡴⢾⣛⠑⢶⣤⣀⣠⠆⠀⠁⠸⠀⠃⠈⠓⠛⠘⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂⢈⠉⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠹⣌⠀⠠⠙⡀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠈⡳⣦⣀⣣⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢐⣄⣀⣤⣴⢟⡉⠱⢦⣀⠀⠀⠁⠀⠀⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⢀⣠⠞⠁⠀⠉⢹⡄⠀⠀⠀⠀⡟⠛⠛⠛⠛⠉⠉⠁⠀⠈⢳⡇⡀⠀⠈⡟⢦⣄⠀⠀⠀⢱⢻
⠀⠀⠀⠀⠀⠀⠀⠘⢻⠴⠤⠤⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣾⠃⠀⠈⢳⡀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠓⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣞⡩⠉⠀⢀⣴⠃⠀⠀⣀⣼⠇⠀⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡷⠯⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠀⠀⠀⠸⣏⣄⣀⣀⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⢿⠿⡿⡿⠟⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣛⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠛⠓⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣄⣀⣀⣤⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡉⠉⠉⣡⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⣼⣿⣿⣷⡄
⠀⠀⠀⣟⢦⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⠁⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⢞⡇
⠀⠀⠀⠹⣄⠉⠲⣼⡏⢳⡀⠀⠀⠀⠀⢰⣿⣿⣆⠉⠛⢉⣠⣤⣤⣈⠙⠋⢀⣾⣿⣷⠀⠀⠀⠀⠀⣰⠋⣿⡴⠋⢁⡾⠁
⠀⠀⠀⢺⡾⢷⣄⠈⣇⠀⠙⢦⣀⠀⠀⢻⣿⣿⡏⠀⣴⣿⣿⣿⣿⣿⣷⡄⠈⣿⣿⣿⠃⠀⢀⣠⠞⠁⢀⡏⢀⣴⠿⣿⠂
⠀⠀⠀⠀⣓⣄⡈⠙⡾⢦⣀⠀⠈⠙⠒⢤⠙⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠉⢡⠔⠚⠉⠀⢀⣠⠾⡖⠉⣀⣔⡃
⠀⠀⠀⠀⠻⡍⠙⠓⢿⣦⣄⠀⠀⠀⠀⠀⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠃⠀⠀⠀⠀⢀⣤⣾⠗⠛⠉⡽⠃
⠀⠀⠀⠀⠀⠈⠓⠦⢬⣧⣄⣀⡄⠀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡀⠀⣄⣠⣤⣯⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⢲⣛⠟⠁⠀⠀⠀⠈⠙⠻⠿⠛⠛⠛⠻⠿⠛⠉⠀⠀⠀⠀⠙⢟⣳⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣞⣚⡩⠭⢓⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠂⠁⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⡘⠄⠠⠀⠢⠔⡲⠄⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢄⠀⡀⠠⠀⢠⠁⠀⠠⢀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠾⠻⢓⣲⡄⠠⡀⠠⡄⠀⠀⢢⡀⢀⢄⠀⢸⢃⠀⠈⢁⠀⠀⠀⡀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠥⢀⠀⠈⢂⠀⡈⠈⠁⠀⠉⠃⠀⠒⠁⠔⠀⢂⣀⠈⠐⠠⡀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠀⠀⠀⠸⡀⠀⠀⠀⠲⠀⠈⠐⠀⠂⠄⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⢀⠀⠀⢀⠀⠀⠀⠄⠀⠓⠀⢸⠀⠀⠀⠀⠀⠀⠀⣱⠄⠒⠂⠈⠆⠀⠇⠀⠀⠀⡌⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⣫⠕⠁⠀⠀⠀⠀⠊⠀⠸⠀⠀⢰⠂⣼⠀⠀⠀⠁⠒⠊⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡡⢀⠂⠀⠀⡀⠀⡌⠀⠀⢀⠀⠀⡅⠀⠙⠠⠄⡒⢒⣴⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠄⠀⠢⢀⠑⢄⠓⠄⠂⠜⠑⠤⡇⢈⢀⠆⡈⠁⠁⠀⠀⠌⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⡀⠀⢤⠈⡄⠾⢀⠀⠀⠀⠀⢀⠇⠸⠁⠀⠃⠀⠀⠀⠀⠀⠠⠈⠸⠀⠀⢁⠀⡄⠀⠀⠐⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡖⠁⠀⣕⠀⠌⢂⠀⠀⠀⠄⠈⠀⠰⠄⠘⡄⠀⠀⣴⠑⠂⠀⠀⠀⠀⢘⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠛⢤⠄⠐⠠⠔⠀⠂⠐⠀⢀⠞⠀⠈⠊⠄⠀⠚⠓⠃⠀⠀⠀⠀⠳⠀⡜⠢⠀⠀⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⡯⠴⡃⠀⠀⠀⡷⢄⡥⠀⠀⠎⠈⡀⠈⠀⠀⠀⠀⣁⠀⠀⢀⢀⠀⠀⠀⠀⢠⠀⣇⠀⢀⠀⠀⠀⠀⠀⠙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠍⠲⠔⠸⡁⠀⠑⠡⠊⠇⠀⠈⠳⠈⠂⠀⠀⠈⠄⠒⢎⠁⠀⠀⠀⠀⢨⠀⢠⠁⠀⠀⠀⠀⠀⢄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠃⠊⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠤⠴⠞⠋
⠀⠀⠀⠀⢠⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣶⣶⣶⣶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄
⠀⠀⠀⠀⠈⢧⡈⠲⣴⡟⢦⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡴⢻⣦⠖⢁⡼⠁
⠀⠀⠀⠀⠀⢿⠳⢤⡈⢇⠀⠓⢤⣀⠈⢿⡿⣿⣿⣿⣿⣿⣿⢿⡿⠁⣀⡤⠚⠀⡸⢁⡤⠞⡿
⠀⠀⠀⠀⠀⢨⡷⣄⡉⣟⠲⠄⠀⠈⠉⠢⠁⣸⣿⣿⣿⣿⣇⠈⠔⠉⠁⠀⠠⠖⣻⢉⣠⢾⡅
⠀⠀⠀⠀⠀⠀⠳⢄⡈⠹⡓⠂⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠐⢚⠏⢁⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣯⡽⠤⠆⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⠤⣯⣍⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⣤⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠄⠀⠀⠀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢠⠇⢀⠴⠊⠁⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⢀⡔⠻⠆⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠀⠛⠄⠀⠀⠀⠀⡰⠋⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠹⠁⠀⠀⠀⠀⠀⠀⠀⠘⢳⡤⠿⠒⠒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡠⠖⠀⢹⡄⡀⠀⠀⠀⢀⡴⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⢤⡤⠝⠃⠀⡔⠉⠀⢴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⠁⠀⠀⠀⠛⠒⠖⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣤⣄⠀⠀⠀⢸⡦⠀⠐⠁⠀⠀⢀⣀⣠⠤⠖⠋⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠈⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⣳⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢄⡀⠀⠞⠃⠸⢃⡼⢧⡉⢙⣋⠿⠶⠦⢤⡈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡠⠞⠉⠘⠗⠀⠂⢽⣋⠀⢹⣾⣄⣀⣀⡀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠲⢄⣸⢠⣤⡏⣒⡡⠴⢚⣁⠴⠋⠀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⡠⠀⠀⢀⡟⣃⡴⣟⠭⠓⠛⠉⠀⠀⣠⢾⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣔⠉⣠⠄⣀⡇⣴⢲⣏⡽⠋⠁⠀⠀⠀⠀⠀⢠⡞⠀⡌⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠉⠹⣧⣤⠏⠻⠷⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠇⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⡠⢎⡠⠖⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠉⠙⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠘⡁⡎⠀⢰⢦⡾⠉⢆⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣄⣀⣀
⠀⠀⠀⠀⠐⠓⠒⠁⠀⠀⠀⢸⠙⢶⠒⡶⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣠⠖⠉⠀⢀⣀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠁⠀⣠⠊⠁⠀⠙⢦⠀⡇
⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠛⠛⠦⣄⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⢀⡞⣠⠇
⠀⠀⠀⠠⠚⠓⠒⠒⠊⠀⠀⠀⠀⣀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢢⡀⠀⠘⠓⠊⠁
⠀⠀⠀⠙⢱⡦⠠⠴⠛⣠⠴⠖⠋⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠈⠉⣶⣖⣀⠛⠓⠠⠤⢄⣀⣀⣈⣷⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣴⠒⡄⢸⡉⠢⣄⠀⠀⠈⢦
⠀⠀⠀⢀⡰⠋⠁⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠑⢾⠀⠀⠈⠳⡀⠀⠈⢧
⠀⠀⠀⠈⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠙⢯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠾⢅⡀⠀⢸⠀⠀⠀⠀⣠⣀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⡒⠘⠃⠉⠉⡎⣻⠀⠀⠀⠀⠙⡦⣸⠀⠀⠀⣴⠁⠘⣆⣨⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⠁⣿⠀⠀⠀⠀⠀⠃⢹⠀⠀⢠⡟⡷⣄⡘⠃⠀⢀⣠⠴⠚⠁⠀⠀⠀⢀⡞⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡇⠀⢨⡄⠀⠀⠀⠀⠘⠶⠀⠀⢰⣀⠘⢤⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠎⠁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⡇⠀⠀⢱⡀⠀⠀⠀⠀⡇⠀⠀⣾⠈⠘⠛⠙⠛⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⣃⠀⠀⠀⠳⡄⠀⠀⠀⡇⠀⢀⠉⠒⠢⠤⣤⣀⣀⣀⣀⡀⡠⠔⠋⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢨⠀⠀⠀⠀⠘⠢⣄⠀⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡼⠀⠀⠀⠀⠀⠀⠈⠙⡇⢀⠷⠤⣄⣀⡀⣀⣀⢀⣀⣠⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠠⡿⠋⠀⠀⠀⠀⠀⠈⠉⠁⣄⣀⡠⣄⢠⣄⡀⢀⢀⡀⣠⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠘⠃⠈⠁⠁⠈⠙⠀⠙⠁⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣠⠦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡻⡄⠘⠊⢣⡀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣶⡿⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢱⠶⡇⡀⠀⣸⡤⠤⣤⣶⣶⣿⠿⠿⢛⡶⠿⣭⣔⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⡶⢂⢾⢗⣶⣴⣿⠷⠲⣟⡻⠻⣯⠶⢿⡩⢉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠉⠉⠉⣉⠲⢤⡀⠀⠀⠀⡇⠿⣷⡇⣾⣿⣟⣽⣟⣲⣟⣛⣻⣿⣷⣾⣭⣾⣏⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠂⠀⢀⠀⣿⣷⣄⠙⣆⠀⢀⢇⠻⡸⡇⣽⣥⠽⣦⡽⢯⣭⣿⠭⣶⡿⣭⣤⠕⠋⠀⠀⠀⣿⣿⣷⣀
⠀⠀⠀⠀⠀⢠⣶⣟⠉⠉⢀⠀⣶⡄⠀⡸⢠⣿⣿⣿⡄⠙⢷⣾⡘⢦⣸⣧⢺⡏⡷⢜⢳⣶⡛⣯⡿⣿⣑⣾⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣸⠙⠋⠀⠀⠈⠇⠀⢀⣼⠁⣼⣿⣿⣿⣷⠀⠈⢿⣿⣿⣿⡿⣾⣋⡷⣼⡛⣶⢿⣙⣿⣬⣏⣁⣀⣀⣀⣀⣠⣾⣿⣿⠛⣹⠇
⠀⠀⠀⠀⠀⢸⣦⡀⠀⢀⣠⡤⢠⠟⠁⣸⣿⣿⣿⣿⣿⣧⠀⠸⢿⣿⣿⣇⡌⡹⣧⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣥⠞⠁
⠀⠀⠀⠀⠀⢾⣯⡿⣍⣙⣉⣤⣞⡄⢐⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⠻⣿⣷⣿⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠐⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣦⣾⣿⣿⣿⡿⠋⢠⡖⠀⠀⠀⠀⠀⠈⠋⠛⠛⠛⠋⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠀⠀⠀⠀⢀⠀⢀⢀⣴⡶⠂⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⡀⣠⣥⣤⣾⣗⣻⣁⢀⣰⡐⢂⠀⠈⠐⣌⢳⣷⣦⣀⣀⣠⣀⠀⢀⣀⡀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡀⠀⣠⠛⢻⠅⠀⠀⠀⢻⠏⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠙⢿⡍⠉⠉⠛⠷⡾⠛⠛⢧⡐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣞⣴⠞⠁⠀⢸⡇⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⣽⡇⠀⠀⠀⢻⡄⠀⢀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡼⠁⠀⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢰⡟⠁⠀⠀⠀⠀⠹⣶⣈⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⣠⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⡋⠀⡠⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠧⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢾⣧⣼⡷⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣀⠁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠢⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠉⠉⠁⠹⠖⠂⢤⡀⠀⠀⠀⠀⠀⠀⠠⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⢦⣀⡤⠞⠉⠱⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠰⡎⢀⡠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠖⠳⠎⠀⢠⠈⠑⠲⠦⢤⣤⡤⢀⠀⢤⡤⢤⡄⠀⠐⣠⡿⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠐⣇⡠⡏⠀⠀⢸⠃⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡜⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣤⣤⡤⠾⣴⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⠁⠀⢀⡜⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢧⡀⠀⠒⠒⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠉⢰
⡀⠀⠀⣠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡐⠰⠆
⠀⠀⢠⡼⠆⠀⠀⡀⠀⠀⠀⢀⡀⠂⠀⠠⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠄⢠⡇⠀⠀⠈⠉⠀⠀⢀
⠈⠁⢠⡜⡀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠲⠲⢤⣌⣉⠒⠠⣄⣀⡙⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⣀⠠⠤⠒⣊⣤⠖⠁⠙⢦⣀⠀⠀⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⣌⣉⠓⠚⠛⡿⠛⠛⠛⣿⠟⠛⠛⠉⢀⣀⣀⣀⠠⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠈⠁⠘⠧⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠀⠈⠙⠉⠁⠴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠒⠒⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⢀⣀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠏⠀⢰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠲⠶⠶⠶⠺⠟⠋⠁⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢀⡁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⢨
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠲⣄⠀⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡀⠀⢨⡛⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⢄⠀⣧⡉⣷⣾⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠀⠘⢳⡆⠀⣤⣿⡇⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢆⢸⣸⣧⡰⡶⣏⣳⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⣄⣦⢀⡈⢦⣀⣨⣯⣿⣯⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣻⡄⡤⣀⣻⢿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣤⡟⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢈⣷⣠⣿⣴⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣀⠀⣤⣦⣤⣠⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⢦⡈⡷⡄⣾⡰⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠙⡷⣧⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢤⡴⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣛⢦⣠⣾⣮⣭⣭⣚⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⡾⠛⣹⡟⣿⠙⡟⢟⠻⢿⣶⣦⣍⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠴⠊⠀⢀⡠⣄⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⣿⣏⣠⠞⢁⢣⠃⡧⠇⡈⠇⢀⣿⠻⣷⣍⠺⣾⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢯⡀⠀⠋⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⢾⡟⣿⡞⢏⡡⠞⠻⠽⠀⠈⠳⠃⠈⠋⣄⠈⠻⣳⣜⢷⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡏⣾⢡⣹⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠙⣿⠻⣧⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⢠⡏⢸⡇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠁⠀⡴⣂⠀⢹⡀⢻⡄⡇⠀⠀⠀⠀⠀⠀⡴⠉⠙⣦⠤⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⢨⠱⣾⠇⢠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⢸⡇⢸⢷⢸⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢸⠀⣿⡀⠸⣌⡸⠀⠀⠀⢄⠀⠀⠀⢀⡆⠀⠀⠀⣠⡇⢠⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠘⣠⡿⡏⠲⣀⠀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⣠⠞⠁⡇⢸⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⣦⣿⠁⡇⠀⠀⠉⠒⠤⣤⣀⣀⣀⢠⡤⠲⣿⡁⠀⠀⠘⠮⣷⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡏⠀⠀⠀⢀⠴⠊⣿⠀⢀⡠⠴⠳⣄⣷⠙⠦⣀⠀⠀⠈⡶⢻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⣿⡀⠀⠈⠳⠦⣼⣿⡦⠋⠀⠀⠀⠀⢹⡏⠓⠚⠉⠀⠀⡇⢀⠱⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⡇⡇⠀⠀⠀⢀⠇⡇⢥⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⡦⠈⢆⡃⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⣵⠃⠇⠀⠀⢀⡌⢸⠀⠸⡄⠀⠀⠀⠀⡟⢨⢣⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡜⢀⠇⠀⠀⠹⣀⣤⣄⣼⠁⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⡜⠀⠀⠀⠀⡟⠟⠻⠿⠆⢸⡀⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡄⢰⢠⣏⠟⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠰⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠆⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⠶⡄⣄⠇⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠖⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠚⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⣠⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠈⠤⠵⠮⢤⣶⠦⢤⣀⠀⠀⠀⠀⣀⣀⣀⣀⠾⠤⣀⣁⣠⡇⠀⠀⠀⠀⠀⠀⣀⣧⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠈⠉⠉⠉⠉⠀⠈⠙⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠼⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⢶⣎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⣸⠟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠉⠁⠀⠈⣿⠹⣆⡀⠀⠀⠀⣀⣀⣤⠞⠋⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⡞⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⠙⢦⣤⣄⣠⣤⡴⠶⠋⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⠂⠀⠀⠀⢸⣷⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡆⠀⠀⠀⠀⠀⠀⠠⣄⣀⡤⠶⠚⠛⠛⠋⠙⠛⠛⠻⠦⣤⣀⠀⣼⠋⢀⣠⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢠⣀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠻⣧⡀⠀⠈⢉⡴
⠀⠀⠀⠀⠀⠀⠀⣶⡄⠸⣿⡄⠀⠙⣦⠞⠁⣀⣠⣤⣤⣴⠆⠀⠀⠀⠀⠀⠉⠻⣟⠲⠄⠀⠈⠻⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠙⠁⠀⣴⣧⠶⠛⣩⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠸⣇
⠀⠀⢀⣠⡤⠶⠦⣤⡀⠉⠛⠶⣼⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡤⠤⠦⣤⣀
⠀⢠⡟⠁⠀⠀⣀⣀⣽⣦⣄⣀⡟⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣀⡀⠀⠀⠙⢷
⠀⣿⠀⣠⡴⠚⠉⠉⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠙⠳⢦⡀⢸
⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⢀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠙⢿
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⢦⣄⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠶⣤⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡼⢷⡄⠀⠈⠛⢯⣙⠛⠛⠛⠉⢉⣥⠞⠉⠀⠀⣼⠃⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⣴⠏⠀⠀⢻⡄⠀⠀⠀⠙⠷⣄⣀⡴⠋⠁⠀⠀⢀⡾⠉⢳⡄⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡾⠃⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⡼⢿⡄⠀⠀⠀⢀⡾⠁⠀⠀⢻⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⣿⣁⣀⣽⣦⡀⢠⡞⠁⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠁⠈⠉⠉⠀⠈⠳⠟⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢀⣀⣀⣠⣤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⣴⠞⠋⠉⠉⠀⠀⢀⣠⢴⡏⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⣷
⠻⣤⣀⣀⠀⠀⣰⠟⠁⢰⡇⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⢾⣏⣠⡴⠋
⠀⠀⠉⠉⠙⠛⠻⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠙⠶⣤⣀⣀⣀⣀⣀⣀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠉⠛⠒⠲⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣾⣟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠘⠻⠷⠶⠶⢺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣠⡤⣄⠀⠀⢀⣴⠄⢀⣴⠆⠀⢠⣾⡟⢀⣤⠀⠀⣠⡀⢀⣾⣏⡼⠁
⠀⢀⡴⠶⠶⣤⡀⠀⠀⢀⣿⡏⣴⣿⡁⠘⡇⢀⣾⡟⠀⣼⡏⠀⣰⣿⠏⢠⣿⠏⠀⣾⡟⠀⣼⡿⠋⠀⡀
⢰⡏⠀⠀⠀⠸⡷⠀⠀⣼⡿⠀⣿⡏⠛⣾⠗⠻⣿⣀⣴⣿⠣⢶⣿⠷⠖⢾⡏⣠⣼⣿⢀⣼⡿⠀⠀⡼⠁
⠸⣇⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⠛⠚⠋⠀⠀⠉⠉⣼⡏⢠⣿⠋⣇⠀⠈⠛⠉⠀⠛⠋⠸⣧⣠⠞⠁
⠀⠈⠛⠶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⣴⠋⠉⢉⣿⠟⠲⢾⡟⠋⣿
⢰⣇⠀⡴⣿⡄⣰⢻⣷⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠸⣧⣠⡏⠀⠀⠀⠀⣼⣄⡀
⢸⣿⣸⠃⣿⣷⠇⢸⣿⠀⢀⣤⡄⣤⡄⠀⠀⢠⢤⠀⠀⠀⠀⣨⠉⠀⣤⠀⠀⢠⣿⣿⡟
⢸⣿⡏⠀⣿⡿⠀⢸⣿⢠⣿⣣⠇⠙⡿⢤⣤⠈⢻⠦⣤⡄⠀⣿⠀⢠⣿⡆⢠⠈⣿⣿⣿⠆
⢸⣿⡁⠀⣿⡇⠀⢸⣿⢸⣿⠁⠀⡰⠁⣼⡿⢀⠏⢠⣿⠇⣸⣿⣄⡞⣿⡷⠋⠘⠻⣿⡏⣤⣀⣤⣦⣄⣀
⠈⠛⠁⠀⠀⠀⠀⠀⠋⠀⠙⠛⠋⠀⠀⣿⣧⠞⠀⢸⣿⡴⠁⢙⣋⢤⣿⡇⠀⠰⣿⠿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⣠⠖⠚⢻⣦⣀⣀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⢰⡋⢀⣼⡿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⡉
⠀⠸⠥⠂⣠⡿⠋⠉⣸⡷⠀⣰⡿⢡⠇⠀⠀⠀⠀⣀⣀⠀⠀⢙⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⢀⣀⣼⡟⠁⠶⣾⡋⠀⢰⣿⡵⢃⣴⡾⢛⡆⠸⣿⡀⠁⠀⢿⣄⠉⠀⢠⣴⠞⢳⠀⢀⣴⠶⣾⡏
⡼⠉⢸⣿⠙⣦⠀⠈⣿⢀⣿⠋⠀⣼⡟⠓⠋⢡⢞⣘⣿⣆⡠⣋⣻⣷⣠⣿⠟⠚⠋⣰⣿⠃⣸⡟⢀⡖
⢧⡀⠀⠓⠀⠟⠀⢠⣿⢹⡇⢀⡼⠙⠧⡤⠖⠋⠯⡥⠿⠃⠸⢭⠼⠟⠀⠻⢦⠤⠚⠙⠷⠖⠻⣧⠞
⠈⠛⢶⣤⣤⣤⣾⠟⠃⠀⠉⠉

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⢠⡄⠀⢸⡏
⠀⠀⠀⠀⠀⣿⡇⠀⣾⠀⢸⡆⠀⢰⡏⢀⡀⠀⣤⠀⠀⣿⠀⠀⣿⠀⣸⠆⠀⣿⠄⠀⣷⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠄⣼⡇⠀⢿⡀⢸⡇⠀⢿⡇⢸⡏⠀⠰⣿⢻⡇⠀⠀⣿⠀⠀⣿⠀⢸⡇⠀⢾⡇
⠀⠀⠀⠀⠀⠘⠇⠀⠈⠀⠻⡀⠀⠀⠁⠘⠧⠀⠀⠀⠸⡇⠀⠀⠁⠈⠣⠀⠀⢻⠀⠀⠈⠀⠘⠇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣤⠶⢾⣿⠿⠿⣿⣶⣤⡀
⠀⢣⡀⣩⡧⣤⠎⠀⠀⠀⠀⡈⠻⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⠞⢉⡳⢤⣀⣠⣤⣤⣤⠤⢤⣀⡤⠾⡉⠙⢦⣀
⠀⡿⣹⣿⢁⡎⠀⠀⣶⣀⣀⢹⡀⠹⣷⢹⠓⢦⡄⠀⢰⠉⠀⢀⣞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣸⣀⠀⠀⢱
⠀⡇⢹⠇⡜⠙⠉⠉⠀⠁⠉⠉⠱⡀⢹⡈⡇⡴⠁⢠⠊⠀⡤⠊⢿⠁⢀⠔⠉⠓⠒⠒⠒⠚⠲⡄⠀⡟⠻⣦⠀⠈⢢
⠀⣇⢼⡴⠁⠚⠙⠀⠀⠀⠚⠙⠂⠳⣤⣷⡏⠀⠀⢹⠄⢠⠏⠀⢸⣤⡎⠀⣀⡀⠀⠀⢀⣀⠀⠸⣤⣇⡴⠛⣦⠀⢞
⣠⠊⠀⣇⡀⠘⢗⡒⠾⠖⠒⡾⠀⣤⡏⠸⡄⠀⠀⠸⡄⢸⠀⠀⢧⡀⠀⠀⣁⣁⠠⠄⢈⣈⠀⠀⠀⡸⠀⠀⣳⠀⡞
⢧⠀⡴⣏⠓⠒⠬⡓⠦⠖⡞⠚⠉⣁⢧⠀⡽⠀⠀⠀⠳⠞⠀⠀⠀⣿⡷⣄⣘⢯⣉⣉⣡⣯⠤⢿⣿⠃⠀⠀⠙⠚⠁
⠀⠹⡀⠈⡷⠀⠀⢻⠛⣻⠀⠀⠸⡅⢀⣟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⡄⠈⢱⡬⢥⠏⠀⢰⠊⢹
⢀⡴⢳⡀⡇⠀⠀⠘⡦⡇⠀⠀⠀⣇⡞⠈⢧⠀⠀⠀⠀⠀⠀⢀⡜⢇⢠⠇⠀⠀⣇⣸⠀⠀⠸⣆⡎⢣
⠛⠠⠤⠽⣇⠀⠀⣸⣁⣱⡀⠀⣠⣏⣀⣀⣨⠇⠀⠀⠀⠀⠀⠛⠲⠼⢿⡀⠀⢀⣇⣹⡀⠀⣠⣏⣠⡤⠗
⣤⣤⣤⣤⣬⣵⣾⣥⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣮⣤⣤⣭⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠄⠀⠀⢸⡴⠊⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠠⠀⠀⠀⢀⡞⠀⠈⠀⠀⢸⡀⠀⠀⠠⡀⠀⠀⠀⡦⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣾⣤⢤⣾⣄⣀⠀⠀⠀⣸⠁⠀⠀⠀⠱⡄⠀⠀⠇⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⡋⠰⠇⠞⠚⠙⠉⡙⢷⣎⡁⠀⠀⠢⢄⠀⢈⡠⠄⠒⠒⠢⢄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⣠⢞⣽⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⡦⡀⠠⠀⢠⠋⢠⠀⠀⠂⠀⠀⢱⠀⠤
⠀⠀⠀⠀⠀⠀⠺⢣⢊⡇⠶⠀⠀⠈⠀⠀⠄⠀⠈⠁⠀⠠⠦⡿⣿⣜⡄⠀⢸⡀⢫⡀⠀⢀⡀⠀⡸⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠋⠹⠘⠅⠀⠀⣹⣦⢍⣉⣉⠤⠚⢁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡈⠓⠤⣄⣀⡠⠴⠊⢀⠴⠃⠀⠀⠀⠀⠀⣀⠜⠃⠀⡀⠀⢄⠀⠈⠑
⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣉⡶⠢⠤⠤⠤⠒⠊⢷⠤⣀⠀⢀⠀⡠⠊⠁⠀⠀⠀⡇⠀⠸⡄
⠀⡴⠉⡩⢅⠈⣇⠀⠀⢤⣴⠊⢁⡇⠀⠀⠀⠀⠀⠀⠘⡄⠀⢹⠿⠋⠀⠀⠀⠀⠀⣈⠥⢄
⠀⢣⣼⣁⣄⡇⠈⡇⠀⠈⠉⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣹⠚⠁⠀⠀⠀⠀⢀⠤⢺⠔⠈⠚⡍⢱
⠀⢮⡤⢽⣉⡜⠉⣀⠀⠀⠀⠀⣀⣀⠀⡇⠠⠤⠄⡀⠀⣤⣄⣀⣀⡀⠀⠀⠘⠤⣌⠪⣶⡷⠙⡇
⠀⠀⠀⠰⣒⣾⣾⠽⠒⠊⠉⠉⠀⢠⠶⠃⠀⠀⠀⠳⠦⠀⠀⠀⠀⠈⠉⠁⠒⠦⢼⣷⣋⠑⠊⠁
⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⡄
⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠐⠁⠐⠱⢠⠂⠀⠀⠀⠠⠀⠐⠀⠆⠀⠤⠆⠈⠇⢣⠂⠧⠀⠀⠖⠀⠀⠀⠴⠠⠀⠀⠏⠁⠞⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣤⣤⣤⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠀⠀⠀⠀⠀⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣸⠰⠆⠀⠲⠀⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠶⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣄⠀⠓⢀⡰⢯⡑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠉⠀⠀⠙⣦⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠢⣤⠔⠀⡇⠀⠸⡾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠸⠿⠀⠀⠐⠿⠆⢸⡇⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣇⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡀⠀⠀⣠⣤⡄⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠛⠛⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⠀⠈⠉⠀⢀⣴⠟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠙⠛⠛⠛⠋⠁⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠹⣆⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠲⠦⣤⠴⠖⠀⠀⣿⠀⠀⠀⢻⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢋⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠘⠋⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣸⠀⠆⠀⠰⠆⣇⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣿⡀⠀⠀⢀⣿⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⠀⠛⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠉⠛⠲⠚⠋⠙⠓⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠁⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠐⢤⠔⠀⣿⠀⠈⡿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⣼⠀⠀⣿⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣠⠄⠚⠂⠀⢺⡆⠐⠃⠀⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⠀⠀⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠙⠊⠙⠃⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢉⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡴⠛⠉⢻⠓⡶⠤⠄⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠐⠇⠙⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠱⠃⠀⠀⠀⠀⠳⠤⢀⡏⣸⠟⠀⠀⠀⠀⠀⠀⢀⣿⠃⣰⡿⠁⠀⢀⣾⠟⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡂⠀⠀⠀⠀⠀⠀⣸⢡⡿⡶⣠⣾⡖⣰⣷⡗⣼⡟⢡⣟⣴⣧⡖⡼⠃⠀⠀⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢘⣘⣛⣉⣉⣛⣉⣘⣋⣉⠝⢻⡇⢈⢉⣉⣙⡁⠀⠀⠀⠀⠀⠀⢀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣤⣄⠀⣠⡉⢭⣭⠅⣤⠄⣨⡥⢠⠄⣠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⣇⣸⠇⣿⣧⢠⡇⠀⣇⠀⣿⡀⢸⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⡇⣿⣇⢰⡏⣿⠈⡇⠀⡟⠁⣿⠁⢸⡀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⣋⠘⠚⠃⡘⠀⠃⠀⠛⠒⠙⠀⠈⠛⢃⣘⠓⠀⠀⠀⠀⠀⠀⠀⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡸⠀⢠⠎⡹⢀⠤⠤⠤⣄⡀⠀⠀⣠⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡀⠀⠀⠀⠀⠀⠀⡼⠛⠳⠀⣏⠔⡁⠈⣀⡀⣀⢀⡉⠉⣛⠟⠉⠀⠀⠀⠀⠀⠀⢀⠀⡳⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠁⠀⠀⠀⠀⠀⢠⠗⠒⡲⢻⠁⣰⣏⢜⣧⢴⣧⠾⣣⠾⢿⠀⣠⠀⠀⠀⠀⠀⠀⠈⢁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠘⠒⠚⠁⠈⠛⠁⠀⠈⠁⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠀⠞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢦⠠⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠢⣞⠀⠀⠀⠀⢀⡀⠀⠶⠀⠀⠀⡠⠻⠆⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠛⠀⢉⠉⠒⠂⠀⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠔⠀⢠⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀
⡆⣧⠀⣾⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⣇⠔⢩⠆
⠇⠀⠀⠈⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠰⠊⣰⠁
⠈⡄⠀⠀⠀⠉⠛⢠⠄⠷⠀⠀⠀⠀⠀⣤⣀⠀⠉⠂⠀⣀⣀⡀⣀⠀⠀⠀⠀⠐⠧⣀⠙⠀⠀⠀⠀⠠⢀
⠀⠘⠦⣀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠈⣆⠘⠃⠀⠉⠀⠠⠋⠀⢓⠀⠀⠀⠀⠀⢸⠀⠉⠦⠀⢠⠒⠂
⠀⠀⠀⠈⠃⠘⣇⠀⠀⠀⠀⠀⠀⢀⠰⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⡦⠀⠀⠈⠳⠀⢀⡠⠋
⠀⠀⠀⠀⢸⠀⠹⡄⠀⠀⠀⠀⢀⡹⠖⠒⠉⠉⠉⠁⠒⠦⣀⠀⠀⠀⠰⡁⠀⠀⠀⡔⠁⢠⡎
⠀⠀⠀⠀⠀⣧⠀⢳⠀⠀⣀⠔⠉⠀⣀⠀⠀⠀⢀⣀⠀⠀⠈⠲⡀⠀⠀⠘⠀⢠⠞⠀⢠⠟
⠀⠀⠀⠀⠀⢀⣄⣠⣧⡴⠁⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⡄⠀⠱⠀⠀⢤⣠⠋⠀⢀⠎
⠀⠀⠀⠀⠀⢯⠁⠀⢸⠁⠀⠀⠀⠀⠈⠀⠀⢀⣀⠤⠚⢩⡆⠀⠀⣛⡀⣸⠃⠀⢠⠎
⠀⠀⠀⠀⠀⠘⣇⠀⡆⠀⠀⠀⣿⡏⠉⠉⠉⢁⣀⣤⣶⡿⠁⠀⢀⠀⢙⠟⢦⣴⠋
⠀⠀⠀⠀⠀⠀⢹⡀⢡⠀⠀⠀⢻⣿⣶⣾⣿⢋⣉⢀⡼⠃⠀⠀⢨⡟⠁⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⢧⠈⣄⠀⠀⠀⠙⢿⠁⢀⢠⡤⠊⠀⠀⠀⣠⠏⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠓⠶⠶⠶⠶⠖⠋⠉⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠡⡤⠒⠒⠒⠒⠀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠉⠙⠓⠒⠲⠤⡶⠤⠼⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠠⠤⠤⠄⢾
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⠉⠻
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠣⣀⣀⡠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡖⠒⠲⠶⠖⠊⠻⣤⣤⣀⣀⣀⣀⣀⣠⠤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠀⠀⠀⠀⠁⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠧⠴⡇⠀⠀⠀⠀⢀⠞⠀⢊
⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⡇⠀⠀⠤⠒⠁⠀⠀⣸
⠀⠰⢂⠀⠀⢋⠀⠀⠀⠀⣀⠦⠚⠣⠁⠀⠀⠀⠀⠆⢨
⠀⠉⠂⠠⣭⣭⡥⠍⠁⠎⠑⠀⠀⠀⠨⡆⠠⠄⠚⠠⠙
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡿⠿⠿⠿⠿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠸⣯⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⣹⡦⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠁⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⣀⣴⣾⢟⣁⣠⣴⣾⢿⣿⠇⠀⠀⢀⡾⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢻⡄⠀⠀⣾⣿⣶⣤⣀⠈⠻⣷⣤⡀
⣠⣾⣿⣿⠿⠟⠛⠉⠁⠀⢸⣿⠀⠀⠀⣼⣧⣤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣤⡈⣷⠀⠀⣿⡇⠈⠉⠛⠿⢷⣶⣿⣿⣶⣄
⠻⣿⣧⣤⣀⣀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢻⣿⣷⡟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣇⡿⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿
⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⢿⣷⠀⠀⠀⠀⠉⠛⠛⠉⠀⢀⣠⣤⣤⣤⡤⠤⢤⡀⠈⠙⠛⠋⠀⠀⠀⣼⣿⣶⣶⣦⣶⣶⣾⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡶⠟⠀⠀⠀⠀⠀⠀⣰⣿⠃⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠻⢿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠈⣹⣿⠻⠿⠿⣿⣶⣶⣾⣿⣉⣹⣿⠿⠿⠿⠟⠛⢿⣏
⠀⠀⠀⠀⠀⠀⢠⣿⠋⣿⣆⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠻⣷⣤⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠈⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢷⣶⣶⣶⣶⣶⣶⡿⠟⠉⠻⢿⣶⣶⣶⣶⣶⣶⡾⠿⠿⠛⠁
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢀⠒⢄⠀⠂⣤⠔⠢⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡴⠋⡤⠯⠀⠀⣻⡄⠰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢠⠋⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠷
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⡰⠀⠀⢀⡔⢀⠀⠰⠁⠔⠀⢠⠇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢇⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⠀⠈⠀⠃⠀⡆⠐⠀⢠⠇⠀⠘⢰⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈
⠀⠀⠐⢦⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠐⣄⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⡉⠉⠀⠠⠠
⠀⠀⠈⠁⣴⣦⡄⠀⢀⡤⢀⣠
⠀⠀⠀⡀⠈⠉⢁⡔⠻⠇⡉⠣⡄⣁⠉⠁
⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠉⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠢⡀⡠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠘⢋⡷⠆⠀⠈⠀⠛⠐⢶⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠉⢲⣥⠀⣀⠉⠀⠀⠀⠀⠀⠻⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣶⣦⡏⠀⠋⠀⠀⠀⠀⠀⠀⢶⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⢀⠏⠙⠛⠛⠋⠀⠀⠀⠀⢐⠦⠈⢻⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⢠⠃⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠺⡆⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⡀⠀⣤⣀⣀⣠⠦⠴⠊⠀⢰⠁⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⡋⠀⠀⠀⢠⠀⠀⠘⠦⣄⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣤⠮⣀⣀⠀⠀⣈⢷⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣾⣧⣄⣀⣈⣉⣉⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠘⠒⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠰⢮⣉⠉⠉⠙⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⢹⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⣆⠀⠈⣧⠀⠀⢿⠀⠀⢀⣀⣀⣀⡀⠀⠙⠷⠶⣄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⣸⡀⠀⢸⣠⠞⠉⠉⠉⠉⠙⠳⣤⠒⠀⠘⠧⡀⠀⠀⠀⡧⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠙⣧⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⡆⠀⣼⠁⠀⠀⠀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⡀⢸⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠃⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⠀⢈⣉⣾⣇⢸⡇⠀⢙⣮⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣸⠋⣡⠄⠈⠉⠁⢰⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣀⣀⣠⠴⠻⢦⣤⣦⣀⣠⡾⠓⠲⠶⠶⠶⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠱⡀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡄⠀⠆
⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠎⠀⠀⠀⠀⠀⠑⠢⣶⣧⠀⠀⠀⠀⠀⠀⣢⣿⡤⡇⠀⠀⠀⠀⠀⢀⣿⠗⠊
⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⢼⣿⡀
⠀⠀⠀⠀⠸⠃⠻⠀⠀⠀⠀⠀⠐⢢⣼⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠸⡜⡇
⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠎⠘⠄⠀⠀⠀⠀⠀⠰⠀⠡⠀⠀⠀⠀⠀⠀⠐⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⣠⣀⠔⠁⠀⠀⠘⡀⠀⠀⢀⠄
⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠳⢄⣶⣀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠈⠙⢿⣶⠄⠀⠀⠺⣿⠁⠀⠀⠀⠀⠀⠳⣿⡴⠊
⠀⠀⠀⠓⢲⣾⠆⠒⠈⠀⠀⠀⠀⢿⡏⠑⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣰⢿⡟⠀⠀⠀⠀⠀⠟⢻⠀⠀⠀⠀⠀⠀⠀⡟⢹⠀⠀⠀⠘⠃⣇⠀⠀⠀⠀⠀⢸⠋⣷
⠀⠀⠀⠀⠚⠟⠃⠀⠀⠀⠀⠀⠸⠈⠛⠐⠆⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⠀⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣇⠀⢸⣿⡇⢸⣿⡇⠀⢀⣾⡿⠁⢸⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⢀⣿⡿⣿⣇⠀⠀⢸⣿⣿⡀⢸⣿⡇⢸⣿⡇⢀⣾⡿⠁⠀⢸⣿⡇⠀⠀⣺⣿⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⢸⣿⡇⣿⣿⠀⠀⢸⣿⣿⡇⢸⣿⡇⢸⣿⣧⣾⡿⠁⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣄⣿⣿⠀⠀⢸⣿⠃⢿⣿⠀⠀⢸⣿⣿⣿⢸⣿⡇⢸⣿⣿⡿⠁⠀⠀⠀⢸⣿⣧⣀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠿⣿⣿⠀⠀⣼⣿⠀⢸⣿⡄⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⡅⠀⠀⠀⠀⢸⣿⡿⠟⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⢸⣿⡇⠀⢸⣿⡇⣿⣿⣿⡇⢸⣿⣿⣿⡄⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⠀⢸⣿⡇⢹⣿⣿⡇⢸⣿⡏⢻⣿⡄⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠀⢀⣤⣦⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⣿⣿⠀⢸⣿⡇⠀⠀⣿⣿⠀⢸⣿⡇⣿⣿⣿⡇⢸⣿⡇⠀⢻⣿⡄⠀⢸⣿⡇⠀⠀⢻⣿⣆⣠⣿⡿⠀⣿⣿⣴⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠿⠿⠀⠿⠿⠀⠸⠿⠃⠀⠀⠿⠿⣤⠼⠿⢷⣿⣿⠿⠇⠸⠿⠇⠀⠀⠻⠿⠀⠸⣿⣷⠄⠀⠀⠛⠿⠿⠛⠁⠀⠿⢿⣿⡿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⡟⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢠⡞
⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣰⣿⠇⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣼⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠏
⢠⣾⡿⠉⠉⢹⣿⣷⣄⠀⢻⣿⠶⣿⣿⡟⠀⠀⣠⣾⡿⠉⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣿⠋⢻⡄⠀⣿⣿⠁⠀⢠⣿⣿⠀⢰⣿⣷⠀⠀⣿⣿⡇
⣿⣿⠇⠀⠀⣾⣿⣿⠀⠀⣾⠀⢀⣿⣿⠁⠀⣰⣿⡟⠀⢰⣿⣿⡇⠀⢀⣿⣿⠀⠀⠀⠀⣼⣿⡷⠶⠾⠃⣸⣿⡿⠀⢀⣼⣿⡇⠀⣾⣿⣿⠀⠀⢿⣿⡇⠀⠀⢀
⠹⣿⣆⣀⣼⢿⣿⡿⠀⣸⠇⠀⢸⣿⣿⠀⣴⣿⣿⣇⣠⠟⢻⣿⣇⣠⡾⢿⣿⡄⠀⢀⣴⢿⣿⡇⠀⣀⡼⣿⣿⡟⠛⠋⢿⣿⣇⣼⠛⣿⣿⠀⣠⡿⣿⣧⠀⢠⡾
⠀⠈⠙⠋⠁⣸⣿⣧⠾⠃⠀⠀⠀⠻⠿⠛⠁⠈⠛⠛⠁⠀⠈⠻⠿⠋⠀⠈⠻⠿⠿⠋⠁⠈⠻⠿⠞⠋⠀⣿⣿⣿⡄⠀⠘⠿⠟⠁⠀⠹⠿⠿⠋⠀⠙⠻⠿⠋
⠀⠀⣀⡴⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢿⡀
⠀⣴⠋⠀⢀⣿⣿⣤⣤⣤⣤⣀⠀⠀⠀⣤⣤⠀⠀⠀⣠⣤⣤⣄⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⢀⣀⣤⣄⡀⣿⣿⣤⣼⣧⣤⠀⢠⣤⣤⣤⣤⣀
⢸⡇⠀⠀⣸⣿⠃⣿⣿⠿⠿⣿⣷⠀⠀⣿⣿⠆⠀⠀⣿⣿⡿⠿⠀⢠⣿⣿⠿⢿⣿⡆⠀⢠⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠀⢸⣿⡿⠿⢿⣿⣷
⠘⢧⣀⣰⡿⠃⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⣿⡄⠀⠀⣿⣿⡇⠀⠀⣾⣿⡇⠀⠸⣿⣿⠀⢸⣿⡇⠀⢸⣿⣿⠻⣿⣿⡟⠀⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠉⠁⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⢹⣿⣧⠀⠰⠿⠿⠀⢸⣿⣧⠀⠸⠿⠿⠀⣼⣿⡇⠀⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣿⡿⠀⠀⣿⣿⡇⠀⠀⣿⣿⣇⣀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⣿⣿⣇⣀⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⣦⠀⠀⣿⣿⡇⠀⠀⣿⣿⡿⠿⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⣿⣿⡿⠿⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢻⣿⡇⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⠀⠀⠙⣿⣿⡄⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣴⣶⡆⠀⢸⣿⣧⠀⢴⣶⡆⠀⢸⣿⣧⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⢿⣿⡇⠀⢸⣿⣿⠀⢸⣿⡇⠀⢸⣿⡿⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⠃⠀⣿⣿⣷⣦⠀⣿⣿⣷⣦⠀⠘⣿⣿⣶⣾⣿⠇⠀⠘⣿⣿⣶⣾⣿⠇⠀⣿⣿⣷⣶⠀⢸⣿⣷⣶⣾⣿⡿
⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣥⣤⣤⣿⣿⣿⣿⣤⣿⣿⣿⣿⣤⣤⣬⣿⣿⣿⣥⣤⣤⣤⣬⣿⣿⣿⣥⣤⣤⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣈⣄⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⢛⣛⣛⡉⣉⠙⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢩⣖⣦⣶⣆⢸⣿⠃⢹⡇⠸⢷⣿⠀⣿⠉⠉⠉⠛⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⣿⢸⡟⠁⠟⢻⠈⠋⠳⠈⠁⠒⢚⣁⣀⣯⣀⣀⣀⣘⠛⢭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠷⡶⠀⠀⣻⣄⣡⣤⡤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠙⠋⠀⣀⡴⠃⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠠⠀⡇⢨⡄⠀⣼⣡⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⡆⠀⠀⠀⣹⣶⢶⡖⢲⢶⡶⡾⢯⣹⡇⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⢸⡇⣇⢸⡀⠀⠉⠁⠀⢠⣤⡤⢤⠤⣤⢲⣶⢿⡁⢹⣌⣿⠀⠀⠀⠿⠋⠈⢷⠇⠈⠻⠃⠀⠙⠃⢸⡇⣿⡇⢠⣤⡄
⠀⠀⣴⢒⠊⠉⠙⠋⠛⠙⢓⠒⢦⡀⠀⢸⣿⡇⢸⣧⣽⠸⣿⠾⡇⠀⠋⠈⠀⠀⠀⠀⢸⡇⠀⢰⣢⠀⠀⣴⣦⠀⢸⣧⠻⠇⠈⠛⠉
⠀⠀⡧⢀⣀⢉⣭⡉⣩⣅⢠⣤⡀⢻⠀⠈⠈⠀⠈⠀⡁⠀⠁⠀⠐⣦⣀⢿⣠⢿⠀⢰⢟⣧⠀⣰⠿⡀⠀⢸⣻⣦⠈⠿⠀⢠⣦⣀⡀⠻⠃
⠀⠀⢷⡟⢻⣿⣸⣇⣟⣻⡿⢹⡇⡿⠀⠀⠀⠀⣶⣾⡿⣰⠀⠀⠀⠹⡉⣂⡡⠼⠀⣯⣵⡿⠀⣿⠃⢷⡀⣾⣭⣼⠇⠀⠺⣼⢿⣻⠅
⠀⠀⣸⣗⠀⣤⠙⠿⣃⠉⢠⣌⣻⠧⣄⢠⡖⠒⢻⣿⡏⢉⣳⡄⠀⡶⣄⢠⢺⠂⠀⢀⡀⣀⠀⢙⡓⠛⠁⠀⠀⠀⠀⢀⣀⡙⠋⠁⣀⢀
⠀⢸⠁⠈⠉⠓⠒⠚⣉⠉⠉⠉⠀⠀⠘⡇⢳⠚⠹⣿⡏⠉⣹⠁⣤⣷⣿⣿⣾⣧⠀⡸⠖⢶⣉⡳⣆⡵⠀⡶⠉⢲⣤⠟⠁⢸⡆⠀⠻⠟
⠀⢸⣴⢶⣄⡞⣷⣼⢻⡆⣾⢻⢠⡟⣦⣿⢸⡀⠀⣿⡇⠀⡟⠀⢸⣏⠋⠋⣭⡏⠀⠁⠈⠁⢀⣉⡉⠀⠀⣷⡀⠀⠉⠀⠀⣼⠃⣶⣤⡤
⠀⠀⣏⠈⠿⠃⠻⡿⠈⠷⣏⠈⢿⡃⣸⡅⠀⠣⢀⠛⠓⠚⠁⠀⠈⣿⣀⣴⣉⡇⠀⠀⠀⣰⠋⠀⠙⣦⠀⠈⠙⠲⢤⣠⡼⠃⠀⠻⠟⠁
⠀⠀⢿⠺⡧⢮⡥⣬⢤⡴⠶⢋⣛⣬⠾⠃⠀⣼⢁⢹⣠⡖⢒⡄⠀⠈⠉⠉⠉⠀⢀⡴⠒⣿⠀⠀⠀⣿⠞⠉⣶⠀⠀⣽⠁⠀⢀⡤⠖⠂⢤
⠀⣠⡀⠉⠓⠒⠒⠒⠒⠛⠉⠉⠀⢠⣤⡀⢠⡬⠽⡿⠻⣿⠏⣤⢰⣿⣤⣶⠀⣤⠞⠳⣄⢿⠀⠀⢀⣟⣠⠤⣿⡁⠀⠙⢦⠀⡞
⠲⡋⠹⡃⢤⢤⣶⣶⡾⣹⠀⡤⣄⢨⣿⡁⠸⡇⠀⣇⢠⡧⠀⢼⢻⣿⣿⡅⣸⠃⠀⠀⢹⣮⠧⣴⠻⡿⠁⠀⠈⣿⠀⠀⣼⠀⡇⠀⠀⠀⢠
⠘⠛⠉⠁⠘⠚⠉⢁⡀⠀⣠⢿⡅⠺⠾⠇⠀⣇⠀⣿⢸⠇⣀⣿⣸⣿⣸⠇⢻⡀⠀⢀⣾⡏⠀⢸⣿⡇⠀⠀⢀⡿⠀⠴⠃⠀⣸⠶⠴⠒⠋
⢸⠖⢦⠀⠀⣠⠚⣵⠿⠀⢑⣛⣁⡔⢰⠀⠀⠈⠉⠉⠉⠉⠁⣀⣀⠀⠀⠀⠀⠙⢶⠋⣿⡄⠀⣸⡿⠙⣦⡴⢛⣀⣀⡀⠀⢠⡇⠀⣸⣷⣶
⠉⠻⠁⠐⢊⣲⠗⠁⣴⠰⣿⣌⠿⠃⠘⢡⣾⠀⠀⠀⢀⡴⠺⣅⡽⢦⡀⠀⠀⠀⠀⠀⠈⢳⣤⠟⠠⠀⡄⡴⠋⠀⠀⠈⢢⠈⢇⠈⠛⡽⠋
⠘⠃⣠⡤⣤⣁⣀⣀⡈⠙⠋⠀⠀⢀⠴⢭⠭⠵⢦⠀⢯⢌⣓⣉⣫⣭⡽⠀⣔⠀⠀⠡⣠⠀⡅⢀⠃⠜⠐⡇⠀⠀⠀⠀⣸⠇⢸⡆⢠⣤
⠀⠀⣿⠀⠖⠀⢀⣠⡾⣷⣀⠀⠀⡾⢉⢚⣩⢉⡹⣄⢸⢸⣻⢹⢸⣿⠃⠀⣾⡆⠀⠀⠈⢳⡁⢀⠎⠀⠀⢻⣄⣀⣀⡴⠋⢀⡼⠀⠙⠛⠁
⠀⠀⢻⣆⣤⡾⠛⢋⣠⠾⣹⠃⠈⣶⣦⡭⡶⣤⡖⡟⠀⠉⠛⠛⠛⠁⡔⠀⠉⠙⠒⢄⡀⠀⣿⠀⠀⠀⢠⠞⠋⠁⠀⠀⣶⡄⠀⣶⣤⠄
⠀⠀⠀⠉⣷⣤⠴⢛⡵⠚⢡⣄⡄⠹⢾⣷⣷⣿⠼⠁⡠⣠⣶⣄⠀⢺⡄⠀⠀⠀⡀⣠⡗⠀⣿⡀⠀⠀⠸⡀⠠⣿⣖⠀⣀⣠⡆⠘⠁
⠀⠀⠀⠘⠧⠔⠚⠉⠀⠀⢮⢿⠗⠀⠀⠀⠀⠀⠀⠀⣱⢺⡟⡞⠁⠀⠘⡏⡏⣿⣏⣿⠃⠐⠁⠀⠀⠀⢀⡇⠀⠁⠀⣠⣯⡀⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣁⣀⣀⣀⣷⣿⣟⣛⣛⣀⣀⣀⣀⣀⣠⣏⣀⣀⣀⣀⣈⣀⣈⣃⣀⣀⣀⣀
⣿⣿⠛⡻⢛⡛⠛⣟⢛⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⠿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣤⣤⣤⣄⡈⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣤⣤⣤⣤⣀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠀⢸⣧⠀⠀⣿⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⣠⡼⠏⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡾⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠊




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⡀⢤⠄⠓⠀⠀⠐⠀⢄⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⡠⠐⡑⠁⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡀⠄⠊⢀⠌⠀⠀⠀⠀⢀⠤⠀⠠⡀⠀⠸⠡⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣷⣤⡀⡀⠀⡠⠁⠀⠀⠀⠐⡄⠀⡆⢃⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢿⣿⡄⠀⠰⠁⢠⣾⡮⠰⡆⠐⠀⡇⠀⠑⢄⡀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢠⡭⠤⠤⢆⡀⠘⢿⣿⠀⠁⢀⠀⠃⠀⠀⠀⠈⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣿⣶⣦⣤⡿⡀⠀⠀⠀⡀⠊⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⡛⠉⠁⠀⠀⠈⠉⠁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠂⠷⠠⠤⠠⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢠⣄⠀⠀⠀⠤⠀⠐⡀⠅⣂⠕⠤⣀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠑⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠠⠄⠂⠀⣁⠄⠊⠀⠀⠀⠀⠉⠑⠤⣀⠀⠀⠀⠀⠂⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠾⣥⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠘⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢣⠀⠠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣸⢇⠀⠀⠀⡆⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⡧⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠁⠈⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⠀⠀⢀⠔⠁⠀⠀⠀⡦⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠐⢧⠂⡄⠀⡀⠮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢠⡀⠀⠀⢀⡀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⠄⣀⡧⢐⠠⠁⠀⠊⠀⠁⠀⠀⠈⠀⠑⠂⠈⠄⡂⢼⣀⠠⠠⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⢚⣡⠖⡀⠂⠀⠀⠀⣠⡴⣤⡀⠀⠀⠀⠀⠀⠐⢀⠲⣌⡓⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣫⠚⠛⠉⠀⠀⣤⡄⣤⡀⣼⠇⠀⢹⣥⡀⣠⡄⠀⢠⡄⠀⠀⠀⠉⠛⠓⣝⣆
⠀⠀⠀⠀⠀⠀⠀⡿⠁⡀⠀⠀⠀⠀⣿⡇⣿⣷⣿⠀⠀⣿⣻⡇⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⢨⢿
⠀⠀⡄⠤⢀⠀⡜⣰⠂⠄⠀⠀⠀⠀⠿⠇⠿⠙⠿⠀⠰⠿⠙⣷⠿⠷⠾⠺⠿⠾⠀⠀⠀⠀⠠⠐⣆⢳⠀⠀⠤⢠
⠀⠂⡖⡕⢀⣸⢱⢣⠡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠙⠷⠿⠀⠀⢀⣀⠀⠀⠀⠀⠉⠌⡜⡎⣇⡠⢪⢲⠐
⠀⠀⠀⣧⡆⡇⣼⠏⣁⣀⣀⢀⡀⣠⢀⣄⣀⡀⣰⠏⣠⣟⢀⣤⣄⠀⢀⣤⡙⣩⣷⡀⣀⣠⣠⣌⠹⣧⢸⢰⣼
⠀⠀⠀⢿⣷⡷⠃⠀⠈⣻⠉⢸⣧⣿⢸⡏⢸⣿⣿⢸⣟⢋⣈⣿⣏⠀⣿⡏⣃⢾⡿⣿⡟⢸⡷⠆⠀⠘⢾⣾⡿
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠛⠂⠘⠃⢿⡘⣛⠛⠋⠛⠈⠛⠛⠋⠛⠋⠀⠙⠛⠛⠛⠃⠛⠃⠘⠛⠃⠀⠀⣸⣿
⠀⠀⠀⠀⠹⡇⢓⠢⢔⠀⠀⠀⠀⠈⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢳⡄⠀⠀⠀⠀⠀⠀⠀⡢⠔⡂⢸⠏
⠀⠀⠀⠀⠤⢿⣸⣸⡞⠀⠀⠀⣶⣶⡆⣶⠄⣶⠀⣶⣦⢰⣦⢸⡏⣶⣴⡆⣶⣶⠀⠀⠀⠀⠀⢳⣇⢇⡿⠤
⠀⠀⠀⠀⠂⠣⣧⢻⡁⠀⠀⠀⠀⣯⠀⣿⠶⣿⢸⣯⣿⢸⣿⣿⡇⣿⣿⠀⣽⣿⡀⠀⠀⠀⠀⢈⡟⣼⠜⠉
⠀⠀⠀⠀⠀⡄⣌⣷⣳⡀⠰⡀⠌⡛⠀⠛⠁⣿⢚⡃⢹⡞⢣⡙⠃⠛⠘⣧⣙⡋⢀⠠⢀⠆⢀⣞⣼⣡⢠
⠀⠀⠀⠀⠀⠓⠊⠣⡙⢏⠙⢎⠐⢞⠀⠀⠀⠙⠿⠏⠀⠙⠛⠁⠀⠀⠀⠈⠛⠁⡳⠂⡱⠋⡹⢋⠔⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢤⡙⠾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠷⢋⡤⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠓⠤⣉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣉⠤⠞⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠶⠶⠒⠒⠚⠋⠉

⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠙⡄
⠀⠀⠘⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠰⢸⡫⠁⠉⠋⡇⢰⠖⠒⠖⠀⠺⠴⠎⠀⠀⠱⡀
⠀⠀⢨⣿⠀⠠⢠⠀⠁⠸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠱⡀
⠀⠀⣯⡏⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⡄
⠀⢠⣿⠧⠐⠀⠀⠀⠀⠈⠀⢠⠀⡇⠀⠁⡇⠀⠀⠀⠀⠀⠘⣆
⠀⣸⣾⡄⡀⠆⠀⠐⠀⠀⡇⢸⠀⠀⠃⠠⡇⠀⠀⠀⠀⠀⠀⠈⢦
⠀⣿⠉⡄⠀⠀⠀⠀⠂⠀⠀⠸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠛⢾⣅⣀⣀⡀⣼⠀⡄⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⢸⠀⠀⢨⠀⠈⠉⠁⠙⠉⠈⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠔⠐⣀⢀⡀⠄⡀
⠀⠀⠀⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠌⠀⢈⢀⡀⣈⢀
⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠁⠀⠉⠚⢷⠀⡀⠃⠉⠀⣠⠉⠴
⠀⠀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢄⡀⡤⠂
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠠⠉⠒⢯⡐⢄⠀⠀⠀⠁⠐⢧⣑⠄⡀⠀⠀⠀⠀⠀⠃⠀⣰⠊⡐⠉⠁⠀⢒⠀⠀⠀⢰⠀⢀
⠀⠀⠀⠠⢀⣀⢀⡙⠶⣍⣂⣈⣂⠐⠠⠌⣓⢦⣭⣲⣤⡀⠀⢂⠀⢻⡄⢀⠀⠀⠀⠀⠡⠀⠀⢀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠡⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠟⠛⠛⠛⠻⠷⣦⣀⠀⠀⠀⢀⣤⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣼⠃⠀⠀⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠻⠿⢷⣄⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⡄⠀⠀⠀⠙⠻⠿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠞⠋⠁⠀⢰⡦⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡙⠻⣷⡄⢸⣿⣆⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣼⠿⣮⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⡆⠘⣷⠈⢿⣿⣦⡀⢀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⢸⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⡇⠀⣿⠀⠈⣹⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢸⠇⠀⢸⣿⣷⣾⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⣰⡏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⢀⣾⣆⠀⠀⢿⣿⡟⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋⠲⣤⠏⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠟⠉⠛⢿⣦⣀⠙⠛⠋⠁⠀⠀⠀⣀⣴⣶⣶⣿⣿⣷⣄⠀⠀⠀⠈⢿⠋⠁⠈⠙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠆⠼⠿⣷⡟⠀⠀⠀⠀⠀⣿⣿⣿⠉⠉⠉⢉⣿⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⢻⣿⣿⣿⣶⠶⠿⠋⠀⢀⣴⣿⠃⠀⠀⠀⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠿⣦⣤⣀⣀⣀⣀⣤⣴⡶⠶⠶⣶⣾⡿⠟⠃⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣶⣶⡶⠾⠿⠿⠛⠻⣦⣀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⢀⣴⣾⠿⠿⠿⠟⠛⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⠾⠃
⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣾⣿⢿⡇⠀⠀⢸⡇⠀⣿⡀
⠀⠀⠀⠀⢿⠸⣄⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡟⠋⢸⠃⠀⠀⢸⡇⠀⢸⣇
⠀⠀⠀⠀⠸⡄⠘⠷⣄⡀⢸⣿⣷⡀⠀⠀⠀⠀⢠⣾⣿⡿⠤⣄⣸⠀⠀⠀⢸⣷⣄⠀⠙⠻⣦
⠀⠀⠀⠀⠀⠙⢦⣄⣈⠙⠛⠛⠛⠃⠀⠀⠀⠀⠛⠋⠁⢀⣤⠈⣿⠀⠀⠀⡀⠀⡌⢷⣸⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣷⣶⣶⠶⠻⠿⣶⣾⠿⣶⠿⢷⣶⣶⢿⣤⠷⢾⠋⠉⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣴⡾⠋⢹⡿⢻⣿⣿⣷⣶⣤⣾⠟⠛⣋⣩⡭⠭⠥⠤⠶⠶⠒⠒⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡯⠉⠉⠉⠛⠟⠋⠀⠀⠀⠀⠀⠉⠘⠛⠻⠿⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣁⣤⢤⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢆⡀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡭⠞⠉⠀⢀⡼⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⠂⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⣼⠟⡿⠋⠀⠀⠀⠴⢟⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠦⡀⠀⠀⠀⠀⠀⠀⠠⣬⣷⣴⠾⠋
⠀⠀⠀⠀⠀⢰⡿⢸⣧⣶⣤⡀⠀⣴⡋⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⢸⣷⠟⠁⠀⠉⠻⣶⣾⡁⠀⠀⢀⡞⣽⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣻⣷
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⢸⣼⣿⣿⣋⣽⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠋⢠⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣃⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⢀⣤⣴⣶⣤⣄⣀⣼⡇⠀⠀⠀⠀⠀⢀⣤⠄⠿⠉⠙⠾⠏⢳⠀⣠⠴⣿⣧⠬⠭⠭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣧⡀
⠀⠀⢀⣴⠟⠙⠋⢠⣽⣿⠿⠛⠷⡄⠀⠀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⢾⣗⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣤⣌⠻⣶⣄
⠀⢰⡿⠁⠠⣾⣿⡄⣿⣿⢢⣶⡄⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠗⠒⠲⢶⣄⠠⠤⠀⠀⠀⠙⠛⠢⣄⡀⠀⠀⢰⡏⣴⣦⣸⣿⡟⣠⣬⣿⣧
⠀⣿⣧⠀⣤⣭⡍⢁⣴⣦⡘⠿⠇⠀⣧⠀⠀⠀⠀⠀⠀⣒⠀⢿⣶⣦⣤⣶⣾⡿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⠀⠻⢟⣡⣭⡐⢿⣿⠏⣿⡄
⠀⢻⣿⡃⠘⠻⢃⣼⣿⣿⣿⣿⠆⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⢾⣿⣿⣿⣿⡄⣤⣤⢹⣿
⠀⠀⠙⢿⣷⡆⠘⠛⠛⠉⠉⠀⠀⠀⠀⠿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠼⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠈⠻⣿⣟⠿⢫⣿⠏
⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⢦⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⡌⠙⠂⠀⠀⠀⠀⠀⢿⠉⠿⠤⢶⣶⣤⣄⢀⣠⡄⢀⡀⠀⠀⠠⢤⣈⣳⣖⠲⠖⠋⠁⡾⠹⡟⠃⠀⠀⠀⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠓⠦⠤⠄⠀⠀⠘⣇⠀⠀⠀⠀⠉⠉⠉⠀⠙⠋⠉⠉⠑⠚⠋⠉⠀⠀⠀⠀⠀⣼⠃⠀⢿⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠈⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡤⠖⠒⢲⣄⣀
⠀⡴⠋⠁⠀⣀⣀⢀⡀⠘⢣⡀
⢰⡇⡀⠀⠂⠀⠀⠀⠀⢀⢹⠄
⠘⡷⠀⠀⠁⠠⠄⠀⣀⠘⢮
⠘⠤⡄⠸⣄⣀⣀⣤⡏⢠⡞
⠀⠀⠙⣄⠙⠡⠔⠋⢀⡼
⠀⠀⠀⠀⣹⠐⠂⡖⠉
⠀⠀⠀⢐⠁⠀⣱⣳⣄⡀
⠀⠀⠀⡎⠀⢠⠋⠀⠀⠉⠓⢤⡀
⠀⠀⠀⡇⠀⢸⠀⠢⣀⠀⠀⠀⡨⠻⢖⡠⢄⡀
⠀⠀⠀⠇⠀⠈⢦⣀⣈⢷⠦⡼⠧⣄⡀⠉⠓⠮⣕⡂⣤⡄⡀
⠀⠀⠀⢧⠀⠀⠀⠉⠁⠘⡇⠀⠀⠀⠉⠓⠶⢤⣀⠉⠁⠉⠙⣷⣄
⠀⠀⠀⢸⡄⠀⠀⠀⠠⠄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⣴⣿⡻⣷⡀
⠀⠀⠀⠈⣷⠀⠀⠀⠐⠂⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢦⠉⠙⠻⢛⡢⣄⡀
⠀⠀⠀⠀⠘⡄⠀⠀⣀⣀⣀⣀⣣⠀⠀⠀⠀⠀⠀⢀⡸⡙⠈⢣⠀⠀⠀⠈⠙⠛⠷⢶⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⢫⡉⠓⢦⣀
⠀⠀⠀⠀⠀⠸⠋⠉⠉⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠈⢏⠓⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠿⣶⣤⣤⣀⣀⣀⡀⠀⠀⣀⠷⣄⠀⢳⠀⠁⠈⠉⠘⢢
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣉⣉⡿⠿⠿⠾⡉⢦⡈⠉⠁⠀⠘⠁⠄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠘⠫⣉⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢆⣀⠔⠒⠐⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣆⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠫⢅⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡃
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡟⡆⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣁⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣠⣀⣹⠟⠒⠒⢾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⠀⠱⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⡴⠓⠓⠲⣰⣖⣤⣆⣠⣦⠆⠀⢸⠁⠍⣍⡝⠀⣢⢂⡎
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢹⠀⠀⢧⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⠴⠛⡀⠀⠀⢴⡊⠀⠀⠀⠀⠉⠁⣉⢽⠿⠛⡃⠀⢸⣠⣤⡀⢀⡈⡊⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠘⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢸⣀⣴⠏⠒⢄⠀⢳⠀⠀⠀⠀⠀⠘⢆⣀⣤⠞⡇⠀⢸⡀⢀⡆⡏⣕⠳⡄
⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣀⣸⠇⠀⠀⠙⡖⠀⠶⠶⠶⠾⣁⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠈⣸⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠹⣍⠭⠅⠀⠉⣳⠀⠀⠀⠹⠦⠀⠀⠤⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣷⣆
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⡇
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣠⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠿⠿⢿⣿⣶⣶⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⢻⣿⣿⡇⠀⠀⣴⣶⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢿⣿⣿⣿⣿⣿⣇⡀⠀⠘⠟⠛⠀⠀⠀⠻⠿⠏⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠉⠛⠿⢿⣿⡿⢃⣤⣶⣿⡿⠿⠿⢿⣷⣶⣄⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠁⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠙⠛⠿⠿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣤⣤⣤⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠿⠿⠶⢶⣶⣶⣶⣾⣿⣿⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⡝⠛⢿⣿⣿⣿⣿⣿⣛⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢻⣦⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠟⠁⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⡄⠀⢰⣿⣀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⠿⣿⣶⣿⡆⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⣿⡄⢀⣾⠃⠀⠀⠀⠀⣠⡞⢀⣤⣿⠿⠟⠛⠋⠉⠛⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠉⠙⠓⠦⠤⠄⠀⠈⢷⡀⠀⠀⠀⠀⢹⣷⡿⠁⠀⠀⠀⢀⣼⠏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⠾⢿⣦⠀⠀⠀⠈⣿⠀⠀⠀⠀⡠⠿⠳⠶⠶⣦⣤⣤⣀⡀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⣶⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠾⠿⠛⠛⠻⠿⠿⠿⠿⠿⠶⠾⠿⠿⠿⠿⠟⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣛⣛⣛⣛⣛⣛⣋⣈⣙⣻⣛⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣭⣭⣭⣽⣿⣯⣭⣭⣭⣭⣿⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠉⠉⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⡤⠤⠠⠤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡜⢀⡀⠀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⡇⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠒⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢞⡀⢀⣱⠆⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⢀⡔⢃⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆
⠀⡠⠋⠀⠀⡱⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⡞⠁⠀⡠⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⡇⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢁⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡄
⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⢆
⠀⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠳⠄
⠀⢰⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⠰⡄
⠀⠀⠑⠃⠀⠀⠀⠈⡗⠀⠐⠀⠀⠠⠖⠒⠀⠂⡟⠀⠀⠀⠀⠈⠳⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠈⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⢡⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢇⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⠤⠔⠊⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⡠⠄⠀⠠⢄⡀
⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⢰⡀⣀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⠀⠑⠔⠉⠀⠇⡈⡄⢃⠘⡄⠉
⠀⣠⠤⠊⠁⠀⠀⣠⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠡⠞⠁⠀⠀⠀⠀⠀⠀⠘⢄⢠⠈⢁⠃⡌⠀⡇⢠
⠀⢿⢸⡆⠒⠈⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠠⣆⠤⠀⠀⠀⠒⠒⠒⡚⠋⠙⣦⠃⠤⢘⡴⠉⠁
⠀⢸⡌⡇⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠒⠉⡇
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠆⠠⣤⠄⠸⣄⠀⠀⢀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢁⣠⡔⢃⡠⠚⠁⠀⠀⠀⢸⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⡆⠀⠀⠀⠀⠀⠀⠀⡄⠘⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⢬⣭⣥⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣘⠆⠁⣑⠀⠀⠀⠀⠀⠀⠀⠰⣱⠘⣐
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠊⠈⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⡖⢠⠀⡆⡴⠀⠀⠀⠀⠸⡀⢀⠀⠀⠉⠀⠀⢀⣀⣠⣔⡒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⡇⠈⣆⠁⡗⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⣠⠞⠉⠀⠣⣀⣨⠆⠀⠐⡀⠁⠀⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⠀⡧⠀⠿⠀⣇⡀⠀⣴⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⢄⠀⠀⠊⠄
⠀⠀⠀⢀⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⠁⠒⠒⠒⠊⠁
⠀⠀⠀⢸⣷⣀⣸⡇⠀⠀⣠⡤⠀⢰⣢⢶⠆⣾⣧⠋⢠⠛⣶⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⣰⢂⡄
⠀⠀⠠⠚⣿⠁⢸⡇⣼⡇⣿⣼⣧⠾⠃⠺⠴⡿⠻⠤⢠⢲⡿⠄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠆⠀⠚
⠀⠀⠀⠀⢻⡀⢸⣷⠻⡷⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠠⠈⢀⠀⡀
⠀⠀⠀⠀⠈⢧⠎⠋⠀⠀⣴⣷⣷⣦⡄⠀⠀⠀⠀⠀⡀⡆⡇⣿⠀⠏⢸⢸⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⣷⢻⠃⣿⠀⢰⢸⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⢶⠒⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠘⠀⠛⠂⠈⠘⠈⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⢹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⡕⠀⣀⢠⡹⣶⡀⢂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⣀⢻⡄⢻⡌⡿⠾⠛⠊⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠐⠉⠀⠈⠀⠀⠀⠀⣉⡀⠀⠀⠀⢀⡀⠀⣤⢀⡄⠀⠈⢹⡇⢸⡿⠀⣿⡌⠻⠋
⠀⠀⠀⠀⠀⠃⠀⡄⠘⠄⠀⠀⠀⣼⣫⣶⡀⠀⠀⡿⣸⡇⣿⠞⢃⡟⣵⣆⢧⡼⠧⠞⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂
⠀⠀⠀⠀⠀⠡⠀⠀⠠⠀⠲⡄⠀⠈⠁⠉⠀⠀⠀⠛⣹⠇⠛⠀⠈⠛⠉⠉⠀⠀⡀⣀⢀⡀⠀⡀⢀⡀⣀⡀⢀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠬⠁⠀⠀⠀⠀⢸⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣸⢸⡀⠀⢇⢸⡞⢸
⠀⠀⠀⠀⠀⠀⢀⠀⣀⠁⠘⠀⡖⠠⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⢸⠀⡸⢼⠈⢇⢸⡄
⠀⠀⠀⠀⠀⠰⠃⠘⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⢾⣷⡄⠉⠈⠈⠃⠁⠈⠈⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙

⡀⠀⡀
⣇⡀⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠓⣤⣾
⣿⣿⠙⣆⣄⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⡀⢱⣾⣿⣿
⣿⣿⣿⣿⠿⡉⣀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⢏⢢⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠺⣥⣷⣿⣁⢀⡴⠂⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡁⢡⢈⡢⣄⣾⣆⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡾⣿⣂⣼⣤⣸⡎⡹⠀⢰⡄⣠⠄⠀⣄⢄⠰⡀⣦⠀⡀⢲⣀⠙⢄⣠⣷⣏⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣤⣷⣿⣴⣿⣿⣴⣄⣼⢸⣾⣶⣧⢿⣴⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢻⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡇⠀⣿⠇⠀⢀⣴⡾⠟⠛⠻⢷⣄⣠⡾⠟⠛⠻⢷⣦⡀⠀⠘⣿⠀⢸⣿⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣿⠁⠀⣿⠀⠀⣾⠏⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢴⡄⠹⣷⠀⠀⣿⠀⠀⣿⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢰⣿⠀⢸⡟⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⣼⠟⠀⠀⢻⡇⠀⣿⡇⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣼⣿⣶⣼⡇⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢸⣧⣴⣿⣧⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠸⣿⡀⠈⠛⢷⣤⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢀⣤⡾⠛⠁⢀⣿⠇⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠙⢿⣦⡀⠀⠙⠿⣦⣀⠀⠀⠀⠙⢿⣄⣠⡿⠋⠀⠀⠀⣀⣴⠿⠋⠀⠀⣠⡾⠋⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠙⢿⣦⡀⠀⠈⠻⣷⣄⠀⠀⠀⠙⠋⠀⠀⠀⣠⣾⠟⠁⠀⠀⢀⣼⠟⠁⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠙⢿⣆⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⢰⡿⠋⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠘⣿⠀⠀⠀⠀⠘⣿⡀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣀⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⠛⠛⠿⠷⢶⣶⣿⡇⠀⠀⠀⠀⢈⣿⣶⡶⠾⠿⠛⠛⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⢠⣄⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⣠⡄⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⡇⠀⠀⠀⠀⠸⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⠒⠒⠀⠀⣀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢀⡠⠒⠁⠈⠙⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠰⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠰⠀⠀⢈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣄⠀⠀⠀⠀⠀⠈⠉⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠃⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠠⠀⠀⠸⠀⠂⡀⠐⠔⢄
⠀⠀⢀⠨⠦⣄⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠃⠂⠀⡨⠈⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣶⣤⠄
⣎⠂⠈⠀⠀⠀⠃⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠘⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⡟⠀⠀⠈⠉⠁⣤⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠉⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⠀⠀⣤⣤⣀⣀⣈⣛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠹⣿⡿
⠀⠀⠀⢀⠈⠀⠎⣀⠐⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⠀⠀⠙⠻⠿⠟⠁⠀⠑⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠠⠃⠀⢀⡐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⢄⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⢠⠁⠀⣀⠎⠀⠀⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢠⠀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⡎⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠳⠶⠄⠐⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠐⠀⠀⠥⠀⠐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠠⠀⠄⠀⠈⢆
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠀⠠⠀⠀⠱⡀⠀⠀⠀⠀⡠⠤⠤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠈⠄⠀⠈⡄
⠀⠀⠀⢠⡅⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠀⠤⠀⠀⠁⢉⠧⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠱⡀
⠀⠀⠀⡰⠁⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠷⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠱⡄
⠀⠀⡔⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⢸⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠢⡀
⢀⠎⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠈
⡎⠀⠀⠀⠀⣼⠐⠓⢦⡀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣠⠀⠀⠀⠀⣀⠔⠉⠁⠡⡀
⢣⡀⠀⡠⠞⠁⠀⠀⠀⠀⠉⢢⡀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⡐⠁⠀⠀⠀⠀⠘⠢⠄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⢾⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⣻⣿⣿⡝⠷⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠁⢠⣼⣿⣿⢷⠀⠒⠉⣁⣀⣉⠉⠀⠀⠘⠻⣿⣿⣟⡡⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⠙⠉⠐⠀⠀⢰⣯⣽⣯⣽⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠙⢦⣄⣀⣤⡴⠾⣿⠷⠦⣤⣤⣤⠞⠁⠀⠀⢀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠙⢿⠛⠀⠀⠁⠀⠀⣛⠟⠁⠀⠀⢀⡤⡋⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠙⠦⣀⠀⣀⠜⠁⣠⠞⠒⡊⠁⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠑⠦⠄⠀⠠⠔⠊⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠉⠢⣄⢱⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡇⡶⠋⠉⠉⠒⢄⡔
⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠰⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢤⡤⣤⣤⡤⢾⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⡎⠀⠀⠀⠀⠀⠀⢸⠬⢧⡀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠲⠄⠄⠷⠠⠘⠁⠀⠀⠀⠑⠄⠤⣀⣀⠨⠠⠊⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠐⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⡩⠄⠀⠀⢀⡴⢏⡨⠁⠀⠀⠀⠊⢄⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣃⠀⠀⠀⠀⠀⠀⢠⡮⣕⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠋⠀⠀⠀⠀⠀⢰⠗⠥⠀⠀⠀⢈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣀⠀⠀⠀⠀⠀⢀⠢⢀⠄⠀⠀⠀⠀⠀⠐⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠑⠀⡀⢀⠀⠀⠀⠀⠀⢠⠀⢃⠀⠂⠀⠀⠈⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⠀⠀⠄⠀⡀⠀⠀⣔⢂⣨⠜⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠦⡀⠀⠈⠲⠐⠤⠊⠁⠀⡀⢀⠀⠀⠀⠀⠀⠴⢆⣄⠉⠸⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠌⠀⠀⠔⠁⠀⢈⠦⡀⠚⠋⢄⠀⠀⠀⠄⠠⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠄⠄⠀⡠⠀⠀⡀⠐⠁⠀⢀⠰⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠈⠀⠀⠐⠈⠀⠄⠀⠈⠁
⠀⠀⠀⢠⠂⠔⡡⠀⡀⠄⡂⠠
⠀⠀⢠⣏⣀⡨⠔
⠀⠀⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣤⣶⣾⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣤⣤⣀⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⣄⠀⢿⣿⣿⡟⢸⣿⠟⠋⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣬⣥⣴⣿⠏⢀⣰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢿⣄⣤⣾⠀⠰⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢰⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠛⠛⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠏⠇⠀⠀⠀⠀⢠⣿⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠛⠀⢀⠀⠀⠀⢀⣾⣿⠘⠻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣧⡀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⢿⡄⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠛⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠥⣤⣤⣤⣄⣀⣀⣠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⡀⡀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠉⠁⠙⡄⠈⠃⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠁⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠁

⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠂⠀⢀⡤⠀⠀⠀⠀⣿⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠄⠀⠀⠈⢸⡇⢸⡟⢠⡄⢀⣤⡄⠀⡀⣠⣦⢸⡧⣡⠀⣼⡇⢀⡀⣀⠀⣿⡄⠀⠀⠀⠀⢴⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠠⠤⠄⣾⠀⡸⡿⣾⠡⣿⣽⣇⣼⡟⢸⡇⡼⣿⣏⠀⣿⡇⢼⣃⣿⢀⢿⠀⡐⠤⠄⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠔⠁⠀⠙⠃⠀⠈⠋⠀⠀⠘⠋⠀⠉⠙⠞⠺⣧⠈⠁⠳⠂⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢠⠀⠠⠤⠄⡀⠀⠀⢀⡄⠀⠤⠤⡤⠄⠤⠤⠠⠄⠬⠄⠤⠠⢤⠀⠀⠠⠄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⡘⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇⠀⢠⢠⠏⠀⢰⠀⢀⠂⠀⠀⡇⠀⠀⠉⠁⠀⡇⠉⠀⠀⡸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠻⠄⠰⠤⠀⠥⠠⠅⠀⠈⠴⠀⠀⠀⠀⠀⠤⠠⠀⠧⠀⠀⠀⠐⠦⠤⠀⠀⠤⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡄⢠⢠⢐⠂
⠀⠀⠀⠀⠀⠀⠑⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠥⠀⠐⠂⠹⡄⡇⢾⢾⠸⠇⠂⠀⠬⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠊
⠀⠀⠀⠐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠦⣰⠂⠀⠀⢀⠀⠀⠀⠐⣆⠤⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⢠⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠓⢂⣤⠀⠈⠀⡍⠨⢭⡉⢦⡀⠀⠈⠐⠚⠀⢀⣤⡀⠀⠀⠀⠀⠀⢀⡆⠐
⠀⠀⠀⠀⠀⠈⠙⠓⠂⠁⠀⠀⠀⠀⠀⢰⣿⡌⠀⠀⣿⠁⠃⠀⠀⠘⠆⠀⢙⣳⡇⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⡀⠀⠈⠐⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠃⣠⠄⢻⣿⡁⣄⢀⣿⡜⢀⣶⠂⢰⣇⢠⣖⠀⠃⣴⠢⢀⣴⢾⣿⠀⠐⠠⣄⠘⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⢠⣿⠏⢿⡄⠸⢿⡴⠋⣿⣯⢻⣖⠉⢿⡤⠊⠻⠺⣿⡰⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠘⠷⠃⠀⠀⠀⠛⠋⠘⠁⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣴⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄
⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠈⠙⠃
⠀⠀⠀⠀⢹⣿⡿⠿⠟⠉⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⣿⠟⠀⠀⠀⢉⣿⠟⠛⠻⣿⡀
⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢰⡏⠀⠀⠀⠀⣼⠋⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠒⠀⠀⠀⠷⠀⠀⠀⠀⠀⠈⠳⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⢀⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⢿⣿⣧⣶⣿⣿⣿⣿⣿⣦⣤⣤⣄⣀⣀⣀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠙⢿⣿⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠹⣿⠟⢈⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⣿⢉⣿⡟⠉⠁⠀⠀⢻⣿⠋⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠘⠿⠖⠀⠀⠀⠀⢈⣿⠆⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣿⣯⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣤⣤⡴⢶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠋⠛⠁⠀⠉⠀⠀⠀⠀⠀⠈⠻⢦⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⡀⠀⣀⠠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣰⡴⠚⠉⠁⠀⠀⠈⠂⠀⠀⠀⠀⠊⠉⠀⠀⠛⠛⠳⣤⡀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠻⣿⡆⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣾⡿⠁⠀⢀⣴⣿⣹⣿⣿⡆⠀⠀⠀⣾⣏⣿⣿⣿⣦⡀⠀⣼⣿⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⠀⢸⣷⣧⣤⠋⢻⣿⣿⠿⠿⠓⠑⠈⠙⠛⠛⠻⠿⣿⠃⠷⠾⠏⠛⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⠁⠀⢀⡼⠃⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠙⢧⠀⠀⡼⠁⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⣸⡀⠀⠈⠀⠀⠀⢀⣾⣿⣟⣋⣿⣿⣆⠀⠀⠀⠀⠀⣲⠇⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠈⣻⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢹⡀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣴⡿⣿⡄⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠻⣄⣘⣦⡤⠔⠓⠁⠀⠀⠈⠋⠲⢦⣀⣠⣎⡠⠏⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠲⠦⠤⣄⣠⡠⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⢸⡿⢓⠂⢠⢠⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠆⠰⣊⡽⠢⠄⠈⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠠⡀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠒⠠
⢺⡀⠀⠀⠀⠒⠀⠈⠉⠀⠀⠀⠀⠀⢒⡀⠔⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡁⠂⠀⠀⠠⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣬⡍⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠖⠂⠨⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢌⠋⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⠀⠓⠒⢃⡬⠊⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠽⣶⣶⠂⠀⠀⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⠤⣤⣤⣤⡤⠤⣤⣤⠤⣤⣤⣤⢤⣤⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣻⠀⣼⢃⡘⣿⢰⡇⣿⠰⣇⠿⢸⠀⢸⠀⢿⠀⣐⣠⢿⡶⠄⠀⠄
⠀⠀⠀⠀⣷⣶⠀⠀⡈⠀⠀⠘⠛⠛⠛⠛⠋⠛⠛⠛⠛⢛⠛⠛⡛⠛⠛⠛⠛⠋⠀⠀⠌⠉⠁
⠀⠀⠀⠈⠩⠋⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃⠀⠀⠀⢀⡐⠀⢀⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡇⢀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢲⣭⣷⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⡘⢉⡡⢤⣐⠘⢰⢄⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⡁⠈⠊⠏⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠂⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⡀
⣱⠀⠀⠀⠀⡀⠀⠀⠀⠐⠛⠃⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠿⠿⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠂⠁⠀⠀⠀⠀⠂⠀⠀⢀⠀⠁
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠆⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠰⠻⡟⠂⠠⣀⠀⢈⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣾⡏⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣤⣼⣿⣿⣿⢷⢁⣄⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⣻⢿⣿⣿⣿⢸⣿⣯⣷⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡈⢦⡀⠰⣆⣰⠏⢸⣿⣿⣿⣿⣿⡁⢷⢀⡀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣌⠓⢄⣀⠳⡀⢸⡟⣿⣿⡀⣿⣿⣿⣿⣿⣿⡿⣼⣿⣇⣿⣀⣄⣸⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⣌⡳⣶⣿⣤⣽⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣦⡙⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣇⡶⢣⠀⣀⠴⠂
⠀⠀⠀⠀⠀⠀⢈⡓⢤⣰⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⣻⠋⠁⣠⠆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢞⡡⠶
⠀⠀⠀⠀⣄⠀⠈⠹⣦⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣤⠄⠀⣴
⠀⠀⠀⠀⠈⠓⢤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡷⠤⠴⠃
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⢄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠀⢰⠀⠀⠀⡴⠁⠀⠀⠀⠈⢃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⢠⠀⢀⡞⠀⠁⣀⡤⠤⠶⠖⠒⠺⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇
⠀⠀⠀⠀⠈⠦⠊⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠞⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡠⠴⠒⠒⠒⠒⠒⠤⠄⠀⠘⠀⡟
⠀⠀⠀⣀⠄⠈⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠐⣌⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣦⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢰⠁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠧⠞⠀⠐⠀⠀⢀⡠⠴⠒⠒⠓⠲⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢃⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⠀⠘⡟⠛⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢀⣀⠀⠀⢢⠜⠙⠛⢛⠟⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⡜⢁⡄⠀⢰⠃⠀⠀⡴⢃⣀⣀⡤⠖⠀⠤⢄⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠡⡎⠀⠀⠸⣤⡤⠞⠁⠀⠈⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠑⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡤⠤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠳⢄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠳⣄⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣠⠤⣄⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢴⡷⣼⠕⠁⠀⠀⠀⠠⠀⠈⠑⢲⡿⠐⠀⢠⠞⡁⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇⢄⠀⢸⡇⢿⡐⣶⠀⡴⢛⡀⣷⠎⡿⢸⡅⡸⢃⣟⠀⣴⢀⡄⣴⢃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⠀⢸⡇⠸⡇⢿⡐⠃⠺⠆⠻⠐⠧⠘⠛⠇⢸⡗⠈⠧⢾⣱⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠼⠁⠀⠀⠀⠀⠀⠀⢠⣸⠂⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢅⡐⠈⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠓⠔⠛⠋⠀⠀⣠⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⣄⠀⠰⣄⡀⣸⠧⠖⠒⢶⡇⢀⠀⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣃⡿⠀⣹⠆⣴⢛⠂⣾⠀⢰⡿⢸⡇⠸⣄⢧⡹⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠞⠁⠀⠻⠀⠁⠛⠀⢿⡠⠙⠒⠸⡏⢂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⢛⣡⡶⠖⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣠⣶⠿⠋⠁⣠⠟⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢠⣤⣤⣍⡙⠛⠿⢷⣶⣤⣄⣀⡀⠀⣠⣴⡾⠟⠛⠛⠛⠻⣿⣶⣾⡿⠋⠁⠀⠀⣼⠋⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠉⠛⢷⣄⡀⠀⠉⠙⣛⣿⡿⠛⢳⡄⠀⠀⠀⠀⢀⡏⠀⠉⠙⠓⠀⠀⣼⣃⣤⣤⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⣠⡀⠹⡄⠀⠀⠀⢸⡇⠀⢶⣄⠀⠀⠘⠋⣽⠏⠁⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠐⠿⢿⣟⠛⠀⠀⢀⣴⢏⠤⣄⢹⡄⠀⠀⢸⣇⡔⢲⡟⢦⡀⠀⠈⢁⡀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠉⠃⠀⠀⠚⠁⠹⣶⡿⢸⡇⠀⠀⠈⢿⡻⠿⠃⠀⠀⠀⠀⠈⠻⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣀⣀⣀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠃⠀⠀⠀⠀⠀⢀⡴⠋⠀⢮⣥⣶⣾⡷⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠙⣿⡋⠀⠀⡀⠀⠀⠹⡆⠀⢀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⠀⠀⠀⢺⡀⠀⠘⢦⣀⣴⠏⠳⠦⠴⠃⠀⠀⣰⣇⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢷⣶⣤⣛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⠃⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢀⡟⠀⠀⠀⢼⠓⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢿⡈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢸⡇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⡇⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⣷⠀⠀⠀⢹⡎⠳⠆⠀⠀⠀⠘⠋⣾⠀⠀⠀⢸⡇⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠸⣧⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣸⠏⠀⠀⢀⣾⠁⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⠖⠘⢷⡀⠀⠀⠙⢶⣄⡀⣠⡾⠋⠀⠀⢀⡾⠃⠲⠾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣈⣻⣄⠀⠀⢷⡌⣿⡃⣾⠀⠀⢀⣾⣁⣀⣀⣀⣈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠻⢷⣶⣾⣿⠿⢿⣿⣶⣶⠿⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠸⣿⣿⠀⢀⣠⠆⠀⣼⣿⣿⣷⠀⠀⠘⢦⡀⠸⣿⣿⠀⣰⠋⠀⠀⢰⣿⣿⠿⠞⠀⡀⠀⠀⣿⣿⣿
⠀⢀⣀⣤⣶⣿⣿⡟⠋⠀⠀⣇⣘⣻⣿⣯⣀⣀⡀⠀⠹⣷⣿⣿⡿⠁⠀⢀⣠⣾⣿⣧⡀⠀⠀⢧⣠⣴⣾⣿⣶⣄⢀⡤
⠀⠈⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⠉⣿⣿⡇⠈⠉⠁⠀⠀⢸⣿⣿⡇⠀⠉⠉⠁⣿⣿⣏⠉⠓⠆⠀⠀⢸⣿⣿⡏⠉⠉
⠀⠀⢴⣄⣼⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⠂⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⣸⣿⢿⣧
⠀⠀⠀⠈⠉⠁⢹⡇⠀⠀⠀⠀⠀⡿⣠⠞⠁⠀⠀⠀⠀⢸⠏⠸⡇⠀⠀⠀⠀⢧⠸⢦⠀⠀⠀⠀⠀⣿⠃⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠐⠇⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠷⠀⠀⠀⠀⠨⠃⠀⠙⠀⠀⠀⠐⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⡤⠒⠂⢉⣉⣑⣆⡀⠀⢀
⠀⠀⠀⠀⣬⡴⠾⠛⠛⠉⢉⣉⡤⠐⠊
⠀⠴⠊⠁⣤⣤⣶⠖⠚⠋⣤⢿⡇
⠀⠀⠀⠀⣿⣿⠈⢀⣒⣀⠉⣸⠁
⠀⠀⠀⢠⣿⣿⣦⣌⠒⣁⣴⡏
⠀⠀⢀⣾⣿⣿⠿⠟⠀⠘⢿⡤⣀
⠀⠀⣾⣿⠟⢁⠀⠀⠀⠀⡼⠀⡈⠣
⠀⢸⡿⠁⣴⠉⠀⠀⠀⢨⠋⠀⢱⠀⢣
⠀⡘⢁⣾⣿⡇⠀⠀⠀⣜⠃⠀⡘⢃⠈⡄
⢰⠁⣼⣿⣿⣦⠀⠀⢰⡉⠀⠀⡇⠈⡄⠘⡀
⡆⠀⣿⣿⣹⣿⠀⠀⣎⠃⠀⠀⠇⠀⠰⠀⠱
⡇⠈⣿⣿⣿⠇⠀⢠⡙⠀⠀⠀⠸⡀⠀⠡⠀⠱
⠰⡀⢻⣿⣿⠀⠀⣬⠃⠀⠀⠀⠀⢁⠀⠀⠱⡀⢡
⠀⢱⡄⠣⣀⠀⠉⠛⠠⠀⠀⠀⠀⠘⠀⠀⠀⠐⡄⠣⡀
⠀⠆⠈⠰⡀⢉⣦⠀⠆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⣀⢨⡆
⠸⡀⠀⠀⠈⠛⠛⡘⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢻⡇
⠀⠙⠂⢤⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⣦
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡀⣀⡀⢀
⠀⠀⠀⠈⠀⠒⠀⠐⠀⠰⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣀⣤⣤⣀⡈⠳⣄⡀⠀⢀⡀⡀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠿⢿⣷⣾⣿⡀⢠⣞⢻⣛⣀
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠍⠀⡈⠁⠈
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠀⠀⠀⠀⠀⢀⠀⠐⠃
⠀⠀⠀⠀⢀⣴⣤⡇⠀⠀⣧⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣁⢰⠁⠀⢘⡁⡴⡋⡀
⠀⠀⠀⢴⣿⡿⠋⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠈⠀⣶⠄⠈⢀⣦⠁⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠋⠌⠛⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢠⡟⠛⡆⢀⠈⢩⠆⠀⠀⠀⠀⠀⠀⠀⡋⠉⢙⠀⠀⠂⠀⠀⡀
⠀⣀⣰⣆⠀⠀⠀⠀⠰⡍⠬⠆⠀⠀⠀⠀⣸⠉⠉⠇⠶⠀⢺⣦⣠⠁⣾⣦⣾⡀⠀⢀⠤⣄⠀⠀⢸⡷⢀⡾⠦⠀⠀⠚⠉⠙⡆
⠀⣿⣿⣿⣷⠀⠁⡆⠂⣠⢀⣦⣤⠀⠀⣾⣿⣣⣴⠁⡧⢠⣼⣿⣯⠄⡁⢸⣿⡇⠀⠠⠀⢈⡄⠐⠇⠀⢀⣠⡗⢀⡠⢶⡄⢠⡇⠀⠀⠀⣄
⠀⢸⣿⣿⠏⠀⠀⠀⣼⣧⣿⣿⣿⣷⠀⣿⣿⣿⡏⠀⣧⣌⣛⠙⠃⠀⠘⠈⣿⣦⠀⠴⣧⣼⡃⠀⠀⠺⣿⣧⠈⠀⢡⣾⣷⣿⣿⡀
⠀⣼⣿⣿⠀⡇⠀⠦⢻⣿⣿⣿⣿⠱⠶⣿⣿⡇⠀⣿⣿⣿⣩⣵⣤⡀⠀⢀⠹⠛⣁⣶⣾⣿⡇⠀⠀⢐⢟⡟⣳⣄⣸⣿⣿⣿⡙⠁
⠀⣿⣿⣿⣤⡇⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⣶⠇⢨⣭⣭⣿⣽⣿⡿⠀⠀⢡⡄⣺⡿⣿⣿⣟⠑⠀⠀⢼⣿⣿⣿⣿⣯⣭⣭⣉⣥
⠀⢹⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⢛⣿⣿⢠⣿⡿⣻⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿⡟
⠀⢸⣿⣿⣿⡇⠀⢸⣿⡟⣿⣿⣿⡇⢸⣿⣧⣿⡟⠁⢿⣿⣿⣿⡄⠀⠀⣸⣿⣿⠀⠙⣿⣿⣧⠀⠀⢸⣿⠁⢸⣿⣿⣿⢿⣿⡁
⠀⢸⣿⣿⣿⡇⠀⢸⣿⡇⢹⣿⣿⡆⠘⣿⡏⢿⣇⠀⠀⠻⣿⣿⣿⡀⣼⡟⣿⡇⠀⣸⣿⡿⠟⠀⠀⢸⣿⠀⣸⡿⠘⣿⡇⣿⡇
⠀⢸⣿⣿⡟⠀⠀⠈⣿⣧⠘⣿⣿⠅⠀⣿⡇⠘⠿⠄⠀⢀⢸⣿⡜⢿⡿⠀⠛⣀⣠⣿⡏⢀⠀⠀⠀⠸⠿⠀⠿⠃⠀⡘⠿⣿⡇
⢀⣾⣿⣿⠀⠀⠀⠀⠾⣿⠃⢿⣿⡄⠀⠉⣑⡀⠀⠀⠀⠀⠀⠉⠑⠂⠠⠄⠀⠈⢄⣘⡀⠀⠀⠀⠀⠐⠀⠠⡀⠀⠀⠀⠀⠘⠛
⢨⣿⣿⡟⠀⠀⠀⠁⠈⠀⠀⣌⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢸⡟⠁
⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠻⠿⠋⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣀⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣮⣴⣦⣤⣄⣀⣀⣀
⠀⠀⠀⣠⣿⣿⣿⡿⠛⠛⠉⠉⠉⠉⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠙⣿⣿⡇⠈⠛⢻⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⡷
⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣀⠀⠀⠀⣀⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠘⣿⡏⠙⠿⣿⣧⡀⠀⠈⠛⢿⣿⣿
⢠⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢿⡧⠀⠀⠀⠈⠁
⠿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠛⠁⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⠀⢿⣇⠀⠀⠀⠀⣸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⣀
⠀⠀⢀⡀⠠⠓⡀⠀⠀⠄⠀⠦⠊⠛⢲⠤⠀⢀⣀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡴⠛⠉⠋⠀⠄⠀⣐⠐⢀
⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠟⠁⠓⠘⠇⠘⠋⢲⠞⠒⠁⠾⠁⠠⠈⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣸⠟⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠅⠀⠉⠒⠂⠀⠰⠀⠀⢠⠤⠀⠦⠀⠀⠀⠴⠂⢤⠄⠀⠚⠁⠘⠉⠉⠁⠀⢀⠀⠀⠁⠀⢸⢥
⠀⠀⠀⠀⠀⠐⠀⠀⠚⠠⡬⠑⠀⠸⠗⠀⢈⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠥
⠀⢀⣀⣤⣄⡤⠀⠂⠀⠈⠀⠀⠀⢀⠀⠀⠀⠉⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠫⡄⠀⠐⠂⠀⠲⠌⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠌⠀⠀⢄⠘⢁⠀⠀⠘⠁
⠀⠀⠀⡐⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡐⣒⠀⠀⠂⢀⡀⠀⡄⢸⡆⡀⠀⢄⠈⠉⠀⠀⢀⡴⠀⠨⠀⠀⠀⠀⠇⠀⠀⠀⣠⡄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⡀⠄⠀⡔⡷⠀⠯⠼⣧⢼⢦⠼⠷⠄⠀⠀⡖⠀⠀⠀⠀⠐⠀⠀⠚⠂⢠⠀⠈⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠎⠀⠃⠞⠚⠀⠀⠂⡇⠀⠀⠀⠀⠀⡄⠀⠀⢠⡀⢠⠀⠀⠀⢀⠆
⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢖⡦⢀⢻⠀⢾⡘⠺⠈⢿⡚⠊⠓⡆⠀⠋⠀⠈⠀⠀⠀⠀⠀⠠⠈⠘
⠀⠀⡀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⡀⠛⢀⡓⠀⣉⠀⠋⠁⢂⡑⠷⠀⠀⠆⠀⠂⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢨⠅⠀⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⡀⣠⠀⠀⠀⢠⡄⠀⠙⣓⠃⣼⠃⠠⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡾⠀⠦⡀⠀⠠⠄⠀⠀⢀⣀⣀⡀⠀⠀⠐⠊⠛⠀⠀⠀⠈⠀⠠⢀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠂⠀⠀⠂⠀⠚⠋⠀⠀⠀⠀⠈⠀⠝⠲⢤⣉⣀⡀⠀⠉⠀⡀⠀⠄⠐⢊⠠⠸⢀⡀⠀⠀⠀⣀
⠀⠀⠀⣮⢧⢆⣄⠀⠀⠀⠀⠀⠀⠈⠫⠉⠁⠀⠐⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⢀⠠⠀⠄
⠀⠀⠀⠁⠁⠀⠁⢐⢄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣼⡃⠠⠠⠀⠀⠀⠀⠀⠘⢞⡛⣭⡴⣄⣶⠀⠀⠄⠀⠨⠀⠀⡆⢸⠀⡆⡆
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠳⣧⣾⣗⣻⡇⡮⠀⠄⠠⠸⠀⠀⠛⠘⠀⠃⠃
⠀⠀⠀⠠⠄⠐⠆⠠⠤⠀⠀⠢⣀⠀⠆⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠷⠍⠗⠀⢦⡤⢲⡀⠠⣆⠀⠀⠄⠲
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠙⡇⠀⠀⢤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⠀⡀⠀⠀⠀⠛⠀⠀⠲⠄⠀⠀⢀⡤⠘⣷⠀⠀⠀⢀⠀⠀⠠⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣠⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣜⣻⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠁⢉⣩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠊⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⡗⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣷⠠⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡟⣿⠻⣿⣿⣿⡀⢂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠘⣿⠇⣰⣾⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⣀⠉⠀⠀⠀⠀⢠⣧⣤⣿⣿⣿⣿⣿⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⢸⡇⢸⡇⠀⠀⠀⠀⠛⠁⠈⠉⠛⠛⠋⠈⣧⠀⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡚⠀⠀⠀⠀⠐⠀⣤⡀⡀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠁⠀⠀⢀⠌⠀⣠⣿⣿⠿⡀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠂⠀⠀⠨⡽⠋⠀⢳⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠀⢤⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣀⣠⣴⠞⠁⠀⠀⠈⣇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⡄⠐⣲⣿⣶⣈⣀⣠⠖⠀⠀⠐⠀⠒⠂⠠⢤⣀⣤⠀⠀⠀⠐⠐⢩⠻⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠩⠟⠙⠛⢻⠋⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⡶⠶⢦⣤⡀⠀⠀⢅⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣠⠂⠙⣿⡇⠀⠀⠀⢻⣿⠐⠀⠀⠤⡐⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠍⠁⠀⠀⠈⠁⠋⢀⠔⠋⠈⣷⣤⣤⣶⣀⣠⡟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠛⠒⠒⠂

⠀⠀⠀⠘⣧⡀⠀⠀⠀⢠⣤⢲⡴⣲⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠂
⠀⠀⠀⠢⢡⠐⢤⠀⠀⠘⣿⡾⠞⠁⠀⠀⢀⣀⣀⣀⣀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⣀⠀⠀⠈⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆
⠀⠀⠑⢄⠘⠆⠀⠀⢀⡔⢩⠀⠀⠀⠀⠐⠛⢢⡤⠀⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠰⢃⠀⠀⠀⣴⣾⠀⣾⡿
⠀⠀⡀⠈⠁⠀⢀⡴⠣⡈⣿⠀⠀⠀⠀⠀⠚⠃⠒⠒⠀⠤⠅⢀⣤⠀⠉⠁⠀⠒⠠⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠒⢾⣏⣩⠟⠃⠀⠙⠁
⠀⠀⠀⠀⢀⡴⣋⠐⢄⠘⣿⠀⠀⢀⣀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠢⠀⠀⠈⠲⣄⠀⠀⠟⠁⠉⠛⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⡀
⠀⠀⢀⡴⠋⠠⣌⠱⣄⢳⡏⠀⠀⢙⣞⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢁⠀⣤⠌⣢⡀⠀⠀⠀⠀⡀⠀⢤⣞⠓⠀⠈⡿⠇⠠⠅
⠀⢰⡟⠒⠚⠦⣌⣆⠘⣎⡇⠀⠀⢸⠹⣆⣰⠋⣿⠀⠀⠀⣞⡦⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡄⠈⠓⠀⢀⡤⠀⢠⠜⠉⠻⣀⣀⣠⠇
⠀⠀⠙⠦⣄⣀⠀⠉⠳⣿⠇⠀⠀⢸⠀⠙⠃⠀⣿⠴⠚⣹⠋⠀⢴⣏⠩⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡤⠖⠉⠄⠀⠀⢀⣀⢀⣀⣬⠁⠐⢄⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⣿⠭⠭⢭⣛⠲⢤⣠⠏⠀⠀⠀⠾⠋⡜⠑⢩⡟⢛⢶⠲⡶⢶⡶⡖⡻⣏⢹⠙⣄⢰⠺⠆⠀⠈⠒⠚⠲⠀⠀⠀⢰⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠲⣖⣶⣬⡙⢶⠋⢀⡤⠤⣄⠀⠀⠙⠚⠁⣷⠃⢸⣠⣀⡌⢧⠀⡇⠈⠺⠀⠈⠛⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠸⢆⠄
⠀⠀⠀⢴⠶⠒⠒⠒⢒⡶⠖⢦⠀⠀⠉⠒⠾⠭⠿⠃⢠⠏⡴⠶⣌⢳⠀⠀⠀⣀⣤⣄⡈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠐⡧⠀⣤⣀
⠀⠀⠀⠈⠳⣄⠀⠀⣾⡩⠽⠾⠦⣄⠀⠀⠀⢀⣀⠀⠸⡜⡇⠀⠈⢧⡇⢀⣾⠟⠒⢆⢻⠀⠀⠀⢰⣆⠀⠀⠀⢸⠁⠟⠁⠀⢠⠖⢉⡠⢪⠞⢀⠉⠛
⠀⠀⠀⠀⠀⠈⠳⣄⡿⢤⡠⠔⠒⠚⠻⢦⡀⠈⠻⣍⠲⢵⡹⣄⠰⡘⣷⣾⡣⠂⢀⠌⡼⠀⠠⣠⠤⠙⠀⠀⣀⣠⡤⠤⠄⠀⠈⠀⠉⡜⢁⡤⠃
⠀⠀⡋⢋⠢⡀⠀⡈⠓⠴⠛⢦⣀⠤⠤⠤⢽⣖⠺⠿⣅⣀⡉⠻⣧⣧⣿⡟⠁⣀⣴⡾⠥⣤⠆⠀⠀⣴⡙⠒⠻⣄⠀⠀⢀⠀⠀⠀⠀⢈⡉⠤⠤⢀
⠀⢠⠛⢶⣌⠁⠀⣍⢦⠀⠀⠀⠻⡄⣀⡤⠶⢻⡄⠀⡤⠬⠭⠷⢾⠧⠀⣹⣿⣭⣤⢤⠬⠑⣦⠀⢸⡇⠈⠉⢉⠃⠀⠀⢸⠀⠀⠀⡴⠅⠐⠂⠂⠀⠑⡄
⠀⠀⠶⡒⢆⠀⠀⣈⣟⡀⠀⠀⠀⠻⣥⠴⡖⠋⠀⠀⢷⡀⠀⠀⡸⠀⠀⡀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⢠⠏⢧⣀⢀⡼⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠈⠁⠀⠀⡏⢨⠇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠉⠉⠉⡇⠀⢀⠋⠉⠉⡏⠁⠀⠀⠀⠀⠘⢦⠴⠃⠀⠀⠈⢩⡄⠀⠀⡇⠀⠀⠂⡀⠀⠀⠀⡘
⠀⠀⠀⢀⡤⠶⠶⡇⣼⠠⠤⣀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⡇⠀⡘⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠁⠎⠀⢀⠠⠀⠀⡴⠁
⠀⠀⠀⢸⠓⠲⠤⠽⠥⠤⠴⢚⠃⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⢀⣠⣿⡤⠄⠀⣆⣠⣁⣤⠶⠊
⠀⠀⠀⢸⣤⠋⠢⠚⣆⡰⠓⡼⠀⠀⢀⡷⢼⣷⡆⠀⠸⠤⠤⠤⠧⢼⣄⣀⣀⡇⠀⠀⠀⠀⢀⣀⡈⠁⠀⣀⣀⡀⠈⠁⠀⠀⠐⢏⡇
⠀⠀⣠⠼⣇⠀⠀⠀⠈⠁⢠⠇⣀⠀⠈⠿⣤⡼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⢻⠋⠉⢉⣩⣭⣓⠊⠈⢩⣑⢂⠀⠠⠀⠀⠀⠀⢀⣄
⠀⠀⠳⢤⣈⣓⠶⠤⠤⢖⣋⣠⠼⠂⢀⡼⠉⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡇⡞⠀⡰⢹⢋⣭⣭⠳⡄⣿⣼⡛⢠⠁⠀⠀⠀⠀⣸⠀⠙⣻⠷
⠀⠀⠀⠀⠈⠳⣭⣭⡭⠟⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⠀⢇⠘⢆⠠⠀⠢⡀⠀⠀⣇⢧⠀⠱⣼⡜⠿⠿⣣⠇⠀⢠⠁⡆⠀⠀⠀⣴⠉⠉⠳⡞⠁
⠀⠀⠀⠀⠀⣠⣴⣖⠲⣄⠀⠀⠀⠀⢀⡀⠀⢘⠱⡄⢄⠈⠢⡀⠑⣄⠑⠳⠀⣘⣶⡦⠙⢾⣦⣀⠈⠉⠓⠚⠁⠀⢠⠃⢀⠀⠀⢀⠾⡈⠑⠦⢤⡞
⠀⠀⠀⠀⡞⢁⠄⠈⣷⢸⣤⡄⠤⠒⢯⢹⡆⠈⠣⡈⠢⢡⡀⠐⣴⣄⠱⣄⠻⠿⠀⠐⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠁⠀⢸⠀⠀⢸⡓⢌⡑⣒⠞
⠀⠀⠀⠀⢧⠈⠳⠴⠛⠁⠀⠀⣀⡤⠞⠋⠀⠀⠀⠈⠢⡀⠶⣿⠋⠙⡀⠈⠑⠂⠄⠊⠀⠀⠀⠀⢠⡀⢸⠙⡆⠀⠀⠀⠸⠀⢴⠋⠝⡲⠚⠁
⠀⠀⠀⠀⠀⠙⠒⠒⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠔⠁⠀⠀⠀⢀⡀⣀⡀⣹⢆⣀⠷⣄⢑⡗⠐⠀⠀⠀⠀⠈⠳⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠐⠄⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣠⣤⣤⣄⡀⠀⠢⠄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⣿⣿⣿⣿⣿⣿⣦⡀⠡⠸⣧⠙⠲⠦⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠈⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⡷
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⡏⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡀⠀⠀⡄⠀⠀⣠⠎
⠀⠀⠀⠈⡇⠀⠀⠈⠹⠶⢤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣆⠀⠹⢿⣿⣿⣿⣿⣿⡿⠷⠤⠴⠤⠤⠽⠖⠊⠁
⠀⠀⠀⠀⠙⢤⣀⠀⠐⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⢹⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⠀⣿⣿⣿⠟⠛⠻⢿⣿⣿⡷⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠙⡩⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠐⠀⠠⠤⠐⠈⠀⠈⠐⢄⣀⡤⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠔⢀⡴⠋⢳⠶⠤⢤⣄⣀⣀⣀⣀⣤⡄⠀⠀⠀⡴⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⢁⡴⠋⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢡⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡞⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠳⢄⣘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⢮⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⣠⠂⢠⠆
⠀⠀⠀⢠⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⣄⠀⠉⠁⡄⠊
⠀⠄⠀⠀⠣⡀⠄⣀⠀⠀⢀⠀⡠⠀⠀⠈⠒⠀⠈⠉⠙⠆⢀
⠀⠀⠢⢈⠒⠵⠈⢁⡀⠆⠀⠘⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠸
⠀⠀⠄⠈⠁⡀⠐⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⡀⠂
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢹⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢂⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⣤⣤⣹⣄⣡⡀⠀⠤⠤⠤⠐⠒⠊⠉⠀⠀⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢂⠀⠀⠀⣀⠴⠃⠀⠉⠀⠀⠀⠀⡈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢤⡤⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠐⢀⠀⠀⠀⢀⠀⣠⡤⠖⠋⢠⣾⡇⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢰⠀⠈⢋⡀⠈⠉⠁⠀⣀⣤⣾⣿⣿⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡦⢀⡀⠀⠀⠀⠠⠐⠁⠀⠀⠀⢸⠆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡸
⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠙⢿⣿⠋⠀⠁⠀⠟⣻⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠉⠒⠡⠤⠤⠚⡁⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⣏⡀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⣀⣀⣀⠤⠶⢋⠀⠎⢉⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⡳⠀⢀⡅⠀⠁⠒⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠄⢀⣀⠀⠠⠖⠋⠀⠀⢁⢡⡞⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠙⡀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢦⣀⢀⠜⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠠⠐⣊⡤⠾⣍⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⢉⣴⠃⣀⡞⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠘⣆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢆⠉⠉⠉⠉⠉⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡌⠢⣀⠀⠀⠀⣰⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⡙⠛⠛⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠔⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡲⠒⠉⠀⠀⠀⠀⠀⠈⠉⠒⢖⡒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠸⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⡆⠀⠀⠀⢿⣦⢃⡤⠒⠒⠦⡘⢶⠟⠀⠀⠀⢣⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢰⠋⠉⠑⠒⠒⠒⢩⣶⣤⣴⣦⠈⠓⠒⠊⠉⠉⠙⡆⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⡀⠉⣻⢿⣉⣀⠀⠀⠀⠀⠀⠀⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠈⢫⣁⣀⡏⠁⠀⠀⠀⠀⠀⣠⡷⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⠤⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⠚⠁⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⣇⠜⠓⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡟⢦⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⠀⠀⠈⠒⠤⣀⣠⠤⠚⠁⠀⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⠈⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⣀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠀⠀⡰⠉⠑⠒⠒⠀⢸⠀⠀⠒⠒⠒⡉⢆⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠤⣇⡽⢿⣀⣲⣀⡤⠜⠳⠤⣀⣽⣀⡽⠮⣼⣤⠗⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠜⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⡆⠀⠀⠀⠀⠀⢠⡖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⠇⠚⠁⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⠀⢠⡟⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢸⡆⠀⠀⠀⢀⣀⣀⠛⢦⣴⡦⠖⠋⣀⠀⢠⡏⡰⠃⠀⠀⠀⠀⠀⣿⣣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⣷⠀⠈⡿⢻⣷⠀⢰⡏⢀⣿⠀⢸⣿⠀⢠⡟⢀⡇⣸⠏⠀⣾⠀⢀⡶⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡸⢻⣂⡞⠁⣼⡏⠀⣿⠁⣼⡿⠀⣿⡇⠀⣸⡏⠁⠀⣿⣤⠖⣿⠀⣾⡇⢀⣾⡇⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⣼⡏⠀⠀⣿⠁⣸⠻⠶⠻⢧⠼⣿⡇⠀⣿⡇⢀⡜⢻⣿⠀⠛⠞⢸⣇⠞⢹⡇⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢹⡇⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢿⡇⣼⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⡇⠀⣠⣄⠀⠀⣀⠀⢀⠀⣀⣈⡉⠁⠀⢠⡖⢳⡄⠾⠂⣴⡄⠀⣀⣠⡶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢸⡇⢠⣿⠼⡇⢸⣿⢃⢸⠀⣿⡇⢻⠀⠀⣿⠀⣾⡇⣶⠀⣿⠁⢠⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣸⠃⠸⠿⠀⠇⠸⠿⠀⠛⠀⠿⠧⠟⠀⠀⢿⢔⣽⡟⡯⠀⢿⣄⡌⠀⢿⡇⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣽⡇⠳⠊⠀⠉⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠒⠁⠀⠀⠀⣴⡆⠀⣼⡏⢸⠆⠀⠀⢀⡴⠊⠀⠀⢠⡿⠀⠀⢀⣶⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⢰⣿⣇⣠⣿⠗⠋⠀⠀⠀⢾⠀⢀⣠⡴⠟⠁⠀⢀⣾⡇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢸⣿⠀⠀⠀⠀⢀⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⠔⣀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⡟⣰⣿⡄⣴⡏⣹⡆⢠⣶⣤⠊⣿⠀⣼⣿⠎⠌⠀⢺⡧⠜⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠃⣿⠁⣿⢀⣿⠇⢸⣿⡇⢠⡿⠀⣿⡟⢻⡄⠀⡎⢻⣖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⢿⡿⠀⣿⣤⠿⠞⣿⡀⣸⣿⠇⢸⣇⡰⣿⡇⢸⠃⡼⠀⡎⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠈⠉⠁⠀⠀⠈⠋⠁⠀⠳⠞⠁




⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠛⠛⠉⠙⠛⠻⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠻⠟⠛⠉⠁⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠶⠶⠶⠶⠶⣼⣆⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⣼⣥⠶⠶⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⣽⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠻⣿⡿⠀⠀⠀⠀⢸⡇⢰⡇⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⣷⠀⠀⠀⠈⠛⠋⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⢿⣖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢶⣶⡿⠿⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠉⠉⠛⠛⠛⠋⠉⣉⠥⢊⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⣀⣀⠤⠤⠶⠚⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠉⠉

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

⠀⠀⠀⠀⡠⠒⠂⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⠐⢄
⠀⠀⠀⢰⠀⢀⡀⠀⠀⠀⢑⡤⠀⠐⠛⠯⢭⡘⠂⡐⠁⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠸⠀⠀⠈⠱⣀⢞⠁⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠘⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠇⠀⠀⠀⡟⠋⠙⠀⠀⠐⠋⠉⠳⠄⠀⠀⠀⠈⡇
⠀⠀⠀⠀⡘⠀⠀⢐⡠⠒⢄⠀⠀⢀⠄⠒⢤⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢐⠀⠀⠀⣼⠁⣴⣲⡅⠀⠂⢠⡶⡄⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠇
⠀⢀⣀⣀⣈⣉⢁⣾⠄⠿⠟⠤⠀⠅⠘⣿⠃⠀⠀⠀⠀⠀⠀⠈⢇⠒⠐⠊
⣾⣿⣷⣤⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⣄⠡
⡛⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙
⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡶⡄
⢡⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡰⠁⠃
⠀⠓⢄⠀⢈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⡀⠠⠚⠁⠀⠘⡀
⠀⠀⠀⠀⠉⠀⠈⠱⢲⣤⣤⣶⣶⣿⠃⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠟⡻⠉⢙⠃⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢸⠀⠀⢀⠔⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠸⠔⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢀⡰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣀⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⡼⠠⠂⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⢄⠀⠀⠀⠀⠀⡄⠀⠀⠀⡞⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢠⡀⠀⠀⡇⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠂⡇⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⣄⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠳⢄⡇⠀⠀⣆⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠓⠦⠤⠤⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠇⠀⠀⠀⠀⢠⠀⠀⢠⡆⠑⠤⢵⣄⡀⠀⠀⠀⠀⠀⠀⢠⢏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠃⠀⠀⠘⠀⠀⠀⡶⠋⡿⠀⠀⢸⠀⢀⣀⣠⣠⣋⠱⠀⠀⠀⠀⠰⡁⠀⠛⢄⣀⣄⢀⣀⡰⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⡎⠉⠀⠀⠃⠀⠀⡠⠳⢶⠇⠀⠀⠘⠉⡟⠩⠋⠉⠀⠀⣀⠀⠀⠄⠐⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠣⠤⠤⠐⠁⠀⠀⢦⣇⣇⠀⠀⠀⣠⠀⠓⠰⠤⠄⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⠦⢄⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠘⡇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡧⠛⠠⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢸⠇⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠁⢨⠀⠀⠀⠆⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡈⠀⡈⠀⠀⠀⢰⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⡄⠀⡇⠀⠀⠀⢘⡃⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢠⠊⠁⢀⠀⠀⠀⢲⠊⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡴⠁⢸⠀⢈⠀⠀⠀⠀⢣⡄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡸⠋⠀⠀⢄⠀⢸⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⡿⠉⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠆⠀⠠⠏⠈⢹⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠆⠐⢶⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⡉⠑⡄⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⡠⠴⠀⠀⠀⠀⠀⠰⠀⠀⠸⣀⢐⡎⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠘⡿⢠⣶⣤⠤⠄⠒⠈⠁⠀⢀⡠⠔⠉⡰⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡘⠡⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠰⠾⠀⠐⣢⣼⠿⠋⢠⣮⣤⡒⠲⠶⠉⠛⢁⡠⠊⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢰⠁⠀⡄⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣧⠀⢀⠈⠻⠛⠁⢰⣾⠇⢀⡋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠃⠀⠀⢡⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡨⢆⠘⡃⠒⠒⠒⠒⡆⢀⣎⠱⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠶⢁⠔⠁⠘⡀⢡⠀⠀⠀⡰⢀⠎⠈⣆⠇⠀⠀⠀⠀⠀⠨⣀⣀⡀⢀⡌⠀⠀⠀⠀⠀⠘⢤⣴⣶⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⢀⣼⡻⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁