⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡄⣴⣶⢶⣲⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣉⢴⣾⣿⣿⣇⣴⡼⠋⠀⠀⡀⠤⠤⠶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⢻⣺⣿⣿⣿⣿⡗⠁⠀⡐⣅⣊⡀⣠⣲⣤⡈⠑⣁⡠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠉⢶⡏⠀⣰⣿⡭⣵⣿⣛⣳⡀⠀⠈⠉⠉⠉⠋⠃⠡⠆⠛⠙⠳⢧⣄⣉⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⢂⠀⢸⡷⠀⠀⠁⠈⡤⣾⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⢑⣁⣈⣓⣃⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠀⢠⣅⣴⡏⠀⠈⠀⠀⠀⠀⠀⠘⡝⡿⣿⣿⣟⣿⣽⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢓⣋⣉⣙⠛⠂⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡾⠣⠀⣼⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣥⣧⡭⠃⢹⣿⣿⡄⢸⠭⠿⠷⠶⡰⠀⠀⠀⠀⠀⠀⠙⠘⠳⣦⠽⢶⡄⠀⠀⠀
⠀⠀⢰⢿⣱⡿⢀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢈⣼⡻⣾⣾⣿⣿⠉⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣻⡄⠀⠀
⠀⢀⡀⢿⡟⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣷⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡘⢻⢯⠀⠀
⠀⣾⣞⡘⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡞⣿⣿⣿⡟⠾⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⢸⣵⡀⠀
⢸⡟⢺⣥⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢣⣿⣿⣿⣷⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⣷⢻⡄
⣾⣇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢜⢯⠰⣧
⠘⢵⣂⣸⡆⠀⠀⠀⠀⠀⠀⠀⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢠⢟
⢤⡈⢚⣾⡇⠀⠀⠀⠀⠀⠠⠇⣰⠇⠀⠀⠀⠀⠀⢤⡀⠀⢠⣴⣾⢯⢷⣄⠀⠀⣀⣀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢐⠅
⣿⢷⣄⠑⠂⠀⠀⠀⠀⠀⠀⠀⣿⡁⢀⢠⣄⣴⣄⣠⣿⣴⠮⠟⠉⠀⠙⠄⣵⣜⣄⠾⢷⣬⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣾⢏
⢸⡏⢟⣖⡄⠀⠀⠀⠀⢀⠀⠋⠉⢁⣶⣿⣿⣿⣿⣿⣥⣎⠀⠀⠀⠀⠀⡔⠛⣤⡹⣿⣵⣿⣿⣿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⢸
⠀⢳⡄⠈⣷⠀⠀⠀⠀⣼⣽⠟⡛⠟⣳⢿⣿⣿⣿⣯⣿⡻⠀⠀⠀⠀⠀⠀⠀⢩⢧⣍⡛⠻⣿⣿⡿⣽⣿⣦⡀⠀⠀⠀⠀⢀⣿⡏⢠⡟
⠀⠀⠻⡷⣽⡇⠀⠀⣰⠿⣠⢶⡴⠞⡯⠟⡿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢚⡠⠀⠉⠳⠉⠟⠟⣹⣦⡀⠀⢀⡾⢳⠀⠿⠃
⠀⠈⢯⣮⢕⡛⣠⡾⣽⣿⢋⢌⢂⡡⣞⣱⢭⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⢰⣀⠀⠈⠠⠈⠉⠿⣶⣼⣇⡾⠀⠀⠀
⠀⠀⠈⢿⣝⢿⣻⣿⣿⣿⣟⣾⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔⠈⠀⠀⡀⠤⠙⠒⢤⡈⣈⡈⢡⣿⣿⣿⣷⣄⠀⠀
⠀⠀⠀⢐⣿⣿⣿⣟⠿⣝⡊⡍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣶⠟⠂⠉⠉⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⣸⣿⣻⢿⡇⠀
⠀⠀⠀⠘⣷⢿⢿⣯⣶⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢫⡟⠹⠿⣿⣿⣿⣷⡇⠀
⠀⠀⠀⠀⠿⠝⠁⠈⠟⣯⣄⣽⢿⣗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣜⣧⣴⣷⡇⠛⠁⠈⠻⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠁⢀⣀⡈⣟⠷⠶⣤⠤⠀⣀⢀⠀⠀⡀⡀⠀⠀⢀⡤⠖⢛⣋⡉⣐⡺⠁⠀⠋⠀⠀⠀⠀⠀⠘⠿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠁⠉⢀⣀⣄⡶⠷⢽⣥⣴⠞⠋⠀⢠⡖⠕⢁⣐⡯⠗⠰⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠠⠚⠞⠀⠀⠀⠀⠓⠛⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀