Cinnamon roll Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠶⠶⠶⠖⠒⠶⠶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⣄⣤⠞⠋⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⣠⣾⠟⠁⠀⠀⠀⣁⣠⡤⠶⠖⢚⡛⠛⠲⢦⣄⣀⠈⠁⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡼⣻⠋⠀⠀⠀⣴⢞⣭⠶⠚⠛⠉⠉⢉⡍⠛⠓⠶⢯⣝⡓⠶⣄⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⠟⣰⠃⠀⠀⠀⣾⡷⠋⠀⠀⠀⠀⢀⣀⣈⣀⡀⠀⠀⠀⠈⠙⠳⣌⡻⣦⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟⢰⡏⠀⠀⠀⣸⡟⠁⠀⠀⢠⡴⢛⣉⣭⣭⣭⣉⣛⠲⢤⡀⠠⣄⠈⠳⣌⢳⡀⠀⠀⡀⠀⢻⡀
⠀⠀⠀⢠⡇⠀⠀⣦⠀⣾⠀⣼⠀⡾⠃⢰⣿⠀⠀⠀⢠⡟⣰⠋⠁⠀⠀⠀⠈⠉⠻⢦⡙⣦⠀⠀⠀⠹⡎⣇⠀⠘⠃⠀⠈⣧
⠀⠀⠀⢸⠃⠀⠀⠈⠁⡇⠀⣿⠀⠀⠀⣿⣧⠀⠐⠋⠸⡇⢿⣀⣀⣠⣿⠀⠀⣠⠀⠈⢷⠸⡆⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⢿⠹⡄⠀⠀⠀⠙⠶⢭⣭⠵⠋⠀⠀⠁⠀⠀⢸⠇⡇⠀⠀⢀⡟⢸⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⢿⠀⢹⡄⠀⠀⠘⣇⠙⢦⣀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⢀⣠⠟⢠⡇⠀⠀⡼⢡⠟⠀⠶⠂⠀⠀⣿⡇
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠘⣇⠀⠻⣄⠀⢿⠈⠳⢦⣉⡛⠶⠦⢤⣤⣤⡤⠴⠶⠚⣋⣁⡴⠋⠀⢠⡞⣱⠏⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠙⣦⠀⠈⠳⣬⡀⠀⠀⠈⠉⠛⠓⠒⠶⠶⠶⠶⠶⠛⠉⠁⢀⣠⠾⢋⡼⠃⠀⡆⠀⠀⠀⢀⡟⣸
⠀⠀⠀⠀⠀⠘⣿⣄⠀⠴⠋⠈⠻⢦⣀⡀⠙⠓⠶⣤⣄⣀⣀⣀⣛⣀⣀⣀⣠⣤⠴⠞⣋⣡⡴⠋⠀⠀⠀⠁⠀⠀⢀⡾⢁⡟
⠀⠀⠀⠀⠀⠀⠸⣏⠳⣄⠀⠀⠀⠀⠈⠙⠓⠶⠶⠤⣤⣬⣭⣭⣭⣭⣭⠥⠴⠶⠚⠛⠉⠁⠀⠼⠀⠀⠀⠀⠀⣠⠞⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠳⢦⣀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣠⡴⠞⠋⠁⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠛⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠶⠒⠛⠋⠉⠀⢀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠶⠶⠤⠴⠶⠶⠶⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣨⡷⢊⣁⣀⡉⠒⠶⣶⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠇⠀⠻⠷⠬⠯⠿⠟⠀⠀⢈⣿⡆⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠉⠻⢿⣧⣀⣀⡀⠀⣀⡀⣀⣤⣴⡾⠋⠀⢀⢈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⣹⣿⡇⠈⢿⣿⠂⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣠⣿⠿⠛⠉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡃⢸⣿⣿⡇⠀⠈⠹⣧⣵⣄⣀⣀⣀⢀⣀⣀⣀⣠⣤⣴⡷⠾⠿⠿⠁⠀⠀⡀⠨⣷⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⡇⠸⣿⣿⣦⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠁⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⡿⠇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠉⢻⢷⣗⣠⣄⡄⠀⠀⠀⠀⡀⠀⢀⠀⢀⣀⣠⣤⣤⣦⣶⣶⡿⠿⠟⠋⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠀⠀⠀⠀⠀⠉⠻⠿⣿⡶⢴⠶⠷⠷⠾⠟⠿⠛⠛⠋⠹⠉⠂⠁⠀⠀⠀⢀⣴⣼⢣⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢸⡟⠁⢮⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⡆⢸⡏⠁⠀⢻⡄⢠⣶⣤⡄⠀⠀⣀⣦⠄⠀⠀⢀⣄⣀⣀⠀⣰⠟⠛⣇⠘⣇⢈⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣼⡇⢸⠇⠀⠀⢸⡇⣼⡟⠁⣧⠀⢠⣿⣿⡗⠀⢰⣿⠟⠋⠉⠉⠁⠀⠁⢻⡀⣿⠠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣾⠀⠀⠀⢸⡇⣿⠃⠀⢸⠀⣼⠟⠉⢻⡄⣸⠏⠀⠀⠀⠍⠀⠀⢀⣸⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣀⠲⣾⠁⣿⠀⠀⡹⣶⣟⣀⡀⢈⣿⢟⢀⠀⠀⢀⣤⣾⢧⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣽⣿⣾⣿⣷⣧⣽⣯⣿⣿⣿⣮⣦⣤⣼⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⣀⡤⢴⣾⣿⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⡠⢊⡗⡡⠂⣠⠔⢛⣏⣛⡒⠈⢽⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡟⠀⠀⢰⠁⣿⠰⡇⠀⡇⠀⠈⠉⠉⠙⡧⠀⠹⣦⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⣿⡇⠀⠀⢸⡀⢿⡀⠻⣄⠈⠀⠰⠴⠶⠊⢀⣀⣠⡿⠀⢳⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⢧⠀⠀⠘⣷⡈⠯⣰⡈⠉⠒⠂⠀⠤⠾⠿⠟⠉⠀⠀⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠹⣿⣦⠀⠀⠹⣿⡄⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⣀⣠⠖⠋⢰⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⡄⠀⠙⠿⣷⣤⠀⠙⢷⣷⣄⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠀⣶⢏⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠅⡄⠀⠀⠈⠛⠷⣄⡀⠙⠿⢽⣷⣄⣤⣲⣶⣤⣦⡤⠴⣫⡴⠛⣄⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠒⠀⠀⠀⠀⠀⠉⠐⠲⠤⡤⢤⣭⣭⡭⠥⠴⠖⠋⣥⠖⡃⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡄⠴⠖⠀⠀⠀⠀⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢠⢶⠄⠀⢰⣄⢀⣶⣦⠀⡦⠀⠀⣄⠠⣆⠀⣰⠀⡴⠒⡆⣴⡀⢰⡄⠀⠀⢠⠒⢦⢀⡔⠲⢰⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⠘⢶⡟⡇⠳⡇⠀⠀⡏⠀⠈⠶⢹⢠⡅⠀⡇⣿⠘⢾⠃⠀⠀⢸⠀⢸⢨⠀⠀⡇⡇⠀⢸
⠀⠀⠀⠀⠘⠇⠀⡇⠀⠀⡀⢸⠀⠈⡧⡇⠀⡇⠀⡀⠀⠀⠀⠀⢸⢸⡇⠀⡇⣸⠀⢸⠀⠀⠀⢸⢀⠌⢸⠀⢸⢠⠃⠀⢸⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⡇⠁⠀⠀⢠⠃⠆⢸⠀⠀⢸⠈⡇⠀⡇⢸⠀⢸⠀⠀⠀⣼⢧⠀⢸⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠃⠘⠀⠀⠃⠀⠀⠉⠀⠀⠁⠈⠀⠀⠘⠀⠃⠘⠁⠘⠀⠈⠁⠀⠀⠛⠀⠃⠈⠂⠊⠀⠂⠀⠘


⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢉⣥⢖⠪⠛⡿⠿⢛⣛⢓⡲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠅⠀⣰⢋⡴⢣⡞⠁⡴⠚⠉⣭⣍⣩⡁⠒⢮⣽⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⠁⠀⠀⢰⡅⣾⡇⢾⠀⠸⡁⠀⠀⠉⠈⠉⢛⡆⠀⠙⣷⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣼⣿⠀⠀⠀⢸⡇⢿⣇⠘⣧⡀⠈⠀⠲⠦⡶⠶⠋⠀⠀⢀⣿⠇⠈⡎⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣿⡀⠀⠀⠸⣧⡈⢿⡁⣄⠙⠲⠤⢀⡀⠀⢠⣶⣿⡿⠟⠁⠀⢰⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣧⣟⡀⠀⠀⢻⣿⣆⠙⠲⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⣼⠏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⠀⠀⠻⣿⣿⣄⠀⠀⢻⣿⣀⡀⠀⠉⠛⠦⢤⣤⣤⣀⣤⣤⣼⠶⠋⠀⣠⡾⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⣷⠀⠀⠈⠛⢿⣷⣄⠀⠙⢿⣿⣦⣤⡀⠀⠀⠀⠉⠁⠀⡁⠀⠀⢀⡼⢟⣵⠏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡦⠰⠀⠀⠀⠀⠉⠛⠷⣤⡀⠉⠛⠿⠿⣧⣶⣬⣿⣯⣴⠷⠾⢚⣭⡶⢛⣁⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠄⠀⠐⠃⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⠴⠦⡤⠤⠤⠶⠶⠛⠉⠠⣴⢚⠁⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣴⠶⡦⠖⠀⠀⠀⠀⠩⠀⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠐⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣐⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⠄⠀⠀⠀⠀⠤⠤⠼⠛⠛⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡦⠀⠀⣶⡄⠀⡦⣶⡀⢰⡆⠀⠀⢰⠀⣶⡀⠀⣶⠀⣴⠚⢲⢰⣦⡀⢰⠀⠀⠀⠀⡖⠒⡆⢠⡖⠒⡆⣶⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⠘⢦⡇⡇⠙⣬⡇⠀⠀⣿⠀⡇⢱⡌⢸⢀⡁⠀⢸⢸⡇⠳⣼⠀⠀⠀⠀⡇⠀⣿⣘⠁⠀⡇⣿⠀⠀⣿
⠀⠀⠀⠀⠀⢶⠆⠀⡟⠀⠀⠀⠀⣿⠀⠈⡇⡇⠀⠸⡇⠀⠈⢸⠀⡇⠀⠀⢸⢸⡇⠀⢸⢸⡇⠀⢹⠀⠀⠀⠀⡇⢀⡇⣿⠀⠀⡇⢿⠀⠀⣿⠀⠰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⣿⠀⠀⡇⡇⠀⠀⡇⢀⡁⣸⠀⡇⠀⠀⣼⠘⡇⠀⣾⢸⡇⠀⢸⠀⠀⠀⢰⣷⡋⠀⣿⠀⠀⡇⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡆⢸⠀⣿⠀⠀⡧⡇⠀⠀⡇⠎⠀⢸⠀⡇⠀⠀⣿⠀⢇⢀⡿⢸⡇⠀⢸⠀⠀⠀⢸⡅⠳⡄⠹⡀⢠⠇⢠⢀⠀⣧⢀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠘⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠠⠈⠁⠄⠀⠀⠀⠘⠠⠀⠘⠂⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠴⠶⠶⠶⠦⠤⢤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡸⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⢦⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢳⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⣀⡼⠋⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣸⢠⠞⠓⢦⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣤⠤⠖⠋⠁⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠃⢸⠄⠀⡼⢀⣠⠤⠤⣄⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣠⣤⣄⠀⣴⠋⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠛⠀⡼⠁⣾⠁⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⡇⢹⡆⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⢀⡿⠀⣰⠞⠛⠛⠒⢦⡀⠀⣾⠀⠀⠀⠀⠈⠳⠞⠃⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠸⣧⣀⡿⠀⠀⠀⠀⠀⢻⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠶⠶⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠖⠛⠋⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢛⣭⣹⠛⡟⢻⠹⡏⣯⠹⡿⡍⣯⢹⠉⡏⣟⠹⣙⡏⣯⢹⣿⡇⣍⢸⡟⣟⢻⠉⡿⢹⠿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣭⠿⠷⠿⠾⠷⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠿⠶⠷⣾⣧⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣥⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡠⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡤⠤⢄⣥⠄⠀⣀
⠀⠀⢀⣴⠆⣵⢲⣿⠱⠯⠿⢻⡟⣏⣷⡄⡀⠀⠀⠀⠀⠀⣾⠀⠸⣄⠀⠙⣀⠗⢀⠀⢰⠄⠀⠀⠀⠀⠀⣠⡾⡷⠃⡾⠋⠞⠋⡌⣾⣭⠋
⠀⢀⢎⡟⠄⢿⣮⡙⠛⠒⢛⣛⣡⣿⣿⠇⢿⢂⠀⠀⣴⡀⠹⣷⣄⠈⠁⠀⠀⠀⠁⠀⠜⢀⡆⠀⠀⠀⣰⡿⠛⡽⢣⢃⢀⡽⢰⡶⡈⠻⣸⢧⢳
⠀⢸⠈⢿⣄⠀⠉⠉⠛⠛⠛⠛⠋⠉⠀⢀⣼⠇⡆⠀⣩⣟⢄⡈⠙⠳⠤⠤⠀⠐⠚⣁⠄⣀⣀⢰⠀⠀⣿⣷⣷⠰⢋⡤⡈⠱⢛⢱⡇⠀⢹⠘⠗⣇
⠀⢸⠀⠠⡙⠻⠶⢶⣤⣤⣤⣤⣤⡶⠿⢛⣡⡆⠀⠀⣿⣿⡌⠋⢀⡓⠒⠂⢀⣐⠊⠁⣰⡟⢿⠀⠀⢸⡟⣿⠃⢣⣜⠻⡇⠸⣿⠘⡁⣸⡏⡇⡙⣿
⠀⠸⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂⠀⢿⡿⣧⣠⣿⣿⡆⣸⡟⠉⠙⢻⣿⠀⢸⡄⠀⠘⣧⣸⡇⣾⠿⣿⢱⣷⡆⣿⣿⢻⣿⡆⣷⣿
⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠈⠻⣦⣀⣈⣧⡉⠉⠀⠀⣤⣿⣿⣿⠟⠁⠀⠀⠘⢿⣧⣿⠀⣸⢟⠁⣹⣇⠈⢁⣿⣥⣾⠟
⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠉
⠀⠀⠀⠀⢀⣠⠶⠛⠛⠚⠋⠉⠓⢤⣄⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠂⠈⠉⠁⠉⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⣾⠷⠖
⠀⠀⠀⡠⠋⠉⣀⡴⣒⣒⣂⣀⡢⣼⣿⡓⣀⡀⠀⠀⢠⠟⡉⠀⣠⣤⡴⠶⠶⠶⢶⣬⡁⠈⢳⡀⠀⠀⢀⡶⠟⠀⡠⠶⠖⠒⠲⠦⡀⠀⠀⠐
⠀⠀⡜⠁⢠⠊⣹⡝⠁⠀⠀⠈⣇⢾⣿⡇⢹⠻⡆⠀⡟⠈⠀⣴⢛⣥⢶⣿⣿⣿⣶⣍⢿⡄⠈⣧⠀⠀⡾⢃⡄⠀⠀⠀⠀⣀⡀⠀⠀⢢⡀
⠀⢸⠀⠀⣥⣴⢿⠁⣼⠿⡷⠀⢸⢰⡏⡇⠸⠀⢳⠀⡇⠀⣸⠃⣾⣿⢟⡽⢭⡻⣎⣿⡎⣷⠀⢹⠀⢸⣧⡟⠀⠀⢀⠴⠋⢉⡉⠳⡄⠀⢻⠀⢠⡆
⠀⠘⣿⡀⣍⠛⠺⠀⡰⡋⠀⢠⡿⡰⠃⢰⡇⠀⡇⠀⡇⠀⣽⡀⣿⣿⡜⢷⣭⣴⣯⣿⠃⣿⠀⢸⠀⠸⣸⡆⠀⠀⣾⠀⠀⢿⠋⣠⠃⠀⣼⠀⣟⡟
⠀⠀⢻⣧⠘⢌⠷⡀⠱⠾⠍⠛⠊⣁⠖⡡⠀⡸⠁⠀⣇⠀⢸⣇⠻⣯⡻⠷⠶⠾⠟⢃⣼⠇⠀⡜⠀⠀⠙⠁⢲⡀⠻⡄⠀⠀⠈⠀⠀⣠⠇⠀⣹⠇
⠀⠀⠈⠻⣷⣈⠑⢾⠖⠐⡖⣲⠾⠋⠉⣠⡔⠁⠀⠀⠸⣎⠂⠙⣦⡈⠻⠿⠶⠾⠿⠛⠁⠄⣰⠃⠀⠀⠀⠃⡌⠳⠄⠀⠀⠠⠤⠴⠞⣥⠶⣾⠏
⠀⠀⠀⠀⠈⠙⠿⣖⣲⣤⣁⣀⣀⡴⠟⠋⠀⠀⠀⠀⠀⠘⠳⢤⣀⣙⣒⡦⢤⣤⡀⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠠⠶⣤⣀⣠⠾⣷⠘⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⣋⣩⡭⠭⠭⣍⢁⣂⡒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣴⠋⢉⣤⠶⠶⠶⠶⠦⣌⠙⢲⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⣏⠀⢼⡇⠀⣿⣁⠀⠻⢿⣿⡆⠈⣷⠀⢿⣷⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢘⣇⠀⢸⣇⠀⠘⠻⠿⣷⣶⡿⠃⢀⣿⠀⠀⣿⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣿⣂⠀⢿⣧⣄⣀⡀⠀⠀⣀⣠⣿⡟⢀⡄⣵⡿⠀⢺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⣿⣄⠀⠉⠻⠿⠿⣿⢿⠿⠟⠋⣠⣦⣼⣿⠃⡰⢸⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠻⣿⣮⣤⣐⣤⢀⣠⣤⣄⣤⣿⡿⠟⢀⠴⢑⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠙⠟⠛⠻⠛⠛⠛⠋⢉⠡⠔⠈⢑⢵⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢔⣆⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⣭⣥⣽⣷⣾⣶⣷⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⡤⠶⣒⣒⣒⣒⣒⠶⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⣛⡭⠭⠭⠭⠭⣍⡛⠿⣿⣿⣿⣿
⠀⠀⢀⣾⡏⠀⣾⡋⢴⣶⣀⣽⠗⢈⣿⣶⣄⠀⠀⠀⣿⣿⣿⠏⠀⣾⡋⢰⣟⡉⠿⠗⣀⣿⠆⠈⠛⣿⣿
⠀⠀⢸⡏⠻⣦⣈⡛⠓⠶⠶⠶⠚⣋⣵⠟⣿⠀⠀⠀⣿⣿⣿⠀⣦⡙⠻⢦⣬⣭⣉⣩⣭⡤⠖⢁⡄⢹⣿
⠀⠀⠈⢷⣄⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⣰⠟⠀⠀⠀⣿⣿⣿⣆⠹⣿⣷⣶⣤⣤⣤⣤⣤⣴⣾⡟⢁⣿⣿
⠀⠀⠀⠀⠙⠳⢶⣤⣤⣤⣤⣤⣤⠶⠟⠉⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣉⡛⠛⠿⠿⠿⠛⣋⣡⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢉⣉⣡⣤⡤⠴⢤⣤⣉⣉⣉⡙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡺⠏⢀⣠⡾⠛⠉⣁⣤⣤⣤⣤⣤⣤⣄⡉⠙⠳⣤⡀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⡾⠁⠀⣸⣿⠁⢀⡾⠏⠁⢠⣤⣤⣤⣤⠉⠻⣷⡄⠈⣿⣦⣀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢸⡷⠀⠀⣿⣧⠀⠸⣧⣤⣀⣈⠉⠛⢿⣿⡇⠀⢸⣧⠀⠸⣿⣿⡆⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⢸⣯⠀⠀⣿⣗⠀⠀⠙⠻⠿⢿⣿⣷⣿⠟⠘⢀⣼⣟⠂⠀⢸⣿⣿⠀⠛⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⣿⡥⠀⠘⣿⣷⢐⠀⠀⠀⠀⠈⠁⠀⠀⢠⡾⣿⡯⠀⡀⠸⣵⣿⠀⠠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⣿⡅⢀⠘⠿⣿⣿⣶⣷⣤⣤⣤⣶⣾⣾⣿⠋⠀⡴⢣⣽⣿⡟⠀⡇⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠡⡈⢿⣿⣤⡑⢄⡈⠙⠛⠛⠿⠿⠿⠟⠛⠉⠁⠠⣾⣵⣾⣿⢿⠀⡰⠃⣧⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣆⠀⠀⠈⠀⠙⢿⣿⣷⣦⣭⡐⣂⣤⠀⣀⣀⣤⣄⣠⣼⣾⣿⠿⠃⣠⡾⠃⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠈⠹⢿⡿⢿⣿⣿⢿⣿⣿⡿⠿⠿⠟⢋⡡⡔⠞⡭⣫⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠁⠀⢁⣠⠶⣭⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⣤⣄⠀⠀⠀⠀⠐⠀⢀⡀⠀⡀⠀⠄⠀⠘⢣⣟⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣾⣭⣭⣤⣭⣷⣶⣷⣶⣿⣞⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣩⣤⠀⠀⠀⢣⡀⣠⠮⣍⡻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠙⠟⠁⢸⢠⣶⠛⠛⠛⠛⠶⢦⣍⣹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠹⣧⠀⠀⢸⠀⠉⠛⠶⠶⠂⠀⠀⠈⢻⣿⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠁⠀⠀⠈⠳⢦⣼⣇⡀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠀⠈⣿⣧⣄⣀
⠀⠀⠀⠀⢀⣤⠞⠋⢹⣿⢀⡴⣶⡀⣠⣤⣌⣉⠟⠛⠻⠿⠿⠿⠛⠛⠁⣀⣠⡾⠟⢹⡏⠙⠳⣦⣄
⠀⠀⢀⣴⠟⠁⢀⣠⣾⣇⣸⠁⢸⡇⡏⠀⢀⣴⠶⠖⠒⠶⠶⠶⠶⠚⠛⠉⠁⢀⣤⣼⡇⠀⠀⠀⠙⢷⣄
⠀⢠⡿⠁⠀⣠⠟⠁⠸⣿⠃⠀⢸⣧⡇⠀⣿⢁⣶⠷⢦⣄⠀⠀⣠⠖⠛⢻⡇⢸⠃⠘⡇⠀⠀⠀⠀⠀⢻⣆
⠀⢸⡇⠀⢰⡏⠀⠀⠀⠻⣧⡀⠀⠛⠁⢸⡇⠘⡏⠀⠀⠙⠛⠋⠁⠀⠀⠀⣧⣼⠀⢰⡇⠀⠀⠀⠀⠀⠘⣿
⠀⢸⣧⠀⠈⢻⡄⠀⠀⠀⠙⠻⣶⣤⣄⣸⣷⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣴⡿⠁⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠻⣧⡀⠀⠉⠓⠦⠤⣀⠀⠀⠉⠉⠛⢻⣿⣁⡀⠀⠀⠀⣀⣀⣠⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠶⣶⣶⣶⣦⣤⣴⣶⣶⣶⡶⠾⠿⠟⠛⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⣠⠠⢤⡄⣤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠲⣦⣀⣤⣤⡤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢾⣿⣦⣬⣽⡇⣸⣿⣿⡌⢹⣟⠲⣮⡙⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⢣⡏⣼⣷⡌⠉⠁⠐⣵⣿⡿⠀⣈⣿⡂⠈⢿⣦⠈⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠎⢰⡇⠸⣧⠘⠿⣿⣶⡾⠿⠛⠋⢠⣶⣿⠏⠀⣠⣿⣿⠀⢱⣽
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⣿⡀⠻⠷⣦⣤⣤⣤⣦⣾⠾⠟⠛⠁⠀⢠⣿⣿⠋⠀⢺⠃⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⠈⠻⣦⣄⣀⠈⠁⠉⠁⠀⠀⢀⣀⣠⣾⡿⠟⠉⠀⢠⡞⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠲⡄⠀⠙⠻⠷⢶⣶⣶⣶⣿⠿⠟⠛⠉⠀⠀⠀⠲⣯⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠐⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡮⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠶⠶⠷⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⡒⢦⣤⣤⣤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⢿⡿⠶⠾⠟⣼⣿⣷⢨⣿⠙⢦⣙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠏⣾⠸⣿⣇⣠⣤⡿⠿⢃⣴⣿⠁⢨⣿⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣆⠹⣧⣌⣉⣉⣁⣤⣴⠿⠟⠁⢀⣿⡿⠁⢼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠙⢷⣄⣉⠉⠉⠉⠁⠀⣀⣤⣴⡾⠛⠁⢠⡞⣼⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠢⢀⠉⠛⠻⠶⠿⠿⠿⠟⠛⠉⠀⠀⡘⣿⣽⠇⠀⢀⣤⡴⠋⣴⠋⡭⠏⢭⡑⢶⣌⠱⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣵⠞⠁⠀⣠⡆⢸⣇⠘⢷⣄⣙⣛⣠⡿⢠⣿⠄⢹⡆⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣤⣤⣤⣤⣤⣴⠶⠛⠉⠁⠀⠀⢰⠋⣷⡈⠻⣷⣄⣉⣙⣛⣛⣡⣼⡿⢀⣿⣿⠨⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⠘⢿⣧⣄⣈⠉⠙⠛⠛⠛⢉⣰⣽⣿⠏⠈⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣊⡩⠥⠤⠀⠀⣒⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠂⠉⠛⠻⠿⠿⣾⣷⠿⠿⠛⠋⠁⢀⣼⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠃⣰⠏⣡⠴⠶⣒⠒⠶⢦⡉⠳⣌⠑⢦⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠁⠄⢾⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⠂⢰⣿⠀⢷⣄⣈⠛⢿⣷⠀⢻⠀⢻⣷⡀⣷⡀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣀⡀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⣹⣆⠘⣿⡄⠈⠙⠛⠿⠛⠉⣠⣿⠁⠀⣿⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠾⠾⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠠⠹⣿⡀⠘⠿⣶⣦⣤⣤⣤⣶⡿⠋⡰⣷⣿⠃⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠁⠙⢿⣦⣀⡈⢉⠉⠉⠉⢁⢀⣺⣿⡿⠋⡰⢽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣩⣴⡿⠤⠤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠉⠻⡿⠷⣿⡶⡿⠿⠿⠛⣉⠴⢿⣵⣿⠇⠀⠀⠀⣠⣬⠶⠚⢛⣛⣛⣩⡭⠭⠷⠒⠒⠛⡂⠘⣉⣉⣭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⣦⣴⣿⡿⠋⠀⠀⠀⠀⣿⣯⢛⣋⣉⣉⣡⣦⣴⣶⠶⠖⠛⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣶⣦⣾⣴⣦⣶⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⣳⡿⠛⠋⢉⣽⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡧⣠⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⢶⣶⣶⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⠶⣟⢻⣹⣙⣇⣇⣿⣧⣧⣴⣼⣼⣼⣼⣤⣧⣿⣇⣧⣹⣹⣹⣇⡇⣿⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢛⡛⢂
⠀⠀⢀⡄⣠⣤⡞⢽⣿⢳⡶⣲⣄⠀⠀⠀⠀⠀⣴⠀⢨⠀⠘⠉⠆⠀⠀⡄⠀⠀⠀⠀⢀⣴⡶⢊⡶⠱⠟⡀⣼⡳
⠀⢀⣼⠁⢿⣌⣛⡒⢒⣛⣴⣿⠿⢹⡂⠀⢠⡆⠹⣦⡀⠁⠀⠀⠀⠁⠠⠃⡄⠀⠀⢀⡾⠓⠿⡨⠀⣸⢠⡄⠙⢇⣦⠲
⠀⠈⠹⣦⣀⠈⠉⠉⠉⠉⠉⢁⣀⣼⠃⠀⢨⣭⡠⡀⠉⠒⠂⠀⠐⣉⠄⣠⣤⠀⠀⢸⣷⡿⡘⣡⣦⢁⣫⢸⠇⣈⡈⢛⡇
⠀⢠⠀⠂⠉⠛⠓⠒⠖⠒⠚⠛⠉⠐⠃⠀⢸⣿⡇⢀⣤⣄⢁⣤⠤⢤⣤⠏⢹⠀⠀⣾⢹⡇⣰⣮⡝⣘⡛⣤⣤⣿⡃⣌⣇
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⢳⣝⠛⠻⡛⠞⠃⠀⢠⣿⣤⣼⠃⠀⠘⢾⣇⡏⠙⣷⠋⢣⡏⠓⢹⣇⣹⡟
⠀⠀⠀⠈⠉⠒⠒⠤⠦⠄⠀⠂⠈⠀⠀⠀⠀⠀⠉⠛⠿⠿⠶⠶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠙⠻⠶⢷⣶⣿⡷⠶⠞⠋⠉
⠀⠀⠀⢀⣤⠖⠒⠒⠀⠁⠒⢤⣀⠀⠀⠀⠀⢀⣤⠔⠂⠀⠀⠀⠀⠐⡢⢄⡀⠀⠀⠀⠀⢀⠀⠐⠶⠶⠒
⠀⠀⡠⠋⢀⣴⣎⠭⠇⠤⠐⣿⣏⢠⣄⠀⢀⡞⠅⢀⣴⠶⣚⣛⣛⠲⣦⡀⠹⡄⠀⠀⣶⠋⠀⠒⠚⠉⠑⠂
⠀⡀⠀⠰⢁⣶⠀⣤⣄⠀⢎⣻⢿⠈⠉⡇⠸⠀⢀⡞⣵⣿⢿⡿⢿⡻⣎⣷⠀⢧⠀⣼⢡⠂⠀⠀⡠⠤⠤⣄⠀⢢⠀⠀⡀
⠀⢷⡄⡛⠿⠿⠘⠕⠋⢀⡞⣹⠈⣤⠀⡇⠸⠀⢸⢰⣿⣇⢯⣙⣺⣧⡿⢸⠀⠨⠀⢻⣏⠀⠀⡎⠀⢴⠆⢘⠀⢀⡄⡾⡇
⠀⠘⣿⡘⢐⠦⡘⠮⠆⠾⢁⡠⠂⠁⡰⠀⢠⠀⠸⣆⢿⣝⠶⠿⠷⠟⣡⡟⠀⡀⠀⠈⠃⢠⠀⢧⠀⠀⠀⠁⢀⡜⠀⣹⠇
⠀⠀⠙⢷⣌⡑⠿⠀⣐⠰⠞⠉⣠⠔⠁⠀⠀⢣⡀⠙⢦⡙⠛⠷⠾⠛⠉⠀⡰⠃⠀⠀⠀⠄⠑⠀⠀⠀⠐⠖⢫⠖⡺⠋
⠀⠀⠀⠀⠈⠓⠫⠶⠤⠤⠔⠚⠁⠀⠀⠀⠀⠀⠉⠒⠠⠭⠗⠒⠒⠀⠒⠉⠀⠀⠀⠀⠀⠀⠘⠓⠦⠴⠿⠷⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡔⣨⡥⣠⠄⡠⣄⣂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⢾⣧⣄⣼⠀⠈⠉⠛⠛⠁⢈⣿⣿⠆⠀⠑⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⣾⣀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠶⠗⠚⠛⠋⠁⠀⠀⠀⣸⣷⠈⢣⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⣧⣀⠈⠙⠻⠿⢶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠟⠛⢁⣀⡿⠁⣸⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠛⠷⠶⣤⣀⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣦⡶⠟⠛⣁⣤⠾⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣉⣉⣉⣭⡭⠤⠶⠖⠚⠋⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠀⣀⣀⣀⣀⡀⠠⠤⠤⠀⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡐⠰⣦⣦⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠙⠛⠷⠶⠤⠤⠴⠟⠋⠀⢈⣤⢂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠧⣌⣙⠛⠳⠶⠴⠤⠤⠤⠤⠴⠖⢚⣋⣡⠜⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⢒⣒⣒⣒⣛⣛⠯⠭⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠂⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠄⠀⠀⠀⠄⠀⠀⣄⡙⠳⣦⣄⠰⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠀⣴⠃⠀⣞⣀⣠⡶⠂⠀⣸⣿⡆⢸⣿⡆⠈⣿⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡎⢀⣿⡇⠀⢿⣷⣤⣤⣥⣤⣤⣶⣾⡿⠋⢀⠜⢃⠀⢀⡿⠀⢹⠘⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⠉⠑⠄⠀⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠁⠀⠋⣠⠞⠁⠀⡆⢠⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠘⠁⢃⠀⠠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⢀⠜⢠⡞⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠋⠁⠀⠀⢀⡴⢋⡴⠏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣥⠾⠛⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠾⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠖⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠦⠤⠤⠤⠤⠤⠶⠶⠶⠾⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠒⢂⣀⡀⠀⠁⠐⠒⠒⠠⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⢀⠀⠀⠀⠈⠒⠒⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⣀⠀⠀⠈⠒⠦⠥⢬⣍⣙⣳⣤⣀⣀⠤⠤⠒⠀⠀⠀⠀⢀⠜⠀⠀⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠁⠀⠀⠲⢤⣈⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⡀⠀⠠⠖⠋⠁⠀⠀⠀⢀⠀⠀⠈⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠒⠦⢤⣀⡀⠉⠉⠙⠓⠒⠒⠂⠁⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠰⠤⣄⣉⠙⠓⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠀⠉⠁⠀⠀⠀⠀⣀⣤⡀⠀⠀⡖⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⣠⠊⠀⠈⢷⡄⠸⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠏⠉⠙⠛⠻⠿⡾⠁⠀⠀⠀⠈⠳⠤⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠄⢰⣦⡀⠀⢀⣄⣀⠴⠻⢷⣄⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠊⢹⡀⠀⡏⠀⠀⠀⠀⠀⠉⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢸⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠷⡀⠀⠀⣠⡴⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠓⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁

⢀⠴⠀⠀⠀⢴⠰⣦⡛⢒⣛⣤⡶⠛⠀⣀⡾⢠⠀⠀⢰⣶⠂⠀⢠⠂⢀⣤⠐⠆⠀⡂⣠⡆⠀⠀⠐⠢⢤⣒⢤⣄⡀⢀⣀⡠⠖⠀⠀⠀⡆⢰⣜⠛⣚
⠀⠀⠀⠀⠀⡸⣆⡉⠉⠉⠉⠀⣀⣠⠾⠋⠀⠉⣴⠀⠀⠿⠀⡀⢸⡀⠈⠃⠐⠀⢰⠃⢹⡇⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⢀⢷⣀⠉⠉⠉
⢲⡄⠀⠀⠀⢓⠉⢛⠛⠛⠛⠋⠉⠀⠀⠀⠀⡠⠋⠀⠀⠐⢀⠱⢀⠁⠀⠀⣤⠴⣣⢤⡞⠀⠀⠀⢀⠴⠋⢉⡀⣀⠀⢈⢱⣦⠀⠀⠀⠈⡆⠙⡛⠛⠛
⢻⡆⠷⣄⠀⠈⢦⡐⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠶⢄⣀⡴⣶⠘⠗⠋⠀⠀⠀⠰⠃⡠⢺⡿⠒⠂⠘⠂⣽⢿⠸⣦⡀⠀⠘⣄⣢
⠈⠇⠀⢸⠀⠀⠀⠉⠙⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣥⢾⠃⣴⢷⠀⢘⢰⠹⠀⠆⠇⠀⠀⠈⠉⠛⠒
⠀⠸⠃⡘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠋⡵⢪⣶⢓⢀⣀⠀⠀⠀⣷⡌⡌⡙⠀⡸⣁⣠⣟⠘⢀⠾⠀⠇⠀⠀⠀⠀⠀⡀
⠨⠂⡰⠁⠀⠀⠀⣶⠀⢢⠀⠘⢉⠆⡀⠀⠄⠀⠀⠀⠀⣼⣯⡄⣫⠎⢀⡴⣠⠑⢿⢊⠀⠀⠀⠸⣧⡁⠍⣢⡈⢓⡈⣁⡶⠅⢀⠌⠀⠀⠀⢰⡆⠐⣆
⢠⠞⠁⠀⠀⢰⣇⠙⢧⡀⠁⠀⠀⠈⠀⠘⢠⡄⠀⠀⣸⢻⡟⢕⠴⣦⢈⣚⢫⡆⠨⣞⣟⡄⠀⠀⠈⠻⢦⡍⢁⡐⠀⠉⣠⡴⠋⠀⠀⠀⣾⡀⠻⣦⡈
⠀⠀⠀⠀⠀⢰⣮⠲⠄⢉⠐⠂⠀⢈⣡⠄⣠⡄⠀⠀⢻⣼⢣⡿⣷⢯⣘⢏⣈⢠⣶⠄⣽⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣶⡆⠦⠈⡉
⠠⣀⠀⠀⠀⢸⢿⡀⣠⣶⡄⣠⡶⠦⣤⡼⠋⡇⠀⠀⠈⠻⣾⣀⡽⠛⢻⡜⢿⣿⡇⣢⣿⠀⠀⠀⢀⡴⠞⠉⠉⠈⠁⠀⠀⠄⡀⠀⠀⠀⣿⣧⢀⣴⣦
⣤⡂⠑⡄⠀⠘⢷⣍⣉⣟⠓⠋⠀⢀⣼⣯⣤⡟⠀⠀⠀⠀⠈⠙⠻⠷⣿⣧⣤⣾⢧⠾⠃⠀⠀⠀⠞⠀⢁⡴⢟⣛⣛⡒⢦⣄⠊⢢⠀⠀⠹⣮⣉⣙⣛
⣈⣷⠀⣷⠀⠀⠀⠈⠛⠻⠿⠷⠶⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⢋⣾⡿⣿⡿⣿⢷⡹⡇⠘⡇⠀⠀⠀⠉⠛⠿
⠿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠛⠝⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⢸⣿⡽⣇⣛⣼⣸⢇⡇⠀⠇
⣰⠇⢀⠃⠀⠀⠀⠀⢠⡴⣶⢶⡟⣟⣦⠰⡄⠀⠀⠀⠀⣰⡋⠀⠐⠉⠉⠉⠑⠂⠀⠀⠀⠀⠀⢧⠄⢿⡘⣯⡻⠾⠿⠿⢋⡼⠁⠘⠀⠀⠀⠀⠀⣤⡶
⠉⣄⠆⠀⠀⢀⢀⡤⣷⣭⣭⠾⣣⣿⠟⠁⣹⠄⠀⠀⢰⣏⡎⠀⠀⡠⠖⠒⢦⡀⠸⡄⠀⡄⠀⠘⢦⡀⠳⣌⠙⠛⠷⠟⠋⠁⣠⠁⠀⠀⡀⢠⢸⣧⣭
⠘⠋⠀⠀⠀⢹⡈⠿⠦⠴⠶⠛⠋⠁⣠⡶⠋⠼⢀⠀⠘⣿⠀⠀⢸⠀⠰⡟⢀⠁⢀⡇⢾⡇⠀⠀⠀⠈⠙⠒⠛⠒⠀⠐⠒⠚⠁⠀⠀⠀⣷⠘⠷⠤⠶
⢀⠀⠀⠀⠀⡎⠷⣦⣤⣤⣤⡤⠴⠚⠉⠀⠀⠀⡿⠀⠀⢉⠀⣆⠘⠄⠀⠀⠀⢀⡜⠀⣸⠃⠀⠀⠀⢀⡤⠖⠂⠐⠒⠢⢄⡀⠀⠀⠀⠰⡙⢶⣤⣤⣤
⣼⡗⣀⠀⠀⠐⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠐⠈⣁⠀⠀⢀⣛⢩⣞⡽⠃⠀⠀⢀⡴⠋⣠⣴⣂⡒⢠⡐⣼⣿⢠⡀⠀⠀⢣⠀⠆
⠸⡇⠉⢳⠀⠀⠙⠶⣦⣀⣀⣀⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠛⠀⠁⠀⠀⠀⠀⠌⠀⠎⣸⡏⢀⣀⠀⢠⢛⢿⠈⠙⡆⠀⠀⠳⢶⢤⣀
⠀⣧⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢖⡠⣀⣀⠀⠀⠀⠀⠀⣄⠸⠻⢽⠀⢻⠙⠀⣼⢹⠈⣠⠁⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣖⡒⢦⣤⡤⣤⠤⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⢿⡿⠶⠾⠟⢴⣿⡷⠈⣿⠙⢦⣙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠃⣾⠸⣿⣇⣠⣤⡿⠟⠁⣸⣿⠁⢈⣿⡆⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⠹⣧⣌⣉⣉⣁⣤⣴⠾⠛⠁⢀⣿⡿⠁⢰⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠙⢷⣄⣉⠉⠉⠉⠁⠀⣀⣠⣴⡾⠋⠁⢀⡞⣼⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠒⠀⠈⠛⠛⠷⠿⠿⠿⠛⠋⠉⠀⠀⠈⢯⣴⠃⠀⢀⢤⡶⠉⣴⠋⡭⠯⢭⡑⢶⣄⠙⣖⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠞⠁⠀⣠⡆⢸⡇⠐⢷⣆⣙⣛⣠⡿⢠⣿⠄⢸⡆⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣤⣤⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⢸⠉⣷⡈⠻⢷⣤⣈⣉⣛⣋⣡⣼⠟⢀⣾⣿⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢷⣧⣤⣈⠉⡉⠛⠛⠙⢉⣠⣽⡿⠋⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⣋⡤⠤⠤⠤⠄⣀⣐⠂⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠙⠛⠿⠿⠿⠶⠿⠟⠛⠉⠀⢀⣼⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡟⠁⣴⠋⣠⠶⢚⣛⣓⠒⢦⡉⠳⣄⠙⢦⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢾⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⠀⢸⣷⠀⢯⣤⣈⡙⢻⣷⠀⢻⠀⠻⣷⡈⢷⡀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣄⡀⠀⠀⠀⠀⡀⢤⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣆⠘⣿⡄⠈⠉⠛⠻⠛⠁⣰⣿⠀⠀⣿⡇⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠛⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠘⣿⡄⠘⠿⣶⣶⣤⣤⣴⣶⡿⠃⡐⢴⣿⠃⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠘⢿⣦⣄⡀⢉⠉⠉⠉⣁⢀⣺⣿⡿⢉⡰⢥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣞⣥⣴⠿⠄⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠉⠛⠿⠿⠷⠾⠿⠿⠛⡛⢩⠐⠻⣾⣿⠃⠀⠀⠀⣴⣤⡷⢛⣋⣉⣩⣭⠭⠵⠒⠒⠚⠋⣉⣉⣁⣈⣥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣔⣿⡿⠃⠀⠀⠀⠀⣿⣭⢉⣉⣉⣀⣤⣶⣴⡶⠖⠛⠛⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⣤⣿⣼⣦⣾⡾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣹⡟⠛⠉⢀⣰⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣀⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠫⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⡞⣹⠿⣿⣶⣆⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣲⡤⣄
⠀⠀⠀⠀⢠⡖⢱⡎⢯⣼⡷⠙⣏⠳⣦⡀⠀⠀⠀⠀⣀⣼⣇⠸⣧⡿⣬⣛⣿⢘⡆⢹⣧⡀⠀⠀⠀⠀⣀⠠⢾⣄⣉⣩⣥⣾⠿⢫⣷
⠀⠀⠀⢰⣯⡛⢬⣛⠳⠶⠦⠚⢁⡼⢣⡟⣷⠀⠀⡼⣿⣽⣿⣷⣎⣛⠿⠿⠶⠟⣁⣾⠟⣿⡄⢀⣴⣷⡙⠳⢶⣦⣭⣤⣶⣶⣿⣿⢟⣤
⠀⠀⢠⣾⢯⡻⠶⣬⣍⣉⣉⣩⣭⡶⠛⣠⣿⠀⠀⢿⣌⠻⣧⣝⡲⢬⣉⣚⣛⣋⣉⣥⡾⣻⠇⢸⣿⠟⠊⢳⣦⢤⠌⣩⡍⣭⣤⠶⢻⣿⠂
⠀⠀⠈⢿⣥⣟⡛⠶⠤⠤⣥⣤⠤⠖⢚⡵⠟⠀⠀⠈⠻⢷⣦⣉⡙⠻⠶⠶⠶⠿⣷⣻⠾⠃⠀⠈⠻⣿⣴⣅⠪⣿⣾⣞⣄⣠⣤⣴⣿⡿
⠀⠀⠀⠀⠈⠉⠛⠛⠒⠶⠤⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠾⠿⠿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⡴⣾⣟⡛⠋⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⠀⠂⢀⢀⡀⡰⡄⠜⡦⣺⢲⡟
⠀⠀⠀⠀⢠⢺⠃⢠⡟⠁⣰⣿⡏⠷⡀⠀⠄⠠⠀⢀⣼⠀⡀⠘⠼⠏⠞⠅⠚⠓⠋⠀⠁⠀⠨⠁⡀
⠀⠀⠀⢠⡇⠈⠀⢲⠿⠿⠟⠋⠀⢀⡿⢱⡀⠀⠀⠒⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣶⣶⠶⣀⣄⡤⠶⠶⢲⡀
⠀⢀⣾⠉⠀⣤⣤⣿⣯⣥⣤⡴⣾⠽⢡⣾⡇⠀⠀⠀⠀⠀⠀⠀⣀⣰⡟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣨⡭⠤⠚⣋⣭⣷⣶⣶⢿⣯⡁
⠀⢸⣏⣴⣖⠀⢀⡰⠟⠿⣢⣯⡴⣊⣹⠟⠀⠀⠀⠀⠀⠠⢔⣼⠇⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣯⡵⠖⠛⠉⠉⠻⢶⣤⣿⣗⠺⣝⣶⣤⡄
⠀⠀⠉⠛⠷⠶⣿⣿⣷⣶⠿⠿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠒⠙⠣⡌⠀⠀⡀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠃⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠉⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠈⠉⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⠃⣠⣶⣿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⢉⣛⣿⡷⠀⠀⢀⣼⡿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠁⠈⢿⣷⣿⡏⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣾⠿⠿⠛⠋⠀⣠⣴⡿⠋⠀⢀⣾⡟⢿⣧⣀
⠀⠀⠀⣠⣾⣿⣿⡟⢻⣿⡀⠀⠀⠙⢿⣷⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⡿⠟⠋⠀⠀⣠⣾⠟⠀⠈⣿⣿⣷⡀
⠀⠀⣴⡿⠋⣾⡟⠀⠀⠻⣷⣤⡀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⣰⣿⠃⢻⣷⡀
⠀⣼⣿⡇⠀⣿⣇⠀⠀⠀⠈⠛⠿⢷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⡿⠟⠋⠁⠀⠀⣠⣶⡿⠃⢀⣼⣿⣇
⢸⣿⢿⣧⠀⠘⣿⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⣀⣤⣶⡿⠟⠁⠀⢴⡿⠟⢹⣿
⣿⡏⠈⢿⣧⡀⠈⠻⢿⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⠿⠟⠋⠁⠀⣠⣤⣄⡀⠀⠀⠸⣿
⣿⡇⠀⠀⠻⠿⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⣀⣄⣀⠀⠀⠀⢻⣿⠛⣿⣆⠀⠀⣿
⠹⣿⡄⠀⠀⢀⣤⣤⡀⢠⣶⣤⣤⡀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣤⣄⡀⠀⠀⠀⣿⡟⢻⣷⡀⠀⢸⣿⠀⠘⣿⡆⠀⣿
⠀⢻⣷⠀⢀⣿⡏⢻⣷⠀⠈⠙⠛⠁⠀⣼⡿⢿⣷⡀⠈⠿⢻⣿⡿⠋⠉⠉⢻⣷⠀⠀⠀⣿⡇⠀⢿⣧⠀⠘⣿⡇⠀⣿⡇⠀⣿
⠀⢸⣿⠀⣼⡿⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⣿⡇⠀⢠⣿⠏⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⠇⠀⢸⣿⠀⠀⣿⡇⠀⣿⡇⢠⣿
⠀⣿⡏⠀⣿⡇⠀⣼⡿⠀⢀⣾⣿⣷⣾⠟⠀⢀⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⡆⠀⣾⡟⠀⠀⢸⣿⠀⠀⣿⡇⠀⣿⣇⣸⣿
⢀⣿⡁⢸⣿⠁⠀⣿⡇⠀⢸⣿⠀⠙⠉⠀⠀⢿⣿⡇⠀⣿⡇⢠⣶⡄⠀⠀⠀⣿⡇⠀⣿⡅⠀⠀⣸⡿⠀⠀⣿⡇⠀⢸⣿⠟⠋
⠀⢿⣧⣼⣿⠀⠀⢻⣷⣤⣼⡿⠀⠀⣴⡄⠀⢸⣿⠁⢰⣿⡇⠀⠉⠀⠀⠀⠀⣿⣇⠀⣿⡿⠂⠀⣿⡇⠀⠀⣿⣇⣴⣿⠋
⠀⠈⠙⠋⠻⢿⣦⣄⡉⠉⠙⠟⠀⠀⠈⠁⠀⣼⡟⠀⢸⣿⠟⠀⠀⠠⣾⠆⠀⢻⣿⠀⣿⣷⠀⠀⢻⣷⠀⣰⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣦⣶⣄⣀⡀⠀⣿⡇⠀⢸⣿⠀⢀⣀⠀⠀⠀⠀⢺⣿⢀⣿⣧⣤⣴⣾⡿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣷⣤⣾⣿⣶⣾⣿⣷⣶⣾⡿⠿⢿⣿⠟⠛⠉⠉
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⠞⢋⣩⡴⠶⢖⠶⠶⣭⡙⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⣡⣴⠖⢛⣩⣭⣍⣙⠓⢦⣌⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣰⣿⣏⠀⢾⣿⡀⠺⣿⣥⣴⠿⠋⣀⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⠏⠀⢸⣿⡁⠐⣿⣅⡐⠛⢛⣀⣼⡿⠀⡀⠉⢻⣿⣿⣿
⠀⠀⠀⣿⡏⠻⣦⣄⡙⠛⠷⠶⠶⠶⠶⠟⢛⣡⡾⢻⣿⠀⠀⠀⢸⣿⣿⣿⠀⣶⣄⠙⠿⣶⣤⣍⣉⣉⣉⣉⣥⡴⠞⢁⡄⠈⣿⣿⣿
⠀⠀⠀⢻⣧⠀⠈⠙⠛⠿⠶⠶⠶⠶⠶⠿⠛⠋⠀⣼⡏⠀⠀⠀⢸⣿⣿⣿⣆⠸⣿⣷⣦⣤⣀⣉⣉⣉⣉⣉⣁⣤⣶⣿⠃⣸⣿⣿⣿
⠀⠀⠀⠀⠙⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣁⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣤⣤⣬⣉⣉⣉⣩⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⣤⠤⠤⠴⠤⢤⣄⡉⠙⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣏⠁⢠⡿⠀⢴⣉⣉⠙⣦⡈⠻⣷⡄⠙⣦⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢸⣇⠀⠙⢿⣶⣬⣉⣉⣠⣾⠇⢰⣿⡇⠀⢹⡇⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⢽⣧⠈⠻⣿⣤⣄⠈⠙⠛⠛⠛⢋⣀⣽⡿⠁⢨⣿⣷⠀⠀⠽⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠈⢿⣧⣆⣀⠉⠛⠿⠿⠾⠷⢾⠿⠿⠟⢀⢘⣿⣿⡟⠀⢠⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⡁⠂⢄⠙⠿⣿⣷⣶⣤⣠⣀⣠⠄⡠⣠⣴⣵⣿⡿⠋⠀⠀⣾⠃⡼
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠂⠀⠉⠙⠻⠻⠿⠿⠿⠿⠛⠛⠉⠁⠀⡀⡠⣶⢏⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠠⢄⢦⣷⣁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣤⣵⣿⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣯⣤⣀⣀⣠⠔⣠⣳⣭⡯⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠲⠦⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠎⢧⡠⡀⢒⣒⡲⢦⡀⠀⠀⢸⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠀⠈⠳⣄⣀⣈⣁⣀⣤⠞⠁⡔⡴⠔⠁⣹⠈⢹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⢿⠙⢦⣀⠉⠉⣑⣲⣒⣒⣤⣠⠔⠚⠒⣚⣡⠤⠖⢃⡀⡇⠀⣹⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢿⠸⡘⣄⠄⣈⣉⡉⠉⠀⠀⠀⠉⠉⠉⢉⣭⣥⣤⣤⡾⠋⣉⡠⠖⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡸⡀⠙⠮⣍⣉⠉⠙⠢⠔⠚⠉⠉⠓⠒⠋⢀⣀⣠⠤⠖⠋⠁⡀⡔⠒⠴⢺
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠉⠉⢢⣌⠉⢉⣓⠒⠒⠒⠒⠒⠋⠉⠉⠀⠀⢐⡼⠛⠛⠚⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠒⠋⠁⠙⠦⠠⠴⠚⠉⠙⠢⠤⠒⠋⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⢤⣄⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⠤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠠⠤⠤⠄⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⣠⣴⣦⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⡐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢢
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢠⠁⠘⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠱⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⡠⠃⠀⢠⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠀⠘⠀⠀⠀⠀⠈⠢⡀
⠉⠋⠙⢿⣿⣿⠿⠿⢷⠦⠴⠀⢠⠊⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠃⠈⠀⠀⠀⢀⣀⠤⠆⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⡘⠉⠏⠉⢣⠉⠉⠉⠂⠈⠈⢣⠀⠈⢆⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠔⠀⡴⠄⠂⠄⠅⠀⠁⢠⣄⠀⠀⠀⠀⠀⠑⠤⢀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⠊⠑⠀⠒⠒⠙⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣡⢖⢟⡭⢛⣩⠭⠭⠽⢒⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠀⣰⢱⡏⡞⠀⡏⠀⠸⠛⠛⢦⠈⢳⣌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣼⡇⠀⠀⣿⢸⣇⠹⣄⠀⠀⠦⠤⠴⠋⡀⣠⡿⠀⡍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⣧⠀⠀⢹⣆⠹⣔⣌⠁⠂⠀⠀⠴⠿⠟⠋⠀⢀⡿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⣿⣦⠀⠀⢻⣷⠀⠙⠲⢦⣀⣀⣀⣀⣀⣀⣼⠚⢁⡺⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣦⠀⠈⠛⢿⣆⠀⠹⣿⣦⣄⡀⠀⠉⠉⠉⢉⠁⠀⡠⢞⡵⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠜⠂⢀⠀⠀⠉⠛⠦⣄⣉⠛⠻⠾⠶⠿⠶⠟⣚⡯⠶⢋⠴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢛⢋⣋⡉⠁⠀⠛⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⢰⠛⠂⠂⡷⡄⣶⡷⡄⡇⠀⢠⡆⠿⡄⡼⠃⡞⠉⡆⡷⡀⡇⠀⠀⢸⠉⡆⡞⠉⡆⡇⠀⡇
⠀⠀⠀⠀⣄⠀⡎⠀⠀⠀⡇⠘⡇⡇⠘⡇⠀⠘⡇⡄⠈⢠⢰⡆⠀⡇⡇⠙⡇⠀⠀⡏⠀⠗⡆⠀⡇⡇⠀⡇⠀⣤
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⡇⠀⡇⡇⠀⡇⢠⠁⠃⡇⠀⢸⠸⡇⢸⠀⡇⠀⡇⠀⠀⣷⡞⠀⡇⢀⡇⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠳⠴⠀⠇⠇⠀⠒⠇⠀⠃⠈⠀⠀⠇⠀⠸⠀⠃⠼⠀⠇⠀⠇⠀⠀⠇⠙⠄⠃⠰⠃⠦⠄⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⠏⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣦⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⠙⠲⠤⢤⣤⣤⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠈⢳⡀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢈⡇⣠⠤⣄⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠀⠀⠀⢀⣠⠾⠋⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡞⠱⡇⠀⢈⡇⠀⢀⣀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢧⣤⠇⢀⡼⢡⡞⠉⠉⠉⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⢳⡄⢻⡄⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡾⠁⢸⡇⠀⠀⠀⠀⠘⡇⠀⢀⣤⣤⣤⣀⡀⠀⠀⣰⠃⠀⠀⠀⠘⣧⣨⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠻⣤⣴⠇⠀⠀⠀⠀⣼⠁⠀⡏⠀⠀⠀⠈⠙⣆⠀⣯⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠃⠀⠀⠀⠀⠀⡿⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⢀⡠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠉⠋⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠴⠒⠦⣀⣀⣀⣠⠔⠓⠲⠒⠊⠀⠀⠀⢀⡤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠈⢃
⠀⠀⠀⠀⢠⠖⠃⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣀⠀⢀⣤⣠⣄
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠳⣄⠀⠀⠀⢀⢀⡄⠤⠤⠄⣠⠔⠀⠈⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⠛⠁⠀⠀⠈⢳
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢦
⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠤⠤⠆⢀⡀⠀⠀⠀⠀⠀⣶⠀⠈⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠃⠀⠀⠐⠀⠀⢀⡤⠟⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠔⠲⣄⠀⠀⠀⣠⠖⠦⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡒⠒⠒⠀⠈⠁⠀⠀⠐⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⢀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠁⠉⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠒⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⢀⡶⣀⣀⣀⡀⠈⠋⢉⡀⠀⠀⠀⠀⠀⢀⠤⠤⠄⡤⢤⠤⠄⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠒⠚⢹⡍⠉⡇⠈⠈⠑⡎⠛⢤⡄⠀⠤⢀⣠⣀⡀⠀⠠⡀⢠⡀⡀⠀⠀⠀⣀⣈⣀⣉⣉⡉⣉⠆⠐⠒⠂⠙⡀
⠀⠀⠀⠀⠀⡈⠀⡘⠢⠤⣄⣀⣀⡀⣧⢰⠀⠀⠀⠀⡇⠀⠐⠀⢠⠖⠀⠀⠀⠛⠀⠲⣄⠀⠀⠀⠀⡠⠊⠉⠁⠀⠉⠉⡯⠁⠀⠀⠀⢀⣀⠃
⠀⠀⠀⠀⢠⠉⠸⢡⠀⠀⠀⠀⡀⢀⠁⢸⠢⢄⠀⠀⡇⠀⡆⡔⠁⢠⡄⠀⠀⠀⡒⠁⠘⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠⢁⠀⠀⡀⠀⠈⠋⠸
⠀⠀⠀⠒⡌⠒⠣⣀⠀⠀⠀⠀⠋⢸⡄⠸⠀⡠⠀⠠⣇⠀⡇⠉⢤⡤⢤⠄⠚⠂⠁⠚⠃⠙⠒⢂⠦⡀⠀⢀⠀⠀⣀⠸⣜⡆⡌⠑⠒
⠀⠘⠂⢰⡿⠆⢰⣤⣾⠉⠁⠀⠸⡌⠀⡆⠍⠄⠤⠶⣿⠀⡏⠃⠀⠀⠀⢠⡀⠀⠀⠀⠶⠀⠀⠉⠢⠌⢋⠉⠉⠁⡸⢆⣸⠀⠘⠂⠁
⠀⢠⠄⣸⢂⠠⡉⢁⢐⡛⠉⠴⠦⠗⠀⠇⣦⣤⣤⣄⣿⠀⢇⡄⠀⡰⢀⡈⢀⣀⣐⣀⣀⣴⣠⢖⣀⡀⠉⠀⠋⠀⠀⢀⢹⡁⠀⠀⠀⢠⢢
⠀⠠⠄⣗⠂⠠⠇⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⢁⠄⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠒⠒⠚⠒⠛⠊⠀⢀⡀
⠀⠠⣰⠃⠀⢽⠀⠄⣠⡜⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠘⠄⠰⠿⡞⠏⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⡄⠀⠀⠀⠀⠘⠁
⠀⠀⡿⠒⠩⠼⠛⣀⠀⠀⠀⠀⠀⠀⡠⠊⠁⣀⠀⣀⠉⠲⢄⠈⠁⠀⣇⡡⠸⠖⠻⠒⠻⠶⠽⠶⠛⠛⠚⢉⠤⠒⠀⠀⠐⠢⢄
⠀⠀⠙⠢⢄⣀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠐⢁⠔⠒⠢⣍⢢⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣠⠔⣈⠁⣐⠢⡀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣂⠐⢆⡠⠀⡇⠀⠟⠆⠈⠄⢇⡸⠤⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⣀⠀⢠⡄⢠⠁⠎⠀⡤⡀⠑⡈⡄⢸⡀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠶⣄⠈⠂⠀⠰⠊⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄⠘⣇⠀⠢⣀⣉⣁⡠⠃⡰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠈⣁⠈⠠⠚⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠆⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠶⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠘⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠐⠂⡠⠛⠛⠀⠀⠀⢀⠄⠐⠒⠒⡀⠒⠢⠤⡀
⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⢠⠀⡐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢥⡀⠀⠀⠀⠀⠈⠁⠂⠀⠂⠐⠒⠀⢨⠉⠉
⠀⠀⠘⠠⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⢄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡘
⣀⣀⣀⣛⣓⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣂⣁⣂⣀⣈⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢁⡴⣺⢍⡩⠟⢛⣩⣍⣉⣟⡒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠁⠀⡰⢋⡾⢡⠏⠀⡞⠉⢀⡶⠦⣦⣀⠉⠳⣏⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⡃⠀⠀⢰⡇⣾⡇⢸⡄⠈⢄⠀⠀⠀⠀⠀⣹⠇⠀⠘⣧⠈⠷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢰⣿⡇⠀⠀⠸⣇⠸⣷⡀⠳⣄⡀⠀⠘⠒⠛⠋⢁⣠⣠⣶⠟⠀⢸⡌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⢧⠀⠀⠀⢿⣆⠙⢧⣒⡀⠉⠉⠀⠀⠀⠼⠿⠿⠋⠀⠀⠀⣻⡇⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⣿⣦⠀⠀⠈⣿⣧⠀⠉⠛⢶⣦⡀⠀⠀⠀⠀⠀⠀⢄⣨⠾⠋⠀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣄⠀⠀⠛⢿⣷⣦⠀⠈⢿⣶⣦⠀⠀⠀⠉⠙⠛⠶⠶⠶⠟⠋⠉⠀⢤⡾⣣⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢟⡁⠀⠀⠀⠙⠻⢷⣤⠀⠙⠻⣿⣷⣦⡄⣀⡀⣤⣀⣰⣂⣀⡤⢖⣩⡼⢋⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠘⣇⠀⠄⠀⠀⠀⠀⠉⠛⠶⠤⣄⡈⣉⣉⣛⣛⡛⣛⣋⣩⣥⠖⢛⣉⡶⢺⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⣳⠉⡆⠀⠀⠁⠠⠀⠀⠀⠀⠀⠉⢉⠉⠙⣉⣉⣉⡩⠀⠄⠀⠹⡁⠁⠹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠘⠟⠉⠛⠀⠀⠀⠀⠀⠁⠀⣠⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡘⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⠿⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡄⢠⢠⣆⠀⢠⢰⣄⠀⣦⠀⠀⢠⠀⣤⡀⠀⣴⠀⣠⠖⢦⢠⣄⠀⣴⠀⠀⠀⢠⠖⢤⡀⣠⠖⢦⢰⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⢸⡏⢣⣸⢸⠈⢦⡿⠀⠀⣼⠀⠈⠳⡔⢹⢀⡃⠀⢸⢸⡏⢧⣼⠀⠀⠀⢸⠀⢸⡇⡋⠀⢸⢸⠀⠀⢸
⠀⠀⠀⠀⠀⣶⠄⢀⡇⠀⠀⠘⢸⡇⠀⢹⢸⠀⠀⣷⠀⠀⢸⠀⡀⠀⠀⢸⢸⡇⠀⣸⢸⠇⠀⢿⠀⠀⠀⢸⠀⢸⢣⡇⠀⢸⢸⠀⠀⢸⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⢸⠀⠀⣿⠀⣄⢸⠀⡇⠀⠀⣼⢸⡇⠀⣿⢸⠀⠀⢸⠀⠀⠀⢸⣖⠁⠸⡇⠀⣾⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⠄⣼⠸⡇⠀⢸⢸⠀⠀⠯⠰⠁⢸⠀⠇⠀⠀⢿⠀⢇⢀⡇⢸⡄⠀⢸⠀⠀⠀⣾⠈⢦⠀⢇⢀⡟⢸⣀⡀⢸⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠒⣒⡒⠒⠒⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠉⢀⣴⠶⠛⠋⢉⣉⣉⡉⢉⠘⠲⢦⣄⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡵⠋⠀⣶⡟⠀⢠⡾⠛⠛⣉⣉⣙⡛⠻⣶⣀⠈⢷⣄⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢸⡇⠀⢰⣿⡇⠀⣿⣁⣀⠈⠛⠿⣿⣷⡄⠈⣿⡀⠸⣿⣿⡆⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⢸⣇⠀⢸⣿⠅⠀⠘⠿⢿⣯⣶⣶⣾⠟⠒⢀⣾⡇⠀⠈⣿⣿⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣿⣤⠀⢻⣿⡄⡂⠀⠀⠀⠉⠉⠀⠀⢰⣿⣿⠇⢀⠈⢧⣿⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠠⠘⢻⣿⡀⠀⠻⢿⣿⣷⣶⣤⣤⣤⣶⣶⣿⡿⠃⢠⠾⣼⣿⡟⠀⡂⢽⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠡⡈⢿⣷⣮⡀⢄⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠰⣯⣾⣿⢟⠃⡰⢃⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠀⠙⠿⣿⣶⣦⣄⣢⣤⣀⣰⣤⣤⣢⣶⣿⣿⠟⠋⣠⢾⣏⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠈⠛⠿⠻⠿⠿⠿⠿⠿⠛⠛⠛⣉⣤⣒⢛⣱⣭⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠁⠈⠁⣀⣅⣉⣌⣿⣿⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀⣀⡤⠤⠤⠤⡄⣠⣄⣀⡤⣷⣶⣶⣾⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⠀⢀⡀⠀⠀⠀⠀⠐⠀⠐⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠙⠻⣿⡆⡀⠈⠐⠂⠀⢀⡈⠁⠀⠀⢀⡀⡔⠁⢀⠀⠆
⠀⠀⠀⠀⠀⢀⡠⢾⡿⢿⡏⣇⡀⠘⠂⠈⠹⠔⠀⠀⠂⠐⢦⠀⠀⠀⠙⢁⠠⡊⠈⢠⠃⡀
⠀⠀⠀⠀⢠⠏⠀⠙⠁⠘⠗⠀⡇⠠⣀⠀⠈⠒⠒⠀⠤⠠⠤⠀⠀⠀⠊⡀⢀⡤⠞⠀⠀⠈⣰⠂⡀
⠀⠀⠀⢀⡟⡴⢦⠀⠀⠐⠀⠘⠏⠀⠀⡁⠙⣆⠖⠂⠐⠚⢢⠠⠈⠑⠊⢻⡜⢀⠀⠀⠀⠐⠁⢀⠼
⠀⠀⠀⠘⣿⠃⠸⣄⠀⠀⠀⠀⠀⠀⠈⠈⠙⠂⠒⠁⠤⠄⠄⠁⠐⠒⠒⠉⠁⠀⠀⠉⢀⣄⢰⠃⠀⢤
⠀⠀⠀⢰⣿⡀⠀⢹⢠⠋⠓⠖⠒⠲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠒⠖⠋⠈⣾⠃⠀⣸⣧⡀
⠀⠀⠀⠀⢿⣿⡀⠘⠛⠀⠀⠀⠀⠀⢸⡆⢀⡞⠉⠉⠳⠦⠤⠂⠉⠹⣆⠸⠃⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠙⠸⣷⣄⡂⠀⠀⠀⠀⠀⢨⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⣠⣶⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠴⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⢦⣤⣤⣄⣤⣦⠶⠶⠴⠶⠟⠛⠋⠁




⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠔⠒⠒⢦⡀⠀⠀⠀⠙⣦⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⡿⠀⠀⠀⠀⣠⠿⠖⠀⠀⢀⣿⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣻⣃⠀⠀⠈⠐⠦⠤⣀⣀⢀⣠⡦⠞⠛⠉⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⢣⣅⡒⠲⠦⢤⣀⣀⣀⡀⢀⣀⣄⣀⣀⣀⣒⣬⣾⣿⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣭⣥⣬⣭⣤⣾⣷⠿⠿⠛⠋⠉⠀⠀⣠⢄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠦⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣀⡴⠞⠛
⠀⠀⠀⠀⠀⠀⡇⠀⠠⡀⠀⣴⡽⠷⣬⣵⣄⠀⢀⣄⣠⣄⡀⠀⠀⢀⣠⣀⡀⢁⡀⠀⣀⣀⣤⡴⠟⠋⠀⠀⣴⡤⠠
⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠉⠛⠻⠷⡾⠿⠾⠿⠾⠟⠿⠛⠛⠛⠉⠉⠀⠀⠀⢀⣀⠀⠙⢠⡆
⠀⠀⠀⠀⠀⠀⢳⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠶⠒⠋⠁⣀⠀⡹⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣝⠇⢀⣀⡀⠀⠀⠀⠀⣰⣯⣏⠀⠀⠀⠀⠀⠀⠤⠞⠛⠛⠻⢿⣏⢦⠀⠀⢤⣺⣟⣵⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢀⡟⣱⣄⠀⣶⡋⢽⡇⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⡄⠀⢸⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣻⣧⣴⣯⡒⢶⣶⣾⠄⠀⠀⠀⠀⣀⣄⣠⣀⣠⣤⡀⠀⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠶⠿⠷⠶⠴⠶⠶⠿⠷⠞⠛⠋⠉⠁






⣿⠿⠿⠿⢿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣉⣑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠰⠯⠤⠄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠙⠳⣦⠀⠀⠀⠠⡀⠀⠀⢀⡠⠒⠁⠄⠀⠀⠀⠀⠀⠀⠈⠃⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣯⢀⠀⢀⡠⠂⠀⠀⠀⠀⠀⡈⠀⠒⠀⡀⠀⠀⠠⠄⠐⡀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⠓⠠⢄⠰⠑⠲⠬⡁⠀⠀⠀⠀⠀⠀⡀⣀⡠⠔⠉⠢⡤⣆⠠⢁⣤⣀⣀⡠⢧⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠈⠀⡀⢀⡖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠓⠶⠞⠂⠉⢳⠀⠲⡑⠤⢀⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⡎⠑⠀⠀⡸⣉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣞⣉⣉⣢⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣀⣀⡠⠎⢁⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢢⡀⢀⠀⠀⢀
⠀⠀⠀⡠⠒⠖⠉⠀⠀⠀⠀⠈⠑⠢⢄⡀⠤⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠒⠢⣀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠀⠀⠈⠀⣀
⠀⠀⠊⠀⠀⠀⣤⠀⠀⠀⠀⠰⠆⢠⠀⠉⠀⠀⠀⠉⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠐⠀⠁⠀⡀⠀⠀⠀⠀⠀⢀⠌⠈
⠀⠀⠀⢠⡀⠀⠁⠀⠈⠂⠈⠀⢀⡼⠦⣀⠀⠀⠀⠀⠈⣒⡰⠁⠀⠱⢄⣀⣀⡔⠤⡀⠀⠀⠠⠠⠐⠀⠀⢰⠂⠀⠈⠁⡆⠀⠄
⠀⠀⡴⠃⢈⡱⠒⠒⠒⠒⠊⠻⣁⡈⡆⠀⠈⠀⠀⢠⠔⠁⠘⠦⠤⠊⠀⣏⡀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠨⠁⠂
⠀⠀⠀⠀⣇⠁⣀⠐⣀⡆⡀⢀⠁⡞⠀⠀⠀⠀⠀⠐⠄⠒⠤⠀⢄⠈⠔⠂⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣂⣈⡁⠀⠀⣀⣄⡀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢛⣩⠤⠒⢐⠂⢈⠉⠙⠷⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠁⠀⠻⣅⢈⣆⣠⡇⢈⠀⠀⠆⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢒⣒⠲⢄⠀⠀⠀⠀⠀⠀⠀⣷⣧⣄⠑⠲⠶⠶⠨⠭⠥⠒⣡⣴⣦⡴⣶⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣎⢠⠌⣷⠀⢻⠲⡄⠀⠀⠀⠀⣿⢿⣍⡑⠀⢀⣠⣤⠀⠀⣉⣼⣿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠿⢤⣈⣁⠴⠃⢀⡟⠀⣿⡀⠀⠀⠀⢿⠂⠈⢛⣶⣿⠿⢿⠷⠶⠛⠋⠁⣴⣶⣿⠏⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣠⣴⠃⠁⢰⣿⡇⠀⠀⠀⠈⠓⠾⣿⣿⣿⣶⣦⣤⣤⣤⣤⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⢩⣯⡿⠶⣤⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣯⣀⣀⣼⠿⠛⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⢠⡶⢲⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⢟⡥⢤⣤⡀⠈⠃⢀
⠀⠀⠀⠀⢀⡿⠀⡟⣸⠆⣴⡔⣷⢠⣶⢺⡆⢠⡞⣦⢀⣶⢺⣦⢺⡆⣠⠞⣧⢠⣦⢺⡆⠀⠀⠀⢠⣟⠙⣿⣧⣸⣴⣦⣿⣿⡆⠀⠈⣇
⠀⠀⠀⠀⢸⡇⠀⢀⡿⢠⡟⢸⠏⣼⠇⣾⢃⣿⢠⡟⣸⡇⣼⠃⡿⢠⡿⢤⡟⣼⠃⡾⢁⠀⠀⠀⢸⣿⡄⠘⠻⢿⣿⣿⡿⠟⠀⠀⣠⣿
⠀⠀⠀⠀⠈⠛⠒⠉⠛⠙⠃⠙⠊⠛⠀⠛⠋⠛⠉⣛⠙⢀⡛⠀⠛⠈⠛⠊⠀⠛⠈⠛⠁⠀⠀⠀⣨⣿⣿⣧⣤⣀⣀⣀⣀⣠⣴⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⢆⡟⡷⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢞⡟⣠⡏⣿⢠⣟⡞⣸⣣⠇⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡟⠈⠃⣿⢣⡿⢸⡏⠠⣿⢁⡔⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠋⠀⠈⠋⠁⠙⠋⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠠⠀⠄⠄

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠶⠖⠈⠙⣯⠷⢦⠉⠓⠶⠆⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠋⠒⠋⠀⠀⠀⠀⠀⠀⠉⠙⠓⠋⠉⠉⠛⡄⠀⠀⠀⠀⠀⣀⣤⠛⢦⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⡌⠀⢠⣦⠀⠀⣀⣀⠀⠀⢰⣶⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠈⡆⢀⢰⡎
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⣀⣀⣀⣤⡾⠧⣄⠈⠁⠀⠠⣀⣨⡇⠀⠀⠀⢀⠤⢼⡓⢤⢄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠋⠁⠙⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣠⠇⠀⠜⠲⠶⠠⠄⠸⠗⠤⠒⠶⠶⠛⠀⠠⢧⣀⣀⠀⠀⣀⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣠⠔⠻⡀⠀⣀⠀⠀⠀⠹⣈⠁⠀⠀⠀⣀⠀⣸⠈⠑⠦⣤⣀⣀⣀⣠⡴⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠚⠋⠁⠀⠀⠙⢺⠉⠱⣄⠤⠤⠤⠤⠄⠤⠞⠉⡛⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⡤⢷⣀⠤⠔⠒⠒⠒⠒⠠⢄⣾⣁⣀⣀⢀⣀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠢⡼⠃⠀⠙⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠋⠀⠈⠷⠒⠲⡄
⡇⠀⠀⠀⢀⡾⣄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠷⣄
⡇⠀⠀⠻⣍⠀⠈⡟⠃⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠘⠇⢐⠃⠀⠀⠁⠀⠀⣧⡀⢀⡀⠀⠀⠀⠀⠀⢸⠇
⡇⠀⠀⠀⠶⠒⠲⠇⠀⠀⠀⠀⠀⢧⣀⣀⣠⢦⡀⢀⡼⠉⠓⠂⠄⢀⣀⣈⣁⣀⣀⣀⡠⠤⢞⠀⠉⠉⠳⠤⠴⠚⠳⠖⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⣱⡖⠀⣀⣀⣤⠤⣤⣀⡀⣀⣤⢊⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠃⠈⢸⠋⠁⠀⠀⠀⠀⠀⠉⠙⠇⠀⠘⢦⣄⣀⣀⣀⣀⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⠒⠛⠋⠉⠀⠈⢡⠔⠚⡁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⡎⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⣦
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠸⡿⠀⠀⣀⢀⡀⠀⠸⠿⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⣀⣠⡤⠖⠛⡤⠤⡀⠀⠀⠀⠸⡠⠁⠀⠀⠀⢀⠤⣼⠛⠲⢤⣤⣀⣀⣀⣀⣠⡴⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠘⣤⣤⠼⠶⠶⠶⠶⠶⠶⠶⠶⠶⢧⣤⣤⠃⠀⠀⠀⠀⠈⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠙⢻⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠉⠳⡄
⡇⠀⠀⠀⠀⠀⠀⣀⣠⠟⠧⣀⡀⠀⠀⢸⠃⠀⢶⣀⠼⠸⠀⠰⡿⠀⠀⡀⠀⡀⠀⠸⡿⠀⠈⠆⠑⠤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡇⠀⠀⠀⠀⠀⠀⠈⡆⢀⡠⡎⠀⠀⠀⠀⠳⣄⣀⣀⡤⢧⣀⣀⠀⠀⠀⠹⣀⠁⠀⠀⠀⠀⢀⡶⢤⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⣤⡴⠋⠳⢤⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣏⠈⠓⠆⠦⠤⠄⠤⠤⢦⡶⠾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣠⣀⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠤⠐⠒⠀⠀⠐⠚⠦⠤⠾⠄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠉⠀⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠂⠉⠀⠀⠀⢀⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠛⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⢨⠛⠲⠶⠤⠤⣤⠤⠴⠖⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⡤⠖⠋⠈⠳⠄⣀⣀⠀⠀⠀⠀⢀⣀⣀⡠⠴⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⡄⣰⠋⠀⠀⠀⠁⠀⠀⠀⠩⣄⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⢸⠀⡆⠀⠀⠀⠋⢠⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠒⠘⠦⠾⠶⠧⠴⠓⠒⠔⠃
⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣳⡶⣿⣴⢶⣾⢿⣼⣿⣛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⡆⢡⣖⣴⣀⡠⢤⣅⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠸⢿⣦⣼⣀⣀⡈⠉⡉⠀⣨⣿⡿⠂⠀⠹⣀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡆⠸⣷⣄⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣠⣿⠇⠈⣆⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠘⢷⣤⣀⡉⠙⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠓⠚⠋⢉⣀⣤⠞⢁⣠⠏⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⠶⠦⠤⢤⣤⣤⣦⣤⣴⠶⠶⠾⠛⣋⣩⡤⠶⠛⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠖⠲⠒⠒⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠺⢢⣈⣩⣤⡄⠀⠀⠀⠀⢀⡄⢀⡑⠊⡀⠀⠀⠀⠀⠀⠘⢷⣌⣈⣥⡄⠀⠀⠀⠀⠀⡠
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⣀⠤⣀⠠⡄⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⡁
⢀⠐⡟⠀⠀⠀⡂⠰⠒⠀⠀⡆⡀⠀⠈⣿⠀⢸⠀⠖⠈⠀⡄⢾⠀⠀⠀⢐⠀⠖⠆⠀⠀⢀⠀⠀⢻⠀⢠
⣨⡴⠃⠀⡘⢧⣌⠀⠀⠀⠄⡀⣤⡀⠀⠀⠐⠌⠀⠀⡤⢞⢤⠞⠀⢀⠻⣄⡁⠀⠀⠠⡀⢠⣄⠀⠀⠈⠂
⠉⠀⠀⠀⢻⣄⠄⢉⠀⣠⡬⢴⡇⢳⠀⠀⠀⠐⠢⠖⠗⠙⠁⠀⠀⢘⣧⠤⠉⡀⢀⡤⠥⣾⢘⡄⠀⠀⠐
⠀⠀⠀⠀⠘⣿⡤⠿⣷⠟⢀⣼⡿⠋⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣧⠼⢿⠞⠁⣠⣿⠟⠁
⠰⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⢀⢸⡀⠢⠈⠘⠀⢀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⢀⠰⣇⠰
⢀⣉⠀⠀⠀⠀⣠⣴⡒⠖⠤⠀⠀⠀⣹⣂⡙⠂⠄⠀⢐⡀⣈⠀⠀⠀⠀⢠⣤⣖⠲⠦⠄⠀⠀⢸⣇⡈⠓
⠞⢹⠀⠀⠀⡠⢀⣀⣀⠀⠰⡀⣆⠀⣿⣇⣠⣦⢠⡶⠤⣴⠋⡇⠀⠀⢀⠄⣀⣀⠀⠀⢄⣤⠀⢸⣿⣀⣶
⠶⠞⠀⠀⠆⠀⠉⠠⣤⢱⠀⠡⠉⠀⠈⠳⢬⣯⣉⣀⣴⣿⠞⠁⠀⡖⠀⠈⠁⢤⠙⡄⠸⠈⠁⠀⠓⢦⣽
⠀⠀⠀⠀⢷⠔⣄⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢹⡆⢦⡀⠀⠈⣠
⠀⠀⠀⠀⠀⠛⢷⣌⣩⣤⠄⠀⠀⠀⠀⢀⠄⢀⠭⠭⠄⠀⠀⠀⠀⠀⠘⠿⣌⣉⣥⡤⠀⠀⠀⠀⢀⡴
⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⡠⠤⢄⠐⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡄
⢠⠐⡏⠀⠀⠀⣂⠐⠙⠀⠀⠆⡄⠀⠀⠿⠀⢸⠀⠚⠀⠀⡆⢿⠀⠀⡀⢀⠀⠊⠆⠀⠐⢠⠀⠀⢻⠀⠰
⣠⡴⠃⠀⡈⠷⣌⡁⠀⠀⢂⠀⣴⡄⠀⠀⠘⠌⠀⠀⠤⣮⢴⠏⠀⢀⠻⢤⣉⠀⠀⠔⡠⢠⣄⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢦⡄⢀⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡁⠀⠀⠿⠾⠀⠀⢈⡷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠻⣄⣙⠲⠦⠤⠤⠴⠖⣋⣴⠏⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠈⠳⣤⣀⡉⠙⠛⠛⠛⠛⠋⢉⣀⡴⠟⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠛⠦⣤⣈⣉⡛⠛⠛⠛⠛⢛⣉⣁⣤⠶⠛⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣿⠲⣦⣬⣍⣉⣉⣉⣉⣉⣉⣩⣤⠴⠖⠋⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⣿⠀⢸⢡⣍⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠀⠀⠀⢸⠀⠈⠙⠓⠶⢤⣄⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠦⠄⠀⠀⠤⠴⠶⠖⠛⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠚⠋⠉⠉⠀⠀⠈⠉⠙⠓⠶⡒⠒⠦⠤⣤⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⠶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⢘⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⠉⠀⠀⠀⢠⣠⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⠉⠛⠒⠶⠶⠶⠶⠶⠚⠉
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖⠋⠁
⠀⠀⠀⠈⠛⠲⠶⠖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⢉⡿⠛⠛⠛⠛⠉⠉⠉⠉⠀⠈⣷⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⠞⢀⠘⡆⠀⡼⠁⠀⠀⠀⠀⠀⢸⡄⣄⠈⣧
⠀⠀⠀⠀⠀⡔⠫⠽⠷⣶⣶⣒⣲⣶⣶⣤⡼⡧⢤⡀⠈⠙⠁⠀⠛⠚⠋⠀⠀⡠⠦⣼⡧⠞⠀⡿
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⢹⣀⣀⣀⠀⠀⠀⠀⢀⡞⠁⢀⣿⣀⣤⠞⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣾⣀⣉⡉⠉⠉⠙⠛⠛⠳⠦⠞⠁
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⡇⡇⠈⠉⠉⣩⣵
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣇⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢲⡤⠤⠤⢤⣤⣄⣀⣀⣀⣀⡀⢘⣽⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠒⠒⠒⠻⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⠛⠛⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⡠⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⠃⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⡆⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢧⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣰⣯
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⢀⣀⡀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⢀⣤⠞⠁⢸⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣰⠃⡏⠀⢙⡆⠀⠀⠀⠀⠉⠛⠒⠲⠶⠤⠤⠴⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⣀⡇⠀⡼⢁⡞⠋⠉⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠛⣦⠐⣇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠁⢸⡆⠀⠀⠀⠀⢹⠀⢀⣠⣤⣤⣄⡀⠀⠀⣼⠃⠀⠀⠀⢸⣄⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠻⣤⣼⠇⠀⠀⠀⢠⡟⠀⣾⠁⠀⠀⠀⠙⣆⠀⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠒⢂⣀⡀⠀⠁⠐⠒⠒⠠⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⢀⠀⠀⠀⠈⠒⠒⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⣀⠀⠀⠈⠒⠦⠥⢬⣍⣙⣳⣤⣀⣀⠤⠤⠒⠀⠀⠀⠀⢀⠜⠀⠀⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠁⠀⠀⠲⢤⣈⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⡀⠀⠠⠖⠋⠁⠀⠀⠀⢀⠀⠀⠈⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠒⠦⢤⣀⡀⠉⠉⠙⠓⠒⠒⠂⠁⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠰⠤⣄⣉⠙⠓⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠀⠉⠁⠀⠀⠀⠀⣀⣤⡀⠀⠀⡖⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⣠⠊⠀⠈⢷⡄⠸⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠏⠉⠙⠛⠻⠿⡾⠁⠀⠀⠀⠈⠳⠤⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠄⢰⣦⡀⠀⢀⣄⣀⠴⠻⢷⣄⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠊⢹⡀⠀⡏⠀⠀⠀⠀⠀⠉⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢸⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠷⡀⠀⠀⣠⡴⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠓⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢂⡠⠀⠀⡍⠀⢾⣏⣾⣅⣤⠒⡶⣤⣄⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⢋⠀⠐⢿⣷⣦⣴⣁⣀⡀⠀⠉⠉⠀⠀⣸⣿⡿⠃⠀⠈⢣⡀⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠁⣾⣇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⢀⣿⡷⠈⢦⠈⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢰⣇⡀⠈⠙⠻⠿⣷⣶⣤⣤⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠟⠋⠀⣀⡾⠃⢀⡷⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠻⠷⣶⣤⣄⣀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⡀⣀⣤⣴⡶⠟⠋⣀⣴⠟⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠙⠛⠛⠓⠚⠲⠷⠿⠾⠿⠾⠿⠿⠟⠛⢛⣋⣩⣤⡶⠾⠛⠋⠁⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⠤⣄⣀⣘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⠛⠛⠒⠒⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⢠⡾⠛⣉⣭⣭⣍⡙⠳⣶⣄⠈⠳⣖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⣿⠀⢀⣿⣁⠀⢿⣴⣦⠀⢿⡆⠈⢻⣷⠀⠈⣷⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠸⣿⣄⡀⠙⠿⣷⣴⣠⣦⣴⣿⠇⢐⣿⣿⠀⡀⣿⡇⠀⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣷⡀⠙⢻⣷⣶⣀⠈⠉⠙⠛⢋⣁⣄⣼⣿⠏⢀⣼⣿⣗⠀⠀⠜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣷⣷⣀⡈⠙⠛⠻⠿⠿⠿⢿⠿⠿⠟⢁⡔⣻⣿⣿⠇⠀⢀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡯⡉⠢⢀⠙⠻⣿⣿⣶⣦⣄⣠⡀⣠⠄⡀⢀⣴⣮⣾⣿⡿⠋⠀⠀⡺⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⠉⠂⠌⠉⠙⠛⠿⠿⠿⡿⡷⠿⠿⠟⠛⢉⠀⠀⠀⣠⢶⣟⡀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣡⣅⣇⣊⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⢁⣸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣴⢤⠤⠀⠀⠀⠀⠀⡀⡠⡸⢶⣶⣾⡷⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠾⣥⡿⠶⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡤⠤⠒⠒⠒⠒⠒⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠈⡌⠩⡗⠒⣶⠋⢹⣴⡚⠉⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡤⣄
⠀⠔⠁⠙⡳⠀⢰⡦⠀⣤⠃⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠇⢠⠗⠲⣤⠔⢦
⠀⢡⠤⠄⠷⣶⠂⢰⡄⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⣉⠆⢀⣅⠀⠛⢤⠤⢄⡀
⠀⠸⡆⠀⠀⠘⠒⠋⠀⠀⠀⠀⢀⡀⣧⠀⠀⠀⠛⠁⠀⢀⠀⡀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⢳⡀⠀⠀⠈⠉⠀⠓⡖⠂⣩⠤⠾⠛⣄⣠⡔⠁
⠀⠀⠉⠠⣀⣀⠀⠀⣀⣀⡤⠖⠋⠀⠈⠣⣄⡀⠀⠀⠀⠈⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠳⠔⠫⣃⠀⢀⡱⠀⣧
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢦⡤⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠚⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠑⠊⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⠉⠉⠃⢄⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠉⠙⣦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣽⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠢⠤⠤⠤⠤⠤⠤⠤⠤⠴⢤⣀⣀⣀⠴⠧⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠤⠤⢤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⣁⣠⣤⡴⠶⠶⠶⠶⠶⠤⠤⢤⣄⣉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡿⠋⢀⣠⣼⠛⠉⢀⣠⣤⣤⣶⣶⣦⣤⣤⣀⡈⠙⠻⣦⡀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢡⡟⠀⠀⣸⣿⠁⠀⣸⡿⠋⠁⢠⣴⣤⣤⣤⠈⠙⢿⣶⠀⠈⣿⣦⣀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣼⡇⠀⠐⣿⣿⠀⠀⣯⣦⣀⣀⠈⠙⠻⢿⣿⣷⠀⠀⢿⣇⠀⠹⢿⣿⡦⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⡆⣿⡇⠀⠀⣿⣿⠀⠀⠈⠿⣿⣿⣿⣾⣦⣶⣿⠋⠂⢀⣾⡿⠄⠀⠘⣿⣿⡄⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣿⣂⠀⠹⣿⣦⠀⠄⠀⠀⠀⠉⠙⠛⠉⠁⠀⡠⣿⣿⡗⠀⠀⢘⣋⣿⡇⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⡀⢹⣿⣭⠠⠀⢻⣿⣷⣶⣌⣰⣂⠀⠀⠀⣀⣠⣤⣿⣾⠿⠀⢠⡗⢴⣿⣿⠄⢠⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠣⡀⢺⣿⣧⡀⠄⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⣰⢃⣸⣿⣿⡗⠀⡘⢨⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠑⢄⠛⣿⣷⣦⣍⠖⠤⢀⣀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣞⣳⣿⣿⣟⠑⠁⣴⣇⣸⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠀⠀⠀⠀⠈⠹⢿⣿⣿⣷⣦⣬⣴⣒⣀⣤⣶⣶⣞⣷⣿⣿⣿⡿⠋⢁⡴⠞⢑⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠿⠻⠿⠿⡿⢿⠿⠿⠟⠛⠋⠙⢉⡠⠴⡚⠛⠴⣥⡾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⡀⣀⡤⡞⣬⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⠄⠀⠀⠀⠀⠊⠀⢀⡀⠀⡀⠀⠤⠀⠀⠘⣠⣇⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣯⣽⣟⣐⣉⣉⣳⣐⣛⣒⣘⣒⣞⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠉⠙⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠊⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⣄⣀⣠⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡸
⠀⣠⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠻⠟⠀⠀⠀⠸⠔⠊⠉⠁⠀⠀⠀⢀⡴⠦⡞⠁
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣠⠤⠖⢻⡀⠀⢸⡆
⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢉⡷⠒⠦⠤⢤⠤⠊⠀⠹⠋⠉⠁⠀⠀⠀⠀⠑⢲⡞
⠈⠣⣄⠀⠀⠀⣀⣠⠤⠒⠁⠀⠀⢠⠏⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⠴⢦⠀⠀⣄⣀⣀⣀⣀⣠⠤⣄⠀⠀⢸