Dory Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⡠⠚⢁⣀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⢪⠔⢋⡽⠒⢋⠥⠒⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⢊⡔⢁⡤⠞⢀⡔⢁⡴⣋⠤⠒⢛⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣶⣖⢉⣠⣯⡤⠶⣟⣩⣵⣯⢔⣒⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⣿⣿⣿⢟⣽⢞⣻⣿⣿⣻⣿⡭⠿⠿⣷⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⣯⣿⣿⣿⣿⣿⢣⣿⣿⡿⣿⣶⣾⣿⣿⣿⣿⣶⣯⣝⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⡾⣿⡛⠛⣻⣼⡟⣿⣿⣿⣿⣏⢾⣿⣿⢟⣯⢻⣿⣿⣿⣿⣟⢿⣿⡿⣿⣿⣟⣥⣴⣶⣿⣿⣿⣿⣿⣭⡙⢿⡇
⠀⠀⠀⣠⣾⣿⣿⣿⢸⣿⣿⢟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣿⢹⣿⣿⣿⡇⣿⣿⡎⣿⣿⣿⣿⣿⣻⣿⣽⣿⣻⢿⣿⣦⢻
⠀⠀⠠⣿⣿⣿⣿⣿⣷⣥⣾⣿⣿⣽⣿⣽⣿⣿⡿⣷⣭⣽⡿⣟⣵⣿⢏⣾⣿⣿⡿⢡⣿⣿⣿⢿⣿⠭⠭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠈⠙⠿⣿⣿⣿⣾⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⠟⣱⣿⣿⣿⣿⣼⡿⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⡿⠟⣡⣾⣿⣿⣿⣟⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠿⠿⢟⣫⣵⣾⣿⠿⢟⣩⣴⣿⠿⠛⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡗⢾⢟⠛⠛⠛⠛⠓⢿⡏⢹⠿⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⣦⠙⢦⡀⠀⠀⠀⠳⣄⠢⠈⠺⡕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠧⠀⠑⠀⠀⠀⠀⠈⠑⠄⠀⠸⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠉⠐⠤⡀⠀⠐⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠁⠂⢄⠀⠈⢳⣤⡀⠈⣦⣤⡈⢳⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣙⣾⣦⣿⣿⣷⣿⣿⣿⣿⣿⣦⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣟⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣨⣟⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣉⣒⣦⡀
⠀⠀⠀⠀⠀⢍⡙⠶⢤⡀⠀⠀⠀⠀⡀⣠⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⣌⣻⠿⢲⣦⣤⡀
⠀⠀⠀⠀⠀⣁⠠⠀⠀⠙⢷⡀⠈⠳⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣷⣶⡝⣿⡟⢩⣟⠤⠐⡏⣛⠿⠗⢿⣿⢷⡏⠭⡉⢿⠢⣄
⠀⠀⠀⢀⠒⠂⠈⢑⣴⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡻⢿⠿⣧⢿⢣⣾⠇⠀⠀⠁⡨⠟⠋⠿⢻⣷⠶⣻⠅⢰⣴⣥⠤
⠀⠀⠀⠀⠠⠬⠤⠀⠀⠐⡻⣿⡿⠿⢿⣿⣿⣽⡻⠏⠉⠠⠚⣞⣿⣿⣻⣷⣿⣵⣾⣿⣿⣶⣄⢀⡜⢯⣧⠀⠀⢈⡛⣿⣿⠁⢻⣏⡔
⠀⠀⠀⠐⡀⢈⠁⠀⠈⢈⡤⠃⠀⢰⠹⣮⡻⣷⣄⡁⠀⢀⠈⠠⠿⢷⠿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣦⡌⠿⣷⣄⢈⣧⠏⡎⠀⠸⠋
⠀⠀⠀⠀⠃⠀⢈⡤⠞⠁⠀⠀⠀⠀⠀⠻⣷⣌⠻⣿⣥⣄⣠⡄⡠⢀⠀⡜⡻⢿⣿⣿⣿⣿⣞⠯⠸⢻⣶⣤⣭⣏⠉⡰⠋
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠻⣷⣤⣍⠻⢿⣷⣶⣥⣿⣷⣥⣆⣾⣿⣿⡟⠀⢀⣤⡠⠟⠚⠁⠠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣶⣶⣭⣭⣭⡿⠩⠍⣍⣭⣭⣭⣯⣥⣶⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⣿⣿⣿⡿⠟⣋⣤⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠉⠁⣰⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠚⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣟⠛⠛⠻⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣁⣤⠾⠟⠛⠛⠛⠶⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡴⠟⠉⠀⠀⠀⣠⡤⠴⠦⣤⣍⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⣠⡾⢋⡶⠋⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠈⠙⣆⠻⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⡀⠀⠀⠀⢀⣼⢏⣴⠋⠀⢀⣠⣤⣀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⣧⠀⠀⢠⡾⣥⡾⠁⠀⣰⠏⠁⠀⠈⠛⠀⢀⣤⣶⡾⠿⠿⠷⣦⣄⠘⡇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠸⣿⣿⡆⣰⡟⣠⠟⠀⠀⢠⡏⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠙⢷⣷⠀⢀⣠⣼⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇⢿⣯⣴⠏⠀⠀⠀⢸⠇⠀⠀⠀⠀⢠⡏⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⣿⣆⣸⣿⣿⠘⣿⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣧⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣷⣦⡀⠀⢿⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⣿⢿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⡇⢣⢹⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⠏⢻⣿⣿⣿⡗⠀⢸⠀⣰⢿⡿
⠀⠀⠀⠀⠀⢰⡇⠀⠙⢿⣦⡀⠀⠀⠀⢿⡛⢯⠸⡀⢆⢿⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠟⠁⠀⣀⡴⠋⠀⢸⡿⠿⠛⠁⣠⠏⣰⡏⣸⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢿⣦⡀⠀⢸⣷⠀⢆⢱⠘⡘⣧⠀⣀⡀⠘⡇⠀⠀⢠⣦⠀⠀⠀⠀⠉⠉⠉⠛⠉⠁⠀⠀⠀⢸⡧⣤⠔⠊⠁⢠⣿⢀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⠙⠻⣦⠙⠾⣷⡈⢆⢣⠱⢻⡞⠁⠙⡆⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⢠⣿⠇⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠠⡈⠢⢌⠳⢾⡛⢷⡈⢎⢧⢻⣷⠀⠀⡇⣿⠀⠀⣾⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⣿⡟⢠⡿
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠠⢀⡁⠢⢍⡢⣻⣎⢷⡌⢌⢻⣿⡇⠀⡇⣼⠀⠀⣿⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⣾⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠄⣈⡁⠒⠬⢽⣿⡇⠻⣎⡆⢿⣿⡴⠃⡿⠀⠀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁⣸⣿⠟⠁
⠀⠀⠀⠀⠀⢸⣤⣶⣶⣶⣾⠿⠿⠿⠿⢿⣿⡖⠛⠁⠀⠙⢿⣌⢿⣧⣼⠃⠀⠀⢿⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⢀⡈⣇⠉⠲⢤⣄⣀⣈⣿⣎⢿⡇⠀⠀⠀⢸⡇⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⠀⠀⠀⠀⠀⠀⠀⠙⢧⣻⡀⠀⠀⠈⣷⠀⠀⠀⠀⠉⠻⢦⣤⣀⣀⣀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⣿⣶⣦⣤⣤⣤⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠿⠚⠓⠛⠚⠒⠲⠶⠤⢤⣄⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣖⣒⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠔⠁⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠿⠀⡘⡄⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠐⡀
⠀⠀⠀⠀⣠⠊⠀⠀⠀⠁⠀⡅⠘⡀⠀⡎⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡉⠀⡀
⠀⠀⠀⣐⣌⠁⠰⣄⠀⠀⠠⠁⠀⣠⠞⠀⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡍⠀⠤⡁⠢
⠀⠀⠀⠐⠦⡽⣆⠀⠳⠄⠀⠀⡴⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠈⠢⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠾⢄⣀⣀⢀⣀⠀⠀⠀⣀⣀⣀⡀⢀⣀⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠪⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣽⣯⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣽⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡠⠂⠀⣠⠞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡔⢁⠔⠉⠀⡀⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⡴⠊⡔⠁⠠⠂⠀⣠⠎⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣉⢷⡾⠤⣄⣀⠤⠚⢁⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣾⣿⣵⣋⣤⡒⢩⠤⣒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠙⠋⠉⠉⠉⠉⠉⠙⠛⠻⢷⣿⣖⡭⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⣤⢀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢺⣷⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣀⠔⠉⠀⠈⣹⠇⣼⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡤⢭⡆⠀⠀⣀⠤⢒⣈⢇⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣻⣅⠀⠀⠳⠞⠁⠀⢸⠀⢹⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣯⣴⣾⣟⣉⠀⢀⣼⠀⠀⢸
⠀⠀⠀⠀⠀⠻⣿⡻⣧⠀⠀⠀⠀⠀⢸⡆⣸⡇⠀⠀⠀⠀⣾⣁⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣿⣿⠷⢬⡅⡸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠻⣼⣧⡠⠀⢀⡴⠟⢼⣯⡴⠶⠤⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡌⠙⠛⠯⢝⠓⠀⡁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⡟⠁⠀⠘⢿⡯⢍⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⡼⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣿⣇⠀⠀⠀⠀⠈⢦⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡏⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⠛⢃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡈⠙⠛⠛⠷⠶⢦⣤⣤⣤⣤⣤⣤⣶⠾⢟⡛⢀⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢻⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣾⣷⣼⣷⣽⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢻⣿⣿⣿⣿⣿⣿⣻⣏⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣇⣿⣿⣿⣿⣿⣿⣿⠿⡟⠿⣻⠟⢻⢻⡟⢫⣽⣼⣿⡟⢶⠦⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠙⠻⢿⣿⣿⡿⠛⠛⡉⣉⠌⠀⠐⠀⠀⠉⠈⠉⡟⣖⣁⣿⣿⡟⠁⠀⠀⠈⣷⣤⢀
⠀⠀⠀⠀⠀⠀⠠⣷⣿⣿⣶⣴⡾⣿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣿⡇⠀⣿⠌⡻⢿⣷⡷⡄⠀⢀⣾⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠈⢻⣦⡙⢦⠱⠝⠂⠀⠀⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠯⠟⠛⠡⣤⣴⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠷⡆⠈⠉⠂⢱⣄⣀⠀⠀⠘⣃⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣆⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣙⣿⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣖⣤⠤⠤⠦⠠⠄⢠⣀⡀⣀⣢⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⡺⠳⠺⠚⠋⠋⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢻⢿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣁⠔⠊⠀⣠⠖⠉⠀⣠⠜⠉⠉⣩⠟⠓⠒⢦⠤⣄⠀⠀⠀⠀⢀⣀⠤⠖⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠵⠒⠚⠛⠉⠉⠉⠉⠉⠛⠛⠓⠒⠲⠮⢤⣀⣠⠞⠁⠀⣠⠃⣀⡤⠚⠉⠀⠀⣀⡇
⠀⠀⠀⠀⢀⡔⢉⠤⢄⠉⢆⠀⠀⠀⣠⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠉⠙⠲⠴⠗⠋⢁⡠⠤⠒⠊⠉⠀⢷
⠀⠀⠀⣠⢾⠀⢧⣀⡸⠂⢸⣀⠀⢏⣀⠀⠀⢀⣀⣀⣀⠝⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢁⣀⣀⣀⣀⣀⣀⣸⡆
⠀⠀⡴⠁⠈⠣⣄⣀⣠⠔⠉⢨⠳⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠒⢉⣉⣁⣀⣀⣀⡀⠀⠀⠀⢘⡄
⠀⢸⣁⡀⠀⠀⠀⠀⠀⠀⢠⠧⠤⣈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢤⡴⠉⠓⢤⡀⠈⠉⠉⠉⠉⠉⠉
⠀⠈⢣⡉⠁⠀⠀⠀⢀⡴⠛⠲⠤⢄⣉⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⠒⣲⠞⠁
⠀⠀⠀⠉⠢⣄⡀⠐⠉⠑⠒⠂⠤⠄⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠛⠒⠒⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⣀⣀⣀⣀⣀⡤⠤⣴⠒⠚⠙⠣⠤⠤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠣⣀⠈⡇⠀⠀⠈⠙⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣟⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡝⠿⢿⠟⠋⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⣿⣿⣿⣉⣤⣤⣬⡙⠻⢆⡿⠀⢐⣜⣦⣀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢸⡟⠉⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣿⣿⣿⣿⡿⠛⠉⠉⣉⣻⣿⣆⠀⢸⣴⣶⣶⣶⡄⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⡀⠀⢿⣿⣿⣿⣿⡟⣰⠀⠀⠻⣿⠟⣁⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⣿⣿⣿⣿⠳⢤⣀⡈⣉⣿⣿⣍⡻⢗⣻⠀⠈⠛⡇
⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣿⢫⣷⣮⣟⣻⣟⠿⠄⠀⠂⢰⡄⠀⠎⠒
⠀⠀⠀⢨⡛⣦⡀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡧⠙⠃⠈⠀⠀⠀⠱⡀
⠀⠀⠀⢨⡛⣾⣿⣦⣄⡀⠀⠀⣠⣾⣿⣿⣿⣿⣏⣿⢿⣿⣏⣿⣿⣿⣿⣿⣿⡯⠉⠀⠀⠀⠀⠀⡤⠤⢶⣀
⠀⠀⠀⣾⠻⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢊⣿⣿⡹⡏⣿⠛⠛⠛⠀⠀⠀⠀⣀⣤⣾⣷⣿⣶⣿⠆
⠀⠀⠀⢛⠻⢾⣿⣟⣾⣿⣿⣿⣦⣄⣀⢨⣿⣿⣿⣍⣽⣿⣿⡇⡔⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⢿⢿⣿⢿⣏
⠀⠀⠀⠘⠻⠶⣾⣽⣛⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠷⣶⣨⡿⢃
⠀⠀⠀⠀⢱⣶⣶⡾⢿⣿⣿⣿⣿⣷⣾⣿⠟⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⡙⢶⣄
⠀⠀⠀⠀⠀⢢⣤⠾⢛⣿⣿⢟⣽⣿⠟⠁⠠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⣦⢻⣇
⠀⠀⠀⠀⠀⠀⠱⣤⠟⣠⣿⡿⠋⠁⠀⠀⠀⠈⢆⡀⠀⢀⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢤⡄⢀⣀⣸⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⣿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⣠⣴⣟⣋⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣜⠁⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⢿⣇⢂⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠃⠀⠈⠃⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣼⠏⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠎
⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣾⣿⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣀⣤⣴⣶⣾⡆
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣽⠛⠿⠿⢿⣿⣿⣿⡧
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡉⠛⠻⠿⠿⣿⣿⣿⣿⣍⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⢿⣿⣿⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣄⠀⠘⣿⠿⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣉⣭⣭⣓⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⣿⣿⣿⣍⠓⠶⢤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣴⣿⣿⣿⡿⠿⣿⡟⠋⠉⠉⠁⠀⠀⠀⠀⢹⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢡⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⣨⢧⡀
⠀⠀⠀⡌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⢾⠀⠀⣿⡀⣈⢦
⠀⠀⡰⠁⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡴⠀⠃⠀⠸⣿⢏⢸⡇
⠀⢠⠃⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⢀⠔⠁⣠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⡠⠂⠀⠀⠹⣆⠞⠀⠀⠀⠀⠀⣠⢤
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣀⣐⣛⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⠄⠒⠉⡔⠁
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⠊
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⡿⠁⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣧⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠘⡀⠤⣀⠀⠀⠀⠀⠀⠀⠁⢀⠃
⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⢄⠉⠉⠛⠻⠿⢿⣶⣤⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠉⠓⠒⣒⣒⡖⠁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠄⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠘⣯⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠖⣿⡏⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣼⡇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣰⡟⢀⡴⠺⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⣠⣾⡯⠞⠁⠀⠀⠈⠙⠢⣄⣀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠛⠨⠼⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⠊⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠎⠀⡠⠊⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠂⠀⠰⠁⠀⡠⠃⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡌⢀⢤⠁⠀⡴⠁⠀⡠⠊⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢁⡌⠂⣠⢎⠂⡠⠞⠀⣀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⢀⢻⠀⢾⠈⢴⡃⢡⠟⣌⡤⡎⠁⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠸⣈⠆⡇⠣⢡⠙⠌⣠⠋⡹⢻⣭⣄⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣙⠒⠙⠧⠹⡇⢜⢣⠆⢹⠺⠳⡟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠣⠹⠀⠐⠁⠈⠀⠓⠐⠸⡂⠈⠀⠀⠈⠀⢢⡕⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢡⠊⠄⠐⠀⠀⠀⠀⢀⣴⡄⠀⠀⠁⢠⠀⢄⠀⠈⠈⡁⠡⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠄⠀⠀⠤⢂⠅⢈⠀⢀⠄⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠻⠀⡆⠁⠀⠤⢄⣔⢃⠠⠁
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠰⣠⠄⠀⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠇⣻⠤⢀⠐
⠀⠀⠀⠀⠐⠠⠀⠀⣀⡄⠀⠀⠀⠘⠂⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠪⠌⠀⠑⠰⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡐⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣⡀⠁⠀⠀⠀⠀⠲⡶⠶⠶⣄⠈⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣃⠑⠀⠀⠀⠀⠀⠀⢢⠠⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⠳⢾⣏⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠛⠛⠂⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠠⣀⠀⠑⢄⣀⡼⠖⠒⠛⠋⠉⠙⠛⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠒⠦⣄⡀⠈⠑⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣵⣦⡀⠀⢠⡿⠛⢻⡿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⠀⠉⢳⡞⢡⣿⡶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠳⣤⡟⠀⣠⠋⠀⢀⡼⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢤⡉⠳⣦⡿⠁⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠿⢧⡐⠁⢀⡴⠋⠀⢀⡼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠹⣶⣿⠃⢰⡇⠀⢀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⢶⠉⢀⡤⠞⠉⢀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠠⢤⣠⡿⣿⠀⢸⣣⠞⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⢰⣷⣿⣿⣿⣷⡄⠀⠀⠈⡟⠁⠠⠔⠈⠉⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⣤⣤⣿⡇⡇⠀⢸⡏⠀⠀⢀⣀⡀⠀⠀⠀⢳⠀⠀⠸⣿⣯⣈⣿⣿⡿⠀⠀⢠⣧⡀⠤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡏⠈⠙⢿⡇⣷⠀⢸⡇⢀⣾⣿⢿⣿⣷⠀⠀⣸⠀⠀⠀⠙⢿⣿⣿⣟⣁⣠⠴⠃⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡭⡿⠋⠑⠢⣷⣿⠀⠘⣧⣸⣿⣷⣴⣿⣿⢂⡴⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣧⣥⣤⡴⠶⣿⢹⡇⠀⠹⡏⠙⠛⠻⠛⠻⢿⣅⡀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⢀⣴⣿⣏⡉⠉⠉⠉⡇⢸⡇⢸⣇⠀⣿⡇⢻⡄⠀⢻⡄⠀⠀⠀⠀⠈⠦⡬⠯⣁⠉⣹⠋⠀⠀⠀⠀⠀⠀⢠⠏
⠀⣼⣿⣟⡀⠀⠀⠀⠀⣷⠈⣷⠀⢿⡀⢹⡇⠀⠙⣆⠀⠹⣆⠀⠀⠀⠀⠀⠈⠒⠚⠋⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⣿⣿⡏⠁⠀⠀⠀⠀⠹⣆⢹⣆⠘⢧⢸⡇⠀⠀⠈⠳⢤⡈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⢹⣿⣿⠉⠀⡀⠀⠀⠀⠹⣦⠙⣦⠈⠳⣿⣆⡀⠀⠀⠀⠙⠳⢦⣍⣛⣲⣶⣤⣤⣤⡤⠶⠚⠋
⠀⠈⣿⣿⣷⠋⠀⠀⠀⠀⠀⢈⣳⡬⠷⣶⠺⠿⢻⠶⢲⠖⢲⠖⠒⢺⡿⣿⣿⣿⡿⢄
⠀⠀⠈⢿⣿⣶⡃⢀⠔⢀⡴⠋⠀⠀⠀⠸⣷⣄⠀⠀⢀⡠⠀⠀⢶⣌⣘⣡⠏⢩⣥⠞
⠀⠀⠀⠀⠙⠻⢿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⣄⡀⠀⠐⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣠⡀⠀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠳⠰⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠶⠛⠉⠉⠉⠉⠀⠐⠷⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠺⣿⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠤⠖⠒⠒⠲⠀⠀⠠⠀⠀⡀⠀⠐⠄⠀⠀⠂⣠⣳⠈⢿⣦⢸⡑⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠒⠂⢤⣄⢀⠐⢢⣀⠀⠀⠀⡀⢻⣿⣧⠸⣿⣧⣿⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⢤⣤⣉⠻⠦⡀⢀⠁⠀⠀⢿⣸⣧⣿⡟⣿⣿⣿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⠓⠒⠒⠓⠒⣬⡗⠀⠀⠈⠀⣠⠘⣿⡏⢿⣾⡷⠿⣿⣇⡇⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⠢⡙⣿⡟⠀⠑⣀⣀⣨⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣭⣼⠏⡿⣁⡭⢀⣺⣟⣿⡻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣺⣗⣨⣶⡿⠟⠁⢁⠀⡠⠘⠀⡈⣻⠋⢸⢿⣿⣿⣿⣿⣿⣿⠿⠏⣀⡿⠛⢋⣙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⣴⣲⣶⢖⣼⣾⠇⠈⠙⠃⡁⠀⠀⠁⠀⡒⠸⠁⣟⡄⠇⠀⠀⠟⠛⣻⢏⣴⡶⠋⠀⠻⠙⠃⠀⠀⣽⢦⡀
⠀⠀⠚⠛⠓⠀⠀⠀⠀⠀⠀⢠⠘⠦⡤⣬⣭⣥⠚⠉⠀⠀⠀⠀⠁⡀⠄⠈⠡⢶⡆⠀⠀⠷⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠙⡗⢶⣄
⠀⠐⣀⠠⠀⠀⢀⣀⠀⠀⠀⡤⠀⠀⠀⠀⠄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠛⢛⣿⣶
⠀⠀⢯⣗⣀⠀⠀⡀⣠⢶⣠⣤⡴⠄⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠏⠘⠆⠀⠀⠀⠀⠀⠀⠀⣠⠆⣾⣯⣀⣅⠈⠁
⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⢻⣿⣧⣦⣀⣄⠀⠂⠐⠈⠀⠆⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣔⡟⢠⡄⠈⠲⣤⡐⡀⢱⡄⣾⣯⣠⣼⣿⣷⣈⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢭⣙⣷⣆⣈⠀⠀⠀⠁⠐⠀⠀⡀⠤⠀⠀⠀⠀⢀⢋⠉⠁⠀⠀⠂⢠⡤⠀⠙⠧⣤⣶⠡⢠⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣦⣷⠀⠄⠀⠀⠡⡄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⣤⠀⡀⠐⢀⣤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢒⣩⠭⠀⠿⡛⠁⠂⠄⡀⠁⣈⣀⡀⠀⣀⠀⠀⢀⠀⠀⣠⡶⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠬⢽⣿⡷⠒⠋⠀⠘⠛⠛⠂⠀⠾⠥⠀⢀⣥⣶⣶⣾⢅⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠸⡿⠟⠿⡫⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⡀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠓⠒⠊⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠒⠛⠢⣄
⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⢀⡞⠉⢀⢰⣶⣠⡀⠀⠀⡰⢅⠀⠀⢀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣼⠀⠀⠀⠀⠀⢙⣿⣀⣤⣶⣀⠲⡠⠁⣠⣢⠤⠀⠀⠀⠀⠘⠳⢦⣄
⠀⠀⠘⣄⠀⠀⠐⠋⠋⠉⠉⣙⣻⣿⡷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⠶⣄
⠀⠀⢀⡞⠱⠦⠤⠒⠊⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠝⠳⡄
⠀⡰⡯⠐⠲⣆⠀⠀⠀⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢰⡄⠀⢀⡃⠒⠀⠀⠀⣈⣴⡶⠶⠶⠾⢤⡄⣠⡤⣴⢂⠠⠲⠆⢀⠀⠀⠀⠀⠀⠀⠃⠠⡌⢳⡶⠾⠟⠒⠦⠴⢿⡓⣦⣄⣀
⠀⠙⣺⠛⠳⠶⢒⣋⣉⣉⣀⣀⢀⣤⣴⠿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠘⣷⣆⢸⠀⠀⠀⠬⢷⠁⠍⠏⠉⠓⠲⠦⢤⣤⣤
⠀⢀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⡔⠀⠘⣉⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣋⢸⠀⠀⠀⢀⣸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠻⣧⣸⣠⣄⣀⢀⣐⠀⡉⠠⣩⣴⡼⠟⢫⣤⡙⢿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡧
⠀⠀⠀⠈⢹⡋⠛⠛⠛⠛⠒⠛⠛⠛⢩⠀⠀⣼⡯⠔⠉⠉⠓⠆⣤⣶⣤⣀⡀⠀⠄⢄⡀⢀⠀⠀⠀⡞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⢷⣦⣀⡀⡀⠀⠀⣄⣀⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠰⠀⠀⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠁⠈⠙⠿⢼⣐⡜⣁⢀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣠⣀⠀⠀⢠⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠿⢧⣤⣥⣶⠾⠶⠛⠛⢶⣙⡀⡏⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⠀⠀⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⣄⣀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣿⡟⡇⡀⡄⠀⠂⠀⠂⠀⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣱⣹⡡⡐⣐⡀⡀⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣵⣿⣿⣿⣟⡙⠐⢡⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠮⢼⣔⣐⣃⣩⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢛⠽⢻⣶⣄⠀⠀⠀⠀⣀⣤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠀⠁⠀⠉⠈⡟⠓⠀⡤⠾⣽⣶⣿⣿⣿⡷
⠀⠀⠀⠀⠀⣺⣦⡀⠑⡄⠀⠀⣀⣀⡀⠀⢸⠇⠀⢸⠇⠀⠀⠈⠙⡿⠛⠁
⠀⠀⢄⡀⠀⠙⠉⡇⠀⣸⠴⣾⣿⣿⣷⡄⠟⠀⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⣴⡶⢶⣾⣿⠷⣆
⠀⠀⠁⢁⣈⣁⡼⠁⡰⢃⠀⣹⣿⣿⡶⣿⠀⠀⠀⢸⠁⠀⠀⠀⣏⠀⠀⢸⣇⣀⣼⣿⣷⣄⢿⣄
⠀⠀⠀⠀⠈⠛⠦⢞⡵⠋⠻⣿⣿⣿⠾⠁⣶⠀⠀⣿⠀⠀⠀⠀⣿⡀⠀⠚⠿⠿⢿⣿⣿⣟⣓⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤⣤⣤⣬⣽⠿⠆⠀⢿⣶⣶⣿⣿⣿⣿⣶⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⣿⠀⠀⠀⠀⠈⠛⢿⣿⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⣴⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⣿⣿⣿⣿⣿⢟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠛⠛⠋⠉⠉⠉⠙⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀⢀⣼⡷⠈⠲⢶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⢁⣀⣀⣀⣀⠈⠙⢿⣿⠙⣥⣚⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⣠⣾⡿⠿⠟⠛⠿⢿⣶⠄⠱⣷⣶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⣸⣿⠋⠀⣠⣤⣤⡀⠀⢺⣿⡄⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣿⣏⠀⢸⣿⣿⣯⣾⠄⠀⣿⣧⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⢹⣿⡀⠈⢿⣿⣿⠟⠀⢠⣿⡏⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠻⣿⣦⣀⣀⣀⣀⣴⣿⠟⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⡀⠈⠛⠿⠿⠿⠛⠋⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣶⣦⣤⣤⣤⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢀⠄⠀⠀⣀⠐⠈⠀⠀⠀⠀⠀⠀⠁⠒⣅⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣦⣤⣄⣠⣶⣶⣶⣄
⠀⠀⠀⠐⠁⠀⠀⠀⠨⠆⠀⠀⠀⢀⠀⠀⠸⠀⠀⠀⠌⢂⠀⠀⠀⢠⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⡇
⠀⠀⠀⡇⠀⠀⠚⠀⠀⠀⠀⠀⠀⠜⠂⠒⠂⠒⠒⠀⠤⢈⡔⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡆⢹⣿⠃
⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⢄⢘⠀⠀⠀⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⠉⠁⢀⠀⠀⠀⠀⠐⢡⠘⠁
⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠘⠑⠀⠀⠀⠈⢙⠀⠀⠀⠀⠘⠿⣇⢿⣿⣿⣿⡿⠃⠀⠠⣿⡆⠀⠀⠘⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠀⠀⠀⠈⠀⠁⠀⠔⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢀⡀⠀⠀⢀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⡀⠀⠀⠀⠀⠐⠂⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⣈⠣⡀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣒⠖⠲⡒⠒⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡀⠀⠀⠀⠀⡈⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣿⣦⡀⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⣿⣿⣿⣿⣿⠣⢌⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠒⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠘⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡌⢸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠢⡀⠀⢀⡜⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠓⠌⣲⠿⠀⢀⠄⠀⠀⠀⠈⠣⡀⠰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣆⠞⢀⡼⠁⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⡄⣀⣸⠿⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠙⡶⠋⠀⣠⣟⣡⣀⣀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⢈⣳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠉⠉⠃⢀⣀⣀⠀⠀⠀⠀⠀⡀⠀⣠⡄⡄⠀⢄⡄⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⢀⣴⠟⠁⣼⡇⠀⠀⠀⣼⠇⠀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣠⣾⢀⣠⠄⠀⢀⣀⣌⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣾⠃⠀⣰⣿⢁⣤⣤⣼⣿⣤⠀⡩⣀⣀⠀⣠⡀⢀⣤⡄⣸⡿⠁⣤⠀⣘⢻⡉⣰⡏⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⣀⣤⣿⢳⡿⢃⣼⣿⣿⡏⡰⣿⡟⡹⢣⣿⡴⢫⡿⢁⡿⠁⣼⠏⣰⡏⣸⣿⠏⣾⢋⡼⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢸⡏⠁⣼⣿⢾⣣⠏⢸⡏⢿⣣⠁⢿⣉⡔⠹⡿⠁⢿⣁⡼⣇⡴⣯⠜⢿⡼⣿⠏⡸⡏⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠘⠇⠀⢿⡟⠀⠁⠀⠀⠀⠀⣁⠀⣀⠀⣀⢀⣀⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⡯⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⣿⢢⣿⠸⣧⣼⣿⡇⠈⣧⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⣠⠤⠶⠾⢿⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⠿⠟⠛⠉⠉⠉⠉⠙⠒⢸
⠀⠀⠀⣀⣠⣴⣶⣿⣶⣶⣴⣤⣀⣉⠙⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠛⠋⣉⣥⣤⣶⣴⣶⣶⣦⣤⡄⠀⠀⢸
⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⢦⣀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣤⠖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⢸
⠀⠀⠀⠉⣉⡻⡀⠀⣿⣷⣶⣾⣿⠉⠓⣍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⠔⠻⣿⣿⣭⣿⣿⠆⠈⠙⠛⠛⠋⠉⠀⢸
⠀⠀⠀⠈⠻⣿⣿⣦⣞⣻⡿⠿⠫⠤⠶⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⣦⣀⣹⣿⣿⣿⢟⣀⣀⣤⣾⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⠶⠿⡄⠈⠙⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠁⠀⠀⠀⡀⠀⠀⠢⡀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣀⠀⠀⠈⠑⠤⡀⠈⡢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠉⠐⠦⣀⠀⢈⠞⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠲⠄⠀⠀⡼⠁⠀⡰⠋⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠲⠤⣄⠀⠀⡙⡌⣰⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠜⠁⠀⣠⠞⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⢤⡈⠛⣰⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡠⠊⠀⠀⣠⠞⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢳⢀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⢀⡠⠐⠉⢀⣠⠴⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠐⠂⢤⡎⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⣀⣷⠀⠀⠀⠀⠁⠠⠐⠂⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠶⠤⢤⢸⠇⢸⠀⡇⠀⠀⠀⣠⣾⣿⠛⢢⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⢦⠠⠄⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⡦⠀⠀⠘⠀⢸⠀⣷⠀⠀⠀⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢼⠉⠁⠐⢤⡸⡇⢹⡀⠀⠀⠹⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡂⠀⡀⠀⢲⡆⢷⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣴⣾⠁⠀⠀⠀⠈⡇⠀⡇⠀⣷⠀⢸⡇⠸⡆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣾⣿⠋⠉⠁⠀⠀⠀⣇⠀⣷⠀⢹⡀⠀⡇⠀⠹⡄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⢹⡄⠹⡆⠈⢷⠀⣧⠀⠀⠙⢆⡈⠲⣤⣀
⠀⠈⣿⣿⡶⠒⠀⠀⠀⠀⠀⠻⣄⠹⣄⠀⠳⡸⣆⠀⠀⠀⠉⠓⠦⢬⣭⣿⠴⠆
⠀⠀⢻⣿⣷⡠⠔⠀⠀⠀⠀⠀⠈⠢⡈⠳⣄⠈⠊⡓⠦⡀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢴⣶
⠀⠀⠀⢻⣿⣧⣀⠔⠀⢀⠀⠀⠀⠀⠀⠀⠈⣧⡈⠀⠌⠀⠀⠀⠀⠀⣀⠀⢈⠄⠈⠈⠳⢀⠆
⠀⠀⠀⠀⠙⢿⣿⣦⣴⣁⡀⠂⠀⠀⠀⠀⠀⠈⠻⢶⣤⡤⠔⠁⠀⠀⠉⠛⠒⠚⠁⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉

⠀⠀⠀⢀⡤⠒⠚⠉⠉⠙⠒⠲⢤⡀
⠀⢀⡜⠁⠀⠀⠀⢀⡤⢤⡀⠀⠐⠈⢣⡀
⠀⢸⠀⠀⠀⠁⣰⠃⠀⠀⠙⢦⠀⠈⠆⢻⡀
⠀⢸⠀⠀⠓⠒⠉⠙⡄⠀⠀⠘⡆⠀⠀⠀⢧
⠀⠘⢆⠀⠀⠀⠀⣀⠟⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠈⠙⠊⠉⠉⠀⠀⠀⠀⢀⡇⠀⡀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡂⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⡠⠖⠋⠓⢦⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢱⠀⠀⠀⠈⠧⠐⠒⠒⠉⠋⠀⠈⠉⠉⢙⠒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠫⠭⠍⠉⠀⠀⢀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠀⠀⠀⠀⢀⠀⠈⠈⠓⢤
⠀⠀⠀⠠⠖⠒⠊⠀⠀⠁⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠱⣄
⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠔⠣
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⡀
⠀⠀⣀⠞⠀⠀⠀⠠⠠⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡
⠀⠀⠣⠶⣈⣩⡅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⢤⡚⢢⡀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⡖⠚⢀⠀⠀⠙⢯⠁⠒⠒⠒⠒⠒⠒⠒⠹⠁⠀⠱⠀⢀⠼⠀⠙⣆⠀⠀⠘⡆⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⣀⣤⡴⢥⣤⠀⠀⣔⠁⠀⠀⢀⢸⡆⠀⠃⠘⣉⣁⣀⣀⣀⣀⠈⠑⠀⠄⠠⣄⣀
⡠⣀⣠⠖⠉⠒⠤⠤⠔⠀⠂⠤⠇⠄⠈⠀⠠⠞⠒⠒⠒⠒⠶⠶⠒⠋⢀⣠⣴⣆⠀⢀⠀⡥⢀⣈⣉⡡⠤⠻⠀⠀⠠⠇⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⣀⡀⠉
⢧⠄⠒⠒⠉⠁⠒⠒⠒⠀⠒⠀⢖⣦⣦⠤⠜⠈⠁⠂⠉⠑⢲⠄⡠⠚⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡤⢂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⡰⠉⢀⣀⡀⠈⠄⠀⠀⠀⠀⠘⠀⢀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⠁⢀⠔⢀⡆⠀⠀⠀⢀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⡄⠈⠉⠁⠀⠀⢀⡀⠃⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠈⠑⠂⠀⠀⠂⠁⠀⢀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⣄⣀⣀⡦⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡷⣿⣿⣿⣷⣶⣶⣦⣿⠏⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣞⡛⢿⡇⢻⡿⣿⣿⠿⡎⠉⢁⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⣦⣤⣬⣽⣿⣷⡠⡁⠐⠶⠿⠃⠀⣰⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣗⡒⠻⢿⣿⣿⣾⣦⣄⣀⣀⣼⣿⣿⣿⣿⣿⣟⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡆⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⢳⣦⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡿⡏⠙⢻⣿⣿⣶⣀⡀⡀⣉⠙⠛⠛⣻⣿⠘⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠁⢀⡀⣿⠿⣿⣿⣿⣿⣿⣧⣴⣿⣿⢿⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣹⡿⣿⣟⣿⣿⣿⢿⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⢩⣿⣿⣷⣿⣿⣿⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⢸⠛⠛⢛⣿⡟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠰⣤⣴⡦⡰⠛⠁⠀⠀⠈⠐⠄⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⠀⠀⡀⠀⠀⠀⠀⠎⠀⣿⣿⡷⢲⣶⣿⣷⠁⣤⡀⡀⠀⠀⠀⠀⠈⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢷⣿⣿⣟⣦⣍⣩⣾⣿⣶⣾⣿⣷⣆⡀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⣿⡀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠙⠈⣽⢃⠁⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠸⡟⠿⠿⣿⠟⠟⠙⠃⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⣶⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠼⣿⡃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠄⠀⠀⠐⠂⠠⠀⠀⠄⠀⠀⠀⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⢴⠾⠋⠶⣴⣦⣀⣠⠀⠀⠶⣦⣔⣋⣽⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⡼⣏⢀⣀⠀⢰⣮⣻⣿⣿⣿⣆⠸⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⠿⠶⠤⠀⠀⠠⣿⣦⣼⣿⣿⣿⣿⣿⣿⣆⠰⣦⠀⠀⠀⠀⠀⠀⢃⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣌⡃⠀⠀⠀⠀⣴⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠂⠘⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⢰⠄⠰⣓⠂⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⡆⠘⣯⠅⠀⠀⠘⠁⠙⠚⠁⠀⠀⢯⣀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢳⡈⠋⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠸⣤⠞⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⡀⠙⠋⠀⢀⡴⣾⠟⠒⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠠⠀⠀⠀⠴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡀⠁⢀⡀⠀⣾⠸⡇⠀⠀⢀⠀⠀⠀⠀⠐⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠉⠀⠀⠀⠁⠀⠘⢦⣉⣒⡶⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⢀⣦⡀⠁⠀⠀⠋⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣆⡆⠀⠀⣼⡤⠀⠁⠀⠀⠀⠀⠀⠤⠀⣰⢿⣦⠀⠀⣀⡀⠀⠀⠀⠈⠟⠁⠀⠰⠂⠀⠉⣻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡈⠀⢀⠀⠘⠀⣠⣿⣄⠀⠂⠀⠀⠀⢰⠇⢹⡘⣇⠘⠃⢹⠀⠀⠉⠀⢠⣄⠀⠀⠀⠀⠈⣡⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⡀⠀⢀⡼⠃⣼⠸⡆⠰⠆⠀⣰⠋⢀⡞⠀⠈⢁⡴⠋⠀⠆⠀⡴⠻⡏⢷⠀⠀⠀⠀⠓⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢹⡆⠀⢁⡴⠋⠀⢰⡇⠀⢹⣄⣠⠞⠁⠀⣾⣁⡠⢀⡞⣠⠶⡄⢠⠾⣇⢀⡟⠈⠳⣄⠛⠀⢘⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠄⠀⠈⢀⡄⠀⠈⢳⣴⠋⠈⠻⡄⠀⠈⠋⠉⠀⠸⡇⢻⡀⠡⡀⠀⠙⣾⠁⠀⣤⠈⠃⠀⢨⣄⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠄⠀⢀⠾⡿⣆⠀⠀⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠹⣄⢳⡀⠙⠀⠀⠀⠀⡴⣿⢧⠀⠀⠛⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⢦⠀⠀⢠⣷⡀⠀⠀⢀⣤⣀⣀⣀⣀⡀⠹⢸⠇⢀⣿⡀⠀⢀⡴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⣠⢞⣟⢦⡀⠐⢫⣯⡓⠀⢀⡾⡴⠀⠀⢠⢠⣿⣆⠋⠀⢋⣿⡙⠀⢀⡾⣿⠳⡄⠰⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠀⡴⢛⣟⠢⡀⠐⣫⣯⡛⢀⣞⡁⠙⠓⠒⠋⡼⣻⣘⣦⠐⢫⣿⣝⠂⢠⠞⣿⡳⡄⠘⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡴⢛⣟⠳⡄⠜⣩⣯⡙⠆⢉⣉⣙⠛⠒⠞⠛⢋⣉⡀⠰⣫⣿⣝⠆⡠⢞⣿⡛⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣫⣏⠳⢦⢚⣵⣷⣍⠂⠰⠆⣄⠰⠶⠶⠀⣀⠰⠆⠘⣡⣿⣌⠃⡴⢋⣿⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠑⠀⢋⣴⣷⣌⠓⠈⣼⣿⣄⢉⡉⣴⣿⣆⠁⢚⣡⣿⣮⡓⠀⠋⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⡷⣌⠓⢈⡴⡿⣆⠐⢀⡴⣿⢦⠀⠋⡴⣿⢦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠾⡿⢮⠀⠈⡼⡿⠦⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣀⠈⢁⠘⠋⢹⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠞⠁⡠⠊⠀⡠⠊⠁⢈⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⣴⣁⣀⣜⠀⢀⠔⠁⠀⡐⠁⠀⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣚⡋⠉⠉⠉⠉⠉⠉⠙⠓⠶⢮⣀⡠⠊⢀⠼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠈⠳⣎⣀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠒⠒⠲⠤⠤⠤⠤⢄⣀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠘⡷⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠤⣄⠀⠀⠀⠀⢀⣀⣀⠀⠈⠑⢤⠀⠀⠙⡄⠀⠀⠀⠀⡧⠙⣧⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠱⡀⠀⠸⡀⠀⠀⠀⠀⠀⠸⣇⢈⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢇⠀⠀⠀⡗⠀⠀⢹⡅⢈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⣉⢱⠀⠀⠀⠀⠀⢀⣤⠶⠾⠶⢶⣄⠀⠀⠀⠱⡀⠸⡀⠀⠀⡇⠀⠀⠀⢻⡄⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⡼⢠⠋⣠⣹⠇⠀⠀⠀⢠⠟⠁⠀⡀⠤⣀⠈⠻⣄⠀⠀⢣⠀⢡⠀⠀⡇⠀⠀⠀⠀⣿⠿⣿⠟⠒⠒⠒⠛⠛⠛⠉⠉⠉⠉⠀⢀⣿⣿⣿
⢀⣀⣀⣀⡀⠀⠀⣇⡌⢸⣿⣿⠀⠀⠀⠀⡞⠀⢠⠊⣴⣶⣌⢳⠀⢹⡄⠀⠈⡆⠘⡀⠀⢧⠀⢀⡴⠊⠁⣀⠻⢿⣿⠆⠒⠀⠀⠈⠉⠉⠉⠁⠀⠀⣽⣿⡁
⠸⣿⡟⠉⠉⠛⢲⣿⠸⣌⣹⠃⠀⠀⠀⠀⢹⡀⠘⣄⠻⠿⠋⡼⠀⡼⠀⠀⠀⢧⠀⡇⠀⣈⡶⠋⢀⣤⣊⣀⠠⠴⣿⡶⠖⠤⠤⠄⣀⣀⠀⠐⠒⠚⣿⣿⠃
⢀⣿⡿⠂⠤⠄⣼⠈⢣⠜⠁⠀⠀⠀⠀⠀⠀⠑⢤⣈⣑⣒⣋⡤⠞⠁⠀⠀⠀⢸⠀⡇⠀⢼⣒⠉⠁⠀⠀⣀⣤⣴⡿⠃⡒⠒⠂⠤⠤⢀⣈⠉⠁⠐⢿⣿⡄
⣸⣿⠦⠤⠤⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⠉⠀⠀⠀⠀⠀⠀⠀⡼⢰⠀⠀⠀⢸⠙⠲⣄⣠⣿⠏⠉⡐⠂⠄⡁⠒⠢⢄⡀⠀⠉⠒⠠⣾⣿⡇
⣿⣯⠀⢀⡠⠔⢻⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⡩⠚⢸⡆⠀⠀⠀⠀⠀⠀⢀⠇⡎⠀⠀⠀⢸⠀⠠⠀⡍⢹⠁⠒⠤⡁⠢⢄⠉⠂⠄⡀⠁⠂⢀⣠⣿⣿⡇
⢸⣿⠋⠁⡠⠔⠉⣧⡀⠈⠙⢟⡛⠩⠍⠒⡖⠉⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡎⡼⠀⠀⠀⠀⡎⢠⠃⢰⣀⣸⢁⠢⢀⠀⠑⠤⡁⠢⡀⠈⠑⢤⣴⣿⡿⠟⠁
⢸⣿⣤⠞⠀⠀⠔⠀⠳⣤⡀⠀⠙⠲⠤⣰⣄⣠⠤⠚⠁⠀⠀⠀⠀⠀⣠⢎⡜⠀⠀⠀⢀⠜⣠⣦⠶⢋⠙⣿⢦⡑⠄⠑⠢⡀⠈⠢⡀⠀⢀⣠⣿⣿
⠘⢿⣇⠀⢀⠎⠀⠰⠀⢨⠙⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢞⡥⠊⢀⣀⣤⣴⣿⣫⣁⡄⠀⠀⠐⣿⡇⠹⣆⠀⢀⠈⠢⡀⢈⣦⣼⣿⣿⠁
⠀⠈⢿⣿⣏⠀⠀⠃⠀⠀⠀⡇⠀⢈⠉⢛⣶⣶⠶⠴⠮⠥⠤⠶⠾⣷⠚⣏⢻⡁⡙⢦⣉⠉⠛⢷⣶⣬⣶⡿⠁⠀⠈⠻⣶⣿⣶⣿⣿⡿⠛⠛⠁
⠀⠀⠀⠙⠿⢷⣾⣤⣤⣶⣄⣤⠀⢀⣦⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠷⣷⡌⡂⡈⢹⣦⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣤⣾⡟⠾⣦⣴⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢴⡦⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠿⠃⠀⠀⠈⢿⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣤⣴⣶⣶⣦⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡴⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡞⢸⠏⠠⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡿⠀⠀⢠⠁⠐⠀⠀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠆⡰⢁⠂⡼⠀⠈⠗⠒⠛⠛⢻⡆⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⠾⠶⠷⣾⣴⣇⣀⡜⡀⠀⠀⠀⢸⡇⣰⠋⡠⠋⠉⣻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠁⠀⠈⠉⠙⠓⠶⣤⣙⠻⢿⡳⢦⣀⠀⡼⢠⠇⠀⠀⢀⠜⠁⠀⢙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⡄⠉⠳⣦⡉⠳⣌⠻⢤⠎⠀⠀⠀⠀⠀⡠⠞⠉⠘⣿⣷⡀
⠀⠀⠀⠀⠀⣠⣞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠁⠀⠀⠀⠀⠀⠀⣀⠴⠚⢻⣿⡇
⠀⠀⠀⠀⣰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠀⠐⠢⣀⠀⠀⠀⠹⣆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⡇
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⣠⣤⠄⡀⠈⢢⡀⠀⠀⠈⢧⡀⠳⡀⠀⠀⠀⠀⠀⣀⣀⣸⣿⠃
⠀⠀⢰⠇⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⣿⣿⣧⣠⣾⣆⠀⢇⠀⠀⠀⠀⢳⡀⢳⡀⢠⠤⢄⣀⣀⣀⡾⠋
⠀⢀⠞⠉⠁⠀⠀⠀⠉⠒⢄⠀⠀⠀⢰⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⡼⠀⠀⠀⠀⠀⢳⠀⣇⠸⠤⠀⠒⠚⠓⠒⠒⠒⢦⣄
⢀⡏⠀⠀⢀⣴⣾⡿⠓⢤⠀⢣⠀⠀⠈⢆⠀⠀⠀⠙⠻⠿⠿⠋⢀⡴⠁⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣿⡇
⢸⠀⠀⠀⢸⣿⣿⣷⣶⣾⡇⠀⠄⠀⠀⠀⠑⠦⢄⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣸⠀⡏⠀⠀⠀⠀⠐⠠⠤⣀⣀⣰⣿⠇
⠸⡆⠀⠀⠘⣿⣿⣿⣿⡿⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠁⠀⠀⠀⠀⢄⡀⠀⠀⢉⣿⡟
⠀⠙⢄⡀⠀⠀⠉⠉⢉⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠀⢀⡾⢠⣷⠦⡀⠀⠀⡀⠀⠈⠙⢲⣾⡿⠁
⠀⠀⠈⢿⡙⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⠐⡆⠀⠀⠀⠀⢠⠞⣱⠟⠁⠀⠙⣆⠀⠀⠓⢤⣠⣾⡿⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠊⠁⢰⠅⣠⠃⠀⠀⣀⣴⣯⠞⠁⠀⠀⠀⠀⠈⠳⣤⣤⣾⣿⠟
⠀⠀⡠⠄⠂⠉⠷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠆⠀⠲⠚⠋⠁⣀⣤⡾⠿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠸⠄⠀⠐⠧⠀⢨⠛⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⢟⡛⠁⠀⢀⠀⠈⢱⣦
⠀⠀⠀⠰⣤⣀⣀⡼⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠰⣄⡀⠈⣏⠢⢤⣤⣥⠶⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⠤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢩⣤⠟⠒⠒⢄⠈⡆⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢻⡃⠀⣴⣧⠄⡖⠁⠉⠒⢄⠀⠈⢯⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠣⣄⣈⣉⠜⠀⠀⠀⠀⠀⢣⠀⠀⢧⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢳⢸⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⠠⠠⠂⠀⠀⠀⢸⡄⡇⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⠃⠀⠀⡰⠁⡀⠀⠀⠀⠀⣀⡼⠖⢟⣛⣒⣭⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⢀⣀⣠⠴⠋⡴⠃⠀⠀⢠⠃⡌⠀⢰⡤⠒⠉⢀⣀⣬⡴⠾⠿⠃
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⡠⠊⠀⠀⠀⠀⢸⠀⡧⠔⢁⡤⠒⠈⠁⢸⢀⡇
⠀⠈⢧⣉⣑⠢⢄⢠⠒⠦⠤⠤⠴⠚⠉⠀⠀⠀⢀⠀⠀⡸⢊⠤⠊⠀⡇⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠉⠉⠓⠦⢌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡀⠔⣇⠀⠑⠤⠁⠀⠀⢠⠃⡎⠀⠀⠀⡴⡫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⣀⠜⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡸⠋⠁⠀⣠⠎⣊⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠀⢀⣀⣘⠦⠴⠊⠁⠬⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣒⣤⣤⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⢤⣀⣀⣀⣀⣀⣀⡠⢤⠒⠫⣀⡏⠀⠀⠈⠑⢦⡈⡑⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⠭⣭⣭⣤⠤⠬⠖⠊⠁⠀⠀⠀⠀⠀⠀⠱⡌⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣦⠀⠀⠀⠀⠀⢠⠃⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⣒⣺⠇⣠⠶⢷⠀⡌⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠶⠿⣿⣿⣿⡟⣦⣼⠚⡇⢠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣉⠉⠛⣇⠀⠈⣿⠟⠀⢸⡟⣆⠹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⠷⣆⠘⣧⣰⡏⠀⣠⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢻⠁⡠⠬⣿⣷⡘⣿⣇⣼⡏⠀⠈⢿
⠀⠀⠀⣀⡀⠀⢀⣀⣻⣿⣧⣴⣿⣿⣿⣿⣿⣿⠎⠸⣷⡀⣀⣿⣷⢸⣿⣿⣷⠊⠀⣸
⠀⠀⣾⣿⣿⣷⣾⣿⣿⣶⢟⣽⠿⣿⣿⠿⠿⣧⣀⡀⣈⣩⣿⣭⣿⣼⢻⣿⣟⠉⣡⠏
⠀⠀⢿⣿⣿⣿⣿⢿⣾⣧⣿⣟⣢⡘⢿⣷⠀⠙⠻⣿⡿⠿⡿⠿⡿⢿⣿⠉⠙⠛⠁
⠀⠀⠀⠙⠛⠉⠀⢶⣽⣿⣿⡿⣧⣃⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠻⠿⠿⠯⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⣿⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣠⡞⠁⠀⠀⠘⠉⠀⠀⣤⣯⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠿⠄⠀⠀⠀⠀⠀⠈⠉⠻⣝⠳⢶⣋⢀⣠⠤⠖⠂⠀⠀⠈⠉⠛⢿⣿⣦
⠀⠀⠀⣠⠴⠖⠲⠯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⠻⣦⡙⠻⣄⣠⠤⠶⠒⠚⠉⠉⠁⠀⢻⣿⠇
⠀⢠⠎⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⣀⠤⠴⠤⠤⣀⠀⠈⠀⠘⣷⡄⠙⢧⣤⠤⠶⠶⠒⠒⠒⣶⠿⠋
⠀⡏⠀⠀⠀⣴⣿⡏⣲⡀⣷⠀⣠⠎⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠸⡼⡄⠈⢷⡄⠀⠀⠀⣠⠞⠁
⠀⢧⠀⠀⠘⣿⣿⣿⣿⢇⡟⢀⡏⠀⠀⣠⣶⡶⢦⡀⠀⢹⠀⠀⠀⣧⢳⠀⠸⣿⡏⠉⠉⢿
⠀⣸⠓⢤⣀⣈⣛⣛⡽⠋⠀⠈⣇⠀⠰⣿⣿⣷⣾⡧⠀⢸⠀⠀⠀⣿⢸⡄⠀⢿⣷⡀⠀⠀⠳⣄⡀
⠀⣿⢀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢦⡀⠻⠿⠿⠟⠁⣠⠏⠀⠀⠀⣿⢸⡇⠀⢸⢸⣧⣠⡤⠄⠈⢿⣦
⢀⡿⠋⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠓⠒⠒⠒⠋⠁⠀⠀⠀⢰⡏⣸⠀⠀⣸⠀⣿⣆⣀⡀⠀⠀⣿⡇
⡟⠦⠈⢲⡄⠀⠀⠀⠒⠶⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡏⢀⣴⠏⠀⣿⢿⠀⣀⣠⣴⠟
⢻⣌⣂⣾⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢡⡞⢠⣿⠋⠀⢰⡇⠈⣯⡉⠉
⠀⠈⠙⠛⠛⢶⣄⡀⠀⠀⣾⡿⠉⠉⠓⠶⣤⣀⡀⠀⣠⡾⠋⣠⠟⠀⣼⡏⠀⢀⣿⠁⢠⡏⢹⡦⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣿⡗⠚⠒⠒⠀⠀⠀⠉⠉⠙⠛⠋⠁⠀⢠⡿⠀⢀⡾⠃⢀⡾⠁⢸⡇⠀⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡤⠤⠶⠖⠒⠂⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⠟⠁⣠⡾⠁⢠⡿⠁⠀⠀⢀⣀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⢀⣠⠤⠂⠀⠀⡀⠀⣠⣋⡴⠚⠁⣀⡴⠋⢀⣴⡿⠁⠀⠀⠤⣀⠀⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡉⠀⠀⣠⠔⠋⣠⠔⠉⠙⠳⢦⡞⢋⣠⣴⠿⠋⠀⠀⠀⠢⣄⠀⠉⠲⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠿⠷⠞⠋⠁⠀⠀⠀⠀⠀⠻⣏⠉⠀⠀⠀⠀⠀⠢⡀⠀⠙⢦⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢰⡀⠀⢆⠀⠘⢦⣀⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣧⡀⣈⣦⣤⣾⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⣾⠃⠀⠀⢳⣿⡟⠀⣦⠀⠀⠂⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠈⠀⠀⡀⣠⣞⣧⡄⣴⡟⠀⠀⠀⠸⡹⣷⣄⣷⠃⠀⠀⠸⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠠⡀⠙⠛⠾⣿⣿⣏⠀⠀⢀⠀⠀⠰⠉⢻⣿⠒⠀⠀⠀⢳⡄
⠀⠀⠀⠀⢀⣤⡶⠊⠈⠛⠷⠀⠀⠀⠀⠀⠀⠀⠙⢯⣻⡀⠀⠀⢀⠀⠀⠾⢿⣦⡀⠀⠀⠈⠻⠄⠀⠀⠀⠀⣀⡀⡤⠀⠀⣴
⠀⠀⠠⢶⣯⣿⡇⠀⠀⠀⠀⠈⠛⠷⣽⡀⡀⠀⠀⠀⠈⠙⠀⠀⠈⠀⠀⢠⡿⢹⣱⣄⡀⠀⠂⠀⠀⠀⣦⡀⠈⠋⠀⢀⣾⡟
⠀⠀⠀⠀⠀⢉⠻⣄⡀⠀⠀⠀⠀⠀⠈⠛⠿⣴⣄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠙⣽⢟⡟⣦⠀⠀⠀⠀⠉⠻⠛⠒⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢯⣷⣄⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⠁⢈⣿⠃⢎⡆⠀⠠⢄⠀⠀⡀⠴⠄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠁⠀⠀⠀⠀⣾⠀⠈⠁⠴⠿⠃⠀⠀⠀⠀⢀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠀⠌⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣌⡀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⣤⠀⠀⠀⢀⣆⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⢾⠏⠀⣘⣴⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠈⠛⠲⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⣁⠔⠁⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⢶⣼⣿⣷⠀⠀⣹⣿⡇⠀⢴⣧⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⣋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⣇⣿⣿⡇⠀⣿⣷⢠⣿⣇
⠀⠀⠀⠀⠤⢀⣀⣀⡈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢥⣸⣿⣿⢺⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣰⣴⣬⣧⠀⠀⣠⣤⣀⡀⣀⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⠒⠲⣾⠫⣴⣶⣿⡏⠐⠲⣞⢠⡫⠁⠙⢷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⡀⠀⠀⠀⠌⢸⡿⠋⠉⠉⠀⠱⣸⣆⡁⠀⢈⠋⢳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠃⠀⣼⠿⠶⢀⢞⠁⡀⠀⠀⠀⢠⣿⣿⡇⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⢴⡞⠉⠁⠀⢋⠂⡸⠃⠀⠙⣦⠀⠀⠸⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠜⠀⣿⠇⡀⠀⠀⣸⣴⣥⠄⡠⢶⡻⡧⠀⢠⣴⠎
⠀⠀⠀⠀⠀⠀⣇⡘⠀⢰⣿⢋⣀⠀⣤⡿⣿⠁⠊⠀⠈⠉⠀⢦⡀⠷⠸⡀
⠀⠀⠀⠀⠀⠘⠿⠇⠀⣼⠟⠋⡀⠀⠈⠻⣾⣆⠀⠀⢰⡷⠁⠀⢷⣀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣤⣾⡄⠠⠀⡠⠂⠁⠀⢀⢸⣥⡀⠀⠈⠻⣄⠀⠀⠙⠳⣤⣀⡀⢄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⠿⣿⣣⣾⡁⠀⠀⠀⣼⡿⠉⠻⢗⢦⣄⣀⠉⠒⠠⠤⢄⣉⠳⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠉⠉⠉⢹⣷⣭⡴⠊⠀⠀⢰⠋⠀⠈⣿⡄⠀⠀⠀⠈⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠽⣿⡸⣿⣄⣠⢶⣯⣤⡴⠤⢉⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⢡⠉⠻⢿⠘⠁⢉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡶⣞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡼⢇⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⡾⢇⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣷⡤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⠀⠀⣀⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣶⡏⡏⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⡁⠀⣀⣀⡄⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠛⠛⠛⠋⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠛⠛⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠤⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⠞⣿⡇⠀⠀⢀
⣀⣠⣤⣤⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⠟⠁⢀⣾⡏⠀⣠⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⢸⣿⠃⠀⠸⣿⡇
⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⣿⣿⣷⣯⣝⣛⣻⣿⡿⠿⠿⣿⣛⣻⣿⣿⣿⣿⣿⡿⠗⠘⢷⣦⣄⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣤⣄⡀⠀⢩⡿⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣥⡾⢠⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡧⣀⢳⡜⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣌⡲⣯⡳⣄⠙⠛⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠟⠟⡁⠀⠑⠑⠄⠙⢿⣿⣕⣿⣿⣌⠑⠴⠿⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣭⣉⣉⣠⣴⣿⣧⣷⠶⠛⢶⣤⣀⡈⡙⠛⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣷⣤⣭⣻⣿⣿⣷⣶⣷⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠐⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠱⠀⠀⠀⠀⢠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⠳⡀⠰⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠠⢀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣄⠀⢻⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠐⠀⠤⢀⡀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⠀⠈⠁⠀⠀⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠜⠦⣀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠀⠀⠀⢉⣖⠒⠀⠉⡀⠀⢀⠀⠀⢀⠀⢄⡂⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⡀⠣⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠚⠓⠀⠀⠀⠘⣿⠁⠤⡀⠈⠂⠈⠑⠀⠈⠧⣀⠈⠐⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠑⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⡞⠀⠦⡀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⣿⡇⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠂
⠀⠀⢀⡀⠡⠤⠢⠀⠁⠸⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠴⠊
⠀⠀⠓⠀⠈⠢⣀⠣⠄⠈⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠦⠤⠤⠤⠀⠄⠀⠀⡀
⠀⠀⠖⠒⠒⠒⠊⠒⠒⠒⠒⠒⠒⠒⠛⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠂⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠑

⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠈⠉⠛⠶⠶⢤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⠀⠄⠀⢀⣡⣤⡦⡀⠀⠀⠀⠉⠀⠂⠀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠌⠛⠉⠉⠉⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠈⠉⠛⠁⠠⠁⠀⠂⠀⠠⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠉⠀⠈⠉⠛⢿⣴⣯⠆⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡇⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠑⠢⣄⡀⡀⢀⣀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢒⣠⣦⣤⡀⢀⡀⠀⠠⣄⠀⠀⠘⠿⠈⣻⠛⡩⠛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣿⣿⣿⣿⣿⣿⣶⡈⠳⣤⡀⠈⠀⠀⠒⠛⠁⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠻⠓⠈⠈⠉⣂⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣸⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⢬⠤⣀⠀⠈⡴⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠊⠀⠠⠀⣽⡆⠙⣤⣾⠃⠆
⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠷⠾⣻⠀⠐⣆⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢄⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⠿⢿⣿⡇⠀⠀⠀⠁⠐⠤⠄⠐⠁⠀⠀⠀⠀⠀⠄⠂⠒⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⢶⣶⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠈⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠐⢤⡀
⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣦⣀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠻⣿⣶⣤⣤⣄⣀⠀⠀⠈
⠀⢇⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⣠⡶⣱⠛⠀⠈⠛⠿⣿⣷⣶⣴⣾⣿⡿⠀⠀⠀⠀⢀⡬⡿⣿⣿⠀⠈⡆⠀⠈
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⣴⠟⠉⢰⡏⠀⠀⠀⠀⠑⠦⣬⠉⢻⡟⠋⠀⠀⢀⠔⠈⠀⠀⠀⠈⠛⢁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢠⠟⠀⠀⠀⠀⠀⠀⣠⠞⡁⠛⠀⠀⡱⠄⡨⠆⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣘⠃⠀⠀⠀⠀⠀⢠⡏⠰⠁⠀⢀⠈⢠⠂⠀⠀⢀⠠⠄⠐⠚⣀⣤⡀⠸⣯⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⢸⠀⡆⠀⢀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡈⠻⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠁⠀⡌⠀⠀⡸⢀⠂⠄⠀⠀⢀⡀⠀⡀⠀⠀⢀⠙⣄⠀⠙⢦⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⠀⠀⠰⠃⢨⡀⢠⠀⢠⠔⠁⡆⠆⠀⠀⢰⠁⣤⣶⣤⠀⢀⣥⣤⡗⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⣜⢠⠃⠀⠀⢰⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠿⢋⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢂⣀⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣈⠅⠀⠀⠀⠀⠀⠀⠈⠁⣤⢸⣇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⢠⢥⠆⠙⠢⠀⠀⠉⠳⣦⣤⣤⡤⠤⠖⠋⢬⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⣿⣒⣏
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠁⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣔⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠔⢦⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠂⠀⢀⣴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠁⠈⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠈⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⣄⣀⣈⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠚⠃⠉⠉⠉⠉⠙⠳⢆⣤⡠⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡄⠀⡦⢘⡇⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⡩⠒⠙⢦⡀⠘⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡇⠀⡷⣾⠀⠀⠀⠀⢠⠃⢀⣤⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⣎⣀⣤⡄⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡀⠀⠀⢀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢄⠀⢧⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠈⡇⠀⠀⢸⠀⠀⠀⢰⣶⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠁⠀⢻⡀⠀⢸⠀⠀⠀⠸⠿⠃⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠍⠁⠀⠈⣧⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠂⠀⠀⠀⠀⠀⢠⠃⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠙⣦⠀⠀⠀⣀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⡒⢶⣶⣤⡄⢹⡄⠀⠈⠓⢦⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣶⣿⣿⣿⡶⠚⣷⡗⠂⣄⠀⠀⠀⠀⠈⠙⠲⠦⢤⠤⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠜⠛⠿⠿⠿⠧⠤⠿⠛⠀⠈⢧⡀⠶⠶⠶⠶⠶⠶⣾⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡧⠀⠀⠀⠀⠀⠀⠗⠀⠈⠛⠲⠤⣄⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⡛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢷⣦⣤⠀⢠⣾⠟⠁⠀⠀⠘⠿⠿⠿⢿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠛⠉⠉⠛⠛⠻⢷⣦⡄⠀⣠⣾⡿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⠟⠋⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⢠⣼⡿⠉⠠⣶⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣠⣾⠟⠛⠉⠉⠉⣀⣴⠿⠋⠀⠀⠀⠹⣷⡀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣠⣾⡿⠉⢠⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⠟⠋⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⣤⣴⡿⠋⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣤⣀⣀⣠⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡈⠭⠉⠁⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⠔⠀⠀⠀⠀⠀⡈⡚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠈⠀⢣⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢃
⠀⢠⡀⠀⠀⠀⠀⠀⠰⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠚⠄
⠀⠀⢻⣄⠀⠀⠀⢻⢦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⠢⣄⠀⡀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣷⠄⢀⣾⣷⡀⠀⠀⠀⣴⡇
⠀⡀⠀⠀⠀⠀⡉⠅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠂⠈⠙⠛⠃⠁⢀⠔⢹⡇
⠀⡇⠀⠀⠀⢀⠀⠄⢸⡇⠐⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠀⣸⡗
⠀⠁⠀⣀⣀⡌⣦⣀⣼⣿⠀⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡷⠈⠀⣀⡴⠋
⠀⡴⠋⠀⠀⠀⠀⠉⠈⢿⡀⠀⠘⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⡥⠶⠋⠁⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢤⠘⡄⠙⢦⡀⢰⡀⠀⠀⠀⠀⠈⠳⣄⡀⣀⡜⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡄⠀⠙⢦⣷⡀⠀⠀⠈⣄⠀⠈⠉⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡰⡄⠀⠀⠙⢧⡀⠀⠀⠈⠂⡀⠀⠀⠀⢀⡄⠴⠋⠙⠛⠛⠛⠃⠰⠆⠀⢠⣀⡞⠳⠞⠛⠛⢷⠀⠀⠈⠉⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣦⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡴⠋⠀⠀⠄⠀⠀⠈⠘⡣⡀⠀⠀⠀⠟⠉⠙⠖⠢⠄⠘⠋⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣤⣤⠴⠊⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⡄⠀⠀⠀⠀⠀⠘⡄⠐⢆⠀⢢⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠘⢄⠀⠀⠀⠀⠀⠠⡀⠘⡀⠀⠆⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣆⣤⣤⡀⠀⠀⠀⠀⠀⠘⡌⡀⢡⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⡦⠈⠻⣿⡷⠀⠀⠀⢀⠀⠀⠰⠀⠈⢧⠀⠀⠀⠆⠀⡇⠀⣄⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠞⠀⠀⠣⣀⡤⠟⢉⡇⠀⠀⠉⠒⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠠⣤⡤⡤⠤⠤⠶⠶⠛⠁⠀⠀⠀⠀⠀⢠⠞⠀⠰⢯⣤⡴⠞⠁
⠀⠀⠀⢀⡀⠀⡴⠒⠆⣴⡏⠀⢸⣷⣆⠀⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⢠⠋⠀⢸⡄⠀⠈⠃⠀⠀⠀⠉⠉⠀⠀⠠⠂⢱⠀⠀⠀⠀⠀⠀⢤⡶⣌⣁⣤⣤⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⠀⠀⢸⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠈⠦⠠⠼⢥⣌⡀⠀⠑⢤⡀⡀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⡤⠖⠋⠀⠀⠀⠸⢷⣄⣠⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⠙⠛⠓⠶⡶⠟⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠤⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠂⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢠⠔⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⡀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⢤⠤⠀⠀⠘⠦⣀⢀⠔⠀⠀⠀⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠢⣄⣀⣀⣀⣀⣀⠤⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⣶⠵⠞⠛⠛⠳⣦⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡿⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⠇⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡜⢰⡿⠀⣾⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⡰⢃⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡼⠁⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⣧⡀⠀⢊⠀⣼⡏⢠⣿⠿⡛⢿⠛⣻⡿⣿⡿⠷⠀⡜⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⣿⣷⡀⠨⢰⣿⠁⣼⠃⠄⠘⠻⠛⠁⠘⢾⣶⡧⢼⡀⠠⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢜⣀⣿⡟⢠⣿⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢹⠀⡠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣹⣿⡇⢸⣿⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⢤⣤⡖⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⠢⣽⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠍⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣱⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠁⢸⣿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⣿⡄⠙⣿⣿⡄⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⢻⣇⠀⣿⣿⣷⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢸⣿⣿⣧⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⢿⣿⣿⣷⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠘⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⣿⡟⡏⠻⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠟⣸⠁⠀⠘⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠃⢰⣇⣆⠀⡀⡆⢠⣀⣀⣠⣄⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠙⡏⣤⡇⣇⡸⢸⠸⡿⠘⣀⣀⣀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠔⡒⠉⠉⠀⠀⠈⠀⠀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⣄⣀⣀⠀⠀⠀⢀⣀⣀⡀⠀⢀⡠⠔⠁⠀⠘⠐⠒⠦⠆⢀⡀⠀⠀⠀⠀⠀⢈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠘⢅⣀⣀⡼⠋⠀⠀⠤⢚⣁⠀⠀⠀⠀⠀⢈⡏⠉⡽⠃⠀⣀⣈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢢⡄⠀⢰⠉⠈⢣⠀⠀⢤⠀⡸⠀⢠⢧⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣖⡄⠆⠀⠠⣌⡦⠖⢮⡴⠁⠀⡿⠯⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣠⡏⠋⠀⡠⠁⠀⠀⠶⠝⣃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠐⠒⠒⠂⠈⢉⠉⠙⠊⠉⠀⠀⠀⠀⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⠬⠄⠒⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠤⠀⢸⠇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡦⣀⠎⢀⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠈⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠂⡋⡀⣇⣀⡀⠰⠂⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢣⡍⠙⢉⡍⠀⠉⠙⢰⣶⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣬⡁⠀⠀⠈⢙

⠀⢀⠀⡀⠀⢀⢀⠀⡀⣀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠉⠉⠑⣤⢀⣀⢀⣠⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠦⢤⣀⠀⠀⠀⢰⠃⠀⠀⠀⢀⡀⠀⡀⢠⡀⢀⠀⠀⠀⠀⠘⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⢤⡀⠸⣄⡀⠀⠀⢸⢻⣶⢷⣭⡸⡾⢇⡀⢀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠙⢄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠳⡍⠒⠀⢤⠔⠒⠒⢤⣠⡤⠖⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠒⠲⠤⢠⠃⠀⠀⠀⡀⠀⠀⠈⡟⡄⠤⡔⠀⠁⠀⠀⣈⣑⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣀⡼⢧⢔⡖⠊⣡⠖⠲⡟⠀⠀⢀⣬⡓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡇⠀⢸⠿⢦⡞⠀⠀⠀⡇⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⡄⠀⠀⠀⢷⣤⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠇⠘⠢⠤⠶⢴⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⢎⡀⠀⠀⠀⠐⢆⠀⠉⠑⠒⠢⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡰⠁⠀⠁⠙⡄⠀⠀⠀⠀⠈⢱⠒⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣩⠭⢄⠀⠀⠀⠀⢡⠀⠀⠀⠀⠐⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠉⢉⠀⠀⠀⠈⣥⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠂⡰⠳⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢣⢀⣜⣁⣀⣈⡢⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠀⠏⣀⡀⠀⢸⠷⢾⡌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢰⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠇⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡆⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⢁⠠⠤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠜⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣉⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡶⡆⢬⣷⡦⠦⠦⡐⠀⠐⠐⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣻⣷⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣙⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿⣿⢿⣿⠾⠟⠋⢿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣶⣶⣙⣻⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⠿⠟⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⣿⡿⢿⠿⣿⣿⢿⣉⢛⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⡆⣿⣿⣷⣾⣿⣿⣻⣿⠿⣿⣿⣷⣯⡴⠀⢠⡽⣿⣿⣿⣦⣹⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⡿⠙⣩⠷⠀⠉⣽⣿⡏⠙⢿⣿⣿⡟⠁⠀⣿⣿⡈⠙⠷⣾⡉⠀⠀⠉⢿⣿⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⣿⣿⠿⠛⠛⠋⢙⣋⣉⣠⣤⢁⣀⣀⣀⡛⠿⠿⣄⠀⣿⣿⡀⠀⠀⢛⣋⣡⣤⣤⡤⠤⢤⣤⣄⣀⠉⠉⣙⣻⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣦⣄⣀⣉⣉⣀⡠⠞⣡⣾⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⡜⣿⣿⣽⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⡇⢼⣿⣿⣿⠿⠿⣿⣿⣿⣿⡟⢻⣿⣧⣿⣿⣿⣿⣿⡇⢸⣿⣯⣀⣼⣯⢻⡟⠀⢸⣿⣿⠟⠃⣸⣿⣿⠟
⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣼⣿⣿⣿⣿⣯⡾⠃⠀⣰⣿⣿⡇⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡸⣿⣿⣿⣂⠀⠘⠿⣿⣿⡿⠿⠛⣩⣟⠁⠀⠀⠄⠹⣧⠉⠉⠛⠋⠉⠁⠀⣠⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣏⡹⣿⣿⣶⣤⡄⠀⠀⠀⣠⡼⠻⣇⣤⡄⣀⢠⣤⡼⠷⣄⡀⠀⠀⠀⢾⣿⣿⠿⣡⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⡷⠹⣾⣭⣭⣤⡤⠶⠒⠋⠁⠀⠀⠀⠙⢧⣿⣼⠃⠀⠀⠀⠙⠛⢶⣶⣾⣷⣶⣋⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⢿⣿⣿⣿⡆⠀⠒⠀⠂⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⠠⠍⣠⣿⣿⣿⡿⣟⣾⣿⣾⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣷⣂⣱⡶⠊⠁⠀⠀⢠⣿⣧⡀⠀⠀⠀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⡿⣿⣿⣿⡿⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣷⣄⠁⠈⠙⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠻⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣷⣦⣤⣤⣴⣦⣤⣶⣿⣿⣿⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠛⣿⣿⡿⠛⠿⠋⢈⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⢐⠉⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢠⡾⠿⠟⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡼⠋⠉⠉⠛⢿⡆⠀⠀⢀⡎⠀⠀⠀⠀⠊⠈⠻⣿⣦⡀
⠀⠀⠀⢀⠄⠈⠉⠉⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢀⠂⢀⣀⠀⣀⣾⠡⢤⣮⣤⣤⠤⠤⠤⠾⣥⣀⢴⣍⠀⠀⠀⠀⠀⠀⠀⠄⠚⢿⣷⡀
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠠⠶⠐⠋⠁⠉⠉⠁⢸⡇⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠙⢦⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠈⠒⠀⠀⠐⠀⠀⠀⠀⠀⣀⣤⠒⠉⠛⠓⠲⠦⣤⣀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠁⠲⣤⡀⠀⠀⠀⢻⡀⠹⡆⠀⠀⠀⠀⠀⠈⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠘⠛⠒⠲⠦⢤⣀⡈⠙⠳⢤⡀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠘⡇⢠⡇⠀⠀⠀⠀⠠⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠑⠶⣤⡉⠳⣤⡈⠙⠶⣤⣀⠀⠀⠀⠀⠘⣇⠀⢀⣧⠼⠖⠂⠠⢤⣀⣠⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢂⠠⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⠙⢆⠀⠀⠈⠙⢦⡀⠀⠀⣿⣴⠟⠳⣦⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⡀⠈⢳⡈⢣⡀⠀⡁⠀⠀⠉⠉⠛⠧⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠈⠰⠀⠀⠀⠀⢿⠀⠀⢱⠈⣷⠀⢡⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⣠⣾⡿⠷⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣴⣿⣷⡇⠀⠀⢀⠈⠀⠀⠀⡆⢸⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⣿⡟⠁⠀⠀⠈⠓⠢⢿⡄⢠⠋⠀⠀⣀⣡⣀⠀⠀⢿⣿⠟⠀⠀⠀⡼⠀⠀⠀⠀⡇⠀⣷⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⣼⡷
⠀⠘⣿⡧⠄⠀⠀⠀⠀⠀⠀⢧⠈⢄⠀⠰⣿⣿⠃⠉⠙⠋⠁⠀⠀⣠⡾⠃⢠⠀⠀⠀⡇⢠⡿⢋⠁⠀⠀⠀⠀⠀⠀⢂⣰⣿⠃
⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠑⠂⠉⠁⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠆⠀⠀⢸⣠⠞⠁⢼⣦⣄⣀⣀⣀⣀⣴⣿⠟⠁
⠀⠀⠀⢻⣿⣅⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⢀⠎⠀⢀⣤⠟⠁⠀⠀⠈⠙⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠙⢿⣷⣆⡀⡀⠀⠀⣠⠻⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⢀⠔⢁⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⠉⠐⠤⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠢⡀⠀⠸⡇⠀⠀⠀⠀⡀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠑⠆⠀⡇⠀⠀⠀⠐⠁⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠑⠄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⡌⠀⠀⢃⠀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠉⠁⠑⢢⡄⠀⠀⠀⠀⠀⡄⣀⣤⠨⠿⠀⠉⠁⠠⠀⠀⠒⠓⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⡀⠾⡀⠀⡀⠤⠀⠤⠤⠘⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢙⡿⠄⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⢀⣉⣣⡐⠀⠂
⠀⠀⠀⠀⠀⡴⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡏⠀⣰⣾⣿⡏⠠⢠⣿⣿⠃⠙⠤
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡀⢀⣠⣤⡌⠙⢶⠄⣠⡿⠀⠀⠻⠿⠟⠁⠀⠀⠠⢀⡀⠄⠀⠐
⠢⢄⡀⠀⠀⢷⠀⠀⠀⠀⠉⠲⣤⣀⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠙⠦⣰⠆⡿⢘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠗⢹⡆
⠀⠀⠈⠀⠒⠘⠃⠠⠤⢀⣀⠀⡆⠩⠏⠛⠶⢤⣀⠀⠈⣦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠁⠃⡜⢀⠀⠀⠀⠀⠀⠠⠒⠒⡈⠀⠀⢀⣼⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⠀⠀⠀⠈⠙⢦⡈⢧⡀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢠⠙⢄⠳⣄⡀⠀⠀⠀⠀⢀⣀⣤⣲⠟⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠉⢢⡙⢦⡀⠀⠀⠀⠹⣷⡀⠀⠀⢀⣴⠙⣄⠀⠑⠦⠍⣉⣉⣀⣉⢿⣽⠞⠡⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⠀⠀⠀⠀⠜⠀⠘⢆⠈⠲⣄⡀⠀⠈⠛⠿⠒⠉⠙⢷⣤⣙⢶⣤⣤⣤⠴⠲⣇⠠⡥⠦⠰⠧⠄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⠄⠓⠉⠀⠀⠀⠀⠀⠀⠈⠢⡾
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⠘⠃⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠈⢄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢠⠇⠀⡠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠀⠀⠀⠀⠀⠘⣦⡀⢀⡎⠀⠰⠁⠀⠀⠀⢀⣠⠖⠀⠄⢀⡀⠈⠳⡀⠀⠘⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠁
⠀⠀⠀⠀⢠⠎⠀⠐⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠉⠛⠤⠴⠆⠀⠤⠄⠚⠉⡌⠀⠀⠀⠀⠀⠒⠠⢧⡀⢶⡀⠀⢀⣠⠴⠋⠁⠀⠀⠜⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢌⡉⠉⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠞⠁⠐⠔⠀⠀⠀⠀⠙⢧⡤⠄⠃⠁⠀⠀⠀⠀⠀⠀⡰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⢦⠀⠀⠀⠀⠘⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡾⡀⠀⠀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣠⣴⣶⠷⠋⠀⠀⠀⠀⠀⢰⣿⠁⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠿⣤⡴⠋
⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢸⡇⠀⠀⠀⢠⡄⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⣿⢠⠀⢠⠈⣷⢰⡆⠀⣿⠀⠀⠏⢷⣄⣿⠀⡐⠀⠀⠀⠀⣿⡟⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢿⣄⣙⡅⢀⡧⢸⡇⢠⣿⣀⣾⣤⠟⠁⠘⠛⠀⠀⠀⠀⠀⠻⣷⣄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣸⡧⠈⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⠁⣀⡤⠖⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣇⣀⠼⢁⡾⠋⠀⠀⠈⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⣴⠟⠋⠉⠙⢧
⠀⢀⡴⠶⠖⠛⠒⠒⠶⠦⣾⠥⢤⣄⣀⣠⣤⠟⠁⠀⠀⠀⠀⠀⣀⡀⣄⠀⠘⠇⣼⠃⠀⠀⠀⢀⡴
⠀⣎⠀⠀⠀⠀⢰⡄⠀⢀⡇⠀⠀⠀⠀⢀⣀⡀⢀⡴⢦⠀⣇⠞⠙⣷⠀⠀⢰⡼⠁⠀⠘⠷⠶⠟⠁
⠀⠈⠓⠶⠶⠶⠛⠁⠀⢸⡇⢀⠴⣦⢰⡏⣸⡇⣾⢀⠞⢀⣿⢀⣰⡏⠰⣨⠟⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡌⡰⠃⢸⣇⢉⡰⠿⣦⡤⠊⣿⠈⠁⠈⠁⠀⠀⠀⠉⡞⡂⠀⠀⠀⠀⠀⢀⡴⢤
⠀⠀⠀⠀⣠⠴⠶⣄⠀⠀⣿⠀⠻⠶⠈⠉⠉⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⡰⢋⡟⢀⡿⠀⣾
⠀⠀⡠⠊⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠇⠀⠀⠀⠀⣈⡁⠀⣀⠒⣷⡠⢺⡆⢸⡇⠀⣿⠃⢸⡇⠸⣧⡠⢿⡀⠀⠀⠀⠀⢀⡀⠤⡤⢄
⠀⠜⣠⠞⣀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣈⠁⢠⡄⠴⣆⡐⢩⡇⢸⣿⠀⣿⠁⣾⢀⢼⣇⡔⠛⠀⠘⠋⠀⠀⠀⢸⡇⠀⠀⣠⠖⠉⠀⠀⠈⣯
⠀⣼⠇⠀⣟⠀⡿⢀⡀⠀⡄⠀⣿⢀⡟⠀⢸⡏⠀⣿⠀⣾⣁⠼⠇⠀⠛⠀⠙⠋⠀⠉⠀⠀⣤⠶⠚⠛⠒⠒⢾⡷⠤⣴⣥⣤⣤⣤⣴⡶⠛
⢠⣿⣄⠀⠙⠊⠁⣾⠁⢸⡇⠀⣿⠸⣇⠀⠿⠇⠀⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣼⠁⡰⠇
⠀⠈⠙⠛⠶⣦⡀⢿⣀⡜⠷⠴⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣠⡤⠴⠛⠁⢠⠁⡆
⠀⠀⣶⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠐⠲⡄⠀⠀⠀⠀⠀⠀⡎⠀⠱⣤⠄
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠊⠀⠀⠀⠀⠀⠀⣸⠁⡶⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢠⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⠾⠋⠀⠋
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⣦⠤⠤⢄⡀⢧⠀⠀⠀⠀⢠⠖⠉
⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠘⢣⣶⠄⢱⠈⣳⣄⠀⠀⡏⠙⠒⠲⢤⡀⠀⠀⢀⡤⠒⠒⠢⠤⠴⠊⣹
⠀⠀⠀⠀⣜⠁⠁⠀⠀⠀⠀⢠⡉⠉⠘⢿⠁⢼⡆⢰⡃⡄⠀⠧⠄⣈⡷⠖⠉⢀⠀⠄⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠹⡤⣤⠀⠀⢀⢠⠞⡃⠀⢀⠾⣤⠀⡇⠀⠀⡌⠀⢄⠀⡉⣀⡀⠀⠂⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⢶⠀⢾⡷⡈⠀⠈⠀⡠⠶⢤⠄⡀⠤⠄⠈⠀⠀⠂⠀⠉⣼⠏⠒⣚⠛⠊⠉
⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⣀⡠⠊⠀⠀⣸⠃⣣⠀⠀⠀⠛⠀⢀⣰⠞⠁⠀⠀⠘⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢏⡉⠙⠛⠂⠉⠁⠈⠳⠤⣄⣀⣀⣀⣀⡠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣀⣀⠀⠈⠑⠒⠒⢂⡸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⠿⢛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠟⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⢈⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⡿⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⢛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣤⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖



⠀⠀⠀⠀⠀⢠⠄⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⢊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡴⠁⡴⢃⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠴⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠈⠃⢄⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡸⠀⢀⠥⢸⡁⠀⢠⠀⠀⠀⢀⡠⠤⠄⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⢸⢀⠃⠀⠀⡷⠔⠚⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡄⡀⡇⡠⢂⠘⠦⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢳⢁⡇⣪⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢡⠐⠀⡀⠀⠀⠀⠀⠉⡁⠒⠤⢀⡀⠀⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡧⣀⡠⠂⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⡀⢰⠉⡇⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠣⡀⠀⠀⠀⠀⠐⡈⢄⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠑⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢰⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡈⠣⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⡇⡈⠒⠤⢀⡀⡛⢶⡊⡁⠔⠈⠋⠰⠜⡁⠀⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠑⠢⡰⡇⣹⡉⢍⠀⠀⠀⢄⠀⠀⢱⢀⠇⡘⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠨⡿⠳⣀⢂⠀⠀⠀⠀⠉⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⠇⡆⠈⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠄⣀⠀⡀⠀⠀⠠⣄⣔⠡⠏⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠐⠁⠀⠀⠀⠀⣇⣋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⢄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠚⡟⠢⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣤⣜⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⢤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠚⠛⠛⠀⠀⠀⠈⠐⠒⠒⠒⠨⠏⠤⠀⠄⠄⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠌⠛⠛⠛⠻⠿⠿⠷⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣀⡀⠒⠂⣠⣤⠿⠿⠿⣷⣄⠀⠀⠀⠀⠣⡀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠴⠉⠀⢀⣶⠏⠉⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠉⣄⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣶⡀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠛⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠔⠛⠻⠟⠉⠙⠛⢻⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠻⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣠⣤⣾⣤⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠉⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⠀⠀⠀⢀⠈⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠐⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⣀⠀⠰⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠁⢠⣤⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠘⠁⠀⢰⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣘⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠈⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣀⣀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠙⠉
⠀⠀⠀⠀⠀⠀⢀⡿⢷⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠛⠛⠠⣤⡀⠀⠀⠀⣤⣤⣶⡆⠀⢤⣤⣤⣤⠀⣠⡾⠋⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠶⠛⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⠿⣄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠘⠀⠀⠀⠀⠈⠁⢰⣿⣿⣷⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠀⣀⠀⠀⠀⣿
⠀⠀⠀⢴⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠉⠉⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠁⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⢉⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⢀⡀⠤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠁
⠀⠀⠀⠀⠙⢿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⠃⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃
⠀⠀⠀⠀⢰⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠛⠛⢠⠀⠀⠀⠀⠄⠀⠀⠀⣠⣤⡿
⠀⠀⠀⠀⠀⠀⠙⠛⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠗⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⣼⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⣴⠟⠁⠀⠀⣠⡶⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣴⠟⠁⠀⢠⡴⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⣾⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣦⠉⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⣿⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡀
⠀⣴⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠙⣤⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠉⢷⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠙⢳⣤⡀⠀⠈⠛⢦⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠡⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣤⠐⠛⠓⠚⠛⠛⢤
⠀⠀⠀⠀⠀⣀⠾⠃⠈⠁⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠉⠁⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⢠⡌⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠘⠇⣀⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣴⣦⣤⣀⣠⡟⠛⠀⠛⠛⠁⠀⠘⢻⣤⣤⣤⣤⣤⣤⣤⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠖⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡾⠒⠛⠁⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢤⣤⣼⣼⠃⠀⠀⠐⠶⠤⣬⣛⡦⣤⣀⡀⠀⠀⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⡭⠖⠚⠛⡟⢻⠃⠀⠀⢤⠒⠶⣦⣤⠄⠀⠈⠁⠀⠉⠉⠛⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡵⠻⣄⠀⠀⠀⠁⠸⣄⠀⠀⠀⠀⠀⢈⡤⠄⢠⡀⡈⠙⠻⢖⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⢡⣄⣀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠉⠀⠀⠈⡇⠹⠄⠀⠀⣹⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣧⣤⠄⠉⠙⠓⣶⣲⠀⠀⠈⢧⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣧⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⣼⣷⣄⠐⠛⠉⠉⠳⠄⠀⢀⣴⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣆⢠⡤⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣻⢤⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠶⢾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣧⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⠃⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠌⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⠃⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠀⡎⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠈⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⠀⠀⠀⢡⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠡⡀⠀⠈⣆⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠄⠋⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢈⣄⠠⠼⠆⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢐⠃⠀⠀⠀⠀⠀⢀⠃⡀⠄⠂⠉⠁⠀⠀⠀⠀⠀⠁⠤⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡘⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢳⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡰⢣⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⡇⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⢃⠀⡁⠀⠀⠀⠀⠀⠀⡇⡰⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠈⢆⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢄⡰⠚⠁⠁⠀⠀⠀⠀⠀⠀⢳⠃⠇⠀⠀⠀⠀⣶⣿⣦⡀⠀⢘⣿⣷⡀⠀⠀⢄⡄⠀⠀⠀⠀⠸
⠀⠀⠀⡘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠏⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠈⡼⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠘⠻⠿⠁⠂⠀⠈⡁⠀⠀⠀⢀⠃
⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡿⠀⠆⠁⠀⠀⠀⠀⣀⣄⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡌
⠀⠀⠀⡇⠀⠀⠀⢢⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⢸⣿⣿⠇⠀⠻⠿⠁⢀⢀⡀⠀⠐⠒⠐⠀⠐⠒⠒⠠⠤⠤⠴⠶⠒⠛⠋⠁⠀⠀⡜
⠀⠀⠀⢡⠀⠀⠀⠘⣆⠀⠀⠀⠀⠸⠀⠀⠸⡄⠀⠀⠄⡈⠙⠛⠀⠀⠀⠀⠀⡌⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⣀⠘⠀⠀⢀⡞
⠀⠀⠀⠘⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠀⣀⠞⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⡌⠀⠀⢠⠎
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⡤⠤⠒⠚⠁⠤⠴⠋⠀⠀⠀⠸⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⣰⠀⣠⠃
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠔⠀⠶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡔⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠁⢳⣄⣀⣀⣠⣤⡶⠟⢡⠞⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠈⠳⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⠀⠀⠀⡆⠠⠉⠉⠙⠋⠁⢀⠄⠁⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⠁⠁⠀⢠⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠳⡄⠀⠀⠀⠀⡀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠎⠀⢰⠆⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠘⡄⠀⠀⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⡜⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠰⠀⠀⠀⠀⠀⠱⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠐⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠆⠀⠀⠀⠀⠀⢡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠚⠛⠛⠛⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠂⠢⠤⢀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⣀⣀⠀⠀⠠⠤⠤⠤⠄⠈⠒⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⠀⣀⡀⢰⣶⡆⢠⣄⣀⣤⠀⠀⣼⠓⠒⠒⡞⣷⡀⠰⢤⣴⡄⢰⣦⠀⢀⢀⣀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠆⢠⠏⠲⠟⠀⢥⣾⡁⣸⣟⠧⢸⣇⣼⣀⡀⠿⠙⣷⡿⢋⡉⢿⣾⣍⣧⣜⡏⣹⣧⠀⣠⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡴⣆⣤⣄⣤⡄⢤⣤⢼⣿⣸⣿⠈⠳⡏⠻⡟⢩⡌⢠⣸⡷⠻⣇⠘⠛⠀⠈⠙⠿⢿⣽⣿⣿⣏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣉⣛⠿⠉⢿⣯⣿⣿⡏⠀⠻⠿⠟⢓⠋⢠⣦⡏⢻⡇⠹⠟⠀⠄⠀⠀⠀⣐⡀⠀⠀⡤⣄⣈⢙⣫⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣸⣿⣧⣽⣧⢿⡏⢘⠿⣿⣟⡙⢾⣷⢯⣽⣧⠈⣧⠁⢲⡇⢤⣖⠈⣽⢛⣿⣯⣿⠀⢹⣿⢛⢿⣦⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⣿⣧⣬⣇⣸⣯⣿⣤⣤⣿⣿⣷⣿⣷⣖⠛⠛⢻⣿⣿⣿⣴⣇⣿⣾⣿⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠛⠲⠿⠿⢿⣿⣿⣿⡿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⠟⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠀⠀⠉⠙⠻⣿⣿⣟⣩⣤⣠⣴⠲⢲⣄⢀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡶⠿⠖⠛⠋⠉⠁⠀⠀⠀⠈⠉⣽⠒⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⠈⠝⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣰⠆⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⡋⠹⠉⠻⠃⣤⡐⠿⠛⠷⢤⣄⣀⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠖⠉⠀⠀⠀⠀⢰⠇⣼⠀⠀⢸⠀⣇⠀⠀⠀⠀⠈⠉⠻⢷⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⣠⡟⠀⣿⠀⠀⠈⣧⠈⢣⡄⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠿⣤⣴⣿⣀⣀⡀⣻⣧⣀⣿⠶⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠉⠉⠉⠉⠉⠀⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡄⡠⠊⠀⠀⠀⡠⠀⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠃⠉⠀⠀⠀⠀⢰⠃⣰⠏⠀⣸⢀⣀⣀⡤⢀⡄⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡤⠶⣐⢘⠇⠟⢠⡞⣁⡴⠁⠈⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠘⠤⠴⣪⠁⠀⠀⡔⠊⠅⢆⠠⠐⠊⠁⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠐⢇⡿⣴⠊⠴⠀⠒⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠌⠷⣤⠀⡼⢠⠇⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣵⠁⡎⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡸⠇⠀⢠⠎⡝⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠁⠸⡄⠨⠜⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⢋⡂⠀⢣⡀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢣⠀⢸⣷⠤⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢋⠻⣨⡆⣀⠄⡠⠤⠐⠂⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠣⠞⠈⢠⡔⠒⠒⠈⠙⢄⢠⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⠀⠀⠀⡠⠘⢡⠀⢀⠃⡑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠀⠀⠀⠈⠀⠉⠢⢤⡀⠂⠀⠠⠓⠮⢔⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⠀⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⢼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣡⢌⢂⣱⣶⠀⠤⠄⠀⣀⣀⣤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢀⠇⠀⠢⣁⠇⠀⠀⠀⠀⠀⡘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠿⠤⢀⠶⠒⠒⠂⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠁⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠤⠔⠁⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠙⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣀⣠⠴⠶⠒⠚⠓⠦⢼⣦⡀
⠀⠀⠀⠀⠀⡀⠤⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡴⠟⠉⠀⠀⠀⠀⣀⣀⣀⣀⡩⠙⢦⡀
⠀⠀⠀⠀⠘⠀⠀⢈⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣠⠶⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠳⣄⠙⣦⣀
⠀⠀⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⡼⣿⡇⠀⠀⠀⠀⠀⠀⣠⠟⢡⡾⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⣬⠿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢻⣿⡀⠀⠀⠀⢀⡾⠋⡰⠋⠀⠀⣠⠖⠒⠒⢤⠟⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠛⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣧⠀⠀⢠⡞⢁⡾⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠛⠳⣦⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣿⠸⣇⢠⠋⢀⠞⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣠⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡄⢻⡇⣠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠈⢳⡀
⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⢸⣇⠀⣸⣿⠣⠈⢷⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⠀⢸⣷⣶⣄⠀⠀⢡⠀⠀⢀⢠
⠀⠀⠿⣿⣦⡀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠘⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⢀⠄⠀⢸⣿⣿⣿⠀⠀⢨⠀⢠⠎⣤
⠀⣾⠀⠈⠻⣿⣄⠀⠀⠀⠀⢸⡿⠻⠃⠡⠀⠂⢻⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠛⠿⠿⠟⠁⠀⢀⡠⠃⠀⠀⢸⡿⠿⠋⠀⠀⠌⢠⡟⢠⡇
⢰⡇⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢹⡄⠈⡀⠀⠘⡈⣧⠀⠀⠀⠀⠘⡀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠲⠂⠐⠶⠈⠁⠀⠀⠀⠠⢸⡇⢀⡀⠆⠁⢀⡾⠀⡼⠁
⣾⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⡏⢻⡄⠰⠀⢂⠁⠸⣆⠐⠀⢂⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣾⠃⢠⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣸⢿⡄⠀⡈⡀⢀⢻⡀⠀⠸⠂⠇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠤⣸⠇⠀⠀⢀⣾⠃⠀⣼⠃
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠳⣄⠻⣆⠰⠀⠂⡼⣇⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⣿⠀⠀⣰⣿⣿⠀⣰⠏
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⣆⠁⠈⡠⢻⡄⢠⡄⠀⠀⠀⢸⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠟⠁⢿⣿⣿⠋
⠸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢈⡷⠘⢧⡀⠀⢞⣷⠎⠀⡇⠀⠀⢸⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠀⠀⠀⣨⠟⠁
⠀⣤⣴⣶⣶⡾⠿⠟⠛⠛⠛⠻⢿⠟⠓⠈⠀⠀⠈⠳⣥⠈⢿⣆⡸⠀⠀⠀⢸⡇⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠔⠊⠁
⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠙⠲⠤⣀⣀⣀⣙⣧⡘⢻⡅⠀⠀⠀⠘⣧⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⡇⠀⠀⠀⠀⠉⠀⠉⠈⠳⡌⢷⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡆⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣮⣙⣒⣤⣤⣄⣤⣤⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠶⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠓⠂⠠⠤
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠛⠛⠉
⠀⠀⠈⠐⠦⢤⣤⣀⣀⢀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠶⠶⠖⠒⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢻⡆⣤⠶⠶⣤⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣸⣇⣿⠀⠀⣿⢸⡇⠀⠀⣿⢠⡶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⢹⡇⠀⣿⢸⡇⠀⠀⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⡴⣿⠀⠀⣿⢸⡇⠀⠀⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⢀⣠⣿⣀⣀⣿⢸⡇⠀⢀⡿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠋⠁⠈⠉⠉⠁⠀⠙⠛⠋⠁⠙⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠂⠘⠀⠀⠂⠂⠀⠂⠂⠀⠀⠐⠀⠀⡀⢠⢘⠀⠀⠀⠀⠐⠀⡄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣿⠿⣿⡆⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠉⠉⠀⠈⠁⠈⠛⢿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠿⠋⠚⡘⠄⠀⠀⠀⠀⢠⠈⢉⠋⠛⡿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠋⠁⢀⡀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠈⣠⣀⣀⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣬⣤⡄⠀⡀⠀⠀⠀⠀⠀⡀⠀⢠⢎⣥⣽⣿⣿⣶⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣶⣿⣯⣿⢟⣿⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⢼⡿⠛⢻⡆⠀⠀⠄⠐⡖⢀⢸⣟⣷⣴⣾⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠓⠴⠞⡉⠀⠁⠀⠀⠀⠠⢦⣾⣿⠿⢿⣿⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⡵⠶⣽⣤⠁⠰⠆⠀⠀⠸⠟⣣⡾⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣶⠆⠏⠹⢮⡀⠀⠀⠀⣠⢎⣥⣶⣍⠫⣿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⢼⣿⣿⡤⣤⣴⣿⣿⣷⣭⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠻⢿⠿⠟⣟⣠⣧⠽⢽⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠝⣽⣯⣰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀
⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣼⣷⣭⣿⣥⣥⣯⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡏⠀⣸⣿⣿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠁⠀⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡟⢠⡾⣿⠉⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⠁⣾⣿⣿⡃⢰⣿⠋⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢹⣿⡏⠀⠸⠏⢠⣼⣿⢏⣶⣿⠃⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠈⢻⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠉⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠾⠿⠿⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⡖⣀⡖⠶⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠈⠁⠶⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠐⠒⠀⢰⣶⣶⠀⠐⠂⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⢩⡝⠛⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠐⠚⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣉⣹⣿⠶⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠉⠛⠓⠂⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⢷⣦⣄⠀⢀⡴⣶⣿⡇⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠐⠛⠀⠉⠛⠛⠉⠀⠛⠛⠃⠀⠀⠀⡌⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠧⠀⠀⠀⠀⠀⠀⡌⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣀⠀⠀⢤⡄⠀⠀⢠⣷⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠛⠷⢿⠇⠀⢀⣾⣿⣿⣧⣄⣈⡻⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⣴⣶⣬⣿⣿⣿⣿⣿⣿⣷⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠇⢬⡔⠿⠛⠻⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⠁⠐⠲⠖⣠⣶⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠠⣄⠀⣼⣿⣿⠟⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠄⣀⣸⣿⣿⠟⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠿⠿⠿⠿⠿⠿⠶⠶⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣟⣻⣯⣛⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣭⣽⣿⣯⣭⣯⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⢀⣤⠖⠚⠉⠉⠁⠒⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⣻⣿⡿⠛⢻⣿⣿⣦⡀⠀⢸⣿⣷⢹⡄⠂⠀⠀⠀⠀⢀⣤⣾⣿⠋
⠀⠀⡠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⣿⣿⣿⣿⡀⠀⢿⣿⠇⠁⢀⠁⠀⠀⣾⣿⣿⡿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃⠀⠀⣿⣿⣿⣿⡇⡠⠊⠀⠀⠀⢿⡆⠀⠀⣿⣿⣿⡇⠐
⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠠⠐⠈⠀⠀⠀⢀⣿⣿⣿⣿⣸⣧⣀⣠⣴⣿⠘⣿⠀⠀⢿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠋⠁⠁⣿⣿⣿⢸⡿⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⡏⣼⠁⠀⠀⠀⠛⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⢀⣴⣿⣿⣿⣿⠁⠀⠀⢰⢸⣿⣿⣇⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢛⣿⣿⣿⣿⡇⠀⠀⠀⠘⢸⣿⣿⣿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿⣦⠉⠃⢄⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠘⣿⠀⠀⠀⠈⠀⠀⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠉⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣰⠟
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠙⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⢠⡟⠀⠀⠀⠈⠉⢂⣀⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠿⠋⠀⠀⠀⠀⣠⠞⠛⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⢿⠀⠀⠀⢠⡾⠀⠀⣼⠋⠀⠀⠀⠀⠀⠘⣷⡇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣠⠞⠁⠸⡆⠀⢠⡟⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⣀⣤⢶⠇⠀⠀⢀⣠⠞⠉⠀⠀⠀⠸⡄⢠⡾⠋⠁⠉⢷⡀⠀⠀⠀⠀⠀⠀⣿
⢠⡞⠋⠀⠀⠀⠀⠐⠛⠳⢦⣀⠀⠀⠀⠀⠹⣾⠁⠀⠀⠀⠸⣇⣀⣀⠀⠀⢀⣼⠃⠀⠀⠀⣀⣀⣠⠤⠤
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢠⣿⡀⠀⠀⢠⣤⡿⣾⣿⣠⣴⠿⠓⠖⠒⠉⠉⠁⠀⠀⠀⢀
⡇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⡽⠷⣄⣠⠼⣻⠃⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟
⢻⠏⢿⣀⣠⡤⠶⠒⠚⠒⠒⠲⢤⣀⣀⣳⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠑⠒⠲⠶⢶⡶⠞⠛⠉
⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢀⡞⢋⡩⢍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢈⣉⠉⣀⠴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠽⠛⢹⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣠⠇⠈⢧⠀⠀⠀⠀⠀⣀⣤⠶⠖⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⢉⣄⠀⠘⡄⠀⢀⡠⠚⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢻⡄⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠝⢧⡀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢆⠀⠙⢦⡀⣼⢣⡄⠀⠀⠀⠀⠀⠀⠀⢢⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠳⣤⠞⢻⠋⠛⠥⣄⣀⣀⠀⢀⡟⠙⣯⣽⡍⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⠀⠀⠈⠀⠈⠀⠸⡀⠀⢹⡉⠁⣈⡁⣿⣅⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⢠⠃⠀⣀⣈⡏⠉⠉⠁⠀⠀⠉⠉⠲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣸⣄⣠⡟⠀⠀⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣨⠀⢸⡇⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⡘⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⡾⠀⡷⠶⠶⠶⠶⠒⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣛⡅⢀⣹⠆⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠖⠋⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡿⢿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠇⣸⠀⠹⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣋⣉⣉⣓⠂⠿⠓⠒⣚⣁⣉⣙⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⠀⠀⠀⣴⡆⠉⣽⡎⢻⣷⡂⠀⢀⣤⠀⢀⠀⠐⠒⠳⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⣤⠀⣀⠀⣀⠀⣠⠟⠉⢻⣦⡀⠀⣰⡟⠘⢿⣦⡀⡠⢻⡤⢤⠀⣛⠓⢲⣿⡀⢸⣿⣤⣤⢸⣿⠀⠀⠀⣀⠤⣶⣤⣄⣈⠉⠛⠛⠗⠒⠈⠀⠀⡀⠔⠒
⠀⠀⢻⣤⠙⠃⢩⡾⠋⠀⠀⠀⠘⣿⣤⡿⠀⠀⠠⠝⡻⠁⠈⣧⠛⢛⣋⣤⣼⣿⣥⣼⣿⣌⡀⠀⠀⠠⠔⠉⠀⠀⠀⠈⠉⠛⠿⣷⣦⣄⡀
⠀⠀⡨⣶⡄⢰⣿⢉⣈⠀⣀⠀⠀⠘⢋⣀⣤⢀⣤⠘⠀⠀⠀⡽⠞⠋⠉⠉⠀⠀⠀⠉⠉⠛⠿⣷⣦⣀⠀⠀⠀⢀⠠⠰⠶⣶⣄⣀⠉⠉⠁
⠀⠀⣇⡛⠁⢸⣿⠸⣿⡄⣿⠀⣷⡄⢸⠿⠛⢸⣿⠀⠀⠀⠊⠀⠀⠀⣠⡴⠶⠿⠛⠻⠿⢷⣶⣤⣙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠠
⢰⣿⢉⣁⡀⠸⣿⠀⠀⠀⣿⠀⠁⣠⣦⣀⡐⢺⣿⠀⠀⠀⠀⠀⡠⠊⠁⢀⠤⠖⠚⠛⠛⠿⣾⣿⣿⣷⡈⠙⢿⣦⠀⠀⠀⢀⣠⣀⠀⠀⠉⠀⠀⢀⠠⣤⣄
⢸⣿⠸⠿⠃⠀⣿⡇⣶⡆⣿⣷⣦⢸⣿⠿⣿⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠙⣿⣿⣿⡄⠈⢻⣷⡀⠀⠀⣭⣿⡿⠶⣦⠤⠞⠁⢸⣿⠉
⢸⣿⣠⠤⣄⠀⣿⡇⠻⠃⣿⣿⣿⢸⣿⠀⡄⠀⣿⣷⠀⠀⣰⠀⢀⠀⠀⠀⠀⠀⢀⡴⠊⢹⡿⠀⢸⣿⠹⣿⡀⠀⢿⣧⣰⡇⢸⣿⣿⣆⢀⣀⢀⠀⢸⣿
⢸⣿⣿⠀⢿⡀⠸⣻⣤⣄⣿⠇⠀⠈⣿⡀⣷⠀⣿⡟⣦⠀⣟⣀⣇⣀⣀⣀⡠⠞⠁⠀⠀⣸⡇⠀⠠⡿⠀⢿⡇⠀⢸⣿⣿⡇⠘⠸⣿⣿⢸⣿⣾⡇⢸⣿
⢸⣿⡬⣤⣾⡃⠀⢻⣿⠙⠿⡶⣤⡀⣿⡇⣀⣠⣿⣷⣿⠿⢻⣿⣿⣏⠉⠛⠛⠲⢶⣤⣀⣿⠀⠀⠰⠃⠀⣼⠃⠀⢀⡟⣿⡇⢀⠀⣿⣿⣸⣿⣿⡇⠸⣿⡄
⡾⠋⠉⢿⣧⢰⡄⠈⢿⣇⠀⠀⠀⣩⣿⡿⠛⠛⣿⠃⣻⣆⣼⠇⠈⢿⣧⡀⠀⠀⠀⠘⣿⡏⠀⠄⠀⠀⡰⢣⣤⣶⣾⠁⣿⡇⠠⠀⢸⣿⣀⣼⢿⡏⠀⣿⡇
⡁⣄⠀⢸⣿⠈⠁⠀⠘⣿⣆⣠⣾⠟⠁⠀⠀⢰⡟⠀⠘⠿⠋⠀⠀⠈⠻⡷⠄⠀⠀⠀⢻⣿⠀⣀⡀⠀⠀⢻⣿⣿⣿⡀⣿⡇⢀⡇⢸⣿⡁⠄⠚⠃⠀⣿⡇
⡇⠉⠀⢸⣿⡀⣿⡇⠀⠘⣿⣏⠁⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⣀⠤⣴⣶⣶⣆⠀⠀⢸⡿⠈⠉⠀⠀⠀⢸⣿⣿⣍⣉⣿⡇⢸⠃⢸⣿⠆⠀⠐⠂⠐⠛⠁
⡇⢼⣧⠀⣿⡇⠈⢀⣀⣀⣸⣿⠀⠀⣠⣴⣶⣏⣻⠀⠀⠀⠀⢸⣿⡄⠿⠿⠛⠃⠀⠀⣿⣇⠒⠒⠀⠀⠀⠘⠛⠛⠋⠉⢿⣇⢘⠀⢸⣿⡇⠀⠘⣿⡆
⡇⠈⠉⠀⠿⠋⠉⢹⣿⡀⠈⣿⡇⠸⠿⠾⠛⠋⠹⣇⠀⠀⠀⠈⣿⣇⠀⠀⠀⡀⠄⣺⡿⠁⠐⠂⢀⠀⠀⠀⠀⢀⡀⠤⢾⣿⠚⠃⢻⠛⢻⠀⠀⣿⣇
⠇⠀⠀⠀⠀⣴⡖⠚⠛⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⣿⡂⠀⠀⠀⢠⣿⠇⠀⠀⢀⣠⠄⠒⠈⠀⢹⣿⠀⠘⣿⠀⠀⢸⠀⢸⠀⠀⢹⣿
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⣿⣇⠀⠀⠐⠀⠀⢘⣷⡀⠀⠀⢤⣿⠇⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⣤⡄⠀⣸⣿⠻⣷⣾⠀⠀⣸⡀⣸⡀⠀⢸⣿
⠀⠀⢰⣿⠉⠛⠉⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠉⠻⣷⣄⣾⠏⠀⠀⠀⠀⣿⡇⠠⠤⣤⣼⣿⠀⣿⡇⠀⢸⣿⠄⣿⣿⡇⢸⣿⠀⢹⣿⡆⢸⣿
⠀⠀⢸⣿⠀⠀⠀⢸⣷⠀⠀⠠⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⢻⣷⡟⠃⠀⠘⠟⢠⣿⢳⣿⡌⠙⠁⣸⡿⠁⢸⣿
⣀⣤⣼⠿⠀⢀⣴⢟⣿⠀⠀⠀⠀⢀⠔⠉⠛⢿⣦⣄⡀⢀⣤⠾⣿⠟⠛⠛⣳⠾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠤⠼⠿⠧⠙⠛⠲⠞⠉⠀⠀⠘⠛⠀⠤
⣿⠀⠀⠀⢀⡾⣿⠀⣿⡇⠀⢀⣴⠋⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⡀⠀⠀⠈
⠛⠁⠀⣠⠟⢰⡿⠀⣿⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠒⠲⢦⡄
⠀⠀⣴⠋⢀⣿⠃⠀⢻⣷⢸⣿⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢻⡀
⠀⣼⣧⣀⣼⡏⠀⠀⢸⡿⢸⣿⠀⠀⠀⠀⠀⠋⠀⠀⠀⣠⡞⠁⠀⠀⠈⣿⣧⠀⠈⡇
⠀⠀⠈⠉⣿⠓⠋⠉⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⡀⠀⣀⠸⣿⡀⠀⣿
⠐⣿⡟⠾⠷⠶⠤⣶⡆⠀⠀⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⣿⡷⣿⡿⠊⡿⠁⣿⡇⠀⢻
⠀⠛⣡⣴⣄⡀⠀⢉⣤⣄⣀⣻⣧⠀⠀⢸⡆⠀⠀⠀⠀⢿⡇⠹⢿⡾⠁⠀⣿⡇⠀⢸⡄
⠖⠈⠁⠈⠉⠉⠉⠀⠀⠉⠉⢹⣿⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⣇⠀⢸⣇
⠀⢠⠾⣷⣄⡀⠀⣠⣶⣄⣀⣀⣿⡆⠀⠀⣷⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡉⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣖⠉⠙⠒⣶⠋⠀⠀⠙⠲⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⢿⣿⣿⣷⣄⠀⠈⠳⣄⠀⠀⠀⠈⠓⢦⡀⠈⢳⣄⠀⠀⠰⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠀⠈⠙⠻⠿⣷⣤⣀⠈⠳⣄⠀⠀⠀⠀⠙⣄⣼⠃⢀⡰⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢔⣷⣄⠀⠈⠉⠛⠲⢬⣑⣤⡀⠀⢀⡾⣇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠂⡐⢠⣾⠟⠁⠀⠀⠀⡠⠖⠒⠋⠉⠀⠀⠙⢻⠇⠀⠀⠀⢠⢦⡹⣿⣿⣿⣛⠓⣚⠷⠠⠤⢀⣀⡶
⠀⠀⠀⠀⠀⠄⢠⡛⢢⣀⡅⠀⠀⡀⠀⠠⢀⣿⡏⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⢆⠙⠿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠘⡧⠐⡏⠀⠀⠀⠈⠀⠀⣼⣿⠀⠀⣦⠤⣄⣀⡻⠋⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⣶⣾⡷⢒⡊⠉⠻⣇⠀⠠⢄⠑⢄
⠀⠀⠀⠀⠀⣠⡔⢻⠀⣇⠑⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⢆⠀⠀⠉⠁⠀⠺⠿⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣋⠤⠄⠀⠘⢷⠀⠀⡱⡀⠱⡀
⠀⠀⠀⢠⢼⠀⣇⢈⠀⠹⣀⠔⢲⠄⠀⠀⣿⡇⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣇⣲⣆⣀⠀⠘⣇⠀⢸⡘⡀⠁
⠀⠀⠀⠹⣌⣳⠞⠉⠀⠀⠁⣴⠋⠀⠀⡠⢹⣿⠀⠀⢀⣤⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⡯⠀⢀⣿⡀⠀⠑⠃
⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢸⡇⠀⠀⡜⠀⠈⢿⣇⠀⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣄⣼⣦⠠⢀
⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢈⣧⠀⠀⡥⠀⠀⠈⢿⣧⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⢸⣿⠈⠈
⠀⠀⠀⠀⠀⠀⠰⡟⠛⠈⠀⢹⣆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣤⣶⣿⣿⡿⠋⣼⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣦⠤⠒⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠋⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣀⣤⠾⢻⢟⠟⣿⣿⣶⣶⣶⣾⣿⣿⣿⣯⣤⣤⣤⣤⣤⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⢻⣆⢀⣠⡴⠞⠋⠉⠀⠠⡇⡞⠘⠁⠀⢟⠔⢁⡞⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢀⣄⠖⢹⠁⠀⢀⡴⠣⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣀⣤⣤⡟⢸⠁⡆⠀⢠⠎⣠⠞⠁⠀⠀⠀⠀⣶⡾⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⠾⠟⠛⠉⢩⡟⠀⠈⢠⠀⡴⢡⠞⠁⠀⠀⠂⠉⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡿⠀⠀⠈⣀⢞⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢤⣦⣄⣠⣤⡐⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠺⣿⣿⣿⡶⠈⠛⠛⠛⠛⠑⢶⣬⣀⣶⣄⣠⠠⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣇⡐⣶⣾⣷⠆⠀⠀⠈⠛⠿⣿⣾⣿⣿⣿⣿⡉⠑⠀⠀⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢿⣿⣿⡯⢿⣿⣿⡿⢀⣶⣾⣷⠆⠀⣤⣍⡉⠛⠛⠛⠁⠀⠀⠀⠀⢰⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⣿⣿⣧⡀⠀⠀⠀⠘⠋⠀⠈⢀⡄⠋⣫⡠⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣋⠉⠈⠴⣿⠷⢆⠉⠳⠀⢠⣾⢁⣶⠟⡄⠀⠀⠀⠀⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⢀⠴⠁⠀⠈⠀⣠⣾⣿⣷⠈⠻⠂⠀⠀⠀⠀⠀⢠⣽⠿⣇⠀⢹⣿⡿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠐⠋⠀⠀⠀⠀⢠⣿⣿⣟⠠⢀⣤⣾⠀⠀⠀⠀⠀⢽⡟⠀⠃⣀⣘⡿⢣⡸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣧⡈⢹⣷⠀⣟⠀⠀⠀⠀⠀⣰⣿⡷⠂⠀⠘⣀⣿⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣴⣦⠀⠀⠈⠿⠝⠦⠹⠀⠿⠿⠇⠀⠀⠀⠩⠟⠀⠀⠀⣀⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣮⣷⣖⣶⣦⣤⣤⣤⣄⣴⣶⣶⣶⣶⣦⠤⠴⠿⠿⠛⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠟⠁⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⠆⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣴⣧⠀⣾⣿⠄⠀⠀⠀⠀⠀⢀⡏⡀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⠀⠉⠀⠀⡄⠀⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡐⠠⠀⠀⠀⠀⢀⠃⠀⠀⠠⠀⢸⡇⡠⠤⢄⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠀⠂⠄⡀⠀⠀⠉⠓⡂⠀⢀⡴⠁⠀⠀⢀⠍⣀⠞⡄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠚⠉⠀⠀⠀⢀⣮⠞⠁⠈⡐
⠀⠀⠀⣴⠋⠁⠀⠢⡜⠉⣉⡍⠧⠐⠒⠈⠉⠛⠁⠉⠓⢦⡀⠀⢄⠀⠀⠀⠞⠁⠀⣔⠎
⠀⠀⣸⠃⠀⠀⠀⠀⢀⠀⡈⠀⠀⠀⠀⡴⠁⠀⠀⠁⠀⠀⠐⡄⠀⠓⠤⣀⣠⠴⠞⠁
⠀⠀⣿⠀⠀⠀⠘⠀⡄⠰⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠀⢹⡄⠀⠀⢀⠀⡆⡇⠀⠀⡌⠀⠀⠀⠀⠀⠀⣾⠟⢁⣴⠞⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠒⠊⠀⠀⣏⠓⢤⡊⢀⠀⠀⠀⠑⢄⣀⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠘⣄⠀⠀⠀⠀⡈⠉⠉⠉⠉⠉⠀⠀⠀⣴⡄⣠⡄⠘⣆⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠙⠒⠦⠤⠤⠥⠶⠀⠀⠀⠀⠀⠐⠉⠀⠉⠁⠀⠘⠁⠈⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⣀⣠⠀⠀⠰⢄⣀⣀⣠⠆⠀⠀⠀⠀⠀⡀⠀⠀⠂⣀⠈⠂⣤⡃⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⢿⠔⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠀⡀⡠⠆⠀⢄⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠠⠤⠤⡁⠀⠀⠀⠀⠀⢉⡄⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄⠀⠀⣤⣀⣠⣿⣿⣿⣆⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⣾⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⢟⣯⣷⣶⣿⣻⡷⣞⠏⢙⣛⠿⠿⢿⣿⣿⡿⢿⣟⣯⣿⢟⣿⣿⢏⣫⣝⢮⠛⠻⠿⣛⡿⠇
⠀⠀⠀⠀⠀⠀⠈⣓⣊⣉⣭⢅⢂⣱⢿⠟⣫⢽⣥⣞⣭⡈⢐⣥⣽⣿⣷⣦⣶⣶⣾⣿⣿⣛⡵⠾⢽⣾⣿⣯⣧⣲⡭⠷⣒⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠯⠛⠋⣉⣭⣭⣏⣛⠻⢿⣓⣯⠴⣭⡷⠿⡿⠿⣶⡿⢿⡿⣯⣷⣶⣯⠭⠿⠟⠛⣒⣙⣻⡵⠾⢛⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢝⣛⣒⣒⣋⣝⣻⠶⣬⡯⠭⡁⠶⣛⣿⣯⢿⣿⣿⣷⣶⣯⢭⣩⣍⣄⣐⣙⣹⢷⡗⠶⣛⡭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢴⢶⣶⡿⠻⢽⣛⡫⠽⠶⢾⣛⣭⠽⣖⡿⢷⣾⣒⣿⣿⣿⣲⡶⠦⡠⠤⠶⢷⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣿⠧⣔⡦⢬⣍⡉⠀⠤⢖⣋⣶⣿⣯⢵⣶⣶⠶⣖⣺⣷⣈⡲⢶⣄⣈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠦⢊⡅⢒⣶⣶⠦⠭⡿⣶⣙⣠⡑⠶⣾⡿⢿⣿⣧⣒⡫⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠪⠭⣠⢽⠟⣛⠫⣉⣹⣿⣿⡿⠿⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢦⣷⡄⠀⢀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡄⠀⠀⠀⠀⠀⠀⠀⠤⢾⣿⣿⡸⡈⠃⢰⢽⠆⠀⠴⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣀⣤⠴⠞⠒⠒⠊⠟⣛⠋⠀⠀⠈⠁⠀⠊⣉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠈⠀⠀⠒⢬⢴⡄⠀⠈⠱⣦⣄⠀⠀⣠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⡟⠃⠀⠠⡝⢋⡘⠀⠘⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⠀⢾⠘⠇⢀⡆⢈⡁⠘⠁⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣞⠀⢇⠈⡿⠄⠙⠐⠷⠦⡄
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⠈⠀⠀⠄⠀⢀⢳⢺⠁⢠⡀⠠⡀⠀⠑⠂⠀⠤⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠘⡘⢌⡌⢎⢧⠈⠇⠀⠘⠀⠀⠀⠀⠀⠀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⠛⠬⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠻⡯⠵⠖⠂⠰⠋⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠤⣀⡀⡿⡾⠿⠛⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠤⢀⠀⠀⠈⠹⡓⠒⠻⠀⣾⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⢷⠄⡤⠿⠨⠻⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠈

⠰⠶⠲⠶⠒⠲⠶⠖⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠖⠒⠒⠲⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠖⠒⠒⠲⠶⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠖⠒⠖⢶
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢲⣶⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠄⠁⠹⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠘⠛⣦⣶⠀⢹⡄⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⢸⣧⣤⡿⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠒⠺⣷⡞⠁⠀⠗⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠃⠛⠶⢄⣠⠴⠂⢀⠈⠛⠂⠀⠀⠀⠀⠀⢸
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢸
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠛⠋⠀⠀⠀⠀⠀⠀⠞⠀⠆⠁⣀⣀⡀⣲
⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠙⠻⠁
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⣤⣀⠀⢀⠀⡀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠄⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠁⠀⠰⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢻⡋⠀⠲⠀⣦⣤⠄⠀⢾⣄⣤⠋⠐⠀⠀⠀⠇
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢄⠀⢀⡈⠀⠀⠀⣿⠿⣿⣴⡆⢀⣴⠆
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠁⠀⠀⠀⠁⠀⠉⠀⣹⠀⠀⠘⠛⠛⠁
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠠⠀⠀⠠⠀⠴⠁⠀⢀⣴⠉
⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢤⡾⢉⠂⢠⠖⠀⠆⠀⠀⢀⡞⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢣⡄⠀⠰⠶⠊⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢋⣁⠶⡁⠆⡠⡝⠂⠀⢠⣏⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠾⡋⢘⠃⠀⠘⢡⠞⠙⠀⣀⢀⣈⣙⡃⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠖⠻⢯⡵⢼⠅⠈⢹⠄⢠⠖⠀⣠⣴⠿⠛⠫⠽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⡇⠀⠀⠀⠀⠀⢀⣤⡿⠂⠀⠼⠓⣠⠔⠛⠁⠠⠄⠀⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⡇⠀⠀⠀⢀⣠⣿⠉⣱⠊⠀⠤⠌⠁⠀⠀⢀⡀⠀⢀⣿⠀⠀⠀⠂⠶⢠⡄⠠⠆⠠⠸⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢘⠁⠀⠐⢠⣿⣿⡁⢀⠙⠋⠁⢀⠀⠀⠶⠀⠀⠃⠀⣼⠯⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⡇⠀⠀⣼⣿⡍⠁⠘⠀⢤⡆⡘⠃⠀⠀⠀⠀⢀⣴⣿⡆⣀⣀⣄
⢸⡇⠀⢸⣿⣯⠡⢀⠛⠦⠀⢰⠃⠀⠀⠀⠀⢠⣿⢿⠛⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣀⣠⡀⢀⣀⣀⣀⡄⣀⠀⡄⣠⡀⣠⠀⠀⠀⠀⠀⠀⠠
⢸⡇⠀⠀⠘⠿⠶⠾⠷⣦⣤⡘⣀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠉⠁⠈⠉⠉⠉⠃⠉⠙⠁⠉⠁⠉⠁
⢸⠁⠀⠀⠀⠀⠀⠀⠘⡟⠙⣿⠙⢓⡾⠛⣋
⠘⠀⠀⠀⠀⠀⠀⠀⣴⠃⣼⠿⠄⠀⠀⠠⠈
⢰⡇⠀⠀⠀⠀⠀⠀⠈⠁
⢸⡇
⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣠⠖⠛⠛⠓⣆⠀⢀⣠⢶⡛⠉⢉⡇⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⡀⠀⠰⡇⠀⠀⠀⢧⣀⣀⣀⡤⠏⠠⡏⠀⡾⠛⠻⣯⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠈⣿⡇⠀⠀⢳⣄⠀⠀⠀⠈⠉⣀⣀⣄⡀⠉⠋⠛⢦⣤⡟⠈⠙⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⢰⣿⠇⠀⠀⠀⢹⠇⠀⠀⢠⣞⡥⠔⠂⣷⣀⡀⠀⠀⠈⠙⠲⠶⠋⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⢸⡀⠀⠀⠘⠦⠤⣶⠻⠥⠬⠍⣷⠀⠀⠀⠀⠀⣶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⢧⡀⠀⠀⠀⠀⠉⠓⠒⠖⠒⠋⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀⠈⠁⠀⠀⠀⠈⠛⢦⣤⣀⣀⡤⠞⢦⣀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠙⠛⠋⠉⠁
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣾⠉⠉⡇
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡆⠀⡴⠲⣄⠈⠓⠚⠁⠀⠀⠀⠀⠀⠿⢿⣦
⠀⣠⣾⢃⡴⠶⠒⠲⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠳⠶⠋⠀⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⣿⡇
⣰⢫⡇⠈⢠⡶⠶⠀⠀⠀⠀⠀⠉⠛⢶⡄⠀⠀⢀⡴⠿⣦⠀⠀⠀⠀⠀⠻⠿⠀⠙⠻⢷⣦⣤⣴⣿⠃
⣿⣼⠀⠀⠈⠀⣠⠖⠀⠀⠀⠀⠘⣧⠀⠛⠀⠀⠈⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠹⣿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠘⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣼⠁
⠀⠸⡆⠰⠉⢠⡀⠀⠀⢀⠀⠈⢳⠀⠀⠀⠀⠀⣷⡤⠞⠁
⠀⠀⠹⣦⡀⠀⠙⠛⠛⠉⠀⠀⠈⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠈⠙⠶⣤⣀⣀⠀⠀⠀⢀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠁

⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣾⣿⠟⣛⠫⡿⣆⠀⠀⠈
⠈⠙⠻⠿⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠄⡵⠉⠁⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣦⣀⣀⣄⣤⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⠛⢾⣿⣿⣷⣶⡖⠚⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣶⣦⣀⢀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣦⣤⣶⣦⣶⣦⣤⣀⠀⢀⣠⣤⣀⣀⣀⣀⣿⣟⠀⠀⠀⣀⣤⣄⣀⣀⣀⣀⣤⣴⣶⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠖⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⠿⣿⠿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠛⠁⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⣤⠤⠦⠠⠦⠀⠀⣤⣤⣤⣠⣤⣤⡀⣠⣤⣤⣄⣠⣀⣤⣤⣠⣙⣷⢆⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠘⠛⠋⠉⠉⠙⠿⠟⠛⠿⠟⠹⠛⠛⠉⢻⣿⣿⠿⣿⣿⣿⣿⣿⠿⠛⣿⡿⠻⢿⣯⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠖⠛⠀⠀⠀⠀⠀⠩⠇⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠩⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠷⣦⡄⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠇⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠘⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡧⢤⡀⠀⠀⠘⣧⡀⠀⠀⣠⢤⣿⡀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⠀⠂
⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠈⢳⡄⢳⠀⠀⠀⠘⣧⠀⢸⠃⠈⠀⠄⠀⢸⠈⠀⠀⠀⠀⢠⣶⡖
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢳⡄⠀⠀⠸⣆⠸⡄⠀⢀⡀⠀⢸⢸⠀⠀⠀⠀⠀⠉
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⡆⠀⠀⢻⡄⠀⠀⢀⡇⠀⠈⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠛⠀⠀⠸⣷⠀⠀⣼⠁⠀⠀⠸⡰⠀⠀⠀⠀⠀⠀⠐⠶⠶⣶⠶⠾⠋
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣤⣀⣀⣸⠏⠀⠀⠁⠀⠀⢀⡄⠱⢤
⠀⠈⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠦⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠈⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢰⠇⠀⠀⠀⠀⠀⠀⢾⠋⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠳⡘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠻⣧⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⢀⠀⠀⠀⠀⠀⠾⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⡿⠀⠀⠀⠀⠀⠀⣠⡤⠶⠿⢋⣉⣙⣭⢨⣟⡹⢿⢷⡀⠀⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣾⣿⣷⠇⠾⠟⠛⠛⠛⠋⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⣀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡀⠀⢠⡿⣡⣿⠋⠀⠀⠀⠀⣀⠠⠀⠀⡀⠤⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠙⢦⣄⠀⣄⠀⠀⠛⠋⠀⢸⡇⢹⣯⠀⠀⠀⠀⠩⠀⠀⠀⢀⡀⠀⣀⣀⣽⠀⠀⠀⠀⠀⠖⠋⠁
⠀⠰⢶⣄⠀⠀⠀⠈⠳⣌⠃⠀⠀⠀⠀⢸⣿⣤⣼⣦⠀⠀⣠⣴⣶⣶⠖⠀⠀⠙⣻⣭⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠖
⠀⠀⠀⠉⠛⢦⣀⠀⠀⠈⠳⣄⠀⠀⠀⠸⣾⣾⣿⡛⠁⠐⠋⣴⠿⠷⠂⠆⠐⣎⠫⠥⠀⣧⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠛⠉⠉⠁⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠈⠁⠀⠀⠀⣻⠿⡿⠗⠀⠀⠀⠀⠋⠉⠀⢀⠀⠘⣦⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⣀⣀⣖⣒⠿⠭⠭⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⢿⠉⡇⠠⠀⠀⠀⠀⠀⠀⢀⠐⠒⠚⠉⠰⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡛⠀⠀⠀⠀⠀⠀⢰⢃⣠⠤⠴⠖⡂⠜⢸⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢤⡤⠀⠀⠀⠀⠀⠙⢶⢇⡀⠀⠲⣄⠉⠈⠀⢰⠞⠉⡑⠢⣼⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⢀⣼⣏⢳⣤⡀⠙⠂⠀⣴⠫⠴⠚⠉⠑⢿⠀⠀⠀⠀⠀⢦⣀⣀⣀⢀⠠⣤⠤⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠰⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠑⢍⠻⢿⣶⣴⡇⠀⠀⠒⠋⠉⠀⣳⠀⠀⠀⠀⠠⣄⣀⡀⠈⠈⠉⠉⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⣧⠀⠀⠙⠲⢄⣽⠀⠀⠀⠚⠁⠘⠉⢈⣧⠀⠀⠀⠀⠒⠂⠉⠉⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣇⠹⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠐⢡⠟⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠋⠻⠿⠟⢛⠿⠛⠛⠁⠀⢻⣆⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣿⠀⠉⠀⠀⠉⠉⠙⠻⠷⣶⣤⣀
⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⢦⣾⡟⠁⠀⠀⠀⠀⢀⡼⢻⡆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢿⡳⡄
⠀⠀⢠⣿⠏⢳⣄⠀⠀⠀⢀⡀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⣸⠞⠁⠈⠓⢤⡀⠀⣠⣾⠀⢸⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠸⣧⢹⡄
⠀⠀⣾⠏⠀⠀⢻⣆⠀⠀⢸⠃⠀⠀⠀⠀⠙⠿⠂⢀⣴⣾⡧⢄⡀⠀⠀⠀⢳⣴⣿⣿⣇⠀⣿⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡄
⠀⣸⡿⠀⠀⠀⠀⢻⡆⠀⢸⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠙⣄⠀⠀⠀⢻⣿⣿⣿⡄⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠁⠘⣷
⠀⣿⠇⠀⠀⠀⠀⠈⠿⠀⡿⠀⠀⠀⣀⣴⣿⣿⠿⠁⠀⠀⠀⠀⠀⠘⢆⠠⠟⣠⣿⣿⣿⣧⣿⠀⠀⠀⠀⣸⠁⠀⣀⠀⠀⠀⠀⠀⠀⢸⣇
⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠏⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣿⡄
⣾⠇⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢚⣥⡾⠸⠟⢻⣿⣿⣿⣿⠀⠀⢠⡟⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢹⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡀⠀⠀⢀⠀⢀⣀⠀⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡝⢛⣽⠍⣥⢹⣠⣝⣿
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣿⣤⣿⣯⣿⣷⣼⣿⣾⣷⣤⣤⣤⣤⣤⣤⣀⢀⢀⢀⣀⣀⣠⣤⣄⡀
⠀⠀⠈⢻⠅⠴⡖⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢃⡾⢸⠸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠙⠿⣿⣿⠿⣿⣯⡐⠚⡛⠛⠿⠿⠿⡿⠿⠿⠟⢋⣉⣤⣾⢀⣿⣯⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⣿⠯⣉⣩⠭⢍⣙⣛⡻⠒⠒⠚⠛⠋⠉⠉⠉⠁⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠟⠛⠒⠒⠒⠒⠂⠐⠬⢭⣍⣑⣚⡒⠒⠒⠒⡠⠾⠛⠐⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⣠⣶⣶⡄⠀⠀⠀⣰⣿⠋⢹⡆⠀⣸⣿⡇⣀⠀⠀⢀⡄⢀⡠⢊⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣿⡿⠀⢸⡇⠀⣿⣿⣿⣿⡇⠀⠊⠀⠀⠀⢁⠄⠂⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⡇⠀⡾⠀⠨⢿⣿⣿⣿⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⡇⡼⠃⠀⠰⠾⠷⢾⣶⠶⣶⠶⠶⠷⠿⠶⠶⠶⠶⠶⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⢀⣀⡴⠒⢦⡀⠀⢠⣤⣤⠀⣠⣦⡀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣾⣿⣿⠀⠀⣷⠀⣿⣿⣿⠀⣿⢸⡇⠀⣾⣿⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣿⣿⣿⠀⠸⣾⠁⣸⣿⣿⡵⠟⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⠇⠀⠈⢿⣿⡇⠀⢀⡾⣿⣿⡈⢷⣤⣏⡴⢻⣿⣿⠀⢠⡟⠛⠻⣿⣿⡀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡤⠏⠀⠀⠀⠈⠻⠿⠶⠞⠁⠈⠻⠷⠶⠋⠉⠀⠀⠙⠿⠶⠋⠀⠀⠀⠙⠻⠷⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢶⡒⢿⡛⠻⡟⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣿⣤⢿⡦⢿⡶⠶⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⣼⣯⠙⠓⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡾⠀⣾⢁⣼⢁⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⣤⡀⠀⢀⣄⠀⠀⣤⠀⠀⣠⣤⡄⠀⣠⣤⠀⠀⣤⢀⣄⣤⣤⣠⠀⣤⠀⢠⡄⢠⣤⣄⡀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⢸⡏⠻⣦⠈⣿⠀⢀⣿⠀⣾⠋⠀⠀⢠⡿⢹⡇⠀⣿⠀⠉⢹⡏⠉⠀⣿⠀⢸⡇⢸⡇⠉⣿⡄⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣨⣿⠀⢸⡇⠀⣿⠀⣿⡄⣸⡇⢸⣧⣤⣤⠀⢸⡇⠘⣿⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⢸⣧⣶⠟⠀⣿⣧⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⢻⡆⣹⡇⣠⡿⠀⢸⣧⣿⠀⠸⣧⠀⢀⣤⢸⡇⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⣼⡟⢷⣄⠀⢻⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⠇⠻⠿⠛⠀⠀⠈⠿⠃⠀⠀⠙⠷⠟⠁⠸⠇⠀⠙⠿⠋⠀⠀⠸⠇⠀⠀⠙⠷⠟⠀⠻⠃⠀⠹⠃⠈⠻⠾⠛