Turkish Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢶⠖⠋⡳⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⡰⠁⡰⠃⢀⠞⠁⠀⠀⡸⠓⢢⡀
⠀⠀⠀⠀⠀⠀⡴⠉⠎⢬⡅⠀⠈⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠃⡰⠁⡰⠁⢠⠋⠀⠀⢀⠞⠁⠀⣸⠉⠑⡄
⠀⠀⠀⠀⢀⠞⠑⢒⡈⠉⡖⠆⠀⣹⠀⠀⠀⠀⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⢰⢃⠃⢰⠃⠰⠁⣰⠃⠀⢀⡴⠋⠀⠀⡴⠃⠀⢀⡇
⠀⠀⠀⠀⡈⠀⠀⢸⠀⢘⠱⠂⡰⠃⠀⠀⠀⠀⠀⢸⠃⠀⠱⡀⢀⣠⣤⠴⠾⠶⡤⣯⣠⡃⠠⠃⠀⣠⠞⠀⢀⡤⠊⠀⠀⡠⠊⢹⡄
⠀⠀⠀⢠⠁⠀⠀⡸⠀⠁⠐⠋⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡟⠉⠰⡄⠆⠐⠀⠀⠀⠈⠙⢷⣄⡞⠁⣠⠔⠋⠀⣀⠴⠊⠀⣀⠜⢳
⠀⠀⠀⡌⠀⠀⣠⠁⠀⠀⠀⡄⠀⠀⠀⠀⣀⡴⠛⡄⠀⠀⡄⡟⠀⠀⡇⠀⢀⠀⠠⠀⠀⠀⠀⠙⣦⠚⣁⠤⠖⠋⢀⣠⠴⠚⠁⠀⣠
⠀⠀⢠⠀⠀⡰⢋⠀⠀⠀⠰⡏⠉⠉⠉⠉⠁⠀⠘⡌⠀⢰⣧⡇⠀⢰⠃⠇⣸⠀⠂⡀⢠⠀⠀⠀⢹⣯⠤⠴⠒⠋⠁⠀⣀⣠⠴⠚⠁
⠀⠀⡎⠀⢸⢃⡈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⣼⡿⠀⠀⠈⠌⢠⠇⠀⠠⠁⠆⠠⠀⠆⠈⣧⠠⠤⠔⠒⠚⠉⠁⢀⣀⣀⣠
⠀⢰⠀⠀⠎⠌⠀⢀⠀⠀⢂⠀⠀⠀⠀⠰⠐⠀⠀⠀⣠⠿⠗⠒⠦⣄⠀⠂⠀⠀⠀⡼⢠⠃⡰⠀⢰⡧⠤⠤⠔⠒⠒⠛⠉⠉⠁
⠀⢨⠀⡜⡜⠀⠀⠠⠀⠘⠁⠀⠀⠀⠀⠆⠀⣀⠤⠊⠁⠀⠀⠀⠀⡿⣗⢦⡀⢀⡔⣠⠃⢠⠃⠆⣾⠡⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⡞
⠀⠘⢞⠁⠀⠀⡠⠀⠀⢸⣀⠐⡁⣂⣬⠼⠊⠁⠀⠀⠀⠀⠀⠀⣰⠃⢸⠀⠙⢯⡴⠃⣠⢃⠞⣼⠋⠑⠒⠲⠤⢤⣄⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠉⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠃⠀⠀⠀⠙⣾⣡⢎⣾⡁⠈⠐⠢⠤⣀⣀⡀⠀⠉⠉⠉⡿
⢼⠀⠀⠀⠀⠀⠐⢊⠟⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⣀⠀⠲⠃⠀⠀⠀⠀⢌⢳⡟⢤⡈⠑⠢⢄⣀⠀⠀⠉⠉⠓⠒⡞⠁
⢈⡷⢤⣤⣤⡤⠞⠁⠀⠀⠀⠀⠻⣄⠀⠀⠀⣀⡤⠖⠫⠀⡀⠀⢱⠊⠀⠀⠈⠢⡀⠀⠑⡙⣦⡉⠳⢄⡀⠀⠉⠒⠲⠤⢤⡴⠃
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢯⣤⣄⣀⣀⣀⣬⠖⠁⠀⠀⠀⠢⡀⠉⢦⡀⠈⢿⠉⠢⣄⡉⠓⣦⣤⣤⡤⠞
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠀⠀⠀⢸⠀⠀⢹⠓⢤⡀⠀⠠⣀⠈⠲⣄⠉⠲⢾⠀⠀⠀⠉⠉⠁
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⡠⠃⡸⠀⡇⡘⠀⠀⢸⠁⠀⠉⠳⢤⣀⠙⠲⢤⣙⣲⠞
⠀⠘⢦⡀⠀⠀⢀⣀⠤⠒⠁⠀⡠⠚⠁⡰⠁⡰⢱⠁⠀⠀⣼⠀⠀⠀⠐⠤⠄⢉⣉⠉⣀⡇
⠀⠀⠀⠙⢦⣍⡀⠀⠀⠠⠐⣁⡠⠔⠊⠀⠐⡴⠁⠀⣀⡼⠉⠑⠲⣤⣤⣀⣀⣒⣲⠞⠃
⠀⠀⠀⠀⠀⠈⠛⠲⠶⣬⣭⣤⣤⣄⣤⣴⡤⠶⡿⢩⠇⠀⠀⠀⠀⢸⡂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠃⡎⠀⠀⠀⠀⠀⠈⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠁⠀⠀⠀⠀⠀⢠⡟⠘⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣄⣐⣒⣒⣲⠲⠴⠃⣿⠀⢀⣠⡤⠴⣚⡅⣠⢂⣧⡙⢢
⠀⠀⠀⠀⠀⠀⠀⠦⠭⠭⠽⢯⡵⣆⣬⠴⢊⡼⠧⣙⢌⡕⢻⣋⢧⡾⢁⡾⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣭⢭⠭⠴⠖⠚⠋⠀⠀⠀⠀⢹⣉⣛⣫⡴⠋
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⢿⣆⠘⣣⢴⠿⠃⠀⠀⠀⡉⢀⣦⠀⠀⠐⠁⠀⠀⢱⠏⠻⠆⠀⠘⢿⣆⣢⣴⡤⠀⠀⠀⡀⢀⢀⡤⠀⠀⠀⠀⠛
⠀⠀⣼⣶⣦⣌⡏⠁⠀⢀⣴⣷⣆⡀⠙⠿⡿⢀⣴⣶⣤⡄⠔⠲⢆⢀⣶⣦⣤⣠⠊⠈⣡⣴⣶⣤⣄⠙⣮⣾⠁⣠⣾⣶⣀⠛⠛
⠀⢺⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠈⣿⣿⣿⠟⠋⠀⠀⠘⣿⣿⣿⣿⠏⠀⢸⢿⣿⣿⣿⣿⠧⠈⠻⡈⢻⣿⣿⡏
⠀⠀⠈⠉⠛⠀⠀⠀⣠⠶⠦⡄⢀⡀⠀⠀⠀⣤⡀⢉⣤⠶⠀⠀⠀⠈⠉⠙⠏⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⠀⣱⣤⣌⠁
⠀⠀⠀⣤⠀⢀⠀⠀⠉⠀⠀⠡⠏⠙⠦⠀⠀⠈⠛⠎⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠠⠋⠀⠈⢃⡞⠻⢦
⡇⣀⠀⣿⡿⢋⣴⣶⣶⣄⠔⠒⢦⣶⣿⣿⣷⣦⡐⠚⠋⢀⣧⣿⣤⠂⢸⣿⡾⢻⣦⠀⠀⠸⡜⠁⣠⣾⣿⣶⣆⠀⢠⠤⣄⠀⣷
⣿⣡⣤⠆⠀⠸⠿⣿⡿⠋⠀⠀⠛⠛⢿⣿⡿⠛⠃⠀⠀⢸⣿⣿⣧⣤⡴⠋⢀⣀⡉⠀⣀⣤⠀⠀⠻⠻⣿⠛⠁⠀⠁⠀⠀⢲⣿
⠋⠈⠀⠀⠀⢤⣄⠈⣥⠶⠂⠀⠀⠀⢨⡛⠁⢀⣠⠄⠀⠈⠿⠋⠉⠁⠀⠀⢀⡙⠛⠶⠛⠃⠀⠐⢶⣄⣠⠶⠒⠀⡄⠀⠀⠸⣿
⡴⠀⠀⠀⠀⠀⠙⠓⢀⠀⠀⠀⠀⠀⡀⣡⠶⠿⠃⡀⠀⢠⡰⢠⡞⠀⠀⠀⠘⠿⢇⣀⣴⡦⡀⢀⠀⢙⣀⡀⠀⢸⣿⠀⠀⡀⠆
⡁⢀⣴⣿⣦⡀⠀⠚⠛⢁⣠⣿⣷⣴⣹⠁⠀⣠⣾⣿⣧⡄⠹⣿⡆⢠⣷⣶⣴⣀⠎⠀⠀⠀⣿⣼⣀⡞⠉⠁⠐⣿⡅⠀⠀⠹⣾
⢅⠀⢿⣿⡿⠁⣠⠆⠀⠸⢿⣿⣿⡿⠋⠀⠀⠈⢿⣿⡟⠁⠀⠀⠙⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⣀⣈⠁⢀⣤⠀⠈
⣠⠶⠦⡄⢀⣾⠋⠀⠀⠀⠀⠈⠻⠁⠀⠀⣴⠶⢦⡃⠀⡀⠀⠀⠀⠀⠉⠙⠃⢀⣴⠃⠀⠘⡿⠟⠀⠀⠀⠀⣈⠛⠳⠟⠋
⠋⠀⠀⠠⡞⠙⠷⠀⠀⠀⢰⡆⠀⠀⠀⠐⠁⠀⠀⢡⡞⠙⢧⡀⠀⠀⢰⡄⠀⡾⠋⠀⠀⡀⡆⣠⡆⠀⠀⠀⠻⠷⣐⣴⣶⠄
⣦⣄⡰⠒⢦⣠⣶⣶⣶⣄⢿⣿⠟⢁⣴⣶⣤⡀⡠⠤⣆⠀⣷⣆⠀⠀⠸⣿⠟⣁⣠⣀⡀⠹⣶⣏⠀⢀⣴⣶⣄⡔⠁⠀⠀⢀⣶
⣿⡿⠁⠀⠼⠿⣿⣿⣿⠿⠧⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⣆⣈⠉⢀⣠⡔⠀⣾⣿⣿⣿⣿⣦⠈⠻⡀⠈⣿⣿⡿⠁⠀⠀⠐⣾⣿
⠻⠁⢀⡴⠀⠀⢈⡿⠋⠀⠀⠀⠀⣄⡀⢉⣤⠖⠀⠀⠀⣈⠛⠻⠜⠛⠁⠀⠀⠈⢻⡟⠁⠀⠀⠀⣱⠶⢦⡁⠀⡀⠀⠀⠀⠈⠉
⠀⠼⠟⠁⠀⠀⠀⢓⡀⠀⠀⠀⠀⠈⠻⠎⠀⠀⠀⠀⠀⠹⠿⣄⣠⣶⠆⠀⠀⠀⠙⡀⠀⠀⠀⠀⠋⠀⠀⢡⠟⠹⠦⠀⠀⠀⢠
⣷⠏⣀⣴⣦⡀⢸⠎⠀⠀⣼⣼⣇⡤⠐⠛⠋⠀⠀⣠⣶⣦⣰⠁⠀⠀⠀⣠⣤⣬⡗⠁⠀⣼⣿⣧⣦⡀⡰⠲⢆⢀⣠⣤⣤⣀⢸
⠁⠈⢻⣿⣿⢏⡞⠀⠀⢰⣿⣿⣯⣤⡴⠀⠀⠀⠀⠹⣿⣿⠃⠀⠀⠀⢼⣿⣿⡿⠟⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⠿⣿⣿⣿⡿⠷
⠀⣤⢤⣉⠁⣾⠇⠀⠀⠈⠿⠟⠉⠁⠀⠀⠀⢠⡴⠶⣌⠀⡀⠀⠀⠀⣈⡀⠙⣠⡤⠀⠀⠈⠉⠛⠀⠀⠀⠀⢦⣄⠀⣻⠏
⠘⠁⠀⠈⣴⠛⠷⡀⠀⢄⢰⢠⠖⠀⠀⠀⡀⠈⠀⠀⠈⡾⠙⠧⠀⠀⠈⠻⠎⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⢷⠙⡄
⣶⡄⢀⠴⢤⣴⣾⣿⣶⣌⣷⣿⠀⣰⣶⣿⣷⣀⠀⠰⠒⣦⣴⣷⣄⠀⣀⡀⠾⢿⣦⠀⠀⠸⣿⡿⠋⠀⣰⣰⡇⣀⠀⠏⢀⣴⣿
⠟⠃⠀⠀⠘⠻⣿⣿⣿⠿⠧⠉⣄⠙⣿⣿⣿⠿⠀⠀⠀⠈⢿⣿⠟⠀⠈⠻⣦⣀⡉⠀⣠⡴⠁⠀⠀⢠⣿⣿⡿⠷⠖⠃⠸⠻⢿
⡶⠆⠀⣤⡀⠀⣘⠟⠁⢀⣠⠀⠙⣷⣜⠃⠀⠀⠀⠀⣴⠖⢦⡀⢀⡀⠀⠀⢀⡙⠛⡾⠛⠁⠀⠀⠀⠘⣿⡿⠃⠀⠀⠐⢶⣄⣨
⣟⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣟⣛⣿⣟⣛⣻⣟⣻⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡆⠀⣼⣿⣿⣁⣠⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⠀⣿⣿⣿⠿⠛⠛⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⠀⢀⣾⣿⣿⣷⣿⣿⠁⠰⠀⠀⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡏⢽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠋⠇⣸⡇⢿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣁⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⡟⢘⣿⣶⣶⣿⣿⣿⣿⡏⡙⠛⠿⠿⡿⢷⠠⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣐⠻⡟⢱⠉⢈⢿⣿⢿⣗⢀⡀⠀⠀⢀⠈⢀⣾⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣉⠓⢿⣇⢻⣿⣿⠀⠀⠀⡀⠀⣀⣾⢏⣿⣿⣿⢷⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣘⣿⡏⢷⡀⠀⢀⣴⣿⢋⣾⢟⣭⣿⡿⣿⣝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣇⢸⣷⠀⣼⡿⢻⡟⣱⣿⠻⠿⣿⣿⣿⣞⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⣭⣭⣭⣭⣼⣿⣃⡟⣼⡿⠋⣠⡴⣻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠈⠻⣶⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣦⠀⠀⢨⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⠈⢿⣿⡿

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢿⡿⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠿⠷⣦⡄⠰⢿⡿⠆⢠⣴⠾⠿⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⣴⣷⣄⠈⢛⣶⣿⣿⣶⡛⠁⣠⣾⣦⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠃⢀⡟⠉⣽⣿⣾⣿⣿⣿⣿⣷⣿⣯⠉⢻⡀⠘⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢶⣤⠞⠁⢀⠛⠻⡿⣷⣿⣿⣾⢿⠟⠛⡀⠈⠳⣤⡶⣿⡇
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣤⣄⡀⠀⣿⣧⣴⠟⠛⣿⣿⠛⠻⣦⣼⣿⠀⢀⣠⣤⣿⣶⣶⣶⣤⣀
⠀⠀⠀⢠⣾⠟⠋⠉⣿⠟⢷⡀⣹⣿⠷⣮⣍⣁⣤⣾⠏⠹⣷⣤⣈⣩⣵⠾⣿⣏⢀⡾⠻⣿⠉⠙⠻⣷⡄
⠀⠀⢠⡟⢡⣤⣾⣇⠀⣀⡾⠃⢈⣥⠶⠚⣫⡿⣿⡁⠀⠀⢈⣿⢿⣝⠛⠶⣬⡁⠘⢷⣀⠀⣸⣷⣤⠌⢻⡄
⠀⠀⣼⠁⣠⣿⠟⢻⣿⡅⠀⣴⠏⣠⣄⣾⠋⠀⠘⢿⡄⢠⡿⠃⠀⠙⣷⣠⣄⠹⣧⠀⢨⣿⡟⠻⣷⣄⠈⣧
⠀⠀⣿⣼⠟⢁⣠⣤⣽⣦⣼⣟⡀⠙⢻⡏⠀⣠⣤⣬⣿⣾⣥⣤⣄⠀⢸⡟⠋⢀⣻⣧⠶⣭⣤⡀⠀⠻⣧⣿
⠀⠀⢿⣏⣴⡿⠋⠁⣶⡄⣿⣯⠙⢷⣼⣿⠰⣿⣿⣿⣿⣿⣿⣽⣿⠆⣾⣧⡾⠋⣽⣿⢠⣶⠄⠙⠳⣄⢹⡟
⠀⠀⠈⣿⣯⡶⠿⠿⢿⣦⣹⣿⣆⠀⢿⣿⡇⠀⠹⣿⣿⣻⣿⠏⠀⢸⣿⡿⠀⣰⣿⣯⣴⡿⠿⠿⢶⣼⣿⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠛⣿⡿⠂⣿⣿⣿⢾⠆⠘⢿⡿⠋⠰⡷⣿⣿⣿⠀⢿⣿⠛⠁⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣹⡿⠃⠀⣰⣦⣼⣧⣴⣆⠀⠘⢿⣏⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⠀⠀⠺⣿⣿⠟⠻⣿⣿⠗⠀⠀⣈⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠶⣪⡁⢩⠉⢀⣻⡿⠃⠠⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡏⢰⠀⠣⠾⠁⠈⠀⠿⠃⠀⠀⡀⠀⠋⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⠀⠁⠀⢀⡤⡤⢀⡶⣤⠀⢤⡀⠈⠀⠐⣀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⣀⣠⣶⢾⣿⣿⣿⣿⣶⣿⣿⣄⠀⠀⠊⠰⢤⣄⡘⠁⠁⠒⠉⡀⠀⠀⠀⠀⣜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠧⢐⡂⠀⠀⠀⣾⡈⠙⣿⢽⣾⣇⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠙⣿⣬⡄⠀⡴⠷⡆⠀⠈⠈⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣫⣼⣛⠁⠆⠀⣠⣾⢿⠄⢰⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠠⠉⣽⡇⠠⢒⠟⠁⠀⠀⣀⣀⠹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⣻⣿⣿⠟⠀⠐⠋⠹⠏⡀⠁⠈⠈⠹⠛⠿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⡇⠀⣄⣠⡤⠀⡉⠁⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠐⡘⡿⣿⣿⣿⣿⣴⡀⢶⡀⢠⣿⢇⠚⣛⡙⠁⠠⠡⠔⡶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣻⡇⠀⠀⠀⠀⠀⣠⣟⣆⠂⡀⢀⠃⠀⠀⠇⠁⢸⠛⡻⣿⣿⣿⡆⣵⣿⣵⣾⣭⣭⡽⡅⠀⠀⠠⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣩⡏⠉⠀⠀⠀⠀⣠⣾⣿⡿⠏⠃⢁⠀⡜⢈⣠⣷⣶⣾⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⠤⠄⣀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠀⠀⠀⡀⣴⣄⡄⠀⠇⠙⣿⣾⣾⣾⣷⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣷⣿⣿⣿⠏⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠄⠀⠀⠀⠀⠀⢠⡿⣧⢣⡄⡌⠃⢘⢻⣿⣿⣿⣿⣿⣯⣿⣿⣟⡿⢯⣿⣿⡯⠻⣿⣿⢋⡤⢉⠒⠤⣐⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⠀⠀⠀⠀⠀⣸⣯⠜⡛⡷⠁⠀⢸⣀⡿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠶⣼⡏⣰⠤⢄⡹⣿⡻⣦⡁⢢⡶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⢠⠀⠄⢀⣴⣧⢻⢛⣄⠏⠀⣘⡄⡽⠓⣽⢻⠿⣿⣯⡿⣿⣷⣼⠟⢣⣴⢏⣀⠒⡁⠈⢳⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣶⣯⣿⣿⣕⣙⡈⢰⠁⢘⢡⢶⣷⢠⠿⣧⣾⣿⣿⣿⣿⣧⣏⣖⡗⡶⢮⣽⣍⣖⠸⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣿⣿⣶⣵⣳⣵⣾⣾⣿⣶⣿⣯⣾⣿⣟⣿⣿⣿⣿⣿⣷⣭⣛⣿⣟⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⠛⠉⠙⣯⠙⠻⢿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠟⠀⠀⠀⠀⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠋⠉⠈⡁⠁⠄⠤⠁⠄⡀

⡿⣯⡉⢙⣆⡾⠛⠀⣿⣃⣊⢴⠁⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⠈⡦⣑⣘⣿⠀⠛⢷⣰⡋⢉⣽
⣇⢈⡟⠉⣹⡃⠀⣞⣿⠪⠑⡽⣸⣓⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣚⣇⢯⠊⠕⣿⣲⠀⢘⣏⠉⢻⡁
⣨⡽⠗⠺⠕⢁⣤⡿⣅⡈⡤⢲⡟⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢻⡐⢤⢁⣨⢿⣤⡘⠮⠗⠞⢯
⠛⠀⣠⢤⣤⡿⠛⣠⠸⡴⣣⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣜⢦⠂⣈⡛⢿⣤⡤⡄
⠿⢻⡻⡛⡁⠹⢐⡦⢐⣴⢻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡟⣦⡂⢤⡢⠏⢈⢛⢟⡟
⢊⣜⣕⡤⢠⣋⣭⠾⣻⡶⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡖⣟⣿⣋⣙⣿⣻⢲⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣟⠷⣭⣙⡄⢤⣨⣣
⠥⣤⢶⢺⣟⣫⠿⠛⠉⠀⠀⠀⠀⠀⠀⣠⡴⣛⣿⠾⡟⣉⢭⢤⠔⠢⡤⡭⣍⢳⠷⣿⣛⢦⣄⠀⠀⠀⠀⠀⠀⠈⠛⠿⣍⣻⡗⡶⣤
⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣭⠟⣫⠖⡚⠠⠀⠰⡅⣊⣁⢨⢆⠄⠄⠓⠲⣝⠻⣭⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⡿⣡⠁⡤⠉⣳⣴⣟⡟⠛⠛⡛⠛⢿⣻⣦⣞⠈⢤⠉⣌⢿⡝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⡟⣸⠡⢧⣰⣿⠟⢀⡀⣀⣠⡿⢿⣄⣀⢀⡀⠻⣿⣄⡼⠎⣇⢻⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡿⣨⠀⡂⣴⢿⠀⠰⣵⠟⢹⠗⢦⡴⠺⡏⠻⣮⠆⠀⡿⣦⢐⠀⣍⢻⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠃⣗⠕⠦⣿⠋⠀⣼⢷⠖⠻⣦⣸⣇⣴⠗⠲⡾⣇⠀⠉⣿⠵⠪⣺⠘⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠰⡁⢎⢸⣿⠀⣿⡇⢈⡷⠶⢾⣷⣿⡷⠶⢾⡁⢸⣽⠀⣿⡇⡱⢈⠆⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡤⡯⡢⢖⣿⣀⠀⢻⡾⢦⣴⠟⢹⡏⠻⣦⠴⢷⡏⠀⣠⣿⡲⢔⢽⢠⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣷⣙⠀⠅⠻⣾⠀⠰⡻⣧⣸⡦⠞⠓⢴⣇⣴⢟⠆⠀⣷⠟⠨⠀⣃⣾⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣽⣦⢹⡠⡚⠙⣿⣦⠈⠁⠉⠙⣷⣶⠋⠉⠈⠁⣴⣿⠋⢓⢆⡏⣴⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⣧⡙⡀⠃⡂⡽⠻⣯⣷⣤⣬⣤⣤⣼⣽⠟⢯⢀⡚⢈⢋⣼⣣⠟
⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣛⣦⣝⠮⢥⠐⠐⠰⡇⢍⡩⢘⠆⠂⠂⡬⠴⣋⣴⣛⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤
⡒⠛⠾⠼⣯⣝⣶⣤⡀⠀⠀⠀⠀⠀⠀⠙⠷⣭⣿⢶⣧⣝⣚⠚⠢⠔⠓⣓⣫⡬⠶⣿⣭⠞⠋⠀⠀⠀⠀⠀⠀⢀⣤⣶⣫⣽⡧⠷⠛
⢌⢫⡫⠓⠐⣍⣛⢶⣽⠷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠧⣯⣿⣍⣩⣿⣽⠽⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⠾⣯⡶⣛⣡⠃⠚⢝⡝
⣶⣼⣵⣥⡁⣰⠨⠗⠨⠻⣼⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣧⠟⠥⠚⠅⣆⢈⣬⣮⣧
⣤⠀⠘⠚⠛⣷⣮⠉⠠⡳⡝⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⢫⠞⠄⠉⣤⣾⠛⠓⠋
⢉⣳⡶⢴⡢⡌⠛⣷⡋⢁⠓⠼⣧⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣾⠅⠚⡈⢙⣾⠛⢡⢔⡦⢶⣞
⡏⢈⣧⣀⣹⡅⠀⢯⣿⢔⡠⣳⢹⡭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢭⡇⣞⢄⡢⣿⠽⠀⢨⣏⣄⣼⡁
⣷⣟⣁⣨⠏⢷⣤⠀⣿⡍⢌⠺⡀⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⢀⠗⡩⢩⣿⠀⣤⡾⠹⣅⣈⣻

⠀⠀⠀⢸⡿⣿⣿⠟⠙⠛⠙⠛⠋⠛⠋⠛⠙⠛⠛⠛⠙⠛⠙⠋⠋⠛⠙⠛⠋⠛⠙⠛⠙⠋⠻⣿⣿⣿⡇
⠀⠀⠀⢸⣿⠟⠁⣠⢶⣻⣗⡻⠛⠛⠛⠳⣛⣿⣛⠛⠛⠛⠛⢛⣿⣛⠟⠛⠛⠛⢟⣻⣟⡳⣄⠀⠱⣿⡇
⠀⠀⠀⢸⡇⠀⡏⠷⣏⡶⠷⣏⡷⠂⠰⢎⡱⠷⢎⡵⠆⠰⢾⣱⠾⢾⣹⠖⠀⠾⣉⠾⢷⣩⠾⢻⠀⢸⡇
⠀⠀⠀⢸⡇⠀⡇⠀⠶⣏⣏⡁⠀⠀⠀⠀⣉⣿⣱⠆⠰⠆⠰⢾⣹⣉⠀⠀⠀⠀⢈⣹⣏⡶⠀⢸⠀⢸⡇
⠀⠀⠀⢸⡇⠀⡇⠶⣏⡷⡷⣍⡷⠄⠰⣎⡱⣷⢏⡳⠆⠰⢾⣹⢾⢾⣹⠦⠀⢶⣉⢶⡶⣙⠶⢸⠀⢸⡇
⠀⠀⠀⢸⡇⠀⡇⠀⠀⣙⣏⡷⠆⠰⠀⠰⣏⣟⡉⠀⠀⠀⠀⢈⣻⣹⠶⠀⠆⠀⠾⣹⣋⠁⠀⢸⠀⢸⡇
⠀⠀⠀⢸⡇⠀⡇⠶⣏⠷⡶⣍⡶⠄⠰⣞⡱⣶⢏⡳⠆⠰⢾⡹⢶⢮⣹⠦⠀⢶⣋⢶⡾⣙⡶⢸⠀⢸⡇
⠀⠀⠀⢸⡇⠀⡇⠀⡾⣝⣟⡁⠀⠀⠀⠀⢉⣛⡹⡆⠠⠆⢰⢯⣻⣋⠀⠀⠀⠀⠈⣙⣋⠷⠀⢸⠀⢸⡇
⠀⠀⠀⢸⡇⠀⣧⡶⣋⢷⡶⢝⡶⠄⠰⣞⡹⣶⢏⣳⠆⠰⢾⡹⣶⠮⣳⠦⠀⢶⣫⢷⡾⣙⣶⣼⠀⢸⡇
⠀⠀⠀⢸⡿⣦⡀⠙⢮⣽⢾⡽⣤⣤⢤⡴⣭⢿⡭⣤⢤⡤⡤⣭⢷⡯⣷⣤⣤⡤⠯⡵⣯⡵⠋⠀⣰⣿⡇
⠀⠀⠀⢸⣷⣿⣿⣦⣄⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣠⣤⣤⣤⣤⣠⣤⣤⣴⣿⣿⣻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⣒⠊⣭⠤⣲⣀⣀⣖⠨⣭⠑⣒⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣁⢀⣻⣥⣿⡶⢾⡟⢻⡏⢹⡟⢻⡷⢶⣿⣬⣟⡀⣈⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢱⣄⣽⢟⡉⠿⠐⠛⠈⠉⠀⠀⠀⠀⠉⠁⠛⠢⠿⢉⡻⣯⣡⡎⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡑⢶⣴⠟⣧⠎⠁⢀⡀⢠⡄⠐⠖⢸⡇⠲⠀⢠⡄⢀⡀⠈⠱⣼⠻⣦⡶⠊⡢⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⢘⣷⢟⡩⠟⠀⠀⠰⠆⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠰⠆⠀⠀⠻⢍⡻⣾⡃⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠇⠟⣾⢧⡌⠁⢀⠰⠆⠀⠀⠀⠀⣄⡀⠀⢼⡧⠀⢀⣠⠀⠀⠀⠀⠰⠆⡀⠈⢡⣼⣷⠻⠸
⠀⠀⠀⠀⠀⠀⡸⠘⢳⡿⣤⠀⠀⣈⠻⠂⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠰⠟⣁⠀⠈⣤⣿⡞⠃⢇
⠀⠀⠀⠀⠀⢠⠇⠗⣾⠷⡆⠀⠀⠉⠀⠀⠀⠹⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠉⠀⠀⢰⠾⣷⡻⠨⡄
⠀⠀⠀⠀⠀⡘⠘⢺⡿⠶⠀⠀⣘⣁⠀⠀⣀⣄⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⣠⣀⠀⠀⣈⣃⠀⠀⠶⢿⡗⠃⢣
⠀⠀⠀⠀⠀⢡⢠⢼⣷⠶⠀⠀⢩⡉⠀⠀⠉⠋⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠙⠉⠀⠀⢉⣍⠀⠀⠶⣾⡧⡄⡌
⠀⠀⠀⠀⠀⠘⡆⡦⢿⡶⠇⠀⠀⣀⠀⠀⠀⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣆⠀⠀⠀⣀⠀⠀⠸⢶⡿⢼⢰⠃
⠀⠀⠀⠀⠀⠀⢱⢠⡼⣷⠛⡀⠀⢉⣴⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠰⣦⡉⠀⠀⠟⣾⢧⡄⡎
⠀⠀⠀⠀⠀⠀⠀⡆⣦⢿⡟⢃⡀⠈⠰⠆⠀⠀⠀⠀⠋⠁⠀⢺⡗⠀⠈⠙⠀⠀⠀⠀⠰⠆⠁⢀⡘⢳⡿⣴⢰
⠀⠀⠀⠀⠀⠀⠀⠱⡀⢨⡿⣮⣑⣦⠀⠀⠰⠆⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠰⠆⠀⠀⣴⣊⣵⢿⡅⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡡⠾⠻⣦⡟⢆⡀⠈⠁⠘⠃⠀⠦⢸⡇⢴⠀⠘⠃⠈⠁⢀⡰⢻⣴⠟⠷⢄⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡸⠋⣻⣮⣁⣶⠂⣤⢀⣀⠀⠀⠀⠀⣀⡀⣤⠐⣶⣈⣵⣟⡙⢇⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡉⠈⣽⡛⣻⠷⢾⣧⣼⣃⣸⣧⣼⡷⠾⣟⢛⣯⠁⢉⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠭⢄⡛⡚⠽⠉⠉⠯⢒⢓⡠⠭⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠰⣿⣷⣄⣄⣀⣀⣤⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣶⡶⠤⣰⣧⣴
⠀⠀⠀⠀⠀⢙⣿⣭⣛⣉⠉⣹⣿⣿⠀⠀⠀⠀⠀⣀⣀⣤⡴⠴⠒⢻⣏⣉⣀⣀⣴⣷⣷⠿⠋⠭⠁
⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠀⢹⣿⣿⣷⣶⣖⣋⣹⠿⠿⠓⠓⠛⠛⠛⠉⠉
⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣯⠁
⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⢒⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⣀⢀⠀⠀⢀
⠀⠀⠀⣼⣿⣿⣿⣿⣟⣛⡈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠟⣻⡿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⡆⢠⢀⠀⡀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⢘⡘⠿⣻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈
⠀⠀⣿⣿⣿⣿⣿⣯⣰⡈⢓⣿⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⣷⠀⡀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⠟⠁⠀⠰⣶⣤⠀⠾⠟⠛⡶⢤⣴
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⠶⠶⠾⠛⠛⠉⠀⠀⠾⠷⠗⠀⠀⠐⠧⠶⠈⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣤⣀⣈⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣷⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣿⣿⣿⣿⣿⣷⡟⣿⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣾⢯⣿⣿⣿⣹⣿⣿⣗⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣻⣿⣷⡹⣿⣿⣿⣿⠿⠟⣉⣉⠉⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡧⣿⣷⣌⣿⣷⣽⣿⣋⣠⣴⣦⣌⣿⣿⣧⣴⣶⣌⠟⠛⢿⣿⣿⣿⣿⣿⣿⡉⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⢟⣿⣿⣛⢻⣿⡏⢉⣉⡉⢿⡿⠛⠻⠉⠉⠙⠛⠻⠛⠛⠳⠀⠻⣿⣿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣴⣾⢿⣿⣿⣿⡏⢠⣿⣿⠟⠃⠀⠌⣑⢄⣤⣶⣶⣿⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⣿⣷⣿⣽⡟⢁⣤⣶⠟⠋⠀⠀⠀⣠⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⡀⣤⡈⠉⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⣿⣿⠇⢘⣿⣇⠀⣠⠂⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣇⠸⠀⡌⣉⣰⡁
⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⢻⢿⣿⡏⢰⣿⣿⣷⠀⢡⡘⣟⣻⣿⣿⡿⠛⣋⠙⣿⣿⠃⡐⠠⣾⣿⣆⢀⠈⠙⡻⠛⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣾⣾⣿⣄⣸⣿⣿⠁⢀⢿⠹⣿⣿⣿⠛⠂⠞⢡⠜⠂⠄⠂⠈⠀⠘⢻⣿⣆⠀⠀⢳⡀⢿⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣕⣺⡟⣿⣿⡏⢰⣿⣇⠀⢰⠹⡟⢿⣉⠷⢤⢈⠛⡁⡄⢴⣻⡄⠂⠀⠀⠈⠹⣿⢀⠀⠀⠁⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣻⣿⠇⠻⡿⠟⢂⠠⣛⠗⣚⣤⠃⡰⣶⣋⠙⢓⠠⢛⣿⣶⡁⠀⢰⣄⡜⢀⣀⠀⠀⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⡇⣰⣿⣷⠶⢌⡳⣎⢹⣿⣄⡚⡵⠿⣿⣴⡋⣠⣿⠿⠛⠓⠐⠿⠛⠓⠶⣤⣄⣠⠊⠉⠙⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠘⠸⣿⣿⣯⡿⠙⢨⣻⠏⣁⣷⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢫⣿⣷⣾⠟⢿⡗⠀⠘⠧⣽⡝⢿⣼⣿⡿⠛⠀⡆⢘⢀⡄⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⢠⣿⡅⠀⠀⡀⢹⣷⣿⣤⣽⢅⢸⠀⣇⢻⢤⣱⡄⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣡⣼⣷⣿⣿⣿⣟⠃⢄⠙⠛⢇⠰⡳⢝⠤⣠⡄⠀⠀⠀⠐⠃⢀⡀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⣿⣻⣿⢃⣄⠈⠳⣑⠪⣱⡛⢾⣵⡝⢾⣖⠒⡄⢺⠂⠈⠁⢀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠏⠠⢌⠂⠀⣩⡐⠨⣍⣓⠾⣣⣿⣽⣿⣿⣾⡆⡠⣏⣷⣧⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⣿⣿⣿⠏⢇⡂⣀⠮⣑⢛⡁⢌⢔⣀⣽⣷⣷⣿⣿⣿⣿⣿⣿⣴⣿⣇⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡟⣼⠟⣿⣳⣾⣽⣿⡜⣿⡿⠾⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢸⡏⠀⠙⠻⢿⣿⣤⣽⣷⡿⠿⠛⠛⠛⠛⢿⡏⠛⠛⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢡⣀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣿⡃⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠳⠯⣉⡀⠀⠀⠀⠀⠀⠀⠚⠹⠏⠛⠷⠤⠍⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⢒⠋⡉⢉⠉⠉⡍⢉⢛⡒⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢋⠡⠀⣀⡡⠬⠄⢒⡒⠒⢒⣒⠒⠒⡒⠢⠥⢍⣐⠠⠌⡙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡁⢄⣡⠔⣊⣍⡥⣊⣓⣎⠤⠭⠧⠶⠬⠯⠥⠬⣳⣂⡑⢎⢉⣑⠢⣍⡐⢨⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⢄⡠⠞⠩⠶⣆⠴⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⠬⣇⡠⢭⠲⣄⡠⠌⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠱⢈⡴⢫⠒⣺⠜⠋⠀⠀⠀⠀⣀⣠⣤⡔⠒⠒⣲⣖⠒⠒⢲⣤⣄⣀⠀⠀⠀⠀⠙⠺⣗⠂⣝⢦⡐⠊⠳⣄
⠀⠀⠀⠀⢀⡜⠡⢆⡴⡫⠶⡣⠛⠁⠀⠀⢀⠴⢒⠛⠁⠀⠀⠀⠙⡞⠁⠈⢳⠋⠀⠀⠀⠈⠛⡖⠤⡀⠀⠀⠈⠑⢟⡂⢜⢦⡰⠈⢣⡀
⠀⠀⠀⢠⠎⠤⢡⢎⡤⣣⠛⠀⠀⠀⡠⢾⠥⣠⡃⠀⠀⠀⠀⠀⡼⠀⠰⠆⠀⢧⠀⠀⠀⠀⠀⢘⣄⠬⡶⢄⠀⠀⠀⠑⣝⢄⡱⡅⠆⠱⡄
⠀⠀⢠⠋⡌⡰⢃⡐⡴⠁⠀⠀⣠⠊⣀⣲⠀⢀⠈⠑⠢⣀⢀⠀⠇⠀⠀⠀⠀⠸⠀⡀⣀⠔⠊⠁⡀⠀⣔⢀⠑⣄⠀⠀⠈⢧⣿⠘⢆⠡⠙⡄
⠀⢠⠏⡐⣰⠑⢋⡜⠀⠀⠀⡴⠋⠁⠀⠸⡀⠈⠃⠀⠀⠈⠳⣘⠀⠀⢀⡀⠀⠀⣃⠞⠁⠀⠀⠘⠁⢀⠇⠀⠈⠙⢧⠀⠀⠀⢷⢉⡎⣆⢂⠹⡀
⠀⡞⠠⢡⢧⠞⡜⠀⠀⠀⣾⠁⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⡤⠞⠋⣉⣉⣉⣉⠙⠳⢤⣀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠈⣷⠀⠀⠀⢻⠲⡹⡄⠀⢳
⢰⠃⡃⡞⢨⢰⠃⠀⠀⡼⢰⡀⠀⠀⠀⠀⠠⠵⣄⢀⠔⢁⣤⣺⣽⡽⠾⠷⢯⣟⣗⣤⡈⠢⡀⣠⢮⠄⠀⠀⠀⠠⢀⠋⢧⠀⠀⠘⣶⡃⢷⢘⠘
⣼⠠⢠⠓⡋⡞⠀⠀⢠⣇⠴⠛⠊⠉⠁⠀⠈⠉⢹⠏⣰⣻⡾⢋⠁⡀⠀⠀⢀⠈⡙⢷⣿⣆⠹⡏⠉⠁⠀⠉⠉⠙⠚⠤⣸⡀⠀⠀⢻⢘⠜⡄⠆
⡇⣈⢸⢡⠇⡇⠀⠀⣸⠙⢦⡀⠘⠓⠀⠀⠀⠠⡎⢰⣟⡾⠁⢈⠀⣡⡶⢤⣌⠒⠁⡈⢿⣿⡆⢱⠄⠀⠀⠀⠚⠃⢀⡴⠋⡆⠀⠀⢸⡛⡐⡇⣁
⡇⠀⢸⠸⡚⡇⠀⠀⢸⡰⠋⠉⠲⢤⣀⡀⠀⠀⡇⢸⢿⡇⠀⠀⠰⣏⠀⠀⣹⠆⠠⠀⢸⣿⡇⢸⠀⠀⢀⣀⡤⠖⠉⠘⠆⡧⠀⠀⢸⣠⠇⡇
⡇⢉⢸⢸⠃⡇⠀⠀⢸⡇⠀⠀⠀⠀⠂⢬⡭⠟⢇⠘⡽⣷⡀⠀⠀⠙⠳⠞⠋⠀⠀⢀⣾⣿⠃⡸⠻⢭⡥⠐⠀⠀⠀⠀⢸⡇⠀⠀⢸⠒⡅⡇⡉
⢻⠠⠘⡆⣢⢣⠀⠀⠘⣧⠀⠀⠀⢀⠔⠁⠀⠀⠘⣄⠘⣽⢗⣤⡀⠀⠀⠈⠀⢂⣠⡺⣿⠃⣠⠃⠀⠀⠉⠢⡀⠀⠀⠀⣸⠃⠀⠀⣘⢊⢠⠇⠆
⢸⡄⡁⢧⢣⠸⡄⠀⠀⢹⠑⠤⡴⠃⢀⡀⠀⠀⠀⠈⢣⡈⠙⢽⣿⣷⣶⣶⣾⣿⡯⠛⢁⡔⠁⠀⠀⠀⢀⡀⠘⢦⠤⠊⡏⠀⠀⢠⣇⡔⡼⢨⢠
⠀⢧⠀⠘⡆⡇⢣⠀⠀⠀⢧⣰⠁⠀⠉⠁⢀⣀⡠⢔⣻⠉⠓⢤⣄⣉⣉⣉⣉⡠⡴⠚⠉⡟⡢⠤⣀⡀⠈⠉⠀⠈⣆⠼⠀⠀⠀⡞⢰⢰⢃⠂⡼
⠀⠈⣆⠡⠹⡌⣢⢣⡀⠀⠀⠫⡉⢹⠋⠉⠉⠀⠀⢁⠇⠀⠀⠌⠀⠀⡸⢇⠀⠀⠡⠀⠀⠸⡈⠀⠀⠉⠉⠙⡏⢉⠝⠀⠀⢀⡼⡞⢡⠏⠌⣰⠁
⠀⠀⠘⣆⢂⠹⡜⠌⡳⡀⠀⠀⠙⢤⡄⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⡰⠃⠈⢆⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⢠⡤⠋⠀⠀⢀⢞⠤⢣⠏⡘⣠⠃
⠀⠀⠀⠘⢆⠰⠘⢆⠇⡹⢆⠀⠀⠀⠙⢦⣄⣀⣂⣸⡄⠈⠃⢀⠔⠁⠀⠀⠈⠢⡀⠘⠁⢠⣇⣀⣀⣠⡴⠋⠀⠀⠀⡠⣋⡸⡰⠃⠒⡰⠃
⠀⠀⠀⠀⠈⢣⡁⠌⠳⡌⢧⠱⢄⡀⠀⠀⠈⠓⠤⣀⢳⡠⠖⢃⠀⠀⠀⠀⠀⠀⡸⠲⢄⡜⣀⡤⠚⠁⠀⠀⠀⡠⠚⡼⣠⠞⠱⢈⡜⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡠⠌⠳⣅⢰⡙⠦⣄⠀⠀⠀⠀⠉⠑⠂⠂⠴⠶⠤⠤⠶⠮⠔⠔⠚⠉⠀⠀⠀⠀⣠⢔⢋⠎⣩⠞⠁⢆⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡐⠊⡑⠬⣉⠦⣙⢒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣖⣋⠴⣉⠽⠊⡑⢂⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡃⠌⣙⠲⢤⣑⠌⠙⢭⣛⣲⣒⠲⢒⣖⠒⣒⣖⣛⡫⠓⠦⣊⡤⠔⢋⠡⢈⡡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⡐⠂⠍⣙⠒⠂⠦⠬⠭⠥⠬⠭⠵⠦⠒⠒⢋⠉⠁⢂⣡⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠬⣅⣁⣘⣀⣀⣃⣈⣨⠥⠤⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⣴⣺⣿⡿⠿⢿⡟⠑⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡠⠐⡶⠒⢠⣌⣿⣧⣴⣥⡀⠀⢠⣌⢹⣷⣶⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠁⠀⢰⠶⠚⠛⣓⣼⢿⣿⠀⠀⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡆⠀⠀⢠⣶⣶⠃⡀⢰⣲⠂⠀⠀⠀⠀⠀⠈⠚⢻⡇⠀⠈⠩⣅⠈⠭⣿⣄⣀⣰⣿⣦⣄⣤⠉⠀⠀⠀⠀⠐⢤⣴
⠀⠀⠀⠀⣲⠉⢀⠀⣾⣿⠁⠀⠀⠈⣿⣷⠀⠀⣆⠐⠒⠠⣭⣿⢀⡔⠀⠀⠉⣿⡖⣀⡻⣿⣿⡿⢿⣿⡟⠿⠻⠻⠟⠏⡿⡿⡟
⠀⠀⠀⠀⣿⣀⢠⣶⢻⣿⠀⡀⠀⠀⠒⣠⣤⢄⣿⡯⠭⣧⣽⡿⣼⡇⢰⣶⣦⣿⣿⡟⠒⠘⢯⣤⠄⣼⡇⢸⣼⣼⣧⣴⣿⣷⣧
⠠⣤⢤⣤⣿⣿⣥⣿⡿⣶⢶⡖⣾⣿⢿⣿⣿⢸⣿⣿⣺⣿⣿⣾⣿⣿⣄⣉⣻⣿⣿⢿⡟⣖⣖⣶⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠙⠋⠋⠁⠐⠛⠈⠟⠉⠉⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠛⠈⠓⠛⠛⠛⠛⠂⠙⠛⠙⠉⠘⠉⡟⠉⠋
⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣭⣬⣥⣭⣭⣭⣥
⣿⣿⣡⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠉⠀⣀⠀⡀⠌⠘⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠙⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢄⠀⠀⠀⠀⠀⠠⠀⠀⠄⠈
⠀⠀⠀⠀⠀⢀⡤⠔⠒⠢⡔⠁⠀⠀⠀⠀⠀⠘⡄⠴⠶⢄⠀⠀⠀⠀⠀⠀⢪⠁⠀⡖⠒⠂⠘⡀⠀⠀⡄
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⢦⠁⠘⡓⠀⠀⠘⠒⠂
⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠤⠤⢄⣄⠠⠤⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⡤⠤⢆⠀⠀⠀⠀⠀⠄⠀⠉⣅⡀⠠⠤⠄⣥⠀⠀⡀⠑⡇⠀⠀⠀⡘⠀⠀⠀⠀⠂⠒
⡰⠁⠀⠀⠀⠑⠠⡀⠐⠁⠠⠐⠁⠈⢀⠀⠀⠀⠀⠀⠀⠀⢱⠃⠀⠀⠐⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠘⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡠⠋⠀⢀⠀⠀⠀⡀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⢄⠀⠀⠀⠀⡀⠀⣀⡀⣐⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠸⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⡴⠊⢁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠙⢤⢀⡀⢀⠀⠀⡄⠀⣀⡀⠀⠀⠀⠈⢽⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⡉⠉⠃⠀⠀⠀⠀⠀⠀⠀⢸⠅⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⢣⠀⠀⠀⢠⠀⠈⢄⠀⠀⠀⢀⠀⠊⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠈⠣⡀⠀⠀⠠⠀⢀⡱⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠈⠙⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⡀⠠⠀⠆⠠⠛⢔⢄⠀⢠⡾⣓⣙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣤⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⠽⡏⡏⡇⡹⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠜⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣬⣧⣤⠶⠶⢰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠴⠐⠘⠄⡁⢉⡳⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠐⠀⠀⠀⠀⠘⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡖⣀⠀⠀⠀⠀⠀⠀⣠⡚⣬⠄⡢⠰
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠂⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⢹⠂⠀⠀⠀⠀⢰⣫⠄⠉⣠⠲⡄⠀⠀⠀⢠⣤
⠀⠀⠁⠀⠈⠁⠀⡀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⠐⠂⠈⣜⣣⠝
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢄⠘⠃
⠀⠀⠀⠀⠿⠀⠑⠀⠀⠌⢃⠀⠀⠀⢠⣴⠶⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⡀⠠⢢⠤⡀
⠀⠀⠀⠀⠀⠂⡐⠀⠀⠀⢬⠀⠀⠀⠾⣿⣷⠣⠈⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⠀⠄⢠⡾⢭⡈⠐⠂
⠀⠀⣀⡀⠒⠐⠀⠠⠀⢂⠈⠀⠀⠀⠹⠉⠀⠒⠘⠂⠚⠀⠀⠀⠀⢀⣤⣤⢀⣀⠀⠀⠀⢀⠀⠀⠁⢀⠊⠁⠀⢀⠄
⠀⠈⠀⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠀⠠⣽⠇⠼⣯⠄⠀⣀⣴⡖
⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⠰⢿⡄⠿⢶⢞⡹⣶⣶⢏⡳⡶⠿⢠⡿⠆⠀⢀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡹⠞⡷⢺⣿⣄⡀⣾⣺⣇⡼⢧⣸⣇⣷⢀⣠⢿⡗⢾⠳⢏⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢾⡥⣴⢟⣈⣻⣾⠛⣯⡹⣌⠁⠈⣡⢏⣽⠛⣷⣟⣁⡻⣦⢬⡷⠁
⠀⠀⠀⠀⢠⣀⣴⣆⣾⣶⣦⣸⣏⠙⠁⣷⢃⢈⡭⢳⡞⢭⡁⡘⣾⠈⠋⣹⣇⣴⢶⣷⣰⣦⣀⡄
⠀⠀⠀⠀⠈⢻⣤⡍⠀⠹⣾⠛⢤⣤⠤⣇⡏⠀⠀⠹⠏⠀⠀⢩⣼⠤⣤⡤⠛⣷⠏⠀⢩⣤⡟⠁
⠀⠀⠀⠀⠀⡀⣸⢗⣚⣻⣏⡻⡉⢐⠋⠉⠋⣠⡄⢸⡆⢀⣄⠙⠉⠙⡃⢉⢟⣹⣟⣓⡺⣇⢀
⠀⠀⣀⣰⠷⡟⢳⣮⣉⡽⠆⠙⢧⣋⣄⡀⢀⣉⠁⠀⠀⠈⣉⡀⢀⣠⣙⡼⠋⠰⢯⣉⣵⡞⢻⠾⣦⣀
⠀⠀⠉⠻⡶⣦⡼⢟⣉⣳⠆⣠⡞⣍⠋⠁⠉⢉⡀⠀⠀⢀⡉⠉⠈⠙⣩⢳⣄⠰⣞⣉⡻⢧⣴⢶⠟⠉
⠀⠀⠀⠀⠀⠁⢹⡮⢭⣽⣯⣵⣁⠠⣄⣀⣄⠙⠃⢸⠇⠘⠋⣠⣀⣠⠅⣈⣮⣹⣯⡯⢵⡏⠈
⠀⠀⠀⠀⢀⣼⠛⣃⠀⣰⢿⣤⡚⠛⠒⡏⣇⠀⠀⣰⣆⠀⠀⣸⢳⠒⠛⠓⣤⡿⣆⠀⣘⠛⣧⡀
⠀⠀⠀⠀⠘⠉⠻⠏⢿⠷⠟⢹⣏⣠⡀⡿⡌⢈⣓⡼⢧⣚⡁⢡⢿⢀⣄⣹⡏⠻⠾⡿⠹⠟⠉⠃
⠀⠀⠀⠀⠀⠀⠀⢀⢾⡓⠻⣮⢉⣽⢿⣤⣿⣱⢋⡀⢀⡙⣎⣻⣤⡿⣯⡍⣵⠟⢚⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣏⣱⢦⡷⢼⣷⠋⠁⢿⢹⡏⢳⡞⢹⡏⡿⠈⠙⣾⡧⢾⡴⣎⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠰⣾⠃⣶⠾⢮⣱⠿⠿⣎⡵⠷⣶⠘⣷⠆⠀⠈⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠉⠀⠐⣻⡆⢲⣟⠂⠀⠉⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣫⡒⣼⣧⠚⣕⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡥⢁⣻⣿⣿⣟⡈⠦⣗⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡝⠻⢙⠻⣥⡞⢑⣮⠟⡏⠟⢫⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⢨⣊⣽⢵⣏⣺⢠⣽⣮⣄⣳⣸⡦⠯⡑⣴⠀⡀⠤⠤⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⣚⡛⣳⢶⣿⢰⡗⢚⢷⣼⠗⠚⠿⡧⣻⣬⢻⡿⣡⣿⢸⡷⠓⠺⠧⡿⢍⣻⡇⣺⢷⠻⠙⣭⢢
⠀⠀⠀⠀⠲⢦⣵⣼⡆⣤⢿⠮⡁⢾⣕⡎⠀⠀⠀⠀⠱⣎⣰⡶⢿⣆⣹⠞⠀⠀⠀⠀⢸⣯⢷⢒⡒⣿⢶⣰⣷⣾⡴⠛
⠀⠀⠀⠀⡴⣊⣿⣿⢿⠖⢻⡉⣑⢶⣜⣳⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣞⣧⡾⣫⣍⡽⠓⡾⡿⢿⢭⡳⡀
⠀⠀⠀⠀⢷⡙⡄⣺⡼⡗⢒⣿⣿⣖⢋⣉⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣭⢳⣿⣿⡏⢱⠷⣟⡀⣎⡾⠃
⠀⠀⠀⠀⠀⢙⣾⢭⢢⠘⣢⣭⣽⠡⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠇⣲⡼⠶⣛⡼⠱⢽⣏
⠀⠀⠀⠀⠀⢸⡰⡖⢲⢟⣲⠶⠭⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠯⠾⢿⡯⣷⢳⢇⡏
⠀⠀⠀⠀⠀⠀⠑⠾⣼⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠊
⠀⠀⠀⠀⠀⠀⢀⢴⠖⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⢳⠢⡀
⠀⠀⠀⠀⠀⢰⡇⠾⡤⣼⡽⠶⣒⡖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣻⡐⠿⣯⡜⠾⢋⣱
⠀⠀⠀⠀⠀⣈⣿⣒⣰⢡⠽⣛⢻⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣗⣘⣙⡟⢶⠸⢬⡺⢯⣀
⠀⠀⠀⠀⡾⢃⠃⠽⡺⡯⠤⣿⣿⠟⣌⣋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣭⡌⢿⣿⡧⠖⣿⢹⢆⢡⡙⡆
⠀⠀⠀⠀⠱⠍⣻⣿⣾⠧⣴⣁⣩⢶⢛⣥⠋⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠳⣬⢻⢮⡥⣼⠶⣺⣿⣿⡯⠕⠁
⠀⠀⠀⠀⠰⠖⢻⢻⠏⠹⢺⠔⠩⢾⡫⢧⠀⠀⠀⠀⢠⢮⡀⠿⠾⠟⣨⠷⡀⠀⠀⠀⣠⢯⣽⡒⣒⢼⠛⡂⣿⢻⡙⠿⠄
⠀⠀⠀⠀⠀⠀⠘⢬⣭⣽⠾⣾⠠⣯⢭⣲⢟⣶⠤⡶⡿⣸⣏⣱⣿⣎⢿⡜⣷⠦⢴⣾⠻⣯⠴⡷⣰⠟⠺⣴⡭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠈⠀⢸⠫⣙⡟⢯⠼⡌⢻⢿⡋⡸⢎⠟⣶⣡⢞⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣍⣬⣃⡯⣞⠳⣤⢟⣳⢵⣸⣬⣩⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⢂⢡⣿⣿⣷⣌⠔⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠮⠥⠊⣿⠳⠭⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡐⠻⠽
⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⠀⣀⣀⣀⡀⡠⠄⠀⡀⠆⠀⠈⠁⠉⣀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠿⣴⣦⡄⠐⠤⠄⠤⠀⡀⠀⠀⠀⠀⠛⠥⡤⠶⢤⠀⠀⢤⠠⣀
⠀⠀⠀⠀⠀⠀⠘⠃⠐⠂⠐⠄⢀⠀⠀⠀⠲⢶⣾⠑⢶⡶⠶⠒⠀⠰⠂⠀⡈⠁⡀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣐⣀⡀⣉⠡⠠⠠⠄⣀⠀⢀⣄⢀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⢄⠐⠀⠀⠀⠅⠒⠦⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢




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

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⣄⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⢀⣷⣿⣿⣶⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠈⠀⠄⣢⣶⣾⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠨⣾⣿⣿⣿⣿⣦⠀⠀⠀⣴⣾⣦⡀
⠀⠀⠀⢨⣭⣽⣿⣟⣿⣿⡿⣿⠀⠭⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣽⣿⣟⣇⠀⢺⠿⠿⡿⣿⡆
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣷⣀⡌⣻⣷⣶⣾⡇⠀⠀⠀⠀⠀⣀⣾⣷⠇⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠂⢻⣿⣿⣿⣿⣿⣿⣿⢻⡗⣾⡿⣷⣿⡄⠀⠀⠀⠀⠀⠻⣿⠎⠃
⠀⠀⠀⢸⣽⣽⣤⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⡷⣏⣼⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⢴⣾⣿⣿⣿⣿⢻⣿⠀⣿⣿⠑⢻⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄⠀⠀⢸⣿⡿⠘⣿⣇⢀⣯⠀⣿⣇⣶⣿⣿
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣘⡇⠀⠄⡈⡏⠛⠁⠙⠙⠋⢻⠀⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣠⣿⢥⡄⠀⣀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⠀⠠⣾⣦⣀⠘⣿⣿⣿⣷⣤⣿⣿⣼⡇⣤⣿⣼⣿⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣅
⢈⣁⣏⢻⣿⣿⣿⣛⣛⠛⠻⠿⠿⣧⡈⠁⣹⣿⣿⣿⠃⠀⠀⣿⣴⣯⣤⡄⠀⠀⠀⣦⢻⠛⡾⢯⣁⣰
⢸⣿⡟⠚⣿⣿⣿⣿⣿⣇⣤⣤⣤⣽⣿⣿⣿⡿⠿⣿⣇⣄⠀⣿⣿⣿⡏⠀⣠⡀⢸⣿⣿⣿⣷⠀⠈⠻⠇
⢸⣿⣿⣴⣼⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⣿⣿⢠⡼⢹⣈⡟⣻⣿⡿⠿⠥⠻⠿⠿⣿⣿⣿⣿⢻⣶⣾⣾
⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠤⢤⡤⠘⠁⠸⢿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠭⠟⠻⠟⣿⣿⣿⣧
⠀⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡦⠄⠀⠀⣿⢏⠁⠀⠀⠀⠀⠀⠀⠠⣤⠙⣛⣿⣿⢿⣿⣿⡟
⠀⠒⣿⠿⣿⣵⣼⣿⣯⡙⠛⠿⠿⠋⠉⠛⠓⠂⠙⠒⠾⠼⠀⠀⠀⡀⠀⠀⣀⠉⠋⣳⣖⣀⣀⣰⡖⠶⠒
⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣈⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠤⠤⠾⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣤⣤⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⣀⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡿⡌⠋⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⢠⣾⡤⣵⣿⢵⣿⣦⣀⣀⣠⠚⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⣇⠀⠀⠀⠀⢸⡿⠗⠒⠒⠒⢿⣟⠙⠉⠙⠓⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⡀⠀⠀⣠⡿⠑⠚⣄⠃⡍⠶⣿⣦⡀⢀⣠⡄⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣛⣷⣄⣾⣿⠇⢀⡐⢮⡚⠗⢀⡀⣿⣿⣆⣿⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⡻⠰⡄⠀⠈⠉⠀⠀⡟⠸⣿⣿⣿⠤⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠄⢿⣇⣸⣿⡻⣄⠀⠙⠈⣶⣷⠏⢨⠀⢠⡾⣿⣿⡘⠒⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣲⠈⢿⣿⣿⡷⠌⠐⠂⠀⠈⠉⠀⠀⣒⣫⣴⣿⣿⠈⣡⡒⢦⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡩⣟⡉⢻⣿⣷⠶⠦⠤⠬⠥⠤⠴⠶⣿⣿⣿⠛⣻⢁⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⢝⢿⣷⣦⣤⣴⣴⣤⣤⣾⣿⠟⠵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⡸⢣⢇⢔⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢱⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⠀⠈⠀⢀⠴⠙⢻⣶⠖⠀⠀⠀⠀⠐⠀⢀⠀⠀⢉⢶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠀⠀⠀⠀⢠⢡⣛⠻⠿⣧⠀⠀⠀⠀⠸⠋⠘⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢀⠐⠿⣳⡆⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣢⠇⢰⡄⠀⠀⢩⠶⣝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠌⠀⠀⠀⣠⠀⡌⠣⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡴⣰⢰⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⡀⠀⠀⠀⠈⠀⠠⢦⣄⠉⠀⠂⠀⠁⣊⢞⢔⣭⣠⠄
⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠒⠲⢿⡢⠀⠀⠀⠜⠁⠄⡽⠷⠭⠤⠀⠄
⠀⠀⠰⠄⠀⠈⡹⢦⠀⠀⠀⢀⠀⠄⠀⠋⠸⣄⡄⠂⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠨⠙⢒⣨⣍⡙⠃
⠀⠀⠀⣤⢀⠀⢨⠷⠠⠀⠀⠐⠻⠀⠀⠀⠁⡤⢿⣥⠀⠀⠀⠨⠀⠀⠠⠄⢀⠀⢀⠀⠀⠲⡤⡙⢾⣛⠅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠶⡶⠀⠄⠀⠀⠠⠂⢴⡧⡎⠀⠸⠀⠁⠀⢘⡛⠓⠭⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠓⠁⠃⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⣶⠀⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡀⢀⣀⣀⣠⣄⣀⣤⣀⣄⣠⣀⣀⣘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⣫⠝⢤⣭⣞⠳⢿⣿⣿⣶⣻⣯⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣟⡛⠿⣿⠛⠙⠉⢸⡏⢹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣬⡋⠄⣿⣄⣈⣠⣾⣧⡘⣧⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⣻⡋⠁⣼⣿⣿⣿⣙⣇⠱⠤⠄⠳⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠿⣎⣘⣩⣴⣿⢿⡉⠛⠛⣿⢶⣤⣤⣤⣜⣫⡿⠻⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢹⣷⣼⣿⡿⠿⠚⣩⣴⠿⠂⠠⠢⣿⣽⣷⡟⣠⠇⠈⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠴⢀⡾⣿⢻⣿⣏⣱⠐⠝⠶⠔⠀⠀⠘⢽⡿⠟⠈⣟⣲⠂⠀⠑⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣶⡿⢏⢹⡿⠛⡾⢣⡀⠀⠀⠀⠂⠀⡐⣣⡶⡎⢲⠻⠟⣧⡄⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⡀⠈⠡⢜⣿⡶⡷⠇⠀⠒⠛⠙⠁⠀⠀⠀⠈⠀⠉⣝⢻⣤⢾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⢰⣠⠀⠀⣧⣺⣶⢷⠦⢀⡤⢶⡄⠐⠀⠀⡆⢰⠀⢈⣼⣯⡏⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⠂⠀⡁⠀⢀⡾⢻⡉⣟⢰⣶⡷⠀⠄⠀⠀⠀⠈⠁⠀⠈⣭⣷⠞⡛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠙⢿⣟⣷⣤⠗⢮⣙⣷⠗⠋⠈⠉⢙⠭⠞⡷⣠⣄⣀⣲⣤⣶⢟⣡⠘⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠼⢿⡏⣀⣾⣝⢀⠀⠀⠀⠀⠀⠀⢼⣭⢷⣭⣝⣿⣛⠀⠀⣠⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣻⣏⣿⣁⠿⡄⠀⠸⠤⠟⠀⠀⣺⣏⣼⠷⢾⡿⢋⠆⠀⠛⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⠛⣶⢳⣮⣄⣁⣀⡠⣔⣏⡧⠬⠶⠿⣘⡷⣬⢶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣄⣄⣈⠁⢸⣿⢉⠻⢍⠀⢠⣤⠀⠀⢾⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠱⣦⣽⣼⣦⣶⣦⣄⣠⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣮⣥⣭⣉⣉⣈⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⣿⣿⣿⣿⣿⣧⣹⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⠛⢛⣽⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⣧⢸⣸⡸⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⣀⣈⣤⠀⢀⠀⠀⠀⢬⣓⣬⣾⣿⣿⣟⣥⣐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡆
⠀⠐⠀⠀⠁⢡⣙⠃⠒⠤⠀⠀⠀⡦⠶⣿⣿⣿⣿⣿⣿⡭⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠠⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠐⢛⡩⢻⢿⢿⢟⢮⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠀⠀⠀⠈⠐⠻⠸⠸⠘⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠐⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⡈⣐⡚⣼⣄⣤⠁⠀⠠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠄⠪
⠀⠀⠀⠀⠀⠀⠀⠂⡩⠙⣿⣿⡁⠖⠀⠠⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⡡⠢⢓⠉⠀⠂⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡆⢻⡿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠿⢃⡿⢬⡉⡩⣵⣀⢔⢥⣒⢪⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡕⡲⡬⡢⡀⣮⢍⢉⡭⢿⡘
⡛⣏⠑⣦⡨⣹⣰⢃⠆⠇⢛⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢛⠘⠰⡘⣆⣯⢅⣴⠊⣹
⡇⡨⣆⣢⠏⠁⢸⣤⢊⡔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⡑⣤⡇⠈⠹⣕⣰⢅
⠑⢛⠴⢚⠒⣶⣚⠘⠬⠥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠥⠃⣓⣶⠒⡓⠦⡟
⠔⣕⠬⠅⢊⠴⠆⡇⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢸⠰⠦⡑⠨⠥⣪
⡸⣘⢛⡐⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡎⣥⣝⡎⢱⣫⣬⢱⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⢂⡛⣣
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢸⢰⠖⡡⣀⡐⢙⠔⠢⡫⢂⡀⢌⠲⡆⡇⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣒⡄⡭⠡⠤⡥⠖⣥⢄⡠⣬⠲⢬⠤⠄⢭⢠⣒⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⡡⠁⡆⢀⣰⡫⠹⡊⢸⡇⢑⠏⢝⣆⣀⢰⠈⢌⠣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣭⢰⠸⢡⠏⣏⡊⠻⢆⣹⣼⣧⣏⡰⠟⢑⣹⠹⡌⠆⡆⣭⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡳⠽⢓⠕⠁⢟⣊⣈⣓⣾⢡⣶⣶⡌⣷⣚⣁⣑⡻⠈⠪⡚⠯⢞⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡵⣲⡬⡢⡀⣮⢍⢉⡭⢷⡘⠿⠿⢃⡿⢭⡉⡩⣵⢀⢔⢥⣖⢮⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣛⠸⠰⡘⣆⣏⢅⣴⠎⣹⢻⡟⣏⠑⣦⡨⣹⣰⢃⡆⠇⣛⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⡑⡀⠇⠈⢹⣕⣰⢅⢸⡇⡨⣆⣪⠏⠁⠘⢀⢊⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠭⠃⣓⡐⠒⡓⠦⡛⠊⠑⢛⠴⢚⡒⢂⣚⠘⠭⠥⠂
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢸⠸⠦⡑⠩⠡⣪⠢⠔⣕⠬⠍⢊⠴⠇⡇⠻⠆
⢡⠩⣬⠡⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢇⡛⣋⢇⡸⣝⢛⡸⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠈⣥⢍
⠢⡫⢒⡀⢌⠲⠆⡇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢸⠰⠖⡡⢐⡒⢝
⡠⣼⠲⢬⠤⠿⢭⢠⣒⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡒⡄⡭⠿⠤⡥⠖⣧
⡇⢑⠏⢜⣆⡀⢸⠛⢌⠣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⡡⠛⡇⢀⣰⠣⠹⡊
⣧⣏⡰⠟⢑⣻⠹⡌⠆⡆⣬⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣥⢰⠰⢡⠏⣟⡊⠻⢆⣹
⣦⡌⣷⣚⣁⣑⡻⠈⠪⡚⠭⢜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡣⠭⢓⠕⠉⢟⣊⣈⣓⣾⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢣⠀⢠⠀⢠⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠂⢸⠀⠂⢀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⢉⣀⡀⠀⠀⠐⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣼⡿⠛⣷⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⡀⡼⣿⣦⣤⣝⠂⠐⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠔⠈⡀⠐⠁⡉⠀⠑⢀⠁⠈⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠄⠀⠀⠁⠠⠀⠡⠀⠀⠀⠑⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⢠⠀⠀⠀⠈⠀⠀⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠠⠀⢠⠃⠀⠀⠂⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠄⠂⠠⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢠⢰⣖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣤⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⡀⠀⠀⠀⢽⣦⠄⠀⠘⢉⣿⣖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢢⣌⠈⠀⢁⠝⠳⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠂⣸⢰⣾⢏⡞⣼⣷⠀⡠⠀⠖⠀⠀⠀⠀⢉⢿⣭⡅⠀⡀⠀⡀⢠⢠⢠⡆⡀⠀⢀⣉⠋⠁⠀⠀⠐⠿⣝⠿⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡙⢦⠡⣔⠈⡏⡾⠐⡿⣫⠞⣠⠾⡃⣷⡟⠰⠀⠈⢷⠿⠷⢤⡈⠃⠳⠈⠋⣘⢿⢔⣅⣤⡄⢆⣠⠀⡀⠀⢦⣛⢿⡃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⠌⢀⠁⠘⠀⠃⠀⣠⠖⡡⠎⣲⡿⢷⣛⡯⠀⢰⠁⠎⠀⠒⠾⢿⠎⠀⠀⠐⢁⠤⠿⠿⢾⢵⠟⠇⠌⠃⣀⠘⢏⠛
⠀⠀⠀⠀⠀⠐⠛⠛⢺⣿⡢⠶⠁⠀⠀⠀⠔⠁⠀⢴⣩⣵⣾⣯⣶⣤⣤⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠐⠉⢹⣥⣭⣉⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⣂⣀⠀⠈⠉⢀⠀⠉⠀⠀⠀⢐⣚⣢⣬⣤⠤⠶⠶⠶⠶⠤⠀⠀⠀⠀⡀⢚⣤⡆⢠⡀⠀⠙⢦⣍⢾⣕
⠀⠀⠀⠀⢀⣩⠴⠒⠂⢀⡠⠄⠀⠀⠈⠀⠀⠀⢈⠄⠀⠤⣽⡿⢶⣦⣤⡀⠀⠀⠀⠈⠐⡿⡻⣠⠈⠇⢀⠀⠸⣌⠛⠂
⠀⠀⠀⠀⠀⠔⠪⠀⠀⠜⡴⡀⣢⡄⠄⣀⠀⠀⠀⠑⢧⣤⡉⢙⣯⣓⠶⠄⠀⠀⠀⢠⠀⡇⣥⡟⣦⣶⣿⢿⡷⠈⡀
⠀⠀⠀⠀⠀⠠⢒⡥⢆⣴⡾⣣⣾⠃⠀⢿⡄⠘⠀⠀⢀⢰⡾⣷⢭⡛⠗⠀⠙⢦⣄⠲⡙⡆⢸⠛⣽⢃⣿⡿⣠⠞⢁⣤
⠀⠀⠀⠃⠀⠀⢉⠔⠹⣿⡟⣹⠏⢠⠀⠉⡇⠀⡐⠀⠀⢳⣧⡀⠑⢽⣲⢦⣐⠢⠙⠧⠙⡆⢸⠀⠁⠐⢋⡼⣫⢖⣫⣤⣀⣠⠤
⠀⠀⠀⠀⠠⠀⠀⠀⠔⠙⠰⡝⠰⢀⠇⠀⠅⠠⣧⠂⢈⣆⠉⢳⣀⣤⣄⣙⣶⡕⠠⠦⡀⠀⠈⠀⢀⠼⠋⠜⣉⠵⢚⣫⡭⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠆⠄⠀⡆⡆⣴⣿⣄⠘⡜⠃⠀⠉⠰⠾⠻⠿⣍⠺⠃⢀⡀⠀⠐⠋⠀⢀⠚⣶⠾⠿⠿⠿⠿⠶⠶
⠀⠀⠠⡀⡀⠶⢲⣧⡀⠀⡀⠈⠳⣅⢘⠏⡏⠏⣽⣣⢊⡤⠀⢀⣀⡩⠤⠀⠀⠀⠀⠤⠀⠀⠐⠈⠀⠨⣍⡽⠶⠶⣖⣚⠛⠛⠛⠻⠆⠀⢠
⠠⠭⣧⡄⠀⠀⠚⣉⣿⣞⣛⢳⡄⢈⠀⠃⠁⢠⠖⠕⡹⢾⡶⢯⡤⠖⡛⠋⢉⡠⠄⠀⠀⠀⠁⠀⠀⠀⢀⠠⡀⠰⢶⣽⠻⠷⣶⣤⡄
⠀⠴⠀⠀⠀⠀⠈⠛⢪⣭⣛⠛⠿⠃⠠⠀⠀⠁⢠⣓⡚⣛⣛⣳⣖⠩⢒⠀⡴⡠⠂⢘⣔⠠⠂⡆⠀⠀⠀⠙⢮⣦⣄⠩⣻⢭⣓⢶⣄⢀
⠀⡀⣺⣴⠂⡆⠀⠙⣾⣿⡿⠂⢀⠀⠀⠀⠀⠀⠙⠈⠩⣵⢶⣤⣩⢖⣥⠖⣠⣶⢏⣼⡿⠀⠀⣷⠀⠘⠆⠀⢀⠨⣪⣷⣮⣝⠿⡿⠋⡛⢦⣆⡀
⠀⠀⠋⠃⠀⠀⣰⠠⡙⠊⠃⠰⢶⡀⣦⠀⣄⠀⡀⠙⢶⣌⡹⣿⡓⠙⡡⢊⣿⣵⢏⡿⠁⠀⠀⢻⡇⠀⠀⡀⠀⠱⣽⡈⠛⢿⡳⠆⠈⢠⣞⡿⣷
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠊⢴⣿⢺⠃⠀⢻⠀⠀⠀⢸⣏⠻⡪⠁⠈⠀⡠⠫⢃⢮⢃⠆⢣⠀⠈⡇⠀⣇⠇⠀⣦⠙⠻⣏⡀⢀⠀⠀⠀⣄⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠎⠂⡇⠀⠀⣿⠀⣦⠙⢆⠀⠀⡀⠀⠁⠀⠈⢎⢊⢀⠊⢠⠀⠁⣰⣿⠀⠈⡞⡧⠐⠻⣿⡟⠐⡇⠀⠨⡟⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⡘⠀⢸⢸⠀⠹⠁⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠇⠸⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⢀⠀⢄⠀⠠⠀⠂⢀
⠀⠀⠀⠀⠂⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠈⠀⠈⠀⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⡒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠢⠀⡀⠁⠈⢈⠀⠀⠀⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠄⢀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠄⡃⠰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⠄⢳⡀⡿⠣⢀⣗⠅⡀
⠀⠀⠀⠀⠂⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢒⡙⠦⠤⠅⠀⠐⡡⠴⠃⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢋⠛⠇⠀⢀⢩⣐⢒⡖⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡟⣤⠊⡠⢸⣀⣈⣳⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢁⡜⢣⢘⠁⣯⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⣠⣤⣠⣄⣤⣄⢲⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⢼⠃⣤⣿⣿⣤⠈⡧⠖⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣤⣄⣀⠛⢨⡇⠛⣀⣠⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢶⣤⢄⣤⡄⠀⣠⡤⠈⣻⣟⡻⠷⣠⢭⡳⣼⣧⢞⡥⢄⠾⠟⣻⣟⠁⣤⣄⠀⢠⣤⡠⣤⡶
⠀⠀⠀⠀⠀⠀⢀⣫⣍⣼⠀⢻⣿⣿⢻⢋⡅⢦⢳⠀⠛⠠⣧⢻⡿⣼⠆⠛⠀⡞⣵⢈⡙⡟⣿⣾⠛⠀⣧⣭⣝
⠀⠀⠀⠀⠀⢠⣼⣃⣠⣬⠀⡾⢀⣟⡈⠳⣝⡈⢼⡄⡀⣤⣱⢸⡇⣎⣤⢀⣀⡧⢁⣫⠜⢁⣛⡈⣧⢀⣤⣄⣺⣧⡀
⠀⠀⠀⠀⢠⡶⠛⣿⠿⣌⣀⢧⠻⣌⡁⠀⠀⣿⡄⠺⢇⣈⣡⣼⣧⣈⣉⡨⠟⢠⣛⠀⠀⢈⣡⢟⡟⣈⡡⠿⣿⠻⢶⡀
⠀⠀⠶⣾⡧⢳⡄⠛⠃⣈⣭⣿⣷⣜⠳⣌⡷⠀⣥⠀⢈⣽⢋⡵⢮⡙⣫⡁⠀⣬⠀⢿⡡⢟⣣⣾⣿⣭⣁⠚⠋⣠⡞⢼⣷⠦
⠀⠀⠀⠘⢼⣉⣀⣰⠋⢱⢒⠲⣶⢭⡙⢶⣤⠾⢋⣹⡏⠙⢫⣴⣦⡝⠋⢿⣇⠻⠿⣤⠶⣋⡭⡶⠖⡒⡎⠹⣄⣀⣹⡆⠃
⠀⠀⠀⠀⠈⠁⣹⣿⠾⣈⠉⠀⠀⠶⠟⢐⣿⢹⡏⣥⣾⡀⠀⠸⠇⠀⢀⣷⣭⢹⠃⣿⠀⠳⠖⠀⠀⠉⣙⠷⣿⣏⠈⠁
⠀⠀⠀⠀⠀⠀⠟⢻⡋⠭⠝⠲⠶⠵⠆⠛⠹⣶⠇⠟⠙⠛⠀⠀⠀⠀⠛⠋⠻⠹⣶⠍⠋⠰⠎⠶⠖⠭⠭⢹⠟⠟
⠀⠀⠀⠀⠀⠀⣶⡼⣅⣛⣣⠖⠳⡲⠂⣤⡰⢿⡆⣦⣠⡤⠀⠀⠀⠀⣤⣄⣴⢰⠿⣦⣤⠰⢖⠞⠢⣜⣛⣸⣧⣶
⠀⠀⠀⠀⢀⣀⣽⣿⢶⢀⣄⠀⠀⠖⣦⠸⣿⣸⣇⣛⢿⠁⠀⢰⡆⠀⠈⡿⣛⣸⡆⣿⠀⣴⠶⠀⠀⣠⡀⡶⣿⣏⢀⡀
⠀⠀⠀⢠⢻⣉⠉⠹⣄⡻⠤⠖⢟⣉⡥⠞⠛⢷⣆⣽⣇⣠⣚⠻⠟⣓⣄⣼⡏⣴⠾⠛⠳⢬⣉⡿⠲⠤⢇⣠⠋⠉⣩⠗⡄
⠀⠀⠺⢿⢇⡼⠃⣤⠄⢉⣹⢿⡿⢫⡴⢫⡷⠀⡛⠀⢈⣻⣌⡳⢞⣡⣝⡁⠀⢛⠀⢾⡝⢦⡝⢿⡿⣍⡉⠴⣤⠙⢧⢺⡿⠗
⠀⠀⠀⠀⠘⠷⣤⣿⣶⣉⠁⡞⣼⢩⡀⢀⣨⣽⡃⢴⡎⢉⡙⢻⡟⢋⡉⢁⣦⠘⣭⠀⠀⢈⡙⣦⣷⢉⣉⣶⣿⣤⠾⠁
⠀⠀⠀⠀⠀⠈⢹⡍⠙⢋⠀⢷⠨⣭⠀⡞⣴⢢⡍⡇⠁⠛⡹⢸⡇⢏⠛⠈⠈⡗⡈⣝⢦⡈⣭⢁⡟⠈⡙⠋⢩⡍⠁
⠀⠀⠀⠀⠀⠀⠨⣽⣏⢿⢀⣾⢿⣿⡤⡿⢀⡭⠞⠁⣠⠐⡟⣸⣷⢻⡆⣤⠀⢧⡻⢈⣡⣧⣿⠿⣦⠀⡟⣹⣭
⠀⠀⠀⠀⠀⠀⠀⠿⠛⠊⠛⠃⠀⠙⠃⢀⣽⣦⣴⡶⠑⢚⡵⢻⡟⢮⡓⠊⢶⣦⣽⣯⡀⠛⠉⠀⠘⠛⠑⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠛⠋⠉⣤⢘⡃⣤⠉⠙⠛⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠴⢺⡀⠛⣿⣿⠛⢀⡗⠦⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠧⠙⠛⠙⠋⠛⠋⠼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠰⣶
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⠀⣶⡶⠸⡆⠀⣸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⢦⡀⠀⢻⠟⠀⠙⢦⣽⣥⠾⠁⠀⣦⠀⢀⣇⠀⢰⠆⠀⣦⠀⢀⣆⠀⠀⠀⢠⡄⠀⣠⣇⠀⣾⠀⠀⢰⣀⠀⠀⣀⠀⡀⠀⠀⢀⣄⠀⢀⡆
⠀⠈⠀⣀⣻⣋⣠⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⢦⣙⣟⣤⠟⠀⠀⠘⢦⣙⣟⣠⣄⡀⠀⠹⣦⣙⣯⡴⠃⠀⠀⣙⣿⣤⠴⠋⠀⠙⠶⣤⣘⣟⣠⠞⠁
⠀⠀⢸⡍⣿⣿⠀⠀⠀⠀⢀⣼⠋⠻⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠙⠂⠀⠀⢹⣿⡇⠀⠀⣞⠹⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡇⢀⡀
⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⡾⠁⠀⠀⠙⣧⠀⠀⠀⣿⢻⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠙⠀⣿⠻⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠐⠀⠀⠐⠠⠌
⠀⠀⠀⠀⢠⡾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣄⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⣿⢋⡿⠋⠙⠁⠀⠀⠀⠀⠀⢐⣯⣽⡛⣿⡏⠛⠁⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠳⠀⠘⠀⢰⡃
⠀⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⠛⢷⣄⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡄⠄⠀⣠⣤⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⡀⠀⢈⣻⡆⠘⢿⣿⣿⣿⣷⡿⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠟⠁⠀⠀⠀⠀⣾⣿⡄⠀⠀⣾⣿⣇⠀⠀⡌⠻⣷⣶⣸⣿⣿⣏⣀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⣦⣤⡻⢿⣋⣠⡄⢟⢆⢸⡿⣿⣻⡟⣿⣿⣿⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣯⡿⣧⣬⣭⣥⣴⡶⠟⠋
⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⣿⣟⣯⣴⣮⣥⣼⣿⢿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⢙⣛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣻⣷⣸⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⡷⠶⠶⠾⠀⠀⠸⠶⠶⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⠙⣿⣹⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⣿⣿⣿⢸⣿⢸⣿⢹⣿⢻⣿⠟⠘⠿⠘⢛⣿⠟⣿⡏⠁
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⠁⠉⢸⣿⢸⣿⢸⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠉⢸⣿⢸⣿⠀⠀⠀⠀⠐⠿⠃⠿⠃
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿

⣯⣿⡉⠉⢻⡄⣸⠷⠁⠘⣿⠣⢊⢠⡎⢸⣥⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⢱⡄⡑⠜⣿⠁⠈⠾⣇⢰⡟⠉⢉⣿
⡇⠈⢻⠖⠟⢻⠇⠀⣠⢾⡯⢍⠣⣰⠇⣾⠭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠭⣷⢸⣆⠔⡫⢽⠧⣄⠀⠸⡟⠻⠲⡟⠁
⠛⠶⣿⣡⣵⢟⡂⠀⣸⡾⠏⠬⠂⠉⣰⡿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢿⣆⢉⠐⠥⠙⢷⣇⠀⢐⡻⣦⣈⣿⠶
⢶⡟⠉⠁⠈⠈⣱⣺⡯⡙⠖⢒⡾⢰⣿⣡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣿⡄⢳⡒⡲⢋⢽⣗⣎⠁⠉⠈⠉⢳
⣁⠀⣠⡞⣲⡾⣏⠫⠄⠅⠰⠞⣱⠿⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠿⣎⠓⠆⠰⠤⠝⣹⢷⣖⢲⣀
⠿⡛⣏⢏⡋⡅⢸⢁⣰⠆⣡⡾⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⣷⣎⠐⣆⡈⡇⢨⢙⡹⣹⢛
⠚⣰⢉⣢⡄⠀⠚⣉⣵⡞⣿⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⢺⢻⣿⣛⣛⣿⡟⡗⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⢻⣮⣝⡳⠄⢡⣔⡙⣂
⣊⣉⣩⣥⣴⡾⠟⣹⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣯⣵⡾⠿⢛⣛⣉⡩⢍⣉⣙⡛⠻⢷⣮⣽⡿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣟⠻⢷⣦⣬⣍⣉
⣭⣿⣧⡧⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⡼⢟⣉⡤⠃⡘⠫⡣⠍⡤⢤⠩⢘⠝⠃⠈⣬⣉⡻⢧⣿⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⢼⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡿⢏⠰⠏⢁⡇⠈⣨⣡⣹⣤⣶⣶⣥⣏⣌⣅⠃⢸⣨⠹⠆⡹⢿⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣶⢏⡴⠆⠰⠒⣢⣹⡾⠯⡼⠋⠀⢉⡍⠀⠉⢧⠽⢷⣏⣔⠒⠆⠰⢤⡻⣶⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣿⠃⡼⠥⠵⣌⣺⡯⠏⡀⡀⢀⣀⡼⠷⠾⣧⣄⡀⢀⢀⠹⢽⣗⣡⠤⠮⢧⠘⣿⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣾⠏⣁⠠⡒⣠⡾⡏⠀⠨⣵⢟⢛⣿⠷⣔⣦⠶⣿⡙⡻⣮⠅⠀⢹⢷⡄⢒⠄⣈⠹⣷⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣒⡿⢰⠯⡢⣅⣺⡗⠋⠀⣰⣿⣴⠼⣧⡀⢸⡇⢀⣼⠦⣦⣿⣆⠀⠙⢶⣗⣨⣔⠹⡆⢿⣂⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⡸⠃⠥⢢⣿⡄⢀⢶⡟⢙⢧⣀⣈⣿⣻⣛⣿⣁⣀⣼⢃⢻⡶⡀⢠⣿⡔⢬⠘⢇⢸⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⢱⡄⡓⠜⣿⠃⠈⠾⣇⢢⡟⠉⢉⣿⣽⣭⣿⡉⠉⢳⡔⣼⠷⠁⠘⣿⠣⢚⢠⡎⢸⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠩⣷⠸⣖⠕⡋⢽⡧⣄⠀⠹⣟⢹⢲⡟⠁⢸⡇⠈⢻⠖⡟⣿⠏⠀⣠⢼⡯⢝⠫⣲⠇⣾⢍⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢿⣆⣉⠀⠥⠸⢷⣇⠀⢐⡻⣮⣌⣿⡶⠛⠝⠶⣿⣩⣵⢟⡂⠀⣸⡾⠉⠬⠂⢉⣰⡿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⣿⡄⢳⡢⢒⢋⢽⣗⣆⠁⠁⠈⠙⢻⡶⢶⡟⠋⠁⠈⠈⣰⣾⣯⡙⣖⣖⡿⣠⣿⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠿⣎⠓⠆⠸⠄⠝⣹⢷⣖⣳⣀⠀⣈⣁⠀⣀⣞⣲⡾⣏⠉⠁⠁⠙⠘⣽⡿⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⣷⣎⠐⣆⡈⡇⢠⢙⡹⣹⢛⠿⠿⡛⣏⢋⡋⡸⢉⢙⣓⢃⣙⣟⣛⡛⠋
⣛⣿⡟⡖⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣿⢳⣮⣉⡓⡀⢠⣔⡕⣆⠓⠚⣐⢪⣢⡌⢀⢛⣋⣽⡟⣿⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⢻⢻⣿
⢍⣉⣙⡛⠻⢷⣮⣽⡿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣟⡻⢷⣦⣬⣍⣉⣑⣊⣉⣩⣥⣶⡾⢛⣻⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣯⣥⡾⠟⣛⣋⣉
⢄⠩⢌⠝⢃⠐⢬⣉⡻⣧⣿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⢮⣼⣿⣭⣭⣿⣧⡧⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⡼⢟⣉⡤⠃⡘⠫⡡⠉
⣶⣥⣏⣎⣁⠃⢸⡈⠹⠄⡹⢿⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡿⢋⠠⠏⢑⡇⠘⣨⣡⣹⣬
⡉⠀⠉⢧⠽⢷⣏⣔⠒⡆⠰⢦⡻⣶⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣶⢏⡴⠆⢰⠂⣢⣹⡾⠯⡽⠋
⠾⣧⣀⡀⢀⢀⡹⢽⣗⣡⠦⠬⢷⡙⣿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⢇⡼⠥⠴⣌⣺⡯⢏⡀⣀⣀⣀⡼
⣴⠾⣿⡉⡻⣮⠅⠀⢹⢷⣄⢒⠄⣈⢹⣷⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣾⠏⣀⠠⡒⣠⡾⡏⠀⢨⣵⠟⢉⣿⠶
⡇⢀⣼⠦⣤⣽⡆⠀⠘⢲⣗⣨⡔⠽⡆⢿⣒⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣒⡿⢰⠏⢢⣅⣺⡷⠋⠀⢸⣧⣤⠼⣧⡀
⣿⣯⣁⣠⣼⠥⢽⡶⡀⢠⣿⡔⢬⠘⢇⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⡇⡸⢋⡤⢢⣿⡄⢀⢶⡿⠜⣧⣀⣈⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⢸⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠹⣷⡀⠈⡇⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢻⣧⠀⠀⢰⠃⠀⠈⠀⠀⠀⠀⢀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⣄⡀⠀⠐⠲⢤⣀⠀⠈⢻⣷⡀⠀⣿⠀⠀⠏⠀⠀⠀⠀⠀⣠⣶⡿⠋⢁⣠⣤⠤⠄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠈⠳⣄⠀⠹⣷⠀⢹⡇⠈⠀⢀⡖⠀⢠⣾⠟⢁⡴⠚⠋⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠒⠢⠄⡀⠀⠙⠻⣦⡀⠀⠈⢳⡄⢹⣇⢸⡇⠀⣠⠟⠀⣴⠟⢁⠞⠁⠀⠀⣀⣤⣶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢢⠹⡄⣿⠀⠁⣰⠏⢀⡾⠋⠀⠁⠀⣠⣴⠿⠛⠉⠀⢀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⠿⢷⣶⣦⣤⣀⡀⠀⠂⠈⢷⡀⠀⠱⢸⡇⢠⠏⢠⡞⠁⠀⣀⣴⠟⠋⠁⠀⠄⠒⠉⠉
⠀⠀⠀⠀⢀⠀⠀⠀⢀⣁⣀⣀⣀⣀⠀⠀⠉⠙⠛⠷⣦⣀⠀⠻⡄⠀⠋⡇⡜⢀⠟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢶⣤⣄⡀⠒⠉⠳⢦⡙⡄⠀⢰⢀⠎⢀⡜⠉⠠⠀⠀⣀⣠⣴⠶⠟⠛⠉⠉⠁⠤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⠶⠶⠶⠶⠶⠤⠤⠉⡙⠳⠦⣄⠀⠑⠄⠀⠀⠈⠠⠋⢀⣠⠴⠚⣛⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠈⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠡⠒⠛⢉⣉⡉⠉⠉⠙⠛⠛⠛⠿⠶⠄
⠀⠀⠀⠀⠁⣀⡴⠖⠋⠉⠀⠀⠀⢀⣀⣤⣤⠴⠶⠖⠒⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡉⠉⠉⠙⠛⠻⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⣠⣴⠾⠛⠉⣡⠄⠂⠀⠀⢀⡠⠀⠁⡠⠀⢀⠀⠀⠀⠀⠐⠢⣌⠙⠷⣦⣄⡀⠀⠀⢀⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠂⢀⣴⡿⠟⠁⠀⣰⠞⠁⠀⠀⢀⡴⠋⠀⣠⠞⠀⢀⠎⠀⠀⡌⠀⠰⡀⢈⠙⢶⣄⠙⠻⣶⣤⡀⠉⠓⢦⣄⠈⠁⠀⠄
⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⢀⠞⠁⠀⠀⠁⣠⠏⠀⠀⣼⠃⠈⢀⡞⠀⠀⠀⠸⡀⠀⠹⣆⠀⠀⠈⠻⣦⡀⠙⠻⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⣾⠁⠀⠀⣼⠃⠀⠀⠀⠀⣧⠀⠀⠘⣧⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣾⠇⠀⠀⢸⡟⠀⠀⢀⠀⠀⢸⡆⠀⠀⠘⣷⡀⠀⠀⠀⠹⣿⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠁⠀⠀⣸⡏⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⠘⡇⠀⡄⠀⠘⣷⡄⠀⠘⢆⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⣿⠁⠀⠂⠀⣿⡇⠀⠀⢹⠀⠀⠀⠃⠀⢷⠀⠀⢹⣷⡀⠀⠘⣧⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢻⡇⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⠀⠀⠀⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠐⡍⠀⠀⠋⠃⠀⠀⠀⡤⠠⠀⠀⠀⠀⠨⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢤⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠦⢤⡄⠀⠀⠀⡀⠀⠀⠄⠉⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⣄⠀⠀⠀⣠⠐⡀⠀⠀⢀⠔⠁⠐⠀⠀⠀⠀⢀⠄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢄⠁⢂⡤⠐⠀⡆⠀⠘⠉⡐⠂⠤⡰⢶⣀⠈⠒⠃⠀⠂⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠚⡌⠀⠀⠀⠐⢡⠀⠀⠀⠁⠀⠐⠚⠀⠐⠐⠃⠀⠊⣀⠀⠀⠘⠁⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⣀⠠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢁⣀⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⡀⠀⢠⠀⠀⠀⠑⣀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠉⠀⡀⠈⠈⠀⠀⠀⢀⡤⠤⠀⠉⠀⡀⠙⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡀⠠⠖⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠱⠀⠐⠁⠠⠴⠒⠶⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⠉⠀⡀⢀⠴⠛⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠈⠀⡇⡌⡀⠠⠂
⠀⠀⣠⠆⠀⣀⠘⠉⠁⣤⣀⠈⠁⡤⠀⢀⣉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠐⠤⡁⢠⢀⡜⠐⠕⡊⠀⠠
⠀⠀⠀⣠⠞⠁⣠⠴⠂⢀⠀⠠⠄⠀⡀⠈⠉⠀⠘⢦⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠠⠄⣉⣁⢈⣛⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠀⠃⠆⠴
⠀⠀⠀⠋⡠⠀⡀⠀⠐⠋⠀⡀⠀⣀⠈⠃⠀⠀⠐⡄⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠄⢀⢄⠼⡟⡿⠁⡝⢅⠁⡀⠈⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠘⠁⣰⠁⡀⠀⡀⠘⠁⠀⠙⠀⢠⠀⠘⡄⠸⠄⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠈⡁⢈⢊⠄⢋⠈⠈⠂⠁⠀⠁⠀⠀⠀⠀⢒⡀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠋⣸⠁⠸⠁⢀⠀⡄⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠦⠑
⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡞⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣤⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠛⢉⣀⡀⢆⠈⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠣⠀⢿⠀⠀⠈⠀⣴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡤⠬⣻⡾⠷⠆⠈⠉⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⢄⠀⢸⠀⠘⠀⡼⠁⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡔⢡⠎⡿⡙⠂⠲⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⡀⢀⡠⠀⠀⠂⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠈⠀⠘⢀⡇⠃⢠⠀⠁⠀⠀⠀⠀⠀⠈⠛⠛⢋⡁⠀⠠⢍⡾⢄⡒⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠈⠘⠆⠁⠀⠂⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠈⠉⢀⣠⠖⠁⠀⠁⡀⠀⢠⡀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠐⢃⡀⠐⠂⠀⠈⠁⠀⣴⠃⠀⣿⠀⠀⠓⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠐⠀⠈⠀⠀⠤⠈⠓⠀⠀⠀⠀⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠀⠊⡀⠀⠀⠀⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠡⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢈⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⣎⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠛⡗⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀
⠀⠀⠀⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣒⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠬⠭⠍⣵⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⣀⣠⣋⡛⠒⠒⠖⠴⡇⠀⠀⠀⠀⠈⠁⠛⠃⠀⠀⠀⠀⠀⠉⠲⠤⠼⠾⣀⣀⡄⠀⠀⠀⠀⢠⠞⠉⠀⠉⠙⠢⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡉⠉⡉⠐⠒⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣠⠒⠒⠹⡄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⠡⢀⡤⠤⢷
⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢾⡏⠉⠙⠲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠤⠞⠛⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣸⠀⠀⢠⣶⡄⠀⠀⢸⣧⠀⠀⣀⡗⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⣰⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⣰⠃
⠀⠀⠀⠀⡤⠠⢤⣠⠔⠒⢢⠀⠀⠀⠀⣾⡷⠤⠤⠤⡏⠀⠀⣾⠇⢷⠀⠀⠘⣿⠒⠋⠁⢠⡶⠒⠢⣄⠀⠀⢿⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢙⠾⡅
⠀⠀⠀⠀⢇⠀⠀⠁⠀⠀⣸⠀⠀⠀⢐⣿⠇⠀⠀⢰⡇⠀⣼⣯⣤⣼⡇⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠈⡇⠀⠈⣿⡞⠁⠀⠀⠀⣠⢄⣠⢤⠀⠀⠀⠳⣏
⠀⠀⠀⠀⠈⠳⣀⠀⠀⡰⠃⠀⠀⠀⠸⣿⠀⠀⠀⢸⠀⢰⣿⠀⠀⠀⢹⠀⠀⢿⡆⠀⠀⢸⣇⣀⣠⡴⠃⠀⠀⣾⡇⠀⠀⠀⠀⠙⢄⣡⠞⠀⠀⠀⠀⢸⡄
⠀⠀⢠⠀⠀⠀⠈⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⣼⡏⠉⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠻⠃⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣴⡞⠉⠓⢦⠀⠀⠀⢸⣧⠀⠀⣰⡞⠛⠲⡄⠀⠉⠉⣿⡏⠉⠀⣀⠀⠀⠀⠀⢸⡇⠀⠙⢦⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⣠⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣸⠀⠀⠀⣼⡇⠀⠀⣿⡇⢀⣠⠇⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⢸⠇⢸⣷⠀⠀⠘⡇⠀⠀⠀⠀⠈⣿⡄⠀⢠⠇⠀⠀⢸
⠀⠀⢀⡀⠀⠀⠀⢸⣷⠶⠚⠧⣄⠀⠀⣿⠇⠀⠀⣿⡿⣍⠁⠀⠀⠀⠀⣿⠀⠀⢸⣧⣀⣀⣼⠀⠈⣿⠀⠀⢠⡇⠀⣰⣿⡀⠀⠘⣿⣀⡞⠀⠀⠀⢸
⠀⠀⠁⠑⠙⠆⠀⠈⣿⠀⠀⠀⢸⠀⠠⠿⠄⠀⠀⣿⡇⠈⠳⠀⠀⠀⠀⠿⠀⠀⣿⡇⠀⠀⡿⠀⠀⣿⣀⡠⠏⠀⣰⡟⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣠⠞⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢀⡇⠀⠀⠙⠉⠀⠀⣰⡟⠉⠙⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡶⡄⠀⠀⠰⠟⠀⠀⠀⠾⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⡆
⠀⠀⠀⠀⠀⢀⣠⡀⠀⣀⡉⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠄⠀⠀⠀⠀⠀⠀⣞⠑⠞⢱
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⠉⢳⠦⣄⡀⠀⠞⠀⠀⠠⠖⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⣠⠤⠴⢆⠀⠀⠘⢦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠘⡏⠑⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⣋⣉⣩⣤⡤⠖⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠
⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠀⠸⡆⠁⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣁⡨⠤⠔⠒⠋⠉⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠙⠁⠀⠀⠀⠀⢸⡀⢀⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠉⠀⠀⠀⣀⣠⢤⡤⢴⣛⡦
⠀⢀⡤⢤⡀⠀⠀⠀⠀⢠⠗⠋⠀⠀⠀⠀⠀⠖⢦⣀⣀⡀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢸⣓⣮⣽⠯⠽⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤
⠚⠉⠀⠀⠙⠢⠤⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠠⠁⢸⠋⣡⢿⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⠌⠀⣵⠘⠉⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⣻⠐⣱⣾⣤⡆⠨⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢀⣈⣤⣿⣿⡿⢇⡤⠀⣤⣿⣿⠟⠃⠂⢽⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢨⢠⡂⢠⣴⣿⣿⣿⠿⠣⢀⠠⣘⣿⣿⣿⠇⠀⠰⣼⣿⣿⣿⡺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⡿⠋⡁⢀⡀⣢⣿⣿⣿⣿⡿⢰⣀⣴⣿⣿⣿⣿⡇⢨⣄
⠀⠀⠀⠀⠀⠀⡀⠀⢠⣾⣿⡏⢣⢈⡅⣼⣿⣿⣿⣿⣿⡏⠜⢲⣱⣿⣿⣿⣿⣿⣿⣺⣿⡀
⠀⠀⠀⠀⠀⠀⠁⢣⣾⣿⣿⢙⣆⠉⢁⣿⣿⣿⣿⡿⠛⠃⢒⣾⣿⣿⣿⣿⣿⣿⡯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡘⡏⠉⢻⣿⣿⣿⣿⣿⡥⡂⣐⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⡩⡻⠛⢿⣿⣿⣿⡟⠋⡰⠻⣬⣿⣿⣿⣿⣟⣛⣝⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣱⣟⢻⣿⣿⣿⣿⡍⠃⢱⢟⣿⣿⣿⣿⣿⣿⢎⣽⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣛⡞⣾⣿⣿⣿⣿⣥⠈⢟⣹⣿⣿⣿⣿⡿⣧⣾⣿⣿⣿⣿⢃⣀⣀⣀⡀
⠀⠀⠀⢸⣶⣾⣣⠀⢹⡷⠊⠈⢻⣿⣿⣿⣿⠧⠄⣠⣿⣿⣿⣿⡿⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠈⣩⣿⢯⣶⣾⣧⣀⡀⠈⣙⣻⡏⠉⠀⠀⠀⢀⣹⣟⣿⣿⣽⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠟⠛⠋⠉⠙⠻⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⢠⣿⡾⢛⣼⣾⣧⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠨⣯⣵⣿⠟⢋⣤⣴⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠙⣿⢋⣴⠿⠋⡡⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡋⠃⠰⣤⣁⣠⣤⠄
⠀⠀⠀⠀⠀⠀⣠⣼⣿⣇⠀⠀⠘⢿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣤⣠⡇⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣤⣶⣟⣧⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠰⠐⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣀⣿⠿⠆
⠀⠀⠀⠀⠸⣿⣿⣿⠟⢿⣿⣿⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⡿⠿⠷⢶⣠⡄
⠀⠀⠀⠀⠀⢿⣟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠾⠷⢞⠻⠛⠛⠛⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⢀⡀⠀⠀⢲⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠿⢁⣄⣀⣾⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣫⣴⣦⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⠀⣿⣿⠟⠿⢿⣿⣿⣷⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢀⣿⠟⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⣃⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⡿⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡇⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠀⠀⠸⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣤⡀⣉⣉⣥⡶⠚
⠀⠀⣰⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⣨⣿⣿⡀⢙⣿⣿⣀
⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣾⡇⠀⠀⢰⣿⣧⣿⡇⢸⣿⣦⣿⣧
⠀⠀⠀⠀⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠛⠛⠉⠀⠀⠀⠈⠀⠀⠉⠃⠀⠋⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣄⢀⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⡟⠀⣤⣴⣦⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠛⠋⠁

⠀⠀⡈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠒⠈⠳⡀
⠀⢰⠀⠀⠀⠀⠈⠁⠐⠒⠒⠤⠤⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠒⠒⠒⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠪⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠈⢫⠒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⣀⣤⠔⠈⢡⠃
⠀⠀⠀⠀⡆⠀⠀⢩⠙⠒⠠⠄⢀⡠⠀⣀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⢁⣀⠠⡀⠦⠐⠈⠁⠸⠀⠀⢸
⠀⠀⠀⠀⡇⢰⡄⢸⠀⠀⠀⠀⠀⠀⠈⠁⠐⠊⠠⡄⠀⠀⠰⢄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠛⠀⡁⠀⠀⠁⠀⠀⠰⣤⡄⢸
⠀⠀⠀⢰⡵⠃⠸⡰⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⢠⠀⠀⠀⠀⠈⢡⡀⠀⠹⡄⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠻⡄
⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠠⠡⣀⠀⠀⠀⢠⠀⠀⠀⣀⠀⣀⠙⣄⠀⠜⢢⡤⠖⠋⠀⠀⢀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠑⢄⠀⢉⢠⠴⠁⣉⡀⠉⣀⠛⠳⡄⠙⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢂⠾⢀⠔⠋⠉⠀⠀⠉⠙⠢⡉⣤⢀⠔⠘⠀⠘⠓⢦⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⢱⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠓⠄⡀⠀⠀⠀⢀⡄⡼⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠓⠄⠘⣶⡶⠶⠶⠶⢾⠇⢠⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠸⠀⣤⣀⠊⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠲⢄⡀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠴⠛⣫⠟⠣⢖⡀
⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠫⡀⠀⠚⠃⠶⠭⠬⡍⠉⢁⡱⠤⡀⠀⠀⠁⠈⠀⠀⢡
⠀⠈⠁⠀⠀⠉⠢⣄⠐⠀⠀⠀⠀⠱⠇⠀⠀⠀⠀⢀⡤⠐⠉⠁⠀⠀⠀⠈⠓⠢⢄⠹⠒⠛⠊⠐⠋⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸
⠀⠄⠐⠀⠀⠀⠀⠀⡆⠀⡰⠒⠖⠒⠶⢧⡱⡖⣶⠀⠄⠀⢀⠘⠃⡄⠀⢤⠃⠄⠀⡳⠃⠀⠀⠠⡦⠄⡴⢈⡀⠀⡠⠐⠒⡄⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠃⠀⡄⠀⠀⠀⠀⠐⡋⣴⠂⠀⠁⢌⠀⠀⠀⣤⠀⠀⡄⠀⠛⠙⠺⣥⠓⢦⠶⡮⢷⡬⢶⣦⣄⠛⠌⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡀⠬⡖⠀⠂⠡⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠹⠒⢶⠙⠚⣆⠀⢈⠇⢀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠭⣄⠁⠀⠀⠀⠀⠀⣠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠠⠀⠀⣸⠀⠀⠹⣦⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⢈⣁⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⢄⠉⠘⢄⡄
⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⡎⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⡓⠀⠀⠈⠐⠂⠄⢄⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⠀⡀⠣⡀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢀⠔⠉⠓⠦⣄⡀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠂⠤⡤⣉⣐⠂⠀⠠⠤⠤⠔⠚⠋⠁⣠⡤⠔⠁⠀⠀⠀⠀⠀⠉⠳⠀⠂⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣅⡼⠀⠀⠀⠀⠀⠩⠈⠉⠛⠛⠛⠙⠒⠋⠈⠭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠖⠓⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠄⠐⠒⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⢠⡄⠀⠀⢀⡆⠀⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠐⢤⠴⠃
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠈⠢⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⠜⠀⠈⠳⣄⠀⠀⢀⡗⠀⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣀
⣿⢻⡟⢿⢛⣟⣛⡛⢿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣿⣿⣛⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⣸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣆⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢳⣹⡀⠀⠀⢲⣷⣗⠀⠀⢸⢡⡇⠀⠀⣴⡆⠀⠀⠀⢀⡴⢺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠏⠀⠀⠀⠀⠀⠀⢳⣷⠀⠀⠈⠉⠀⠀⠀⣾⣸⠀⠀⢰⠟⠁⠀⢀⡴⣫⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡢⣄⠀⠀⠀⠀⢻⣧⠀⠀⣤⡀⠀⠀⣯⠇⠀⠀⠀⠀⠀⣠⣮⠞⠁⠀⠀⠀⠀⣠⣖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢷⡄⠀⠀⠀⠻⣆⠀⢧⢳⠀⢰⡿⠀⣠⡆⠀⢠⡾⠋⠁⠀⣠⣄⠀⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠹⣆⠘⣾⡀⢸⠇⢰⡷⠃⠴⠋⠀⠀⠀⠐⢿⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠮⢭⣓⣲⠤⣄⣀⡀⠘⠦⣙⣦⡉⠀⠘⠃⠈⠀⠚⠁⠀⢀⣤⣾⠟⠀⠀⣀⣀⡤⠤⢶⣒⣛⣛⡭⠷
⠀⠀⠀⠀⠀⣤⣴⣒⣦⡤⠀⠀⠀⢠⡤⢭⣉⡙⠛⠻⠷⢶⣤⣍⡓⠀⠀⠀⠀⠀⠀⠀⠚⠋⣭⠴⠶⠿⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢒⣺⠽⠟⠛⠉⠀⢀⣤⠆⠀⠀⠀⠀⢀⡀⠀⣤⡀⠉⠑⠒⠋⠀⢰⣿⣗⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⣉⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⣖⡽⠁⣠⠆⠀⢠⠀⠈⣷⡀⠈⠻⡷⣄⠀⠀⠀⠀⠉⠀⠀⠉⠻⠭⣓⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣴⣴⠄⠀⠉⢠⣾⠃⠀⠀⢸⡆⠀⠻⡇⠀⠀⠙⢮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡷⠀⠀⠀⠀⠟⠋⠁⢀⣴⡿⠁⢀⣿⠀⠈⣷⠀⠀⣴⣶⡄⠀⠀⠙⢦⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣴⡾⠃⠀⠀⣠⢯⠞⠀⠀⡼⡟⠀⠀⣿⡆⠀⠙⠛⠁⠀⠀⠀⠀⠙⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠞⠀⠀⠀⣰⡷⠃⠀⠀⢀⣧⠇⠀⠀⢻⣧⠀⠀⠀⢰⡄⠀⠀⠀⠀⠈⠳⢤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣿⡄⠀⠀⠈⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠘⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠰⢄⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⠂⠀⠀⠀⠀⠀⣠⠏⡐⠶⠃⠀⠀⠀⢀⡐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⢀⣞⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠡⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⡵⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠤⣌⠆⠀⠀⠀⢰⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢥⠊⠀⠀⢔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣤⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⡀⠀⠀⠀⢤⡐⠀⠁⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡀⠀⠈⠢⡤⠀⢄⠀⠀⠀⠀⠀⠀⠠⣎⢂⢈⡰⠂⠁⠀⠀⠀⠀⢈⡤⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠉⢆⠀⠀⢄⡀⣠⠀⠀⠀⠀⡖⢢⠀⣩⠜⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡐⠀⠀⠀⠑⡄⠀⠀⠀⠑⢤⡈⢆⢙⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠒⠣⣰⣁⠁⠑⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⡠⠊⠈⠢⡀⠀⠀⡠⣅⡜⠉⠀⠀⠀⢀⠊⠈⠲⠀⠀⠀⠀⢀⣠⢉⠀⠐⠗⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⢀⠔⠁⠀⠀⢀⠜⠓⢄⠑⠉⠈⢢⠀⠀⠀⠀⠢⠄⠘⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⡰⠃⠀⠀⡠⠖⠁⠀⠀⠀⣁⠦⢀⡀⠡
⠀⠀⠀⠀⠀⠀⡌⠌⠀⡠⠊⠀⢀⠤⠊⠀⠀⢀⠠⠒⠉⠀⣀⠠⠘⠋
⠀⠀⠀⠀⠀⡐⠌⢀⠔⠁⡠⠐⠁⢀⡠⠐⠈⣀⠠⠐⠊⠉
⠀⠀⠀⠀⢰⠏⡠⢃⠴⠊⡀⠄⢂⠡⠔⠒⠉
⠀⠀⠀⢠⣏⣨⢔⣡⠔⠍⠒⠉
⠀⠀⢠⡿⠟⠛⠉


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

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⣾⢟⣛⣟⣛⣟⣛⣛⣿⣛⣛⣻⣛⣻⣟⣛⣛⣻⢛⣻⣻⣛⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣻⣛⣻⣻⣛⣻⣻⢷⡄
⠀⠀⠀⠀⢸⡏⣏⠶⢊⠟⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⠛⢵⡎⣿⢿⡇
⠀⠀⠀⠀⢸⡧⣿⠟⠀⢀⣰⠿⢏⣩⠭⣍⡹⠭⠉⠉⠉⠩⠽⣉⡽⢭⣉⠉⠉⠉⠉⠉⠉⣉⣭⢯⣍⡻⠍⠉⠉⠉⠩⢟⣩⡽⣍⡹⠻⣄⠀⠀⠻⣿⢸⡇
⠀⠀⠀⠀⢸⡧⡇⠈⢰⡟⣥⣞⠫⣵⣶⣦⠝⣳⣦⠀⢠⣶⡛⢥⣶⣶⡍⢛⣦⠄⠠⣴⡞⢩⣶⣶⣮⠙⣶⡤⠀⢤⣞⠋⣵⣶⣦⠝⣳⣮⢻⡆⠀⢸⢹⡇
⠀⠀⠀⠀⢸⡏⡇⠀⢸⡇⠀⢉⣛⠶⣭⡴⠛⠉⠀⠀⢀⠈⠙⠶⣭⡵⢞⣫⠁⠀⡀⠀⢍⡳⢮⣭⠶⠛⠁⠀⠀⠀⠈⠛⠶⣭⡴⢚⡉⠀⢨⡇⠀⢸⣽⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡏⠀⠸⣛⣥⠶⣤⣀⠀⠀⠀⠀⠀⢀⣠⠶⢦⣝⡻⠀⠘⠃⠀⠼⣫⡵⠶⣤⡀⠁⠀⠀⠀⠀⣀⣤⠶⢮⣛⠃⠀⢹⡇⠀⢸⣼⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡃⢴⣟⡩⢶⣿⡶⢍⣻⡦⠀⠰⣾⡋⠵⣾⣷⠌⣙⣶⠄⠠⢶⣟⠡⣶⣿⡦⢉⣷⠦⠀⢴⣞⡉⢶⣿⡶⠍⣻⡶⠸⡇⠀⢸⢸⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡇⠀⠈⠙⠲⣭⠖⣫⡅⠀⢀⡀⠀⣍⡳⢮⡵⠛⠉⠀⠀⠀⠀⠉⠛⠶⡥⢖⣫⠁⠀⣀⠀⢈⣝⡳⢬⠶⠋⠁⠀⠀⡇⠀⢸⢻⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡇⠀⢀⣠⡴⠶⢮⣝⡓⠀⠉⠁⠀⣛⣥⠖⠶⣤⣀⠀⠀⠀⠀⢀⣠⠴⠲⢮⣛⠂⠀⠉⠀⠘⣋⡵⠖⢦⣄⡀⠀⠀⡇⠀⢸⣾⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡃⠶⣯⡑⠾⣿⡷⢊⣹⠶⠀⠰⢿⣉⠲⣿⡿⠆⣹⡷⠆⠀⢾⣏⡱⢾⣿⠶⣉⣿⠖⠀⠶⣿⣁⠶⣿⡷⢎⣹⠷⢠⡇⠀⢸⣺⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡆⠀⢠⣍⡳⠶⠞⠋⠀⠠⠀⠀⠀⠉⠛⠶⠶⣫⣥⠀⢀⡀⠁⢨⣝⠳⠶⠛⠉⠀⠀⠀⠀⠀⠉⠳⠶⢞⣫⡄⠀⣸⡇⠀⢸⢺⡇
⠀⠀⠀⠀⢸⡯⡇⠀⢸⡇⠀⢘⣩⠶⣛⠶⣤⡀⠀⠀⠀⢀⣠⡴⢞⡳⢮⣛⠀⠈⠃⠀⣚⣭⠞⡛⠦⣄⡀⠀⠀⠀⢀⣠⠴⣛⠶⣭⣃⠀⢸⡇⠀⢸⣺⡇
⠀⠀⠀⠀⢸⡯⡇⠀⠸⣧⡺⢯⣐⠿⣿⠿⣂⡽⠗⠀⠐⢿⣅⡺⢿⡿⢒⣭⠿⠂⠐⠿⣯⣐⠿⡿⠗⣨⡿⠗⠀⠺⢯⣅⠺⢿⠿⣂⣽⢿⣴⠇⠀⢸⣺⡇
⠀⠀⠀⠀⢸⡯⣿⠦⠀⠀⠙⣦⣍⣛⣶⣛⣩⣒⣀⣀⣀⣀⣮⣙⣳⣞⣉⣀⣀⣀⣀⣀⣀⣉⣓⣶⣋⣱⣂⣀⣀⣀⣐⣎⣛⣶⣚⣉⣴⠋⠀⠀⣤⣿⢸⡇
⠀⠀⠀⠀⢸⡇⣇⠶⢇⣦⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣤⡷⢆⣿⣺⡇
⠀⠀⠀⠀⠘⢿⣭⣽⣿⣽⣽⣽⣭⣽⣭⣭⣽⣭⣽⣭⣭⣭⣽⣭⣯⣿⣭⣯⣯⣭⣯⣯⣭⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣵⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⡷⣠⣆⠠⠔⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣒⠀⠀⠘⠻⣿⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡭⠶⣷⢀⡘⠓⣀⠘⠁⠈⢠⠰⠘⠀⢠⡀
⠀⠀⠀⠀⠀⢙⠀⣿⠀⠀⠀⣸⣿⡆⠡⠅⣎⠀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠚⢀⡈⠡⡄⠉⠶⡀⠴⠦⠰⢆⢁⡀⠖⣈⠠⠌⣁⠈
⠀⠀⠀⠀⠒⡰⣴⣿⣧⣤⣴⣿⣿⡞⠈⠁⠀⠀⠀⠉⠒⠀⠀⠠⠄⢤⡤⠶⢀⡐⢃⡀⠛⠄⡤⠘⠀⠀⠀⠙⠳⠴⠮⠰⠦⠁
⠀⠈⠁⠀⡰⠉⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠘⠓⢠⠐⢢⠀⠅⢀⠐⡦⡀
⠀⠀⠐⠈⠀⠀⠀⠀⠹⣿⠿⢿⣻⠅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠠⣌⣀⢚⡀⠈⣀⠘⠠⡆
⠀⠀⠀⠀⠀⠀⠠⠅⠀⡜⠀⡀⣶⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣾⣶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠅⣁⠀⠠⠀⠀⠘⠀⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⢀⠒⠠⠟⠀⠁⠒⠩⢀⡀⠀⠒⠉⢈⡁⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣶⠉⡀⢤⣄⡓⢠⡅⠨⠒⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠸⢷⣄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⠛⢶⠹⡊⡴⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⣶⢏⢹⣿⡐⠢⣜⠐⠀⣣⠔⢒⣿⡏⡹⣖⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⠁
⠀⠀⠀⠀⠘⣿⣏⣾⣺⠁⠙⢽⠻⡟⠑⡼⠂⣰⢿⡟⣧⠙⢿⣦⡑⠂⠘⢊⣴⡾⠋⣾⢛⡿⣆⠐⢤⠊⢹⠿⡯⠋⠉⣗⣷⣻⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣡⣿⣭⣒⡬⢄⡁⠠⣕⣻⠃⢾⠧⠟⣤⣦⡍⠛⢦⡴⠛⢩⣴⣤⠷⢾⣷⠘⢟⡫⠄⢈⡠⣥⣖⣽⣿⣬⣿⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣉⡽⣿⡿⣷⣌⠄⠩⢙⡲⠛⠉⢰⣿⣿⡏⠀⠘⠋⠀⢹⣿⣿⡆⠹⠛⠖⢏⠌⠐⣡⣾⢿⣿⢧⣘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⢟⡄⢙⣿⡌⢠⡆⢀⡀⠰⠄⢸⣿⡇⣤⣠⣆⣤⢸⣿⡃⠰⠄⢀⡀⢰⠄⢁⣿⡋⢠⡻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢰⣷⡇⠀⠁⡿⡏⢠⢒⡟⢢⢹⣾⠳⢞⣷⡏⡔⢳⡒⡆⢹⣿⠈⠀⢸⢿⡄⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣗⡇⠀⠀⡇⢠⠌⠉⢸⡟⣸⠛⠃⠘⠛⣇⢿⡇⠉⠡⡄⠺⠀⠀⢸⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⢿⣳⣶⣾⣧⣿⡀⠀⠀⢀⣿⣼⣷⣦⣞⡿⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣽⣆⣸⢿⢧⡀⢀⡼⡿⣅⢰⣯⣾⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣶⡏⢀⡄⢠⡀⢹⣦⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠉⠀⠀⠙⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣿⣿⡿⢃⠄⠀⠀⠠⡘⢿⣿⣿⠃⡏
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⡆⠈⠉⣴⠋⢰⡇⢸⡆⠙⣦⠉⠁⢰⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣬⣷⣶⣶⣄⠙⢦⡀⠀⠀⠀⢿⣦⣰⡇⢚⠺⠇⠸⠋⡓⢸⣆⣴⡿⠀⠀⠀⢀⡴⠋⣰⣶⣶⣾⣥⣤⣀
⠀⠀⠀⠀⠀⠀⠈⣉⡿⠿⣿⣿⡿⠓⠀⢻⣶⠀⠀⠀⢹⣿⠘⣿⣿⡄⣠⣿⣿⠃⣿⡏⠀⠀⠀⣶⡟⠀⠚⢿⣿⣿⠿⢯⣉⠁
⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠠⠖⠒⠶⡶⢿⣦⡀⠀⢈⣭⣤⡉⠋⠀⠀⠙⢩⣤⣭⡀⠀⢀⣴⡿⢶⠶⢒⠲⠆⠀⠀⠀⠈⢡
⠀⠀⠀⠈⣷⣄⡏⠀⢀⠀⣀⠺⠶⣞⢡⣼⢆⡉⢱⠚⠊⠀⢰⡋⢰⣇⣸⡆⢝⡆⠀⠑⠛⡎⢉⣰⣦⡌⣳⠶⠗⣀⠀⡀⠀⢻⣠⣾⠁
⠀⠀⠘⠢⢼⣿⣿⣶⡌⣦⠘⢷⢦⠈⠈⠿⠛⠀⠛⠂⣖⠀⠀⢵⡀⠋⠙⢁⣮⠀⠀⣲⠐⠚⠀⠛⠿⠁⠀⡴⡾⠃⡴⢡⣾⣿⣿⡧⠔⠁
⠀⠀⠀⠀⠈⠻⣿⣿⡇⠘⢦⡋⢰⣿⣿⡇⠀⣐⠻⣦⠈⣿⠀⠀⢙⡶⢶⡋⠀⠀⣿⠁⣴⠟⣂⠀⢸⣿⣿⡂⣉⡴⠃⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠒⢤⣤⣀⣠⣬⣿⣮⣅⠋⡤⣄⡙⠛⠂⠀⣬⠣⡆⠈⠁⠘⠁⢰⠜⣥⠀⠐⠛⠋⣠⢤⠙⣨⣵⣿⣥⣄⣀⣤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⢾⠁⠐⠊⠱⠚⠉⠹⠒⠀⠀⠀⠀⠀⠀⠒⠏⠉⠳⠞⠑⠂⠈⡷⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⢾⡀⠠⢄⡰⢤⣀⣰⠤⠀⠀⠀⠀⠀⠀⠤⣆⣀⡴⢆⡠⠄⢀⡷⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠤⠚⠛⠉⠙⢛⣿⢟⡋⣄⠓⠃⣡⣤⠄⠀⢓⠔⠇⢀⡀⢀⡀⠸⠢⡛⠀⠠⣦⣌⠙⠚⣠⢙⡻⣿⡛⠋⠉⠛⠓⠤
⠀⠀⠀⠀⢀⣴⣿⣿⡇⢠⠞⣉⠸⣿⣿⡇⠀⠩⣴⠟⢀⣿⠀⠀⣨⠷⠾⣅⠀⠀⣿⡀⠻⣦⠍⠀⢸⣿⣿⠇⣀⠳⡄⢸⣿⣿⣦⡀
⠀⠀⢀⠔⢺⣿⣿⡿⢃⠞⢨⡾⠞⠀⢀⣶⣤⠀⡠⠄⠭⠀⠀⡿⠁⣄⣠⠈⢻⠀⠀⠭⠠⣤⠀⣤⣶⡀⡀⠳⢷⡄⠳⡘⢿⣿⣿⡗⠢⡄
⠀⠀⠀⢀⡿⠋⣧⠀⠈⠀⠉⢴⠶⢯⡘⢻⠏⣁⡸⣤⢄⠀⠸⣅⠸⡏⢹⠇⣪⠇⠀⡠⡤⢏⣈⠹⠟⢃⡽⠶⡦⠉⠀⠁⠀⢸⠙⢿⡀
⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠰⠦⠤⠶⠷⣾⠟⠁⠀⠈⣛⠛⣁⣄⠀⠀⣠⣈⠛⣚⡁⠀⠈⠻⣷⠾⠶⠤⠴⠂⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⢀⣉⣷⣶⣿⣿⣷⡄⠀⣼⠿⠀⠀⠀⣸⣿⢠⣿⣿⠃⠸⣿⣿⡄⣿⣇⠀⠀⠀⠿⣧⠀⢤⣾⣿⣿⣶⣾⣉⡀
⠀⠀⠀⠀⠀⠀⠉⠛⢛⡿⠿⠿⠏⣠⠞⠁⠀⠀⠀⣾⠟⠹⡇⢬⢴⡆⢰⡦⡅⢸⠏⠻⣷⠀⠀⠀⠈⠳⣄⠙⠿⠿⢿⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠇⢀⣀⠻⣄⠸⡇⢸⠇⣠⠟⣀⡀⠸⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⣿⣿⣷⡌⠂⠀⠀⠐⢡⣾⣿⣿⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣀⠀⠀⣀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠻⣇⠈⠁⠘⠁⣸⠿⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⢀⠉⠀⠀⢎⣱⠀⠀⡀⠀⠀⠈⠐⠣⣠⠇⠀⠀⠘⠗
⠀⠀⠀⠀⠠⠀⠊⠀⠃⠃⠀⠀⠀⠁⡄⡄⠀⠀⠀⠘⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠈⠀⠠⠀⠂⠀⠀⣀
⠀⠀⠀⠀⠠⣲⠀⠀⠀⠀⠀⠁⠂⢄⠀⠑⠀⠀⠀⠠⠠⠀⠀⠐⠈⠀⢠⠀⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠰⠔⠹⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⢀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠂⠈⠀⠀⠀⠟⠀⢀⠀⢠⢢⠀⠓⠲⠁
⠀⠀⠀⢒⠊⠢⠀⠁⠂⡀⠠⠀⠐⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⡈⠉⠀⠒⠀⠄
⠀⠀⠀⠘⠈⠃⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⢔⠆⠀⠀⢁⠢⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠣⠃⡀⠁⠀⠀⠀⠐⠰⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠰⠍⠆⠀⠀⢹⡤⠼⠁
⠀⠀⠀⠀⠀⢀⠁⡠⠀⠀⠔⢁⠐⠁⠀⠀⠀⠀⠐⠟⠀⢠⠀⠰⠭⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠮⠆⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⣩⢈⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠂⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁