Jackal Emojis & Symbols

⠀⢀⣀⢀⡀⡀⢠⣥⣌⠢⡀
⠀⠈⢹⠟⠻⠟⠹⠸⣿⡆⠐⣤⣄⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠈⠃⣠⣿⣿⣿⣿⣦⣄⡀
⠀⣸⣤⣴⠟⠛⠀⠀⠀⢀⣿⣿⣿⣿⢿⣿⣿⣿⣧⣄⡀
⣼⣿⣿⣿⣷⠆⠀⠀⣄⠀⣼⠀⠘⢿⣯⣿⣾⣿⣿⣿⣿⣷⣄⡀
⠘⠻⣿⣿⡿⠶⠦⣶⣯⡀⠀⠀⠀⠈⠻⢟⣬⡏⠎⣩⡝⢐⠟⠿⠧⢴⣤⣦⣦⣶⣴⢶⣠⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠂⠀⢠⣮⠛⠩⠄⠈⢀⣁⠀⠞⠂⡚⠛⠻⠿⠉⠛⢋⣛⠟⢿⣸⣟⡳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠀⠟⠀⠂⠀⠉⠁⠀⠘⠁⠛⠈⠿⠈⢛⠀⠈⢫⢠⡏⣁⣨⣝⣿⣛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⣀⠰⠀⠒⡁⠒⠀⠃⣶⢠⡆⠲⠶⢿⠙⠅⠛⠇⠀⠀⠉⢈⡡⣈⣂⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡃⠤⠀⠆⠁⠀⠆⠀⠀⠀⠀⢀⠄⡀⣀⠀⣤⠀⢰⠆⠟⠈⠉⠈⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡇⠀⢻⣘⣃⡀⢸⡌⣄⠀⠀⠘⠓⠀⠹⣃⠀⠗⠀⡶⠆⣠⠘⠻⠎⢶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣼⠿⠙⠷⠠⣾⣷⣄⢻⠄⢠⡦⣤⣜⣼⣶⣦⠀⠁⠀⠙⠐⣿⠆⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠓⠀⣤⢈⡉⠛⠛⠿⠷⠶⠿⡿⠿⠿⠛⠛⢣⡘⠇⠰⠆⣾⣦⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣉⢠⡄⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⢠⠀⠶⡖⢏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⣀⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣍⡽⢯⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⢹⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⢽⢿⣾⡿⢋⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢹⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠇⠙⣿⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠸⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡤⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⡿⠋⠀⠀⠀⣸⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⣻⢛⣥⢾⣿⣟⠠⣤⡤⠄⡀⠀⠀⡠⠀⠀⠄⠟⠿⢶⡶⢿⡗⣲⣳⣆⣿⣛⣡⡿⣤⡄⠀⠤
⣤⣤⣤⣤⣤⣤⣭⣾⣥⣤⣭⣤⣬⣭⣭⣭⣭⣥⣤⣬⣭⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣭⣥⣭⣭⣭⣭⣭⣯⣭⣭⣤⣤
⣿⣿⣄⣭⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⣕⢠⡀⠀⠀⠀⠀⠀⢀⡤⣲⠏
⠀⠀⢡⡳⣌⣳⠤⡤⠐⢲⠡⢈⡏⠀⠐⣡⠃⢸⠀⠀⠀⢰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡆
⠀⠀⠀⠑⣜⡟⠀⠁⠀⠀⠚⡞⠃⠀⠀⠏⠹⢸⠈⣷⠚⢸⠅⠒⢸⡳⣾⠎⡐⠷⡟⢒⡃⠀⠀⢨⣼⡖⠺⠏⢐⡇⠁
⠀⠀⠀⠀⠘⣏⠡⠀⠈⠅⢔⣧⢀⣀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠈⠁⠀⢀⡼
⠀⠀⠀⠀⠀⠘⠺⡯⠝⠋⠀⢾⡣⠌⡿⢿⠻⡿⠿⠲⡲⠴⢟⠻⠍⣉⠪⡓⣛⣽⢿⣗⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠛⠊⣠⡼⠀⢜⢀⣈⣷⣵⣤⣭⠤⠮⠔⠛⠁⠀⠀⠀⠙⠂⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠒⠀⠀⠀⠀⢊⠟⠋⠙⠛⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠐⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠁⢀⣶⠄⠀⠀⢰⠄⣰⡏⣀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠳⡀⠀⠈⢸⣇⣤⠄⠤⠀⠠⠀⠀⠐⠊⢹⠇⠀⠀⠘⢰⡿⣏⠈⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠦⠀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⢤⣟⢧⢹⡿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⣇⠙⣆⠹⡞⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢻⣆⡘⢆⢹⣆⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢫⢳⠸⡇⢻⣷⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡇⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡎⢸⢰⠁⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠎⠈⢀⠎⠎⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣐⢃⣗⡂⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠑⠊⠘⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⠀⠀⢀⡠⢦
⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢿⣄⠙⡎⡱⠋⢀⡏⡄
⠀⠀⠎⠀⠀⠁⠀⠀⢰⠀⡀⠀⠀⡀⠀⠀⠀⢠⢔⡶⡂⢰⠀⣳⠇⠀⠀⠀⢀⣦⠇⠀⠀⠀⠀⠚⢴⡇
⠀⠰⡀⠈⡹⠉⢐⣉⠻⢮⠟⠟⠛⠉⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠋⠀⠲⠄⠀⠞⠀⢵⡿
⠀⠀⠈⠈⠀⠀⠀⠀⣀⣠⠤⠖⠛⠉⠉⠋⠛⠗⠛⠉⠋⠉⠙⠋⠉⠉⠉⠃⠘⢢⠈⠊⢀⣀⠀⠃⡎
⠀⠀⠀⠀⠀⠀⣠⠎⠤⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⠀⠓⠂⡙⡋⠀⢼⠁
⠀⠀⠀⠀⢀⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠀⠈⠀⠀⢀⠀⠀⠐⠟
⠀⠀⠀⠀⢸⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠰⠇⠀⠀⠃⠘⠂⣠⠃
⠀⠀⠀⠀⢈⢠⣔⡀⠀⠀⠀⠀⠀⢀⠄⣢⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⡤⢴⣤
⠀⠀⠀⠀⢸⡏⠻⣄⢠⢎⠀⠀⠀⢨⣤⣿⡷⢤⣄⡀⢀⣀⠀⣸⣍⣴⠀⠀⣼⠀⣤⠟⠁
⠀⠀⠀⠀⠘⣇⠀⠈⢣⡊⠀⠀⠀⢖⡾⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣧⠀⠀⡷⢿⠋
⠀⠀⠀⠀⠀⠙⣧⠀⢻⣇⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⣾
⠀⠀⠀⠀⠀⡰⣷⣡⣾⠋⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣏⠏
⠀⠀⠀⠀⠀⢰⡁⡟⢏⠃⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⢀⢀⠀⣧⠀⣿⣇⠀⠀⠀⢀⠀⣀
⠀⠀⠀⡠⣄⣘⣧⣷⣌⠳⡈⠴⠗⠴⠶⢺⡒⠀⠐⠲⠼⠶⠶⠷⠯⠤⠿⠤⡜⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠈⠈⠉⠉⠙⠓⠛⠚⠐⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣥⣦⠀⠀⠀⢀⡤⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⡏⢹⢀⣤⠞⡟⣸⣿
⠤⢠⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢨⠻⠻⢷⡴⠂⠀⠈⠲⡿⡟
⢳⠻⣼⡄⢶⠐⠀⠳⡀⠀⢘⡲⣼⣶⡁⠟⠐⠋⠨⠇⠀⠀⢐⠸⠏⠁⠇⠸⠿⠀⠀⠀⢸⠘⠺⠋⠁⠀⠀⠀⠀⢿⠁
⠸⠔⠃⠃⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣐⣊⣀⣀⡀⠀⠀⠀⣀⠠⣤⢦⠈⠁⠀⠀⡶⢆⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣲⣍⣿⣭⣯⡿⠛⢹⠟⠑⠟⠻⢫⢛⣉⣾⣡⡶⡞⢸⠄⡀⠀⠲⢄⡀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠍⠉⠉⠛⠛⠻⢿⣷⣾⣷⢾⡞⢹⡐⣝⣸⠚⣧⢐⢃⠇⠠⠂⠁⠀⠀⠀⢙⡷⠚⠫⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠿⢿⣯⣴⣿⣇⠀⣻⢸⠁⠀⠀⠀⠀⠀⠀⣲⠏
⠀⠀⠀⠀⠀⠀⢀⠁⡔⢠⡄⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⡿⠋⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⡆⠀⠇⢰⠃⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⢀⠀⠀⠀⠀⠀⠀⠃⢀⡇
⠀⠀⠀⠀⠀⣸⣳⡏⢰⣦⢧⡇⠀⠀⠀⣀⡷⢀⢀⡘⡄⡀⠀⠀⠀⢀⡴⣧⠀⠤⠀⠀⡀⠖⡢⠊
⠀⠀⠀⠀⠀⡿⣿⠀⠸⣾⡟⡅⠀⠀⡴⡙⠏⢉⡞⠉⠙⠛⠛⠓⠂⠉⠀⠛⣯⠘⠀⢰⡵⠊
⠀⠀⠀⠀⣼⢳⠇⢠⣶⡏⣷⠆⠀⠀⢡⡆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠀⢸⡇
⠀⠀⠀⣼⠋⠀⢀⣞⡞⢁⣿⠁⠀⡴⡻⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡇⠆⢸⡇
⠀⠀⣼⠃⢀⣴⡶⠟⠀⣸⠃⢀⠈⠀⢠⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢧⠀⢈⡇⠀⠄
⠀⣰⣳⡞⠿⠛⠁⠀⣰⣏⢀⡎⣀⣀⣏⣴⣦⣤⣼⣵⢞⣤⡴⣶⣦⣀⡀⣼⣤⢸⢠⡈⣷⠀⣘⢥⣀⣤⣴⡠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠙
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⡀⢀⠐⠁⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠤⠡⡀⠀⠀⠁⠢⡀⢀⠞
⠀⠀⠀⠈⠊⠉⠓⠛⠀⡰⠂⠀⠀⢀⢎
⠀⢀⢀⠀⠀⠀⠀⠀⡐⠁⠁⠀⠀⠀⠀⠑⠐⠂⠀⠒⠒⠒⠤⠤⠤⠤⠤⢄⣀⡀
⠰⠤⠤⣥⣀⣀⡠⠄⠊⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠐⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆⠀⣎⠀⢀⣀⣀⣀⣀⣠⠤⠚⡇⠀⠀⠀⠠⠋⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠇⡀⢠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢉⠂⠅⠰⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣘⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠇⡯⠠

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣿⡆
⠀⠀⠀⠀⠀⠀⣠⡾⢿⠛⠿⣿⣶⡄
⠀⠀⠀⠀⣀⡴⠷⠽⠂⠀⠠⣿⡿⠻⢶⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠐⠛⠁⢀⠀⠈⣻⣷⠛⢿⣿⠇⠁⠀⣢⣬⣯⣿⡗⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠃⠀⣼⣿⡟⠀⣼⠃⠀⢠⣾⣿⣿⣿⡏⠈⢠⣼⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠃⠀⠀⢨⣿⣇⠀⠈⢠⣴⣿⣿⣿⣿⠛⠀⢠⣿⣻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⢸⣿⣿⣿⣿⠧⠀⣀⠸⣹⣿⣿⣿⣇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠻⣿⡆⠀⠈⠙⠉⠉⠀⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠘⣿⣿⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣨⣿⣶⣿⣿⣿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⢠⣴⣶⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠿⠿⢻⡿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠧⢀⣚⠿⠛⠛⠋⠉⠀⠀⠛⠉⠋⠁⠀⠀⠀⠀⢧⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⢀⣴⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣷
⣸⣿⠏⠀⠈⠙⠛⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠛⠉⠀⠈⢻
⣿⣿⠀⠀⠀⢀⠀⠀⠈⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠉⠀⠀⢀⠀⠀⠀⢸
⣿⣿⠀⠀⢠⣿⣿⣦⡀⠀⠀⠀⠙⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠁⠀⠀⠀⣠⣾⣿⣧⠀⠀⢸
⣿⣿⠀⠀⢸⣿⣯⣍⡁⠀⠀⠢⣀⠀⢈⠻⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⡄⢀⡤⠂⠀⠀⣉⣭⣿⣿⠀⠀⢸
⣿⣿⠀⠀⢸⣿⣿⣦⣍⠁⠀⠀⠈⢳⡄⠳⣌⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢋⡴⠋⣴⠏⠀⠀⠀⢈⣥⣾⣿⣿⠀⠀⢸
⢻⣿⡆⠀⠈⣿⣿⡷⢦⣀⠀⠀⠀⠀⠙⣦⡈⠳⣄⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⡴⠋⣠⡞⠁⠀⠀⠀⢀⣠⡴⣿⣿⡏⠀⠀⣸
⢸⣿⡇⠀⠀⢿⣿⣿⠶⠤⠀⠀⠀⠀⠀⠈⢿⣄⠈⢷⣄⠹⣿⣷⣤⣶⣶⣾⣿⣿⣶⣶⣦⣴⣿⡿⢃⣴⠟⢀⣴⠏⠀⠀⠀⠀⠀⠠⠴⢾⣿⣿⠇⠀⠀⣿
⢸⣿⣷⠀⠀⢸⣿⣿⡷⣦⡄⠀⠀⠀⠀⠀⠈⢻⣦⠀⠹⣷⡌⠻⠛⠋⠉⠁⠀⠀⠉⠉⠙⠻⠋⣴⡿⠁⢠⣾⠏⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⠀⠀⢠⣿
⠀⣿⣿⡀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣨⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡇⠀⠀⢸⣿
⠀⢻⣿⡇⠀⠀⠸⢿⣿⣯⣉⣀⠀⠀⠀⠀⠉⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠈⠁⠀⠀⠀⢀⣈⣩⣿⣿⠿⠀⠀⠀⣿⣿
⠀⠘⣿⣷⣤⠀⣠⣀⠈⠻⣿⣿⣿⠟⠁⠀⢀⡼⠋⠀⠀⠀⠀⠀⢄⠀⠠⣽⣿⣿⡤⠀⢀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠙⢿⣿⣿⡿⠋⢀⣠⡀⢠⣴⣿⡿
⠀⠀⣿⣿⡏⠀⣿⣿⣿⣦⠈⠛⠁⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠘⢿⠟⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠙⠋⢠⣾⣿⣿⡇⠀⣿⣿⡇
⠀⠀⣿⣿⡇⠀⠹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠀⢿⡀⠀⠀⣸⡏⠀⢀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠁⠀⣼⣿⡇
⠀⠀⢹⣿⣷⢀⣴⠏⣠⠎⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠘⡇⠀⠀⡿⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠈⢦⡘⢿⣄⢠⣿⣿⠃
⠀⠀⠀⢿⣿⣿⠃⣼⡏⠀⠀⣾⡇⠀⠀⢤⣤⣄⣀⡀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⣀⣀⣤⣤⠄⠀⠀⢿⡆⠀⠈⣿⡄⢻⣿⣿⠏
⠀⠀⠀⣼⣿⠃⣸⣿⠁⠀⠀⣿⡇⠀⠀⠀⠈⣹⡟⢻⣿⣶⣄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⣾⣿⠛⣿⡏⠀⠀⠀⠀⣼⡗⠀⠀⢹⣿⡀⢻⣿⡄
⠀⠀⢰⣿⣇⡄⠉⢉⠀⠀⠀⠹⣧⠀⠀⠀⠀⠹⣇⠀⠈⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣈⠀⢀⡿⠃⠀⠀⠀⢀⡿⠃⠀⠀⢈⠉⠁⣠⣿⣷
⠀⠀⠛⢻⣿⠁⠀⢿⡆⠀⢀⠀⠙⠀⠀⠀⠀⠒⢬⣿⣿⣭⠄⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢨⣽⣿⣯⡔⠂⠀⠀⠀⠚⠁⢀⠀⠀⣼⡇⠀⢹⣿⡛⠃
⠀⠀⢀⣿⣧⡄⠀⢹⣇⠀⠘⣷⡀⠀⠀⠀⠠⣀⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢂⡠⠄⠀⠀⠀⣠⡟⠀⢀⣿⠁⠀⣤⣿⣧
⠀⠀⠈⠉⣿⣁⠀⠐⣿⡄⠀⠹⣿⣦⡀⠀⠵⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡶⠁⠀⣠⣾⡿⠁⠀⣸⡗⠀⢀⣹⣏⠉
⠀⠀⠀⢸⡿⣿⡀⠀⢛⣷⡀⠀⠙⢿⣿⣷⣶⣿⣿⣿⡿⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠘⣿⣿⣿⣿⣶⣿⣿⠟⠁⠀⣰⣿⠋⠀⢸⡿⣿
⠀⠀⠀⠀⠀⣿⣷⡀⠈⠙⠳⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠀⠀⠰⠟⠁⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠟⢿⣧⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣦⣼⠟⠇
⠀⠀⠀⠀⠀⠀⢸⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠉⠈⣿⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠁⠀⠀⠀⣿⡟⠈⠁⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣀⠀⠀⣦⠀⠹⣿⠀⠀⠀⠸⠇⠀⠀⠀⠀⠹⠀⠀⠀⢸⡿⠁⢠⣆⠀⢀⣀⣴⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡄⠀⠻⡆⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡼⠃⠀⣼⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣷⠀⠀⠁⠀⢴⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⢰⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⡓⢦⡸⣅⣀⠀⠉⠁⢀⣀⡽⣠⡶⡃⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡈⢿⣷⡽⣿⡇⠀⠀⣿⡿⣱⣿⠏⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣛⠿⠾⣿⢶⣾⣿⠾⢟⣣⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⣿⣾⣷⡾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣾⣶⣶⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣿⣿⣷⣶⣷
⣿⣿⣿⣀⣀⣠⣤⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠍⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠟⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠄⠀⡀⠙⠀⠀⠀⠀⣀⡆⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⠤⠤⣡⣤⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠠⠃⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⢤⠋⠀⠁⠉
⠀⠀⠀⠀⡔⠀⢠⠀⠀⠀⠐⠀⠀⠐⡀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⢀⣨⠀⠀⠀⠀⠀⠀⡀⠂⡀⢨⣲⠆
⠀⠀⠀⠘⠁⢀⡏⠀⠀⠀⠀⢤⠀⠀⠈⠹⣦⣀⠙⠶⣆⠀⠀⠀⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢲⠈
⠀⠀⠀⠀⡆⠠⣹⣞⡀⣤⠀⠈⠳⣄⡀⠀⠈⢿⣧⣐⣿⣦⣔⣱⡆⣦⠠⠀⠀⠀⣀⠈⢀⠀⢀⡈⠖⠁
⠀⠀⠀⠀⠣⢀⠰⢻⣄⠘⠁⡀⠀⠁⠹⠳⡄⠀⠀⠉⠉⠓⠿⠶⢿⡀⠉⠉⠐⢉⡵⠏⠽⠚⠉
⠀⠀⠀⠀⠀⠙⣄⣛⣿⣷⡄⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⡎⠃⠘
⠀⠀⠀⠀⠀⠀⠹⣸⠃⣻⡇⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⢈⠘⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢆⡀⠇
⠀⠀⠀⠀⠀⠀⠈⡏⣼⡀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠀⠀⠁⢀⣀⠠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠷⢄⣈⣉⣉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⢢⡀⠀⠠⠠⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⡆⠙⢦⣤⢤⡤⣠⠞⠁⣤⢹
⠀⠀⠀⢀⠴⠖⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠸⡏⣿⣄⠀⠙⠂⠴⠃⠀⢤⡟⢸
⠀⠀⠀⠞⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⢹⢴⠋⠀⢖⠀⡌⡇⡇⠀⠀⠀⠀⠀⠀⣷⣼⠁⠀⠀⠀⠀⠀⠈⠛⢥⣾
⠀⠀⢰⠀⠀⠶⢶⡶⠂⠠⠖⠲⢘⣴⢲⣧⣚⠦⡴⢻⠀⠀⠀⠀⣀⡿⠈⠉⠀⠉⠁⠈⠀⠉⠁⠁⠀⠀⠀⠀⢀⠚⡹⠃⠀⣄⡀⠀⠀⣂⣤⠀⢒⣙⣦⡄
⠀⠀⠘⢦⣀⣀⠜⠀⠀⠳⠤⠎⠚⠘⠚⠈⠒⠀⣁⣀⣀⣀⣀⣀⣉⣁⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠼⣿⠄⡀⢀⠈⡛⠀⣀⠉⢁⠀⠉⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡴⠒⠉⠓⠉⠈⠉⠊⠁⠹⠖⠙⠁⠈⠉⠉⠈⠉⠋⠉⠈⠁⠁⠈⠉⠀⠍⠱⣄⠈⠏⠁⣀⣉⠀⡸⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢉⡀⠁⠤⠄⠈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠱⡤⡄⠀⠿⠿⠘⠁⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢰⡄⠀⠀⠀⠐⠐⠂⠘⠈⣹⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢋⠋
⠀⠀⠀⠀⠀⠀⢠⠟⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡶⠂⠀⠀⠰⠀⠀⠷⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠠⢉⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠔⠀⠀⠀⠈⠁⠀⢀⡆⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣦⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⣿⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀⢠⡶⠆⣣⣴
⠀⠀⠀⠀⠀⠀⣼⣸⠙⢿⡄⠀⢀⣴⠁⠀⠀⠀⠀⠄⣁⢠⣿⣷⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⣚⡑⢡⣶⠁⠀⠀⣼⠁⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⢸⡏⡆⠀⠙⢦⡘⢠⠂⠀⠀⠀⠀⠘⣋⡿⠋⠉⠉⠉⠛⠷⣦⣤⢷⢮⣤⢾⠿⠶⣟⠏⠀⠀⢰⡇⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠈⣧⢠⠀⠀⠀⣹⡌⠠⠀⠀⠀⠀⠏⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠀⠀⢸⡟⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠘⠎⢧⠀⠐⢷⣿⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠁⠀⢸⠇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎⢲⠀⣽⣿⠃⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠇⣾
⠀⠀⠀⠀⠀⠀⠀⢠⠛⡝⣤⣷⣿⢁⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⠿⡁⠋⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣇⠀⠘⣏⢺⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠠⠂⣹⢀⢹⠠⠙⣦⡀⠳⢠⣤⡀⠀⣠⣠⣔⣀⣄⣀⠨⣉⣀⢹⣧⣤⣀⣠⣁⣒⢃⠈⣿⠀⠀⢧⣼⣦⣡⡴⠬⠶⠚⠀⠁⠉⠀⠀⡀
⠀⠀⠀⠀⠦⠘⠦⢴⣦⢿⣼⢾⣦⣈⢣⠀⢙⠛⡍⠙⠋⠉⡬⣥⣀⡄⠀⠉⠉⠉⠉⠉⠋⠛⠉⠉⠋⠙⠋⠁⠙⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠑⠉⠋⠋⠘



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡎⠀⣧⠀⠀⠀⠀⢴⣿⠋⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢙⣿⡇⢠⡟⠀⠀⠐⠛⢽⣇⣀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⣟⠻⠟⢁⣤⡴⠛⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣤⠀⢭⣀⣁⢰⣁⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠰⣦⣄⢠⣄⢤⠀⣤⣠⠀⠠⠤⡤⠤⡤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⣀⣌⣙⡻⣿⣤⠈⢁⣀⣓⠒⢢⢀⡼⢻⠛⡛⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠁⢘⡟⠋⠻⢿⣿⣤⣆⡀⠈⠁⢚⣃⠈⣻⣿⣏⣿⣿⡿⠃⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠁⠀⠀⠀⠀⣀⠐⠮⠁⠉⠀⣶⣦⡄⢩⠏⣿⣯⣿⣿⠟⠋⠁⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣇⠀⡃⠀⠀⠀⠀⠀⠀⠀⢠⣴⡛⡋⠀⣼⣷⣿⣿⠟⠁⠀⣰⡄⠀⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡟⠀⣿⣿⡟⠁⠀⠀⢠⣿⣤⣾⣿⣿⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠛⠀⠀⠀⠀⢨⣿⣿⣆⢻⡿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠀⠀⠀⠀⣠⢆⠀⠀⠸⠇⠈⠉⡀⠀⠀⠐⢠⣿⣿⡏⣙⣿⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣴⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠈⠁⢻⣟⠁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢀⣺⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡜⠃⠃⠀⢾⣄⠁⠠⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠿⣏⠉⠁⠀⠀⠀⠀⠀⢠⣠⣶⣿⣿⢷⡄⠀⠀⠀⠉⡄⢠⣿⣿⡏⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⡄⢀⠋⠁⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠇⠀⣇⠀⠀⣤⠀⠀⠸⣿⣿⣗⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠙⠀⠀⠈⠁⠀⢾⣿⣿⣿⣦⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢻⣿⣿⣿⣿⣧⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠙⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠃⠀⠀⡀⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢠⣀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠈⠋⠉⠉⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡏⣧⢀⡤⡾⣱⣿⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠿⢷⡴⠈⠀⠱⡿⠇
⠀⠀⠘⠛⢶⡄⡦⣂⠘⠄⠀⢘⠶⠷⠁⠛⠘⠁⠙⠀⠀⠐⠚⠃⠙⠘⠻⠀⠀⢈⢟⡛⠉⠀⠀⠀⠀⡛
⠀⠀⠀⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⢤⣤⣤⣤⡥⣤⣤⢤⡤⢠⠄⣐⡞⠆⠀⠀⠘⠛⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠟⠿⢷⣿⣿⣿⣍⣴⣩⡬⠄⢱⠇⣶⡟⢺⢿⠃⡃⠆⠀⠉⠰⣤⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠈⠀⠀⠀⠀⠈⠙⠛⠿⣿⣷⣟⣼⣾⠁⣵⡴⠊⠀⠀⠀⠀⢀⣴⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⡿⠃⠀⡀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢰⢀⠅⠸⠁⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠰⠂⢀⠀⠀⠀⠀⠀⠃⣰⠇
⠀⠀⠀⠀⠀⠀⢀⣿⡿⢰⣿⣿⠀⠀⠀⣤⡗⠄⣤⣵⣤⣀⣀⢀⡔⣿⣄⡖⠀⢠⢂⠔⠁
⠀⠀⠀⠀⠀⠀⣸⣿⠃⣘⣿⣟⠀⠀⡌⡸⠁⡼⠀⠀⠀⠉⠀⠀⠀⠀⣷⠁⠀⣿⠁
⠀⠀⠀⠀⠀⣰⠏⠁⣰⣻⠃⣿⠀⢀⣴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⣃⠄⣿
⠀⠀⠀⠀⣰⠋⢀⣤⣿⠁⣸⠋⠀⠈⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣻⠀⡀
⠀⠀⠀⣠⣧⠾⠿⠋⢀⣠⣏⢠⣁⣀⣜⣴⣆⣤⣯⣶⣤⡴⣶⣔⣀⣸⣆⢻⣀⣿⡄⣘⣤⣠⣤⣦⠂
⠀⠀⠀⠉⠀⠀⠈⠙⠉⠉⠋⠉⠁⠀⠀⠁⠁⠈⠀⠀⠈⠀⠀⠉⠉⠉⠈⠙⠋⠁⠁⠀⠈

⠀⠀⠀⠀⠀⡰⣧⠀⢀⣠
⠀⠀⠀⢀⡴⣿⣿⢔⣽⡞
⠀⠀⣠⠎⠀⠉⠿⣿⣿⣥
⢀⡴⠃⠀⠸⣷⠄⠀⠚⠸⢦⣀
⢼⡿⠀⠀⢀⣀⣀⠀⣤⣄⣀⣠⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⢷⠀⠀⠘⠿⢿⣷⣦⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠙⠛⠛⠛⠶⣤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⢭⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⡘⣷⡄
⠀⠀⢻⣄⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠃⠀⠀⠀⠀⠀⠀⡇⠹⣿⣆
⠀⠀⠈⠻⣿⣄⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⣿⣆
⠀⠀⠀⠀⢸⢻⠃⠀⣾⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⡟⢻⣇⠈⢻⣿⣆
⠀⠀⠀⠀⣸⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⢸⡇⣿⠻⣆⠀⣿⣿⣷⣤⣀⣀⡀
⠀⠀⠀⠀⣿⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⢻⣿⣄⠙⢶⣿⣿⣿⣿⣿⣿⣿⠥
⠀⠀⠀⠀⡇⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢮⠳⣄⠙⠿⠻⠿⠟⠃
⠀⠀⠀⠀⡇⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡞⡆⣿
⠀⢀⣀⡼⢡⡿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡼⠀⡇⣿
⠀⠯⣤⡴⠟⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡼⡡⠖⠃⡟

⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣏⣡⢃⡀
⠀⠀⠀⠀⠀⣼⣟⣟⢟⡦⣷⢿⣿⣦⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣽⣿⠿⡏⠁⡈⠺⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣫⡿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠘⠷⠴⠒⣷⣿⡧⢞⣸⣿⣿⠿⣿⣿⣼⣿⡁⠹⣽⣿⣿⣯⡿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣯⣿⣭⠁⠊⣼⣿⣿⣿⣿⣿⣶⢹⠟⠁⠀⠈⢹⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢘⣣⣦⡀⣿⣿⣿⣿⣿⣿⣇⡄⢀⣴⠐⢀⣸⣿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⠏⠉⠋⠈⡽⠁⠀⠁⠀⠈⢿⣂⣻⢃⡰⠾⣿⣿⠀⢟⡿⢿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⠉⠀⠀⠈⠉⠳⣆⣈⠙⡛⣻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡎⠀⠀⢷⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣆⠀⠀⠀⠀⠀⠈⢻⣏⠉⠛⠛⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣒⣠⠊⠀⠀⠀⠀⠙⠥⠆⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⢀⡙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠵⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠀⠀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡞⣧⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⣻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⣿⡟⢿⡷⠀⠋⠛⠛⣿⡿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⠰⡝⠻⣦⣵⣥⣦⠶⠶⠟⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢿⣧⢀⣤⣈⡉⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⢏⠖⡈⢻⣷⣿⣧⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣧⡟⣿⣿⣿⣿⣿⣾⣿⣻⡟⣿⣫⣾⣿⣿⣿⣿⣷⢏⠀⠁⠈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⢿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡟⣿⣿⣹⣿⣿⣿⠷⠆⠠⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠷⠆⢰⣿⣿⡿⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠷⣿⣿⣿⡿⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⠇⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢋⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠹⢁⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠟⠁⠸⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸⣟⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⡡⣝⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠋⣿⡾⠃⠰⢤⣤⡈⢿⣆⠂⢶⡴⣢⣤⣠⣶⣝⣷⣔⣚⠣⠖⠀⠸⣿⠸⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢃⣴⡆
⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⠀⠀⠀⠀⠈⠙⠻⠿⢷⣦⡄⠀⠉⠿⠋⠻⠿⣿⣿⠷⠤⣀⠀⢿⡖⣿⠀⣤⣤⣤⣤⣤⣿⠛⡙⠻⢿⣾⣿⡃
⠀⠀⠀⠀⠀⠉⠳⣤⣾⣿⡀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⠤⣄⡁⠚⣷⢿⣦⣄⠀⠉⠹⠿⣿⣿⡠⡖⠲⠤⣤⡁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠀⠀⠀⢀⣄⠠⢠⣾⡆⠀⢊⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⠅⠀⠀⠈⠑⠲⠤⠉⠁⠀⠀⠈⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠂⠸⠍⠉⠉⠀⠀⠀⠬⠅⠩⠤⠖⢢⡄⢄⡤⢠⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡶⣿⠿⢺⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣶⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⠟⡿⠃⣉⠷⡔⢯⠠⢟⣿⡏⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⢿⠇⠈⣉⠹⡏⠛⠟⠿⣿⣿⣿⣿⡫⡭⢡⡘⠀⠀⠸⠗⠄⢀⠈⢀⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⠳⠆⠁⠀⠉⠀⠀⠁⠀⠀⠃⢰⢿⢻⣿⣷⡕⡀⠳⢤⠀⣀⡠⠘⠃⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢸⡇⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⢈⠕⠀⠋⠿⢈⡓⠼⠋⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠃⡢⠀⠀⣨⣤⡖⠳⢤⣠⣄⡀⣠⣦⣄⡀⠀⠀⠀⠁
⠀⢀⡴⠾⢿⣟⡿⢟⡩⠂⠀⣀⡠⠤⣼⡿⠿⠀⠀⠀⠀⠉⠉⠉⣿⣿⡟⠾⠆⠘⢄
⠀⢸⡷⠛⠉⢡⠒⡋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠀⠀⠙⢳⣌⣁
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣅
⠀⠀⠀⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠆

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⢲⢄⠲⣄⡀⠀⠀⠀⠀⢀⡠⠖⣡⠎⠀⢀⠀⠀⢀
⠀⠀⠈⢮⠳⣤⣹⠒⢲⠐⠒⠫⢰⠂⡞⠀⠀⢹⣰⡁⢸⡄⡀⠀⠀⢳⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡆⠀⠀⢸
⠀⠀⠀⠈⠣⡘⡟⠀⠈⠀⠀⠀⠛⡞⠋⠀⠀⠸⠏⡹⢈⡇⢹⡖⠛⢸⣅⠐⠂⡟⣳⣻⠎⡁⠏⣾⠗⣘⡃⠀⠀⠀⣥⣸⡔⠛⠯⢀⢻⠸
⠀⠀⠀⠀⠀⠹⡟⢛⠀⠀⠚⠀⡴⣧⡀⠀⠀⠀⠋⠀⠀⠀⠉⠁⠂⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⢀⡇⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠹⣤⣶⢐⣶⠂⠈⣽⣎⡉⢳⣲⡦⢶⡶⣶⢤⣤⡤⢤⣤⣶⣒⠒⢚⡓⢯⣿⡟⢶⢶⣤⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍⠀⠀⠀⠸⣗⣉⠜⠉⣱⠀⢹⡈⠁⢸⡎⣌⠑⠢⡈⢘⡶⣈⣢⠔⠛⠉⠙⠓⢽⡛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠰⠚⢟⣀⣰⣤⣤⣤⣷⡾⠶⠶⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠁⠀⠀⠀⠈⠡⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠈⠂⠀⠀⠀⢀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢁⣾⡆⠀⠀⠀⢸⠄⢰⣟⢀⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠱⣄⠀⠀⠁⢸⣗⣀⣀⣀⣀⡀⣀⠀⠠⠤⠐⠛⢻⡇⠀⠀⠀⠇⢰⡿⣿⠉⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢳⡀⠀⠈⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⣠⡟⣇⢹⡷⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⣿⠙⠸⡆⠻⣄⣬⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⣧⠀⠻⡄⠹⣆⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠹⣷⣄⠹⣆⠸⣧⡔⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢹⠘⡆⢻⠀⢿⡷⣜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡜⢀⡇⡎⠀⠈⢻⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡼⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⠀⣸⢱⠃⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠬⢸⡃⡀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢛⣯⡔⠠⣠⡥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠚⠂⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⡀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⢀⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⣍⡀⠀⢀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⡀⠀⢀⣩⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣷⡂⠀⠀⠱⣌⠢⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠔⣡⠎⠀⠀⢐⣿⣿⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣿⡯⠀⠀⠀⠈⢧⡙⢦⡻⣷⣴⣶⠶⠶⣶⣤⣾⢋⡴⢋⡼⠁⠀⠀⠀⢽⣿⡟⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠸⣿⣯⣀⠀⠀⠀⢨⠗⠈⣛⠈⠁⠀⠀⠀⠀⠈⢁⣛⠀⠺⡅⠀⠀⠀⣀⣽⣿⠇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠻⢿⣭⣄⡀⠀⠀⣤⠞⠁⠀⠀⠀⣴⣆⠀⠀⠀⠈⠳⣄⠀⠀⢀⣠⣭⡿⠟⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢰⣷⣦⠙⠋⠁⠀⠞⠁⠀⠀⠀⠰⡄⢻⠟⢠⠆⠀⠀⠀⠈⠳⠀⠈⠻⢋⣴⣾⡆⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⡿⢋⠀⢀⠀⠀⠀⠀⠀⠑⢦⡀⢻⡀⢀⡏⢀⡴⠂⠀⠀⠀⠀⠀⡀⠀⡙⣿⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡞⣱⠏⢠⡏⠀⠠⣄⣀⡀⠀⠀⢻⡌⠀⠀⢠⡟⠀⠀⣀⣀⣠⠄⠀⢻⡀⠹⣎⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠟⠀⠘⣧⠀⠀⠸⡏⠛⢳⣆⠀⠀⠀⠀⠀⠀⣰⡞⠛⢹⠅⠀⠀⣼⠃⠀⠻⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠁⢺⡀⢀⠈⠀⠀⠀⢿⣾⡏⠙⠀⠀⠀⠀⠀⠀⠋⢽⣷⡗⠀⠀⠀⠁⡀⢠⡗⠈⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠂⠸⣇⠈⣷⣄⠀⢴⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⡦⠀⣠⡾⠁⣸⠃⢐⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠀⢿⡄⠈⠻⣷⣾⣿⣟⠀⠀⣴⠀⠀⠀⠀⣦⠀⠀⣿⣿⣷⣾⠟⠁⢠⡏⠀⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣇⡄⠀⠀⠀⠉⠻⣿⣿⠀⠀⢹⠀⠀⠀⢀⡏⠀⠀⣿⣿⠟⠁⠀⠀⠀⣠⣸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⣦⠀⠀⠀⠀⠻⢿⡆⠀⠸⡇⠀⠀⢸⠇⠀⢸⡿⠟⠀⠀⠀⢀⣴⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⡀⣄⠸⣇⠀⠀⠃⠀⠀⠈⠀⠀⣸⠃⣤⢀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡄⠙⠀⣠⣴⣶⣶⣦⣄⠀⠋⢠⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣦⣽⣭⠉⢉⣭⣧⣴⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⣿⣿⣤⣴⣿⢿⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⣄⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⣦⠀⠀⠀⢰⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢿⣧⠀⢀⢠⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠋⠿⢷⠎⣼⡿⣹⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣃⢈⣠⠂⠠⠂⠀⢏⢞⣿⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⣿⣦⣤⡽⠟⠛⠻⣛⣀⣉⣿⣿⣷⡄⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠠⠒⠀⠀⠀⠩⣹⡷⢶⠾⡿⣿⡎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠐⢄⠀⠀⠀⠀⢰⣿⣶⣿⣧⣭⣿⣿⣄⣿⠁
⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀⢀⣾⣤⣴⣦⣼⣿⣦⣤⣾⡟⠃⠘⡏⠙⣿⢸⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠘⠋⠉⠀⠀⠀⠀⠙⢿⣿⣿⡅⡀⢣⡳⢐⣵⠟⣽⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠷⣚⣤⡾⢟⣵⠞⣡⠛⠹⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠀⢿⣻⣭⡾⢛⣵⠟⠁⠀⠤⣀⣙⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣇⢦⡿⢟⣥⣾⡫⠁⡅⢘⡴⢛⡭⠿⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⠉⣤⢸⣿⡟⠋⢡⠐⣂⣴⡟⣴⠋⠀⠀⡀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⠏⣼⠟⠃⠋⣠⣾⣿⡟⣼⡟⠤⠄⠠⣌⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠈⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⣰⢶⡖⣀⣠⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⡎⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⣩⠀⢀⣀⣀⡀⢉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⣉⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣭⣉⣉⣙⣶⣲⠄⠀⠀⠀⠀⠀⠁⢀⣀⣐⣻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠈⠙⠻⠿⠿⣿⣯⣿⣭⣤⡄⢀⣀⣀⣠⣤⣠⣿⣻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠙⠛⠙⠛⠋⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⣼⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⣠⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣄⣤⡄⣰⡟⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⣿⣀⡹⢧⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣍⣼⣿⣿⣿⣿⣿⣿⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⠙⠛⣥⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⣡⣾⣿⣿⣿⡇⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⣿⣿⣿⣯⠃⠉⠁⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣽⣿⣿⣿⣿⣿⡇⢀⣤⣶⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢛⣿⡇⠈⣿⠿⢟⠉⢀⣤⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡏⠀⣿⣿⣿⣿⡇⠀⢸⣀⣼⣶⣿⣿⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣷⣾⡇⠀⢀⣉⣀⣸⡇⢀⠘⣿⠟⢻⣟⣿⣧⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⣿⠟⠙⢻⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣼⣯⣿⠉⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠻⠀⠀⠀⣿⣿⣟⣻⣿⣥⣤⣿⢿⣋⣽⣿⣿⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡛⢷⠷⣤⢀⣼⣿⣿⣿⣶⣯⣿⣹⣿⣯⣿⡿⠃⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣯⣀⣀⣸⣿⣿⣿⣧⡈⠉⠉⠛⠛⠛⣻⣿⣇⠀⠀⠀⣸⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⣾⣷⡄⣀⠀⣿⣿⣿⣿⣷⣤⡀⠶⢀⣰⢿⣎⠿⣦⣤⣾⣿⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⢬⡿⣭⣥⡴⣿⣿⣿⡻⠿⣏⣿⣟⠉⠁⢙⣿⠄⢈⡉⣿⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⡇⠀⠻⣿⣻⣿⡿⣿⢿⣿⡷⠶⢾⣿⠃⠸⢿⣿⣿⡷⣿⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡞⠀⠀⢷⠀⠀⠙⣷⡉⠀⠉⠉⣿⣯⣀⢘⣟⢀⣧⡄⢸⣿⣿⠿⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⡀⠀⠀⢨⠁⠀⠈⠛⠋⣣⠍⢸⡟⢉⣽⠁⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣖⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⢰⣦⠀⢰⡆⢰⡦⠀⢰⡆⠀⣶⠶⣶⡄⠰⢶⣶⠆⢀⣿⡟⠛⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⣿⣩⣿⣇⠀⢸⡿⢷⣼⡇⢸⡇⠀⢸⡇⠀⣿⠶⢾⣇⠀⢸⡇⠀⠀⠻⠿⢶⣶⣤⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⣿⡄⠸⠇⠈⠻⠇⠈⠿⠶⠾⠃⠀⠿⠶⠾⠏⠠⠾⣿⠆⠐⣶⣦⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣾⣿⠀⠸⣧⡀⠀⠀⠀⠀⢀⣼⠇⠀⣿⣷⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠂⣼⣿⣿⡆⠀⠿⠿⢷⣒⣒⡾⠿⠿⠀⢰⣿⣿⣧⠐⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⣿⣿⡇⢀⡆⠀⢸⣿⣿⡇⠀⢰⡄⢸⣿⣿⣿⠀⢸⣧
⠀⠀⡀⠀⠀⠀⠁⠠⡸⣿⡇⠀⠹⣿⡿⠁⠘⠻⠄⢸⣿⣿⡇⠠⠞⠃⠈⠿⣿⠟⠀⢸⣿⢇⠄⠈⠁
⠀⠀⠀⠀⠂⢰⡀⠀⠀⣸⣿⡆⣤⡀⠀⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠀⠀⣤⢰⣿⣏⠀⠀⢀⡆⠑
⠀⠀⠀⠁⠀⠈⢳⣠⣾⣿⡿⠉⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠁⢿⣿⣷⣄⡞⠀⠀⠈
⠀⠀⠀⢀⡖⡀⠈⠱⡝⣿⣷⣤⡄⠀⠀⠉⠟⠁⢀⠀⠀⠀⠀⡀⠈⠻⠉⠁⠀⢠⣤⣮⣿⣿⠋⠁⢀⢶
⠀⠀⠀⠈⠀⠁⠀⣀⢁⡿⠿⠿⠿⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠾⠿⠿⢿⡀⣀⠀⠀⠀⢁
⠀⠀⠀⠀⡔⠀⠀⠸⣿⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠘⣿⠇⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣇⡿
⠀⠀⠀⠀⠀⠈⠀⠀⠈⢳⣾⣭⣟⠛⠛⠛⠛⠻⠇⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⣻⣭⣷⡞⠁⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠉⢁⣀⣀⣀⣀⣈⣀⠀⠀⣀⣁⣀⣀⣀⣀⡈⠉⠉⠩⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⠁⠀⠂⠀⠀⠀⠘⣿⣿⣿⣿⡏⠉⣋⣙⠉⢹⣿⣿⣿⣿⠃⠀⠀⠀⠐⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣛⣛⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⠇⠈⠛⠛⠃⠸⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠒⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠙⠟⠁⠀⠙⠋⠀⠈⠻⠋⠀⠙⠟⠁⠈⠻⠟⠁⠈⠛⠁⠀⠙⠟⠁⠀⠙⠋⠀⠉⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⢹⣾⡏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⣿⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡇⢸⡄⣿⠉⣽⠟⡛⠳⢦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡶⢻⡈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⠉⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡾⠃⣠⠞⢷⡀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⢴⣶⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣠⠏⢀⡾⠁⠐⠛⠻⣦⡀⠈⠉⢙⣿⡟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠏⠀⠈⠀⣴⠀⢠⡀⠀⢷⠀⠀⣾⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡏⢀⡾⠀⣼⠃⣀⣸⡇⠀⢸⡇⠀⡇⢠⠀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠀⣸⣡⣴⠛⠛⢯⣹⡇⠛⢸⡇⠀⡇⠸⠀⣯⡽⠟⠛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⠃⠙⠳⣄⡀⢹⡇⣶⢸⡧⢤⡇⢀⠀⡏⢀⣠⠴⠋⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠁⢸⠇⠀⠀⠀⠀⠙⢻⡇⣿⢸⣧⣤⡇⢸⡇⡿⠋⠁⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⢸⣇⣿⢸⡇⠀⣇⣸⣇⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠛⠒⢾⠀⠀⠀⢸⣧⠀⠈⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⣸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⠛⣓⢻⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣟⡛⣛⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁



⣿⣟⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⠀⢠⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣶⠀⠀⣶⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠂⠀⢰⣶⠄⠠⣶⡆⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠣⣿⣷⠜⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⠿⡛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⠀⠄⠀⠁⠈⠢⠀⠀⠀⠀⠄⠁⠀⠀⢠⠀⡞⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠋⠑⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠂⠙⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠟⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠟⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⢘⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⡃
⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⢛⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠨⡛⠛⠛⢛
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⢻⠇⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠚⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠛⠛⢂⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡐⠛⠛⠛⠏
⠀⠀⠀⠀⡁⢃⠀⠀⠀⠘⠛⢛⠛⡃⠀⠁⠨⠀⡁⠀⠀⠀⠀⠀⠀⢨⡀⠅⠐⠀⢘⡛⢛⠛⠃⠀⠀⠀⡘⢁
⠀⠀⠀⠀⠈⢄⠁⡀⠀⠀⠈⠛⠛⢛⠂⡄⠈⠀⠉⠓⠒⠶⠶⠒⠚⠈⠀⠅⠠⠐⠛⢛⠛⠁⠀⠀⢀⠈⡀⠁
⠀⠀⠀⠀⠀⠀⠠⠈⠀⡀⠀⠀⠈⠻⠃⢫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡝⠘⠻⠁⠀⠀⢀⡄⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⡀⠀⠀⠰⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⢀⠄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠂⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢊


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢰⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡆⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⢾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡧⠇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⡇⣾⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣷⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢠⣧⢿⡌⣷⣀⣤⣤⣤⣤⣤⣤⣀⣾⢁⣿⣾⡄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡇⠘⣿⡄⠀⠀⠀⠀⢀⣿⠃⢸⡧⢻⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢹⡇⠸⡟⡴⠋⢷⠀⠀⠀⠀⣾⠙⢦⣾⠇⢨⡛⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⠻⣆⢸⡷⣴⢦⣘⡆⠀⠀⢰⣃⡶⣦⢿⡇⠰⠟⣆⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣴⠋⡄⢸⡟⠀⣯⠀⠹⠤⠤⠤⠭⠏⠀⣹⠀⢻⡇⢠⠙⣦⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⣸⠡⠆⠀⣿⠁⠀⠘⢦⡀⡀⠀⠀⢀⢀⡴⠃⠀⠈⣿⠀⠰⠈⣧⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇⠈⡀⣼⠃⠀⠀⠀⠀⠈⠣⠈⠀⠜⠁⠀⠀⠀⠀⠘⣧⢀⠀⢹⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡀⠀⠻⣆⠀⠷⣄⣀⣴⢠⡇⢸⡄⣧⣀⣠⠾⠀⣰⠟⠀⢀⡸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⠂⠀⢹⣆⠀⠈⠻⣿⠉⠀⠀⠉⣿⠟⠁⠀⣰⡋⠀⠀⠉⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⠀⠀⠀⠀⠙⢦⡀⢸⡟⠀⠀⠀⠀⢻⡆⢀⡴⠋⠀⠀⠀⠐⠂⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⠆⡀⠀⠀⠐⠀⠈⣷⣾⠁⠀⠀⠀⠀⠈⢷⣾⠁⠀⠀⠀⠀⢀⠰⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠀⠀⠈⠂⠀⠀⠀⠀⣿⠁⢠⡇⠀⠀⢸⡄⠈⣿⠀⠀⠀⠠⠂⠁⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡟⠒⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢿⣷⣾⠿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠒⢻⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡼⠁⡌⠱⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠎⢡⠈⢧⡀⠀⠀⠀⢀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⣏⣷⣄⣠⡞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⡦⢴⣉⣁⣈⣉⡆⣼⠋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⣄⣠⡾⣹⠃⠀⠀⠀⢸
⠀⠀⠀⠀⢰⢦⣾⡉⣼⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢩⣟⠁⠀⠀⠦⠀⠀⠀⠀⠴⠀⠀⠈⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢁⣿⡴⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠞⡩⢧⠸⣟⠶⣤⡀⠀⢄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣀⠄⢀⣤⠶⣿⠇⡜⢍⡳⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⣧⠈⢣⠙⣅⣠⣽⣷⣄⠑⠀⠀⠀⠁⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⡁⠀⠀⠀⠀⢊⣠⣾⣯⣄⣨⠋⡴⠁⣼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠹⣆⠄⠣⡈⢷⣄⠐⠛⠻⣄⠀⠀⠀⠀⢠⡸⣯⠛⠷⣄⠀⠀⣠⠾⠛⣽⢇⠜⠀⠀⠀⠀⣰⠟⠛⠂⣠⡜⢁⠜⠀⣰⠏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢎⠄⠑⢄⠱⣀⣴⡞⠉⢳⡌⠃⠀⠀⠀⠹⣆⠀⠙⣆⣰⠋⠀⣰⠇⠀⠀⠀⠘⢡⠞⠉⢳⣦⣀⠌⡠⠈⠀⡰⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠢⡈⠛⢿⣢⠄⠻⣆⠀⠀⠀⠒⣿⢷⡄⢙⡋⢤⡾⣿⠀⠀⠀⠀⣰⠟⠠⢔⡿⠛⢁⡔⠀⢠⡜⠁⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠢⢄⠙⠢⢴⡿⣦⠀⠀⠀⣿⠀⢻⡌⢷⡟⠀⡿⠀⢀⠀⣼⣿⡦⠔⠋⣠⠔⠋⢀⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠁⠢⢄⡉⠙⢧⠁⠀⠸⣷⡾⡀⢀⢳⣾⡆⠀⠀⡼⠋⢉⡀⠔⠈⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠁⠁⢸⣆⠀⠀⣿⠙⣇⢘⠃⣿⠀⠀⣰⠇⠈⠁⠀⢀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⢀⣀⡀⢸⣇⠀⢻⠦⡇⢹⠴⡟⠀⣸⡇⢀⣀⡀⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠻⡄⠚⢿⡀⢸⣆⣡⣌⣰⡗⢀⡿⠓⣠⠟⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠑⢼⡇⢸⡇⢻⡏⢸⡇⢸⡧⠊⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠾⠉⢙⠏⠉⠖⠋⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⠦⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠿⢛⣋⣉⣉⣻⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠁⠙⠺⠿⠿⠿⠿⠿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠰⣶⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣟⠀⠁⠀⠀⠀⠄⢀⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⠿⠯⠿⠿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠿⢿⣿⣿⣿⣿⣿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⣀⣤⣤⣠⣤⣶⣦⣀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣮⣈⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢼⣿⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣮⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠘⠿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣻⣿⡎⣿⣿⣿⣿⢛⣿⣿⣿⣾⣿⡿⣯⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣻⣟⣍⡉⢻⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣷⣛⣿⣤⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢰⠋⠀⢹⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠗⣢⣤⣭⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣉⣿⣿⣿⣇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⣿⣿⡟⠿⢷⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⣿⡟⢻⡰⣮⣣⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⣿⣮⣿⣾⣧⣂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣼⣿⡌⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣯⠙⠣⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠟⣸⣿⣿⡿⠿⣿⣿⣿⣿⡀⠧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣿⡇⠀⢸⣿⣿⣿⣷⣀⠘⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠄⣿⡟⢃⣀⣿⡇⠀⢹⣿⣿⣿⣿⡟⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣷⣿⣯⣭⣽⣿⢟⣿⣿⡗
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⣿⣿⣇⣸⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⣿⣯⣉⣾⣿⣿⡇
⣀⣤⣶⢾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠉⠀⣹⡟⣼⣿⣷⣽⣧
⢿⣿⣿⣶⣌⢰⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠛⠒⢶⣿⠇⣿⣿⣿⣿⣿⣷⡄
⠈⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣼⣿⣿⡷⠀⠀⣀⡿⢸⣿⣿⣿⣿⣿⣽⣿⣄
⣠⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⡟⣿⠿⢿⣽⣿⣿⡿⢿⣿⢿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣷⣄⣴⣿⢃⣿⣿⣿⣿⣿⣿⡟⣫⣽
⣿⣿⣿⣿⣿⣿⣿⣧⡻⣿⣿⣿⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⣷⣿⡷⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⢋⣾⣿⣿⡆
⣍⡻⠿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣟⣭⣿⣽⣧⣿⣿⣿⣯⣽⣆⣼⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣤⣘⣻⢀⠙⣿⣿⣿⣿⣿⣿⠏⣾⣿⣧⣸⣷
⢻⣿⣷⣌⡙⠿⣿⣿⣿⣿⣷⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⡟⣿⣷⣿⣾⡿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠉⠁⠉⠀⠙⣿⣿⣯⣽⣿⣼⣿⣿⣿⣿⣿
⠀⠙⢿⣿⣿⣦⣈⠛⠻⠿⣿⣿⣿⣮⡻⠿⣹⣏⠙⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⡛⠉⠙⠛⠀⠒⠀⡁⠠⣼⣿⣿⣿⢻⣿⣿⣿⠿⢿⡿
⠀⠀⢸⣿⣿⣿⣿⣷⣶⣤⣄⣈⣉⣹⣿⣦⡟⢿⣤⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⠦⡀⠀⠀⠀⠈⢻⣿⣿⣿⣟⢠⣿⣿⣿⣇⡨⣵
⠀⠀⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣭⣻⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⣧⣄⣀⡀⠠⣼⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣦
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣎⣿⣿⣿⣿⣿⣿⣿⣜⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢠⣍⠿⠁⠉⣻⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⢿⣿⣿⢏⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣣⣶⣌⡉⠀⠐⢿⣿⣿⣭
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡝⣿⣼⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣷⡄⠉⠛⢿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡟⣸⣟⡻⠿⣿⣿⣿⡿⢿⣿⣿⣿⡎⢻⣿⣦⣿⣿⣿⣦
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣴⣾⠏⣹⣿⣯⣟⣛⣋⣩⣤⣶⣿⢻⣿⣿⣿⣿⡏⠋⣀⣋⣤⣍⣀⣄⣠⣿⣿⣿⣧⠀⢹⣿⣿⣷⣟⣿⣧⣾
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⣀⣼⠏⣼⣿⡋⣻⣿⠛⠉⣿⣿⣿⡍⣿⣿⣿⣿⣿⣿⣟⣏⣹⣿⡯⠍⠉⢙⣿⣿⣿⣿⠀⢀⠻⢿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣦⣴⣤⣤⣶⣾⣿⡟⢸⡿⠿⠿⠿⠿⠂⠀⠛⣱⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⠿⠟⠛⠛⠿⣿⣿⣿⣧⣽⠀⠈⠳⢤⡄⣀⣠⣴⣾
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⠿⡻⠍⠁⠚⠁⣿⡇⢸⡿⠀⠀⢀⣤⣄⠀⢠⣙⣻⣿⣿⣿⣿⣿⣿⢇⣀⠀⠠⠿⠶⢶⣾⣿⣿⣿⣿⡇⠃⠀⠀⠀⠀⢹⣿⡟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠆⠀⠀⠀⠀⠀⠠⠊⠙⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡌⠄⠀⠀⠀⠀⠀⣼⠁⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⠄⠀⠀⣀⠀⣿⣇⠈⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠈⢊⠤⠤⠄⠼⡏⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠙⠿⠁⠀⠀⠀⠀⣀⣄⣌⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣓⣁⢀⡀⠀⠐⠲⠦⣼⣿⡛⠻⣿⡄⠀⠈⠢⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⢛⣉⣉⣉⡀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡾⠛⢛⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠠⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢲⣿⠿⠿⠿⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢺⣤⣴⣶⣾⣿⣿⣿⡉⠂⠀⠤⢤⣤⣤⡤⠨⣍⢀⣐⣒⠒⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠖⠺⠛⢋⣉⣡⣤⣤⣤⣴⡀⠀⠀⠀⠀⠙⢻⡾⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠖⢳⣾⣿⠿⠟⠛⠋⣉⣉⣱⡀⠀⢂⠀⣸⠈⣶⠶⠶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢒⠂⢻⣁⣠⣴⣶⣿⡿⠿⠟⠛⠳⡀⠀⢦⣿⡄⢳⣶⣶⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢍⠻⡛⢿⣿⠟⣉⣠⣴⣶⣾⣿⠿⠿⡒⠺⡟⢷⡛⣷⣶⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠣⡊⠳⢌⡙⢟⣩⣴⣶⣿⠿⠿⡼⠽⠈⠍⢚⣳⣶⣶⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡢⡈⡩⠘⢿⣉⣥⣶⣶⣿⠿⡞⠟⠛⠛⡙⣷⠶⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣔⠌⡝⡻⣋⣭⣴⣶⣶⣿⣶⢲⣓⡮⢿⡶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⢉⣛⡙⠭⠭⠹⠸⠼⠼⢚⡫⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣼⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡥⠠⢀⠀⠘⢿⣿⣿⣿⣿⠷⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢙⢷⡄⠀⠀⠀⠀⠀⠀⢠⠋⡜⠀⠀⠧⠀⠃⣸⣿⣿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⡁⣠⠀⠀⠀⠀⠀⠀⠀⢀⢀⣧⠔⣶⣿⡇⡄⢸⣟⣿⣬⣛⡀⠀⠀⠀⠀⠀⠀⢨⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⡀⠀⠀⠀⠠⠀⠀⠀⢹⣷⡌⠛⡿⡇⣸⣿⡿⣩⢞⡽⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⡄⠀⠀⣷⣄⡀⠀⠀⠀⢛⢶⠁⣧⡽⠩⠉⣔⣯⡶⠋⠀⠄⠀⠀⢰⣦⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠘⠛⠻⣿⣆⠄⠀⠀⠘⠶⠬⠛⠉⠩⠑⠈⢀⣀⣠⣤⠀⠀⠸⠗⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠺⣿⠛⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⡘⣧⠀⠀⠀⢸⠀⠀⢀⡠⢄⢄⠢⣑⠬⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠛⠚⠷⣤⣄⢸⡠⡐⢕⠈⠢⢑⢌⡢⣥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠠⡀⠀⠀⡆⠀⡤⣔⠀⢠⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡟⠗⠦⡐⠑⢌⡢⣑⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠳⠀⠈⠠⠄⠣⠴⠁⠍⠂⠸⠀⠸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠂⠀⠀⡂⠀⠀⠀⠻⠶⣌⡢⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠦⡱⣄⠸⡀⠀⠃⠀⠐⠀⠀⠀⢑⠻⣾⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠈⠒⠒⠤⣄⣐⠜⡃⡈⠻⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣶⣾⣿⣾⣛⣿⣿⣷⠀⠀⠀⠀⠀⠀⣼⠀⢸⡟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠏⣦⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣧⣤⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣹⣿⣷⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡿⣏⣱⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣷⣿⣿⣆⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⠿⣿⣿⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⣿⠀⣿⣿⣿⣦⡐⣽⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⣃⣤⢤⣄⣤⣤
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣇⣴⣿⡆⢿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣛⣿⣿
⠀⠀⠀⢰⣶⣟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⣤⡿⣿⣿⣿⣆
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣨⢧⣿⣿⣿⣿⣧
⠀⠀⠀⣰⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣫⣾⡆⠀⠄⠀⠀⠐⠀⠈⡆
⠀⠀⠘⢿⣝⡻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠜⢿⣿⣿⣿⢳⣿⣿⣇
⠀⠀⠀⠀⠻⣿⣦⣙⠿⢿⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣬⣿⣶⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡂⠀⠀⢹⣿⣿⢣⣿⣿⣦⣄⠀⣀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠏⣼⠟⢛⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⡆⢠⡙⢿⣷⣿⣿⠀⣦⠂
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣟⣽⠿⠿⣿⠿⢿⣿⣏⠻⣷⣿⣿⣆⢈⣽⠏⣸⠿⣦⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠛⣺⢟⣼⢿⣷⠶⣶⣿⣏⣿⣿⣿⣥⡶⣶⡶⠶⢾⣿⣿⠀⠻⣿⣿⣿⠟⠁⠜⠻⣄⠀⠁
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣶⣶⣶⢶⣾⣿⢸⠟⠛⠛⠀⠉⣿⣿⣿⣿⣿⠿⠿⢛⣋⣓⣿⣿⣿⠁⠐⠂⢤⣤⣾⢿⡆⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠉⠁⠀⢘⣇⢸⣤⣶⣾⣆⣸⣾⣿⣿⣿⣿⣖⢀⣬⣭⣿⣿⣿⣿⡄⠀⠀⠈⠿⡀⠀⢹⡄⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⡶⠟⠛⢿⣌⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠣⠀⠀⠿⠶⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⠿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠉⠛⠿⠟⠟⠀⠀⠿⠿⠀⠸⡿⣿⡿⠿⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣇⠘⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⢻⣀⣽⣇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣷⣿⠁⠈⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠂⠚⠛⠁⠀⢲⣼⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠞⠛⠋⠁⠀⠀⠀⠀⠀⣸⠉⡧⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⣶⡂⠚⠿⠿⠋⠛⠀⠀⠀⠀⣯⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⢀⡄⣗⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢿⠀⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣡⡎⢦⣤⡿⢺⣿⣿⡿⠋⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣶⣤⣶⣾⢼⣿⣿⠁⢠⠖⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣭⠷⣌⡟⢩⠹⣇⢸⣿⡇⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣩⢳⢶⣧⡷⡿⣿⡀⠀⠀⣼⡀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠸⠙⠓⠋⠉⠀⠀⠚⠁⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣓⣒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⢛⣛⣿⣯⣭⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣟⣛⣛⠙⠉⠀⠈⠉⠉⠙⠛⠛⠛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⠿⡃⠀⠀⠀⠄⠀⠀⠐⢿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⣿⣿⣿⣿⣿⡿⠟⠇⠀⠀⠀⠀⠀⠒⠀⠿⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠿⠿⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣷⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⡀⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡩⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⣷⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⣤⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⣤⣀⠀⠱⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣸⣄⡀⠀⠐⣿⠀⢿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣏⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⢆⠀⠹⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⣿⣿⡇⢻⠀⢣⢀⣤⣄⠈⠉⠻⢿⣿⣿⢿⣿⡿⠀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣼⡄⠀⠋⠀⠀⠑⣄⠀⠀⠙⣫⣿⣿⠇⣰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⣳⣴⣿⡏⢻⡿⢠⣿⠛⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⣿⣄⠀⠀⠀⠀⠘⢿⣿⡷⣼⠃⣼⡟⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠘⠿⠟⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡧⣷⢸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⣶⠻⢿⡙⣣⡅⠚⣻⣿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢫⠀⠳⠌⣽⡘⠛⠉⠱⠞⠗⠌⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠛⠛⠟⠃⣠⡤⠄⢹⠈⠉⠉⡙⠻⣿⣿⣿⣧⡑⡗⠰⣎⠀⠐⠀⠛⠑⣂⠰⣤⠤⢤⣀⣈⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⢿⡏⠛⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠁⠸⣻⣍⠿⠿⣷⡌⣄⠙⢶⣄⣀⡢⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠈⣿⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠀⢈⡍⠁⠘⠩⠿⣈⡝⢾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠈⠸⠔⡄⠀⠂⢀⣤⡢⠾⠧⣄⣠⣄⡀⣀⣷⣄⣀⠀⠀⠀⠐⡑
⠀⠀⢀⣤⣶⣾⢻⣿⡿⢛⡆⠀⠀⠈⢀⣀⣰⣿⣿⠇⠀⠀⠀⠉⠉⠛⠙⣿⣯⣽⠷⣶⡄⠘⡀
⠀⠠⣯⣴⠶⠚⢋⡭⠔⠉⡀⠠⠐⠉⠁⠀⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠇⠀⠙⠻⣦⡀
⠀⠀⠛⠁⠀⠀⡇⡠⠊⠁⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡤
⠀⠀⠀⠀⠀⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠄
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⣀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⠟⠀⣽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢘⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⢀⠠⠂⢀⠹⢃⠀⠀⠀⢀⣀⣠⠠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠂⠒⠀⠀⠈⠉⠀⠄⠀⠀⠀⠉⠁⠈⠉⠁⠒⠂⠐⠊⠀⠄⠀⠩⠀⠀⠂⠀⢀⡀⠉⠉⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠐⠈⠁⠘⠀⠀⠀⠄⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⡀⢀⡠⠀⠯⢁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠤⠞⠀⠀⠖⠀⠠⡀⠃⠀⠀⠀⡠⠀⠀⠂⠐⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⢙⠏⠍⣿⠟⠧⠤⠼⠿⠋
⠀⠀⠀⢀⡐⡱⠂⠤⢀⡀⢀⠀⠈⢀⠈⠀⢀⠀⠀⠀⠈⢁⡅⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠁⠆⠈⠀⠀⣈⢻⠻⠃
⠀⠀⢠⡞⠀⢰⡆⠀⠀⠀⠘⠀⠀⠨⢃⣀⠀⠄⠘⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠀⠀⠀⠀⠀⠀⠠⡀⠚⢠⡐⢬⣹⠋
⠀⠀⢸⠀⢠⣞⠀⠀⠀⠀⠀⢤⡆⠀⠐⠛⢻⣦⣀⠈⢳⢿⡀⠀⠀⠀⠀⠠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⠙⡶⠁
⠀⠀⢀⠄⢰⣻⣦⠇⢀⣤⠀⠈⠳⣄⠀⠀⠀⠙⣿⣷⡀⢼⣿⣠⡴⢣⣤⢴⣥⣄⠄⠀⠀⠀⣀⠹⠀⠀⠁⠘⢳⠖⠁
⠀⠀⠘⡅⠈⢧⣻⣏⠀⡻⠄⠀⠀⠘⠙⣶⢤⠀⡈⠉⠛⠟⠿⣿⣿⣼⣿⡌⠛⠖⠲⢢⠄⢚⣥⢖⣞⡭⠾⠃
⠀⠀⠀⠀⢶⡀⣷⣿⣦⣌⠀⠋⡀⠁⠀⠀⠘⣧⠆⠀⠀⠀⠀⠀⠀⠉⠉⣷⠀⠀⡄⠀⢠⣟⠉⡼⠁
⠀⠀⠀⠀⠀⢿⡶⣿⠟⣿⡇⠘⠁⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⢀⡏⠀⠃⢧
⠀⠀⠀⠀⠀⠈⢶⠏⣈⣿⠇⢀⠄⠀⢰⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠈⠹⠀⢠⢸
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠏⡀⠁⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⠀⠀⢿⣦⠘⡇
⠀⠀⠀⠀⠀⠀⠿⣅⡇⢈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠰⡈⠿⣮⡀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠶⠀⠈⠆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠃⠰⡀⠈⣷⣦⡀⠐⠰⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⣄⠀⠀⠀⠀⠚⠒⢢⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠙⠛⠲⠤⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠄⠷⠀⠀⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⢤⣤⣤⣤⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠰⠚⠉⠁⠉⠒⠿⢿⣿⣴⣽⣿⣯⣛⠉⢹⡟⠛⢿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠘⠇⠈⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡎⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⣼⢀⣴⡿
⠀⠀⣿⣶⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣂⠠⠖
⠀⠀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣮⣁⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣾⣶⣶⣼⣶⣾⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣴⣶⣦⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣬⣰⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡟⢿⣷⡀⠉⢻⡘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣏⣽⣿⢿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢟⣿⣿⣄⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢸⣿⣿⣿⣿⠉⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡁⠀⠀⠀⡺⢟⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⢈⡴⠁⠀⠞⢻⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣾⠀⣸⢷⡇⠀⠀⣾⣿⣯⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣯⠼⠷⢧⣼⣿⣿⣿⣷⣤⣸⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡤⠀⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⣿⣿⣿⣄⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠋⠉⣩⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣥⡬
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣠⣤⣶⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⣀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⠢⠀⢐⢀⠰⡆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣬⣤⠈⢉⡄⢤⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠈⢈⢼⠠⠥⠄⡿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠈⠙⠀⠐⠁⠀⡤⠤
⠀⠀⢆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⣁⡀⠀⠀⠀⠀⠀⠀⢤⢤
⠀⠀⡤⠻⡁⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⣿⣷⣷⣶⣶⠶⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈
⠀⠀⠀⠀⢹⠒⢦⠀⠀⠀⠀⠺⠃⢀⠀⢹⣿⣏⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡾⠟⠂
⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠐⣦⢻⡄⣾⣿⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⡆⠿⠋⠀⠀⢨⣇⠀⠀⠀⠀⠀⢰⣾
⠀⠀⠀⠀⠀⠀⠘⠿⠀⠰⢦⡀⠈⠻⣑⡯⠵⠿⠃⢀⠀⢰⡖⠀⠀⠀⠀⡁⠀⠀⠀⠀⡸⡟⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⣤⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⢈⣲⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⡴⢄⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠒⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠢⢄⡈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⡇⠀⠀⠀⠀⢸⣏⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⣿⠀⠀⠀⠀⣿⠋⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢧⣿⡆⡄⠠⢰⣿⣾⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣠⣾⣿⣿⣿⣿⣷⣄⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢸⣿⡻⣿⣿⣿⣿⢿⣿⡇⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣼⢿⣿⣾⣿⣿⣷⣿⠟⣧⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠐⣿⣦⡙⣿⣿⣿⣿⢋⣴⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⣗⠈⠛⢿⣿⣿⡷⠟⠁⣾⣥⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠙⣿⡟⢶⣄⢈⣿⣿⠅⣠⡶⢻⣟⢉⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⣹⣿⣿⠉⣅⠀⠙⢻⣿⣿⡟⠋⠀⣠⢉⣿⣿⡁⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡍⠙⣿⣷⠉⠳⣤⣸⣿⣿⣇⣤⠞⠋⣿⣿⡁⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣮⡛⢙⣷⡀⠈⣻⣿⣿⡟⠁⢀⣾⡉⣩⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⣤⡤⠼⠿⠿⠧⢤⣬⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣘⣿⣷⣟⠛⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡛⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡐⢄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⡿⡿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠱
⠀⠀⠀⠀⠀⠀⠀⢸⡏⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣿⡿⣿⣏⣀⣼⣿⣿⣧⣉⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡃⠈⣯⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⡅⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢨⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⣻⢷⣽⣿⡇⠀⠀⠀⠘⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣰⣿⣿⣿⣾⣝⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⢕⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⡶⣶⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢽⣿⣿⣿⣿⣿⣲⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⣸⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⣁⡀⠀⣿⣷⣾⠉⠛⠻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⣿⡿⠀⠀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡟⣷⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⣿⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡈⡇⢹⠶⣾⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⡼⣧⠃⠈⠈⠁⠙⠃⠈⠉⠙⠛⠓⠒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡴⢋⡴⢛⣆⠀⠠⣄⣀⣀⣀⣀⣀⣰⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡞⠀⠞⢀⠈⠈⠳⡄⠀⢠⡟⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡞⢠⡄⢠⠏⠀⡇⠀⢹⠀⢸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠘⠁⣾⣠⠟⠺⣟⡇⠰⢸⠀⢺⠸⢰⣏⡿⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡀⢰⠏⠈⠳⢤⣀⡇⢺⢸⠶⢾⢀⣸⣇⣠⠖⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⠀⠀⠀⠀⠈⡇⢼⢸⠖⢿⢸⡷⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣤⣼⠀⠀⢠⡄⠀⠳⠾⠾⠀⠸⠾⠷⠃⢀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠖⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠲⠒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠹⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠉⠉⢹



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡦⠊⠙⠻⠋⠋⠓⢦⣄⠀⢠⠀⠀⠀⣠⡴⠶⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠐⢀⡦⢻⡇⠀⠀⠈⣥⠖⠻⠟⠛⣦⣭⣭⣭⣿⣃⠀⠀⠀⠀⠀⣠⡄⠀⠷
⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠃⠸⠁⣆⠀⠀⠈⠓⣒⠒⡛⠁⠀⢀⣀⣀⠀⠀⠀⠀⣀⡐⢿⡇⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⢿⡄⠐⠋⡆⠀⠀⠀⠿⠀⢷⣄⠀⠺⣧⡽⠀⢀⠷⠈⠋⣡⣼⡇⢀⡀⠀⠘⠀⠁
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣧⡀⣼⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⢨⡆⠀⡸⢻⣿⡇⠨⠃
⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⡤⠾⡈⢧⠀⠈⢠⣤⣼⣶⡄⣀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⢰⡗⠀⢸⠻⡇⠀⢀⡐⢂⠄
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⡴⠁⠀⠄⠒⢬⡁⠀⠀⠀⠉⠉⠀⠀⠀⣀⠠⠁⠀⠀⠀⡀⠀⢀⡿⠀⠀⡎⢸⡇⢄⡠⠃⣼⠁
⠀⠀⠀⠀⠀⠀⠹⢦⣠⢀⡾⠁⠀⠀⠀⠀⠸⠛⡆⠀⠀⣀⠤⠟⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⣼⡇⠀⠀⠇⠸⡇⢠⣧⠘⠘
⠀⠀⠀⠠⢂⠀⠀⠀⠉⡿⠁⠀⠀⠀⣀⣀⠀⠀⡀⠀⠘⠁⠀⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠛⠀⠀⣶⠀⠀⢣⣿⣠⠗⠀⠀⡄
⠀⠀⠀⠐⠆⠀⡀⠀⢸⡇⢀⠚⢋⡉⠀⠀⣷⠀⢿⠀⠀⠀⠀⣏⠈⠓⠰⢆⠀⠀⠀⠀⠂⠚⠂⠀⠀⠀⠀⡀⢸⢣⠟⢀
⠀⠀⠀⠀⠀⠀⠁⠀⢸⠁⣿⠀⠀⠀⠁⠒⢧⣤⣽⣄⣿⠀⠀⣿⠔⠈⠀⣨⣤⡶⠁⣀⠀⣀⠀⠀⠀⢀⣀⡃⣸⡏⠀⢡
⠀⠀⠀⠀⠀⠀⡀⠃⠸⠆⣙⠷⢀⡀⠀⠀⠀⠈⠛⠉⠙⢦⡐⣧⡤⠔⠊⠙⣄⠼⠋⠁⠀⠁⢰⠇⠀⠀⠈⢡⡹
⠀⠀⠀⣈⠙⣦⢗⢠⡴⠀⠀⠀⠀⠸⣿⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⢀⡤⠒⢿⠀⠀⠀⠀⢀⠈⣠⠄⠀⠀⣾⠃⢀⣤⡄
⠀⠀⣀⢉⡴⠃⠀⠾⠚⠓⠀⠐⡀⠀⢿⣦⠤⡄⠹⠛⠛⠶⠶⣤⠞⠉⡇⠀⠀⠀⠀⠀⠐⠞⢿⠷⠂⠀⢰⡌⠀⢁⣀⡀
⠀⠈⢁⣴⣿⡀⣄⡐⠶⡀⠀⢐⠀⠐⠘⡝⠀⠀⠀⢠⠀⠀⢠⡟⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣦⠀⠀⠿⠻⡷
⠀⠀⢨⢋⡴⢳⣼⠻⠀⠼⠀⠀⠠⠦⠀⠚⡤⣤⣤⣀⣀⣤⣿⡇⠀⢂⠀⠉⠲⣄⠀⠀⠀⣞⠓⠒⠀⢰⠀⠀⠀⠶⠆⡄
⠀⢈⠃⢠⡄⢈⠁⣀⣠⣆⢀⡀⠀⠂⢀⡖⠀⣭⣭⡭⢿⢿⠧⠄⠀⠀⠀⢀⣀⠈⠑⠲⣦⣈⠑⠂⠐⠋⠀⠀⠀⡀
⠀⠘⠶⣬⠷⣷⡆⠼⣆⠉⠿⣄⠀⢀⡯⠈⠭⠐⠀⠾⢿⣿⠿⣧⠀⠀⠀⠸⣧⠀⠀⠀⠀⠙⢦⣀⠈⢀⠃⠀⠖⠃⠰⠃
⠀⠈⡽⢣⠤⢼⠉⠘⣻⠃⠾⡆⠁⢨⠛⢀⠠⠔⢣⣾⢻⡿⠀⠸⠇⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⢉⠂⠈⠀⠀⠀⢶⠶⠅
⠀⠀⠀⢈⡿⠀⢀⡞⠁⠈⠁⠀⠀⡧⠊⠁⠀⠀⠛⠕⣉⠃⠀⠠⡇⠀⠀⢠⣤⠀⠀⠀⠀⠀⢀⡜⠀⠀⡄⠀⠀⣭⣍⠄⠀⠀⠁
⠀⠀⢀⡼⢀⡰⠋⡀⠀⠀⠈⠄⠈⣖⠀⠀⠀⠀⠁⠀⠆⠀⠀⠀⣿⠀⠀⠘⠑⠆⠀⠀⠀⡀⢼⠁⡀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠂
⠀⢸⡯⠴⣉⠰⣦⣶⠶⠏⠀⠀⢤⣍⠠⠀⠀⢀⡀⠀⠀⢀⡀⠀⢸⠆⢀⠀⡷⠄⠰⠐⠀⠐⡎⠀⠁⡠⠀⢰⠀⣦⢠⡀⠀⢀⡆
⠀⠈⠀⠚⣠⣞⠁⢰⡟⠒⠀⠀⢸⣧⡤⠖⠂⠉⠁⠚⠓⠟⠀⠀⠀⠀⠈⠁⠛⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢁⣨⡀⠈⠈⠁
⠀⠀⠀⣠⣿⠟⡻⠋⢹⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠐⠲⣲⡶⠀⠀⢘⠃⠀⠀⣀⠐⠈⢦⡀⠀⠁⠀⠀⠰⠆
⠀⢠⣴⠃⠀⠘⠁⠁⠀⠀⠈⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠿⡇⢀⣴⣈⠀⢀⠄⠁⠀⠀⠀⠻⣦⣄⢖⠲⣤⡀
⠀⠘⠁⠀⠀⢢⠀⠀⣀⠀⠀⢨⠁⠀⠀⠀⠀⡀⠀⠄⠐⣴⠀⠀⠀⢄⠀⠀⣠⠖⠙⣎⠻⣿⣯⡖⣄⠀⠀⠀⠀⠙⣌⠻⣷⢼⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣾⠀⠀⣠⡀⠀⠀⠀⣀⠈⠀⢠⠀⠀⣼⣀⡊⠀⠀⢸⡅⠀⠈⢿⡟⢮⡡⣄⠐⢀⠀⠘⣧⠉⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠁⡠⠤⠠⡍⠡⠠⣿⠁⠀⠀⠀⠁⠀⠀⠘⡏⠀⢰⡄⢈⡤⢄⡾⠄⠀⣀⠈⢳⡤⠽⠆⠒⠚⠦⢄⡐⠋⠙⠃
⠀⢀⣤⠔⠀⠠⢶⡉⠀⠀⠀⠁⠀⢀⠃⠀⠀⠀⢠⣀⡀⠀⠋⠻⡀⠈⣷⠀⠤⣸⠄⢄⣠⡄⠙⠀⠀⠀⠀⠀⢀⣀⣀⡈⠙⣿⡇
⠀⠈⠀⠀⠀⠀⢀⡨⠟⠓⠰⡇⠀⣻⠀⠀⠀⠀⠀⠈⠑⡒⠀⠀⢳⡀⠘⠀⢀⠇⠀⠀⠀⠈⠑⠂⠤⢄⡄⠒⠉
⠀⠠⡤⠒⠂⠐⠪⠀⠀⠀⢰⣇⢠⡉⠑⠢⢄⣀⣀⠒⣯⣀⣄⣀⠠⣇⠰⠇⢈⡀⠀⠀⠀⡀⣀⠀⣀⣀⣀⡥⠖⠚⠛⠓⠒⠲⠆
⠀⢀⡀⠀⠀⠀⠀⢀⡑⢂⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣶⣁⠀⠀⡈⠛⠛⠟⣛⣻⣿⣉⣁⣀⠀⠀⠀⠀⠠⠤⠒⠲⠆
⠀⠈⠁⠀⠀⢀⡴⢀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠉⠈⠉⠈⠉⠠⣿⠉
⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠘⠛⠓⠛⠛⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⠈⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿