Celebration Emojis & Symbols

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

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

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

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

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


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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠻⢿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣶⣶⣶⣄⠉⠛⠛⠉⣠⣶⣶⣶⣶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠠⣄⣠⣟⠀⠀⠀⠀⠀⣀⣀⣺⣦⠀⠀⠀⠀⢀⣼⣃⠀⠀⠀⠀⢀⣟⣀⠀⠀⠀⠀⠘⢶⣷⠞
⠀⠀⠈⠉⡿⣍⠁⠀⠀⠈⢿⣿⣟⠁⠀⠀⠀⠠⣤⡿⠷⢤⡄⠀⠀⠀⢸⡯⡅⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠼⠑⠃⠀⠀⠀⠀⠚⠑⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠏⠁⠀⠀⠀⠀⠀⠞⠘⠇
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠻⣮⡉⣫⡾⠃⠀⠀⣠⣶⢿⣦⡄⠀⠀⢠⢴⣿⣿⡦⡄⠀⠀⠀⣀⣴⣀⡀
⠀⠀⠀⠙⣿⡛⠁⠀⠀⠀⣿⣿⣈⣿⡿⠀⠀⠈⠲⢿⡿⠗⠁⠀⠀⠀⢹⠿⣯⠁⠀⠀⢠⣤⣿⣽⣇⢀
⠀⠀⠀⠈⠳⠃⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠚⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠛⠚
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣤
⠀⠀⢉⣶⡟⡛⢦⡀⠀⠀⢰⢿⡆⠀⣄⠀⠀⣤⠠⡆⢰⠄⣤⠀⠀⠀⣀⠚⣿⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠸⣇⠘⠃⣸⠃⠀⢠⡟⠛⣿⡈⠛⠁⠀⠈⢷⣿⣿⡾⠁⠀⠀⠘⠻⢀⣿⠀⠀⠀⠀⠈⢠⣿⡄
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⢀⣤⠶⣤⡀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⣠⠴⢦⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢠⣄⣀⣀⡀
⠀⠀⢸⣿⣴⣿⣷⠀⠀⠀⣠⣾⣿⣦⡦⠀⠀⠀⣿⡀⣠⣿⡀⠀⠀⠰⠐⠖⡶⠟⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⢹⣷⣿⣿⠁⠀⠀⢸⣏⣛⣹⡇⠀⠀⠀⢈⡉⠉⠉⠉
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⡶⠆⠀⠀⢠⡀⠠⣶⠄
⠀⠀⠀⠀⠘⣿⡿⠂⠀⢸⡇⠀⢀⡼⠻⠀⠀⢀⣠⡍⣤⡉⣷⠀⠀⠀⠐⣡⣰⣶⠀⠀⠀⠓⠦⠥⠤⡶
⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⣇⣞⣉⣀⣀⠀⠀⠋⠈⢦⣍⣤⠟⠀⠀⣺⣇⣿⣟⣿⠀⠀⠀⠀⠰⣷⠄

⣠⠤⣴⣶⣶⣶⣶⣶⢒⡤⢤⡀⠀⠀⠀⠀⢀⣠⣠⣤⣤⣤⣤⡤⠤⣄⣠⣀⠀⠀⠀⡀⣠⠴⣄⣀⣀⣀⣀⡀⠀⢀⣀⠦⢄
⢧⠀⠘⣿⣿⣿⣿⣿⠼⠂⢀⡇⠀⠀⠀⠀⢎⠀⠉⣿⣿⣿⣿⣿⡇⠍⠁⢨⠀⠀⠀⠉⠣⡀⢹⣿⣿⣿⣿⣿⣿⣷⠹⢀⠜
⠀⠑⠠⣽⣿⣿⣿⣿⡤⠖⠋⠀⠀⠀⠀⠀⠈⠢⣀⠘⣿⣿⣿⣿⡝⢀⠤⠃⠀⠀⠀⠀⠀⠠⡈⠛⠿⣿⣿⣿⠿⠗⢏⠅
⠀⠀⠓⠟⢿⣿⣿⡟⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠃
⠀⠀⠀⠀⠈⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀
⠀⠀⠀⠀⠰⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⢀
⠀⠐⢶⣬⣉⡋⠠⠓⢒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢊⠨⣭⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡄⣤⣌
⠀⠀⠀⠹⢉⣾⠘⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡗⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠴⠛⢻⡓⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⣠⣶⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⣴⠿⠿⠿⠿⠿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣠⠆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⠓⣦
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⠒⠛⠃
⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⢀⣀⣀⡀
⠀⠀⢠⣾⣽⡿⠿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣶⢀⣪⣿⣿⡿⠟
⠀⠀⣽⣿⣿⠆⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣶⡶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣲⣿⣿⣿⠏
⠀⠀⠈⠿⣿⣿⣿⣯⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠉⣯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠻⣵⣿⣿⡿⠏
⠀⠀⠀⠀⣿⣭⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣀⣿⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⠷⢁
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⣷⣔
⠀⠀⠀⣾⣿⡟⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣿⡏
⣤⣤⣤⣯⣥⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⢞⣱⠆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⡐⠠⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦⡀
⠀⠀⠀⠀⠀⣀⣿⣿⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠉⣿⣿⡄⠀⠀⠀⠀⢀⡃⡐⠁⢠⡆⠀⢡⠐⡀⠀⠀⠀⠀⠀⣰⣿⣧⢸⣿⢹⡆
⠀⠀⠀⠀⠀⠙⠁⣿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣿⡿⠁⠀⠀⠀⠀⠐⡎⢷⡀⠠⠇⠀⣸⢅⡖⠀⠀⠀⠀⠀⢿⣿⣿⡾⢋⡼⠃
⠀⠀⠀⠀⠀⢀⣰⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⣿⣶⡀⠀⠀⠀⠀⠀⠹⣞⡅⠀⠀⠈⣃⠾⠁⠀⠀⠀⠀⠀⢀⣙⣲⣖⠋⡀
⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⠶⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠰⠻⢶⡾⠛⠁⠀⠀⠀⢠⣤⣄⣴⣿⡿⠙⢦⣠⣤⠀⠀⠀⢸⡁⢹⣿⣿⣿⣿⠸⠁⣹⠀⠀⠀⠀⠀⠀⠀⣷⣿⠃
⠀⠀⠀⠀⠀⣠⣬⣧⣤⡀⠀⠀⠀⢀⣿⣿⡞⢋⣰⣿⣯⣿⣿⡀⠀⠀⠀⠑⠶⣿⣿⣿⣿⡧⠖⠁⠀⠀⠀⠀⠀⠀⢀⣸⣟⣀
⠀⠀⠀⠀⢸⣿⠛⡿⢻⣿⠀⠀⠀⠀⠀⠀⠈⠚⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠻⢿⡇
⠀⠀⠀⠀⠸⠿⠾⠷⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠾⠇

⠀⠀⠀⠀⢀⢔⣮⣗⡢⡀⠀⠀⠀⠀⠀⠖⢸⣿⣿⣿⡆⠲⠀⠀⠀⠀⠀⢀⠠⠀⢀⡀⠀⠠⢀⠀⠀⠀⠀⠀⣄⣀⣀⣀⡀⣀⣀⣠⡀
⠀⠀⠀⠀⡦⣿⡛⢛⣿⢰⠀⠀⠀⠀⠀⠈⠊⢿⣿⡿⠔⠁⠀⠀⠀⠀⢐⠂⡆⠀⢸⡇⠀⠈⠄⠂⠀⠀⠀⠀⣿⣿⣿⢟⣵⣿⣿⣿⡇
⠀⠀⠀⠀⠰⣝⡿⢿⣫⠖⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠨⡄⢷⡀⠾⠷⠄⡼⠁⡍⠀⠀⠀⠀⣿⡿⣣⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢺⣿⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣻⣷⡆⠀⠀⠀⠀⠀⠀⠛⣦⡅⢀⣀⠠⣤⠞⠀⠀⠀⠀⠀⠉⠀⠁⠉⠻⣄⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⣿⠛⢛⣛⠇⠀⠀⠀⠀⠀⠀⣔⣉⣯⣉⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⠁⠀⠀⠀⠀⠀⠰⠒⠄⣶⣶⣶⣶⠠⠒⡆
⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⠿⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠿⢧⠀⠀⠀⠀⠀⠀⠀⢂⠀⣿⣿⣿⣿⠀⡰
⠀⠀⠀⠀⢀⣀⣼⣁⣀⡄⠀⠀⠀⠀⠀⠀⠈⢑⣶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠏⠔
⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠉⢻⡇⣶⠲⣶⢠⡤⣤⡤⣤⢤⣤⢤⡄⣴⠖⣶⢰⡟⠉⠀⠀⠀⡄⢰⠀⡄⠀⡄⢠⠀⠠⠀⡄⢀⠀⢠⠀⣴⠀⣆⢀
⠀⠀⠈⠀⠉⠀⠃⠘⠃⠘⠀⠛⠀⠇⠘⠁⠘⠀⠁⠀⠁⠀⠀⠀⠀⠙⠛⠒⠛⠲⠳⠼⠦⠾⠤⠿⠼⠧⠞⠗⠛⠚⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠠⠄⢀⠔⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥
⠀⠀⠀⠀⢀⡎⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣛⣛⣃
⠀⠀⠀⠀⠚⠄⠀⠐⠂⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⣾⡜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠿⠿⠿⣂
⠀⠀⠀⡾⢀⠀⢀⡄⠚⠁⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠈⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠄
⠀⠀⡼⣡⡾⢃⣬⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⣶⣾⣷
⠀⣰⡿⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠠⠆⠐⢂⠒⠆⠰⠄⠰⠄⠀⠀⢷⣮⣭⣝⣛⣛⣭⣥⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠚⠀⠛⠀⠸⠂⠘⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠁
⠀⠀⠀⢀⣤⣄⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠹⢾⣿⣿⣿⠿⣿⣿⣿⡶⠁⠀⠀⠆⠀⡆⠀⢰⠀⠖⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠷⠀⠓⠐⠃⠀⠒⠀⠃⠀⠀⠀⠠⣤⣾⣷⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣶⣶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⢀⣤⣴⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⡶⠂
⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏
⠀⠘⣿⣿⣿⣿⡿⢿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠹⣟⣿⣿⣿⡿⠃⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠷⠄
⠀⠀⠈⠋⠀⠘⠀⠈⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⢴⣦⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⣰⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠉⢿⣮⡛⠛⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⡄⠀⢶⠆⠀⣶⠄⢀⣄
⠀⢰⣿⣿⣿⡯⣳⣿⠃⠀⠀⠀⠀⠀⢸⡇⠉⣇⣷⠄⢸⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣄⣸⣧⣠⣿⣠⡾⠉
⠀⢸⣿⣿⣿⣯⣿⡏⠀⠀⠀⠀⠀⠀⠘⣷⣄⠈⠉⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠃
⠀⠈⠉⠛⠛⠓⠛⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠒⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⢒⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄
⠀⠀⢀⣝⠉⣀⣀⠈⢻⣆⠀⠀⠀⠀⢸⣿⣄⠀⢀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⣿⡄⠀⠀⣴
⣠⠾⠻⠟⠁⠿⠿⠃⢸⡿⠀⠀⠀⠀⠀⢻⣿⣀⣾⣿⣿⡗⠀⠀⠀⠀⠀⠀⠉⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⣿⣷⠀⠛⣿⠛
⠃⠀⠀⠺⣶⣤⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣸⣟⠀⠀⣸⣿⣇⡀⠉
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣛⡴⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡄⠀⠘⢀⠀⠀⠀⠀⣀⣀⣚⣛⣛⣛⣂⣀⡀
⠀⣼⣹⣿⡅⢸⣿⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠀⠲⣶⣿⣿⡶⠂⠀⠄⠀⠀⠀⢻⡈⣯⣿⣿⣿⠏⣼⠃
⠀⢿⣚⣿⡇⢸⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠿⡇⠀⠠⠀⠀⠀⠀⠀⠙⠚⢿⣿⠟⠚⠁
⠀⠈⠻⣾⣿⣿⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢿⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈

⠀⠀⠀⠀⠀⣠⡿⡇⠀⠀⠀⠀⠀⠀⣤⡄⠀⣤⣿⣤⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣘⠿⠃
⠀⠀⠀⠠⠚⠁⢠⣤⣄⠀⠀⠀⠀⠀⠘⢷⣄⣀⣛⣀⣠⣄⠀⠀⠀⠀⠀⠀⠬⠿⣾⣿⢷⡴⠆⠀⠀⠀⠀⠀⠀⢰⡶⢶⣶
⠀⢀⣀⡀⣿⣷⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⣛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⠀⠀⠀⠀⠀⣴⣤⣤⣾⣿⣼⣿⣀⣀⣀
⠀⠸⠿⠇⠿⠿⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢼⠃⠀⠀⠀⠀⠀⣿⡗⣼⣿⣿⣿⣿⣿⢂⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠸⠿⠧⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠄⢠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣴⣶⣶⣄⠀⠀⠀⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠶⣀⢢⡈⠀⢀⢀⣀⣀⡈⢡⣼⢧⣀⡹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈
⠀⣹⣿⣿⣿⠇⣤⣶⣿⣗⢻⣿⠀⠴⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣤⣴⣶⣷⡄⠀⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣡⣄⠀⠀⠆
⠀⣿⣿⢿⡟⠀⣙⣣⣿⣿⡆⠃⠀⠀⠀⠀⢰⣿⣿⡟⣌⣥⠀⠀⠀⠀⢿⣿⣿⣿⣟⡁⡆⣼⠀⣤⠈⠛⠿⠃⢰⣧⡹⢿⣿⣇
⢾⣯⣿⣾⣧⣼⣿⣿⣽⡟⠁⣀⣿⠄⠀⠀⠀⠸⠟⠃⣿⣿⠀⢸⣷⡄⢼⠻⠛⢿⣿⢿⡆⠀⠀⠉⠀⠀⠀⠀⠀⡿⠟⠈⢻⣿⡇⢸⡿⣷⣦
⢰⣯⢁⠙⣿⣿⣿⠋⠀⠀⠀⠉⠉⢀⡴⠟⠀⠛⠂⠀⠈⣿⠀⠀⠉⠀⠀⠀⠀⢸⠁⠸⠇⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣀⡤⠀⠀⠷
⣼⠟⢘⣧⠈⠁⠁⠀⢀⡘⡀⠀⠀⢠⡇⢾⠆⢀⡄⠀⢾⣿⡇⠈⠀⠀⠀⠀⠀⠈⠀⢀⣀⠀⡤⠀⠀⠀⠀⠀⠈⠀⠀⣿⣆⠙⣧⠀⢠⣤⣴
⠀⠀⠛⠛⡀⠀⢠⣾⣿⣿⣧⣴⠇⣾⠀⠸⠇⢠⣿⠃⣾⡟⢡⠀⠀⠀⠀⠀⢀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⠆⠀⡔⣿⣿⣿
⢀⣀⠀⢘⣻⣷⣾⡿⠛⠛⠀⠆⣀⠋⡤⠀⠀⠻⠋⠀⠟⢐⡂⠀⠀⠐⣉⣁⡈⢀⠀⢺⣙⠁⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⣿⣿⣿
⠘⠻⠏⠀⢿⢿⣿⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⢿⣇⡀⣴⣿⣿⣷⣄⣿⣿⣿⣿⡮⠀⠀⠁⠀⠀⠀⠀⠠⢶⡀⠀⠀⠀⠻⢿⣔⠺⣾⣇⠈⠻
⣰⣶⠗⠀⠀⠊⠉⠀⠀⠀⠚⠿⣿⣿⠇⠀⠀⠈⣿⡀⠟⢿⣿⣿⣯⣿⣿⡿⠛⠁⠀⠀⠀⠀⣀⡀⠀⠀⠈⣷⡄⢠⣶⡶⠀⠈⠓⠻⣿⡆
⠈⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⠛⠀⠰⢄⣴⡻⢿⣆⢨⡿⠿⠿⣿⣯⡄⢠⣶⠾⠀⢰⠛⠿⢟⣀⣀⣠⣼⠿⠮⠁⡀⣠⣠⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠉⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣸⡟⠺⠃⠀⠀⠉⠋⠠⣀⡅⠲⠀⢠⣶⠃⢺⣿⠏⠈⣥⠀⠀⠀⠈⠛⠋⢀⡀⠀⠀⠐
⠀⢴⣶⡇⠀⠀⢠⠽⢃⡀⠀⠀⠀⠀⠁⠀⣠⣶⣦⡈⠁⣤⠀⠀⠀⠀⣀⡀⠛⠤⠀⠀⠸⠫⠀⣈⠉⠀⢀⡉⠀⢶⣦⠀⠀⣰⠿⠏⠽⠈⣗
⢰⣾⣿⡿⠀⠀⣶⠀⠈⣡⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣄⢰⡦⠀⠀⠀⡿⠓⠀⠀⠐⢁⠔⠀⠀⢙⣀⠀⣿⡄⠀⠀⠛⠀⠀⠉⠀⠀⠀⠐⠛
⠈⠉⠀⠀⣀⠀⢸⣶⡿⠃⠀⠀⠀⠀⠰⣤⣝⡛⠁⡈⢧⢸⡇⠀⠀⠀⣴⣾⠀⠀⠀⡖⠀⡀⢸⣿⣯⠁⠙⠿⠲⡷⠀⠀⠀⠀⢳⣤⠀⠀⢠
⠀⠀⠀⢸⣇⠀⢸⡿⠁⢀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⡦⢠⠤⢸⡏⠀⠀⠐⠉⠘⠻⡿⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀
⠀⢀⣤⣤⣤⡐⠛⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠋⡹⠀⠀⠀⠀⠀⠀⢀⣬⢉⣇⠒⠀⠀⠀⠀⠀⣩⠃⣸⣇⠀⢺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣻⣿⣿⣿⡏⠀⢰⣶⣧⣶⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠻⣥⣌⣬⣥⣦⡀⣿⠛⠂⠀⠸⣟⣹⣿⣷⣿⣿⢃⡀
⠀⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⢠⣾⣿⣷⡄⣠⠀⠀⡀⢰⣿⣿⣿⣿⣿⣷⣤⣤⣴⠆⠀⠉⠉⠉⠉⠀⢹⣿⣿⡇
⣼⡿⠿⠿⠁⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣷⠸⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⢿⣄⡀⠀⠀⢀⣸⣿⣿⣿⣷⣶⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠘⢄⠀⡠⠁⠀⠀⢠⢊⡠⠔⠊⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠚⠓⠒⠒⠒⠒⠒⠒⠛⠂⠀⠀⠀⠈⠁⠓⠂⠒⠈⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⢩⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢤⠤⡤⠄⠶⡐⡟⠠⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢘⡀⢱⠁⡘⠀⠀⠀⠀⠀⣀⣠⠁⠀⠀⠹⠉⠀⠑⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠊⠀⠒⠀⠈⠃⠀⠀⠀⠄
⢀⠀⠀⠀⠀⢐⠈⢙⡎⣞⠉⢐⠀⠀⢰⠁⠀⠈⢄⠀⠀⠠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠁⠀⠀⠀⠀⠀⠁⠈⡅⡇⠀⠁⠀⠀⠈⢆⠀⠀⠀⡓⠲⠷⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠤⢀⡅⣇⠠⠆⠀⠀⠀⠀⠈⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⡍⠆⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠉⠆
⡀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠔⣁⠠⠘⠃⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢀⠔
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⠙⠛⠛⠙⠋⢛⠄⠀⢦
⡄⢀⡠⠊⠀⠀⠀⢀⣀⡤⢺⠓⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠢⣀
⠉⠁⠐⡖⡶⡀⠘⠣⣸⠈⠘⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠀⢠⣦⣘⣁⣴⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠓⠄⣀⣠⡇
⠀⠀⠀⠉⠀⠈⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠘⡤⠤⡇⢹⠠⢬⠃⠀⠀⠀⡸⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠈⡆⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⡇⣸⠀⢸⠀⠀⠀⠀⡇⠀⠀⠈⣦
⠂⠀⠀⠀⠀⢀⠎⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠓⠚⠐⠊⠀⠀⠀⢸⣀⢀⠀⠂⡠⠃⠀⠀⠐⠒⣤
⠷⢀⠀⠀⠀⢾⣀⠀⠀⠀⣉⠆⠀⠀⠀⠀⣠⠐⣑⣊⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠺⢦⢥
⠒⡎⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠘⠉⠉⠁⠉⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠒⠲
⠀⡇⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤⠀⠀⣀⠃⠀⠀⠀⠀⠀⡠⠚⣍⢢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠
⠉⠀⠀⠀⠀⠀⠃⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⠀⠄⠊⠁⠀⠀⠀⠀⠌⠀⠀⠑⡒⠉⠐⡄⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠈⡄⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠈⢆⠀⠀⠀⠇⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠈⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠜⡆⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠱⠤⡼⡄⠔⠉⠀⠀⠀⠀⢀⠤
⣉⢢⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢉⡹⢒⠐⠤⡠⢤⠖⠀⠀⠁⠀⠒⠚⠀⠀⠀⠀⠀⠀⠀⣀⣔⣈⣁
⠈⠉⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠋⠀⠑⠎⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⡀
⠀⠀⠀⠀⠀⢀⠂⠀⠁⠉⠉⠁⠀⢢⠀⠀⠀⠀⠀⡼⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡠⠚⣌⢢

⣰⡶⠀⠲⣶⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⢸⢉⣉⢹⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠢⠀⠄
⢽⣇⠀⢀⣿⠅⠀⠀⠀⢈⣿⣻⡅⠀⠀⠀⠀⢸⠐⠒⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⠀⠀⠀⠀⠀⠄
⠀⠛⠓⠛⠃⠀⠀⠀⠀⠈⠁⠘⠓⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛

⠀⢶⣦⣶⠂⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠀⢠⡿⣥⠀⠀⠀⠀⠸⣧⣾⣷⣴⡇⠀⠀⠀⢲⡞⠰⠠⠤⠀⠀⠀⠀⠢⣿⣿⠕⠀⠀⠀⢰⣶⣾⣿⣷⣶
⠀⠻⣤⡾⠀⠀⠀⠀⠘⠁⠀⠀⠈⠑⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡜⢣⠀⠀⠀⠀⠀⠀⠈⠛⠁

⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⡇⢀⣤⣀⠖⠀⠀⠀⠀⠀⠀⢀⣤⣾⠀⠀⠀⠀⠐⠿⠈⠀⠀⠀⠀⠀⣤⣴⣧⣤⠀⠀⠀⠀⣼⣯⡊⠙⡆
⣇⢋⣀⣁⣀⠀⠀⠀⠸⠇⠿⠻⠟⠿⠀⠀⠀⠀⠐⣿⡖⠀⠀⠀⠀⠀⠿⠿⠿⠿⠀⠀⠀⠀⠙⠢⣝⠴⠃
⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⡖⠒⠒⣒⡒⡄⠀⠀⠀⣠⣴⣮⡭⣄⠀⠀⠀⠀⣙⡿⣏⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⢀⣼⣿⣿⣷⡶
⠧⠭⠤⠭⠤⠇⠀⠀⠘⢔⡻⠿⠃⠁⠀⠀⠀⢸⣿⠴⣻⡇⠀⠀⠀⠰⠮⠽⠯⠽⠆⠀⠀⠀⠻⢿⣿⡿⠃
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠈⠻⣦⡀
⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠀⠈⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⠁⠀⠀⠀⠀⢈⣿⣦⡀
⠀⠀⢀⣴⠟⠁⠈⠻⣦⡀⠀⠀⠀⠀⠹⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠏⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⣦⡀
⠀⠀⠀⠻⣦⡀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠈⢻⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⡟⠁⠀⠀⠀⢀⣴⡟⠁⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣹⣷⠶⠟⠛⠛⠉⠙⠛⠛⠻⠶⣾⣏⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠙⣷⡶⠟⠉⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠉⠻⢶⣾⠋⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⢠⣾⠋⠀⠀⣠⡶⠟⠋⠉⠁⠀⠀⠈⠉⠙⠻⢶⣄⠀⠀⠙⣷⡄⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡿⠁⠀⣠⡿⠋⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⢿⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⣼⠏⠹⣧⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⡿⠀⢀⣀⣤⣤⣤⣼⠏⠀⠀⠹⣧⣤⣤⣤⣀⡀⠀⢿⡆⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠈⠻⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠁⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⣿⡀⠀⠀⠀⢸⡟⠀⠀⢀⡀⠀⠀⢻⡇⠀⠀⠀⢀⣿⠁⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡄⠀⠘⣷⡄⠀⠀⣼⣧⣴⠾⠛⠛⠷⣦⣼⣧⠀⠀⢠⡾⠃⠀⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⢿⣄⠀⠈⠻⣦⣄⠙⠉⠀⠀⠀⠀⠀⠀⠉⠋⣠⣴⠟⠁⠀⣰⡿⠁⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣹⣷⣄⠀⠀⠙⠻⠶⣦⣤⣤⣤⣤⣴⠶⠟⠋⠀⠀⣠⣾⣏⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠶⠶⢶⣾⠋⠀⠙⠷⣦⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣠⣴⠾⠋⠀⠙⣷⡶⠶⠶⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣠⡾⠟⠛⠛⠷⠶⠶⠶⠶⠾⠛⠛⠻⣷⣄⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⢱⣿⣿⣿⣧⡀⠉⠉⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣿⡿⠀⠈⣿⡿⢀⣀⣀⡀⣿⣿⣿⣰⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠰⣿⠇⢸⣿⣿⣇⠛⠋⠁⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⣾⣿⣷⡸⠛⠉⢸⠁⢀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠿⠋⢹⡇⠀⣀⡘⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⠟⠉⣿⠀⢀⣘⢳⣾⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢹⡇⠀⢀⠛⣶⣿⣧⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢳⣾⣿⠀⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠘⠟⠿⠀⠻⠿⠗⠘⠿⠛⠃⠻⠿⠟





⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠄⡀⠀⢤
⠀⠀⢏⢀⠀⠀⠀⠀⠀⠒⠁⠀⠀⣀⠀⠀⡼⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠠⠘⠆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠙⣆⠀⠀⠀⠠⡠⡄⠀⠀⠀⠘⠉⠂⠀⠀⠀⢇⡠⠀⠈⠉
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠅⠤⠒⠁⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠂⣤⠁
⠀⠈⠀⠀⣴⠀⠀⢀⡀⢰⡆⢢⠀⠀⢠⠀⠀⠀⡤⠠⡀⢰⡄⣀⢀⠀⢤⠄⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠙⡀
⠀⠀⠀⠀⡟⠀⠃⣼⢡⠀⡇⠁⡆⠀⠈⣧⠀⠀⢿⠐⠄⢸⠀⣿⠀⠀⢸⠀⡏⢀⠸⡆⠀⢠⠄⢳⡐⠀⠀⠄
⠀⠈⠀⠀⠁⠀⠘⠃⠀⠀⠁⢠⡇⠈⠀⠇⠀⠀⠸⠤⠂⠈⠀⠟⠀⡀⠈⠀⠃⠀⠀⠃⢠⠟⠂⠀⡇⠀⠰
⠀⠀⠀⠈⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠆⡄⡈⠀⠐⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⡄⠀⠁
⠀⠈⠀⠀⠀⠆⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢗⡂⠨⠈⠐⢱⠀⠀⠀⠎⠑⠊⢁
⡀⠀⢀⠀⢀⠖⠁⠤⡀⠀⠀⡤⠀⠀⠈⠂⠐⠄⠄⠀⠀⠀⠀⢠⣤⠴⠦⠒⠛⠁⠀⠀⠈⠢⠠⠁⠀⣀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢸⡀⢍⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡀⠀⠀⠀⠴⠀⠀⣠⢄⡠⠲⡴⠒⡤⠒⡤⠲⠔⠲⠀⠀⠀⠛⠁⠀⠀⣀⡤⣾⢢⠀⣀⣀⣠⠤⠃⢇⣀⣀⡀
⠀⠀⠈⠘⠉⠁⠀⠀⠀⡀⠀⡇⠈⠀⠠⠀⠀⢉⠓⢶⢤⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⢋⡉⠀⠀⠀⡀⠉⠒⣄⢀⣠⡀⡰⠊⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠈⡇⠀⢧⠀⠀⠀⠀⠘⢡⡄⠘⢀⠜⠉⠉⠟⠒⠲⠒⠒⠶⠒⠲⠒⠒⡂⢉⠋⠀⠈⢆⠇⢀⡀⠁⠀⠀⠀⠁⠀⠀⡷⠋⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⢂⡀⠘⡄⠸⡄⠀⡄⠀⠀⢈⠁⠀⠃⠀⠒⠀⠸⡔⠁⢀⡀⠘⣤⠁⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣠⡀
⠀⠀⠀⠀⠀⠁⠀⠉⠙⢦⡘⢆⠱⡀⠃⠰⣦⣾⠁⠀⠀⡀⡀⣀⡀⠀⠀⠘⠃⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠚⠃⠀⠀⠂⠀⡏⢡⣄⠐⡎⠀⠆⠀⠨⢾⡁
⠀⠀⠀⢀⠀⠀⠀⠄⠆⠄⡙⠌⠃⠀⠀⠀⠙⠃⠀⠀⠘⠛⠉⠉⠉⣀⠀⠴⠀⠜⠇⠀⢆⢀⠀⢠⡗⠚⡁⠀⠀⠀⠀⣈⠁⠀⡇⡀⠁⡀⠇⠀⠀⠀⢈⣿⡆
⠀⠀⠀⠀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠈⠀⡠⠂⠉⢱⠀⠄⠀⠀⠀⠈⠀⢀⠀⢠⣄⠀⠲⣄⣯⢀⠀⠜⠃⠀⣰⣄⡀⠀⠠⠄⠀⡯⡐⢃⠄⣷⠀⠀⠀⢀⣿⡇
⠀⠀⠀⡞⠁⠀⠀⠀⠈⠱⡄⠀⠀⠈⡀⢸⣁⡉⠤⡇⢐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠦⠀⠁⢡⠀⡈⢀⠀⡠⠛⡼⠢⠀⠀⠁⠀⠁⠙⠓⠒⠛⠀⠀⠀⠤⠖⠃
⠀⠀⠀⡁⠀⠀⠀⠀⠀⢣⢹⠀⠀⠀⠠⠈⢇⠀⠀⠁⠠⠄⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠙⢸⠀⠇⢀⠞⠀⠀⠀⣀⡀⠀⠀⠁⠀⠂⠰⠀⠖
⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⢁⠄⠓⠤⠃⡐⠀⠀⢀⡔⣒⠀⣄⠀⠐⠓⠀⠀⠨⠀⠀⡞⠀⠀⡀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⡉⠑⣄
⠀⠀⠀⠀⠳⣄⠀⢀⡴⣫⠎⠀⣄⣀⣀⠀⠈⠀⠠⠀⠀⠀⠀⢸⡑⠂⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠉⠀⠀⠀⢠⠞⠉⠲⡄⠀⡴⠁⠀⠀⢘⠀⢸
⠀⠀⠒⠓⠀⠀⣝⡿⠿⠀⣠⡐⢉⠰⡁⠀⠀⠀⠸⠡⠀⠀⠀⠘⡀⠈⠉⠇⠀⡰⣦⢶⢾⠎⡇⠀⠀⠀⠀⠲⠂⠀⠀⡇⠀⠀⠀⠘⣾⠀⠀⠀⠀⡜⢀⡏
⠀⠀⠀⢠⡀⠀⠀⢣⠀⠀⠀⢠⠁⠉⠃⠀⠀⠀⠀⠀⠀⣤⠄⠀⠑⠄⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⠞⢠⠞
⠀⠀⠀⢸⠆⠀⠀⢠⠁⠀⠀⠀⠀⠀⣀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⠔⢺⡄⠐⠒⡂⠖⠂⠀⠀⠈⢦⡀⠀⠀⠀⢠⠞⢁⡴⠃⠰
⠀⠀⠀⠰⡃⠀⠀⠀⡆⠀⠀⣀⣀⣀⣷⣍⡀⠀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⢊⠉⠀⠀⢸⠅⠀⠛⠂⠤⠀⣀⠀⠀⠀⠙⠢⢄⡀⡠⠚⠁⢠⡆⠀⠀⠿
⠀⠀⠀⢚⡄⠀⠀⢠⠁⠀⣀⣨⠷⠀⣿⠀⠭⢩⣉⣍⠉⣭⠭⣍⠩⣤⠖⠀⡦⠖⣽⣠⠴⠆⣸⣠⠤⠒⠒⠈⠉⠉⠀⠀⠤⠀⠀⠀⠽⠗⠀⠀⣀⠀⠁⡀
⠀⠀⠀⢈⡆⠀⠀⠀⠇⠀⠳⣄⠀⠀⣿⠀⠘⢠⠞⢺⡀⡷⢮⡁⠀⣾⠀⠀⢰⡾⠃⠀⢀⡴⠋⢀⡠⠖⠚⠉⠉⠓⠦⡀⠀⠀⠀⠀⠐⡇⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠠⣗⠀⠀⠸⡀⠀⠀⠈⠑⠦⣜⣦⣤⣄⣀⣀⣀⣁⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⠁⠀⣰⢋⡤⠖⣋⣉⠙⢲⡀⠹⡄⠀⠀⠀⢘⠀⠀⠀⡠⢄⠠⢄
⠀⠀⠀⠐⢏⠀⠀⠀⠃⠀⠰⠀⠀⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠎⡠⠊⢁⡀⠙⡄⢷⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢉⠔⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠃⢀⡀⠴⠀⠀⠀⠀⡔⠦⠲⠚⠖⠓⠳⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠁⠀⠁⠈⠀⠁⠸⠀⠇⠀⠀⠀⠰⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⡀⣀⣀⣀⡀⣀⣀⣀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀
⣿⢿⠿⠿⢿⢟⡻⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣛⣛⣻⣿⣟⣻⣛⣻⣛⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠀⢸⣿⣶⡦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⢸⣿⣿⠗⠀⢰⣤⣤⣤⠀⢠⣤⣤⣤⠄⠀⣤⣶⣶⠆⠀⠹⣿⣿⡇⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠈⣿⡿⠃⠀⠀⢻⣿⡏⠀⠀⠘⢿⡿⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣶⣄
⠀⠀⠀⠀⠀⠀⣰⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠆⠀⠀⠀⠀⡶⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⣾⣷⠆⠀⠀⠀⠹⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠸⡿⠀⠀⠀⣴⡯⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢰⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢿⠇⠀⠀⢠⣿⡄⠀⠀⢸⣷⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣼⣄⠀⠀⠀⣼⣤⠀⠀⠀⣰⣇⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡄⠀⠀⠘⠿⠇⠀⠀⠀⠛⠃⠀⠀⠀⠉⠃⠀⠀⠀⠛⠋⠀⠀⠀⠿⠿⠀⠀⠀⣴⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⡀⠀⠀⠀⠀⠿⠋⠁⠀⣿⣶⡆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠻⣿⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⢹⡿⠋⠀⢻⣶⡶⠀⢰⣶⣤⠄⠠⣤⣶⠆⠀⢶⣾⡇⠀⠙⢿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠀⠀⠀⢿⠏⠀⠀⠹⡟⠀⠀⠈⠛

⠀⡀
⠀⠁

⠀⠀⠀⠀⠀⡤⠤⢤⡤⢠⠀⣀⣀⢀⡀⣀⣀⡀⣀⢀⣀⣀⢀⢀⣀⢀⢀⡀⠠⠤⡄⣤⠤⠤⠄
⠀⠀⠀⠀⠀⠱⠀⡰⠁⠈⡄⠀⠄⠀⢂⠀⡈⠀⠑⡈⢤⠃⠈⠀⢀⠌⠀⢣⠀⡐⠀⠘⡀⢐⠁
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠐⠊⠀⠀⠈⠖⠁⠀⠀⠱⠃⠀⠀⠘⠞⠀⠀⠀⠓⠁⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠞⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠦⠊⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣄⠅⠉⠀⠀⠀⠠⠙⡄⠀⠀⠖⠙⢴⠈⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠂⢠⣉⡭⠋⠀⠀⢀⡄⠀⠈⠁⠀⠉⠀⠠⡄⠐⠂⠀⠘⠀⢠⡄⠀⠀⠐⢖⠒⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⡠⠼⣷⡀⢲⠄⢈⠠⣄⠀⠰⡆⠺⣄⠀⠈⢦⠀⡀⢾⢵⠉⠀⠀⠀⢀⣈⡠⡞⢶⠛⠁⠀⠀⡀
⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⡥⠯⣒⠁⠀⠰⠕⢵⠋⠁⠀⢸⡨⠚⠑⢦⡇⠀⠀⠀⠈⠁⠀⠈⠾⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣒⡒⢦⡀⠀⠈
⠀⠀⠀⠁⠀⠀⠞⡱⠒⠢⡙⣆⣀⠊⡉⣉⠉⠉⠉⠀⠉⠀⠀⠀⠀⡈⠈⠀⠁⠠⠠⢠⠈⠄⠑⣀⣠⠿⠉⠀⠀⠈⢆⢳⠀⠀⠉
⠀⠀⠄⠀⠀⢸⣸⠀⠀⠀⠒⠚⠛⠒⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⡓⢒⠒⠂⠀⠂⠐⠐⠒⠚⠉⠉⠁⠀⠀⠀⠀⢻⢸⠁⠀⠒
⠀⠀⠄⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⡄⢈⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢊⠔⡡⢀⠔⡡⣂⢸⠀⠀⠀⠀⠀⠀⠀⡌⢸
⠀⠀⠀⠀⠀⠘⢸⡀⠀⠀⠀⠀⠀⠃⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⢊⠔⡡⢊⠔⡁⠊⠀⠀⠀⠀⠀⠀⡘⢠⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠡⢇⠀⠀⠀⠀⠀⠸⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢊⠴⢈⠔⡡⢊⠔⠃⠀⠀⠀⠀⢀⠜⣠⠏
⠀⠀⠀⠀⠀⠀⠐⢟⣆⠀⠀⠀⠀⠀⢆⠀⡊⠀⠢⠀⠀⠀⠀⠀⠀⠀⠐⡡⢚⡡⢊⠔⡡⠆⠀⠀⠀⠀⣠⢊⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢮⡷⡀⠀⠀⠀⠈⡆⠀⠆⠀⠑⠀⠀⠀⠀⠀⠀⣫⢔⡡⢊⠄⡊⡐⠁⠀⠀⢀⠔⣠⠊⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡢⣄⠀⠀⠈⢀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠔⡡⢂⠕⣪⠊⠀⢀⡠⢐⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢝⣢⢤⣀⡑⣄⠀⠂⠀⠀⠀⠀⢐⣡⡺⣿⣭⡥⣴⣶⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠷⠦⣄⠀⢀⠬⢓⡥⠚⠛⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠕⢐⡺⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⡰⠖⣟⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠸⠇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠢⢒⠔⠉⡑⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡁⠀⠀⠀⠀⠀⢀⠕⡈⠢⢀⢀⢈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⠿⠧⠄⠾⠋⠭⠤⠿⠿⢿⠿⠿⠿⠿⠿⠧⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠟⠛⠛⠒⠒⠒⠒⠒⠒⠚⠛⠚⠚⠛⢺⠌⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢌⢼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣿⣯⣺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⣀⠸⡀⠀⠈⠀⠀⠀⠰⠛⠛⠃⠚⢒⢂⠶⠖⡷⢋⡞⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠋⠙⠉⠛⠐⠛⠓⠓⠓⠓⠛⠟⠺⠞⠟⠛⠛⠟⠩⠓⠩⠂⠩⠒⠝⠊⠔⠚⠊⠓⠉⠊⠂⠒⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⡶⠂⠀⠀⠀⠀⢠⡿⠟⠛⠛⠿⣿⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⣾⣿⣿⣿⣿⣦⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠘⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡿⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠈⠛⠿⠿⠋⠀⠀⠈⠛⠿⠿⠛⠁⠀⠈⠛⠿⠿⠛⠁⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣶⣶⣶⣶⣶⣶⣄⠐⣶⣶⣶⣶⣶⣆⠐⣶⣶⣶⣶⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡄⠰⠶⠀⣀⢀⣤⣄⠀⠐⣀⠀⠀⠀⣀⡀⢀⣤⡄⠀⡤⢤⣤⠀⠀⠀⠀⠀⡸⠛
⣶⠀⠀⠀⠀⠀⠉⠉⢁⠀⠀⠀⠀⠀⠀⠙⡿⠁⣾⢶⡏⠀⠀⠈⠟⢑⢘⡫⡅⠀⣥⡽⢤⣿⡷⠀⡀⠀⠀⠀⠰⡿⠃
⠩⣿⣶⠀⠀⢀⣺⡗⡈⡇⠀⠀⠐⠀⠀⣠⣤⡌⠛⣈⡀⠀⠀⠀⡀⡀⠿⣀⠀⠀⡿⡅⢀⠛⠀⠀⠟⠀⣤⣀⡎⢀⠀⠀⢰⠂⣧
⣤⣾⣿⡧⠀⢠⡅⠀⢃⡀⠀⠀⠀⠀⢸⣿⣿⡿⣠⠈⠀⠀⠀⠀⣿⠇⠀⠀⠒⠠⠇⠀⢘⡃⠀⣿⡀⠀⠈⠟⠛⠋⠁⠀⠀⠐⠚
⠉⠉⠀⢀⡀⠀⣧⣾⣿⣿⠀⠀⣠⣤⣤⣛⠋⢁⣾⡄⠀⠀⠀⠀⠑⣊⣤⡀⢰⡇⠀⢀⣿⣿⠧⠙⠿⠀⠀⠀⣀⣺⣿⣤⢄⣀⡠
⠀⠀⠀⣿⣅⠀⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠤⢸⡏⢈⣀⡎⠁⠛⠿⢿⠁⠀⠀⠀⠀⢸⠟⠋⠁⠹⠿⠀⠉⠳
⠀⠀⠀⠉⠻⡞⠉⠙⣿⣶⣿⡟⠉⠉⣝⠋⣩⠇⠀⠀⠀⠀⠀⢠⡀⠉⠛⠉⠁⢀⠀⠀⢠⡀⠀⠀⠀⠀⢈⠛⠘⠷⢠
⠀⠀⠀⠀⠘⠃⠀⠀⠙⠛⠋⠀⠀⠚⠛⠛⠋⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠋⠀⠀⠘⠛⠃⠀⠀⠀⠈⠀⠀⠀⠙

⠀⠀⠋⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠂⠑⡄
⠀⡀⠀⠀⠀⠀⠁⠈⠉⠐⠒⠂⠤⠤⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠔⠒⠂⠀⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡏
⠀⠀⠀⢃⠈⠑⠦⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⡄⠴⢺⠁⠀⢰
⠀⠀⠀⢸⢀⡀⢸⠀⠀⠀⠀⠉⠐⠒⠠⠄⣀⠀⠐⢀⡀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠰⠖⠂⠁⠀⠀⠀⠈⣄⡀⢸
⠀⠀⠀⣼⠖⠱⣢⠀⠀⠀⠀⠀⡀⠀⡀⠂⡈⠀⠀⠀⠙⣀⠀⠘⡄⠀⠀⠀⠀⡠⠁⠀⠁⠀⠀⠀⠀⠀⠹⡕⢾⡀
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣀⢈⣀⠀⠀⠀⡁⠀⠀⠀⠀⡀⢣⡀⠈⠢⡠⠔⠊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠑⠄⠀⣁⠴⠃⣉⡀⢉⡈⠋⢦⠘
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠈⣀⠃⠔⠉⠀⠀⠀⠀⠑⢌⢱⡠⠂⠉⠈⠉⠒⣄⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠗⡈⠀⠀⠀⢀⡀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡰⠠⡁⠀⣀⣀⣀⣀⣀⣤⠀⠐⠀⠀⠀⠀⠀⠀⡰⠀⠀⠘⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢠⡘⠋⠁⠈⠉⠁⡰⠇⠀⠀⠀⠀⣠⠖⠁⠀⠀⣠⠼⣳⢄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⡊⠀⠠⠆⢤⡒⣛⠓⠂⢲⣄⠀⠀⠀⠑⠂⠀⢃
⠀⠀⠈⠉⠐⠢⣀⠘⠀⠀⠀⠐⠗⢀⠀⠀⠀⣀⠀⠋⠂⠀⠀⠈⠒⠢⢄⠲⠐⠲⠡⠞⠁⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⢀⠖⠲⠒⠶⠦⠱⢶⡆⠡⠀⢀⠘⠠⠄⠠⠐⠤⠀⠷⠃⠀⠀⢤⠤⠔⢉⠀⣀⠄⠒⣀⢘
⠀⠀⢀⠀⠀⠀⠀⣇⢼⠀⡠⠀⠀⡀⠀⠘⡰⠆⠀⠀⠆⠀⠀⠰⠄⠀⠄⠀⠉⠛⢳⠊⢲⠚⠖⡳⡴⠶⢦⡉⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⢹⡶⡄⠺⠀⠁⠐⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⢣⠈⠹⡆⢠⣇⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠈⠀⠀⠀⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠀⠤⢺⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠐⢊⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠈⠄⠀⠙⠂⠤⡀⠀⢀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢰⠀⠸⡀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠒⠦⣄⡀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠈⠐⠠⢀⣉⡐⠂⠤⠤⠤⠤⠐⠊⠁⣀⠤⠊⠁⠀⠀⠀⠉⠓⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠇⠀⠀⠀⠀⠩⠉⠉⠋⠛⠃⠐⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⡀⠤⠀⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⣶⠀⠀⠐⢁⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠴⠙⢦⡀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠊⠀⠀⠀⠉⠒⠒⠊⠀⠀⠀⠀⠀⠈⠢

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣀
⣿⣛⣛⣛⣛⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣽⣿⣯⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣀⡤⢤⡤⠤⢤⡤⠤⢤⣠⠤⣄⡤⢤⣤⢤⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⣀⡀⠀⣠⡴⣤⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣰⠟⠉⣿⠀⢿⡄⠈⣧⣴⠶⠶⢶⡿⠓⢀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⠀⣼⠃⠀⣰⡟⠀⠈⠛⠶⣯⣤⡀⢠⣿⠃⢀⣾⠁⠀⡜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⢀⣴⠟⣠⠶⣶⠀⢰⠁⣼⠃⣾⡏⢀⣾⠇⢠⠎⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠞⠛⠁⣼⠋⡴⣿⢠⠃⢸⢇⢸⣿⣰⠋⠻⠖⣡⣤⣾⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⢿⡜⠁⠻⠃⠀⠈⠁⠀⠛⠁⠀⠀⡞⢁⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠿⣿⡟⠛⠁⢀⣤⠀⢀⣤⠀⢀⣤⠀⢀⣴⠀⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣠⠆⢠⣿⠁⠀⢀⣾⡟⠀⣼⣿⢠⢿⣿⢠⣿⡏⢠⣿⣳⠏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣸⡿⠀⢀⠞⣿⡇⡸⢹⣇⠏⣼⣧⠏⣿⢀⣿⡟⠁⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡇⢠⠎⠀⣿⣰⠃⠸⠏⠀⠹⠏⠘⠷⠋⣿⡇⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠋⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠴⠦⠖⠶⠖⢦⠖⠲⠔⠒⠶⠲⠖⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠒⠻⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠐⠚⢻⡿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠚⢿⠟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠐⢺⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠂⠐⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⣰⡄⠘⠃⠀⠀⠀⠀⠀⠀⠄⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠤⢾⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠠⠴⢾⣷⠶⠤
⠀⠀⠀⠀⠀⠁⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠰⡦⠈⢻⡿⢁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢐⠀⠠⡂⠀⠀⠄⠀⠀⠀⢼⠀⢰⠄⠀⠀⡠⡄⠀⢀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠠⠀⠄⡄⡠⢠
⠀⠈⠀⠂⠄⠀⠀⢘⠀⠀⢁⡉⠀⠨⠵⠀⠣⣀⢧⡤⠋⠐⠀⣧⣾⣤⣥⣼⣼⣦⣿⠃⠂⡀⢀⠄⠀⠠⠐⠀⡔
⠀⡄⡄⠀⠑⡀⠐⠨⠐⠀⠄⠤⠀⡀⡃⠀⠋⡊⠅⠙⠆⠈⢀⠉⠉⠉⠿⠋⠍⠉⢁⡀⡀⠝⢂⠰⠿⠀⠶⠶⡀⠸⠟
⠀⠀⢠⠂⠀⡅⠈⠀⠄⠠⢐⡀⠀⠀⢠⠀⠘⠁⢀⠁⡀⠐⠀⠁⠠⠀⠀⢀⢦⡀⢠⡀⠀⠐⠈⠐⠔⠈⠒⠆⠀⠐
⠀⠈⠔⡀⠁⠆⢀⢀⣃⠔⠀⠄⠀⠀⡚⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠓⠀⠘⠀⠀⡯⢘⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠈⠌⠈⠀⠠⠀⠀⠠⠥⠀⠁⣈⠀⠀⠀⠁⠀⠈⠀⠂⠉⠀⠉⢄⠀⠀⠁⢀⢀⠁⡈⢸⠀⠒⠪⠁⠑⠁⠀⠨⠙⡄
⠀⠀⠀⠀⠀⠄⠐⢄⠀⣧⢀⣐⣀⣀⣈⣀⣀⣈⢀⣀⠀⠀⠂⠻⠀⠀⠀⠈⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⢀⠏⠂⠈
⠈⣀⣀⡁⠂⢠⣶⣷⡆⠈⠀⢣⡰⠁⠂⠀⠈⠢⡠⠁⠑⠤⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠛⡄⢈⠀⠐⠀⠐
⠈⣿⣿⡇⠀⠁⠛⠛⢇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠰⠓⠀⠡⣀⠀⠠⠀⠀⠀⠀⡀
⠀⠈⡏⠁⠀⢀⠄⢀⢈⠓⠀⠀⠼⠧⠀⡀⠀⢰⠃⠀⠀⠀⠰⠀⠀⠀⠣⠀⠒⠂⠀⠀⠀⡀⠐⡄⠐⠀⠐⠀⠉⠁
⠀⠄⠃⠂⠀⠈⠀⠀⠂⠀⡠⠀⠀⠀⠀⢀⠀⢈⠀⠃⠀⠉⠈⠈⠀⠃⠀⠀⠀⢠⡀⠀⠐⠀⡀⠈⠀⠀⠐⠈
⢀⡀⠀⣴⠀⢃⠀⠂⡈⠨⠠⠄⠀⠀⠌⠄⡇⠘⣄⠀⠐⠒⠢⠀⠀⠀⡸⠀⠀⠀⠀⠀⠔⠀⠰⡀⠀⢀⠀⠁⠀⠑
⠀⠄⡐⠀⢡⠈⠄⠀⠆⢜⠅⠂⠀⠀⠀⠠⡃⠀⠈⠀⠒⠒⠒⠐⠂⠈⠀⠀⠇⠐⢿⡟⠁⠀⠀⠙⣿⠗⠀⠈⠉⠄
⠀⢠⠁⠀⠀⢃⠀⠁⡀⣤⡁⣰⡀⠀⠂⠈⡀⢠⠄⠀⠀⢠⢀⠐⢀⠀⡁⢀⢄⠀⠈⡀⠀⠀⠀⠀⡏⠄⠄⡂⠉⢨⠐
⠀⠲⠤⠠⠄⠘⠀⢸⠂⠀⠀⠈⠠⠀⢀⠆⠀⠈⠄⣤⠀⠈⠓⠊⠷⠀⠀⠀⠁⢀⠀⠰⠄⡄⡠⠆⠀⠀⠦⠈⠀⠁⠂
⠀⠀⠀⣤⠄⠀⠀⣈⠰⠀⢐⠐⠐⢠⠃⢀⡠⠔⠒⠀⠀⠀⠠⠄⣀⡀⠀⢠⡈⠉⠀⠲⠾⠿⠿⠾⠃⠀⠀⠀⠀⢠⡄
⠀⡰⠠⣤⡌⢂⠀⠈⡁⠀⠀⠀⠀⠈⠉⠀⢀⠤⠀⢀⣀⠤⠄⠀⠀⢀⠀⠘⠁⡋⠉⡖⠂⠀⠒⠖⠒⠒⠂⠀⠁⠈⠁
⠸⠺⠒⡉⡙⠤⠁⠀⠈⡠⠀⠠⠈⠀⠀⠀⡍⠀⠄⢀⡁⢀⠀⡄⠀⠐⠘⠀⠀⠛⠑⠃⠄⠂⠄⠶⠓⠄⠠⠀⠂
⠰⣄⠀⠃⠀⠀⡀⠠⠤⠀⠀⠄⠘⠿⠁⠀⠀⠄⡀⠐⢡⠉⡆⠀⡆⠀⠄⠀⢆⠰⠀⠔⠀⠀⡤⠀⡤⠤⠤⠄
⠀⣀⡐⠂⠈⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⢠⠉⠐⠁⠀⠀⠀⠀⠀⠂⠈⠀⠠⠂⠀⠆⠀⠥⠀⠀⠂
⠀⠀⠀⠀⡄⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡄⠄⡸⠀⢐⠀⠀⠀⠤⡀⠀⠴⠐⠄⢃⠀⠠⠀⢈⠀⠠⠒
⠀⠆⠀⠄⠀⠀⠃⠀⠀⠠⠂⠁⠀⠘⠁⠙⠓⠒⠃⠃⠀⠂⠈⠁⠀⠒⠀⠑⠐⠃⠃⠐⠂⠐⠁⠊⠒⠂⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣾⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣼⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷⠤⠀⠀⠹⠉⠀⠀⠀⠀⢠⣿⣧⡀
⠀⠐⠒⠺⢿⣿⣿⣿⣿⡷⠶⠆⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠾⣿⣿⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⠹⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠻⠋⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣀⠀⠀⠀⠀⠀⠀⠈⢿⡏
⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣇⠀⢘⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣠⠀⠀⢠⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢈⠿⠿⠛
⠀⠀⠛⣿⠟⠀⠀⠹⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠈⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠙⣿⠛⠁⠀⠀⠀⠐⢦⣠⣿⣧⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⢿⡏⠉⠓⠀⠀⣰⣿⣶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠻⠓⠠⢴⣿⣯⠄⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠈⠛⠁⠀⠀⠀⢀⣀⣼⣧⣀⡉⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢡⣤⣾⣧⣤⠄⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢹⡿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⣿⠏⠉
⠀⠐⠒⠒⠿⠿⠿⣿⣿⠿⠿⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣤⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠰⠶⢾⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠤⣤⣿⡤⠤⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠀⠀⠀⠀⠀⠐⠶⢾⣿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠲⠾⢿⣿⡿⠿⠒⠂⠀⢸⡇
⠀⠀⠀⠤⠤⣾⡦⠤⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣦⡤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠠⢤⣼⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⠀⣀⣤⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠶⠶⣿⣿⡷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡤⠀⢤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠋⠉⠉⠉⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠙⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⢤⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⠀⣀⣈⣻⣋⣀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠘⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣿⣃⡀⠀⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⣬⣽⣥⡄⣿⣿⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣳⣶⣶⡰⠶⢶⠿⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⡇⣶⣶⡆⠸⠿⠇⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠻⠿⠿⠿⠳⠿⠃⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⠇⣿⣿⡇⣿⣿⡿⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠠⣿⣷⢀⣻⣟⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢙⣿⣿⡋⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣻⣋⡰⣾⣶⡎⣿⣿⠋⠀⣠⡀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡿⣷⠿⠿⠀⠈⣻⠁⠀⠀⠀⠀⠀⢠⣄⠀⣶⣶⡄⣶⣶⢠⣶⣶⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣧⣼⡇⣿⠉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠹⣦⣭⣯⣄⣭⣭⡄⣽⣭⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠷⠟⠀⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⡇⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⣆⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡾⠀⠀⠀⠛⠛⠛⠋⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⢷⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⡞⠁⠀⠀⠙⢦⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠙⠋⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⡻⣆⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢷⣌⣷⡘⢿⣷⠘⣧⡾⢻
⠀⠀⠀⠀⠀⢰⣦⡀⣿⣇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣦⠉⠛⠁⠈⠉⠀⠛⢃⡟
⠀⠀⠀⢠⣦⣌⣿⡻⣿⢿⡿⣿⣴⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠹⢮⡛⠃⠀⠀⠀⠙⢣⡞⠀⢀⣀⠀⣤⡀⢠⣄⠀⠈⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡏⠀⠀⢸⡝⣿⡇⣿⣿⢹⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡀⣼⢧⢀⡶⣦⢸⡇⠀⣶⠾⣷⠈⠃⠘⠋⢾⡾⢻⠆⣿⠀⠀⢠⣦⡀⣿⡆⢀⣤⡄
⠀⠀⡶⣼⡏⣷⣿⢸⣿⠃⡿⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⣰⠏⠀⣿⢀⠀⢸⡌⣷⡟⣿⣸⢃⣇⣴⡦
⠀⠀⢷⡘⣿⠘⠟⠈⠛⢸⣧⡿⣦⠀⠀⠀⠹⡆⠀⠀⠀⣴⠃⠀⠀⣿⣏⠻⣾⡇⠻⠃⣿⡟⢸⡟⣹⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢁⣴⡃⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⣿⠙⢷⡀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢀⡇⠀⠀⠀⢠⡴⠋⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡀⠈⠷⣄⣀⠀⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠈⣷
⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠘⣧⠀⠀⠀⢸⣇
⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⢻
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠸⠄⠀⠈⠈⠀⠀⠀⠶⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⣤⢀⠀⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠑⠖⠀⡁⠀⠠⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠁⠂⠀⠁⠀⠂⠤⠄⢀⠀⠂⡀⠈⠀⢀⡀⢀⠚⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡔⠆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠄⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⠀⠘⠉⠀⠀⠒⠁⠀⠀⢀⣠⠄⠈⠀⠀⠒⢃
⣶⣶⣶⣶⢶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⣠⣔⣒⠒⠦⢤⣀⡀⠀⠀⠀⠀⠹⠀⢀⣀⠀⠀⢀⠀⣠⠄⠀⠀⣠⠤⢀⠔⢉⢀⠅⠀⠀⠔⠋⠀⠀⠀⠀⠀⣠⢲
⠀⠀⠀⠀⠀⡇⠐⠚⠀⡜⣇⠀⠈⠑⡆⠢⣄⢉⡓⢤⡀⠀⢀⠀⢢⣏⠀⢀⠀⣀⢻⣄⠀⠀⠀⢠⠁⠀⠈⡀⠄⡀⠀⠂⣀⠐⠒⢄⠀⢠⡵⠃
⠀⠀⠀⠀⠀⠘⠀⠀⢰⢇⠈⠣⣀⠀⠄⠀⠈⠣⠉⠓⢿⡄⢸⠇⠞⢈⣷⡏⣼⢏⣴⡟⣡⠀⡀⠀⠀⠀⠈⢀⠠⠤⠖⠒⠈⠐⣄⠜⡆⠀⠁⠞
⠀⠀⠀⢀⡴⠒⢄⠀⢸⠘⢦⡀⠈⠓⠶⢤⣄⣀⣀⣀⡼⠁⢸⠀⣄⡼⠉⠂⠳⠊⣿⡴⠋⢀⣀⡀⠌⠠⠊⠀⠠⠠⠄⣊⡠⠖⢁⡀⠙⢲⡀⠀⢀
⠀⠀⠀⢸⠀⢀⠘⠀⣾⢠⠀⠙⠶⢤⣀⣀⢀⡀⠀⡴⠃⠀⠀⡤⣌⠀⡶⠳⡄⢀⣀⣀⣀⣏⣀⠝⠈⡗⠂⠈⠒⠚⢋⠅⠂⠁⠀⢈⡄⡸⠀⠐⠇⡳
⠀⠀⠀⠈⠳⠜⠠⢀⡇⡞⠀⠀⠀⠀⠀⠉⠥⣠⠞⠁⠀⢠⡌⠀⣿⠀⢧⣠⠓⢩⡏⣠⠉⣡⠀⠀⢸⠀⠀⠀⠀⠐⠁⠀⠀⢀⡠⢊⡄⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣸⢱⠁⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⢸⢣⣠⢏⣎⡇⢬⢇⣾⢰⡇⢀⡟⠀⠀⠀⠑⢄⡲⣄⠀⠤⠀⠒⠉⠀⢸⡇⡇⠀⠁
⠀⠀⠀⠀⢀⠀⢀⡇⠇⠀⢀⠀⠀⠀⣼⠋⠀⢠⡎⠀⠀⠘⠀⠁⠈⠁⠉⠀⠁⢰⠊⣱⣞⠀⠀⣆⣄⣀⠀⠙⢌⢢⠀⠀⠀⠀⠀⠠⡇⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠀⡼⠀⠀⠀⠀⠀⢀⡼⠁⢀⣷⣯⡆⠀⡠⢨⢀⠤⠀⡠⠖⠒⠒⠤⡉⠁⠀⠀⠀⠘⢿⣮⢆⠀⠈⢆⢣⡀⠀⠀⠀⠀⡃⢰⠀⢾⣁⢈⠆
⠀⠀⠀⠀⠀⠀⢣⡐⠤⣄⡀⢀⡞⠀⠀⢾⣿⣯⠀⢀⡱⢁⡤⠒⠚⠶⢤⡠⠄⠒⠾⣑⠢⣄⠀⠀⠘⣟⣿⢃⠀⠈⢦⡱⠤⠤⠤⢔⡡⠟⠀⠀⡡⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠀⠀⠀⣽⣿⣿⠀⠘⠁⡜⠲⣄⣐⣄⡀⣓⠀⠀⣀⣈⣦⠼⣆⡀⠀⢹⣿⣿⡄⠀⠀⠙⠓⠒⢋⣁⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠢⡀⠀⠀⢾⣿⣟⠀⠀⠀⡧⣀⡀⠀⠈⡍⠉⠉⢹⠉⠀⢸⡀⣧⢌⠑⡌⠑⠿⠁⠀⠀⠚⢠⡞⢁⡀⢀⣀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⢠⠞⡉⣲⣤⢀⠄⢷⡀⠀⠈⣻⣿⡳⠀⠀⠗⢄⣉⠁⠒⠓⠀⠀⠘⠒⠈⢁⡠⢺⠀⢣⢸⠀⠀⡠⠖⠚⣋⡟⠲⢅⠁⠈⠉⠳⡄⠀⣷
⠀⠀⠀⠀⠀⢸⠀⣡⠄⢹⡌⢠⠔⢷⡀⠀⠉⠻⠇⠀⠀⠀⢠⠀⠈⠁⡖⠒⠂⠒⡆⠉⠀⣇⢸⡄⠸⢸⢀⡞⢀⡤⠊⠉⠲⣵⢋⡇⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠘⡄⠀⣠⠐⠞⢦⡐⠋⣳⡀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⢹⠘⣗⡡⠃⢸⠀⣸⠀⠀⠀⠀⠈⡇⢹⣂⢀⡶⠁⢠⠇
⠀⠀⠀⠀⢠⣄⠹⣆⠀⠀⠔⠉⣉⠶⢅⡹⠶⢤⡀⠀⢸⠅⠒⠄⢀⠀⣀⠀⢀⠀⣇⡠⠄⠚⡡⡏⠀⠀⢸⡀⠈⢧⡀⠀⠀⡸⠀⡆⣠⠞⠁⢠⠎
⠀⠀⠀⠀⠈⢦⠳⡈⠳⣆⡀⠀⠃⠀⠊⠙⡤⠄⠽⠀⠀⢄⠈⠁⠀⠀⢤⠀⠀⠤⢤⠀⠂⠁⣧⠟⠀⢀⠀⠳⣄⢀⠈⠒⠚⠒⠫⠝⠂⢀⠴⢃⢞⡽
⠀⠀⠀⠀⠀⠀⣍⠚⠆⠈⠙⠲⠤⣤⠤⠖⠁⠀⠀⠀⠦⠀⠉⠓⠲⠤⠴⠤⠤⠤⠼⠔⠒⠋⠀⠀⠀⠈⠀⠀⠈⠑⠪⠥⢤⡤⠤⠔⠊⠁⠖⠋⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢺⡐⠭⣧⠇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣸⣥⣤⠖⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⡂
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⢶⣄⠀⠀⡀⠀⢖⡲⠀⡊⠁⡆⠈⠉⠁⠀⣼⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡝⠛⣏⣹⠄⠀⣠⡄⠉⠈⠁⠀⠀⠀⠀⠀⡟⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⢡⡀⠀⢽⠆⠀⢀⢠⠀⠀⠀⡀⡔⠃⠀⠁
⠀⠀⠀⠀⠀⡀⠖⣀⣀⠀⢠⠖⠒⢄⠀⢿⡀⠀⠀⠀⠀⠄⠂⠀⠠⢇⣹⠃⠀⠄⠒⢌⠂⠀⢀⣼⠃
⠀⠀⠀⠀⣼⣿⠉⠉⠁⠀⠹⣀⣀⠜⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠸⡀⠀⡠⢀⢠⣾⡿
⠀⠀⢀⣴⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⢨⡿⣿⡀
⠀⠰⠟⠁⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⢠⣿⠃⠈⢻⡄⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⢸⠠⠄⠀⠇⠀⠀⠀⠀⣤⣴⣦⣤⠀⠀⠀⠀⠠⠁
⠀⠐⢿⣄⢀⣾⠇⠀⠀⠀⠀⢾⢹⣧⠀⠀⠀⠀⢸⣀⣀⣀⡀⠀⠀⠀⠀⠜⢿⠿⠇⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠘⢿⡾⠏⠀⠀⠀⠀⣀⠠⣶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣾⣷⣤⠀⠀⠀⠀⡀⣠⢤⡀⡀
⠀⠀⢠⡞⠳⡄⠀⠀⠀⠀⣿⠿⠿⠿⣟⠀⠀⠀⢠⣯⣘⣀⣲⠀⠀⠀⠀⠑⢿⡿⠋⠀⠀⠀⠸⠿⢿⣻⠿⠿⠃
⠀⠀⠈⠛⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑

⠀⢰⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀⡤⣲⣤
⠀⢸⢀⠔⠦⠞⠁⠀⠀⠀⣀⣠⣠⡆⣿⠀⠀⠀⠀⠀⣩⠁⠀⠀⠀⠀⠀⣶⣾⣿⣷⠀⠀⠀⠀⣟⠛⢅⢈⡇
⠀⠸⠤⠤⠤⠤⠄⠀⠀⠈⠋⠙⠉⠋⠙⠀⠀⠀⠀⠈⠟⠏⠀⠀⠀⠀⠀⠛⠙⠛⠋⠀⠀⠀⠀⠈⠑⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⢰⣶⣤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣀
⠀⢸⢀⢀⢠⡀⠉⠀⠀⠀⡄⢾⣿⣎⠱⠀⠀⠀⠀⣴⢟⣶⡄⠀⠀⠀⠀⢠⣾⣽⣄⠀⠀⠀⠠⣾⣿⣿⣿⡏
⠀⠈⠂⠋⠈⠁⠉⠀⠀⠀⠘⠤⠛⠁⠀⠀⠀⠀⢠⣿⣕⣼⣧⠀⠀⠀⠘⠛⠘⠃⠛⠃⠀⠀⠀⠈⠻⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡗⣭⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣰⡏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⢰⣟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣷⣾⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠛⠀⠀⠀⢀⣀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣶⣶⠞⠀⠀⠀⢤⣤⡴⠀⠀⣤⡄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⣆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡟⠀⢀⣤⡀⠘⣿⠁⢠⡄⢸⡇⣠⣼⠇⣄⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣷⣾⣿⠀⣿⣿⣿⡇⠙⢻⡇⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⠀⣿⡿⢿⡇⣶⣾⠻⡆⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⠸⣿⡏⠈⣿⠀⠙⠃⣸⡇⠉⠸⠆⠐⠃
⠀⠀⣠⣴⣶⣶⣿⡇⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠸⣿⡿⠃⠀⠠⣿⣿⡀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠁
⠀⠾⠿⠛⠛⠉⠉⣿⣷⣶⣾⣿⡇⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛



⠀⡁⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⡀⠀⢠⡄⠀⠀⡀
⠀⠀⠖⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠉⢇⠀⣰⠃⢀⣀⣛⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠲⠤⠾⠟⠁⠀⠒⠾⠭⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠁⠀⠀⠠⠀⠀⠀⠭⠭⣭⠁
⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠃⠀⠀⠘⠳⢦⡄
⠆⠀⠀⠀⠀⠀⠀⢰⠀⢈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄
⠰⠾⠀⠀⠀⠈⠂⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠀⣤⣾⣦⡀⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠩⣿⡛⠁⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢡⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⠈⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠟⠉⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡄⡄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡷⠀⠐⠦⠤⠃⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈
⢀⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠾⠛⠁⠀⠀⢐⡝⡎⢹⠀⡤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡷⠔⠈⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⠜⠐⠞⠀⠼⠂⠀⠀⠀⠀⠀⠀⢈⣒⣈⣀⠢⣀⠠⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠙⠋⠙⠷⠆
⠀⠀⠀⠀⠀⠘⢣⡄⢠⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠈⠀⢿⡇⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⣿⣿⣿⡿⠃⠀⠀⢀⣠⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠆⠀⠘⠘⠀⠉⠁

⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣷⣆⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢰⣾⣷⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⢿⣿⣿⠛⢩⣿⡍⠛⣿⣿⣿⠀⠀⢸⣿⣿⡟⡉⠒⠝⢿⣿⣿⣿⠀⠀⢸⣿⣿⢰⣖⣒⣦⢹⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿
⠀⠀⣸⣿⡏⠠⣿⣿⣿⠄⢹⣿⣿⠀⠀⢸⣿⣿⣧⠳⠤⢊⣾⣿⣿⣿⠀⠀⢸⣿⣿⢸⣚⣚⢟⡸⣿⣿⣿⠀⠀⢸⣿⣿⣥⠀⠀⠀⣬⣽⣿⣿
⠀⠀⣿⣿⣧⠄⠙⠿⠋⠠⣼⣿⣿⠀⠀⢸⣿⣿⣏⣄⣧⠀⢻⣿⣿⣟⠀⠀⢸⣿⣿⣘⣒⣚⠊⠁⣿⣿⣿⠀⠀⢸⣿⣿⣽⣤⣀⣠⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣾⣾⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⣾⣿⣿⡿⣿⣿⣿⢿⣿⣿⣷⠀⠀⢸⣿⣿⡟⠛⣿⠛⢻⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿
⠀⠀⣿⣿⣯⣻⣿⣿⣿⣿⣽⣿⣿⠀⠀⢸⣿⣿⣿⣄⠀⣠⣿⣿⣿⣧⠀⠀⢸⣿⡟⢿⣯⠁⣹⡿⢻⣿⣿⠀⠀⢸⣿⣿⢩⠁⠀⠈⣭⣿⣿⣿
⠀⠀⣿⣿⣷⢿⣿⣿⣿⡿⣿⣿⣿⠀⠀⢸⣿⣿⡿⢉⣤⡉⢿⣿⣿⣿⠀⠀⢸⣿⡇⠂⣀⣈⣀⡐⢸⣿⣿⠀⠀⢸⣿⣿⣮⣅⠀⢀⣵⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣷⣈⠛⣁⣾⣿⣿⣿⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⢸⣿⣿⣿⡏⠤⢙⣿⣿⣿⣿
⠀⠀⠹⢿⣿⣿⣿⡿⣿⢿⡿⡿⠏⠀⠀⠸⠿⣿⣿⣿⡿⢿⣿⣿⡿⠏⠀⠀⠸⠿⣿⠿⠿⠿⣿⣿⣿⠿⠏⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟

⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⢸⣿⣿⠟⢋⡵⠉⡻⣿⣿⣿
⠀⠀⣿⣟⡍⢭⣿⡉⣿⢸⢿⢿⣿⠀⠀⢸⣿⢸⣿⠟⡻⠿⢣⣤⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠟⢻⠀⢸⣿⠀⠀⢸⣿⡇⣃⢋⢴⣿⣦⢸⣿⣿
⠀⠀⣿⣗⣃⣛⣛⣓⣛⣘⣘⣻⣿⠀⠀⢸⣿⢸⣧⣾⣿⣶⣿⣿⣿⣷⠀⠀⢸⣿⠉⣿⠀⢸⠀⢸⠀⢸⣿⠀⠀⢸⣿⣧⣙⢻⣆⡹⢟⣼⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣈⣉⣉⣉⣉⣉⣉⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣷⣮⣶⣿⣿⣿⣿
⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣄⠀⣬⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠟⡋⢷⣮⢿⣿⣿⠀⠀⢸⣿⡿⠉⠁⠐⠈⠙⢛⣿⣿
⠀⠀⣻⣿⣿⡏⠠⢟⡂⢹⣿⣿⣿⠀⠀⢸⣿⡿⠏⣤⠙⢤⠹⢿⣿⣿⠀⠀⢸⣿⣏⡿⡀⠱⠆⣻⣴⣿⣿⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⢽⣿⣿⣅⣈⣛⣁⣸⣿⣿⣿⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣮⣩⣶⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣦⣤⣤⣾⣿⣿⣧
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⡍⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⡇⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠃⠂⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠇
⠀⠀⢠⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢠⠀⠀⠀⠀⠈⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠈⡇⠲⢄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡠⠊⢡⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⠟⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠈⡀
⠀⠀⢸⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠜⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢇⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠘⢇⢰⠃⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠈⠣⣸⠀⠀⠀⠀⠐⡂
⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⠠⠒⠀⠛⠃⠇⠀⢰⠂⠙⢧⠘⡆⠎⢏⠉⢹⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⠐⠶⠶⠀⠀⠀⠀⢸⠀⠀⠚⠃⠀⢄⠈⠑⠚⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⢸⠑⠂⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠛⠖⠰⠿⠀⠘⠗⠓⠶⠀⠰⠄⠸⠀⠀⠀⠀⠀⠛⠶⠤⠅⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡤⠄⢀⠀⠀⢠⠤⠄⠀⠀⠠⠤⢤⡤⠀⡀⣠⠤⠤⠤⢤⢤⡤⠤⣄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⣆⠀⠃⠀⣆⡄⠀⠆⠀⠀⠀⡇⢈⠄⢸⡇⠀⡇⠀⠈⠀⠙⡀⠀⢆⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠘⡶⠠⠤⠃⢴⡙⢃⠀⢰⠀⠀⠀⡵⢍⠐⠎⠀⠀⡇⠀⠀⠀⠀⢱⠀⠘⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢠⡈⠶⠶⠄⠀⣄⠀⠀⡆⢈⠀⢰⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠈⠃⠀⠀⠙⠀⠋⠉⠀⠁⠈⠃⠘⠁⠀⠉⠀⠁⠀⠀⠀⠉⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⡀⠠⢀⣿⣁⣡⣏⣸⣉⣉⣄⣋⣷⣀⣈⣁⣈⣁⣟⢉⣁⣉⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⣄⠀⢠⡄⠀⡄⢠⡶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⢸⣦⠀⠉⡇⠀⣿⠀⠀⠆⠀⡇⢸⠋⡍⢠⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡶⠀⢸⠞⢧⡀⠷⠤⠙⠒⠂⠀⠾⠃⠚⠀⠰⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠸⠀⠀⠁⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠉⣀⣀⢠⡞⢙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠠⠀⣀⠾⡡⠾⡵⠄⠀⢀⣤⣤⠀⣿⣀⣟⢈⣿⠛⣶
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⡄⣾⣡⣟⠁⣾⣏⣹⠟⠛⠛⠁
⠀⠀⠀⠀⠀⣰⣟⠀⠀⢀⣸⠇⠀⠀⠀⢀⡤⣰⠟⣿⠄⣿⠁⣩⡁⣿⣀⠿⠁⠈⢉⣀⣠⣤⣶⣶⣶⣿⠿⠂
⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⣤⡀⠀⣾⡇⢸⠀⣿⠀⣴⡄⠿⠤⠛⠁⣀⣠⣤⣶⣾⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠈⣿⠠⣿⣇⣿⡄⠛⠒⠋⢀⣠⣴⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⡾⠋⠀⠉⠉⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⣰⡟⠷⢸⣏⣬⣤
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⣤⠀⣠⡶⣶⣦⣿⣩⡤⠻⠶⢻⡧⣭⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⢉⣀⣀⡀⠀⠀⢀⡀⠀⣠⣶⠏⠈⣿⣾⡋⢸⣟⣩⡶⠻⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠛⣉⣽⡷⢶⣶⡟⢻⣿⡏⠘⠛⣿⣿⠈⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠛⣿⣥⣾⣏⢿⣤⡾⠋⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⠁⠀⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡜⠃⣤⡄⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠂⠀⡀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⣆⠐⠀⠀⠀⠀⠀⢀⣠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠛⢠⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⡿⠋⠀⠀⠀⠀⠛⠛⠿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⡐⠈⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⠟⠁⠀⠀⢀⣼⣿⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣄⠒⢿⣿⣿⣿⠟⠂⠀⠙⠁⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠷⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠁⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣨⣿⣇⣸⣿⣁⣸⣿⣀⣽⣿⣀⣿⣯⣀⣿⣇⣈⣿⣇⣨⣿⣇⣸⣿⣁⣸⣿⣀⣽⣿⣀⣿⣯⣀⣿⣏⣈⣿⣇⣨⣿⣅⣸⣿⣁⣸⣿⣀⣽⣿⣀⣿⣯⣀⣿⣇⣈⣿
⣿⡋⢹⣿⠋⣻⣿⠉⣻⣟⠉⣿⣏⠉⣿⡏⢙⣿⡏⢙⣿⡋⢹⣿⠉⣻⣿⠉⣻⣟⠉⣿⣟⠙⣿⡏⢙⣿⡏⢹⣿⡋⢹⣿⡋⣻⣿⠉⣻⣟⠉⣿⣟⠙⣿⡏⢙⣿⡋
⠻⣿⡟⢻⣿⠟⢿⣿⠟⢿⣿⠛⣿⡿⠻⣿⡿⠻⣿⡿⠻⣿⡟⢻⣿⠟⢿⣿⠟⢿⣿⠛⣿⡿⠛⣿⡿⠻⣿⡟⠻⣿⠟⢻⣿⠟⢿⣿⠟⢿⣿⠛⣿⡿⠛⣿⡿⠻⣿
⣾⣿⣷⣾⣿⣶⣾⣿⣶⣿⣿⣶⣿⣿⣶⣿⣷⣶⣿⣷⣾⣿⣷⣾⣿⣶⣾⣿⣶⣾⣿⣶⣿⣿⣶⣿⣷⣶⣿⣷⣾⣿⣷⣾⣿⣶⣾⣿⣶⣿⣿⣶⣿⣿⣶⣿⣷⣶⣿
⣿⣤⣼⣿⣄⣼⣿⣤⣿⣯⣤⣿⣧⣠⣿⣧⣤⣿⣧⣼⣿⣤⣼⣿⣄⣼⣿⠄⣽⣧⣤⡿⢧⣤⣿⣧⣤⣿⣧⣼⣿⣤⣼⣿⣄⣼⣿⣤⣿⣯⣤⣿⣧⣠⣿⣧⣤⣿⣧
⢙⣿⡏⢹⣿⡉⣹⣿⡉⣻⣿⠉⣿⣟⠉⣿⣏⢉⣿⡏⢙⡟⠋⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠏⢉⣿⡏⢙⣿⡋⢹⣿⡉⣹⣿⡉⣻⣿⠉⣿⣟⠉⣿⣏⢉⣿
⣿⠟⢻⣿⠿⢿⣿⠟⣿⡿⠿⣿⡿⠻⣿⡿⠿⡟⠉⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠟⢿⣿⠟⢿⣿⠛⣿⣿⠿⣿⡿⠻⣿⡿⠿⣿⠿
⣿⣦⣾⣿⣶⣾⣿⣶⣿⣷⣶⣿⣷⣶⣿⣷⣾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⣾⣿⣶⣿⣿⣶⣿⣷⣶⣿⣷⣶⣿⣷
⣬⣿⣥⣼⣿⣄⣼⣿⣄⣼⣿⣤⣿⣧⣠⣿⠃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⠿⣄⣼⣿⣄⣼⣿⣤⣿⣯⣠⣿⣧⣠⣿
⣿⡋⢹⣿⡉⣻⣿⠉⣿⣟⠉⣿⣟⠉⠛⠏⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣿⠉⣻⣟⠉⣿⣟⢉⣿⡏⢙⣿⡏
⠻⣿⡟⢻⣿⠟⢿⣿⠟⢿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢹⣿⠛⣿⡿⠻⣿⡿⠻⣿
⣾⣿⣷⣾⣿⣶⣾⣿⣶⣿⣿⣶⡇⠠⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡔⠀⠀⣠⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣽⣶⣿⣿⣶⣿⣷⣶⣿
⣿⣅⣼⣿⣄⣼⡟⠀⠙⠯⠀⠛⠀⠀⠀⠀⠀⠀⡠⠄⠲⠄⢠⡞⠀⢠⠀⠁⣠⠠⢰⡞⠒⢶⡄⡠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣧⣠⣿⣧⣠⣿⣇
⢙⣿⡋⢹⣿⡋⣁⡀⠀⠀⠂⡠⠀⠐⠀⠀⠀⠀⢇⡀⢀⡤⠏⠀⠀⠘⣆⠸⠃⠀⠎⠀⠀⠞⠰⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣟⠉⣿⣏⢉⣿
⣿⠟⢿⣿⠟⢿⣿⠛⡀⠀⠀⠀⠁⠀⠰⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠿⠻⣿⡿⠻⣿⡟
⣿⣷⣾⣿⣶⣾⣿⡦⠀⡀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡀⢰⣶⣶⣿⣷⣾⣿⣷
⣤⣿⣧⣼⣿⣤⣬⠀⠀⢀⠰⠀⠠⡴⠊⡀⠀⠀⠀⠀⠀⣀⠤⢄⡀⢠⠎⠀⠀⢘⠀⡀⢠⣄⠀⣴⠧⡀⢀⡀⠀⠀⠀⠀⠰⠂⠐⠳⠀⠀⠀⣠⣿⣧⣤⣿⣧⣤⣿
⣿⠋⢻⣿⠋⢻⣿⠉⣻⣟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⡁⠀⢀⡰⠋⠀⠀⠠⠃⣼⠁⢠⠇⢴⠁⢰⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣿⡟⢙⣿⡏
⢿⣿⡟⢿⣿⠿⢿⣿⠟⢿⣧⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠀⢠⣿⠿⣿⡿⠿⣿⡿⠻⣿
⣾⣿⣷⣾⣿⣶⣾⣿⣶⣾⡇⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⢸⣿⣶⣿⣷⣶⣿⣷⣶⣿
⣿⣅⣼⣿⣄⣼⣿⣀⣽⣯⣀⣿⣧⣀⠀⣀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣄⣴⣤⣄⣴⣮⣀⣿⣧⣠⣿⣧⣨⣿⣇
⢙⣿⡏⢹⣿⡋⢹⣿⠉⣻⣿⠉⣿⣟⠙⣿⡏⢙⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⢹⣿⡋⢻⣿⠋⣻⣿⠉⣿⣟⠉⣿⡟⠙⣿
⣿⡿⢿⣿⠿⢿⣿⠿⣿⣿⠿⣿⡿⠿⣿⡿⢿⣿⡿⢿⣶⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⠿⢿⣿⠿⣿⣿⠿⣿⡿⠿⣿⡿⠿⣿⡿
⣿⣦⣾⣿⣦⣾⣿⣦⣾⣷⣴⣿⣷⣴⣿⣷⣴⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⢠⣾⣦⣴⣾⣦⣾⣿⣦⣾⣿⣦⣾⣷⣴⣿⣷⣴⣿⣷⣴⣿⣧
⣨⣿⣇⣸⣿⣅⣸⣿⣀⣽⣿⣀⣽⣯⣀⣿⣧⣨⣿⣇⣨⣷⡄⠁⠀⠀⠀⠀⠐⠀⠢⠀⠠⠤⠀⢠⣤⣨⣿⣇⣨⣿⣅⣸⣿⣅⣸⣿⣀⣽⣿⣀⣿⣯⣀⣿⣇⣠⣿
⣿⡋⢻⣿⠋⢻⣿⠋⣿⣟⠉⣿⡟⠙⣿⡟⢙⣿⡏⢹⣿⠋⢳⣤⠈⢳⣶⠀⣀⡀⠀⢀⡀⠁⣶⡟⠙⣿⡏⢹⣿⠋⢻⣿⠋⢻⣿⠋⣻⣟⠙⣿⡟⠙⣿⡟⠙⣿⡟
⢿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⠿⣿⡿⠿⣿⡿⠿⣿⡿⢿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣶⠿⣿⡿⠿⣿⡿⠿⣿⡿⠿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⠿⣿⡿⠿⣿⡿⠿⣿
⣴⣿⣷⣾⣿⣦⣾⣿⣦⣾⣿⣶⣿⣷⣴⣿⣷⣴⣿⣷⣴⣿⣷⣾⣿⣦⣾⣿⣦⣾⣿⣶⣿⣷⣶⣿⣷⣴⣿⣷⣶⣿⣶⣾⣿⣶⣾⣿⣦⣾⣿⣶⣿⣷⣴⣿⣷⣴⣿
⣿⣅⣼⣿⣄⣼⣿⣄⣽⣯⣠⣿⣧⣠⣿⣧⣨⣿⣇⣸⣿⣅⣼⣿⣄⣼⣿⣄⣽⣯⣠⣿⣧⣠⣿⣧⣨⣿⣇⣸⣿⣅⣼⣿⣄⣼⣿⣄⣽⣯⣠⣿⣧⣠⣿⣧⣠⣿⣇
⢙⣿⡋⢹⣿⡋⢹⣿⠉⣻⣿⠉⣻⣟⠉⣿⡏⢙⣿⡏⢙⣿⡏⢹⣿⡉⢹⣿⠉⣻⣿⠉⣿⣟⠉⣿⡏⢙⣿⡏⢙⣿⡋⢹⣿⡋⢹⣿⠉⣻⣿⠉⣿⣟⠉⣿⡏⢙⣿
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⢿⣿⣿⡿⠿⠿⠿⢿⡿⠿⠿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣴⡿⢶⡀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣜⣧⡀⣓⠋⣈⢟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⡄
⠀⠀⠀⢶⣶⣶⣶⡏⣿⣷⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠉⠁
⠀⠀⠀⠸⣿⣿⣿⡇⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣆
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠏⣠⣤⡀
⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷
⠀⠀⠀⣀⣜⠒⠶⠶⠴⠶⠖⢒⣄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡙⠟⠁
⠀⠀⠀⠛⠻⠿⠶⠶⠶⠶⠾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷
⠀⠀⠀⢦⣄⣀⣀⠀⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠏
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠸⠸⠰
⠀⠀⠀⠀⠀⠈⠂⢀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣾⣾⣾⣾⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆
⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⣶⣶⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠦⢥⠀⣸⣿⡄
⠀⠀⠀⠉⠁⠀⣀⡀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣌⣓⠒⠲⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⢦⣍⣉⣉⡽⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿
⣿⣿⣿⣿⣿⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠻⣿⣿⣶⡀⠀⠀⠀⡄⠀⠈⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣷⣾⡿⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⡿⠿⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠓⠀⢁⣀⣻⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠖⠛⠋⠙⠋⠛⠋⢻⡿⢟⣽
⠀⠀⠈⠁⢈⣀⠉⠀⠋⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣀⣠⠤⢄⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢐⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣭⡀⠀⢀⣸⣦⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠢⣄⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠦⣝⣷⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⡿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⢠⡋⢲⠖⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠉⡑⠂⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⣸⠓⣴⠂⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢀⡀⠄⠠⠤⠀⡈⠀⠀⠀⠒⣀⢤⡀⠀⠀⠀⠀⠀⠀⠠⠏⠉⠁⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⢺⣀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠁⢀⠄⡪⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠎⠀⠀⠀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠀⠀⠀⢊⠤⠒⢉⠀⠀⠤⠈⠑⢄⠀⠁⢂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⡄⢀⢔⠁⡚⠉⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠁
⠀⠀⠀⢀⠀⠀⢀⠄⠂⢘⢟⠛⠒⠐⠄⡅⠀⠀⡂⠄⡀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢊⢔⠡⢒⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣀⣴
⠀⠀⢀⠊⠀⠔⠁⠎⢔⠕⡱⡪⠂⠡⡂⢀⠀⢈⠔⡨⢂⠄⠀⠔⠁⠞⠝⡐⠀⣾⢐⣡⠎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡌⠋
⠀⠀⠆⠀⡌⠀⠀⠀⠀⠈⠀⠁⠁⠊⠢⠘⣆⠠⢊⠔⡡⡢⡢⡀⠌⠚⢈⣩⠁⠛⠶⣅⠨⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣀⠀⠀⢈⠁⠀⠀⠠⠂
⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢢⡁⠪⠊⢈⠋⠀⠀⠘⠉⠊⢑⠠⠀⠈⠓⡐⠡⠀⠀⠀⠨⡋⠆⠀⢀⡤⡠⠈⠐⢄⠑⢌⠂
⠀⠀⠀⠀⢃⠀⠀⢂⠀⠀⠀⠀⡊⣂⠕⠊⢅⠠⠄⠾⣷⠃⠀⠀⠀⠀⠀⠀⠁⠂⢕⠀⠀⠘⡎⠴⠀⠀⠅⡂⢀⣠⢖⠎⡁⠀⠄⠀⢡⠀⢂
⠀⠀⠀⠀⠈⡄⠀⠐⡂⠔⡠⢀⢀⠂⠀⠀⠀⠠⠐⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡷⠠⠀⠀⠠⠈⠫⣋⠄⡪⢐⢅⠀⠀⠀⡆
⠀⠀⠀⠈⢂⠘⢄⠀⢐⢅⡂⢀⠍⠀⠀⠀⠀⠄⠊⠅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠔⠅⠀⠀⠈⠀⢱⡨⢐⠕⡠⠂⠀⠀⡆
⠀⠀⠀⠈⠢⢈⠢⡑⠤⡁⠂⢐⢧⠀⠀⠀⠀⠁⡂⠅⣣⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣟⠀⠠⠀⠀⠀⠀⠀⣆⠅⡊⢔⢴⠀⠠⠀⡀
⢀⣀⡰⠂⠀⠂⠀⠀⠀⠀⠁⠈⠘⡤⠀⠀⠀⠀⠐⠡⡹⣆⠀⠀⢂⠄⠠⡀⢀⠄⡠⠀⠀⡼⢑⠡⠊⠀⠀⠀⠀⢀⡡⢊⢔⢅⠕⡠⢃⠔
⠰⠧⡨⠛⠀⠀⠀⠀⠀⠀⠀⠀⢦⡘⢄⠲⢄⠀⠀⠀⠐⠋⠁⢄⠒⡥⠮⠂⠅⡊⠔⣡⣶⣶⣷⠃⠀⠀⠀⡠⢀⣼⡮⢖⣰⡥⠖⠴⠃⣤⣠⡤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠂⠑⠠⢄⡀⣐⣀⢀⡔⠁⢉⠘⣿⣤⡅⠂⠉⣄⡛⢀⣤⣀⠀⠀⠀⣠⢈⣉⣩⠭⠶⠋⠀⠀⠺⣯⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠇⠎⠀⠐⠀⠉⠃⠁⠀⠀⠁⠩⣤⣤⠤⠴⡠⠂⠀⠀⠠⠐⣋⠉⠴⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⡄⠀⡇⠀⠀⠀⠀⡘⠀⠀⠜⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠘⡀⢁⠀⠀⠀⢠⠁⠀⡌⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢡⠈⠀⠀⠀⡄⠀⠜⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠆⠀⠀⠰⠀⠜⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⢰⡆⠂⡌⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣧⡐⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠘⣄⡰⠙⣄⣤⢀⡿⠀⣠⠴⡇
⠀⠀⠀⡀⠀⠀⢠⡄⣽⠑⠾⠀⠈⠃⠀⠙⠈⠃⠰⠞⠁⠐⠇⢀⣠
⠀⠀⠀⠙⢟⠃⠶⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⢩⠃
⠀⠀⠠⣤⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣠⠶
⠀⣀⣀⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⣀⣀
⠈⠙⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠒⠊⠉
⠀⣠⣔⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠦⠄
⠀⠀⠀⠀⣼⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣆
⠀⠀⠀⠈⠁⠀⣯⠴⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠀⡴⠈⠀⣠⠛⢩⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣇⠞⠻⢀⡜⢧⡞⣆⡞⠳⣄⣯⠙⠶⣄⡘⢆⠀⠀⠀⢀⣼⡗⠀⠀⢿⠀⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠟⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠙⠺⣦⠀⠀⣼⠏⠀⠈⠁⠀⠀⠠⡀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⢸⡇⢀⡖⠂⠀⠀⠐⣒⣚⡇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠚⠁⠀⠀⠀⣾⢡⡀⠀⠀⠀⠀⠀⠀⠈⣡⠀⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⣇⠀⣠⠀⠀⣀⠀⠀⣿⡀⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠹⣤⣤⠋⠀⣴⢟⣧⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠖⠟⠛⠛⣡⣠⠆⣀⣀⣴⡿⠋⠘⣿⣷⣄⠀⠙⣿⡳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⣾⠛⠄⠀⠀⠈⠃⠉⠀⠉⠛⣯⠠⠶⣄⠈⠉⠻⠷⣦⡈⠹⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⢦⡀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⣤⣹⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡶⡄⢀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠃⠀⡈⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣀⡀⠀⠀⣦⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣠⡤⠀⢀⣴⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⢿⠇⠀⠀⠀⠉⣿⠨⠲⠕⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠘⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠀⠀⠀⢧⠀⠀⠀⠀⣿⡄⠀⡢⠀⡀⢅⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠈⢣⠀⠀⠀⠸⡇⠂⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⡏⠀⢦⡄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠫⠄⠀⠀⠀⠇⢠⠈⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠆⡀⢀⠀⠀⠀⢠⡄⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠣⣈⣀⣴⠆⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠑⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢀⣿⣿⡄⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⡦⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠉⠀⢩⣷⣦⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠰⣿⠂⠀⢀⣽⡶⣦⡀⠀⢀⡀⠀⠀⠀⢠⡄⠀⠀⠁⠀⢀⡀⠀⢼⣿⣀⠀⣠⣄⠀⠀⢠⠆⠈⠛⠋⠀⣿⣦
⢀⡶⠿⣿⣷⣿⣿⠷⠛⠁⠠⠾⠇⠀⣠⠀⣨⡏⠀⠠⣶⠀⠘⠿⠂⠛⠉⠉⣸⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠛⣿
⣼⡇⢰⡌⠻⠛⠋⠀⠀⢦⠀⠀⠀⣻⠁⠀⠀⣀⠀⢤⣿⣆⡠⠀⠀⠀⠀⠀⠛⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠰⣿⠀⠀⠉
⠏⠀⠛⠛⠀⠀⣠⣶⣿⣿⣤⡴⢰⡇⠀⠀⢀⣿⡆⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠆⠈⣤⡀
⠀⠀⠀⠈⡿⠓⢻⣿⡟⣹⣿⢀⣽⠀⠀⠀⣸⠋⠀⠟⠉⠃⠀⠀⢐⡉⠁⣀⠀⠀⠎⣩⣥⣄⠀⠀⠀⠀⢰⡇⠀⡇⠀⠀⠀⠘⠓⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⣀⢖⢄⠀⠀⠀⠰⠄⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠪⡼⠄⠀⠀⢀⡴⢯⡨⠁⠀⠀⠀⠊⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⠀⠀⠀⠀⠀⢠⡮⣅⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠤⠁⠀⠀⠀⠀⠀⠸⠓⠼⠀⠀⠀⢂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠟⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⢂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠀⡀⠀⠀⠀⠀⢀⡨⠣⢠⠄⠀⠀⠀⠀⠀⠘⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢴⢂⣁⠘⠃⠀⠀⠀⢠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⢄⠀⠀⠠⢄⠀⡀⢎⢠⡨⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠆⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⡠⠃⠀⠀⠀⠻⣈⠖⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠖⠢⡎⠁⠙⠊
⠀⠀⠀⠀⠀⢀⠂⠌⠀⢀⠀⠀⠀⡀⠓⢄⠛⠉⠂⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠔⠁⢀⠀⠊⠀⠀⡀⠔⠂⢄⡀
⠀⠀⠀⠀⣈⠂⡠⠂⡠⠀⠁⡀⠄⠂⠁⠄⠐⠈
⠀⠀⠀⣰⠁⢈⠄⢊⠀⠀⠡⠐
⠀⠀⢰⣷⣤⠵⠚
⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠿⠿⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠨⡆⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⢲⠆⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⡃⠀⠀⠀⢀⡀⢀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠘⣧⠰⣷⢀⡼⠁⣀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⡀⠀⠀⠈
⠀⠐⠀⢸⣷⠀⣸⠃⠀⠈⢹⣿⡏⠀⠀⠹⡄⢴⡷⢀⡏⠀⠸⣄⢰⡷⠀⠀⠀⠻⣄⢰⡷⢠⡏⠀⠠⣷⠄⢀⡴⠀⢦⣀⠀⣾⡆⣠⠏
⠀⠀⣴⢲⣷⡞⠁⠀⠀⠀⣼⠿⣇⠀⠀⠀⠉⣿⣿⠉⠀⠀⠀⠈⣿⣿⡟⠛⠦⠀⠈⢻⣿⡏⠀⢀⡴⣾⣿⠉⠀⠀⠀⠈⣹⣿⡟⠁
⠀⠀⠘⢾⣿⡇⠀⠀⢀⡾⠁⠀⠘⢧⡀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⢸⡿⡇⠀⠈⠇⢸⡿⣆⠀⠀⠀⢠⣿⣿⣿⠀⠃
⠀⠀⠀⢸⣿⡇⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⢸⡇⢹⠀⠀⠀⠈⣿⣻⠉
⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠙⠙⠀⠀⠀⠀⠀⠈⠃⠃⠀⠀⠀⠛⠀⠛⠀⠀⠀⠀⠙⠙

⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⢀⣨⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⢀⣀⠁⠃
⠀⠀⠀⠀⠻⣽⡿⣿⡷⠦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢶⡯⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⠀⢀⠄
⠀⠀⠀⠀⠀⢸⡗⣦⡀⠀⠁⠀⠀⠀⠀⠐⣿⣿⡾⢿⣄⠀⠈⡁⠤⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠀⣀⡁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠙⢷⠀⢸⣿⣷⣶⣦⣿⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠟⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠰⠟⠀⠀⠀⠀⣼⣧⠀⠀⢠⣿⣧⡀⢈⣽⢷⣤⣭⣿⣿⣿⣁⡀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢷⣤⣜⣟⣉⣠⣀⣡⣄⣿⣿⣿⣿⢿⣿⣿⠀⠀⣠⣴⡿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡸⣿⣿⣷⣷⣦⠰⣷⡶⣶⣶⣶⢶⣤⣿⣷⡶⠿⠛⠁
⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡾⣿⣿⡿⢶⣶⣶⣾⡟⣿⡇⣿⣿⣿⣷
⠀⠀⠀⣽⣅⠀⠀⢀⠀⠀⢀⠀⠀⢨⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⣿⣾⣿⣼⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣇
⠀⠀⠀⣿⡟⠙⠋⠉⠀⠀⠈⠙⠛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡇⣿⡇⣿⢾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢹⣿⠻⠇⣿⡇⣿⢸⣿⢸⣿⠀⠈⠀⠀⣿⢸⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠀⠀⠀⢴⠿⠋⠀⠀⣼⡇⠀⠀⠻⠃⠻⢸⣿⢸⣿⠀⠀⠀⠀⣿⠸⣿
⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢸⡿⢸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠠⠤⠈⠂⠀⠀⠀⠀⠠⠨⠑⠀⠀⠀⠀⡀⡀⠀⠀⠉
⠄⢀⡀⠀⠀⠀⢀⠔⠊⠉⠐⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠱⠄⠀⠀⠠⢀⠄⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠙⠀⣀⣀
⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⠊⠉⡢⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠲⡎⠠⢐⢬⠀⡄⡄⠀⠈⡉⢄⡀⡤⠀⠀⠂⠀⠀⠉⢳
⠀⠀⢸⡀⠀⠀⠐⠀⠀⠘⠋⣸⢏⡶⠀⡠⠀⠀⠂⢁⡐⡑⣒⣠⢖⠲⠓⢀⠃⢰⡤⠀⢆⠀⠀⡕⠂⢈⠀⢴⡇⠀⠀⠀⠀⠈⡆
⠀⠀⡸⠀⠀⠀⠀⡀⠄⢀⠸⠃⠁⠀⠀⡜⠀⠂⠐⠀⡛⠁⠚⠁⠀⠀⠀⠀⠃⠀⠒⠂⠁⠉⠀⡈⠀⠘⠀⣸⡾⠣⢤⠀⠀⠸⠁
⠀⡐⠡⠀⠀⠀⠀⡡⡀⠀⠁⠂⠀⠀⠰⡡⣒⠉⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠂⠈⢀⠔⠁⡎⠙⢆⠠⠚⠙⢻⡿⠛⢉⠠
⠀⢀⠆⠀⠀⠀⢠⠀⠈⢆⠱⡈⠠⠀⠊⡀⠝⠂⠜⡾⠃⠰⡗⠀⠀⠤⠀⠀⠁⣠⠀⠈⢀⡜⠁⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⢰
⢐⠕⠒⠠⡀⠀⠈⡕⠄⠈⢆⢃⠔⢁⠞⠃⠀⢠⠔⠁⠀⠁⢈⠀⠀⢢⠠⠤⠚⣚⡆⠀⠉⠀⠀⠀⠀⣜⡦⠄⠀⠀⠀⠃⠀⠐⡆
⠁⠀⠀⢠⠇⠀⠀⠃⠈⠢⡀⠀⡔⠁⠐⠀⡰⠃⢀⡀⠀⠀⣠⠃⠂⠸⠀⠀⠀⠀⠘⣈⣋⡗⠒⠒⠈⢻⠧⢼⠉⠑⠂⣶⠀⠀⠁
⠀⠀⠀⡎⠀⠀⠀⡇⢀⡀⠀⠀⢱⠀⠀⠰⠁⠀⠀⠈⠉⠉⠈⠀⠈⠊⠀⢠⣀⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠂⠤⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠐⠒⠤⡀
⠀⠀⠀⢀⠐⠉⠀⠀⠉⠰⠁⠀⠀⠀⠀⠀⠀⠈⠳⡊⠉⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⡖⠁⠀⠀⠀⠀⠀⠀⠈⢖⠈⠉⠈⠁⠢⣄
⠀⠀⡐⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂
⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡱⢒⠤⠤⠐⢎⡁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠕⠢⠤⠤⠐⣌⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠈⠁⠐⠖⠀⡩⠀⠈⠀⠉⠈⠩⠉⣀⣐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⢰⠂⢈⠡⠀⠀⠀⠁⠈⠏⠡⣀⡒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣇⠘⠉⠣⠀⠀⠀⠀⠀⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠦⠀⠀⠀⠀⠀⡂⠘⠃⢀⠀⠀⠐⠋⠧⡀⠹⠍⠛⠀⠀⠠⡀⠚⠃⡄⠀⠀⠀⠀⢀⠴⢎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠗⠂⢀⠀⠀⠀⠀⢃⠠⢲⣤⠄⠰⠁⢰⠄⢸⠀⢴⠄⠰⠀⢤⡇⠄⠶⠀⠀⠀⠀⠀⡀⠐⠢⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠛⠶⣤⠖⡏⠀⠸⠀⠀⣷⣄⡀⠀⠈⠀⠀⣀⣠⡇⠀⡅⠀⢸⠓⢦⣤⠶⠛⠁⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣄⡀⠈⢻⡇⠀⠙⠉⠈⣿⠏⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⠀⢱⠀⠀⠈⠀⡖⠐⢮⠀⠀⠀⡸⠀⠹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⡆⠀⠀⢀⡇⠀⠘⡆⠀⢠⠇⠀⠀⠙⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠃⠀⠀⠀⠀⠳⣄⣠⠼⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢲⡶⠒⠲⣶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⢸⡇⠀⠀⣿⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⠿⠿⠿⠇⠀⠀⠿⢿⠿⠿⠿⠿⠦