Work anniversary Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡄⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⡀⠀⠀⢸⠀⠀⣀⣀⠀⢀⡀⣀⠀⢀⡀⣀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⠁⠉⠳⣦⣾⠀⡄⠀⢸⠀⣼⠀⢸⠀⣸⠀⢘⠆⠀⢸⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠒⠒⠚⢿⠈⠙⠒⠉⠒⣿⠒⠚⠂⣿⠒⠚⠐⠁⠈⠓⢚⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⢀⠄⠀⠇
⠀⠀⠀⠀⠀⢀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⢸
⠀⠀⠀⠀⡐⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⣤⠄⢤⠀⠀⣤⡄⢤⡀⢀⡄⠀⢤⠀⠤⡀⠀⠀⠄⠀⢤⡀⠀⡠⡄⠀⠀⠤⢤⠀⢠⢤⠀⠀⢤⠀⠀⡄
⠀⠀⠀⢧⠀⠀⠀⠀⡠⣿⠀⡀⣾⠀⠈⡇⡀⢸⠀⠀⡇⡸⡇⡀⠸⡄⢀⠗⢾⡀⠀⡀⠀⣇⣰⡀⠘⠀⢶⠀⣸⡀⡀⠸⡄⡀⢸⡀⢀⡇⡠
⠀⠀⠀⠈⠓⠶⠶⠚⠁⠹⠞⠁⠈⠀⠀⠉⠀⠈⠀⠀⠈⠁⠉⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠈⠁⠉⠉⠁⠀⠉⠀⠉⠀⠀⠉⠀⠀⠉⠡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡸


⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣀⣀⣰⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀⠀⠰⢀⠀⠀⣠⣄⠀⠀⡐⡆⢀⡀⣀⣀⢀⢀⣀⣀⢀⣀⡀⣆⣀⣀
⠀⣹⠀⠐⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠆⠀⣏
⠀⢩⢬⠀⠈⢡⠴⠶⠶⢦⡀⢺⡇⢰⣦⠒⠒⣄⠀⠀⠀⡴⢂⠔⠓⢦⠐⣄⠀⠀⣴⣤⠴⠶⢬⡁⠀⡤⣍
⠀⢛⡀⢰⣴⡏⠁⢰⠀⠀⣹⣤⡄⢰⣉⠀⠀⣼⠁⠀⠸⡇⢸⡀⡹⢸⠀⣸⠀⠀⣐⠀⠠⢀⠂⠹⠄⢀⡛
⠀⣾⢄⠙⠁⠀⠄⠈⠠⠄⠐⠈⠋⢰⣉⢀⡂⣼⠁⠀⢐⠛⣀⡂⠀⢂⡀⢱⠀⠀⠻⣄⠑⠂⢈⣭⣀
⠀⢈⠉⠀⠀⠈⡙⠛⠛⡋⠀⣀⡀⠀⡘⠢⠔⠋⠁⠠⠈⡁⠈⠳⠤⠊⠁⢈⣀⠀⠀⠈⠙⠛⠉⢈⡁⠐
⠀⠀⠀⣄⡤⡀⠀⠀⡎⣴⢋⣭⣍⢳⡌⡆⠀⢔⠀⠐⠂⠈⠢⠀⢀⢮⡾⠛⠙⠻⣯⢂⠀⢡⠎⣩⢌⠙⡄
⠀⠀⠀⠋⠑⠀⠘⠀⣁⣇⢻⣽⣽⢇⣇⡀⠀⠉⠀⠘⠋⠀⠩⠀⠸⣻⡇⠘⠋⠃⢽⢿⠀⢸⠠⠶⢻⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠰⣧⡌⠳⠾⠷⠛⣤⣷⠄⠀⠂⠀⠀⠔⠀⠀⢶⣠⠍⠤⠬⠤⢨⣰⡦⠈⠢⢤⠤⠒⠁
⠀⣀⠀⣀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⢠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠬⢌⠉⠦⠰⠶⠖⠶⠰⡦⢀⠀⠀⣾⢠⣤⠶⠛⠷⠾⠛⠶⣤⡄⣾⢨⡁⢤⡄⠀⠁⠁⠁⠉⠈⣤⠀⣏
⠀⠀⠠⢲⣾⢛⣻⣿⣿⣟⣋⠉⠀⡀⣿⢸⡇⠀⠂⠀⠀⠀⠀⢸⡇⣿⢠⠄⣠⡔⠃⠘⠀⠛⠀⠛⣄⠀⣤
⠀⠀⠐⠀⠓⢈⠙⠀⠋⠙⢱⠖⠀⡅⠀⠉⠙⠛⠶⣦⣴⠶⠛⠋⠉⠀⠐⠀⠀⠆⠶⠶⠶⠶⠶⠶⠀⠀⠑
⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣖⣾⣵⣢⠄⠀⠀⠀⢀⡴⠞⠓⢶⣀⠀⠀⣠⣦⣄⣀⣀⣀⣠⣴⣄
⠀⢸⣍⠀⠄⠀⠰⠭⢀⣽⠃⢠⣾⣟⣿⣿⣿⣿⣿⣷⡄⠠⣟⠀⠧⠈⠷⢹⡆⠀⢹⣿⣽⣿⣿⣿⣽⣿⡟
⠀⠒⠒⠛⠿⢆⡰⠟⠛⠒⠂⠀⠙⢋⢿⣿⣿⣿⡙⠋⠀⠀⠻⣜⡉⠉⣉⠞⠀⠀⢾⣿⣿⡿⠿⢿⣿⣿⡷
⠀⣀⠀⠀⣠⣤⣀⢀⡀⠀⠀⠀⠀⠀⠉⠑⠊⠁⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠈⠁⣀⠀⣀⣤⠀⡈⣀
⠀⣼⠀⢶⠆⠀⠀⠈⠁⠓⠲⠲⠤⢤⣤⠄⠀⢠⠄⣀⣄⠠⡄⠀⢤⠠⠦⡤⠆⠖⠀⠛⠁⠀⠀⠰⡶⠀⣧
⠀⠀⠀⠀⠘⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠆⠙⠋⠰⠃⠘⢃⠀⠀⢀⠀⡀⠀⡀⠛⠛⡛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠋⠉⠻⠆
⠀⠀⣀⣀⣁⣋⣀⣁⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⠲⠖⣀⣀⣀⣀⣀⣈⣀⣀⣀⣈⣀⣁⣘⣀⣉⣀⣀⣀⣀⡀
⠀⠀⠉⣍⣉⣉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠛⠅⠨⠙⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⠉⣭⣭⣉⣉⣉⣉⣩⣥
⠀⠀⠀⠻⠟⡛⡭⠁⢀⣴⠾⠛⠓⠀⣀⠄⠀⣤⢆⣴⢞⣛⣛⠓⢦⡐⣦⡀⢰⡾⠋⡉⢉⡙⢶⡄⢸⣿⣍⡏⢹⣿
⠀⠀⣐⣀⣭⣥⣄⡀⢸⡗⠀⠢⠴⠲⠀⠀⢰⡏⡾⠁⠋⡀⡀⣑⠀⢻⢼⡆⢸⡇⢩⣋⣬⡆⢸⡇⢸⣿⢼⠧⣼⣿
⠀⠀⠉⣉⠫⠽⠄⠀⠸⣧⣀⠀⠘⢀⠄⡀⢸⣏⣧⠀⡀⠋⠓⠃⠀⣸⢭⡇⠸⢧⣀⠀⠊⣠⡾⠃⢸⣿⣿⣿⣿⡟
⠀⠀⠠⣭⣶⣶⡆⠀⠀⣩⠛⠷⠊⠀⠀⠀⢀⣱⣾⣿⣿⣿⣿⣿⣿⣿⣎⡁⠀⠀⠙⠳⠟⠉⠀⢠⠘⠹⣿⣿⡿⠁
⠀⠀⠀⣀⠈⠉⠁⣾⣾⣿⡷⠀⠀⣀⠀⠀⠈⠿⠟⠁⢀⢰⡆⣀⠀⠛⠿⠁⠀⠀⣄⣀⡀⠀⢺⣿⣷⣷⠀⠁⢀⣀⡀
⠀⠀⠤⣿⠟⠂⠀⠈⠈⠉⠁⠒⠻⣿⠄⠀⠀⠀⠀⠐⠐⠛⡛⠃⠂⠄⠀⠀⠀⠀⢿⣿⠛⠿⠈⢉⠁⠁⠀⢰⠈⠣⡷
⠀⠀⣤⠈⠀⠈⠉⠀⠓⠒⠂⠁⠀⠁⣤⠀⠀⠀⣴⣾⣿⠿⠿⣛⣓⣂⠀⠀⠀⠀⣀⣘⣠⣀⣀⣀⣓⣀⣤⠼⠀⢓
⠀⠀⣀⣰⣶⣶⣶⣶⣶⣶⢶⣶⣶⣆⣀⠀⠀⠀⢲⠐⣖⣛⣩⣭⣭⣭⠄⠀⠀⢸⡉⠉⣟⣛⣛⠛⡛⣋⣄⣠⠀⢸
⠀⠀⠿⠿⠏⠉⠙⠋⠛⠛⠋⠉⠻⠿⠧⠀⠀⠀⠈⠙⠛⣛⢛⡛⠋⠁⠀⠄⣀⣀⡀⠀⣀⣉⣩⣬⣥⣭⣵⡷⠞⠁
⠀⠀⠀⣠⠀⠀⠠⠠⠂⠤⠠⠀⠀⣄⠀⠃⠽⠘⠀⣀⣠⣤⣦⣤⣀⡀⠀⡀⠼⠅⣀⢸⠉⢩⣭⣿⣻⣭⠉⢹⣤⡖
⠀⠀⠙⣿⠷⠆⡤⡤⣠⠤⣤⠰⠾⣿⠁⠀⡰⠛⠛⢛⠛⡛⢛⠛⣛⣛⡛⢁⡀⠀⣀⣈⣁⣈⣉⣿⣟⢻⣶⣿⠿⠟
⠀⠀⠀⣠⣤⣤⣤⡀⠁⠀⢁⣠⣤⣤⣤⡀⠹⠶⣦⣶⣶⣶⣶⣶⣷⣤⠷⠖⠀⢀⣙⣟⣛⠛⠛⠛⠋⢀⣀⣀⡀
⠀⢀⣾⡏⣥⣠⣍⣿⣦⢠⣿⡟⡯⣉⡻⣿⡆⠀⣠⢬⣉⣙⣛⣉⣥⢤⡀⠀⣴⣋⣠⣦⣈⣻⡄⠀⣴⡟⣉⠉⢻⣧⡀
⠀⠸⣿⣷⣿⣷⣾⣾⣿⢸⣿⡄⠞⠻⢁⣿⡏⢸⣅⡲⠤⠩⠭⠡⠄⢂⡷⠀⣿⠿⠿⠿⠯⢿⡇⠐⣿⡿⠿⠯⠽⣿⠇
⠀⠀⠙⢷⣦⣤⣴⠿⠁⠈⠻⣿⣶⣶⣿⠟⣡⡀⠨⡛⠲⣤⣦⠶⠚⠯⢀⣤⡙⠶⣬⣨⣵⠞⢁⡀⠘⠿⣶⣶⠾⠋
⠀⠀⣠⣤⡀⠀⣀⢀⡀⠀⢠⡄⠀⠨⠦⠬⠭⠽⠦⠤⠤⠤⠤⠤⠤⠵⠮⠭⠭⢴⠤⠀⠀⢰⢋⡙⡆⠀⠀⠄⠀⠀⠄
⠀⠘⣿⣽⡇⢸⣿⣿⡇⠰⢾⡿⠆⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⢰⡛⢾⣰⣆⡷⢻⡆⠆⢐⣀⡇
⠀⠀⠈⠋⠀⠈⠙⠛⠁⠀⠘⠋⠀⠐⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠇⠈⠑⠂⠙⠋⠐⠊⠁⠀⠚⠁

⠀⠀⡴⠃⢠⡄⠘⢦⠀⠀⠀⠀⡴⠃⠴⡄⠘⢦⠀⠀⠀⠀⡴⠃⢴⡄⠘⢦⠀⠀⠀⠀⡴⠃⣤⡄⠘⢦
⠀⢐⡇⠀⠐⠇⠀⢸⡆⠀⠀⢐⡇⠀⠸⠇⠀⢸⡂⠀⠀⢰⡇⠀⠺⠟⠀⢸⡂⠀⠀⢰⡇⠀⠲⠟⠀⢸⡂
⠀⠀⢳⣤⣤⣤⣤⡞⠀⠀⠀⠀⢳⣤⣥⣬⣤⡞⠀⠀⠀⠀⢳⣤⣥⣬⣅⡞⠀⠀⠀⠀⢳⣤⣤⣤⣄⡞
⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⡴⢃⣄⣤⡘⢦⠀⠀⠀⠀⡴⢣⣄⣠⡜⢦⠀⠀⠀⠀⡴⢣⣄⣤⡜⢦⠀⠀⠀⠀⡴⢣⣄⣠⡜⢦
⠀⢐⡇⠀⠟⠿⠃⢸⡂⠀⠀⢐⡇⠰⠇⠿⠇⢸⡂⠀⠀⢐⡇⠰⠇⠿⠇⢸⡂⠀⠀⢰⡇⠰⠟⠻⠇⢸⡂
⠀⠀⢳⣠⣤⣥⣄⡞⠀⠀⠀⠀⢳⣠⣤⣤⣄⡞⠀⠀⠀⠀⢳⣠⣥⣤⣄⡞⠀⠀⠀⠀⢳⣤⣤⣤⣄⡞
⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⡴⢃⡄⣠⡜⢦⠀⠀⠀⠀⡴⢣⡄⣠⡜⢦⠀⠀⠀⠀⡴⢣⡄⣠⡜⢦⠀⠀⠀⠀⡴⠣⣄⣤⡘⢦
⠀⢐⡇⠘⠗⠿⠇⢸⡆⠀⠀⢐⡇⠸⠟⠻⠇⢸⡂⠀⠀⢐⡇⠸⠟⠻⠇⢸⡂⠀⠀⢰⡇⠰⠏⠿⠃⢸⡂
⠀⠀⢳⣠⣤⣥⣄⡞⠀⠀⠀⠀⢳⣠⣤⣤⣄⡞⠀⠀⠀⠀⢳⣠⣤⣤⣄⡞⠀⠀⠀⠀⢳⣠⣤⣤⣄⡞
⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⡴⠣⣄⣤⠘⢦⠀⠀⠀⠀⡴⢣⣄⣠⡜⢦⠀⠀⠀⠀⡴⢣⣄⣠⡜⢦⠀⠀⠀⠀⡴⣃⣀⣀⣘⢦
⠀⢐⡇⠰⠇⠿⠃⢸⡆⠀⠀⢐⡇⠸⠟⠻⠇⢸⡃⠀⠀⢐⡇⠸⠟⠻⠇⢸⡃⠀⠀⢐⡇⠹⠻⠟⠿⢸⡆
⠀⠀⢳⣠⣤⣤⣤⡞⠀⠀⠀⠀⢳⣤⣥⣤⣄⡞⠀⠀⠀⠀⢳⣤⣤⣤⣄⡞⠀⠀⠀⠀⢳⣤⣤⣤⣄⡞
⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠸⠇⠈⢥⠐⠒⠈⠁⠀⠀⠀⠀⠈⠁⠒⠂⡬⠁⠸⠇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⡏⠁⣿⠀⠁⠐⠀⠀⠀⠀⠁⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⠀⠆
⠀⠀⠀⠀⠀⠆⠀⡀⠁⠀⣦⠁⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠞⠈⣡⠀⠈⢀⠀⠰
⠀⠀⠀⢰⠀⠀⡘⠃⣀⣁⣬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣡⠶⢀⠘⢃⠀⠀⡆
⠀⠀⢠⠀⠀⢘⠋⢀⣉⡐⠀⠀⢀⣴⠶⠾⣶⣶⣤⠀⠀⠀⠀⣴⣶⣦⣤⣤⣤⡖⠀⠀⠶⠋⡀⠙⡃⠀⠀⡄
⠀⠀⠀⠀⠐⠛⠀⢦⣀⠅⠀⠀⣿⣷⡄⠀⠈⣿⣿⠆⠀⠀⠀⣿⠛⠿⠿⠟⠋⠀⠀⠀⠈⣼⠃⠀⠛
⠀⠈⠃⠀⠠⠂⢐⠂⢀⠀⠀⠀⠛⠿⠋⠀⣰⣿⣏⠇⠀⠀⢠⡟⣀⣤⣤⣄⡀⠀⠀⠀⠀⠄⡤⠀⠐⠆⠀⠘⠁
⠀⢷⡄⠀⢀⡄⠀⠙⠋⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠸⠏⠉⠈⠙⣿⣿⣦⠀⠀⠀⠙⠁⠁⢠⡀⠀⢠⡶
⠀⣠⣅⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⠀⠀⢠⠀⠀⢀⣀⠀⠀⠀⢹⣻⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⣨⣄
⠀⠙⠿⠎⠐⢃⠀⠀⠀⠀⠀⠀⢰⠅⠤⣦⣤⢄⣤⣾⠀⠰⣷⣿⠃⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⡘⠂⠰⠿⠋
⠀⠀⣿⣷⠠⢻⡿⠀⠀⠀⠀⠀⠚⠀⠀⠈⠺⠿⠟⠁⠀⠀⠙⠻⠶⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⢿⡏⠔⣾⣿
⠀⠀⠈⢩⣅⢣⠸⣿⡇⠀⠀⠀⠀⠀⠀⢤⡄⢠⠀⡀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣌⣨⡍⠁
⠀⠀⠀⠘⠶⠆⠰⡉⠀⣾⡆⠀⠀⠀⠀⠈⣿⠁⣿⠘⢨⢼⡇⢸⠉⠙⢮⠀⠀⠀⠀⠀⣦⡄⢀⠀⠸⠿⠏
⠀⠀⠀⠀⠀⣽⣿⣮⠀⡙⠁⢸⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⣾⡇⠀⢋⠔⣵⣿⡀
⠀⠀⠀⠀⠀⠈⠉⠩⠄⣬⡀⢈⡋⠘⠿⡿⢠⣴⡤⡀⠀⠀⢠⣤⢠⡄⣾⡇⠀⠙⡡⢀⡁⠠⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⣠⣄⣐⡢⠬⣀⣛⠛⠃⠀⠀⠸⠛⣋⣀⠭⢔⣲⣤⣀⠛⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠋⣠⣶⣷⣬⠉⠉⠉⠉⣥⣾⣶⣄⠙⠿⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡾⢡⣤⠀⠀⠀⠀⠀⠀⢠⣄⠹⡆⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢸⣃⡈⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⣀⣻⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠻⣴⡤⠉⠉⠀⠀⣄⡀⣦⢠⣧⢠⡄⣀⡄⠀⠈⠉⠡⣴⡼⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠹⠶⠶⠀⠀⠀⠀⠀⠀⠈⢿⣶⣾⣿⣦⣾⠏⠀⠀⠀⠀⠀⠀⠲⠶⠾⠁⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠙⠷⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠟⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣦⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⢉⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣍⢡⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡙⠛⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡙⠛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢋⣤⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⡿⢣⡆⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⡗⠀⠀⠸⣆⠀⡧⣞⠀⠀⠀⠀⠀⠀⠀⣦⠻⡶⠾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣿⢣⣶⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠉⠈⠀⠉⠀⠁⠈⠁⠀⠀⠀⠀⢰⣆⢻⣷⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣾⡏⣼⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⡌⣿⣾⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣵⠿⡇⣿⡇⣷⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣴⡇⣿⣇⠻⠿⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⠛⣳⣽⢧⣀⠀⣀⣀⣼⣿⣄⣀⡀⢀⣠⢿⣵⡛⠻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠈⠙⠾⢿⣿⣿⣿⠿⠚⠉⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠉⠻⠆




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⡀⢆⠳⠀⠀⠠⠀⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠲⠃⠀⠀⠀⠧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡘⠆⠀⠀⠰⢃⡄⢀⡀
⠀⠀⢠⡐⠤⠉⠀⠀⢀⠀⡐⠀⠈⠥⠜⣠⠀⠀⠀⠀⣀⠁⠰⠌⠀⠀⠀⠀⠀⠀⠀⠴⠘⢁⡀⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠆
⠀⠀⣦⣹⡏⠀⠀⠀⠊⠀⠈⠳⠀⠀⣿⣩⡄⠀⠀⢠⡈⣨⡅⠀⠐⠐⣦⠀⡒⠒⠀⠈⣏⠈⣤⠀⠀⠐⠗⠶⠀⠀⠀⠈⡇⠠⢭⡀⠀⠀⠶⠺⠂
⠀⠐⢶⡴⣆⠀⠀⠁⠉⠀⠁⠀⠀⢀⡲⣶⠶⠀⠀⣤⡀⣴⠆⠀⠀⠠⠋⠀⠉⢳⠄⠀⢮⣀⣤⠄⠀⠘⠛⣛⠀⠀⢀⠈⠀⠀⠀⠑⠀⠀⣛⠛⠃
⠀⠐⠶⢾⢻⣆⡀⠀⠀⠀⠀⠀⣀⣶⣻⠶⠖⠀⠀⢠⣄⡰⠟⣀⠒⠒⠒⠐⠀⠈⢀⡸⢆⣠⣤⠀⠀⠘⠏⢉⣤⠀⠈⠈⠁⠈⠁⠀⠀⣬⡉⠻⠃
⠀⠀⠐⠿⠛⣹⡇⣷⡀⠀⣰⡏⣿⣽⠛⠗⠂⠀⠀⠀⢀⣤⡈⠋⢼⡆⠀⠀⠠⣷⠘⠇⣤⣄⠀⠀⠀⠀⠻⠃⠀⠟⢀⣤⠀⠀⣤⡔⠿⣀⠘⠛
⠀⠀⠀⠀⠙⢋⣽⣿⠓⠖⠻⣷⣍⠛⠛⠀⠀⠀⠀⠀⠀⠉⣠⡶⠀⠀⠀⠀⠀⠀⢠⣄⠈⠁⠀⠀⠀⠀⠀⠈⠛⢀⣾⡁⠐⠀⢈⣧⡀⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⠰⠁⣀⠀⠀⠀⠀⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠄⢠⠀⣄⠀⡤⠤⠀⠀⢹⣧⠀⠀⠀⠀⢀⠅⠀⠄⢀⣀⡀⠀⣀⣀⠐⠀⠪⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⠀⠀⢈⠤⠋⠀⠂⢢⡀⠀⠈⣿⡂⠀⠀⠀⣒⡇⠀⠀⠓⣸⠇⢰⠭⣍⠀⠈⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡀⠀⠒⠲⠔⠘⠀⠼⠁⠀⣸⣿⠂⠀⠀⠀⢧⢇⠀⢀⡾⣥⡔⢰⣄⣿⠃⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠏⠀⠀⠀⠀⠨⠌⠂⠀⠀⠀⠀⠀⠠⠀⠀⠐⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢀⡿⣧⠀⠀⢰⡖⢇⠻⠇⠀⠀⠀⠀⠀⠀⠈⠰⢞⣱⠦⠄⢠⠆⢆⠁⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠀⠀⠛⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢠⠖⣒⢒⠒⣒⢒⣒⡒⠢⡀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠳⠶⣄⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣤⣤⣤⣤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠂⠀⠀⢀⣄⢀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠟⠂⠀⢠⢦⡀⠀⠈⢳⡀⠀⠀⠀⣤⡶⠟⠀⠀⠀⠀⠀⠀⠙⢵⣤⠄
⠀⠀⠀⠀⠀⠀⢠⢣⠀⠀⠀⢹⣿⠀⠀⠀⠘⠸⠀⠀⠀⢰⡏⠀⠀⠀⠈⠋⠀⣀⠀⠀⣷⠀⠀⠀⣿⠁⠀⠀⠀⣀⢀⣀⢀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⡌⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠂⠇⠀⠀⣼⠆⠠⠠⠀⣂⣠⠅⠰⠀⠀⢸⡇⠀⠀⣿⠀⢀⣤⠀⡡⠀⡄⡄⣤⠀⣿
⠀⠀⠀⠀⠀⢰⠁⠀⣀⡤⡀⣩⢩⡅⣀⣠⢄⠀⢸⠀⠀⢻⠇⠀⠲⢛⡁⠤⠤⢖⣁⠀⢸⡇⠀⠀⣿⠀⠰⠷⠀⠇⠀⠃⠇⠼⠀⣿
⠀⠀⠀⠀⢀⣸⡄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣰⣆⡀⠸⣧⠀⠚⠉⠐⠀⠀⠀⠀⠀⣾⠁⠀⠀⣿⠀⠀⠆⠀⠀⠀⠀⠲⠀⠀⣿
⠀⠀⠀⠀⠈⣻⣿⣎⣻⣷⠾⠿⠿⠶⠾⣿⣋⣴⣿⣏⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢯⣦⡄⠀⠀⠀⠀⠀⠀⢀⢤⣿⠄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠑⠢⡥⠔⠋⠉⠉⠉⠉⠉⠁⠀⠀⠈⠳⠶⣦⣤⣦⠶⠋⠀⠀⠀⠀⠀⠀⠈⠯⠶⠶⠶⠶⠶⠶⠯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⡀⠀⠀⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣤⣤⣤⣤⣤⡶⢶⣆⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠳⢄⠀⠀⠀⠀⠀⣀⣴⡶⠶⠶⠶⠶⠶⠶⠶⣶⣄
⠀⠀⠀⠀⠀⠀⢻⡇⠀⣠⢤⣄⠀⣠⢤⡀⠀⣽⡇⠀⠀⢀⣀⠞⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠸⣿⠉⢀⣴⢲⣤⢀⣴⢲⡄⠈⢻⡏
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠛⢣⡿⢱⣿⢸⣷⠀⣿⠀⠀⡠⠎⠃⢠⠄⢠⣤⠀⠠⠤⠄⠌⠨⠶⣄⠀⣿⡀⠀⠉⢼⡋⢸⣿⢸⣧⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣯⣴⡎⣿⢸⠏⠀⣿⠀⢸⠁⠴⠆⢀⡠⠞⣋⢀⡀⢉⣷⠀⠴⠄⢸⡆⢹⣧⠰⣿⣸⡿⠘⣿⣸⠇⢰⣿
⠀⠀⠀⠀⠀⠀⢰⡏⢠⡈⣭⠉⣤⢠⡥⢤⡀⣿⡀⠈⠳⡄⠀⠀⠤⠤⠀⠠⠆⠨⠴⠀⠀⡤⠚⠀⠀⢿⣆⠀⠅⠄⠤⠤⠄⢀⣿⠃
⠀⠀⠀⠀⠀⠀⢾⣅⡀⠁⡉⠀⣈⠈⡉⠀⣁⣼⡇⠀⠀⠘⠓⣄⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠲⣾⣿⣶⣶⣶⣶⣶⣶⣾⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣄⢉⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⢀⣠⠞⠁⣀⣀⣀⠀⠘⠋⠿⠛⣿⣟⣻⣿⡟⠻⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠈⠉⠉⠉⠀⣴⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠱⠀⠎⠀⢊⡈⢉⠀⠀⣀⣤⣈⢋⣉⣿⡟⣷⣦⣄⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⡛⠍⠚⠈⠘⠨⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢂⠬⠚⠛⠛⡒⠥⡀⠉⢷⡀
⠀⠀⠸⡟⠉⠉⠉⠉⠀⠁⠀⠀⠀⢠⣼⡄⠀⠀⠀⠀⠀⠉⠩⠉⠉⢙⡿⠀⠀⠀⣠⡼⠙⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠘⢧⡀
⠀⠀⠀⢹⡄⠀⠀⠠⣤⡄⢀⡀⣄⣤⡀⡄⡄⣤⣄⣀⣠⢄⠀⠀⠀⡜⠀⠀⠀⠀⡿⠀⠘⠀⠇⠘⠸⠘⠃⠛⠀⠓⠸⠸⠘⠒⠃⠀⠈⡇
⠀⠀⢀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢟⡀⠀⠸⠸⠁⠿⠀⠈⠇⢿⠀⠿⠸⠇⠘⠧⠀⢠⡇
⠀⠀⠘⠛⠒⠒⠒⠲⣤⣤⣄⢄⠀⠀⠀⠀⠀⡀⢀⣤⣤⠖⠒⠒⠒⠚⠛⠀⠀⠀⠈⠛⠖⢶⡂⠀⢄⡀⠀⠀⠐⠀⢀⡤⠀⢀⡴⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡧⣤⠤⣦⣶⡯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠩⢒⡒⠒⡚⡍⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⡶⢛⣩⣍⡛⢶⡄⠀⠀⠀⠀⠀⡐⣡⣾⡿⠛⠛⢿⣷⡌⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣆
⠀⠀⢀⣀⡟⣰⡛⣛⢛⣛⡃⣛⠀⡀⠀⠀⠀⠡⣿⡏⢤⠨⣥⡇⢹⣿⢘⠀⠀⢀⡠⢛⣻⡛⠛⠛⠛⠛⠛⠃⣀
⠀⠀⢸⣇⠇⠳⣓⣐⣀⣀⠐⠂⢸⡇⠀⠀⠀⣆⢿⣷⣄⠀⢀⣡⣿⡟⡸⠀⠀⢸⣇⠸⢿⠇⠶⠶⠶⠶⠶⠂⣿
⠀⠀⠀⠀⠙⢦⣍⣛⣛⣩⡴⠋⠀⠀⠀⠀⠀⠈⢢⣙⠿⠿⠿⠟⣋⠔⠁⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠊⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⣷⣦⡀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⣤⣶⡇
⠀⠀⠛⠿⣿⠿⣿⠛⡿⠿⢛⣻⣭⣭⣴⣿⣧⣿⣶⣤⠀⠀⠀⢠⣴⣾⣿⣾⣿⣶⣦⣿⣙⣿⢻⡿⠿⠿⣿⡿⠟⠁
⠀⠀⠀⠀⠛⠻⠿⠶⠷⠛⠛⠉⠉⠀⠀⠀⠈⠳⢿⡀⠀⠀⠀⠀⣼⠷⠃⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⢀⢔⣴⣶⣿⣿⣶⣤⡠⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢠⠞⣁⠀⣀⡉⢳⡄⠀⠀⠀⠀⡄⠺⠛⠻⠳⠿⠿⠿⠗⢡⠀⠀⠀⠀⢠⡾⢋⡀⢀⡈⠻⣦
⠀⠀⠀⢠⡆⣿⠀⣿⠀⡇⡧⠀⡗⣠⠀⠀⠀⡇⣘⣁⣈⣘⣈⣀⣃⣃⢸⠀⠀⣠⣤⢼⡁⢸⡇⣿⢸⠆⣹⢆⣤⡀
⠀⠀⠈⡲⠷⠸⢦⡉⠀⠉⣁⡼⠃⠿⣞⠁⠀⠸⡙⢿⣿⣷⣿⣿⡿⣣⠇⠀⠀⠈⠿⠘⣷⣈⠁⠀⢁⣰⡟⠘⠟
⠀⠀⠀⠁⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠈⠀⠀⠀⠈⠓⠪⠭⠭⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤
⠀⠀⢠⣿⣿⣾⢷⣶⣶⡶⠶⡶⢶⠶⠶⡶⠶⣶⣶⠶⢶⣶⢶⣒⣶⣖⠶⠶⣶⡶⠶⡶⠶⢶⢶⣶⡾⣿⡾⣿⡆
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠃⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⠓⠛⠚⠛⠛⠛⠃
⠀⠀⠆⠂⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠒⠐⠆⠀⠀⠆⠂⣂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣐⠂⠰
⠀⠀⡄⢀⠉⢹⣷⠰⢀⣠⣀⣀⣤⣄⣄⣠⣭⠉⡅⢀⡀⠀⠀⡌⢀⠉⣍⡀⣤⣤⡠⣀⣄⢠⡄⣄⣠⣭⠉⡀⢡
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠀⠈⠉⠉⠉⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣼⡏⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⣿⢃⡾⢃⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠳⠤⠃⠈⠚⠰⠛⠁⣀⣤⠴⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢻⡄⠀⣶⠦⠀⠀⠤⠖⠋⠉⠀⠀⠀⠀⡀⠀⡀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠀⢸⡇⠀⡟⠀⡠⢤⡄⢰⡄⢲⣴⡶⢹⡦⡗⢸⡇⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠠⢤⡀⠠⠖⢺⡏⠉⡇⢸⠃⣸⡇⣿⣀⠞⢹⡧⠞⢁⡭⢺⠇⠈⡁⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⠀⢹⡆⠀⢸⠁⠀⠇⠘⠓⠃⠛⣿⠀⠀⠸⠇⡀⠀⣡⠅⣴⠀⡟⡟⢸⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢠⣿⡇⠈⠁⠀⠈⠀⠀⠠⠀⠀⢀⠀⡤⠄⣶⡄⡺⣤⠐⣿⠐⢿⡴⠀⠷⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⢀⡞⢸⡇⣀⢠⡄⣤⢰⡆⣾⢸⣇⡎⢸⡃⡰⠹⡗⠳⠝⠃⢈⡠⠤⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡾⠂⢾⡇⣿⢸⡇⠿⠘⠃⠙⠂⠉⠀⠀⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⢘⡆⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇⠀⠀⠠⠤⢤⣀⠀⠀⢀⡴⠒⠉⠀⠉⠉⠐⢺⡧⠤⠤⠄⠊⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡆⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣒⠀⠀⢿⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⣡⠖⡄⠀⠙⠦⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁

⠀⠁⠀⠀⣀⣀⠀⠀⣸⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⢀⠠⡘⠁⢧⠤⠀⠁⠃
⠀⠄⡀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⢀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠦⡜⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠄
⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⢡⠇⡤⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠠⡆⢸⢰⠃⠴⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠆⠶⠀⠀⠀⠞⠢⠀⠠⠀⠑⠀⠲⠘⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠣⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⠀⠘⡀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀⠀⢀⠀⠀⡀⠀⠀⢤⣀⠀⠀⠀⠀⢀⠀⠀⠀⠨⠄⠠⠄⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠠⠄⠀⠀⠀⠀⠀⢃⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠒⠻⠁⠀⠀⠁⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠠⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠁⢀⢈⡀⠀⠀⠀⠀⠀⠐⠂⠂⠂⠆⡀⣀⠀⡀⠀⢀⣉⣁⡼⢲⣺⢶⡆
⠀⠠⠀⠐⠀⠀⠁⡋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠐⠂⠐⠢⡰⠉⠛⠀⠀⠛⠛⠓
⠀⠀⡂⠑⠀⠁⡂⢂⠀⠀⠀⢀⢑⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣒⡀⠀⢀⡀⣂⠀⠀⣀⢀⣀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠳⡆⢀⢩⣿⡿⠿⣫⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡀⢰⣤⣷⣄⡀⢀⣿⣋⡬⠉⠋⠋⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠵⡞⠋⠀⠀⠉⠛⠛⠈⣁⣀⠀⣴⢖⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⢖⠟⠀⠐⠚⠀⠀⠀⢸⠩⠏⠀⠁⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡾⠉⠀⢀⠀⢤⠀⢠⠀⢸⣆⠠⠄⠒⢑⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢄⠣⠀⠲⢤⠀⠀⣇⠐⠄⠈⡁⠐⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠰⣶⣾⣿⣿⣿⡄⢀⡔⣰⠂⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠐⠚⠉⠉⠙⠻⣿⣇⠀⠀⠉⢠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢠⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢼⣿⣇⢰⠀⣸⣿⣿⣟⣛⣉⣿⣿⣿⣿⡀
⠀⠀⠐⡄⠀⠀⠀⡷⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠸⠀⠀⠊⢸⣿⣿⢘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠐⠠⣐⣢⠀⡀⠀⠀⠀⠀⠈⠇⠀⠀⠀⢀⣀⡞⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠐⠲⠟⠛⣵⠀⠀⢀⣿⣿⣿⣿⣙⣫⣝⣿⣿⡏⠀⢻⣿⣿⣿⡋⠉⢭⣝⣳⠄
⠀⠀⠀⠀⠀⠎⢉⡀⣿⠉⢳⡖⠋⠀⠐⠀⠀⠀⣠⡅⠿⠤⠤⠯⠿⢿⣻⣿⣿⣭⣽⣿⣭⣥⣤⣬⣽⣹⡄⠯⠐⠹⠅
⠀⠀⠀⠀⠈⠁⠒⠒⡏⠀⠀⠹⣄⠀⠀⠠⠀⢼⣿⣿⣆⠀⠀⠀⠀⠈⠁⠀⠁⠐⠀⠀⢄⡀⠀⠀⠀⠀⠈⠀⠂⢤⡀
⠀⡀⠀⠀⠐⠀⠀⠐⠃⠀⠀⠀⠈⠃⠀⠀⠀⢸⠻⣿⣿⠳⢤⣀⡀⠀⠀⠀⠀⢀⣤⠒⠛⡿⣷⣦⣶⣶⣶⣶⣶⡶⠂⠁
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡿⣿⠀⠠⠀⢹⣿⣶⠶⠞⣿⣏⠀⢠⠿⣽⣿⢹⠙⠛⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⣿⠿⠂⠀⣿⣿⣿⣿⣶⣿⡝⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⣠⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣦⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣛⣋⣉⣀⣀⣀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣉⣉⣉⣀⣀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⡉⠛⢿⣿⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⢹⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⢁⣼⣿⣿⣿⠀⢿⣿⠃⣸⣿⣿⡇⢸⣿⡇⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣷⣤⣤⣴⣿⠟⢉⣁⣈⣉⣁⣈⣉⣀⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⣉⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⣤⣤⣤⣤⣤⣈⠙⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠾⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⢠⢠⠀⢀⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⢣⠘⠀⠀⠀⠑⠀⠈⠀⠀⠘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡇⠀⠀⢀⣀⠀⡀⣀⡀⠰⠆⠀⢀⡄⠀⠀⠀⣤⠀⠀⣀⡀⠀⠀⠀⠀⣠⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡤⣴⠧⢼⡧⠄⣿⠎⡿⣸⡷⢩⢇⡾⢰⡇⣸⢧⣰⡯⢋⢿⡄⣸⣇⣙⢴⢒⣾⢀⠿⡄⣰⣇⢾⣇⠄
⠀⠀⠀⠀⠰⣧⠔⠁⠀⠀⣧⠀⠋⠐⠗⠙⠁⠸⠊⠙⠉⠓⠃⠀⠈⠛⠁⢼⠞⢱⢋⡷⠈⠉⠷⠋⢸⠗⠉⡡⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠭⠤⠤⠤⠤⠤⠀⠀⠸⠧⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠆⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠒⠢⣄⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠖⠒⠉⠉⠉⠁⠒⠢⢌⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠁⠈⢀⡀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⠢⠀⠑⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⡤⠀⠀⠤⠄⢀⣠⣾⡇⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣶⡶⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠻⠄⠀⠔⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⢠⠃
⡄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⡎
⠱⡀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠀⠀⠈⠂⡤⢆⠀⠀⣀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠑⠦⡀⠄⠀⠀⡀⠀⠀⠁⠂⠤⣀⠈⠢⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠈⠶⠥⣄⠀⠀⠀⠢⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⠁⣀⠀⠀⣀⠜⠀⠀⠈⠢⣀⠌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡠⠖⢚⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⢠⡄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⣀⣤⡀⠀⠈⢦⠈⢢⡀
⠀⠁⠀⠀⠀⢿⡉⢢⡀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠷⠄⠀⠠⡶⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢠⣇⡼⠋⣰⠃⠀⠀⠀⢧⠀⢳
⠀⠀⠰⣟⠓⢮⣳⣄⠱⣼⡇⣠⠏⠀⠀⠀⠀⠀⠀⢀⡾⣫⡴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⣞⢉⣉⡙⢿⣄⠀⠀⢾⡥⠶⣦⠀⠀⢸
⠀⠀⠀⠈⠓⢄⡙⠁⣠⠟⠁⢳⡀⠀⠀⠀⠀⠀⠀⣸⠇⢁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡦⠹⣧⠀⠀⠀⠀⠉⠁⠀⡝⠀⠈⢷⠀⠀⡤⠖⠋⠀⠀⢸
⠀⠀⠰⣏⣉⣈⡁⠰⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠙⢦⣄⡀⠀⠀⢀⣠⡴⠛⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠁⣤⣉⣱⡄⠀⠀⠏
⠀⠀⠀⠀⢠⠞⣡⣄⣀⣀⣄⠙⢦⡀⠀⠀⠀⠀⣠⣿⡀⢸⣇⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⣿⠀⢸⡷⣤⡀⠀⠀⠀⣰⠋⢠⡷⠒⠋⠁⠈⠉
⠀⠀⠀⠀⠘⠋⠀⠈⠉⠉⠈⠳⣄⠙⢦⡀⠀⠀⣧⣂⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢀⣀⣸⠇⠀⢠⡞⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠈⣿⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠀⠀⣿⠁⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⢄⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣠⠞⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠈⢧⡈⠉⠙⠛⠛⢛⡿⠃⠀⠀⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⡀⠈⠻⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣄⣀⠉⠛⠛⠛⠋⠁⠀⣀⣠⡴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣼⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⠀⢀⣠⠶⠛⠙⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⢦⡀⠀⣠⠏⣹⠛⠻⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⢻⡙⢦⣀⡴⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠲⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⠶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢨⠄⢠⣤⠀⠠⠤⠌⠁⢆⡀
⠀⠀⠂⠀⠀⠀⠈⢀⡽⠃⠈⠩⣥⠀⠀⠀⠐⠀⠀⠀⠰⢎⠀⠀⠀⠈⢁⡸⠟⠀⠉⢧⡄⠀⠀⠀⣹⠶⠀⠀⠀⠀⡀⠂⠀⠠⢚⣩⠠⡀⢈⠿⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠐⠃⠃⠐⡋⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠙⠀⠊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠒⠀⠂⠐⠒⠒⠀⠀⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⡀⠀⣤⣤⣦⣶⣿⣷⣤⣦⣤⠀⢀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠉⣁⣀⡀⣀⠀⣄⡈⡉⠁⠀⠀⠀⠀⠀⠀⢠⣦⠶⠸⠇⠻⠅⠻⠁⠸⠭⠔⠶⢶⡖⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣉⠂
⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠁⠉⠉⠃⠒⠀⠀⠀⠀⠈⠀⢀⡀⠀⡀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠦⠀⠐⢂⣴⡿⣛⠻⣿⠟⠛⣻⣄⠀⠀⠠⡆
⠀⠀⠀⠐⠐⠈⢀⠀⣉⢈⡁⣀⠁⠁⠘⠂⠀⠀⠀⠀⠀⢠⣋⡈⡣⠀⢹⠀⢹⢂⡠⢹⡀⡧⡇⡙⡆⠀⠀⢀⠀⠀⠀⣾⣿⣷⠟⣠⣿⣨⡛⢿⣿⡆⠀⠂
⠀⠀⠀⠒⠀⠀⠸⠟⠼⠻⠜⠈⠲⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢀⡈⠀⢿⣿⣃⡚⢛⣇⠾⣃⣾⣿⡇⠀⢀⠈
⠀⠠⢄⣁⠀⠀⠃⠲⠐⠆⠲⠀⠐⠀⠃⢃⣀⠄⠀⠀⠀⠐⠋⠠⠶⠶⠶⣖⠂⣶⣖⡲⠀⠐⠿⠛⠀⠀⠀⠀⠶⠀⠠⠘⢿⣿⠛⣛⣛⣿⣻⣿⠟⠀⠂⠠⠆
⠀⠀⠈⠀⡀⠈⠁⠀⠀⠀⠀⠀⠈⠁⢐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⠿⠿⠟⠛⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⢠⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠾⣿⣿⣻⣓⣒⣒⣚⣒⣒⣓⠘⣧⣤
⠀⠀⠀⠀⡀⠀⠀⢀⣉⣉⣉⢁⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠶⠔⡿⠻⠛⠟⠛⠻⠿⠟⠛⢐⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⢀⡀⠀⣀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢴⣦⢶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢀⡼⠋⠀⠐⢲⡄⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⢉⡉⡆⢉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠐⠼⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⡀⡀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡷⠖⠀⠀⠀⠀⠰⢾⡟
⢀⠀⢀⠀⢀⠀⠀⡀⠀⢀⣀⣀⠀⣀⠀⢀⡀⠀⣀⠀⠀⡄⠀⠄⢠⠀⣄⠀⡄⡄⠀⡤⢀⠄⠠⡄⡄⡄⠀⠀⢀⠠⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⢠⠀⡄⢠⠀⡄⣄⣠⠀⠄⣤⢠⡀⡄⢠⣴⠀⠐⢯⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⡀⢨⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⣀⣀⡾⠀⠟⣴⣿⣯⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠛⠛⢻⣄⠀⢉⣡⠀⢀⡶⢸⠏⢀⡶⢀⡟⠻⣦
⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣶⣿⠇⣼⠟⠛⠛⡇⠀⠚⠁⡄⠀⢨⣴⠿⢃⣴⣿⠁
⠀⠀⠀⠀⠀⢸⣇⢠⣾⣟⣡⡏⣸⠏⢀⣴⣿⣷⣤⣴⣾⣿⣤⣤⣴⣾⣿⣟⣡⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣻⠟⠋⠉⠉⣀⠉⣀⠛⢁⣴⠀⣸⠃⢈⡤⢀⡉⠀⣡⠄⢈⠁⢀⡟⠀⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣤⣴⠞⠀⣿⠀⡟⠀⠰⠃⢰⡏⢠⡿⠃⢨⠁⣼⠟⠀⡍⠀⠞⠀⠘⣉⠀⠉⣿⡄
⠀⠀⠀⠀⣿⠙⠶⠟⠋⠀⣸⡇⠀⢿⣤⣴⣦⡔⠁⣦⣤⣶⠇⢰⣤⣴⣾⣧⣴⠎⣰⣿⠟⠻⢷⣿⠇
⠀⠀⠀⠀⠹⣷⣄⣀⣠⣾⣿⣧⣀⣀⣿⡍⡿⠀⢸⣿⢉⡏⠀⣿⠃⠘⠷⠟⠃⣰⣿⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠙⠛⠛⠋⠘⣷⣤⣿⠇⣿⣄⣰⣿⣆⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠋⠙⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃⠈⠁⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⠄⢀⣤⠟⢠⡟⠀⠀⠀⠀⢀⡴⠛⠉⡉⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⡟⠝⠋⠀⠐⠖⣇⠀⠀⠀⠀⢸⢣⠖⣿⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⡷⠀⠀⠀⠀⠀⡼⠃⠀⠀⣤⡼⢫⠀⠻⣴⡇⠀⠠⡀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣤⣤⡽⠁⠀⠀⠀⣇⡀⠀⠀⠀⠈⢧⢤⠀⠬⣽⢉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠶⢤⣤⡏⣀⣀⣀⣀⡀⠀⠧⣄⣀⠀⠀⢶⡶⠚⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣶⣤⣀⠈⢻⣧⢴⣯⣤⣿⣶⣒⡆⢹⠀⠀⠈⣇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠷⣄⡀⠀⠀⠀⠀⠀⢠⣷⠏⠉⠻⡍⠛⡎⢱⣴⣹⣍⣵⣦⠙⠀⡼⠤⢖⣫⡹⡆⠀⠀⣷⠀⠀⠀⠀⠀⢀⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠙⠶⣤⣀⠀⠀⡿⢸⠀⠀⠀⢻⠀⣹⠢⢶⡘⠶⣻⢥⢚⡼⠁⢠⠏⠀⢹⣿⠂⢀⡇⠀⢀⣠⡴⠞⠋⠀⣸⠃⠀⣀⣄
⠀⠀⠀⠀⠘⣿⠛⠛⠓⠛⠀⠀⠀⠀⠀⠉⠛⢻⡇⢸⡆⠀⠀⠘⡇⠛⣶⢺⣹⣻⡧⠜⣾⠁⠀⣾⠀⠀⢸⢿⣀⡾⢖⣛⠉⠁⠀⠀⠀⠀⠛⠛⠋⣹⠏
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢠⡾⣯⡉⠙⠛⣿⠀⠈⣷⠀⠀⠀⢻⡴⠋⠙⠛⣛⡷⠀⢻⡄⠀⡿⠀⠀⣾⠸⡏⠉⠉⢉⣩⡿⢳⡄⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⡿⠀⠀⠙⠳⢦⣯⣀⠀⠸⡆⠀⠀⡼⠁⠀⣈⣯⡿⠁⠀⠈⣷⢸⡇⠀⠀⣿⢀⣿⡤⠶⠛⠁⠀⠀⢷⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⣾⣤⣤⣴⣭⣿⣧⣀⣠⣤⣿⡼⠷⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠀⠀⠀⢱⣠⠔⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⠙⡄⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣄⠐⢀⡜⠁⠄⠀⢀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠀⢸⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⣻⠟⡝⡟⢷⣶⣤⣀⣀⠞⠁⠀⢀⠀⠀⠈⠧⠀⠀⢈⣀⡀⠈⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠋⢀⡬⠐⠋⠘⠁⠁⠀⠐⠦⠙⢷⣦⣀⠀⠈⠙⠂⠀⡠⠚⠉⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣡⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣯⡣⡀⠒⠀⡼⠁⣰⠃⠀⠁⠀⠀⠀⢳⠐⠚
⠀⠀⠀⠀⠀⠀⠐⠟⡴⢡⣇⠛⠀⡀⠀⠀⠀⠐⠂⠀⠈⠀⢀⠀⠛⢸⣻⡷⣵⡀⠀⠱⡀⠹⣄⣀⣀⡤⠀⢠⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠏⠀⠇⠻⠁⠀⠀⣹⢶⠤⢍⡭⠤⠖⠁⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠦⢄⣀⣀⡠⠴⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⣀⠀⢰⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠦⠤⠤⠤⠤⠔⠚⢿⢄⡀⠀⠀⣀⢀⡠⠊⠁⠀⠀⠀⡇⠀⠀⢇
⠀⢠⠊⢉⣚⠉⢹⠄⠀⢀⣀⣠⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠑⣾⡷⠏⠀⠀⠀⠀⠀⠀⣃⣀⠀⠈
⠀⢿⢠⠋⢀⢱⠈⠓⡄⠀⠞⠿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠞⠁⠀⠀⠀⠀⠀⣀⣴⡉⠵⠮⣗⠒⣄
⠀⣰⠛⢻⠾⠊⡤⠞⠁⠀⠀⠀⠀⠘⠓⠋⢹⡏⠉⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣅⢎⣥⡼⢴⠃
⠀⠈⠋⢉⣓⣚⣆⡴⣦⣀⡠⠤⠤⠒⠒⢃⣸⠇⠉⠉⠁⣇⡀⠉⠙⠓⠒⠒⠦⠤⢄⣀⠉⢱⣌⡹⠯⣀⡼
⠀⠀⠀⠈⠓⣮⠿⠛⠉⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⡀
⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠋⠔⠋⠄⡰⠀⠀⠀⠂⠠⠀⠀⠂⠱⠘⠀⠶⠂⠋⠇⠃⡇⠱⠀⠀⠰⠂⠁⠀⠀⠴⠀⠆⠀⠸⠉⠱⠋⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⢿⢻⠿⡿⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠿⠛⠻⠟⠛⠿⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⡥⠄⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠘⣿⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠀⣾⣷⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡐⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⡤⢴⠆⠀⠀⠠⠂⠀⠀⡠⠀⠁⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢌⣀⣠⡔⢈⡀⠠⣤⠐⠈⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⢹⣧⣼⡷⠀⠀⠀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠐⢻⡀⠀⠀⠀⠙⠈⠁⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠁⠀⢀⠠⠀⠐⠛⠊⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠑⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠇⠀⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠰⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⣽⣷⠇⠀⠀⠀⣷⣿⣫⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⡻⠃⠀⠀⠀⠀⠘⠿⠿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣤⣿⣷⣾⣷⣶⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⣼⣿⡏⠀⠀⠀⠉⠉⠈⠙⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⠟⠋⠛⠛⠿⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠏⠋⠉⠈⠁⠀⠈⢻⣿⣿
⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠘⣿⡇
⠀⠀⠀⠈⣜⠀⠀⠀⠁⡀⢀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠗⠎⠀⠄⠀⠁⠄⠠⠀⠀⠀⠀⠐
⠀⠀⠀⢠⣿⣦⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠠⡉⠈⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀
⠀⠀⠀⣸⣿⣿⣿⣿⠗⠐⢿⣿⣷⠀⠀⠀⠂⢀⠄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡛⠃⠓
⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠈⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎
⠀⠀⠀⠈⠉⠉⢱⠀⠀⠀⠀⢈⠁⠀⢠⠀⠀⠀⠀⠀⠈⠩⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠦⠲⠀⠀⠀⠀⠸⠲⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢒⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠥⡄⠈⢴⠀⠀⠉⡙⠀⠀⠀⠀⠈⡤⠏⠘⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠠⢺⠇⠀⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⡟⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣄⢀⡀⠀⢢⠀⠀⠀⠀⠀⢻⡆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢸⡇⠀⣀⠄⡀⠀⠀⠁⢹⡄⠀⠀⠈⡿⣇⠀⢸⡇⠀⠀⠀⠀⢸⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⣇⢰⡇⣸⣡⢺⣤⣀⡼⠁⣷⢤⡴⠗⠻⠴⢸⡇⡔⠀⠀⠀⢸⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠿⠤⠛⠉⠁⢸⡇⠁⠀⠀⣷⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢠⡟⡸⢁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⡴⢞⠛⢦⡀⠀⠀⠀⡀⠰⡇⠀⠠⠀⣿⠀⠀⣀⠴⢚⡟⠀⠀⠀⣰⠏⠈⢐⣩⡴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣰⠏⠀⢸⡇⠀⠀⢰⠁⢠⡇⢠⠃⠀⣿⢠⡞⠁⣠⡾⠁⢀⡴⠊⠁⠀⠊⣉⣐⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠢⠙⠀⠀⠀⣠⡞⢁⣼⠏⠀⢀⡾⠁⠀⠀⡇⠀⢸⠇⣾⠀⢀⡟⠀⠙⠋⠁⠀⠊⠁⣀⣢⣬⠭⠷⠶⠾⠟⠛⠿⠷⠶⣭
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣼⠟⢠⣾⣯⣤⠞⠫⠐⠀⠀⠀⠧⠴⠋⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣻⡿⠛⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⣀⡀⡠⠖⡄⢰⡷⢲⢴⢏⠇⣠⠔⣠⠀⡼⣲⢲⡇⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠁⣰⡿⠃⢀⢀⠖⣷⢠⡀⠔⣹⢠⠀⢸⡇⡼⢁⡟⠀⠊⣰⠏⡴⠋⠸⣇⣼⠃⢰⡏⣰⢱⠁⣸⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠃⠀⣰⡿⠁⠀⣿⠋⣼⠃⢸⠇⣰⠃⣿⢀⢼⡿⠁⢸⡇⢀⣴⠋⠈⠇⢀⢀⣽⢻⣤⠾⡶⠃⠈⠀⠘⣻⣏⠴⠊
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣰⡿⠁⠀⢠⠏⢰⠃⢀⠞⠀⣇⣸⢷⣊⣈⣁⠀⠀⠛⠛⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡤⠴⠖⣾⠏
⠀⠐⠤⠤⠚⠁⠀⠀⠀⠀⣿⣁⣀⣀⣀⣀⣈⣤⣤⣤⡴⠶⢶⡿⠷⠶⣎⠛⠦⣄⡀⠀⠀⠀⣀⡠⠔⠂⠁⠀⠀⠹⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠙⠶⠶⠋⠀⠀⠀⠉⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠠⡄⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠺⠳⢾⡆⠰⠛⡠
⠀⠀⠀⠀⠲⡀⠘⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⣴⣀⢀⡀⠀⠰⠈
⠀⢰⠀⠀⡀⠑⠄⠀⠄⣀⠀⠀⠀⢀⠄⢀⠔⠀⠀⠈⠑⠒⠀⡀⠉⠉⠉⠆⠀⡀
⠀⠀⠑⢄⠈⠢⣈⡄⠘⠋⠀⢰⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠶⠈⠀⢠⠄⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢦⡀⠂⡀
⠀⠀⠘⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢙⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠉⠀⠀⠊⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢂⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠶⠀⠉⠉⠉⠛⠻⠶⣿⡄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢠⠀⠀⢀⡠⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢦⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠀⣼⣷⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⠘⢷⠒⠂⠐⠒⠒⠊⠉⠁⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢻⠀⠀⠀⢧⣤⣄⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⡷⠀⣀⡀⠀⠀⣀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⡀⠠⠿⢻⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠓⠴⠂⣀⣀⣀⠴⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠐⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠷⣤⣤⣀⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣤⣤⣤⣠⣤⣤⠴⡾⠋⣀⠀⠷⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡅⠀⠀⡇⠀⠈⠁⠶⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⠘⠀⢆⣤⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠈⠁⠀⠀⠀⠀⠀⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⢛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣄⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⣤⡞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⠶⠞⠁⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠴⠞⠉⠀⠻⣆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡴⢾⠁⢠⣼⣁⣀⣀⣀⣀⠀⡴⢶⡞⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢇⠀⠁⠀⠀⠀⠀⠀⠀⠄⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠡⣀⠀⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣤⣤⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⠁⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠉⢢⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠉⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⣠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⠶⣤⣤⣀⣀⣀⣁⣤⡴⠋⠀⠀⢰⠄⠀⠸⡿⠀⠀⠀⣀⠀⠀⠀⣰⠿⠋
⠀⠀⠀⣠⠎⠁⣀⠄⠐⠒⠒⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠋⠀⠀⠘⠁
⠀⠀⣰⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢿⣿⠂⠐⣶⡗⠀⠐⢶⣿⣧⠀⠀⠰⣶⡖⢲⣦⠀⢶⣶⠞⢶⣄⠀⢻⣿⡀⠀⣿⠃
⠀⠀⡇⣸⠃⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢸⡄⠀⣼⣿⠀⠀⣿⡇⠀⠀⢸⢿⣿⠀⠀⠀⣿⡇⠀⣿⠆⢸⣿⡀⢸⣿⠀⠀⢿⣷⣼⠇
⠀⠀⣧⣿⠀⠀⠠⣿⠁⠁⠀⠀⠀⠀⠀⣸⠀⠀⣿⣿⠶⠶⣿⡇⠀⠀⣾⣸⣿⡆⠀⠀⣿⣧⠼⠟⠀⢸⣿⣦⠾⠏⠀⠀⠈⣿⣿
⠀⠀⠹⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⢀⡰⠃⠀⠀⣽⣿⠀⠀⣿⡇⠀⢰⡏⠈⣿⣧⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠹⣧⡀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⢀⣿⠏⠀⠘⠛⠛⠀⠛⠀⠀⠛⠛⠃⠐⠛⠃⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠛⠛⠂
⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢲
⠀⠀⢀⣀⣀⣤⡀⣠⡀⣠⣤⡀⣠⡀⣠⣤⡀⢘⠗⠀⠀⣾⢹⠀⢀⣤⣄⢻⣤⠇⠀⢠⣶⠶⠄⠀⣀⣀⣠⡼⣧⡾⠀⠀⣤⠀⢀⣄
⠀⠀⣾⢋⣼⡿⠀⣿⢰⠏⣼⠇⣿⢡⠏⣼⠇⣿⠁⣿⡀⢻⣿⣀⣿⡧⠏⢠⠟⣷⡀⣹⣧⣀⣠⣾⢋⣼⣿⠀⡼⢳⣦⢸⡟⢀⣾⡿
⠀⠀⢿⠞⠘⢷⡼⢿⡏⠠⣿⣰⢿⡏⠀⣿⣰⣿⣴⠻⣧⡼⠁⠀⢿⣆⣠⠎⢰⡟⣠⢣⠟⢿⡄⢿⠞⠈⢿⡼⢁⣿⢃⡜⠷⠞⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠃⠈⠁⣀⣛⣃⣈⣀⣀⣈⣁⣀⠀⠀⠀⠀⠀⠘⠓⠃⠸⣀⣼⠇⠀⠀⢀⣀⣀⠀⠛⠚⠀⣠⡞⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠶⠦⠤⣤⣌⣀⠀⠀⠐⠋⠉⠉⢳⡄⠀⠀⣿⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠶⠶⠶⠶⠶⠶⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⣀⣤⢼⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⠏⠀⣸⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢰⡏⢀⡟⠀⡰⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡿⠀⣾⠠⠊⢁⡤⣤⡄⠀⣠⣠⣶⡀⢀⡀⣠⡀⠀⡀⠀⢀⡀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠇⠀⣰⠏⢠⡟⠀⢸⡟⠁⣼⢃⡿⠊⢹⡇⣾⠁⢠⡿⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣿⠀⢰⡏⡠⣿⠁⢐⡿⠀⢠⠏⣸⠇⠀⡼⣻⠇⡴⣻⠇⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠒⠒⠒⠶⢤⣄⡀⠀⠈⠀⠀⠘⠛⠀⠸⠋⠀⠿⠊⣼⠇⠀⠁⢤⠿⠄⠊⠁⠛⠋⣰⠟
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠰⠋⠀⢀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠊⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠀⠰⠆⠀⠀⢾⡆⢠⣇⣀⡤⠊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣠⣴⣯⣤⡄⢰⡏⡠⣾⠠⢰⡏⡴⡿⠀⣴⢀⡾⠀⢸⠇⣠⣿⠃⣘⡁⠙⢃⡄⠿⠀⡄⠛⣾⢣⣾⠾⢧⡶⢀⣾⠃
⠀⠀⠀⠀⠀⢀⡤⠔⣺⠉⠁⠀⣿⠀⠀⠁⣿⠏⢰⡇⢠⣿⠎⣸⠃⢰⡇⢸⡇⢀⡞⣾⠋⠀⣰⡟⠁⠀⠙⣓⢀⡛⢠⣾⢇⣿⠋⢠⣿⢁⣾⡏
⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠿⠄⠀⠸⠇⠀⠿⠂⠸⠃⠠⡿⠀⠺⠃⠘⠷⠊⠰⣯⡠⢘⡟⠀⠦⣄⡠⠟⢹⠟⠩⡿⠺⠋⠀⠸⠟⢁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⠀⠀⢀⠔⠁⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⢠⣀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⠀⠀⠐⠤⠀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⣠⡄⣤⢤⡀⠀⠀⠀⠀⠀⣠⣄⡀⠀⡠⣄⠀⠀⠀⠀⠀⢀⢤⡀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⢀⣿⠁⡏⠀⡇⠀⠀⠀⠀⢸⣴⣄⡷⣸⠁⢸⡇⠀⠀⠀⠀⢳⣶⠏⣸⣥⣼⡇
⠀⠀⠀⠀⠀⠀⢀⣸⣇⢻⣠⠇⠀⠀⠀⠀⣠⣾⠛⡁⢿⡀⢸⡗⠀⠀⠀⠀⣜⣯⢳⣿⠛⢻⠇
⠀⠀⠀⠀⠀⣠⢈⣉⡉⡉⢁⠄⠀⠀⠀⠀⢻⠶⠾⠟⢈⡧⠚⠁⠀⠀⠀⠊⠳⠶⠋⠈⠳⠮
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠋

⠀⠀⣰⠇⣄⣰⠋⢲⡀⠀⠀⠀⢰⡾⠷⠖⣰⡆⢲⡄⠀⠀⠀⠀⠀⠦⠀⠀⠐⠂⠀⠀⠀⣄⣁⡄⣰⠂⣠⠀⢦
⠀⢀⣟⣀⣿⣿⣦⣾⡇⠀⠀⠀⠸⠒⢶⣄⣿⡇⢸⡇⠀⠀⠀⣠⠀⠀⠀⠀⠀⣔⠀⠀⠀⠉⠰⠀⣻⢀⣇⠀⡿
⠀⠀⠀⠉⡟⢻⡉⣸⠇⠀⠀⠀⠘⠃⡾⠇⠘⠃⠾⠃⠀⠀⢘⠁⠀⠀⣠⠄⠀⠙⠂⠀⠀⠀⢆⣰⠟⣼⣁⣸⡃
⠀⠀⣄⣤⡁⠆⣩⠁⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠀⠀⠀⠘⠲⠚⠀⠀⠓⠀⠀⠀⠀⠁⠉⠉⠈⠁⠁⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠻⢻⠀⣾⠃⣼⡆⠀⠀⠀⢰⠁⢀⡆⡘⠀⠈⠀⠀⠀⠀⢘⠁⠀⢠⠀⠎⢲⠔⠂
⠀⠀⠀⠀⠀⠀⠰⡟⢪⣶⣿⠀⣿⡇⠀⠀⠀⠈⠀⣸⠃⠁⠀⡀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢤⠻⢹⠇⠸⢆⠾⠀⠀⠀⣼⣡⣴⣅⣴⡴⠼⢤⣤⠀⠀⠠⣾⠺⣄⠆⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⡄⠀⢀⠔⠀⢠⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠇⢀⠎⠀⠀⠈⠂⠀⠠⠔⠒⠉⠁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⡐⢠⢀⡖⢠⢠⠂⣀⡄⣰⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⢀⠀⠀⠈⠀⠀⠀⠉⠸⠁⠀⡜⠉⠈⠀⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⣴⠀⢣⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢴⠇⠀⡎⡀⠐⠀⠀⡀⠐⠀⢀⠀⡀⢄⡀⣠⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⢠⡂⡠⠊⢰⠀⠐⢀⢎⡏⣸⢳⢡⢣⠂⠙⠞⠁⡞⡔⣹⣀⣰⠁⡞⣼⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡀⢀⡄⠀⢀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠤⠔⠚⠉⠁⠀⠀⠨⡀⠀⠐⠁⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠒⠤⠀⢀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⣰⢎⠀⡰⢃⢀⠄⣠⢶⣄⡠⢲⢀⡄⣤
⠀⢠⠀⠀⠀⢀⠤⠊⠁⢸⡞⠁⢈⠈⣰⠋⠉⡼⢉⠁⠀⢡⠋
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⡠⢀⡏⠀⠁⠀⠀⠐⠁⠀⠀⠃
⠀⠀⠀⠀⡞⠀⠀⠂⢚⡾⢥⡞⡴⢰⢠⠆⡆⡌⢠⡆⡄⣤⠀⢶⠀⡰⣄⣀⡆⠰⡆⢠⡆⡄
⠀⠀⠀⠀⠑⠀⠠⠖⠋⠀⠘⠄⢠⡇⠀⡼⠀⠅⠀⠁⠀⠈⠀⠈⠀⠀⠀⠁⢀⠠⠅⠠⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⢀⠀⡀⡀⡠⢸⠠⡂⢠⠠⡀⡄⡂⠄⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢖⠂⣆⠗⠁⠇⠀⠣⠸⠀⠚⠘⠀⠃⠃⠁⠀⠀⡏⢀⠇⠄⠐⢰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠤⠄⠤⢄⠈⠁⠀⠈⢁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠎⠉⠀⠁⠈⠀⢀⣀⠀⠈⠑⠒⠖⠢⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠔⠉⠁⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠠⡉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠐⠢⠭⢥⡝⠀⠀⠁⠀⣀⠖⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠄
⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠷⣮⡍⠁⠈⢣⠀⢀⣀⠆⠁⠀⠈⠙⠔⠆⠤⠤⠦⠀⠀⢀⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⠀⠀⢸⢸⢀⠆⠋⠁⠀⠀⠀⢹⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢇⠀⢁⠏⡼⠀⠀⠀⠀⠀⠠⡘⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⠀⠀⠀⠀⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠈⢢⣀⠜⠀⠀⠶⠀⠀⠀⡀⡄⢂⠀⠀⠀⠰⡇⠀⠀⠀⠠⠦⠀⠀⠣⣤⢠⡀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⣦⣀⠀⠀⠀⠀⠀⢀⣠⠞⠓⢤⣀⠀⠐⠐⠀⠀⠀⠀⢀⡠⠔⠁⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⣿⠐⠒⢲⣙⠷⡀⠈⠑⠀⠓⠋⠁⠀⠒⠒⠂⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⡿⠃⠀⠸⠄⢠⣆⠀⠀⠀⣀⠀⣀⠐⠤⣦⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⣈⠀⠛⠂⢸⠀⠉⠉⠂⠴⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⢀⠄⠉⠁⠰⠦⢼⡀⢀⢀⠀⡀⡀⢄⡒⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠃⠴⠻⠦⠐⠛⠒⠀⠀⢘⠁⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠐⠀⠀⢀⠀⡀⠐⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡁⠀⢈⢩⡀⠀⠀⡀⣄⡄⠀⢈⡁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣼⠃⠀⠀⡰⠁⠀⠾⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡴⠁⠀⠀⣸⡟⠀⢀⣾⠃⠀⠀⠀⠱⠄⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⡹⢀⣘⠆⠀⠳⡄⠀⢰⡿⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⣄⠀⠘⢿⣄⣀⣀⣀⠤⢤⣶⣶⠶⠲⣿⠷⢶⣴⡿⠀⣠⢄⡄⢀⣤⢤⡀⣠⡤⣄⢠⡄⠀⣄⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠳⠶⠴⠖⣺⠝⠋⠀⠀⣸⡏⠀⠈⣿⠇⡾⢁⣾⢁⡼⠁⣸⢱⠏⢠⠏⣼⢁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠘⠦⣤⣄⣀⣠⣤⠴⠖⠋⠀⠀⠀⠀⠐⠛⠀⠀⠘⠛⠈⠛⠋⠷⣿⠛⠞⢡⡟⠓⠋⠘⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠰⠃⠀⠀⠟⠀⢀⠀⠀⠀⡾
⠀⠀⠀⢠⡶⢳⡖⢠⡶⣶⠀⣰⠶⡆⢠⡆⢰⡆⣞⢠⡖⡲⠻⢷⡶⠀⢿⣆⢀⡴⢲⡶⠀⠿⣶⠀⣰⠂⢠⡆
⠀⠀⠀⣿⣠⣿⣁⡾⢀⣏⣰⡏⢸⣃⣼⣇⢸⣧⠋⢻⡋⡀⠀⣾⠁⠔⠠⢹⣿⣡⣾⣡⠌⢼⣇⠴⣯⣴⡟
⠀⠀⠀⠈⠁⠈⠁⠁⠀⠉⠈⠀⠈⠁⠈⠁⠀⠁⠀⠀⠉⠀⠀⠈⠀⠀⠀⠁⠈⠁⠈⠁⠀⠈⢁⡶⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⣼⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⢀⡼⢃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠛⠒⠀⠀⠀⢀⡴⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⢠⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⣄⠀⠀⠀⠀⠛⢸⡧⢸⣿⠀⢆⣶⡄⣶⠒⣦⢰⡖⢲⡔⣶⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠷⠀⠀⠀⠀⢸⡇⠸⣿⠐⠯⠾⠇⣿⠤⠟⢸⡧⠾⠃⠸⡷⠁
⠀⠀⠀⠀⢀⠠⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠀⠐⠛⠳⠤⣤⣤⣤⡴⠃⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠠⠀⠐⠀⠀⣞⡉⢿⣆⠀⣶⡆⠀⢸⠃⠀⣀⠀⠀⠀⣹⣧⠀⠀⢉⣿⡄⠰⠗⠀⠀⠀⡀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠸⣿⡄⡼⣿⡀⡞⢰⣟⡹⠗⢰⡿⠉⣿⢄⣾⠋⢻⡇⢹⣿⠈⣿⡏⢻⡇⢰⡏⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⢻⣿⠁⠸⣿⣀⡀⠸⣷⣠⡿⠈⢿⣄⣼⠇⢸⣿⠀⣿⡇⣸⡇⢈⣗⡞⠋
⠀⠀⠀⠀⠁⠐⢄⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠐⠋⠀⢼⡛⠛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠶⠶⠦⢤⣀⣠⣾⢋⣶⡖⣰⣶⠆⡴⢰⢦⣤⠆⢰⡄⢸⣀⡖⡶⢰⡄⣰⣰⠆⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠁⠿⠘⠉⠃⠛⠘⠈⠃⠙⠀⠙⠀⠘⠀⠛⠘⠊⠃⠈⠃⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡠⡄⡴⡄
⠀⠀⠀⠀⠀⠀⣠⣾⡏⣖⣠⣦⣶⣿⡗⣧⣇⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢀⢸⢀⡍⠠⢧⠸⣁
⠀⠀⠀⠀⠀⠰⡝⢅⣉⣁⣸⠈⠸⣀⢈⡾⣳⡂⠀⠀⠀⠠⢠⡄⠐⠚⠚⠊⠛⢂⠘⠀⢀⠁⡀⡀⡀
⠀⠀⠀⠀⠀⠘⠙⢛⡏⢿⡸⣷⣏⢣⡟⢎⠾⡇⠀⠀⠀⢖⡿⡧⢿⠿⠿⠷⠟⠯⢿⠸⠾⢾⡇⢳⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠉⠁⠁⠉⠈⠀⠉⠁⠀⠀⠀⠉⠀⠈⠀⠀⠈⠉⠉⠁⠋⠈⠁⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣸⣧⡟⣡⠀⢠⣀⢠⣄⣠⢠⠄⠀⠀⠀⠀⠀⢇⢈⡂⢠⡄⢰⡤⢴⠐⠖⢠⠃
⠀⠀⠀⠀⠀⠨⠼⠘⠃⠷⣧⡯⡾⡿⠞⢙⣾⠀⠀⠀⠀⠀⠀⠎⠘⠉⠊⠛⠋⠘⠁⠐⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠠⠇⠀⠘⠁⠀⠀⠀⠀⠰⡆⡀⠀⡇⢸⠁⣸⠀⣴⢸⢠⣆⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠻⠸⠇⢺⠀⢿⠀⡛⣘⠘⠋⠓
⠀⠀⠀⠀⠀⠀⡄⣄⣄⠀⣀⣄⣠⠀⢠⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣇⢻⡏
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠁⠉⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠙⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⢛⡋⠩⠭⠭⠭⠭⠍⣙⣛⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣋⠥⠂⠉⠀⢠⡴⣖⢰⡆⣶⢤⡆⠀⠉⠐⠬⣙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊⠀⠀⠀⠀⠀⠸⠇⠧⠞⠻⠿⠷⠟⠀⠀⠀⠀⠀⠑⢌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⠊⠀⠀⠀⠀⢠⣶⣶⣶⡆⠀⣀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠑⡜⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡡⠁⠀⠀⠀⢠⣴⣿⣿⣿⣿⡇⢰⣿⣿⣿⡿⠛⣿⣿⣿⣿⡀⠀⠀⠀⠈⢎⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⠁⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⡌⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠁⢀⣠⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⢀⣄⡀⠈⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠸⠟⠇⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠆⠀⠀⠸⠿⠇⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠇⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠣⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢸⣿⣿⣿⣧⣠⣿⣿⣿⣿⠃⠀⠀⠀⢀⠜⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡑⡄⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠙⠿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢠⢊⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠌⠂⢀⣠⠔⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢤⣴⠟⢁⡼⢣⣤⡄⣤⢤⠄⡌⣤⢠⢄⡤⡄⣶⠀⢦⡀⣠⢤⡄⣶⢠⡄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠆⠃⣰⡟⠁⢩⡿⠁⠿⠸⠷⠇⠿⠾⠵⠧⠋⠺⠍⠰⠯⠾⠾⠹⠧⠿⠰⠯⠾⣼⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⠞⠁⠀⠀⣈⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣊⣡⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣿⣿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⡟⠉⢻⡟⠿⢿⠿⠻⢿⠻⠟⠻⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⣿⡿⠿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣉⣀⡐⠀⠐⠒⠮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢟⣛⣩⣭⣭⣛⣓⡀⠀⠀⠀⢮⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⠵⣾⢿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢿⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡼⠁⠈⠀⠀⠀⠀⠐⠒⠲⠄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⠀⢀⠤⡀⠀⠔⡡⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡤⣄⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣧⠃⠀⠈⢀⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠁⠀⢰⠚⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⡇⠀⠀⠀⠀⣄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢙⠂⠤⠞⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⠀⠀⠀⠀⠀⠈⣏⠉⠁⠀⣠⠔⣻⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢠⢂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⢇⡉⣉⡠⣺⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡠⠚⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠉⠒⠚⠁⠀⠀⠀⠀⣠⠞⠁⠀⣀⠴⣌⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠀⠀⣀⣠⡴⢾⠁⠒⠒⠉⣁⡠⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢋⡀⢀⡞⢰⠒⠊⠉⠁
⠀⠀⠀⠀⠀⡠⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠒⠒⠒⠉⣀⣤⡆⠀⠉⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡴⠂⠤⠤⠤⠤⠖⠚⠦⠔⠒⠋⠁⡼⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠃⠈⠙⠲⠤⣀⡉⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠲⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠤⣄⢀⣀⣠⠋⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⡭⢷⡄⠀⢀⣀⣀⣀⣈⠑⠲⠦⢤⣤⣀⣀⡀⠀⣀⡁⠀⠀⠀⠀⠀⢸⠀⡟⠈⠀⠀⠈⠉⠉⠉
⠀⠀⠒⠄⠀⠀⠀⠀⠀⡰⢮⡠⠚⠁⠀⠀⠛⠉⠉⠉⠁⠈⠉⠁⠢⢤⣀⡀⢀⠉⠉⠉⠉⠴⡦⠀⠀⠀⢠⠋⡰⠃
⠘⢌⠢⡀⠈⠑⠢⢄⡘⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⠀⣸⠣⠤⠔⣊⡭⠛⠁
⠀⠈⠱⣈⠢⡀⠀⠀⠈⢳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠏⠙⠋⠉⠁
⠀⠀⠀⠈⠑⢌⠳⢄⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣿⣵⣶⣌⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣟⣻⣿⣿⣿⣿⣿⣷⡀⢙⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⣿⣽⣿⣿⡗⡸⡿⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡯⠉⠀⠀⠀⠀⠀⠉⠻⣿⣿⠇⢹⢳⣇
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⣤⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⣠⣤⣤⡀⠘⣿⣯⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣟⡂⠀⠀⠉⠙⠛⠷⠆⠀⢹⣿⣿⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣣⣄⠠
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣯⠳
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⢤⠀⠀⠀⢰⣴⣿⡿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠠⠹⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⡠⠐⢹⣿⣿⣿⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⢫⡑⠒⠒⠈⠁⠀⠀⢸⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢮⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠨⠂⠠⠀⠬⣔⡀⡀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠍⠳⣦⡄
⠀⠀⢔⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠉⠀⠀⠘⡆⠀⠀⠀⢾⣿⠿⣿⡀⠀⠀⠹⣿⡀
⠀⠀⠀⢄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢸⡟⣀⡘⣿⠠⠴⠂⠙⠣
⠀⠀⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠀⠟⠋⠋⠀⠈
⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠘⠀⠀⠀⠰⠶⠄
⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⠔⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠃⣾⠀⠀⠀⣰⠒⢰⠏⠀⢀⡞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⡏⠀⠇⠀⠳⢀⡿⠀⠀⣾⢁⡀⣠⠀⡀⠀⣀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡆⢠⡏⣶⢸⡟⣸⢲⡟⢰⣿⡇⢸⡇⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇⠸⠅⢏⢸⡗⠋⢸⡇⠛⠀⠉⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡠⠀⢸⣇⠀⢘⡇⠀⡄⡈⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⠄⠀⠁⠀⢀⡏⠀⠀⣷⠀⠟⠀⠉⠘⡇⠀⣊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⣾⠀⣤⢻⡀⣴⢂⡔⣼⠇⣴⠳⣿⠀⡖⠐⣷⢸⡇⣸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢿⠈⠓⣇⠸⡇⢼⡄⣿⠀⣿⠘⠇⠀⠇⢸⠁⠻⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⡈⡀⠀⢰⠃⠘⠃⠀⢶⢸⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡄⠀⠀⢰⡄⠀⠈⠑⠲⠂⠊⣿⠈⠀⠸⣆⠀⠀⠀⠉⠞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠⡄⣀⡀⡇⢰⡄⢸⠃⡬⢰⠆⣠⠎⠂⠹⡤⠀⢤⠹⡆⣰⢢⡖⠀⢸⡇⣴⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⠇⠸⠂⡇⠀⠇⢸⠀⢇⠸⡆⢿⠀⠀⢸⡇⣃⠘⢇⡗⠻⠘⠇⠀⠸⡧⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠳⠀⠀⠸⠆⠀⠀⡀⡀⠀⠀⠀⢥⡀⠀⠈⠀⠀⠒⣦⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠠⠞⠁⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠺⡓⠚⠟⠀⢸⡓⣲⠶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⡴⠶⢽⣆⠀⠀⢸⡟⠁⠀⠀⠀⠀⢙⣟⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⣭⡶⠉⠀⠀⠀⠈⠳⣄⡸⢠⠞⠁⣀⣴⣋⣭⠿⠤⣄⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠲⠬⢝⡷⠶⠦⠤⣭⣲⣽⣾⣇⣿⢋⡼⠛⠉⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢈⡽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠰⢾⣉⠉⠓⠒⠶⣶⠴⢿⣏⠀⢈⡟⣚⣋⣉⣀⡀⠀⠀⠀⡏⠀⠀⠀⣠⠖⠉⠀⢿
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⡏⠀⣠⠞⠁⡴⠋⣸⣯⢻⠛⠥⣄⣀⠉⠉⠉⢲⣜⡓⢦⣤⠞⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣴⢯⣄⣀⠀⠀⠀⠀⠀⠀⠀⣧⠞⢽⠀⠈⠁⠀⢻⠃⣼⠀⠀⠀⠈⠹⡿⠭⣙⢻⣿⢿⡀⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⡄⠀⠉⠉⠓⠲⠦⢤⣀⡀⢀⡤⣺⢶⣤⣀⡀⢸⣠⢿⠀⡴⠛⠲⠤⣿⢀⡴⠛⡄⣟⡇⢳⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢲⣷⣥⣡⡋⠉⠉⠁⠈⠟⠀⠀⠀⠀⣰⠋⠀⠀⢷⢸⣿⡈⡇⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢿⡇⢽⠉⠛⠲⠦⣤⣀⡀⠀⣠⠞⠁⠀⠀⠀⠸⡄⣿⣇⢹⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣼⡇⢸⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⠀⠀⠀⠀⣧⢸⡟⡄⢧⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡄⣿⢸⡘⡆⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⡅⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣇⢹⣇⢣⠹⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⡇⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⡈⣿⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⣧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣄⣀⠀⠀⢿⣿⡇⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠺⠧⢧⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⢤⣀⣀⠀⠀⣧⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠿⠶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣴⣶⣶⣶⣶⣦⣤⣉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠙⠛⠛⠛⠛⠛⠟⠻⠿⣿⠂⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠈⠉⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢇
⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⡞⢙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣀⡄⠀⠀⠀⠀⠀⠠⢬⣤⡄⠀⠀⠀⠀⠀⠀⣴⡆⢰⡤⢧⣦
⠀⠀⠀⣀⣢⡷⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠛⠤⢀⡠⣦⡶⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠧⠘⠀⠐⠛
⠀⠀⠀⠐⠋⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠌⣁⠠⡉⠁⢴⣤⣤⣤⡀⠀⣠⣤⣶⣾⠟⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠑⠀⡁⠂⢁⠂⠄⢀⠀⠀⠀⠀⢀⠀⠀⠠⡊⠄⢈⠀⠊⠀⠀⠀⠐⢀⡘⠙⠛⠣⠄⠻⠋⠁⢡⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠂⠀⢀⠤⣀⠨⣀⠄⠆⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠂⠀⠀⠀⠐⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠁⠀⠃⠀⠖⢂⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠠⠐⠻⣀⠇
⠀⠀⠀⠀⠀⠀⡔⣀⣡⠉⠑⠐⠀⠀⠀⠀⠐⠒⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠮⡄⢨
⠀⠀⠀⠀⠀⠀⠃⠘⠁⠑⢀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⢣⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠂⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⡄⡰⠀⡂⢔⡠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⠀⠀⠁⠈⠁⠁⠀⠈⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⣀⠀⠀⠐⠄⣸⠁⣿⠀⠠⢶⡤⠀⣶⢰⡴⠀⣦⠀⣤⠀⢰⡄⢯⣣⢀⡤⡄⠙⠧⣄⠀⢀⢿⣄⠀⣴⠒⣀⠙⡧⣄⠀⣤⠀⢰⡆⠀⢸⠀⠀⢸
⠀⠀⣼⠁⠀⠑⠀⢠⠏⠀⢿⡄⠀⢼⡇⢸⡇⢸⡇⢰⡏⠀⣿⣀⡼⣧⠀⡟⢸⡏⢀⡜⠀⣿⠀⣘⡼⣿⠐⣿⣀⣿⠀⠇⣿⠀⣿⢀⣼⡇⠀⢾⠂⠀⢸
⠀⠀⠹⣄⡀⢀⡠⠏⠀⠀⠸⣇⠀⠀⠀⠘⢧⠈⠀⠘⠧⠜⠁⠁⠀⠛⠒⠁⠀⠉⠉⠀⠀⠛⠖⢹⠀⣿⠀⠀⠀⠙⠞⠀⠻⠄⠈⠁⢼⠇⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠋⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⣿⣶⣶⣾⣿⣿⡄⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣤⣤⣤⣤⡟⠛⠛⠛⠛⠛⠛⣧⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣛⣻⣿⣿⡇⠀⠤⠤⠤⠀⠀⣿⣿⣟⣛⣻⣿
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⣿⣷⣶⣾⣿⣿⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡴⠒⠒⠦⣌⠳⡄⠀⠀⠀⠀⠀⢀⡤⠔⢒⡐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠈⢣⡘⣆⠀⠀⣠⠖⡡⠖⠋⠁⠈⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⢇⠀⠀⠀⠀⠀⢧⢸⣄⡜⡡⠋⠀⠀⠀⠀⡰⢁⡏
⠀⠀⠀⠀⢀⣠⡤⠤⢤⣄⣀⠀⠘⡜⢆⠀⠀⠀⠀⢸⠀⡏⡜⠁⠀⠀⠀⣠⠞⣡⠎
⠀⠀⠀⠰⣏⡠⠤⠠⠤⠤⣄⣉⠓⠺⢎⣣⡀⠀⠀⡞⢸⡟⠀⠀⣀⠴⠊⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢍⡓⢄⣸⠁⣾⡤⣖⠭⠴⠒⠛⣉⣉⣉⡩⠭⠭⣍⣓⣲⠄
⠀⠀⠀⠀⠰⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠋⢻⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢸
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⢸⣉⡧⠀⠑⠁⠀⢸
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⡁⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⢾⢠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺
⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⢻
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴⢢⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⡖⢲⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⢀⣤⡈⠁⠀⠀⣀⠀⠀⠀⠀⢸⢸⡇⠀⠀⢠⣶⡄⠉⠉⢠⢤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠈⠛⠁⠀⠀⠈⠛⠁⠀⠀⠀⢸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠲⠚⠞⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁

⣿⣷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠋⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠙⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣸⡿⠀⠀⣼⡟⠀⠀⡀⠀⠀⠀⢠⣾⠂⠀⠀⢀⣶⠆⠀⠁⢀⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠷⠶⣾⡿⠀⣠⡾⠛⣿⠂⢠⣿⡗⢩⣿⠀⣾⡧⠊⣿⠂⢻⣿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⠇⢰⡟⢁⣾⡇⢀⣾⣯⢤⣾⠏⣼⣿⢤⣼⠟⢀⣿⠃⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢿⣄⠈⠛⠁⠘⠛⣽⡏⠙⠋⠁⢰⡿⠙⠛⠉⠀⠀⠛⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠃⠀⠀⠀⣴⠞⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⡆⢀⣴⡷⠀⠀⢰⣄⠀⠀⣶⠄⠀⠀⠀⠀⠀⠐⠛⠟⠁
⠀⠀⠀⠀⠀⢠⣶⠿⣿⡟⠉⠙⢦⠀⠁⢀⣤⠉⠉⠉⠛⠛⢻⣾⢿⣶⣿⣯⣤⣀⣠⣼⠟⠀⣼⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠹⠅⣰⣿⣀⣀⣤⠏⢀⣠⣌⠉⢰⣛⡆⠀⠀⣼⠏⢠⡿⢁⣭⣭⡍⢉⣡⣤⣴⡟⠀⠀⢠⣴⠶⣤⠀⢀⣴⠆⢠⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⢹⡄⢹⡿⠁⢀⣼⢛⡿⠀⣸⡏⠀⣾⡷⢋⣿⠋⣴⠟⠉⢠⡟⠀⠀⣴⡿⢁⣼⠇⢀⣾⠏⣠⣿⠃
⠀⠀⠀⠀⠀⢠⣿⡃⢀⣀⣤⠟⠁⣿⣧⠶⠋⢰⣿⣥⢾⣿⠀⢸⡟⠁⢼⣇⡤⢿⣤⡶⠻⣧⣴⠞⢿⡥⠊⣿⡤⢺⣿⠔⣿⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠐⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣬⣿⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⠟⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⡟⢐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠸⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡼⣫⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣝⡿⣄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣄⡀⣿⣇⣴⡶⢀⣚⠒⢶⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⣚⣀⢶⣦⡀⣿⡇⣠⡄
⠀⠀⠀⠀⠘⠻⠆⠻⢿⡝⣼⢟⣾⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣝⢿⠙⣾⠟⠁⠿⠋
⠀⠀⠀⠀⠀⢠⣄⠀⠈⠓⢯⣿⠋⠰⣶⠿⠃⠀⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠈⠻⣷⠆⠙⢿⣾⠟⠁⠀⣀⣤
⠀⠀⠀⠀⠀⠈⢉⣀⡀⡁⢸⠃⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⠿⠿⠀⢀⣾⣿⡿⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢿⠐⠀⣀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⢉⡁⠰⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⡈⠜⠀⡉
⠀⠀⠀⠀⠚⠓⠲⣜⣿⣠⡿⡁⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣶⣤⠀⠀⣿⣿⡟⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⢻⣦⣸⢏⠴⠒⠛⠂
⠀⠀⠀⠀⠖⠛⠻⢮⡣⢻⠟⠋⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠻⣿⣿⣷⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⠛⢿⠱⡡⠞⠛⠳⠆
⠀⠀⠀⠀⡴⠖⣛⣳⣅⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⣿⣿⡇⣿⣿⣟⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢨⣶⣛⠒⢦⡀
⠀⠀⠀⠀⢀⣾⡿⠿⣿⣿⡀⠑⠀⠀⠀⠀⠀⣶⣶⣆⠀⠀⠀⢸⣿⣿⡇⢿⣿⣿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⢿⣿⡄⠁
⠀⠀⠀⠀⠈⠿⣧⡆⡀⣿⡇⠀⠁⠀⠀⠀⠀⢻⣿⣿⣤⣀⣠⣿⣿⡿⠀⠘⣿⣿⣧⣀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠁⢀⣿⢃⡰⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⢃⠀⠀⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠀⠀⠀⠘⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⡀⠀⣀⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣿⣾⡞⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⡳⣿⣾⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣹⡿⢿⢣⣿⠻⠆⠀⠀⠀⠀⠀⠀⠈⠏⠧⠛⠞⠯⠇⠀⠀⠀⠀⠀⠀⠀⠞⢿⣮⢷⢿⣿⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣌⠸⣿⣆⠀⠀⠀⠀⠀⢠⡤⡤⣴⢀⠆⡴⢀⣄⠔⠆⠀⠀⠀⠀⠀⣠⣿⡟⢈⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⣳⣬⡻⢷⣦⣀⣀⣀⡀⣀⠀⠀⠀⠈⠀⠁⠀⣀⠀⣀⣀⣀⣤⣾⢿⣫⣶⣯⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣥⡥⢦⣬⣵⡿⠛⠛⣛⣿⣦⠀⣠⣾⣝⡛⠛⠿⣷⡥⣔⢦⣥⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢰⡟⠙⢿⣧⠆⠺⠋⠀⠀⠀⠀⠀⠙⠛⠀⣦⣿⠏⠹⣷⠈⠙⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠇⠀⠀⠀⣠⣴⣿⣿⠟⠛⠉⠉⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⣿⣿⣿⡿⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⢀⣼⣿⠟⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⢀⣴⣾⣿⣿⣟⣁⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠘⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠀⢀⣼⣿⣆⣀⣀⣠⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠰⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠈⠈⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠉⠻⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠲⣶⣤⣄⡀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡈⢿⣧⣴⣶⣾⣿⣿⣷⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣎⣿⣥⣠⣤⣀⣀⠀⠀⠉⠉⣛⣿⣿⡿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣾⣿⠿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠛⠛⠿⢿⣷⣶⡶⠿⠛⠉⠀⠀⠀⠈⠉⠛⠿⣷⣶⣤⣀⡀
⣤⣴⣶⣾⣿⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⠿⣿⣦⣈⢹⣿⣿⠁⠀⠀⠀⠀⠀⠈⢻⣷⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣾⠿⠛⠛⠿⣷⣶⣤⣀
⣿⣿⠻⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠿⠟⠛⠿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠉⠉⠉⠉⠉⠙⠛⠛⠿⣿⣷⣦⡀⠀⠈⠙⠻⢿⣦
⣿⣿⠀⠈⠙⢿⣿⣦⣄⣀⣀⣤⣴⣶⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣶⣤⣀⣀⣠⣴⣿⣿⣿⡿⠿⠿⣿⣶⣤⡀⠀⠀⠀⠉⢻⣿⣆⣠⣴⣶⠿⢿
⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣏⡉⠀⣼⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⡿⠟⢡⣿⠋⠉⠙⣿⡿⠿⢿⣿⡏⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⣿⣿⠋⠁⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠙⠿⣿⣦⣿⡏⠉⠙⠛⠛⠛⠛⠋⠉⠁⢀⣴⡟⠁⠀⢀⣾⡟⠻⣦⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠀⠀⠀⣼⣿⠁⣀⣬⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣇⠀⠀⣀⣀⣤⣶⡿⠟⢻⣿⠁⠀⠀⢠⣿⣿⣿⡿⠟⠛⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣩⣤⣶⣿⡏⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⣿⡍⠻⣿⣷⣦⣤⣤⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠋⠉⠀⠀⠈⣿⡿⠛⠙⣿⡇⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⣿⡇⠀⠈⠙⠛⠛⠛⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣇⠀⠀⢿⣿⡀⠀⠀⠀⠈⠻⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⢿⣷⣄⣠⣤⣴⣶⣿⣿⠆⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠻⠿⠟⠛⠉⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢹⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢿⣷⡀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⢻⣷⡄⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿
⠀⠀⠀⠀⠹⣿⣄⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠘⢿⣾⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣤⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⢸⣿⡇⠀⠀⠀⢀⣠⣤⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⣸⣿⣧⣤⣶⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠿⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡾⣹⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣻⡹⡶⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣥⣿⣛⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣞⣻⣧⣽⢻⣆
⠀⠀⠀⠀⠀⠀⢀⣿⢻⣼⠿⣶⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣤⠤⣤⡀⠘⢳⡤⢿⣼⢻⣇
⠀⠀⠀⠀⠀⠀⣿⠻⣼⠟⢺⠇⠀⠀⣠⠞⣩⣭⠉⠻⣆⢠⠞⠁⣴⢶⠀⠹⡆⠈⢿⠚⢿⡼⢻⡇
⠀⠀⠀⠀⠀⢰⡿⣦⣿⠞⣻⠀⠀⠀⣯⡀⣻⣼⠃⢀⣿⡏⠀⢸⡏⢸⡄⠀⣿⠀⢸⡛⢾⣧⡾⣷
⠀⠀⠀⠀⠀⢘⣷⣌⣿⠞⣻⠀⠀⠀⠈⠹⣟⡁⠐⠿⣿⠀⠀⣿⠀⢸⠃⠀⣿⠀⢸⡛⢾⣏⣴⣟
⠀⠀⠀⠀⠀⠸⣯⠙⢿⣦⠟⣇⠀⢠⠖⢛⣻⣿⡄⠀⢹⠀⠀⢿⠀⡼⠀⢰⡏⢀⡟⢧⣾⠟⢩⡿
⠀⠀⠀⠀⠀⠰⣿⠳⢿⣧⣰⠏⣇⣿⠀⢸⣏⡼⠁⢀⡿⣇⠀⠘⠗⠁⣰⡟⣀⡏⢷⣠⣿⠷⢻⡷
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣾⣿⣄⡟⢹⣷⣤⣤⣤⣶⡛⠁⠈⢓⣶⡶⣿⣥⣴⠛⣇⣼⣿⣦⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠉⣛⣧⣠⡷⢻⢡⡏⡾⡛⡿⣩⢹⣧⢹⠳⠜⣿⣦⣟⡋⢉⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠟⠛⢛⣛⣾⡘⢁⣷⣬⠷⠶⠶⣿⣿⣿⣿⣛⠛⠛⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠻⠦⠾⢿⣵⡲⢶⣽⠟⠛⠙⠳⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠖⠋⠓⢮⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣶⡿⠿⠿⠿⠿⠿⠿⠯⠿⣿⣲⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡾⠗⠋⢉⣠⡄⢰⢶⡄⢰⢶⡆⢀⣦⠀⢠⣉⠑⠻⢷⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠟⠉⠀⣄⠀⠸⣧⠆⢸⣟⣧⢸⢿⡁⣾⣿⠀⣸⠏⢁⡶⢀⡉⠻⣵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠟⠁⠰⣏⡤⠘⣦⣤⠙⠛⠁⣉⣁⣀⣀⣀⣁⠈⠀⠋⢠⡞⣠⣿⣥⠆⠈⠻⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡞⠁⢰⣟⠂⡙⠷⠞⢀⣠⣶⡾⠽⠚⠓⠒⠒⠚⠚⠯⣵⡲⣤⡀⠁⠟⣡⢞⡹⠆⠈⢻⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠉⠳⠟⢀⣔⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⠢⡀⠹⠞⠁⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡄⠀⠀⠀⣰⠫⠉⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠑⠘⢆⠀⠀⠀⢠⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀⡼⢠⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⢀⣿⡿⠻⣿⣷⠀⠀⠀⠀⠈⢇⠀⠀⡄⢧⢀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣧⣧⣇⣇⣆⣰⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠘⠛⠃⢠⣿⡿⠀⠀⠀⠀⠀⠘⣆⣱⣸⣸⣼⣼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡰⠟⠛⠛⠛⠛⠛⠿⠦⢤⣴⠀⠀⠀⢰⣿⡏⣿⣿⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⣦⡤⠔⠿⠛⠛⠛⠛⠛⠛⢆⣄
⠀⠀⠀⠀⢰⠒⠠⠴⢤⣿⠂⠀⢀⣰⣄⡀⠀⠀⠀⢽⣿⠀⠀⠀⣿⣿⣶⣿⣿⣦⠀⣼⣿⠏⠀⠀⠀⠀⠀⣿⡭⠀⠀⠀⢀⣠⣆⡀⠀⠐⣿⡤⠦⠔⠒⡆
⠀⠀⠀⠀⠀⡇⠀⠀⢻⣿⡀⠀⠀⠟⠻⠀⠀⠀⢐⣻⣿⠀⠀⠀⠉⠉⠉⣿⣿⠉⢠⣿⣿⣶⣶⣶⠀⠀⠀⣿⣟⠂⠀⠀⠀⠟⠻⠀⠀⢨⣿⡓⠀⠀⢸
⠀⠀⠀⠀⢀⡇⠀⢀⣼⣿⠦⢤⣤⣤⣤⣤⣤⣤⣤⡼⠿⠀⠀⢀⣀⣀⣀⣉⣉⣀⣀⣉⣉⣉⣉⣉⡀⠀⠀⠿⢧⣤⣤⣤⣤⣤⣤⣤⡤⠶⣿⣧⠀⠀⢸
⠀⠀⠀⠀⠘⠂⠀⠒⠾⠿⠷⠚⢿⠋⠏⠣⠣⠁⠀⠳⣄⠀⠀⠀⠰⣴⠂⣶⠂⢰⣆⢰⣶⡆⢶⡆⠀⠀⠀⣠⠏⠀⠈⠜⠜⠹⠙⡽⠳⠾⠿⠷⠒⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⢀⣠⣴⠆⠈⠳⣄⠀⡀⠃⠀⠓⠂⠛⠙⠘⠋⠂⠛⢃⠀⣠⠞⠁⣤⣳⡄⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⢛⡿⠋⣴⡟⣠⢈⠙⠿⣽⣶⣦⢤⠤⡤⡤⢖⣒⣯⠶⠋⠁⢴⡟⣦⠉⠙⠦⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⣦⡀⠞⣹⠟⢡⣿⣰⢂⡄⣈⢉⡉⣉⡉⢉⣉⠁⣤⣄⠸⣷⣄⠙⣿⠳⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣦⣉⠰⠏⣿⠃⣼⠁⣿⡼⢹⣏⡉⢸⣭⡇⢛⢶⡄⢻⡟⠓⣀⣴⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢿⡶⣤⣈⠃⠀⠿⠃⠸⣧⡤⠸⠏⠧⠈⠛⣁⡤⣴⡯⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠿⣿⣶⣲⣶⣶⣶⣶⣲⣶⣿⠽⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⠆⠸
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣄⠀⠀⠀⣀⠤⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠘⠉⠁⠒⢄⠀⠀⡀⠀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠳⠶⠚⠁⠀⣡⣀⠔⠁⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠒⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⠟⢉⡍⠀⠀⣇⠀⠉⠉⠓⠛⠒⠒⠒⠒⠒⡟⠀⠀⠰⡟⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢈⡶⢹⠀⠀⠀⡇⠈⠐⠒⠀⠀⠤⠄⠀⠒⡾⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⢻⠀⠀⠀⠸⡆⠀⠀⠤⠄⠀⢀⣠⠞⠀⠀⠀⠀⠀⠰⢂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⠶⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠃⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠒
⠐⠂⢉⡆⠰⠒⠈⠀⠀⠀⠀⠁⠒⠂⠤⢄⣉⡑⠢⠤⣀⠈⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢀⣀⠤⠐⣀⠔⠉⢦⡀⠀⠀⢀⠀⠠⣔
⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣌⡉⠒⠺⠛⣿⠶⠶⠶⣶⠶⠶⠟⠉⠀⢒⣂⣈⣭⠤⠔⠒⠉⠁⠀⠀⠀⠉⠓⠀⢧⠘⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡰⠁⠘⠒⠛⠁⡶⠂⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠉⠑⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⡴⠀⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣠⣤⣴⠞⢉⠄⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠢⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⠄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣀⠇
⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠜⠀⠀⠀⠀⠀⢀⡴⠋⠀⡨⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⣰⠏⢀⡴⡶⢀⣿⠃⠀⡠⠊⠀⠀⣤⠖⡆⣠⡟⠀⠀⡔⢁⣴⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠫⠀⣿⠇⠀⣸⡟⡠⠀⡁⠀⠀⣼⠇⡰⢡⡿⠀⡠⠊⢀⣾⡇⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣿⡏⠀⠸⡇⠀⠀⠘⠇⠀⣾⡗⠀⠈⠀⣸⡿⣀⣀⠀⢀⡄⠀⣀⠀⠀⠀⢠⠄⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣀⠀⠀⣠⠖⣆⡀⢀⣿⡕⠲⣆⢠⣿⡟⠀⣿⢴⣿⠀⢠⣿⢀⠔⢸⣷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣿⠀⢠⡿⠀⣹⡇⢸⣿⠀⣸⡟⢸⣿⢁⣴⣿⢸⡇⡰⢹⣿⠁⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⣿⡀⢸⣇⡰⢿⠁⣼⣿⠸⠟⠁⢸⣿⠸⠟⠃⠀⠉⢀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡏⠈⠀⠈⠓⢹⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⠏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⡞⠁⠀⢸⡿⣠⠄⡄⡨⣟⠀⠀⢠⡄⡼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡄⠀⢀⣀⠀⠀⠀⢇⠀⠀⠀⣰⡏⠔⠀⠁⣿⡆⠀⢸⡇⠙⠐⠋⢀⢲⡆⠀⠀⡴⠋⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢀⣀⢰⡟⠰⠁⠀⣾⢁⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣿⡗⠐⠉⠄⠀⢀⠀⠃⢸⡇⠀⢀⡤⢤⣠⠀⠀⡃
⠀⠀⠀⠀⠀⣿⠄⣿⡗⠁⣰⡆⣿⡸⠀⣼⠋⠃⣴⢲⣼⡟⠀⣰⡏⢠⣿⡇⠀⣴⡇⠀⢹⣿⠀⣾⡇⠀⣿⠃⢸⣿⠀⡰⠁
⠀⠀⠀⠓⠀⠙⠀⣿⡇⠀⣿⡇⠸⣇⣸⡟⠀⢸⡇⠀⣹⡇⠀⣿⠁⠀⣿⡇⠀⣿⠀⡌⢸⡟⠀⣿⠃⢸⣿⢀⡼⣿⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣇⢀⠿⣇⠠⠁⠀⢷⡠⠙⢇⢠⢻⣇⠀⢿⡄⠀⢻⡇⢰⠙⠖⠁⠈⠃⠀⣿⠀⠆⠙⠊⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⣈⠁⠀⣀⡀⠀⠀⠀⠀⠈⠻⠜⠀⠉⢀⠈⠓⠁⠀⠀⢠⡾⠱⠀⠻⠎⢀⠖⣹⡆⢻⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⡀⠀⠉⠐⠢⢤⣀⠀⠀⡰⠁⣠⢇⡶⢳⠀⠀⢸⣧⠰⠀⠀⠀⠸⠸⡸⠇⣾⣾⠃⡇
⠀⠀⠀⠀⠀⠠⠞⢁⢴⡄⠀⠀⠀⡔⢹⡄⠀⠀⠀⠀⠀⠉⡝⠛⠉⠁⣼⡇⠌⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠴⠃⣿⣀⠃
⢀⡴⢄⣀⠀⠀⠀⡌⢸⡇⠀⣄⢰⠁⣾⠁⠀⣛⠀⣠⠀⠐⢀⡴⢲⠄⠹⣷⡀⠀⠀⠀⡜⢿⣆⠀⢀⡴⢢⣠⡄⠀⢈⢿⣶⠀⣴⠄⣠
⣿⠁⠘⣿⠀⡰⣶⠃⢸⡇⢠⢹⡇⠀⣿⠀⢸⡏⠀⣿⢀⢣⣿⠡⠊⠀⠔⣸⡟⢠⠋⠸⣷⠈⣿⡄⣾⠇⢺⣿⠀⠀⡎⣼⡇⢸⣿⢠⣿
⢿⡀⣸⢻⣀⠇⢾⠀⢸⡇⡈⠸⡇⠀⣿⠀⣼⡇⡰⢿⡎⠸⣯⠀⢀⠌⠀⣿⠃⢘⡐⠁⠿⠁⣿⠃⢿⣠⠚⣿⢀⠎⠀⢿⣁⠏⠛⢻⣿
⠈⠁⠁⠀⠁⠀⠀⠀⢸⣇⡇⡀⠀⠀⣿⢰⠀⠉⠁⠀⠁⠀⠉⠀⠁⠀⠀⠙⠆⠊⠣⠄⠀⠴⠋⠀⠀⢀⢤⣈⠁⠀⠀⠈⠁⠀⠀⢸⡿
⠀⠀⠀⣠⠴⠒⠂⠉⠀⠉⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⡤⠤⠐⠂⠈⠉⠉⠙⢲⣄⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⠆⠀⠀⠀⠀⠀⠀⣼⠃
⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⠀⠀⠀⠀⠈⠀⠂⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣵⡿⠋⠀⠀⠀⠀⠀⢀⡼⠃
⠘⢿⣄⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠈⠉⠀⠐⠂⠉⠉⠀⠀⠂⠀⠀⠀⠀⠐⠉
⣤⣤⣭⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡼⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⢣⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⢠⣾⡿⠿⠿⣿⣷⡄⢀⣾⣿⠿⠻⣿⣷⡄⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡎⠀⠀⠀⠀⠻⠿⠁⠀⠀⣽⣿⡇⢸⣿⡟⠀⠀⢸⣿⣿⠀⠀⠀⢹⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠟⠁⠸⠿⠇⠀⠀⠀⠿⠿⠀⠀⠀⠀⣻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡯⠀⠀⠀⠀⠀⢀⣶⣿⠿⠋⠀⠀⠀⢸⣿⣷⠀⠀⢸⣿⡿⠀⠀⠀⠀⠬⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣻⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⣾⣾⡆⠀⠻⣿⣷⣶⣿⡿⠃⠀⠀⠀⠀⣝⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠐⣮⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⠞⠚⠻⠗⠉⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⡀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⠀⠀⢀⣀⡀⠀⣀⣀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⠀⠀⣀⣀
⠀⡁⠀⠀⠀⠀⠀⠶⣿⡇⠀⠾⠏⠙⣿⠀⠿⠋⢹⡷⠀⢠⡾⣿⠀⢸⣟⣉⡛⠁⣼⣟⣙⡛⠈⠛⠛⣿⠟⠰⣿⡉⣻⡇⣼⡟⠉⣿⡄⣾⡏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣤⡞⠋⠀⣀⠘⢛⣧⢠⣿⣤⣿⣄⢘⠛⠉⣻⡆⣿⡋⠙⣿⡄⠀⣼⠋⠀⢠⣟⠛⢻⣆⠘⠻⠖⣿⡇⣿⡁⠀⣿⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠿⠇⠀⠿⠿⠶⠶⠀⠻⠶⠾⠋⠀⠀⠈⠿⠁⠘⠷⠶⠟⠁⠘⠷⠶⠟⠀⠸⠿⠀⠀⠈⠻⠶⠾⠋⠘⠷⠶⠟⠀⠙⠷⠾⠟

⠀⠂
⠀⠂
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠙⠛⠛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡴⠚⠋⠛⠓⠦⣄⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⠔⣫⠖⠋⠉⠉⠙⠢⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠳⡀⠀⢀⡜⣡⠎⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⢳⡀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣌⠑⢤⡀⠀⠀⠀⠀⠀⠈⢇⠀⢸⡿⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣙⢦⡀⠀⠀⠀⠀⠘⡆⢘⡇⠀⠀⠀⠀⣠⠔⣫⠖⠋
⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠽⠿⠷⠤⠤⠤⠤⢼⠼⡧⠤⠤⠤⠾⠵⠾⠥⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠏⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠳⠤⠏⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡴⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⠀⠀⠀⢸⠀⡇⠀⠀⠀⠘⠦⠴⠃⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢠⠤⣄⠀⠈⠙⠁⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⡴⠒⣆⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠹⠤⠞⠀⠀⠀⠀⣠⢤⡀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠙⠒⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⠇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⣏⡹⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣴⠲⡄⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⠚⠁⠀⠀⠀⠀⢸⠀⡇⠀⠀⢀⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢯⡽⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣧⣀⣀⣀⣀⣀⡞

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠛⠉⠁⠀⠀⠀⠀⣀⣠⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣷⣿⣶⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⢀⣾⣿⣿⣿⡿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠙⠻⡿⠿⠿⠟⠛⠛⠋⠛⠛⢹⣿⣿⣿⣿⠃⠀⠀⠀⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⡀⠁⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠐⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣀⢄⢤⢠⣄⣀⣄⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣍⣀⡀⠀⠐⠒⢭⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢟⣫⣭⣭⣭⣭⣇⣀⣀⣀⣐⣾⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡵⡺⠟⠟⠛⠉⠁⠈⠉⠀⠀⠀⠈⠉⠹⣟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠏⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⢿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠀⠀⠀⢸⢱⠀⠀⠔⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⠙⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⢠⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣠⠔⣣⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⢦⠀⣀⡄⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡄⠀⠀⠀⠀⠀⢤⠐⠚⠉⠀⡀⣿⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⢂⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠘⢶⠒⠒⣉⢴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⠨⠖⠋⠀⠀⠀⠀⣠⠟⠀⢀⡠⡄⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣄⣀⠀⠀⠀⠀⣀⣠⠴⡿⠥⠒⠒⢉⣀⠟
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢍⠀⣠⠃⡆⠒⠉⠉
⠀⠀⠀⠀⢠⡄⠀⠒⡆⠀⠀⠀⠀⠀⠀⣀⣀⡠⡆⠀⠀⢉⣀⠴⠆⠀⠉⠀⠀⢳
⠀⠀⠀⠀⠀⠤⠀⠁⢁⣀⡠⠜⠒⠒⠒⠒⠒⠚⠳⠒⠊⠉⢀⡞⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡬⢌⣉⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠈⠉⠒⢤⣄⣉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠼⣄⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⣯⠙⡆⠴⠖⠂⠤⠤⠥
⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠊⡠⠚⠉⠹⡦⠴⠖⠒⠒⠒⠤⢀⠉⠉⠛⠒⠲⠶⠶⣂⣀⠀⠀⠀⠀⡏⣸⠁
⠠⡀⡀⠀⠠⢄⡀⢀⠎⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣇⠀⠀⠀⢀⡏⢀⣀⠤⢚⡴⠃
⠀⠑⢌⠲⡀⠀⠈⠙⠦⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣼⠢⠤⠒⠊⠁
⠀⠀⠀⠑⢌⡒⢄⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣭⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢐⠀⠠⡂⠀⠀⠠⠀⠀⠀⠠⡇⠀⣴⠀⠀⢀⠠⡀⡠⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠄⠠⢠⠄⡄⢀
⠀⠈⠀⢐⢅⠂⢠⠐⠠⠀⠈⣈⠁⠀⠭⠖⠈⢀⣀⢇⡠⠋⠢⠀⣿⣴⣥⣇⣴⣷⣧⣸⡇⠀⠀⠀⢠⠀⠂⠄⠐⠠⡔
⠀⡄⡀⠀⠀⠆⠀⡂⡁⠀⢢⠡⡀⠀⠈⠀⠀⠣⠸⠀⢳⠆⠈⢀⠙⠛⠛⢻⠟⠻⠉⠉⠀⠀⠸⠗⠁⢔⡇⠨⣖⠆⡁⠸⠗
⠀⠀⢀⡂⠀⢘⠈⠂⢠⠀⠐⠆⠀⠀⠈⡀⠀⠚⠃⠠⠃⠀⠀⠉⠂⠂⡄⠀⢀⣠⡀⠀⣉⠀⠐⠂⠁⠠⠄⠃⢠⠐⠁⠒⠈
⠀⠔⠤⠀⠂⠄⠐⠠⠘⠠⠌⢊⠀⠀⠀⠃⡀⠀⠀⠂⢰⡄⠂⠀⠀⠀⠣⠄⢸⠀⠀⢰⠁⠆
⠐⡐⠐⠠⠀⡐⠀⢂⣉⠀⠐⠀⠊⠀⠀⠀⠀⠀⠒⠀⠅⠓⠐⠒⡀⠀⠀⠊⢸⠀⡇⠘⠀⡇⠠⠴⡒⠀⠽⠀⠀⠸⠻⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡀⠉⠍⠀⠂⠂⠀⠀⠒⠀⠀⠀⡀⡀⢾⠀⠀⠀⠘⠂⠁⠰⠐⠇⠀⠀⠀⠀⠀⠀⢀⢂⠀⠱
⠰⠀⠀⠒⡤⠁⣠⣤⡄⠘⠋⠻⡉⡙⠋⠉⠉⠛⣍⢩⠋⠀⠀⠀⠀⡀⡄⢀⠂⠀⠀⠀⠂⠀⠀⠐⠀⡀⢆⠀⡐⠄⠀⠀⢀
⠀⣾⣿⡦⠀⠢⢻⣿⣧⠀⠀⠀⠙⢠⠀⠐⠂⠀⠈⠃⠀⢀⣈⣀⡀⠀⠀⠠⠀⠀⠀⠀⡤⠄⠐⡀⠀⠀⠈⠀⠃⠀⠀⠀⠈
⠀⠻⡛⠃⠀⠀⢀⡀⠈⢦⠄⠀⠀⡞⠀⠀⠀⠀⢠⠂⠉⠉⠀⢀⠉⡉⠋⢦⠀⢤⠤⠈⠁⠀⠀⠐⡀⠐⡄⠀⡀⠀⠶⠂
⠀⠀⣧⢀⠀⠠⠆⠈⢂⠀⠁⠂⠉⠁⠉⠀⠀⠀⡌⠠⠄⠀⠄⠨⠀⠀⡆⠐⠅⠀⠀⠀⠀⠀⡐⠀⠘⠢⠁⠀⡀⠠⠀⢀
⠀⠀⠀⢀⠀⢨⠀⢀⠀⡆⡔⠁⠠⠀⠀⠤⢳⠀⠧⠐⠀⢁⢀⡀⠀⠀⠀⠀⡄⠀⠀⠓⠀⠀⠀⠐⡄⠀⠀⠀⠐⠄⠠⣀
⠀⠂⠀⡟⢇⠀⡆⠀⢐⠀⡥⢉⠐⠂⠘⠀⢙⡀⠈⠳⡀⠀⠀⠈⠀⡀⠠⠖⠀⣠⠀⣀⣠⡬⠁⠀⠱⣤⣠⡂⠀⠠⠤⠈⠄
⠀⠃⡌⠀⠘⡀⠁⠤⠊⠘⢄⡂⠀⠀⠀⠀⡪⠂⠀⠀⠀⠀⠈⢉⠁⠀⠄⣄⠀⠉⠀⠙⡟⠀⠀⠀⡀⠸⡟⠁⠀⡀⠀⠁⡀
⠀⢰⠀⠀⠀⠘⡀⠀⡔⠒⠒⠠⠧⠀⠀⠀⡰⠂⡙⠁⠂⠀⢐⡠⠈⡤⠊⠐⠐⠲⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⠁⠤⠠⠴
⠀⠉⠐⠐⠂⠀⠁⢠⠃⡀⠄⠀⠀⡂⢀⡜⠁⠁⠀⢂⠖⠀⠀⠃⠉⠙⠀⠀⡀⠀⣠⡀⢀⡉⣲⣰⡊⣡⠀⠈⠃
⠀⠀⠀⠲⠂⡀⠀⠠⣀⠃⠀⠃⠁⠁⢎⡀⠤⠐⠊⠁⠀⠀⠀⠀⠂⠠⠤⠊⠠⡦⢀⣀⣈⠛⠛⠛⠛⠋⠀⠀⠀⢀⡀⢼⠆
⠀⣜⠑⣶⣆⡱⢀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡰⠂⠀⢰⡤⠒⠂⠀⠀⠀⠀⠀⠁⠸⣀⢸⠉⠀⠈⠉⠉⠉⠉
⠸⠙⠉⣀⠨⠰⢸⠀⠀⠠⠂⠀⠂⠀⣀⠁⠐⠌⠐⠀⠠⡄⣠⠀⢦⠀⠈⠀⠃⠀⠈⠉⠙⠐⠈⠐⠀⠊⠑⠀⠂
⠘⢅⠀⠂⠀⣀⡘⠀⠒⠄⡀⠀⠀⠙⠃⠀⠀⡀⠤⡀⡈⢰⡀⣇⢀⡇⠀⠀⠀⢲⡐⡆⠐⡀⠀⠰⠢⠀⠆⠐⡰⠂
⠀⡀⠈⠃⠈⠠⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢆⠐⠂⡀⠀⠀⢢⠀⠐⠂⠀⠀⠀⠐⠀⠃⠀⠐⠀⠚⠀⠰⠁⠀⠆
⠀⠀⠀⡐⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⡌⢄⡸⠀⢀⡂⠀⠀⠰⢠⠀⠰⠂⠳⠈⡄⠁⠂⠀⢉⠀⢠⠊
⠀⠆⠀⠄⠀⠀⠃⠈⠐⠀⠜⠈⠀⠀⠋⠀⠓⠒⠒⠒⠒⠀⠂⠈⠁⠀⠒⠀⠐⠀⠋⠘⠀⠒⠀⠊⠐⠁⠒⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⢀⠀⠀⠁⠀⠀⠸⡢⠀⡼⠁⢀
⠀⠀⠀⠀⠀⠀⢀⠀⡟⣀⣋⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⢍⡿⣅⡴⠃⠀⠀⠁⠎
⠀⠀⠀⠀⠀⠀⠣⣱⠈⣼⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⡰⡀⠀⡤⢀⡾⢇⣰⠞⠁
⠀⠀⠀⠀⠀⢐⣠⡄⢂⠴⠴⠒⠀⠀⠀⠠⢤⣄⡄⠀⠀⠀⠀⡅⠀⠀⠀⢸⢸⠁⠀⠀⠀⢁⠅⠀⠰⢄⡤⢜⠃⢀⠀⠠
⠀⠀⠀⠀⡄⠀⠀⡀⣁⠜⠛⡁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⢸⢸⠀⠀⠀⠀⢠⢸⠀⢰⢦⣤⠺⠊⡉⠀⠀⠐
⠀⠀⠀⠀⢈⠐⠊⢀⠃⡰⠊⣡⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠸⠸⠄⠀⠀⠀⡘⡀⠀⠱⠷⡸⠒⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠾⠐⠈⠆⢠⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠁⠸⢭⠂⠆⢴⠊⠁⠐⠈⠀⠀⠁
⠀⠀⠈⠀⠀⠈⠲⠔⠸⠦⡁⣢⠀⡴⠅⢀⡀⠀⠀⠀⠀⠀⢰⡼⠀⠀⠀⠀⠀⠀⠀⣠⡣⠂⠀⠰⣇⠀⡆⢸⡇⡀
⠀⠀⠀⠀⠄⠀⠀⠤⢀⡤⠉⠘⠀⠈⠁⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠩⠤⢦⠠⣤⣬⡴⠃⠐⠣⠒⠄⠀⠠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠤⢀⢀⣀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢢⡀⠒⠀⠂⠀⠀⠀⢸⠁⢀⡀⣀⠀⢀⠄⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⢠⠂⠀⠀⢨
⠀⠀⠀⠀⠀⢠⣤⣀⠀⠸⠾⣯⠘⠉⠈⠉⠈⠈⠐⢒⣴⠂⠀⠄⡄⠠⡤⠤⠤⢀⡀⣀⠀⠀⠀⡀⡀⣠⠀⠀⠀⢸⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠃⠛⠋⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⡐⠁⠀⢀⡢⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠉⠀⠀⣖⡾⠃⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⡟⢸⡇⠈⡇⠀⠀⠀⠀⠀⢋⣉⢹⡆⣼⠁⢹⡄⠀⠀⠀⠀⠰⣡⢹⠂⣸⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠉⣇⠸⡇⠀⡇⠀⠀⠀⠀⠀⢁⣨⡞⢁⣿⠀⢈⡇⠀⠀⠀⠀⠀⠒⠳⣄⡿⠐⣻
⠀⠀⠀⠀⠀⠀⠒⠛⠦⠽⠊⠄⠀⠀⠀⠀⢰⢋⣁⣴⡦⠻⠀⠸⠃⠀⠀⠀⠀⢾⣚⣣⡿⠻⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠀⠀⠀⠀⠈⣛⣉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣥⡀⠀⡬⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⣰⠇⢀⢠⠏⠘⣆⠀⠀⠀⠀⢰⡞⠛⠚⢰⡷⠐⣆⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠓⠀⠀⠀⠀⣁⡤⠄⢰⠇⢠⠆⠘
⢠⣿⣀⣸⢸⠆⠀⢽⠀⠀⠀⠀⠐⠚⢳⣤⢸⡇⠀⠯⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⢸⠀⣾⠀⢸
⠀⠁⠉⣿⠹⡆⠁⡾⠀⠀⠀⠀⠚⠃⢘⠞⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠈⠃⠀⠀⠀⠀⠆⠀⠟⢠⣏⠠⣞
⠀⢀⣀⡉⢀⢈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠉⠊⠉⠋
⠀⠉⠉⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢤⣾⣧⠀⣠⠆⢳⡀⠀⠀⠀⠀⡠⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⣠⡄⢷⠀⣼⠀⠘⡇⠀⠀⠀⠀⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠈⢹⡀⢿⠆⢻⠀⢸⠇⠀⠀⠀⡀⠀⠀⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⣐⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡐⠌⢃⠚⡀⠘⠡⠛⡀⠀⠀⢸⠡⠶⠕⠶⠳⠙⠒⠒⣶⠀⠀⠀⢻⠏⠱⠔⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⣀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠒⠢⠤⡀
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡠⠂⡩⠕⠒⠒⠒⢤⡀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⡇⠀⠀⠀⢰⠁⠀⠀⠀⠁⠐⠈⠑⠀⠚⠈⠰⠀⠀⠀⠀⢀⠔⢠⠀⠙⠄⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⡀⢊⠴⠸⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡁
⠀⠀⠀⠀⢃⠀⠰⠉⠕⠊⠀⠀⠀⠀⠆⠀⠀⢠⠀⠀⠰⠁⠈⠀⠡⡌⠀⠳⡅⠀⠀⠀⠀⠀⢱⠀⠇⡜⡀
⠀⠀⠀⠀⠀⠢⣈⠆⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⡘⠀⠀⠀⢠⢀⠀⠀⠀⡀⠈⠑⠠⢀⣀⡤⢤⡤⡈⢠⠃
⠀⠀⠀⠀⠀⠀⠉⠢⣀⡀⠀⠀⠄⠀⠀⠀⡠⠜⠀⠀⠀⠀⠈⡍⠀⠀⠀⠋⠀⠀⠀⠀⠀⠁⣰⢀⠈⡇
⠀⠀⠀⠀⠀⡠⠐⢮⣀⡈⢙⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⡀⠀⠂⠆⠀⠀⠀⠀⢀⡘⠈
⠀⠀⠀⢠⠊⢠⠀⠀⠈⠉⠉⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣤⠄⣉⠖⠒⡖⠒⢰⡬⠝⠀⠀⠀⡄
⠀⠀⢠⡁⠀⡈⠀⠀⠊⠈⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⠀⢀⠎⠀⠉⡡⢰⠢⡴⠎⠊
⠀⠀⡌⠈⡶⠀⠀⠀⠀⠀⡀⢺⠈⠂⠲⠀⠀⠀⠀⠘⠏⠂⢤⠐⠊⢉⡉⠡⢵⡈⠘⢁⡸⠀⢣
⠀⠠⠃⢰⠀⣤⠀⣀⣀⣠⠀⢬⠈⠁⠁⠀⠀⠀⠀⠀⠄⠀⡓⠮⠀⠒⠀⡟⢉⡠⢐⣉⡀⠠⠜⢆
⠀⠈⠓⠈⠀⠇⠁⠉⠁⡉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠄⠀⠀⠐⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠄⠒⠈⠉⡉⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⡁⠀⢠⠚⠤⣀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣒⣒⠖⠂⠏
⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠜⢘⡒⣱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⠀⠀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⢸⣿⣶⣤⣴⣴⣶⣿⡇⠀⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢹⠀⢀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣸⣿⠿⠿⠿⠿⠿⠿⣇⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣤⠀⠳⢤⡤⠞⠀⠀⠀⠀⠀⠀⠀⣿⡿⣯⢿⠿⡿⣿⣿⡇⣀⣀⣂⣀⣀⠀⢸⣿⢿⠾⡿⢿⢿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣿⣿⡇⠉⠉⠉⠉⠉⠀⢸⣿⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⠿⢿⣤⣀⣀⣀⣀⣀⣀⡼⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⠀⢸⣿⠿⠟⠿⠻⠿⣿⡇⠀⣀⣉⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⡄⠀⠀⠀⢀⡞⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣼⣿⣿⠀⠀⠀⢸⣷⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⢸⣷
⠀⠀⣿⡇⠀⠀⢠⣴⣶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠉⠛⠆⠀⠀⣿⡇
⠀⢰⣿⠀⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⣧
⠀⢸⣿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⣿
⠀⢸⡟⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠶⠴⠶⠶⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢶⣶⣶⣦⣤⣤⣤⣤⣶⣶⡶⠾⠿⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⣀⣀⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢀⣴⠞⠁⠀⣀⣠⣤⣄⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⡞⠉⠉⠉⠓⢦⡀⠀⠙⣆⠀⠀⣠⠞⠀⢀⡴⠛⠉⠀⠀⠀⠹⡆⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⠀⠀⠹⣄⠀⠈⢧⣰⠏⠀⣴⠋⠀⠀⠀⠀⠀⠀⢰⠇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢷⡀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠋⠀⣼⠁⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠻⢦⣀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠇⠀⠀⠀⢀⣠⠶⠋⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠉⠛⠲⠦⣤⣄⣿⠀⠀⣿⣠⡤⠶⠚⠋⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠿⠶⠦⣤⣄⣀⠀⠁⠀⠀⠉⠀⠀⢀⣠⡤⠶⠯⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡴⠛⢳⡀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢠⢿⡇⠀⢸⣷⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠏⢸⡇⠀⠀⡇⢻⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⠏⠀⢸⡇⠀⠀⡇⠀⢳⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⢶⣠⠏⠀⠀⢸⡇⠀⠀⡇⠀⠈⣧⢠⡷⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⢸⠇⠀⠀⡇⠀⠀⠸⡟⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⡤⢤⡤⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣀⡀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢹⣷⢀⣤⡀⠀⠀⠀⠀⠀⢠⣤⣤⣰⣦⣿⡇⠀⠀⢰⣿⠁⠀⠈⠻⣿⡆⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣿⢛⡙⣷⣲⣦⣾⡟⣿⣿⣷⣿⠏⠿⢿⣷⢤⣄⠸⣿⡀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣸⣿⢿⣿⣿⠋⢸⣿⠸⣶⠾⢻⣿⢸⡟⠀⠙⠛⠓⠚⠋⢴⡆⣀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠸⠟⣤⡌⠉⢠⣶⠀⠘⠛⠊⠀⠀⠀⠀⢀⡀⣠⡈⠘⣿⣶⣦⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢻⡧⠀⠀⠀⠀⠀⠀⢸⣟⡇⠀⢸⣿⡄⢀⡀⣀⡀⣤⠖⣦⣿⣿⣿⣷⠀⠇⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣸⠃⣶⡄⠀⠀⠾⠗⢸⣿⠃⢀⣼⣿⡇⣿⣿⠿⠿⣿⡔⢃⡼⡿⠹⣿⠌⠈⠚⠉
⠀⠀⠀⠀⣤⣀⣀⠀⢀⣿⣿⣤⡾⠁⠀⣿⣇⣤⡀⣴⡗⢸⣿⠀⣿⣧⣿⣇⣿⡟⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠻⣿⣿⡿⢿⣿⣿⠁⠀⠀⠀⢿⣿⣿⡇⣻⣷⡜⠛⠗⠉⢛⣡⣭⣶⣦⣤⡀⠀⠀⠀⠀⠀⢹⣷⡀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⡼⠟⠈⠛⠁⠀⠀⠀⣠⡞⢋⣶⣶⠆⠘⣿⣿⡆⣴⣫⣿⣷⠀⣿⣧⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣤⠞⠁⠀⣴⠿⣶⡄⠀⢰⣿⡀⠀⣿⣿⡆⠀⢹⣿⣿⢨⣿⣿⣿⣆⣿⣯⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⢸⡟⠀⢸⣿⠀⠸⣿⣿⣿⢹⣿⡇⠀⣸⣿⠇⠘⠛⠃⠉⢉⡤⠖⢿⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠈⠙⢿⣾⡇⠀⢸⣿⠀⠀⠀⠉⠀⣸⣿⣇⣴⠟⠋⠀⠀⢀⣤⠞⠋⠀⠀⢸⣿⡆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠙⠃⢀⣿⡟⠀⠀⢀⣶⣏⣽⡿⠁⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣀⠀⣤⣴⣿⠟⠀⠀⠀⠀⠉⠋⠉⢀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢹⡄⠀⢀⠞⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⣠⠤⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠀⣸⠁⢀⠏⠀⠀⠀⠈⠂⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⡜⠀⠀⢠⠂⣠⢀⡖⢀⠄⡴⠀⢀⡔⢠⠆⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠊⠀⠀⠀⠑⠀⠀⠃⠐⠃⢼⠂⠈⢠⠗⠊⠘⠀⡏⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⢀⡄⢲⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡸⠀⠀⠀⠀⠀⠖⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡾⠀⢀⡇⠀⢄⠀⠀⠀⠠⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢠⠲⠇⠀⠸⠠⡀⣠⢀⡄⣠⢀⡌⡀⣠⢀⣤⠘⣠⠀⣶⠀⠀⢀⠐⣡⢀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡔⠁⢸⠀⡠⠁⡰⢳⡃⣸⢣⢇⡞⣰⡡⠉⡟⠀⢰⠃⠖⠸⠴⣦⣏⣴⣇⣾⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⣀⣀⣈⡀⠀⢀⠀⠀⠉⠀⠁⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⡁⠀⠀⠠⠇⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢠⠠⠌⣙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠐⠛⠂⠌⠱⣄⡠⠔⠠⠤⣄⡀⠀⢠⠇⠀⠀⠀⠀⣠⢯⣛⢳⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡞⢷⡢⣄⠀⠀⠀⠀⠈⠳⡛⠃⢄⡀⠙⠢⡜⠀⠀⠀⠀⢠⡟⠭⠟⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢯⡥⢒⠭⢷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠁⡼⢡⠀⠀⠀⢀⡾⠭⠍⣠⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢯⡷⣕⡥⣞⠡⢚⢦⡀⠦⣈⠢⣤⡽⠶⠾⣥⣫⠄⠀⢠⣞⠭⣩⠔⣡⡞⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠁⠀⠀⠊⠖⠕⡿⣻⠿⣷⣚⣿⠶⠬⣹⢏⠀⠀⠀⠡⠝⢯⣔⣯⣶⣛⣵⣚⣭⠶⠚⠙⠛⠦⣄⡀
⠀⠀⠀⠀⢀⣔⣻⣀⡀⠠⣀⣠⣤⢄⡶⣲⠖⣲⠒⡲⢤⣭⣭⣿⣽⣾⣇⡆⡶⢿⡻⢽⣛⠻⠿⠿⣿⣁⠀⠀⠀⠀⠀⠁⠢⠌⠙⠲⠤⣄⡀
⠀⠀⠀⠀⠘⡆⣟⣡⣴⣟⡫⠞⠱⠋⠘⠁⠈⠁⣈⡤⠗⠚⠉⠚⠑⡹⣾⣽⣿⣶⢬⣀⠀⠀⠀⠀⠀⢨⡝⢦⡀⠀⠀⠀⠀⠀⠈⡩⠖⣀⣭⡷
⠀⠀⠀⠀⠀⢇⠈⢹⣸⡎⠛⠲⢄⡀⣀⠤⣒⠉⠁⠀⠀⠀⠀⠀⢀⣤⡵⠟⠋⠹⢧⣐⢉⠷⢢⣄⡀⠈⢗⡀⠙⣄⠀⠀⠀⢀⣠⢔⡞⡹⣱⡇
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡏⠁⠈⠁⠀⠀⠀⠀⣀⣴⠾⠉⠀⠀⠀⠀⠀⠀⠈⠳⢦⣉⠴⢊⠷⢥⣴⡺⠷⢤⣖⡾⣡⢫⢎⢞⡔⣱⠃
⠀⠀⠀⠀⠀⠀⢙⠲⣄⠀⠀⠀⠀⡇⠀⠀⠀⠤⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡐⠋⠁⠒⠀⣀⠸⡖⡵⢣⢫⢎⣜⡍
⠀⠀⠀⠀⠀⠀⢸⠀⠁⠛⠶⣤⣨⠀⠀⠀⠀⣑⢀⡯⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⢀⡀⠔⠀⣀⡤⢶⢻⣧⠀⠀⠨⢖⠀⡟⡴⣱⣣⢾⡾⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠆⢰⡍⠀⠀⠀⠀⠈⠑⠦⣉⠒⠍⢀⡠⡴⢋⠟⡰⣡⡫⣿⠀⠀⣪⠥⠀⡿⡶⣩⣫⢪⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠏⢸⣦⣀⠀⠀⠀⠀⠀⠀⢠⠙⣎⢟⡔⡵⢣⢞⡔⡕⡕⣽⠀⠠⠔⣊⠠⡟⡴⡱⡳⢻⠃
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠅⢸⡇⠋⠷⣦⣀⠀⠀⠀⣘⠀⣧⢊⠞⡴⣡⢪⣮⣾⡞⣿⠀⢐⡫⠔⢰⢟⡜⡵⣡⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⢀⡇⠀⠀⠀⠉⠛⠶⢬⣛⠂⣧⣃⣾⢴⡟⡹⣣⢎⢞⡇⠀⠽⢚⡡⢸⢎⠎⡴⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⣧⠀⠀⢐⡂⠠⡇⠀⠀⠀⠀⠀⠀⠈⠈⢹⡟⡝⡡⢋⠞⡴⣡⢫⢞⡇⠰⣚⡥⠆⣸⢎⡜⡰⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢢⢀⠀⣿⠀⠀⠐⡂⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⡜⡱⢣⠞⡴⡱⣣⢿⠇⢈⠴⢒⡉⣧⢎⢼⠟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠀⢹⠀⠀⠀⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⢊⠞⣠⢫⢎⠜⡵⣡⢻⠀⠤⢒⡩⠄⣧⢮⢋⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⠀⠀⠀⠦⠀⡇⠀⠀⠀⠀⠀⠀⠐⡀⡷⢋⠜⡡⢣⢎⠞⡴⡱⢻⠀⢊⡡⠖⢋⣷⡣⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡨⢕⠀⣯⠀⠀⠀⠀⠀⠀⠠⡁⡷⢋⠞⣡⢣⢎⢞⡽⡱⣿⠀⡩⢔⣋⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣻⣄⡀⠀⠀⠀⢀⡒⠀⢰⢋⡼⣡⢣⢎⢞⡜⣼⡇⠀⢖⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡠⢶⡪⠅⢸⠎⡔⡱⣣⡯⠞⠋⠙⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀⠀⣀⠀⠀⡀⠀⢀⠀⠉⠓⠮⣅⣸⣎⡼⠛⠉
⠀⠀⠀⠀⠀⠀⡠⢖⡥⢚⡡⢒⡩⠔⣋⠤⢊⣡⠔⢉⡤⠚⢁⠔⢊⡠⠂⣀⠌⢁⡠⢊⡤⢂⡠⠀⣀⠔⢀⡤⠀⣀⠄⡠⢀⡠⠀⣀⠀⡠⢀⡤⢀⡀⢀
⠀⠀⠀⠀⠀⠈⠀⠁⠖⢡⠔⢉⡴⠊⣡⠖⢉⡠⠖⢁⡤⠊⣁⠔⢋⡠⠊⣁⠔⣡⠖⢁⠴⢋⡠⠚⣡⠔⢉⡤⢚⡡⢊⡴⢋⡤⢊⡵⢋⡴⢋⡴⢫⠖⠡⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠀⠐⠁⠠⠊⢁⡴⠋⣠⠎⡡⠞⣡⠖⢁⡴⠋⡠⠊⣁⠔⢉⡴⢋⠔⠁⠴⠋⠐⠋⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠈⠀⠀⠁⠀⠉

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⡀⡄⠆⠀⠠⠤⢆⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠀⠀⡈⠘⠂⠀⠄⠀⡀⠉⠉⠙⠂⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⠤⠤⣄⠀⠀⠀⢰⡣⠞⠁
⡇⠀⠀⠀⢸⠏⢀⠀⢀⠖⢉⡄⢹⡇⠀⠀⠂⠀⠨⠕⢂⠀⠀⡇⠀⣤⣀⣒⣄⠀⠀⢠⡏⠠⠤⠀⣼⣗⠀⠀⠋⠈⠉
⡇⠀⠀⠀⠁⠠⠀⠀⣸⣷⡤⢠⣟⣟⣹⡀⣀⠀⣀⠀⠀⠀⠀⡇⠀⠀⠒⠚⠋⠀⢐⣾⣿⣶⠂⣼⣽⣉⣿⣀⣀⢀⣈⣀
⡇⠀⠤⠥⠀⠀⣬⢴⡟⣿⡟⡏⢏⣸⣙⣃⣋⣸⣼⠃⠀⠀⠀⡇⠀⣀⠀⣀⡠⢤⠶⢻⢻⠋⡏⣿⠠⡏⢺⠀⣇⣰⣇⡞
⡇⠀⠂⠀⠀⢀⡼⠴⣷⣛⡛⠯⠍⠉⠉⠉⠁⣀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⣇⣸⣦⡼⠾⠞⠓⠛⠛⠛⠉⠉⠉⢉⡉
⡇⠀⠀⠀⠴⣖⣊⠉⠁⠀⠀⠸⡖⠀⢀⠶⠚⢁⠀⠀⠀⠀⢰⡇⠀⠀⠈⢋⠉⠁⣀⢄⠄⠀⠀⠀⠀⠓⠀⠀⠀⠲⠙⠒
⡇⠀⠀⠀⠂⠉⠋⡍⠉⠁⠈⠀⠅⠠⠉⠄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠎⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⠦⠤⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⢒⡖⠛⡳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⠰⠡⠄⠏⠺⠓⠋⠚⠁⠡⠁⠓⠘⠛⢠⠃⠈⠀⠈⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠉⠉⠻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⡴⠟
⡇⠀⠀⡀⠀⠀⢀⣀⣠⠠⠄⡤⠘⢖⠶⡒⠒⠉⣀⢉⡇⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⡃⠁⢠⠀⠀⠁⠀⣀⣀⠀⠁⠈⠀⡼⡃⣼⢀⠀⣼⠢⠄⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠉
⡇⠀⠀⠠⣷⠀⠀⠀⠀⡔⢉⡄⢈⡷⠀⠀⠀⢧⢣⡇⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⡚⠁⣴⠏⠀⠀⠀⠀⠀⠀⠤⠶
⡇⠀⠀⠀⢸⠳⠀⠀⠀⠳⣶⢠⡞⠁⠀⠀⠀⣀⣭⠷⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣇⣼⣃⣀⡀⢀⠀⠀⠀⠀⠠⠤
⡇⠀⠀⠀⢸⡇⠀⠔⣶⢸⠏⣹⣀⣏⣸⠀⠀⣧⡏⠀⠀⠀⡟⠀⠀⠀⠀⢀⣐⢈⣿⢀⡟⡀⣿⣀⣾⢁⣺⠤⠤⢤⡀
⡇⠀⠀⠀⠺⡖⠢⡜⠉⣉⣉⡉⠁⢀⣤⣶⣖⣿⠄⠀⠀⠀⣧⠔⠂⢠⠏⣭⢩⡹⡍⡉⡭⣩⢩⡭⢭⣩⡄⡴⠠⠀⡇⠐⠢
⡇⠀⠀⠀⠀⠷⠶⠺⠞⠛⠛⠛⠲⠋⠉⠉⠉⠁⠀⠀⠀⠀⡇⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣠⣞⣀⣠⣎⣀⣄⣠⣇⣀⣤⣀⣀⣰⣄⣀⣳⣄⣀⣙⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢤⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡴⠊⠀⠰⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢰⠀⡘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠇⠀⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡐⢃⠶⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⢉⠔⠁⠀⠀⠀⠀⠠⠈⠁⠀⠙⢁⠲⡀⠒⠒⠒⠶⠀⠀⠀⠤⢠⡄⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⠔⠁⠀⠀⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠉⠐⠂⠤⠄⠉⠐⠛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠐⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠀⢀⡁⠀⠀⠄⢐⠀⠤⠀⢀⣀⠀⠀⣀⣐⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠂⠀⠠⠤⠤⠈⠍⠙⠀⢻
⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠸⠀⠈⡈
⣿⣿⣿⣿⣿⣿⣿⠃⢀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⣤⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⣧
⣿⣿⣿⣿⡿⠛⠛⠃⣤⠊⠀⡀⠀⠠⠇⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠑⣰⣧⠊⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⡄⠀⢫
⣿⣿⡻⣿⣶⣆⣠⣀⠀⠀⠸⠇⡀⠀⣀⣤⠐⠶⣤⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠈⠁⠀⢀⡄⠀⠂⣸
⡟⠛⠻⠉⠿⠿⠟⠟⡻⠧⠤⠤⠷⠟⢻⠶⠖⠒⠆⠘⠗⠀⠀⠙⠒⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢀⠸⡁⠀⢀⢹
⡇⠀⢐⠀⡀⢀⡔⠀⠀⠀⠀⠐⠀⠀⠹⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣤⣀⠁⠀⠘⠀⠀⠀⠀⢠⠎⠀⠃⠀⠀⢸
⣯⠘⢙⠉⣉⠋⠀⠀⠀⠀⢰⡆⠀⠀⠀⠈⢫⠛⢉⠉⠋⠀⠀⠀⡀⠀⠀⠀⠈⠆⠀⠃⠀⠀⠀⠀⢰⠀⠁⠀⠀⢸
⡟⢠⠘⠀⡍⠀⠀⠀⠀⠀⠊⢠⠀⠀⠀⠀⠀⠦⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠘⣀⢸⣾
⡇⠀⢠⠀⠃⠄⡀⠀⠀⠘⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣴⣶⣿⣿⣿
⡇⠀⠀⠀⡁⠀⠀⢢⡄⠣⡀⠀⢧⡀⢴⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠘⢻⡆⠀⠀⠈⠠⠄⠀⠀⠀⢀⣸⠀⠀⢂⡀⡐⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠸⠚⡃⠀⠀⠀⠀⠀⠀⣀⣌⠀⠈⠁⢴⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠸⠀⡇⠀⠀⠉⠀⠀⢔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣤⣀⣀⡇⠀⠀⠂⠀⠀⠚⢩⠁⠀⢀⠀⣠⣄⠠⡄⣤⠀⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠀⠀⠛⠐⠂⠐⠒⠀⠐⠒⠒⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠂⠀⠠⠤⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠛⠀⠀⠀⠀⠋⠿⡂⠀⠄⠠⠄⢀⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⣀⣀⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡖⣶⠀⢸⣏⣷⠀⠀⣴⡖⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣭⡄⠀⣿⣹⠆⠸⠇⠿⠀⠾⢓⣇⠀⠀⡽⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠻⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⣠⠟⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢂⠀⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣠⢾⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⡦⠀⠀⠀⠀⠀⠀⢀⣭⣭⠃⠀⠈⣭⣭⣭⣭⣭⣭⠇⠀⠀⠀⠀⠀⢶⢋⡉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⡱⠿⣿⣿⠀⠀⠰⣿⡏⠛⠛⠛⠒⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠠⣿⣷⣿⣶⣿⣕⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢙⡿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠒⠒⣽⣿⡇⠀⠀⠀⠀⠀⠀⠈⣻⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⢄⡀⠊⣭⡍⢀⡀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠿⢿⣿⡷⠀⠐⠹⢿⡿⣿⠿⠋⠈⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠖⢞⡿⠃⠀⠀⠀⠀⠀⠈⢉⠈⡈⢉⡀⠀⡀⢁⣀⠁⢉⠀⠀⠀⠀⠀⠀⠀⣬⡽⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣠⡶⠀⠀⠀⠀⠀⠈⣿⠁⣿⡀⣸⢧⢨⡿⡅⣓⡅⠀⠀⠀⠀⢠⠤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠷⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠙⠲⣍⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡼⣻⡴⠃⣠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠹⡽⢦⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣰⠃⠀⣏⣸⠃⢰⣖⠂⠰⣏⣷⠀⠓⠒⣦⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸⣏⡄⠀⠧⠸⠆⠈⠉⠁



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⡝⠛⢳⠒⠤⣄
⠀⠀⠀⠀⠀⣀⢴⠾⠃⠁⠀⠉⠷⡦⣀⠀⠀⠀⠀⠀⠀⠀⡠⠞⡤⠂⠀⠀⠀⠀⠀⠐⣬⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄
⠀⠀⠀⠀⠴⠯⠁⢀⣠⠀⣠⣤⡀⠈⠼⠧⠀⠀⠀⠀⠀⢰⠳⠆⠐⢠⡴⣦⣀⡴⢦⡀⠂⠶⢻⠆⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢸⣚⡄⠀⠈⣿⢸⣟⢈⣿⠀⠀⣛⡧⠀⠀⠀⠠⠼⠛⠂⡀⠈⣴⠟⢻⡇⢸⡇⢈⠐⠟⠧⠀⠀⠀⠀⠀⢠⡏⠀⠀⠞⢻⡦⣼⠛⣧⠀⠀⢻
⠀⠀⠀⠼⢛⢃⠀⠠⠿⠤⠿⠼⠏⠀⠐⣛⠣⠀⠀⠀⢀⠰⡗⠀⠀⠸⠷⠾⠟⠷⠞⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠲⣏⢀⢀⣀⢻⣷⣿⠀⣿⠀⡐⣻
⠀⠀⠀⠸⢟⣄⣀⡠⠄⠀⠀⠀⠀⣀⣡⠛⠆⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠀⠔⠻⡁⠀⠙⠛⠁⠈⠛⠁⠀⡸⠗⡄
⠀⠀⠀⠀⢈⢉⣠⣄⠀⠀⠀⠀⣠⣤⡉⡃⠀⠀⠀⠀⠀⠀⠯⠅⣁⣚⠷⣶⣖⣶⢾⣃⣘⡬⠱⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁
⠀⠀⠀⠀⢁⠔⠋⠉⠙⠒⠂⠛⠉⠙⠢⡈⠀⠀⠀⠀⠀⠀⢠⡠⠟⠋⠀⠁⠉⠉⠈⠑⠹⢄⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⠰⠀⠖⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠖⠃⠀⠀⠀⠀⠀⠀⠀⠓⠦⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⢀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠤⠠⠤⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠘⠖⠉⠁⠀⠀⠀⠉⠲⡏⢀⡀⠀⠀⠀⠀⠀⠀⣤⠿⠧⠀⠀⠀⠀⠀⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⢆⣴⠀⠁⣀⠀⠀⣀⡈⠙⢶⡆
⠀⠀⠀⠀⠠⠄⠀⠀⣴⡆⢠⡶⣦⡀⠰⡆⠀⠀⠀⠀⠀⠀⣴⢛⠀⢰⠶⠶⢀⡶⢶⡄⢑⡻⣴⠀⠀⠀⠀⠀⢀⣼⡋⠀⣾⣉⡓⣾⠋⣿⡄⠉⣷⠃
⠀⠀⠀⠒⢆⢀⠀⣾⣹⣇⣿⡇⣸⡇⡀⠀⠒⠀⠀⡐⢀⡤⣿⢁⠀⠘⠛⢶⣼⡇⢘⡇⠀⡙⣯⣄⠀⢂⠀⠀⡈⣿⡄⠀⣿⣉⣿⢿⣄⣿⠃⠂⢸⠊⠁
⠀⠀⠀⣰⠬⠋⠀⠀⠺⠷⠘⠳⠟⠀⠁⠧⣒⠀⠀⠁⠜⠃⢻⣤⠂⡙⠷⠟⠉⠻⠞⢃⠘⣼⠟⠘⠃⠁⠀⠀⠈⠹⣇⠀⠈⠉⠁⠀⠉⠁⢀⠀⠈⠀⠀⠀⠐
⠐⠊⡁⢈⠛⠛⠷⣄⣀⠀⠀⣀⣠⡶⠛⠚⡃⢨⡑⠂⠀⠑⠢⠈⠉⠛⠀⠀⠀⠀⠐⠋⠈⡁⠖⠋⠀⠀⠀⠀⠈⡁⠉⠁⠀⠲⠀⠀⠐⣠⣤⠆
⠈⠉⠉⠉⠑⠲⢄⣀⠉⠉⠉⠉⢁⡠⠔⠚⠉⠁⠉⠁⠀⠀⠀⠈⠛⠑⠒⠒⠒⠒⠚⠉⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⠞⠉⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠴⣆⡤⠽⠯⠤⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⣴⣠⠞⣁⣀⣀⢀⣀⡈⠱⣄⣴⠀⠀⠀⠀⠀⠀⠂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠂⠉⠁⠉⠁⠠⠦⡀
⠀⠀⠀⢀⡀⡏⠀⠋⣸⠏⣿⠈⣿⠀⢸⣀⣀⠀⠀⠀⠘⠄⠀⠁⠒⣴⠶⣦⢀⡴⢶⡤⠒⠉⣀⠀⠁⠀⠀⠀⠀⠀⣼⣉⠀⣠⣤⡀⢀⣤⣄⠀⣙⡆
⠀⠀⠀⠘⠉⣇⠀⣠⣿⡀⢿⣤⡟⠀⢸⡉⠋⠀⠀⠀⢠⢰⠟⣱⠀⣸⠷⢿⣸⡇⢸⡷⠰⣎⢻⢀⡄⠀⠀⠀⠀⣤⣁⠓⠸⣧⣸⣷⣿⠀⣿⠀⠣⣉⡤
⠀⠀⠀⠀⠻⠉⢦⡀⠀⠀⠀⠀⢀⡠⠉⠛⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠷⠟⠁⠻⠞⠃⠐⠈⠁⢀⠀⠀⠀⠀⠀⠈⢃⠀⠀⢦⣼⠏⠻⣤⡿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠚⠃⢨⣷⠀⠀⣼⣇⠸⠛⠀⠀⠀⠀⠀⠀⠉⢐⣶⢀⠤⠠⠄⠀⠠⠄⠤⣀⣶⠊⠉⠀⠀⠀⠀⠀⠈⠉⡠⠄⠀⠀⠀⠀⠀⠀⠠⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣂⣤⣂⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⢠⡏⠀⠀⠀⠀⠀⠀⡴⠋⢀⠃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢰⡏⠁⣿⠀⠀⠀⢠⡞⠉⣼⠁⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡏⠀⠋⠀⠘⠃⢰⡟⠀⠀⣾⡇⣄⢀⡄⢀⡄⠀⣀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣦⠀⡾⢱⡆⣸⠇⣸⠖⣿⢁⣿⣿⠀⢾⡗⠁⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⢰⣇⢺⡇⣿⠰⠟⠀⡿⠺⠃⠉⢁⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⡀⠁⣿⠀⠀⠀⡇⠀⠀⢀⠂⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠘⡀⠀⢉⡞⠈⠈⣷⠀⢸⠀⠤⠋⢠⡄⠀⡴⠂⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣿⠸⣀⣾⢸⢀⣄⠈⡁⣼⠅⢠⣤⣿⠂⢉⡀⣤⡔⢸⡇⢠⡖⣦⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠰⡏⠀⣿⠹⣇⣿⠁⣾⠙⣿⠀⣿⠈⣿⠀⣿⠀⢸⡇⣼⠃⣾⠃⣿⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠻⠄⠁⠹⠄⠻⠀⢿⠀⠷⠀⢻⡀⠙⠂⢈⠁⢿⠀⠉⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⠀⠀⠀⠀⡀⠈⠁⠀⢀⣄⡤⠀⠀⣏⠀⠈⠁⡂⣸⢾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⡄⠀⠀⠜⡇⠀⠀⠀⠉⠐⠃⠉⣼⠀⠀⠀⢻⡆⠀⠀⠁⠀⠞⢿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠰⡦⠀⣤⢀⡇⢰⡎⢰⡇⢠⡄⣶⠀⣴⠋⠃⠙⣧⢀⠀⣌⢻⡄⣴⠋⣶⠀⠀⣿⢃⡞⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢧⠈⠿⢸⡇⠀⠇⢸⡇⣼⡀⢿⡄⣿⠀⠀⢠⡏⢨⠀⠹⢸⡇⢿⠔⣇⠠⠀⣿⡘⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠧⠀⠀⠸⡧⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⠀⠀⠊⠀⠀⠀⣦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈