Women meme Emojis & Symbols

⠀⠀⠀⠀⠀⡠⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠛⠀⠘⡿⠂⠀⠀⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢤⣀⠀⠐⢾⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠰⡄⠀⠀⢀⣤⣶⣆⠇⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁
⠀⠀⠀⠀⠀⠈⠂⠀⠸⠤⢬⠟⠀⠀⡠⡀⢀⠠⠐⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣉⣉
⠀⠀⠀⠑⠀⠄⠀⠘⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⡀⠀⠄⢀⡀⠀⠤⠀⠤⠤⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠄⢀⣀⡀⠀⠀⢀⣀⣀⣐⡀⠂⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠞
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠂⢆⡠⠋⢲⠀⡎⡱⢠⠊⠑⢀⠇⠀⢎⡡⢤⡡⠦⣉⠍⠓⠶⣎⡁⢰⡁
⠀⠀⠀⠀⠀⠀⢦⡄⣠⠎⡙⠘⢔⣹⣔⣁⣔⡡⣧⠎⡖⢣⢹⠥⡶⡪⢒⣭⡤⠼⠣⡬⣢⡜
⠀⠀⠀⠀⠀⠀⠺⢚⠕⢒⣷⢋⠝⣿⣿⣿⣿⣦⡐⡄⢈⡙⣯⠊⡰⢡⡏⠀⠀⠀⠀⠈⢪⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢀⢎⢣⡷⣾⠃⠀⠀⠈⠑⢜⣮⣀⣭⢻⡷⢁⡾⣖⣲⡄⠀⣀⣀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⡎⢡⢃⠎⣆⢱⡏⠀⠀⠀⠀⠀⠀⢻⡄⡸⣼⡇⣼⠈⠙⠋⡏⢽⠿⠷⠑⡄⢸⡄
⠀⠀⠀⠀⠀⠀⢣⡆⡘⡰⠘⠆⣇⡤⠤⢤⠀⢴⣫⣽⡘⡾⢣⠀⡇⠀⠀⠘⠤⡾⠀⠀⢠⠇⠸⡇
⠀⠀⠀⠀⠀⠀⡞⠀⠇⡇⡟⢰⠥⠴⠿⠚⡇⠸⡉⠁⢐⢸⣀⢰⠃⠀⢰⣕⣍⣦⣀⣀⣾⠀⠀⣇
⠀⠀⠀⠀⠀⠀⡇⢠⠀⣆⢹⡄⠀⠀⠀⠀⣧⡤⠗⡀⢘⠸⠙⣀⡤⢶⣿⠹⠛⢅⣉⣉⣉⣻⣶⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢸⢣⠀⠀⠀⢰⣴⣖⣣⣽⢸⢘⠞⠁⣴⢏⣋⢠⠀⢸⠿⣿⡯⢧⠊⢸
⠀⠀⠀⠀⠀⠀⠀⢰⢀⠟⢀⠱⣧⡀⠀⠸⣏⠜⡏⣿⡼⠁⠀⠀⢿⡁⠸⡄⢧⢘⡶⢿⠶⢾⡀⢸⡄
⠀⠀⠀⠀⠀⢠⢇⣮⣊⣦⣌⣡⡈⢻⢯⣀⠻⢭⣴⠟⠁⠀⠀⣠⡾⡿⠦⠼⠉⠝⣡⠎⡇⡈⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠛⠛⢠⣑⠪⣿⡌⢦⡞⠈⡱⠊⠁⠀⠀⢀⣼⠃⣷⠁⠀⢀⡼⡞⡿⠀⡇⡇⣹⡇⠃
⠀⠀⠀⠀⠀⠘⠴⢚⣭⣤⣑⣿⡷⣘⡽⠊⠀⠀⠀⠀⢠⡟⢹⠀⡿⡄⡴⠋⡿⢰⡇⠀⡇⠁⠁⠁
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠈⢻⡗⠉⠀⠀⠀⠀⠀⢠⠟⠀⠘⡆⡂⣿⠁⢰⠇⡘⡇⠀⢹
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢷⠸⣿⠀⣼⠀⣳⠀⢀⣸⠀⣦⠆
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡇⠀⠀⠀⢸⢃⢻⡀⡾⢸⡇⠀⢨⡇⠀⢻
⠀⠀⠀⠀⠀⢸⡙⠄⠀⠠⠤⠤⠤⠄⠀⠀⢴⠇⠃⠉⠃⠀⠀⠀⠳⠜⠳⠧⠬⠤⠤⠼⠀⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⣠⣀⣀⡤⡄⠀⠠⡀⡄⠀⣠⠀⢠⠄⠀⠀⠀⠀⠀⣠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠚⠟⠁⠀⠿⠄⡼⢃⡴⢊⡩⣿⡓⢬⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⣛⣻⣍⣙⡢⡄⠀⠀⢠⠏⢠⠎⠀⠀⠈⢳⣳⠀⡇⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣰⢣⢿⣿⠁⠀⠀⠙⢿⣄⢠⠏⢀⡾⠿⣄⣀⣶⢼⠈⡇⡷⠶⠶⠶⠶⢶⡄⢹
⠀⠀⠀⠀⠀⢠⠇⢸⡜⣇⡠⢄⠀⣀⣞⣿⡏⠀⡜⠀⠰⠏⠇⠀⢸⠀⢿⡇⠀⠀⠀⠀⢸⠁⠀⡇⠀⡠⢄⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⡞⠀⣿⢡⠇⠚⠋⠀⠹⡀⢸⡇⢀⣇⣀⠾⡷⠤⢤⣏⣀⡘⡇⠀⠀⠀⠀⢸⠀⠀⢳⣰⠁⢠⠁⠈⡍⠁⢰⡄
⠀⠀⠀⠀⠀⠀⢰⢻⢸⡀⠀⠀⢉⣬⢅⣸⢣⡼⠋⣀⠰⡄⡶⢲⠶⡞⣿⣇⠀⠀⠀⠀⡎⠀⠀⠘⡇⠀⠀⠘⣃⠀⠀⡸⠁
⠀⠀⠀⠀⠀⢀⡇⣸⠀⠳⣄⠀⠻⣽⠞⣹⠃⠀⠀⠸⡄⣧⣵⡾⣴⠃⣷⡏⠙⣢⣀⣀⣇⣀⣀⣀⣻⢀⠀⠉⠁⠀⢰⣁
⠀⠀⠀⠀⠀⣭⠴⡥⣴⠃⠘⡦⣌⣹⠞⠁⠀⣰⠛⡗⠚⢹⢹⠃⢹⠀⢸⡗⠉⣿⠁⡀⡏⠉⢁⡵⣻⠯⣍⠙⠛⠛⠛⠛⣛⣻⣟⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⡧⠚⠁⠀⠀⡰⣿⡇⡇⠀⡇⢸⠀⠈⡇⢸⡇⠀⣿⣭⡭⠗⠀⣯⣕⠛⢶⣯⣭⣉⢉⡍⠋⢠⣶⣿⠛⢸
⠀⠀⠀⠀⠀⠞⠉⠉⠙⠾⠋⠀⠀⠀⠀⣴⢳⢹⡇⢧⠀⡇⢸⠀⠀⡇⢸⡇⣀⣿⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⢸⣻⢸⣰⠃⣾⠀⠀⡇⠰⣏⠕⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⣭⣭⣭⣭⠭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠞⠀⢻⣿⠸⠻⡀⠛⠀⡇⠀⢰⠃⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⢸⣿⠀⠏⠄⠀⣧⠏⢨⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣯⣽⣿⣿⣿⣽⣷⣤⡀⠀⠀⢀⡤⠴⠯⠭⠽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠯⠭⠽⠭⠭⠭⠭⠭⠽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠯⠭⠭⠭⠭⣭⠭⠭⠍⠡⠩⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⢻⣿⣿⣿⣿⣿⡟⢩⠍⠹⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⡭⢭⠭⣿⣽⣯⣿⣿⣿⡿⠿⠿⣿⣿⣭⠿⠟⠋⠁⠨⠙⢿⣿⡽⣿⡭⠭⠩⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣭⣼⣿⣿⣿⣍⣡⣤⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣶⣤⣾⣿⣿⣿⣿⣭⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢷⠿⠤⠤⢤⣷⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣼⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⠾⠦⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⠁⣘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⣲⠂⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠒⢒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣀⡂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣲⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⠒⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣳⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣻⣿⣿⣿⣇⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣒⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣓⣒⣒⣒⣒⣒⣒⣒⣒⣻⣿⣗⠀⢐⣲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⠂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣒⡒⣒⡒⢒⣺⣿⣟⠒⠀⣀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣀⣒⣀⡈⣿⡿⢿⣿⣿⠿⣿⠿⠿⠿⠷⠿⣖⣒⣲⠶⠂⣼⣛⣒⣂⣀⣐⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣒⣒⣂⣒⠒⢳⣖⣛⣒⣒⣖⡒⠂⡖⠀⢀⠂⠀⣉⣤⣞⣷⣓⡒⣒⢀⣒⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣒⣒⣒⠂⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠐⡒⣒⣒⣒⣒⣒⣒⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣲⣒⣲⣒⣒⣒⣀⣐⡐⢀⠀⢀⣀⡀⣀⡀⣐⣦⢐⢒⣶⣒⣒⣒⣒⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣓⣷⣾⣓⣒⣒⣒⣓⣟⣒⣲⣟⣂⡛⠓⣓⡚⣃⠒⣊⣓⣲⣚⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣶⣲⣶⣶⣖⣶⣒⣓⣒⣒⣒⣒⣒⣒⣒⣶⣿⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠁

⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿
⣿⣿
⣿⣿⣷⣄⣀⣀⡀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀
⣿⣿⣿⡿⠏⠁⠀⢀⡄⠈⣴⣿⣿⣿⣿⣿⣿⣶⣶⠤⠴⠿⣿⢿⡦⢀⣤⣤⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⣿⣿⣿⡧⠀⠀⣴⣿⣇⡈⠛⠿⠿⠿⠿⠛⠋⠁⣀⣠⣼⣿⠿⠶⡆⠉⠛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡿⣿⣿⣅⠀⢰⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⡾⠟⠛⠛⠛⠉⠉⠀⠀⠀⡀⠘⣿⣿⣿⣿⣷⣤⠀⢀⣀⡀⠀⣠⣤⣴⣿
⣿⣾⣄⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣟⠆⠀⠀⢻⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣿⡿⢋
⣿⣿⡏⠀⢐⠀⣄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⢻⣿⣿⡻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⣾⣿
⣿⣿⠁⠀⠸⠀⣿⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠈⠻⣿⣋⠹⣿⣿⣿⣷⠀⠀⠠⢒⣿⣿
⣿⣿⣷⠀⠀⢷⣹⣿⣿⣧⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢿⣷⣄⢻⣿⣿⣇⠀⠀⢙⣿⣽
⣹⣛⡋⠀⠀⠈⠻⣿⣿⣿⠏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠔⠻⣋⠉⠟⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⣿⣿⣆⠀⠀⣭⣥
⣿⣿⡟⠀⠀⠀⠀⠈⠻⣿⣇⢠⡶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀
⣾⣿⣟⠂⠀⠀⠀⠀⠀⠘⣿⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⠆⠀⢀⠀⢹⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⠿⠋⠀⠀⢸⠀⠀⣿⡄⠀⠀⢀⣤⣤⣶⣾⣿⣿⠂⠀⠀⠀⠀⠀⠐⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠀⠀⠀⠀⠸⠀⢠⣾⣿⣆⠀⠈⠻⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⡤⠳⡄⠙⠛⠿⣿⣿⣿⣿⣿⣿⠉⢛
⢿⣿⣿⣶⣶⣶⠖⣀⣤⣄⣥⡀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠀⠀⠙⣶⣤⣀⡀⠉⠹⢿⣿⣿⣿⣿
⢸⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣷⣦⡙⢿⣿⣿⣶⣄⣀⣀⣠⣤⣶⣿⡿⠋⠀⠀⢀⠠⡊⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⠋⠁⢀⠀⠐⠀⠁⡀⠐⡀⠰⡇⢠⣶⣾⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢂⠈⡄⠀⠂⠀⠰⡀⠐⠀⢀⠔⠱⣾⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠆⠸⡄⠈⠂⠀⠀⠀⠀⣡⠏⠀⠈⠛⠿⠿⠿⠿⠛⠋

⣀⣀⣀⣀⡀⠀⠠⡀⢀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡀
⠁⠀⠁⠀⣇⠀⠰⠯⠃⠀⢸⣀⣈⠗⢀⠴⢒⣲⡖⢮⣻⠄⢘⡇
⠀⠀⢀⡤⠛⠶⡒⠒⠦⡀⠀⠀⠀⡴⠃⣰⠋⠀⠉⠓⣝⡆⢸⠇⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⢠⢏⣞⣿⠏⠉⠉⠑⢝⣆⠀⡸⠁⢰⣷⣆⠀⢠⢄⣸⢸⢸⣦⣤⣤⣤⣤⣤⡀⢱
⢀⡏⢸⣸⣿⢀⡀⠀⠀⡨⢿⣶⠃⢀⠇⠀⣼⢹⠉⠁⡞⠈⣿⠀⠀⠀⠀⠀⢸⠃⠈⡇⠀⢀⡀⠀⠀⠀⠀⣀
⡼⠀⣼⡏⡏⠩⠿⠀⠸⡛⠙⣿⠀⣸⠀⢠⣴⣄⡀⢀⡇⠀⢻⡄⠀⠀⠀⠀⣸⠀⠀⢳⢀⠎⢈⡢⠔⠒⠖⠉
⠁⢠⢿⢸⠀⠀⠀⠰⠄⠗⠀⣿⣀⡿⠛⠉⣍⢉⣉⣉⣩⠽⣾⡇⠀⠀⠀⠀⡏⠀⠀⠸⡟⠀⠈⠡⡶⠉⠀⠀⡿
⠀⡞⢸⠈⢆⠀⠀⢰⡿⣏⡗⡷⠋⠀⠘⡆⢸⡘⣦⣇⣸⠀⣿⡗⠦⣀⠀⠀⡇⠀⠀⠀⢷⡀⠀⠲⠓⠂⠀⡜
⠴⣡⠎⢀⡄⠑⣄⠀⠿⣧⠔⠁⠀⡠⣤⣘⠶⣻⣿⠀⡇⠀⢷⡧⠴⡾⠒⠒⡗⠒⠒⢒⣾⣾⠶⠶⠶⠶⠾⠷⠶⠤⣤⣤⡶
⠉⠉⠉⠛⣄⠀⣻⣱⠖⠁⠀⠀⣴⣧⣷⠀⢠⠇⣿⠀⢳⠀⢸⡇⠀⡷⠒⠲⡇⠀⡴⠯⣼⡉⣵⠤⠤⠤⡤⢤⠖⣚⣛⣣⠍
⣠⠤⠤⠤⣘⡤⠟⠁⠀⠀⠀⣼⢹⣼⢸⠀⢸⠀⡟⠀⢸⡄⢸⡇⠀⡟⠛⠉⠁⠀⠛⠷⢦⣬⡿⠿⢶⣤⣿⣤⣤⣿⣽⣧⠤
⠁⠀⠀⠀⠉⠀⠀⠀⠀⢀⣼⣾⠃⣿⡌⡆⣸⠀⡇⠀⢸⠁⢸⡧⢖⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⡶⠬⠭⠭⠤⠭⠭⠭⠤⠤
⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⣿⡆⡇⡇⢷⡇⢰⡇⠀⢸⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⣿⡛⢻⠉⠩⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢩⡾⠇⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠉⠉⠛⠛⢿⣿⡄
⠀⣠⢺⠏⠏⡼⠗⠒⠍⠳⣄⠀⠀⢠⣿⣿⣿⢀⡀⠀⠀⠀⠀⣿⣿⡄
⢰⠃⠙⢠⠀⠀⠀⠀⠀⠀⠘⣆⠀⣸⣿⣿⠛⠾⠏⠀⠜⢣⡀⣿⣿⣇
⡏⢀⠃⠸⠀⢀⣀⡀⠀⠠⢒⡘⢦⣿⣿⡿⠀⠀⠀⠀⠀⠈⢁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⢁⡌⠀⠈⠀⠠⠶⠌⠀⠀⠉⠁⠘⣿⣿⡃⠀⢠⣶⣶⡀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠁⠔
⡈⠀⡇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠄⠈⠉⠁⠀⠈⠉⢛⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠄
⠁⠀⢣⢀⣧⠀⠀⠀⣶⡾⠿⡆⠀⠟⠉⠀⠠⡀⠰⠀⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣀
⡠⢀⠄⢐⡸⡇⠀⠀⡅⠀⠘⡇⠁⣀⣀⣰⡄⠀⡀⢀⣰⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠠
⣵⡅⣚⣉⣠⠙⢦⣀⠙⠛⠋⠀⠀⢀⣾⣿⡏⠀⠂⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⣀
⣿⣿⣿⣿⣷⢀⠀⡿⠋⠀⠀⠀⢠⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠀⢀⣁⠀⠈⠁⠀⣀⠀⢈⠉⠤⠄
⣿⣿⣿⣿⣿⡾⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠛⠛⠓⠒⠚⠛⠚⠳
⣿⡿⠋⠹⠋⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣧⠀⠁⣿⣿⣿⣿⣿⣿⣿⡆
⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⡿⠀⠰⣿⠿⠿⠿⠿⠿⠿⠇


⢀⠀⠀⠄⠀⠀⠀⢠⠠⡤⠀⠤⠀⠀⠀⠀⠀⠄⡀⠄⠀⠀⠀⠀⢠⢄⡠⢀⢤⠀⠀⠀⡄⢀⠄⠠
⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠀⠉⠀⠀⠀⠁⠈⠁⠈

⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⢀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠋⠉⠉⠉⠉⢹⡀⠀⢀⣿⣲⠏⠀⢀⡇⠀⠀⣿⠀⠀⣀⣤⠤⢤⣤⣀⠻⣄⠀⠀⡧
⠀⠀⠀⠀⠀⢸⡇⣀⣈⣉⠉⠀⠀⠈⠛⠒⠚⠋⣠⠞⠉⣠⠖⠻⢦⣉⠳⣟⠁⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⣠⢖⡋⠙⣻⣆⣉⣙⠲⣄⠀⠀⠀⠀⣼⠃⠀⡼⠁⠀⠀⠀⠈⢻⡜⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋
⠀⠀⣴⠃⡞⣽⣷⠉⠉⠉⠉⠳⣜⣦⠀⠀⣸⠃⠀⣸⣓⡦⠀⠀⢠⣄⡠⡇⢹⠀⣷⣤⣤⣤⣤⣤⣤⣤⡀⠀⢧
⠀⣸⠇⢸⢰⣿⡇⠀⠀⠀⠀⠀⠈⣿⣧⣰⠃⠀⣸⠃⠈⢡⡶⡆⠺⠖⢸⡇⠸⣀⡇⠀⠀⠀⠀⠀⠈⢉⡇⠀⢸⡇
⢠⡏⠀⡟⡼⢸⡧⠶⠶⠄⠀⣤⣫⡼⣿⡟⠀⢀⡏⠀⠀⠛⠀⠓⠀⠀⣸⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⡔⢦⡀⠀⠀⠀⠀⡰⢆
⡞⠀⠀⣿⠇⡾⠀⠚⠛⠁⠀⠹⡄⠀⣿⣷⠀⢸⣇⢀⣰⣯⣽⣤⣀⣀⣟⣀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢻⣀⡘⠀⢠⡌⠉⠉⣉⠉⠀⢸⣀⡀
⠁⠀⣴⢻⢸⡇⠀⠀⠀⠀⠦⠄⠟⠀⣿⢹⠀⣸⠟⠋⠁⣄⠉⢀⣀⣉⣉⣩⠿⣷⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⠁⠀⠀⠀⢴⡆⠀⠀⠀⢀⡿
⠀⢰⡇⢸⠈⣧⠀⠀⠀⢀⣴⣯⡝⡇⢿⣸⠟⠁⠀⢲⡀⠸⡆⢹⠀⡍⠉⢣⠀⡟⣷⣤⣀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢻⡄⠀⠀⠠⣼⣤⠀⠀⠀⡎
⠀⡿⠀⡼⠀⠈⠳⣄⠀⠈⠻⣤⡟⠁⣼⠃⠀⠀⠀⠀⢳⡀⣿⣼⣿⠛⣶⠃⠘⡇⠧⠀⠉⣳⢄⣀⣀⣇⠀⣀⢀⣀⢈⡏⢆⡀⠀⠀⠀⠀⠀⢾⣀
⣚⣡⣞⣁⣀⠞⠀⠈⣧⣀⠉⠓⣶⠞⠁⠀⠀⣴⢻⡷⠦⠛⢡⠎⡟⠀⢻⠀⠀⢻⡷⠞⠋⣿⠉⠀⠈⣿⠉⠉⠉⣩⡟⣿⣟⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⢿⠿⣍
⠉⠉⠉⠉⠙⢦⡀⠀⢸⢉⡿⠛⠁⠀⠀⠀⣼⣿⡄⡇⠀⠀⡿⠀⡏⠀⠘⡇⠀⢸⡇⠀⠀⣿⠒⠒⠲⣿⠀⢠⡾⠧⣼⣇⢀⣽⠦⠤⠶⠶⢦⠶⡶⠚⢋⣉⣻⣤⡤
⠀⣀⣠⣤⣄⡈⢷⣀⡿⠋⠀⠀⠀⠀⢀⣼⢹⣼⡁⡇⠀⢠⡇⠀⡇⠀⠀⢿⠀⢸⡇⠀⠀⣿⠶⠾⠛⠋⠀⠘⢿⣦⣤⣬⣱⣯⡾⣧⣤⣄⣿⣂⣀⣀⣿⣟⣿⣄⣀
⠛⠉⠀⠀⠈⠹⡞⠉⠀⠀⠀⠀⠀⢀⣿⢹⠀⣿⣇⢹⠀⢸⡇⠀⡇⠀⠀⢸⠀⢸⡇⠀⢀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣉⣈⣉⣙⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣼⠀⡏⣿⠈⡇⢸⠃⢠⠃⠀⠀⡿⠀⢸⡿⢋⣥⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣬⣭⡉⢉⡉⠉⣉⣉⣉⣛⣒⣒⣒⣒
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⣇⣿⡄⣿⢹⠀⣷⡿⠀⢸⠀⠀⠀⡇⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠚⢻⡟⡛⢻⡟⠋⠉⠉⠭⠿⠿⢿
⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠿⠧⠇⠛⠸⡆⠈⠁⠀⠼⠀⠀⠸⠇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠟⠰⠂⠺⠀⠆⠀⠘⠻⠇⠀⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠉⠀⠁⠀⢀⠀⠀⠀⠀⣀⡨⣔⢈⢣⠀⠙⢢
⠀⠀⠀⠀⠨⠁⠀⣤⠔⢶⣷⣶⣄⠀⠐⠲⡏⠉⢠⠎⠉⠉⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢁⢰⡏⠀⠀⠉⢰⡌⢭⣷⠂⣾⣶⣄⣀⣄⠀⢹⡀⢰⠀⠀⠀⠀⠤
⠀⠀⠀⠀⢀⠀⠀⢂⢹⠀⢀⠀⢀⠄⡃⣰⡏⠘⠀⠉⡀⡍⠛⢘⠂⡇⠰⠀⠠⠀⣀⢀⡇⠀⠀⢀
⠀⠀⠀⠀⢸⠁⠀⡈⠜⠩⠶⠇⠸⠋⠁⢱⡀⡆⠀⣤⣘⣁⣀⣘⠀⠇⠀⠀⠠⠀⠀⠈⠁⠀⠀⠈⡟⠒⠂⠐⠒⠂⡴⢻⠃
⠀⠀⠀⠀⠀⢀⢠⢰⠀⠀⠀⠸⢒⠃⠀⢆⣡⠖⣾⠋⠉⢠⣩⣭⡿⢟⠀⡐⠀⠠⠀⢠⠀⠀⠀⢠⠁⢦⠀⠤⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠘⢸⠀⢦⡀⠀⢾⠫⠺⣦⠎⠀⢾⠃⡆⢄⢩⣽⣩⡇⢸⢰⠧⠀⠀⠀⢰⠀⠀⠀⢸⠀⡞⠡⠴
⠀⠀⠀⠀⠀⣠⢨⢌⣄⠛⣧⡘⢧⡴⠃⠀⢀⡜⠷⠼⠋⢋⡌⠀⢸⣾⣾⠡⠊⠀⠀⠙⠀⠀⠈⠘⠛⠛⠛⠛⠓⠒⠚⠂⠠
⠀⠀⠀⠀⠈⡩⠖⠘⣷⡰⣇⠄⠁⠀⠀⣰⠏⠸⠀⣠⡞⢹⠀⡀⠈⡇⠁⠀⣆⠀⣀⡿⢠⠞⠀⠠⠤⠊⠓⠊⢲⠖⢻⠒⣿⡶⢶⠋
⠀⠀⠀⠀⢠⠀⠉⠑⢿⠔⠁⠀⠀⠀⡴⠁⠠⠈⡶⠁⡇⠘⠀⡇⠀⡇⠀⠀⢉⠀⠀⠀⠀⠈⠛⠛⠚⠛⠒⢒⡚⠛⢻⣿⡾⠗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠘⠎⣇⢰⠃⡆⠀⠀⢰⡇⣆⠀⠀⠀⠈⠛⠒⠀⠀⠀⠀⠀⠚⠛⠶⠟⠛⡃⠓⠒⠂⢂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡐⠓⠤⠀⠀⢂⡹⣼⠘⠀⢰⠃⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣧⣤⣰⣄⣃⣀⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠤⣤⣤⣄⡀⠀⣿⠿⢟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⡴⢲⣞⠿⠛⢀⡙⠉⠀⠉⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠛⢿⣿⡏⠉⠉⠉⠢⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠜⢢⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⣌⣰⡅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠢⠀⠀⠀⠀⠀⠀⠈⠛⠻⠳⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠤⠒⠒⠒⠲⣾⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠦⠀⠀⠊⠉⢲⣶⡶⠒⠒⠤⣀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢢
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡠⠂⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠇
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⡞⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⡄

⣀⣀⣀⣠⡀⠀⢠⡀⡀⠀⣀⠀⢀⡄⠀⠀⠀⠀⠀⣀⠄⠀⡀
⠁⠀⠀⠀⡇⠀⠺⠽⠁⠀⠧⣀⡸⠂⡤⠒⣋⣿⠲⣝⡦⠀⡇
⠀⠀⢀⢔⠛⢺⣉⣓⢦⡀⠀⠀⢠⠎⢀⠞⠀⠀⠉⢪⢣⠀⡇⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣰⢣⢿⣿⠉⠀⠈⠑⣽⡄⢠⠏⢀⡾⡶⡄⣀⣦⢼⡟⡆⡷⠶⠶⠶⠶⢦⡄⢹
⢠⠇⣸⡞⣇⣀⣀⠀⣀⣜⣿⡞⠀⡼⠀⠰⠋⡇⠉⢸⠀⢷⡇⠀⠀⠀⠀⢰⠃⠈⡇⠀⢠⡀⠀⠀⠀⢀⡄
⡞⠀⣿⢣⠇⠒⠚⠀⢻⡉⢸⡇⠀⣇⢀⣶⣶⣄⣀⣏⣀⠘⡇⠀⠀⠀⠀⢸⠀⠀⢳⣠⠃⢨⠒⠂⡀⠋⢸⣀
⠀⢸⢻⢸⠀⠀⠀⠐⣂⣁⢸⢧⡸⠋⡁⠰⡀⡤⢤⢤⠞⣿⡇⠀⠀⠀⠀⡿⠀⠀⠘⡇⠀⠀⠐⡇⠀⠀⢸⠃
⢀⡇⣸⠈⢧⡀⠀⠾⣛⡾⢸⠏⠀⠀⠹⡄⣇⣷⡾⡤⠃⡇⡏⠑⢦⠀⠀⡇⠀⠀⠀⢻⢄⠀⠉⠉⠀⢠⡃
⣊⣴⣃⣠⠂⠘⣦⡈⢛⠖⠁⠀⢰⢺⡒⠟⢻⢻⠃⢹⠀⢹⡗⠚⣿⠉⠉⡏⠉⠉⡩⢿⢿⡛⠛⠛⠛⠛⠛⢛⣛⣿⠿
⠀⠀⠀⠈⢦⠀⣧⠞⠁⠀⠀⣰⣿⣧⡇⠀⡏⢸⠀⠘⡆⢸⡇⠀⣾⣉⣭⡷⠀⣿⣓⠺⢶⣾⣻⠉⠉⡟⠋⢩⣤⣽⠖
⠖⠋⠉⠑⣾⠚⠁⠀⠀⠀⣰⢳⢸⡇⣇⠀⡇⢸⠀⠀⡇⢸⡇⠀⣻⣀⣀⣀⣀⣈⣙⣛⣛⡫⠭⠿⠿⠷⠶⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣾⢸⢻⢸⣰⠃⣼⠀⠀⡇⢸⣟⡭⠗⠒⠒⠒⠒⠒⠒⠿⠯⢭⣭⣭⣭⣭⠭⢭⣿⣿⣛
⢦⠀⠀⠀⠀⠀⠀⢀⡜⠀⣿⣿⠸⢸⡈⠟⠀⡇⠀⢸⠇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⢸⣛⠃⡏⡀⠉⣭⡍⢩

⠀⠀⠀⢰⡂⠒⠲⠂⠀⠲⠤⠖⢠⠖⣂⠴⣒⢦⡶⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⡤⣎⣙⣯⣭⣓⣄⠀⠀⡰⠁⣰⠁⠀⠀⠑⣽⡀⡇⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉
⠀⡞⣸⣿⡇⠀⠀⠈⢻⣆⣰⠁⣰⠛⢣⣤⢴⠒⡇⣇⡟⠛⠛⠛⠛⠶⠈⡆
⠀⠀⣿⢿⠧⣲⡀⢠⠭⢿⡇⢀⡇⠀⣛⡘⠀⢸⠀⢸⡇⠀⠀⠀⠀⡇⠀⢱⠀⡐⠂⣀⡀⢀⠔⡀
⠀⢠⡟⡜⠀⠀⢀⡈⡆⢸⡇⢸⡧⠞⡛⠓⠒⠚⣢⣌⡇⠀⠀⠀⢠⡇⠀⠸⡶⠀⠐⢀⡐⠂⠀⣷
⠀⡏⣇⢳⡀⠀⢠⡶⣶⢼⡽⠋⠀⣆⢹⢸⣉⡋⡇⡟⡧⢄⡀⠀⢸⠀⠀⠀⢷⠀⠀⠼⠄⠀⢠⠁
⠀⣠⠇⣠⠙⢆⠀⠷⣣⠞⠀⢀⢤⣜⡶⡿⡏⢹⠀⢳⣧⠤⡿⠒⢺⠶⠶⠖⣾⣶⠤⠤⠤⠤⠷⠦⠤⣤⣴
⠀⠋⠉⠣⡀⢸⣹⠖⠁⠀⢠⣿⣼⠀⢠⠃⡇⠈⡆⠘⡇⠀⡗⠒⣺⡄⣰⠯⢼⡬⡵⡴⠖⢶⠶⠖⣊⣙⣴
⠀⠖⠒⢦⡷⠊⠁⠀⠀⢠⢧⢿⡿⡄⢸⠀⡇⠀⡇⠀⡇⠀⡏⠉⠉⠀⠈⠛⠲⠾⠟⠛⣶⣾⡶⣶⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⢸⡧⢧⡼⢠⠇⠀⡇⠨⡗⣯⠭⠭⠭⠭⠭⠭⠭⣭⣭⣽⣲⣶⣶⣖⣒⡒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠋⠙⠚⠋⡇⠀⢀⡷⣰⠃⠀⡇⠀⢰⡇⠀⣀⡤⢤⡤⣄⢻⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣈⣉⡁⠀⠀⠛⠒⠚⣠⠞⢡⠖⠛⠓⢮⡻⡅⠀⡇⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⡴⣫⣠⣩⠧⠤⢍⡳⡀⠀⠀⣰⠃⢠⣏⡀⠀⠀⠀⢹⢹⠀⣇⣀⣀⣀⣀⣀⡀⠈⣇
⠀⠀⠀⠀⠀⠀⡞⢰⢣⢷⠃⠀⠀⠀⠙⣿⡄⢰⠃⢀⡟⠛⢳⣤⠼⠝⢸⠈⣇⡏⠉⠉⠉⠉⠉⣹⠀⢸⡀
⠀⠀⠀⠀⠀⣸⠁⢸⡼⢸⢤⢤⡄⢀⣰⣚⣿⡏⠀⣼⠀⠀⠏⠸⠀⠀⡇⠀⢻⡇⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⡔⠢⣀⣀⣀⢀⡴⡄
⠀⠀⠀⠀⠀⠇⠀⣾⢇⡇⠐⠛⠁⠈⢧⠁⢹⡇⠀⣧⣀⡼⢿⠷⠤⠴⠧⢤⡈⡇⠀⠀⠀⠀⢰⡇⠀⠀⢷⡼⠀⠰⠆⣀⢠⠉⠀⢧⡄
⠀⠀⠀⠀⠀⠀⣸⢹⢸⠀⠀⠀⠀⢒⣘⡀⢸⢧⣰⠟⣁⠐⣆⢰⠖⠶⠶⠋⡷⣇⡀⠀⠀⠀⢸⠇⠀⠀⠘⣇⠀⠀⣈⣟⡀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⢀⡇⢸⠀⢣⡀⠀⠰⣟⢳⠽⢹⠎⠀⠀⠘⣆⢸⣼⣶⠧⡔⠁⡇⡇⠈⣳⣄⣀⣸⣀⣀⣀⣀⣻⢂⡀⠈⠉⠁⠀⡼
⠀⠀⠀⠀⠀⣊⣴⠋⢀⡄⠉⣆⡀⠺⢯⡴⠋⠀⢀⡶⡶⠼⠞⡿⣻⠀⣇⠀⢹⡗⠋⢹⠉⠀⢸⡁⠀⢀⡴⣻⠿⣛⠛⠛⠛⠻⠿⠿⠶⢶⣶⣶⡂
⠀⠀⠀⠀⠀⠉⠉⠉⠙⢆⠀⢸⣉⠶⠋⠀⠀⢀⣾⡇⡇⠀⢸⠃⣿⠀⢸⡀⢸⡇⠀⢸⣉⣩⣽⠇⢰⣏⡓⠻⢦⣾⣓⠛⠓⣲⠲⠖⢋⣉⣻⣤⠙
⠀⠀⠀⠀⠀⡤⠶⠒⠦⣈⣦⠞⠁⠀⠀⠀⢠⣯⢿⡿⣷⠀⣼⠀⡏⠀⠈⡇⢸⡇⠀⢸⠀⢀⣀⣀⠀⠉⠛⠳⠾⠛⠛⢻⣶⣿⣤⣤⣼⣿⣿⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢠⣧⣾⢸⣿⠸⡄⡿⠀⡇⠀⢰⠇⢸⡷⣚⡭⠭⠭⠤⠤⠭⠭⠭⣭⣭⣙⣒⣒⣶⠤⠤⠤⠤⢤⣤⣄⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣿⣿⢸⣿⡀⣷⡇⢸⡃⠀⢸⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⣿⡛⢻⠟⠫⠿⠿⢶⣶⣶
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⢿⣽⠘⠘⠇⠉⠀⠸⠀⠀⠘⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠓⠃⠘⠐⠀⠐⠷⠇⠰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠛⠛⠉⠀⠀⠀⠀⠂⠀⣀⠁⠀⠀⠀⣀⠐⠐⠠⢀⠀⠀⠀⠈⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠒⠒⠀⠀⠀⠬⢀⡢⢌⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠈⠢⠍⠂⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢀⠀⣠⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⣠⡶⠛⠋⣻⣿⣿⣿⡷⣦⡀⠀⡀⠀⠀⠀⢀⣹⣷⣄
⠀⠀⠀⠀⠀⣼⢋⠔⡂⠀⠀⠈⠀⠉⠉⠙⠛⠛⠻⣿⡿⠂⠀⠀⠘⠿⣶⠾⠛⠉⢩⣍⠉⠙⠋⠁⢀⣡⣤⣤⣤⣤⡀⠉⢝⢷⡄
⠀⠀⠀⠀⠀⣿⠀⠘⠰⠟⠛⠛⣷⣤⣤⠄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠛⠛⠉⣀⣦⠀⠈⢻⡆⠈⠈⢿
⠀⠀⠀⠀⠀⣿⣄⠐⠄⠀⣸⡇⠀⠀⠀⠀⣠⣾⡏⠁⠀⠀⠀⢀⣀⡚⠳⣦⠂⠠⠤⠄⠀⢀⣀⣤⡶⠟⠋⣻⡷⠦⢀⡿⠀⠀⣸
⠀⠀⠀⠀⠀⠘⣧⠁⠂⢰⣿⣿⣤⡀⠊⠁⠉⠙⢷⣄⣠⡄⠈⠉⠉⠋⠰⢟⣀⣤⣤⠶⠾⠛⣿⠃⢀⣠⣴⡿⠀⠀⠘⣁⠜⣰⡟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠇⣿⠛⢿⣶⣦⣤⣤⣬⣭⣤⣴⣶⠶⠞⠛⠛⣿⠁⠀⣀⣠⣴⣿⡿⠛⣽⠟⠀⠀⠀⠀⣰⡾⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣤⣼⣇⣀⣀⣸⣏⣀⣀⣸⣇⣀⣀⣤⣤⣿⣿⡿⠿⠛⠉⢿⣠⡾⠋⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠙⣧⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣾⡇⠹⣏⠙⣿⠉⠉⣿⠁⠀⠀⢸⡇⠀⠀⠀⢀⣹⣧⡶⠟⠁⠀⠀⠀⡀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠛⠻⠶⠿⠷⠦⠾⠷⠤⠴⠾⠷⠶⠞⠛⠋⠉⡁⠠⠐⡈⠄⢂⣡⡴⠟⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠈⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠅⠀⢀⣡⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠲⠖⠒⠒⠚⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠛⠛⠛⠛⠛⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡄⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠹⡄⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠏⠀⠁⡠⠂⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠐⢦⡀⠀⠱⣤⠎⠀⠀⢀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠌⠂⠀⣻⠛⠐⠉⠢⣴⠖⠋⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠬⠥⠔⢃⠠⠛⠠⠀⠀⠀⠇⢐⢡⣤⣍⠂⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡈⠉⢉⣀⠄⠀⠀⠀⠀⠀⠰⡈⠠⠟⠣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢠⠤⡀⠀⠀⠀⠣⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣤⣀⠀⠀⠀⠠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⢳⣄⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⠟⠁⠘⠫⢟⣟⣀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢁⠤⡉⠀⠕⣢⢹⠏⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⢿⡿⠶⠧⣤⡎⠞⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂⠭⠆⠿⠸⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⠚⠛⠓⠲⠤⠤⠤⢲⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠶⣄⠀⠀⠉⠛⠲⠦⣤⣀⣠⠔⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠶⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⢲⡶⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣦⡀⢀⡄⣤⠀⡀⠀⠀⠀⠀⣻⠶⣾⡷
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⣰⣏⣀⣀⣨⡿⢦⣷⠼⣧⣿⡄⢀⣠⠞⠋
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⢛⡿⠋⠉⠉⠉⠀⠀⠀⠙⠳⣬⡭⠖⠋⠁
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠿⠶⠶⠦⠤⠤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⡩⠭⢹⡆
⠀⠀⠀⠀⠀⠈⠿⠀⢀⣀⠀⢠⢀⡞⢱⣶⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠋⠈⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⠀⠀⠁⠈⠙⣛⣭⣍⣉⠉⠉⠀⠀⠀⠀⠀⠀⠿⢿⠏⠀⠀⠸⠃⠀⢰⡌
⠀⠀⠀⠀⠀⠰⣿⠟⠉⣉⠉⢲⣆⠀⠀⠀⢉⡀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡾⢃
⠀⠀⠀⠀⠀⠀⠹⣤⣞⠁⣾⣿⡿⠀⠀⠀⠀⠉⠡⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⢹⠏⠉⣠⢋⠇⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠁⡾⠀⠀⢀⣀⣀⡨⠃⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠲⠂⠀⠋⠀⠀⠀⣀⣀⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⠀⢀⣤⣴⣚⣭⣽⣿⣉⣩⣭⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⣘⣿⣿⢟⡫⠭⠟⠛⠛⠹⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⢻⠛⠁⠀⠀⠉⠀⠀⠀⠈⠉⠡⠄⠘⠀⠀⠀⠀⠀⠀⠀⡰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⠤⣤⠴⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⢆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠟⢛⣻⠛⠛⠛⠛⣿⠛⡟⡟⡛⡟⣿⠻⣿⠛⠛⠛⡟⢻⣟⡿⡟⢛⢟⡿⡿⢻⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢻
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡔⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠭⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⢛⡛⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠚⠉⠉⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⠁⠀⣸⠋⠉⠳⣒⡿⠛⢶⠦⠀⢹⡄⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢀⠁⠀⠀⠀⠀⢠⡇⠀⠀⢷⡀⠀⣠⠿⣄⣃⣸⠂⠀⠘⡇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⣠⢚⠂⠀⠀⣠⠟⠋⠉⠀⠉⠙⢷⣄⠀⠀⠓⢄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢸⠀⠀⠀⠀⠻⣭⠄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠠⣬⠞⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⠀⠀⠀⢀⣀⣴⡿⠁⠀⣿⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⠀⠀⣀⣈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢹
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠐⠛⠛⠷⠒⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠞⠀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁⠀⠀⢸
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⢦⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁⣠⠴⠋⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠉⠓⠲⠤⠤⣤⣤⠤⠤⠶⠚⠋⢹⣧⠀⠀⠀⠀⠛⠻⠥⠴⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⠀⠀⠀⠀⣸⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⠀⠀⠀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠻⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠚⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠶⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢰⠀⠀⣦⢤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡰⠒⠢⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⣘⠀⣸⠁⢠⠟⠁⣹⠀⢠⣧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡄⠑⠀⠙⠤⠤⣤⠀⠀⠀⠀⠈⠉⠛⠛⠁⠋⠀⠃⠀⠾⠀⢠⠇⣰⠋⠀⣸⠁⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠊⠣⡀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠙⠦⠞⢁⠔⠁⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣞⠁⠘⠢⠋
⠀⠀⠀⠀⠀⣐⠦⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠉⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⠀⢀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣀⣀⣀⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡃⠉⢀⠈⠚⠠⠋
⠀⠀⠀⠀⠂⢰⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⡝⡾⢦⣴⣶⢧⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠈⠫⠀⠀⠁⠀⡀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⣋⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠢⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢠⣄⡠⢻⣦⡀⠀⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⠀⠀⠠⢹⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣾⣯⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⠿⠟⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠿⠻⠻⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠿⠛⠙⣋⡛⡛⠛⠛⣟⣛⣻⣟⣻⣿⡟⣿⢟⠛⠛⡟⣿⣻⣿⣛⣛⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙
⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠒⠀⠀⠐⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⡆⠀⠀⠀⠀⠀⠀⡸⠁⠀⢀⠀⠠⠄⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠁⠐⠠⢀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠧⡆⡖⢁⠀⡠⠀⠐⠃⣼⠆⠫⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢑⡇⢠⠔⠠⣄⠀⡀⢠⣀⠂⠅⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠇⠀⠀⠀⠀⠀⠸⡁⢀⡁⠸⣜⣋⠼⡶⢀⢼⣈⣀⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢈⠀⠀⠀⠀⠀⢠⠝⠉⠀⢰⡋⠀⠀⠉⠉⢳⡤⣄⡽⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢻⡁⠀⠈⠙⠒⠒⠚⠩⣄⡘⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠘⢆⠈⡟⠦⣄⣀⣀⣀⡠⡶⠁⠁⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢧⢳⣦⣀⣇⣀⣬⡴⠁⢀⡜⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣿⣿⣿⣿⠃⣠⠎⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠧⣩⡩⠟⢰⠁⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⠒⠂⢠⠇⠀⠀⠀⠀⠙⠤⢐⣂⣈⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠙
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⡆
⠀⠀⠀⡇⠀⠀⠀⢀⣀⡤⠴⠖⢹⢀⠶⣸⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⢀⡖⠉⠀⠀⢠⠃⠈⠉⠆⢹⠀⠃⠀⠈⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠓⠀⠸⠇⠤⠤⠤⠔⠂⠐⠒⠒⠚⠒⠚⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠒⠒⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣁⠀⠀⠀⠀⠐⠦⣄⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠧⠴⠧⣤⣤⣤⣀⠀⠀⠈⠙⢄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⢶⣶⣶⣤⣤⣤⣉⡙⠓⠦⣶⣄⠀⠈⢦⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡙⠳⡄⠈⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣷⣀⢸⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣸⠉⠀⠀⠀⠉⠙⠛⠿⢿⠟⣛⠉⣴⣿⣿⠸⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣿⠒⠋⢉⡛⠒⠦⠀⠀⢸⣿⡟⢰⣿⣿⣟⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠸⣶⢚⣉⣉⡉⠐⠀⠀⢸⣿⠁⢟⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠹⣏⡡⠤⠄⠀⠀⠀⣀⠇⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⠀⠀⠀⠘⠳⠶⣶⣶⣿⣿⡏⢸⣿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⢶⣶⣶⣀⣉⣉⣉⣭⣴⣿⣿⡟⠁⣠⠟⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢻⠇⢸⣿⣿⣿⣿⣿⡿⠟⠁⣠⡾⠃⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⡏⠀⠸⣿⠿⠟⢛⡽⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⠀⠀⠀⣼⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣴⣿⡀⠀⠀⣰⠏⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣤⣴⡏⠀⠀⠀⣠⠞⠁⠀⠀⢀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠿⠷⠶⠶⠛⠛⠋⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⢛⣙⠛⠛⠛⢻⡟⣻⢻⣛⣛⣿⠛⣿⠟⠛⠛⠟⣿⣻⢻⣟⣻⣻⢻⢛⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠒⠒⠒⠂⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⣠⠞⠉⢀⣠⠤⠖⠒⠈⠉⠫⠩⢉⠙⠒⠤⣍⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠂
⠀⠀⠀⣠⠞⠀⣠⠶⠯⣄⡀⠀⠀⠈⡆⠀⠀⠀⠀⠢⡀⠀⠙⠢⡉⠢⡀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⡰⠁⢀⡞⠁⢀⠞⠁⠉⠑⢦⡀⠀⢠⠤⠄⠀⠚⠀⠑⢄⠀⠘⢦⠙⣄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⢰⠁⢀⠎⢙⠆⠈⠀⠀⠐⠀⠀⢳⠀⠀⠂⠀⠀⢢⠀⠀⠈⡆⠀⠈⢧⠘⡆⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠀⠸⠉⠀⠲⣇⠀⠀⢸⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣧⠀⡇⠀⣀⡀⠀⠀⠀⠐⠀⠀⠀⣆⠀⠀⢀⣇⣀⠀⠀⠀⢸⠀⣠⠏⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢸⡀⢹⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡟⠀⠀⠈⠀⠀⠁⢀⣤⡿⠚⠁⠀⠀⡼⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⢣⠀⠑⠦⣄⣀⡈⠀⠀⠀⠀⣀⣇⣀⣀⣤⡤⠴⠚⠉⠚⠢⠀⠀⠀⣰⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠳⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⠀⠐⠘⠀⠀⠐⠀⠀⣀⡀⠀⢠⣧⣤⡀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⣠⠖⠚⠀⠀⠤⠤⠴⢖⣒⡲⠻⠉⠀⠀⠀⠲⣐⡚⠿⢹⡴⠁⠀⠘⠀⠀⠘⡆⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⠤⠚⠁
⠀⠀⡇⠀⠀⠀⠀⠐⠂⠽⣌⣥⠥⢃⠂⠀⠈⢢⡀⠀⠈⠉⠁⠀⠀⠀⠀⣄⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠈⡙⢀⡜⠉⠉⠁
⠀⠀⠙⠶⠒⢺⠀⠀⠀⢀⡀⠀⠀⢈⠀⠀⠀⠀⡳⠀⠀⠀⣦⠀⠀⠀⢀⠏⠉⠁⠀⠀⠀⠀⠀⢀⣀⢀⡊⠔⠋
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠚⠀⣀⠀⠈⠂⠤⠄⠚⠁⡀⠔⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⠉⠈⠉⠅⠒⠊⠁⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠒⠒⠢⠒⠒⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠦⠖⠒⠚⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠊⣉⣉⣙⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣉⡙⠲⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⠁⠀⠀⠀⠰⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣙⡦⠀⠀⠀⠈⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖
⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⢀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡴⠟⠁⠀⣀⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⢦⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡇
⢠⡞⠁⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠙⢆⠀⠀⠀⠀⢸⡇
⡘⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠉⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢸⡇⠀⠀⠀⢸⡇
⣻⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⡀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⡋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⣇⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⠀⡿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠘⠷⠶⠶⠶⠶⠤⡆⠀⠀⠀⠀⡶⠴⠶⠶⠶⠤⠟⠀⠀⠀⡇⠀⠀⣧⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⠇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⠁
⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡀
⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠦⠤⠤⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⢸⡇
⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⡇
⢧⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡼⠀⠀⠀⠀⢸⡇
⠘⣧⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣴⠃⠀⠀⠀⠀⢸⡇
⠀⠈⠳⣄⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠳⢦⣤⡀⠀⠈⠙⠳⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠉⠉⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⣇⠀⠀⡶⠉⠉⠉⠲⣄⠀⢠⠶⠋⠉⠉⠳⡄⠀⢰⡏⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⣀⣼⣀⣀⣇⣀⠀⠀⠀⣿⠀⢸⠂⠀⠀⣀⣠⣇⣀⣸⣀⡀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢼⡧⠿⠥⠤⠿⢽⡦⠤⠴⣿⠤⢾⡦⠤⠤⣿⠤⠿⠤⠿⠯⣷⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⢿⠶⠾⠃⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠤⠤⠤⠤⠾⠀⠀⠀⠀⢷⡈⢷⣄⠀⠿⠤⠤⠤⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠓⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠛⣁⡴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣴⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣛⣉⣀⣀
⣿⣿⣿⡿⠛⠿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⣄⡄⠀⠀⣤⢠⣤⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠎⡛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠘⠀⠃⠇⠘⠂⠉⠈⠀⠀⠀⠀⠀⠁⠈⠁⠀⢀⡀⢸⣳⡠⠔⠁⠀⠀⢀⡜⠓⢤⡀⢰⠋⠀⠀⠠⠀⠠⠀⡇⠀⣰⣦⡁
⠀⠀⠸⢇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣼⣠⠏⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠸⡆⢄⠀⢅⠀⣐⠼⠁⠀⡇⡜⠃⠀⠀⠀⣀
⠀⠀⠀⠘⡆⡜⠀⠀⠀⠀⣤⠀⡰⠂⠀⠀⠼⢾⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠒⠟⣶⠛⠛⠉⠁⠀⠀⠘⡇⣇⠀⢀⡰⢶⣝
⠀⠀⠛⢄⢻⡇⠀⠀⣠⡞⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⢉⠦⠤⠤⠴⢠⡤⣧⡄⢼⠆⠀⠀⢰⠉⠂⠌⣐⠀⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⣈⠉⢉⣀⠜⠋
⠀⠀⠀⠈⢢⡇⠀⠀⢈⣧⡀⠀⣸⡄⠀⠀⡠⡄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠘⣆⠌⠐⠀⢁⠂⠈⠂⡼⠀⣠⣤⣄⠀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⠛⠙⡍⠀⠀⠀⠉⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⡽⠀⣀⡠⢤⠤⡬⠷⣤⠤⠤⠤⠖⠋⢀⢮⠞⠁⠀⡴⢹⢀⣤
⠀⠀⠀⠀⠀⢹⢠⠶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡿⠋⠀⢸⠁⠠⠀⠀⠀⠄⠈⢦⠀⠀⠀⠀⢸⠘⠒⣦⡸⠁⠓⠊⡼⠀⣾⣿⡆
⠀⠀⠀⠰⢆⢸⡏⠀⠀⡠⠤⠤⣀⣀⠴⠊⠳⡀⠀⠀⠀⠀⣀⡠⣤⠄⣀⣀⣀⠘⣦⠈⡀⠀⠀⠄⠀⣘⠇⠀⠀⠀⠈⠓⠊⠡⡷⠒⡆⣸⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠈⢾⡇⠀⠘⣅⠀⠀⡼⠉⠓⢦⣸⠁⠰⠀⠖⠉⠃⠀⠀⢀⠠⠐⠉⠉⠉⢷⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⠖⢲
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⡞⠁⠺⠇⢠⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣤⣤⠀⢠⣤⡄⠀⣠⣤⡀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠠⠂⢼⠙⠲⢄⣠⠋⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣠⡇⠀⢸⢹⠀⠀⠀⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⡴⠞⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣾⠀⢸⣿⡇⠀⢸⢸⠀⠀⠀⣙⠇⢸
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠠⠍⡇⠀⠀⢀⢏⣌⢧⠀⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⣧⠄⢾
⠀⠀⠀⠀⠠⠀⡷⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠀⡇⠀⠀⢸⢸⣸⢸⠀⠀⠘⠋⠀⠈⠛⠁⠀⠘⠛⠀⠀⠀⠿⠤⠼⠰⠆
⠀⠀⠀⠀⠀⠀⡧⡇⠀⠁⠀⠀⠀⠀⠀⠀⠐⡿⠷⢶⠂⠀⠀⢸⢰⡏⠙⢆⡇⠀⡆⠘⣆⣡⠞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠇⠂⠘⡆⠀⠀⠀⠶⠁⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⢠⣾⡁⢀⣀⣠⠔⠛⠓⢤⣠⠎⠀⠈⠲⣤⡀
⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⢹⡀⠀⠀⠀⢀⠀⢀⠀⠀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠈⠋⠀⠤⠆⠀⠈⠁
⠀⠀⠀⠀⢀⡞⠤⣈⣆⠀⠀⠀⠀⠀⠀⣸⠃⠠⣕⠀⠀⢧⠀⠀⠀⠉⠀⣿⠀⠀⠀⢰⡆⠀⢇⣤⣤⣀⣀⣀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡞⠈⠘⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⣤⡄⠀⢶⠀⠀⠀⠣⠤⠄⣀⣀⣀⣀⣤⠀⠀⢠⣤
⠀⠀⠀⠀⢣⣀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠐⣿⠀⠀⠀⢸⢿⠀⣿⡇⠀⣿⠀⠀⡤⡄⠀⠀⠀⣶⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡀⠙⠿⢿⡿⢿⡿⠿⠿⠿⠿⠛⠀⠀⠀⢿⠀⠀⠀⢸⢸⠀⡇⡇⠀⣿⠀⠀⡇⡇⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢖⣢⣀⣀⣹⣷⣤⡤⠼⢷⣦⠤⠤⠄⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⢸⢸⠀⡇⡇⠀⡿⡆⠀⡇⠇⠀⠀⢸⢸⠀⠀⣷⡇⠀⠐⢶
⠀⠀⠀⢀⣤⣤⠔⠊⠉⡿⠃⠀⠐⠖⠁⠀⠺⠊⠀⠀⠀⠀⠀⢤⡄⠤⠤⢾⠤⠶⠶⠾⠾⠶⠷⠷⠶⠻⠗⠦⠗⡖⠒⠒⣼⠛⠒⠲⠟⠓⠿⠆⠙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠘⠈⠀⠈⠉⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⠛⠛⠛⠛⠛⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠤⠤⠤⠤⠤⠤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⢻⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠋⠉⠉⣙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠖⠚⠃⠘⠒⢲⡆⠀⢸⡇⢀⡴⠋⠀⠀⠀⠀⢸⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⡇⢸⠋⠉⠁⠀⢸⡷⠋⠙⢦⡀⠀⠀⠐⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠓⠚⠀⠀⠀⣰⠋⠀⠀⠀⠀⠙⢦⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠉⠉⠉⠉⠉⢉⡽⠋⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⢼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⣀⣀⣀⣸⣀⣀⣀⣰⣖⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⣀⢀⠀⠀⣀⢀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠁⠸⠄⠣⠜⠀⠘⠤⠘⠸⠑⠇⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠂⠉⠉⠁⠉⠉⠉⠉⠉⠑⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⣤⣀⠀⠀⠀⠀⡴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠸⣧⣄⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠻⣿⡇⠀⢠⠀⣶⣴⠆⠀⠰⣾⣿⣿⣿⣿⡿⠟⠛⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡆⠀⢿⣷⣄⣀⣴⣿⠋⠀⠀⢸⣿⣿⣿⣿⠋⠀⠠⢔⠀⢈⠀⢀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠈⠙⠿⠿⣿⣿⡀⠀⠀⠛⢛⡛⠻⢷⣄⠀⠀⠀⠀⣀⣴⠟⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⣿⣿⠃⠀⠀⢠⡉⢻⣿⣶⣭⡛⠲⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣤⣾⢏⣙⣧⠀⢀⣿⠤⠟⠓⠒⢤⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⢻⠀⢷⣤⡟⠀⠀⠐⣦⠀⠀⢻⠀⢳⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡈⢇⠀⠈⢿⠀⠀⠀⠘⡇⠀⠈⡆⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡈⠣⡀⠸⣇⠀⠀⠀⢻⡄⠀⠙⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀⠁⢀⣿⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣾⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢄⣀⣀⣀⣀⣀⣀⣀⡠⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⠒⠂⠀⠀⠀⠒⠒⠒⠂⠠⠤⠬⠭⠭⠭⠭⠙⠻⠿⠿⠿⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⢀⣠⠴⠚⢉⣠⠤⠖⠒⠒⠂⠀⠉⠉⠑⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠒⠦⠈⠙⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⡠⠔⠉⣠⠔⢋⡡⠴⠒⠒⠉⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠐⠒⠤⣄⡀⠀⠀⠀⠀⠙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠈⠀⡴⠋⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⣶⣶⣶⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⣠⣾⣿⣧⣄⡀⠀⠀⠀⠀⢀⣤⠀⢠⣾⣿⣻⣿⣿⣿⣿⣿⣇⣀⡈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⡆⢀⣀⣀⣀⣀⡀⠙⢿⣶⣄
⠀⣠⣾⢟⠟⠉⠁⣠⣤⣤⣤⣤⣤⣀⠀⠒⠀⠙⠛⠋⠉⠉⣩⡍⠉⠙⠛⠿⣷⣶⣿⠟⠀⠀⠀⠀⠸⢿⣿⣿⡿⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣈⠓⢤⡙⢿
⣼⡿⠁⡏⠀⢠⣾⠟⠉⠉⢁⡉⠙⠻⠿⣶⣶⣤⣤⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⣀⠀⠀⣀⣴⣶⣶⣶⣶⣌⠹⡄⠹⣸
⣿⠁⠀⠀⢀⣿⠏⠀⠀⢀⣾⣿⣦⣀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠻⠿⠿⠿⠟⢀⣄⠀⠈⠉⠀⡇⠀⣿
⣿⡄⠀⡆⠸⣿⡀⠶⢾⣿⣿⡉⠙⠻⢿⣶⣦⣄⡀⠀⠀⠀⠤⠤⠤⠖⠚⢰⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⡀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⡴⠃⣸⣿
⢻⣷⡀⢧⠀⠻⣧⠀⠀⠀⣿⣷⣄⠀⠀⠈⠙⣿⡿⢿⣶⣦⣤⣀⡀⠀⠀⠸⣷⡄⠺⠿⠟⠟⠓⠀⠀⠀⠀⣠⣾⡿⠛⠋⠉⠒⠦⠀⠀⣠⣿⣿⣿⠀⠠⠴⠚⣹⣿
⠀⠻⣷⣄⡙⠲⠄⠀⠀⠀⠈⢿⣿⣿⣶⣤⣀⣿⣧⡀⠀⠉⠙⠛⠻⢿⣷⣶⣬⣤⣀⣀⡀⠀⠀⠀⠘⠿⠿⠟⠋⠀⠀⠀⠀⣀⣠⣴⣾⣿⢿⣿⣿⡆⠀⠀⢰⣿⠃
⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠻⣷⡌⠙⠻⣿⣿⣷⣦⣤⣄⡀⠀⢠⣿⠋⠉⠉⠛⠛⠿⣿⣿⡿⢶⣶⣶⣶⣶⣶⡾⠿⢿⣿⡟⠉⢹⣿⠈⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⣿⡏⠙⠻⠿⣿⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣇⠀⠀⠀⣀⣿⣇⣀⣼⣿⣾⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡁⠀⠀⠀⠀⠉⢹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⣼⡿⠀⠀⠀⠈⠉⠛⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣾⣿⡁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⣿⠉⠉⢉⣿⡏⠀⣼⡿⠁⢿⣷⣿⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡙⠲⢤⣈⠑⠢⢄⣀⠈⠉⠛⠿⠿⣶⣶⣤⣤⣤⣿⣧⣀⣀⣀⣀⣿⣇⣀⣠⣾⣿⣤⣼⣿⣷⣾⠿⠛⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⣈⠙⠲⠤⣈⠙⠲⠤⣀⡀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⡉⠑⠂⠤⢍⣙⡒⠦⠤⢄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⢀⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣄⡀⠀⠈⠉⠙⠒⠒⠢⠤⠤⢄⣈⣉⣉⣉⣉⣉⠉⠉⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀
⢠⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣦⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣿⣿⣿⡿⠛⢉⣉⠙⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⣤⣀⣀⣀
⣿⣿⣿⣿⣿⡏⢀⣀⣸⣿⣀⡀⠸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⡇⠘⠛⢻⣿⠛⠛⢀⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣦⡀⠘⠛⢀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣴⡤⢤⣤⣀⠀⢰⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣤⣴⣦⣄⡀⠀⣠⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢁⣰⣆⡈⢿⠀⢸⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⡁⢈⣹⣿⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠙⢻⡟⠃⣼⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠛⠚⠛⠿⣿⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣾⣿⠀⢸⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠹⣿⣷⣿⢽⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⢻⢛⣟⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠸⢜⣛⣀⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⣤⣾⣿⣿⠿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣀⢀⣠⣤⣴⣶⣶⣦⡀
⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⡗⠀⢠⣤⢀⣀⠀⣀⢀⡀⢀⣀⢀⡀⢀⡀⣠
⠀⢀⣿⣿⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⣿⣿⡆⠀⠀⠀⠈⠛⠿⢿⣿⣿⠃⠀⢸⣿⣿⠿⠿⠛⠁⠀⢸⣿⠉⢉⣉⠋⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⣶⣶⠀⠀⣀⡀⠀⢻
⠀⠀⣿⣿⣷⣶⣶⡖⠀⠀⢰⣶⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢘⣿⠀⠀⢛⡿⠀⠀⢿⡧⠀⢺
⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢕⣂⠀⠀⠀⠀⠀⠀⠀⢸⣿⠲⠞⠛⠶⠶⠛⠛⠖⠶⠛⠳⠒⢿
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠻⠛⠚⠐
⣶⣶⠶⠶⠶⢶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠋⠁⠉⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠛⠉⠉⠛⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⣁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣷⠈⠸⡇⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠰⠉⣵⠨⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣿⣿⣿⣿⣿⡿⠀⠑⠊⠀⠘⡀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⡿⠈⠲⠋⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⣿⣿⣿⣿⡿⠀⣀⣀⢀⣀⢻⠟⠀⠀⠀⠀⠀⠻⣧⣼⣿⣿⣿⣿⡟⠀⣀⣀⠀⠐⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣄⠉⠅⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⠙⠛⠛⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠉⠉⠉⠛⠛⠛⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⡈⠀⠀⠁⠀⣲⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠉⢀⠁⠀⠐⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠉⠀⠙⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠻⠟⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⢀⡀⠀⠀⢠⠤⢄⠹⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⣴⡍⢢⠀⣸⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⢀⣀⣿⣿⣇⠐⠡⣶⣇⢠⢤⣸⡛⢠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠀⠙⠀⠁⣼⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⢠⣿⡟⢿⣿⣿⣷⡀⠊⠀⣈⣛⣁⡈⠈⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢤⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣰⣿⠏⠀⠀⠘⢿⣧⣸⣿⣿⣿⠁⣴⣿⣿⣿⣿⣿⡆⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡀⠉⠙⠓⠀⢸⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡄⠉⠭⠭⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⣀⣀⣤⣾⣿⣿⡿⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣀⣀⣠⠴⠛⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠛⠛⠋⢉⡁⠤⡔⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠉⠉⣉⢁⠀⠀⠐⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠀⠀⠀⠘⠁⠄⠄⠄⠀⠇⠸⠈⠣⠀⠰⠀⠐⠀⠀⠀⠍⠸⠇⠃⠀⠀⠀⠀⠀⠀⠘⠿⠼⠋

⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⠂⠐⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⠀⠀⡥⠀⠀⠀⠀⠤⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢠⡎⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠊
⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⠂⠄
⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⡃⠀⠀⠀⡤⣖⡧⠀⣂⣀⠔⢒⠄⢀⣠⠀⠀⠀⢠⠀⢀⢢⣄⣐⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⡀⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⢰⡌⢇⠀⢀⣼⠀⢠⠔⠀⢠⡜⢸⢀⠇⢀⡠⠮⠂⠀⠀⡇⠀⠀⠙⠦⠀⠙⠁
⠀⠀⠃⠃⠉⠁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠋⠁⠚⠁⠐⠚⠀⠙⠀⠋⠀⠀⠊⠁⠛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠆⠀⠀⠁⠶⠦⠠⠶⠦⠼⠿⠧⠷⠄⠴⠶⠴⠄⠠⠶⠶⠦⠿⠇⠀⠘⠀⠀⣖⠀⠤⠀⢐⡀⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠈⢠⡄⠀⠀⠈
⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠉⢀⣀⣀⡀⠊⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠢

⠀⠀⠀⠀⠀⠀⢠⠖⢉⠙⠆
⠀⠀⠀⠀⢀⡤⣿⡠⣏⢀⢧
⠀⠀⠀⡴⠁⣤⠀⡇⠈⠳⠔⠁⠀⠀⠀⣀⣠⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠤⣄
⢀⡴⠒⠻⡞⢣⡜⢳⡄⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠶⠛⠀⣸⣏⣉⡉⠲⣄⡤⢤⣀⡀
⣏⣠⡟⢠⡇⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣓⡞⠋⠁⣜⠉⣁⡴⠻⣤⠶⠀⢱
⠈⠁⠑⢎⡼⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⢦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠧⡽⠁⠀⣼⠇⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡟⣻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣭⣿⡍⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣍⣡⣿⣿⣿⣿⣿⣿⣿⠿⠟⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⣀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠼⢦⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠺⣉⡶⢤⣠⣼⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠶⠄⢳⡀
⠀⠀⠀⠀⠀⢀⣠⠊⡤⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠻⡤⠗⠦⠤⣞⠓⢦
⠀⠀⢀⣀⠊⣤⠈⠏⠱⣚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠛⠳
⠀⠊⣡⠈⡋⢱⣜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⠛⠲⠖
⠀⠉⢱⣘⡄⠀⠉
⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣿⠛⠛⢿⣼⠛⠛⢻⣴⠟⠛⢛⠛⠛⢻⠀⢸⡟⠛⢻⡇⢠⡟⠛⠛⢻⣿⠛⠋⠉⠉⠉⠛⠙⣿⣶⠟⠋⠉⠉⠛⠻⣦
⠀⠀⠀⠀⠀⢹⡆⠀⠘⡟⠀⠀⠸⡟⠀⠀⣾⠀⠀⠸⠷⠾⠇⠀⢸⣧⡾⠁⠀⠀⠀⢻⡟⢻⡆⠀⠀⡿⠓⠻⠷⢤⣴⠿⠟⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠁⠀⡀⠀⠀⠀⣼⣿⠀⠀⢠⣤⣤⡄⠀⢸⣿⠁⠀⠸⠇⠀⠀⢿⣸⡇⠀⠀⡇⠀⠀⠀⢸⣇⣀⣠⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣰⣧⣀⣀⣰⡏⣼⣀⣀⣸⡇⢸⣇⣀⣘⣃⣀⣠⡶⢶⣄⣀⣈⣿⣇⣀⣀⣷⠀⠀⠀⣸⣉⣉⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠓⣤⠤⠤⠤⠤⠶⢍⡀⠀⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠓⢄⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⡤⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢚⠦⣀⢀⠓⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠁⠀⢱⠀⠑⠂⠔⠂⠤⠤⠤⠴⢂⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣂⣀⡀⢀⡤⠐⠒⢷⡦
⠀⠀⠀⠀⠀⠀⠘⠴⡀⢠⢧⡄⢆⠰⠤⣀⠀⡷⠶⡏⠁⢠⠀⣹⠹⣄⠀⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⡳⠈⠉⠀⠀⠘⠦⠤⠔⠣⢀⠌⠁⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠽⣝⠉⣝⢉⡎⡃⠀⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠛⢆⠈⣷⡱⣤⠜⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⠀⠀⠀⠀⠉⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⡦⠤⣀⠀⠀⣀⣰⠖⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡑
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠜⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠄⠃⠀⠰⡤⠤⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⡩⢷⠈⠉⠉⣹⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⢀⠔⠊⢆⡀⠑⠒⢶⡁⠉⣉⠽⣄⠀⠀⠀⢀⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢋⠉⠉⣷⠀⠙⠤⠤⠋⠳⡀⠐⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠑⠊⠁⢇⠀⠀⠀⠀⡰⠁⠃⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠊⠀⠑⢄⡀⠀⠀⠀⡠⠊⠒⠒⠒⠉⠀⠀⠈⠢⠄⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⣭⠙⠒⠒⠒⠒⢉⠙⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠉⠉⠙⢢⣄⣀⣤⠬⣁⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢃⡼⠁⡏⠀⠀⡀⠈⢻⢶⣧⠀⠀⢀⣠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠋⠩⡀⠀⣸⣤⣀⣉⡰⠃⠸⣄⡤⠖⣉⡽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠑⠦⣝⡋⠀⠀⠀⠀⠀⠀⢀⣀⣤⢚⡡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣞⠣⣄⠀⠀⠀⠀⢀⡎⠉⣿⣒⢒⣺⠋⡹⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠗⠀⠏⠑⠠⡔⠉⡇⢀⠂⠀⢀⠃⣞⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠳⠞⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⡘⢠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠒⠤⢀⡀⢴⢰⠃⠀⠀⠀⡇⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡠⠴⠋⠀⠀⠀⠀⡆⡃⠀⠀⠀⠀⢠⠔⠋⠂⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⠀⠀⠀⣀⠴⠥⡀⠀⠀⠀⡠⠃⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡶⢄⣈⡷⠀⠀⠈⣢⠤⠒⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⠈⢳⠧⠶⢊⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⠃⠀⠀⠀⣴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡟⠀⢦⣀⣀⠀⠀⠀⣀⣀⠠⠜⢄⠀⠐⡠⠀⠀⠀⢢⠉⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢧⣀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠈⠉⠒⠒⢲⠁⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⠀⢸⠀⠈⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡞⠒⠦⢄⣀⠀⠀⠀⠀⠀⢱⠀⡠⠊⠀⠀⠑⢄⠀⠀⠌⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢀⠂⠀⠐⠒⠩⡉⠉⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠙⣳⠃⠰⡀⠀⠀⠀⠀⠀⡆⢠⠂⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠈⢆⠀⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⢨⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣤⡄⠀⠀⠀⠀⠀⠀⣠⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣾⠿⠿⠿⠆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⣿⣦⣀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠙⠻⣿⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⣤⣤⣤⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⢹⠏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⣸⢫⣶⣶⡝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣶⣶⣾⣿⠿⠃⠀⠀⠀⠀⠀⠹⣎⡻⢟⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣠⣤⡴⠞⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⡶⠿⠿⡷⠀⢠⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠄⠤⣀⡤⠔⠢⡀⠀⠀⠘⡷⠤⠒⠉⠀⡀
⠀⠀⠀⠈⠁⡀⠀⡿⠀⠀⡇⢀⡀⠀⠀⠀⢀⡎⠉⠑⡍⠀⠀⠀⢀⣧⢠⡼⠵⢤⣀⣱⠀⠄⠊⠀⠀⢘⠉⢵⠈
⠀⠀⠀⠀⠀⠁⡰⠥⠀⠀⢣⠀⠁⡠⢤⣴⠟⠻⠀⢀⣼⠀⠀⠐⣅⠈⢲⡀⠀⣤⠑⣾⠉⠛⢆⠀⢠⢬⠉⢁⣤⡀
⠀⠀⠀⠀⠀⢠⠃⣠⣀⣠⣌⣆⠀⠣⡴⡅⠀⠀⠙⡿⠿⠀⠀⠀⢈⡉⢶⠬⠦⣄⣠⡏⣦⠤⠚⠀⡈⢊⡴⣋⠜⠁
⠀⠀⠀⠘⢁⣿⣿⣿⣿⣿⣿⣿⣆⠀⣷⠹⡄⠀⣐⣒⣒⡄⠀⠀⢀⣸⠈⢆⣀⡤⠛⠒⠊⠀⠀⠀⡤⣋⠜⢁⣀⡀
⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⡿⢈⠀⢸⠖⠚⠚⠒⠒⠒⠚⣆⠀⠀⠙⠀⠀⠀⠀⣠⣴⠶⢒⡚⠿⣿⠁⠀⠀⢸⣏
⠀⠀⠀⠀⣈⠑⠒⠂⡒⠒⠒⠈⠁⠉⠘⠒⠦⠤⠤⠦⠆⠒⠃⠀⠀⣤⡆⠀⠀⡾⢋⠖⡒⠒⡌⢢⠙⡄⠀⠀⢸⣍⠁
⠀⠀⠀⠈⠚⠁⠀⠀⠻⠯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠒⠄⠴⠀⠀⠈⠁⠀⠀⡇⠸⣀⡛⠘⡜⡸⠀⡇⠀⡆⢸⠮
⠀⠀⠀⠀⢴⢀⡶⠚⢲⡀⠀⠓⠺⠰⠀⠀⠀⠀⠀⠊⠒⠤⠴⠂⠀⢠⣤⠀⣄⠹⣤⠈⢉⠉⠐⣡⠞⠀⠀⠧⠿⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠀⠀⢠⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⣠⠞⠛⠳⡄⠀⢰⡆⠉⠂⣴⠶⠶⠄⠈⢀⡀⠀⢀⡄⠀⣠⠤⢤⡒⠀⢸⣂⣀⣀
⠀⠀⠀⠀⠐⣆⠀⠀⢀⡇⢰⡇⠀⠀⠀⠉⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⢧⠀⢸⡇⢰⡇⠀⠈⠁⠀⢸⠉
⠀⠀⠀⠀⠀⡌⠛⠒⠋⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟⠛⠛⠂⠀⡟⠈⣇⢹⠃⢺⢁⠀⠀⢀⡀⠸⠶⠖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢧⣀⣀⣠⠄⠀⣸⡇⠈⠁⣿⣤⣤⡄⠸⠃⠀⠘⠟⠀⠈⠦⠤⠖⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⢒⣤⣤⡄⢀⡴⣊⠥⢄⠉⢆⠲
⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠠⡆⠀⠀⠘⠀⠈⢫⡂⢠⠛⠒⠠⢼⡀⠛⠑⠙⠀⠀⣀⠁⡀⡄⢠⣾⡔⠁⠀⢀⠃⣼⢠⣤
⠀⠀⠀⠀⠀⠁⢰⠭⡆⢰⠯⡆⠀⡟⡇⠀⠀⠀⡸⠡⠀⠀⠠⠀⠈⠟⢠⣄⣤⠀⠳⣄⢀⡗⠋⠀⠀⠀⢴⣧⡴⠃⢸⠏
⠀⠀⠀⠀⢶⣾⣯⡿⡽⠽⠯⡿⠿⠿⣿⠟⠀⠘⢇⠀⠀⠀⠀⠀⠀⡆⠈⠻⠃⠀⢂⡬⠛⠬⡀⠀⠀⠀⠔⠈⠀⢻⣮⡄
⠀⠀⠀⠀⢸⣿⠀⣶⡇⠀⣿⡇⢠⣿⣿⠀⠀⢀⡠⠣⡀⠀⠐⣂⣀⡇⠀⠀⠀⡰⠉⠀⠀⠀⠉⢦⠀⠀⠀⠀⣦⣠⠟⠁
⠀⠀⠀⠀⢸⣿⠀⣿⡇⠘⠿⠇⠀⠿⣿⡆⠀⡉⣀⢀⠙⠉⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠀⠀⠸⠟⠄⠀⠀⠸⠛⠋
⠀⠀⠀⠰⠿⠿⠿⠯⠿⠿⠯⠿⠽⠽⠽⠿⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣤⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⠿⠛⠉⠙⠛⠿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⢻⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣄⡀⢀⣠⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡿⠟⠋⠁

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⣠⢶⣦⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠁⠀⢰⡞⠲⡇⠀⠀⠀⠀⠀⢹⣮⡿⠀⠀⠀⠛⠛⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠁⢘⠷⡼⣟⠀⡠⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣄⡈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⣤⣤⠞⠻⣿⣿⣿⣿⣿⣶⣌⡙⢦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣤⣆⣀⣀⣤⣠⣀⣠⣤⣤⡶⠶⠛⠉⠀⣠⠖⢿⣿⣿⣿⣿⣿⣿⣿⣎⢷⡀
⠀⠀⠀⠀⠀⢸⠁⡀⠀⠀⢀⡾⠛⣧⣤⡀⠀⠀⠀⡀⠀⢀⣤⢤⣀⡴⠛⠳⣏⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣯⢳⡀
⠀⠀⠀⠀⠀⣾⠀⠨⠃⠀⢾⠀⣸⠁⠈⢻⡶⠶⠦⣄⣰⠛⠀⠀⠻⡅⠀⠀⠙⣆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢳
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢸⣧⣿⡀⠀⠀⢳⡀⠀⠈⠻⣆⠀⠀⠀⣿⠀⠀⣀⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⣇⠀⠀⠀⢹⡆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣿⣿⣿⡿⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⠃
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⢳⡄⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠸⣿⣿⠿⢛⣻⣿⣿⣿⣿⢀⣀⣀⣀⠀⠈⠁⠀⣠⣿⢸⣿⣿⣿⡿⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢷⣴⡏⠀⠀⠀⠀⢸⠟⠁⠀⣿⠛⠒⠒⣾⠁⢸⡼⠶⣿⠏⣠⠞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⠷⣤⣀⠀⢀⣼⠀⠀⢀⣿⣀⣀⣄⣿⠖⠋⣠⠞⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠈⠉⠛⠛⠿⣿⣿⣩⡥⠭⠭⠵⠚⠛⠉⢁⣤⠞⠃⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣤⣠⣀⣀⣀⣀⣠⡤⠤⠤⠴⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢦⣤⣄⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣠⣤⡶⠶⠶⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⡍⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⡤⠤⠀⠤⢤⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠶⣄
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠊⠀⠉⠈⢦⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣠⠵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠁⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡡⠤⠠⠤⠒⠒⠁⠀⠀⢀⡤⠦⢤⡀⠾⢤⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠰⠆⢈⡤⠤⢤⡀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣳⠀⠀⠑⠶⠤⠤⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡤⠞⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⣇⠀⠀⠀⠀⠀⣘⡲⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠋⠙⣦⣄⠀⠀⠀⠀⠀⣼⠙⠲⠴⠚⢹⣆⣀⣠⠴⢻⠋⠉⢉⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠓⠾⣄⠙⠒⠒⠛⣋⣧⡤⠀⠀⠀⢸⣿⠉⠀⢀⡏⠀⢠⠏⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢿⠉⠓⠋⠉⢹⡇⠀⠀⠀⠀⡼⠸⡆⢀⣸⣡⠴⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⢿⡀⠀⠀⢰⠛⠛⣏⠉⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠹⡦⠀⠏⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⣀⣀⣼⡇⠀⠀⠘⢦⣀⣀⣀⣀⣤⠤⠟⠀⢙⡏⠉⠉⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠉⠁⣹⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢸⣇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣿⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⣼⠇⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠓⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⣠⠄⠈⡁⠀⠘⠀⠾⠂⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣦⡠
⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣷⡀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⠷⠾⢓⣆⠀⠂
⠀⠀⠀⢠⡤⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣦⠖⣾⣯⡉⠀⠀⡀⠀⣴⣷⣿⣼⣿⠗⠀⠀⡀⠀⠀⠀⠀⠀⠟⣷⢿⡏⠉⠂
⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠐⣴⣷⣏⣩⡅⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣄⠀⠀⠀⠀⠀⢤⠿⠙⠍⠋⠈⠀⠀⠀⠀⣠⣤⢰⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⡀⢰⡤⠀⡀⠀⠀⠀⠀⢺⡃⢰⡆⠀⠈⡀⠀⠀⠀⠻⠀⠀⡅⢻⠋
⠀⠀⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠁⠰⠆⠀⠀⠈⠁⠀⠙⣦⡀⣿⠀⠀⠀⠘⢶⡰⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢠
⠀⠀⠀⠰⠂⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢶⣴⣇⣀⠀⠀⠀⡀
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⣾⣭⣻⢻⡷⡔⠚⠁
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠈⠀⠀⠐⣟⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⣼⣩⡄⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠁⣼
⠀⣀⠀⠀⠀⠰⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢀⣠⣞⠁⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠘⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠿⠀⠀⠀⠀⠄⠉⠙⠛⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢈⠀⠀⠀⠀⠰⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠈⢘⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠁⡄⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣲⣾⣿⣞⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡚⢲⡄⠀⠀⠘⠟⢻⣿⠛⠃⠀⠀⠂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠎⣰⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠉⠳⡖⠀⠀⢠⠆⠀⠈⠀⠂⠀⠀⠀⡀⠠⢥⣮⣿⣿⣷⡀⠀⠠⠄⠀⣇⠀⠉⢸⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⢠⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⠻⠟⠑⠦⠀⠀⠀⠉⠀⠀⡀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣴⠆⠁⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠒⠀⠀⠠⣤⠉⠀⠀⠄⠀⢨⠀⠀⡀⠀⢼⡴⠁⠀⣀⣀
⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⣀⡴⠒⣫⡟⠁⠀⠀⠀⠀⢰⡀⣠⡔⠀⠀⠀⠛⠀⠀⠀⠀⠀⠗⠀⠞⠀⠀⠈⠁⠐⣴⠛⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⣁⡴⠚⠁⠀⠀⠀⠀⠀⠐⠘⢿⣿⣆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢄⣸⣿⣯⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣸⣧⠖⠚⠙⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⠦⠤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢴⣶⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣨⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⣿⣿⣶⣤⡄⠀⠀⣀⠀⣤⣤⣴⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⢿⣿⣿⡿⠋⠀⢀⣼⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⣤⣴⣦⣤⣤⡙⣄⣮⢦⠤⠚⢉⡱⢄⡈⠑⢏⣤⡶⠋
⠀⠤⠀⠀⠀⠀⢀⣀⣤⢤⣤⣤⣶⣶⣶⡾⠿⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠻⠙⠈⠀⠛⠲⣤⣤⣘⡉⠽⠛⠉
⣠⣤⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠿⠟⠛⠉⠁




⣀⣀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠶⠶⠶⠶⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⢾⣭⣭⣥⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠏⠓⢦⡀⠀⠹⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠹⣄⡀⢢⠹⡆
⠀⠀⠀⠀⠀⢰⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⠤⢶⣶⣤⣄⠳⡀⠳⣧
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡠⠖⠋⠛⠓⠦⣤⡀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢰⣿⣤⣴⣿⣿⣿⣧⢹⡀⠘⣦
⠀⠀⠀⡀⣼⡏⠀⠀⠀⣴⠋⠀⠀⠀⣤⣤⣄⡈⢿⡲⡄⠀⠀⠀⠀⠈⢳⡀⠀⢉⣀⣿⣿⣿⣿⣿⣿⠂⢹⠀⢹⣷⡀
⠀⠀⠀⡇⢹⠇⠀⠀⢠⠇⠀⠰⢷⣤⣾⣿⣿⣿⣎⢡⠇⠀⠀⠀⠀⠀⠀⠱⣄⠘⢿⣿⣿⣿⣿⣿⠏⢀⡼⠀⠀⢧⢧⡀
⠀⠀⠀⣧⡞⠀⠀⠀⠘⣶⠀⢠⣼⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⠿⠿⠭⠥⠴⠋⠀⠀⠀⠘⡆⣧
⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⠀⠀⠙⠿⠿⠿⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠒⠚⣉⠉⠉⢉⣽⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢋⣯⣀⡴⢦⠔⠛⠋⠓⠒⠋⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⢿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⣀⣤⣄⣠⠴⠒⠲⠦⣄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠖⠛⠃⠀⠀⠈⠁⠀⠀⠀⠸⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠘⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡁⠀⠀⠀⠀⠀⠀⠀⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢯⣹⡶⠲⣼⣩⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⢸⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠸⡆⠘⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠉⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣴⣷⣿⡂⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠄⠂⢀⠠⡿⣿⠿⠋⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣜⠀⠀⢀⠠⠀⢷⠀⠐⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠰⠁⣴⠈⣀⡀⠀⠀⢀⡙⢸⠇⠲⣮⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⣠⡙⢰⠁⠙⠲⡒⠁⠘⣹⢉⡖⢳⠨⠤⠤⠒⢂⠞⠁⠀⠀⠀⠀⢀⡸⠀⠀⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡉⠘⠆⠀⢁⢡⣌⡜⢁⡭⢠⢈⡬⠂⠐⠛⠁⠀⠀⠀⠀⠀⠀⢈⠀⠈⠀⠰⠀⢾
⠀⠀⠀⠀⠀⠀⠀⢻⣀⠤⠼⣇⠀⠳⡀⣸⡉⠀⢀⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⢈⠉⠛⠒⠢⠤⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠑⣄⠈⠂⠀⡠⠋⢀⠔⠉⢙⡿⠃⠀⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⠀⠢⡘⠁⠀⠀⠀⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⡈⠣⡀⠀⡀⢐⡅⠀⠀⣞⣠⠆⠀⢀⡤⢤⣴⣶⠄⣄⣈⠙⠓⠶⠤⢬⣒⣁⣙⣋⣀⣀⡠⠏⢀⣠
⠀⠀⠀⠀⠀⠀⢀⡽⠮⠍⠀⠀⠉⠼⢠⣯⡀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠁⠀⠀⢈⣉⣉⣓⣒⣒⣢⣤⣤⡀⠉⠁⠐⠛⢿⡅
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠀⠀⠉⠉⠛⢶⣄⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⠉⠳⢌⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⠃
⡼⠁⠀⠈⢆⠀⠀⣀⡀⠀⠀⠀⢶⠘⠻⣆⠀⠀⢀⡤⠂⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⠀⠀⠁
⢷⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣤⣀⣄⣦⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒
⠈⢷⡀⢦⠀⣈⣆⠀⠀⠀⠀⠀⢰⣲⡀⠀⠀⢠⣤⣄⠀⠀⢄⡀⠀⠀⢘⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠏⠀⠀⠀⠀⠀⣄
⠀⠈⣷⣾⣇⠹⣿⣧⠀⠀⠀⢀⣿⢿⠆⠔⠛⠃⠊⠚⠻⣶⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠛⢉⣡⣴⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠘⣿⣿⣆⠹⣿⣆⠀⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠫⠶⡀⠀⠀⠀⠀⠀⢷⣠⣶⣾⣿⣿⣿⠶⠚⠋⠁
⠀⠀⠀⠘⣿⣿⣦⡟⡿⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⣍⠀⠀⠀⠠⣙⣦⣄⠀⠀⠀⢀⣀⡀⢠⠤⠖⠁⠀⠀⣠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⢦⣄⣠⣜⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⡀⠀⠀⠀⠀⢀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⠻⣿⣶⣌⠙⠿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢣⠀⠈⠻⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠹⢦⣄⣠⣀⡤⡤⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠾⣿⣷⣴⠿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢻⡆⠀⠀⢀⡴⠛⣉⡉⠙⢷⣄⣠⡾⠋⠉⠉⠛⢶⡀⠀⠀⢰⡟⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⠁⣼⠋⠁⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⠀⠀⣿⡀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⠀⠀⠘⢷⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣼⡛⢷⣄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡾⢛⣧⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⣷⡀⠙⢷⣄⠀⠈⠻⢦⣄⣠⡴⠟⠁⠀⣠⡾⠋⢀⣾⠃⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠈⢷⡄⠀⠙⢷⡄⠀⠀⠉⠉⠀⠀⢠⡾⠋⠀⢠⡾⠁⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠻⣦⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⡀⢀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠂⠠⢄⣀⣀⠠⠤⠶⢀⠀⠤⡄⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠟⠒⠻⢤⣀⠀⣀⣐⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠰⢠⠏⢿⠁⠀⠉⠙⣶⣦⡀⠀⠀⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠊⢅⠀⢘⢦⣀⣁⡼⠁⢇⣠⠔⣉⢽⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡰⠀⠀⠀⠈⠑⠬⣙⡁⠀⠀⠀⢀⣀⢠⠤⠎⠡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡾⣝⠢⣀⠀⠀⢀⡼⠀⡝⠭⠭⡟⣁⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⢈⢀⠃⠈⠐⠁⢰⠀⠃⠀⠰⢀⠇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢱⡀⠀⠀⠀⡘⡠⠀⠀⢠⡆⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡜⠀⠈⠁⢉⠁⠁⠀⠀⠀⠃⡠⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢈⠄⠀⠀⢀⣠⡊⠀⠀⠀⢀⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⢄⡀⡯⠀⠀⠑⣄⠠⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⠀⠈⢳⠤⠖⡊⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠣⠄⠀⠀⠀⢠⠄⠒⠁⠤⠀⠤⠀⠀⠀⠳⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠤⢀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⢸⢄⡀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⡀⠀⠀⡈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠠⠀⠀⠉⠒⠒⠠⠐⢦⠀⠈⠉⠒⠒⠂⠤⢤⡄⠐⠁⠀⠀⠀⠈⠀⢀⠄⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠒⠉⠀⠨⡀⠀⠀⠀⢀⠂⠂⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⢠⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣟⣟⣿⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣿⣟⣻⣛⣻

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣄⣀⡀
⠀⢸⣭⣙⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣷⣦⡁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⠛⣿⣿⣷⣤⣘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⡇
⠀⠀⠹⣿⡿⠀⠸⣿⣿⡿⢿⣷⣌⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠋⠉⠘⣏⣡⣴⣾⣿⣿⣿⣿⣃⣀⣀⣉⠉⠉⠉⠁
⠀⢠⡀⠹⠇⠀⠀⢹⣿⠃⠘⣿⣿⣷⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢟⣡⣶⣿⣷⣿⠟⣫⣿⣿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⢸⣦⠀⣠⣾⡄⠀⡟⢀⠀⣿⣿⣿⣿⣧⡙⢆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⣁⣤⣯⣭⣶⣶⣾⡿⢻⡾⢟⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣾⣿⣿⣧⠀⢀⣾⡀⣻⡏⢸⣿⣿⣧⠈⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣠⣾⣿⡇⢛⣀⢸⣿⣿⣿⣧⢰⠀⠀⠀⠘⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣿⣸⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠙⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⡿⠟⣻⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⣼⣷⣶⣶⡶⠶⠦⣤⣀⡀⠀⠀⠉⠋⢸⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣶⡷⡿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡟⠀⠀⠀⠀⠀⣽⣿⣿⣷⣿⣿⣿⣶⣮⣽⣓⠄⠀⠀⠀⠙⠿⡿⢡⣿⣿⣿⣶⣿⣿⣿⣧⣼⡆
⠀⢸⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡟⢠⣿⠁⠀⠀⠀⢀⣾⣿⣿⣟⠉⠹⣯⣽⣿⠟⢿⣿⣷⣦⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣯⣽⣽⣿⣁⡸⢿⣿⣿⣿⣿⡗⢀⡿⠃⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣶⣼⣦⣤⣤⣤⣿⣿⣯⠃⠀⠀⢀⣸⣿⣿⣿⣿⣭⣭⣭⣭⣽⣛⡁
⠀⠀⠀⠀⠈⠉⠙⡛⣻⣷⣦⣏⠐⢹⠧⠟⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠉⠹⠟⠛⢛⠠⠤⠅⣈⠉⠉⠛⠻⠇
⠀⠀⣀⠤⢐⡒⣚⣓⡛⠟⠉⠉⠳⠎⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠙⡇⠀⠀⠞⠁⠸⣯⣽⣶⠖⠈⡀
⠀⠐⡥⠀⠘⣧⣿⣿⠏⠀⠠⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣲⠁⠀⠀⠀⢄⡐⠛⠛⠀⠀⠀⠐
⠀⠀⠒⠠⠀⠀⠉⣢⠤⠌⠒⠀⠘⣆⠀⠐⠀⠀⠈⠙⠻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢢⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠐⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⢈⡿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⠤⠔⠊⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢣⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠙⡆⠀⠀⠀⠀⠀⢠⡄⠄⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣤⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠠⠴⠤⠥⠆⠠⠤⠀⣒⡂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⢉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣯⣽⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣭⡍⠉⠛⠛⠿⢿⣿⣿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⠟⠀⠀⣠⣤⣶⣟⣷⣦⡀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⡀⠀⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡷⠀⠈⠙⢻⣾⠛⠋⠀⠀⢀⣤⣾⣿⣿⠏
⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⠿⠛⢁⣤⣶⣾⠏⣻⣶⣄⠀⣴⣿⣿⡿⠛⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⢸⣿⣿⡿⢀⣿⣿⠟⠀⣿⣿⡟
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠸⠶⠀⠀⠀⠀⢀⠐⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⠀⠂⠀⠤⠀⠄⢀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡂⢀⠀⠀⠀⠀⠀⢠⠀⡁⠀⠃⠀⠂⠠⠄⠠⠀⢀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⢀⠴⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠐⠀⠤⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡠⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⡏⠘⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠶⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠂⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⢲⣤⠤
⠀⠀⠀⠀⢀⢤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠢⠼⠛⠹⣄⠀⠂
⠀⠀⠀⠠⠽⠊⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠠⠤⡌⠁⠤⠄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠠⠤⠜⠈
⠀⠀⠀⠄⠚⠫⠃⠀⠀⠀⠀⠀⠛⠌⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠙⠐⠢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠒⠛⠒⠓⠒⠒⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⢈⡠⠄⠠⢄⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠠⠤⠀⠠⠀⠤⠀⠠⠀⠀⠀⠄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢨⠉⠀⠀⠀⠀⠉⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣒⣒⣦⣄⡀⠀⠀⠀⠀⠀⠈⢀⡀⡠⢤⡄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⠛⣛⣷⠖⠃⠀⠀⠀⠀⠀⠀⠿⣿⣯⠬⢇⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠳⣄⠀⠤⠄⠀⣀⡞⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠘⢅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠲⠤⣄⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⠂⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⡤⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠳⣀⣀⣀⣀⣀⣀⡀
⢀⣀⣠⠔⠚⠉⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠄⠀⠔

⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢰⢋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠠⠁⠠⠬⠐⢂⠀⠀⠀⠀⡦⠀⡐⠉⢂⢀⡀⠀⠀⠀⣀⣧⡵⠖
⠀⠀⠀⠀⠀⣥⠜⠁⢢⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠸⡀⠁⠐⠀⠂⢉⡜⠀⠀⠀⠈⢢⡠⣯⡟⣍⣈⠏⠀⠀⢼⠁⢈⡇
⠀⠀⢀⠀⡀⠀⠀⠰⢀⠀⠀⠘⡁⣤⠁⠠⡀⢀⠀⠀⠑⠤⡄⠀⡠⠎⠀⠀⠀⠀⠐⣁⣸⠨⢵⡋⠑⡀⢀⡴⠚⢯⠉
⠀⠀⠈⡉⠅⠀⠠⢂⠌⠀⠀⠀⠐⢄⠀⠀⠐⣄⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠄⠈⠉⠀⠀⠈⠉⠚
⠀⠀⠀⢰⣶⣿⣷⣷⣀⠀⠀⠀⠀⠈⠰⢤⡾⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠀⠑⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⡈⢀⠀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠀⠀⠀⠠⠘⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⡠⢊⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠉⡇⠠⠀⠀⠀⠀⠀⢻⣷⠄⠀⠠⠊⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡦⢄⠤⠖⠁⠀⠀⠀⠀⠀⠠⣠⣶⣶⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠢⠄⠄⠊
⠀⠀⠀⠀⠀⠠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡡⠀⠀⠀⠀⠈⢤⡐⢀⠆
⠀⠀⠀⠀⢠⠁⠏⠀⠀⠀⠄⢀⠴⠀⠀⠀⢠⠿⢿⠿⣿⣿⡿⠷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠂⠐⠔⠁⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠒⢀⠸⠈⠂⠀⠀⠀⠀⠀⠀⢂⡀⠀⡰⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣈⠁⢈⣤⣤⡗⠀⠀⠀⠀⠀⢠⠊⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡍⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂
⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⡆⠀⠄⣀⠀⠀⠀⠀⠀⠀⡠⢐⣤⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠠⠐⠁⠀⠑⢩⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇⣀⣀⠀⡄⠀⠀⠀⢰⡸⠏⠟⢀⢰⠀⠀⠀⠈⡀⣬⢢⠀⠀⡠⡂⠥⠀⠠⠁
⠀⠀⠀⡁⡄⠀⠐⠒⠄⠅⠀⠀⠀⠀⠀⣠⣴⡾⠛⠻⢿⠃⠀⠀⠀⠀⠀⠃⠈⠄⢉⡀⠂⠀⠀⠀⠐⠠⢙⢠⣌⠜⢁⠠
⠀⠀⠀⠑⠈⠀⠒⠨⠈⠀⠀⠀⠀⠀⠠⡈⠛⠃⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⣀⣰⠘⠋⠈⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠓⠂⠈

⠀⠀⠀⠉⠙⠛⠉⡇⠀⣘⣆⡔⠀⢰⠀⢀⡔⠀⠀⠀⠀⠀⠀⣠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⣀⣧⣤⣌⣙⠀⠀⠘⠶⠴⠋⣠⠞⢉⣭⣟⠲⣽⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠤⠴⠶⠖⠒⠒⠒
⠀⠀⠀⠀⢠⢞⣷⣤⡼⠦⠬⣝⢆⠀⠀⢀⡞⠁⡰⠁⠀⠀⠙⢮⢧⠀⡇⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉
⠀⠀⠀⢠⡏⣸⣼⡿⠀⠀⠀⠈⢻⣧⠀⡞⠀⣰⠿⣖⡀⢠⣤⢸⠸⡆⡷⠶⠶⠶⢶⣶⡄⠘⡇
⠀⠀⠀⠾⠀⣿⡏⡧⠶⣦⠀⢠⣒⣻⣿⠁⢠⠇⠀⢼⢹⠈⠉⣼⠀⣷⡇⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⡤⡀⠀⠀⠀⡠⢦
⠀⠀⠀⠀⢰⣿⣸⠁⠉⠉⠀⠸⡄⠨⣿⠀⢸⡀⣠⣖⣦⣀⣀⡏⠀⠸⡇⠀⠀⠀⠀⢰⠃⠀⠘⣆⡜⠀⡬⠉⠩⡍⠁⢸⡦
⠀⠀⠀⠀⡟⣿⢹⡀⠀⠀⢈⣢⣍⣰⡿⣄⠿⠋⠁⣌⢁⣈⣉⣩⡽⣶⡇⠀⠀⠀⠀⢸⠀⠀⠀⢿⠁⠀⠀⢻⢃⠀⠀⡼⠁
⠀⠀⠀⣸⢃⡞⠀⠳⣄⠀⠺⣟⡷⢏⡟⠁⠀⠈⣇⠸⡜⣇⣎⣈⠆⡏⡗⠦⣄⠀⠀⢸⠀⠀⠀⠸⣧⡀⠈⠋⠉⠀⣴⣁⢀⣀⣀⣀⣀
⠀⠀⠀⠰⠿⠤⣴⠃⠘⣧⣈⢛⡷⠚⠀⠀⡴⣶⣬⡶⣻⢿⠁⣇⠀⢳⣧⡤⢾⠗⠒⢻⠒⠒⠒⣲⣿⣟⠛⠛⠛⠛⠛⠛⣋⣽⣿⣛⠷
⠀⠀⠀⠀⣀⣀⠈⢧⠀⣿⠼⠋⠀⠀⢀⣼⣷⣽⠀⢠⡇⢸⠀⢹⡀⢸⡇⠀⢸⠶⠶⣾⠀⣰⡿⢴⣧⣬⣗⡖⠚⢻⡟⠋⢡⣶⣿⡛⣁
⠀⠀⠀⠉⠉⠉⠙⡾⠛⠁⠀⠀⠀⢀⣾⡼⣿⣿⠀⢸⠃⣾⠀⠘⡇⢸⡇⠀⢸⠛⠛⠉⠀⠙⠻⠶⠶⠿⣿⣛⣷⡾⠷⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⡇⣿⡟⣇⣸⠀⡿⠀⢠⡇⢸⣧⡤⢾⣖⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣺⣿⣿⣿⣿⣿⣭
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠⠏⢿⣿⡇⣿⡇⢿⡟⢀⡇⠀⢸⡇⢸⡷⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⣰⡟⣻⡿⢋⡟⡉⠉⣿⣯⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠇⠁⠻⠈⠁⠸⠇⠀⠼⠁⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠋⠈⠁⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢰⣿⣿⡿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠿⢿⣿⣶⣄
⠀⠀⠀⠀⣿⣿⠿⠦⠶⢿⣿⣷⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣿⣿⣿⣿⠋⣀⣶⣀⡈⣿⣿⣿⣿⠀⠀⠀⠀⢰⣶⣶⣿⣿⣷⣷⣷⠀⠀⠀⠀⣿⡏⠉⠉⠁⠀⠀⠉⠉⢹⣿⡆
⠀⠀⠀⠀⢠⣤⣴⣾⣷⣦⣤⡄⠀⠀⠀⠀⣿⣿⣿⣿⡈⠛⣿⡛⠃⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⣿⣿⡏⠉⠉⠀⠀⠀⠀⢿⣿⣶⣶⡆⠀⢰⣶⣶⣾⣿⠁
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣀⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⢰⣦⣤⣤⣤⣠⣄⣤⣤⣤⣤⣄⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣄⣾⣿⣿⣷⡄
⠀⢸⡇⠀⣴⡄⠀⢀⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⡇⢀⣿⡇⠀⣿⡇⠀⢰⣶⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⡿⠁
⠀⢸⣧⠤⠾⠥⠤⠼⠧⠤⠴⠯⠤⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣉⣿⣽⣷⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠋
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠓⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⠀⠀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠆⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⢋⣴⣉⢻⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠞⠳⣆⠁
⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠛⠻⠿⢿⡏⠀⠸⣿⠿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣌⡙⣉⣾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢦⡴⠏
⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠙⢹⡇⠀⠀⠅⠀⠀⠀⠀⠀⠈⠙⠚⠚⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⣠⣬⣭⠑⠄⠆⠀⠀⠀⠀⠀⣴⣶⡿⠛⡓⢶⡄
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣹⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢾⡷⢠⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⡇
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢄⡤⠴⠋⠀⡂⠀⠀⠀⠀⠀⠈⢙⡟⡟⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⡴⠋⢢
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⣄⠀⠀⠀⠀⠀⠑⢄⠀⣰⣾⣿⣷⣄⠀⠀⠀⢰⠀⠀⠀⣠⠞⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠙⢯⡻⣿⣿⣿⣷⠀⠀⠀⢇⢀⡾⠁⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⣿⠟⠀⠀⠀⠈⠻⢤⣀⣀⡠⠔⠁

⠀⠀⠀⠀⠀⠀⠒⠰⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⡄⠀⠀⠀⠀⠀⢠⣴⣶⣦⣀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⣾⣶⣶⣷⣒⡂⠀⠀⠀⣿⣿⣿⡿⢻⣿⣿⣿⣿⠀⠀⢀⠄⠀⠀⠀⢀⣴⡿⠣⡀
⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠉⠹⠿⣿⣿⡄⠀⠀⢛⣛⣣⣱⣾⣏⢟⣛⡛⠀⠀⠸⣷⣶⣤⣴⣿⣿⣴⣶⠇
⠀⠀⢳⠀⠀⣧⢀⡼⠀⠀⠀⠀⢸⣿⣿⣤⠀⢠⣤⣿⣿⡇⠀⠀⠀⠹⣿⣿⣇⣼⣾⠟⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠳⠤⠼⠋⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠾⠿⠿⠿⠇⠀⠀⠀⠀⠈⠙⠿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠛

⢀⣤⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣿⣿⡆⣀⡀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡆
⠀⠀⠳⣄⠑⣄⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡅⢾⣿⣿⣷⠄⠀⠀⠀⣀⣿⣿⣛⠛⢳⠀⠀⠀⠀⠠⠾⠴⣿⡶⡲⢦⡀
⠀⠀⠀⠀⠛⢄⢱⡀⠀⠀⠀⠀⢀⣬⣿⣿⣏⢾⣿⣿⣤⠀⠀⠀⣾⠉⢘⠲⠛⣷⢺⡀⠀⠀⠀⠀⠀⠀⣯⡪⢈⣼⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠻⢆⠀⠀⠀⠀⠻⠿⢻⣿⣾⡟⠿⠟⠀⠀⠀⢿⡀⠈⠁⢠⡟⣸⡏⢄⠀⠀⠀⠀⠀⠈⠉⠉⡟⡣⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⡈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠄⢀⡞⡁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠇⢈⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠘⢂⡀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣄⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡤⠄⢀⣴⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⢿⣄⢘⣿⣇⢦⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣀⣠⣿⣦⠿⠃⠀⠹⣆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⠚⠋⠉⠁⠈⢿⡄⠀⠀⠀⠸⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠙⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠶⠀⠠⠦⣄⡘⣧⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⢰⠀⠑⠈⠃⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⣀⠴⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣃⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⢸⡏⢳⡀⠀⠀⠀⠀⠿⣿⡾⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⣸⡇⠈⣷⠀⠀⠀⠀⣰⠉⠀⠀⠀⠀⢸
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸
⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡄⣰⠏⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣷⠋⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠻⠯⠤⠤⠤⠤⠭⠭⠭⠽⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣭⣙⣒⣒⣒⣒⣒⣒⣒⣒⣚⣩⣬⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠁⡏⢹⠉⡏⢹⠉⡏⢹⠉⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠾⣦⣧⣼⣤⣧⣼⣤⣧⣼⣤⠷⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠿⠿⠿⠿⠿⠿⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠶⠶⢶⡶⠶⠶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠻⠶⠶⠶⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠀⠀⠀⠀⢀⡴⡖⢶⡄
⠀⠀⠀⠀⠀⢀⡴⠶⣤⣤⣄⡀⠀⠀⣿⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⣿⡀⠀⠀⣴⠟⢮⣁⣼⡇
⠀⠀⠀⠀⠀⢸⣄⣀⣸⠐⠚⣻⠀⠀⣿⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⠆⠘⣧⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠋⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣉⣸⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⣦⠧⠸⠞⢲⣦⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢤⡀⣰⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠛⠛⠻⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⠛⢉⡷⠮⠭⠳⣄⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⢀⡎⠘⠁⡀⠈⠀⠀⠀⠀⠈⢧⠀⠀⣿⣿⣿⢿⣾⠓⠀⠴⣂⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⠀⡘⠰⡇⠀⠀⠀⠀⠀⡠⠌⢧⢸⣿⣿⡇⠀⠀⠀⠀⠀⠛⢡⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡏⠠⠁⢀⠂⠀⣉⡝⠂⠀⠐⠛⠀⢿⣿⣿⠀⠀⣠⣤⣄⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⢸⠡⠁⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⠛⠛⠋⠀⠰⠿⠿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⢀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢸⡆⡆⢧⠀⢆⠀⠀⠀⢀⣤⣴⣆⠀⢸⠿⠋⠁⠀⠀⡄⠀⣦⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⢸⠁⡇⢈⠱⡸⣇⠀⠀⠚⠋⠁⣅⠠⠀⠀⠠⡀⠈⠄⠀⠀⣀⣼⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢸⣜⡔⡡⠤⠂⠻⣄⠀⠰⣤⣤⠊⠀⠐⢋⣶⣿⠆⠀⠀⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠈⠁⠀⠀⠀⠈⣁
⠀⠀⠀⠀⠀⢘⣾⣿⣶⣶⣶⠁⡌⣿⣦⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠠⠄⠀⠰⠆⠀⠀⠀⠠⠤⠀⠀⠠⠀⠬⢳⣄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇⠃⠛⠁⠀⠀⠀⢠⣿⣿⣿⣿⠀⢀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠠⢴⣶⣄⣀⣀⣤⣶⣦⣐⣀⣭⣅⣄⣐⣀⣜⡸⠂
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⠟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⢸⢱⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠏⢁⠄⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⠅⠂⠀⢄⡂⠀⠀⠀⠈⠀⠠⠄⠁⠀⠀⠀⠈⢀⠠⠖⠀⣰⠀⠀⠀⠇⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⢶⣤⡀⠀⣠⣴⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠈⢻⡾⠋⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⢸⡏⠈⢻⡆⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢰⡟⠀⢹⡇
⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠈⣿⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣦⣀⣴⠿⢶⣄⠀⠀⠀⠀⠙⠷⠾⠛⠁⠀⠀⠀⣠⡶⠿⣦⣀⣴⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠈⠛⢿⣦⡀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣴⡿⠋⠁⠀⢀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠉⠻⣦⡀⠈⠛⣷⠀⠀⠀⠀⣾⠛⠁⢀⣴⠟⠉⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠿⠷⠷⠶⣶⣾⡾⠿⣷⠀⠀⣾⠿⢷⣶⣶⠶⠶⠾⠿⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠿⢿⡇⠀⣿⠀⠀⣿⠀⢸⡿⠿⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠀⠀⠿⠶⠾⠷⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠲⠛⠒⠚⢻⡆⠀⣹⣦⠟⠀⣾⠀⠰⣏⠀⣀⣤⢤⣤⡐⢾⡁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣠⣭⣉⡀⠀⠙⠛⠚⢡⡞⢉⡴⠚⠷⣭⣻⡏⠀⡏⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢠⢾⣯⣭⡽⠶⠮⣝⣦⠀⠀⣰⠏⢀⣞⡀⠀⠀⠀⢻⣿⡀⣇⣀⣀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢠⠏⣾⣿⡟⠀⠀⠀⠈⢻⣧⣠⡏⢀⡾⠻⣿⣦⣾⡿⢺⠼⣧⡟⠛⠛⠛⠛⠛⣿⠀⣷
⠀⠀⠀⠀⠀⢀⡿⢰⣿⣿⡧⠶⣦⠀⣴⣿⢿⣿⠀⣸⠃⠀⢻⠻⠃⠀⣿⠀⢿⡇⠀⠀⠀⠀⠀⡟⠀⢸⡆⢀⡴⢄⠀⢀⡀⣠⢶
⠀⠀⠀⠀⠀⢼⠁⣸⣿⣽⠀⠋⠉⡀⠹⡆⢸⣿⠀⣿⣤⡼⢿⡷⠤⢤⣧⣄⣘⡇⠀⠀⠀⠀⢸⡇⠀⠈⣧⡜⠀⢶⠉⠉⡍⠁⠘⣧
⠀⠀⠀⠀⠀⠀⢠⡟⡏⣧⠀⠀⠀⢉⣬⣧⣼⢿⣴⠟⢡⡀⢷⢰⡶⢶⢶⡞⣿⣏⡀⠀⠀⠀⢸⠃⠀⠀⢻⡇⠀⢀⣹⣏⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⣼⢁⡇⠘⢦⡀⠀⢿⣝⡿⢻⡟⠁⠀⠈⢧⢸⣯⣷⠿⡴⠃⣿⡏⠙⢲⣄⣀⣸⡀⠀⠀⠈⣿⣄⠈⠉⠉⠀⢠⣏
⠀⠀⠀⠀⠀⢸⣧⣞⣁⡼⠃⢹⣦⡘⢻⡶⠋⠀⢠⡞⣿⠾⠟⣿⣻⠀⣷⠀⢻⡷⠚⢻⠋⠉⢹⠉⠉⢉⡽⣿⢿⡛⠛⠛⠛⠻⠛⠛⣛⣿⡿⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢈⣧⠟⠋⠀⠀⢠⣿⣿⣿⠀⢸⡇⣿⠀⢸⡄⢸⡇⠀⢸⣋⣛⣿⠄⣼⣟⠲⠷⣴⣟⣻⠛⠛⣟⠿⢋⣭⣿⡷⠆⡇
⠀⠀⠀⠀⠀⣠⠖⠛⠛⢶⣽⠞⠁⠀⠀⠀⢠⢿⣸⣿⢻⡀⢸⠁⣿⠀⠘⡇⢸⡇⠀⢸⠉⠉⠀⠀⠈⠛⠻⠶⠿⢿⣻⣿⣾⣿⣶⣶⣿⣿⡷⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣾⡍⣿⡎⣇⣿⠀⡏⠀⢸⡇⢸⡷⣚⣭⣭⡭⠭⢭⡭⠭⢿⣭⣽⣿⣗⣒⣒⣲⣖⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣿⣿⡇⡿⡇⢿⡏⢠⡇⠀⢸⠇⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢻⣿⡟⣿⠛⠛⣻⣻⠻⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠛⠃⠁⠛⠀⠀⠘⠃⠀⠚⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠛⠁⠃⠋⠀⠙⠋⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠧⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡾⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡞⠁
⠀⢀⣤⠶⠶⠶⠶⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟
⢠⡟⠉⠢⡀⠈⠠⡀⠀⠈⠙⠶⣄⣿⠛⠒⠒⠒⠓⠛⠛⠋⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⢧⠀⠀⠈⠳⣄⠈⢦⡀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⠘⣆⠀⠀⠀⠈⠳⣄⠙⢦⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠸⣆⠈⢢⡀⠀⠄⣀⠈⠳⢄⠙⢦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠁⠀⢀⡾⠁
⠀⠘⢦⡀⠙⢦⡀⠀⠀⠀⠀⠑⢄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⢦⣀⠈⠓⠶⢤⣤⣀⣤⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⠶⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠉⢉⣽⠟⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠾⠋⠁⠠⠄⠀⢀⡤⠞⠉⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⢀⣀⣠⠴⠛⠁⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⡠⠚⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⠦⠤⢤⣄⣀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⣠⠖⠁⠀⣠⠖⠉⠀⠐⠀⠀⣠⠎
⠀⠀⠀⠀⣠⣴⡛⠛⠲⢤⣀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢴⣟⡁⢀⣠⠞⠁⠀⣀⣀⡤⠖⠋⢁⡼
⠀⠀⠀⣰⠏⠈⠙⠲⢦⣀⡈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠈⠉⠉⠉⠉⠉⢉⣀⣠⡤⠶⠋
⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⢹⣏⠑⠦⣄⡀⠀⠂⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢦⣤⢿⡆
⠀⠀⠀⠀⠻⣆⠀⠀⠉⠓⠒⠤⠤⣀⣀⣀⣀⣬⠽⠶⠒⠉⠀⢀⡿
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⠀⠀⣀⣀⣀⣤⡴⠞⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⢈⣛⣭⣹⣿⣿⠝⡟⣽⣿⢹⣿⡟⢽⣿⣿⡿⠿⢿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣽⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡏⣿⡷⣮⣼⣿⣿⣬⣟⣫⡾⢫⣵⢟⣋⡰⢮⡓⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣟⣻⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡟⡩⣶⡦⠘⠶⠮⣝⢿⣿⣿⡟⣵⣿⢣⣿⣿⣿⣷⡜⡎⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣛⣿⣿⠙⣿⣿⣸⢾⣿⣿
⠀⠀⠀⠀⠀⢈⡾⣵⠑⣼⣿⣿⣿⣮⠪⢻⡿⣱⣿⢇⣂⡽⡿⡯⢝⡇⣷⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣺⣶⠿⠿
⠀⠀⠀⠀⠀⢸⡇⡇⡇⡿⠿⢿⣿⣟⣣⠈⢱⣿⡏⣾⣿⣣⡇⣿⣾⡇⣿⠘⢸⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣿⢏⠘⡃⢉⢿⢏⡙⢿⣿⣿
⠀⠀⠀⠀⠀⢸⠇⣸⢱⣟⣭⣽⣿⡰⣾⡇⢸⣿⠹⣿⡟⠩⠻⠿⡿⢸⣿⠀⢸⣿⣿⣿⣿⣿⡿⢿⣮⡿⢿⡷⠈⠛⠘⠋⠠⣾⣍⣿⣿⣦
⠀⠀⠀⠀⠀⠈⡄⡏⣿⣿⣿⣿⣝⣧⣿⡇⡸⡿⣀⣴⣾⢳⡿⠿⠶⠶⣂⡀⢸⣿⣿⣿⣿⡟⠈⠿⠟⠃⣸⣿⡃⢀⣂⣄⣺⢟⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⡇⣿⡹⣿⣿⡟⢁⡐⠎⡇⢣⣾⣿⣯⢻⡇⣧⠻⠳⡷⣻⢠⢸⣿⣿⣿⣿⣯⣿⣷⢛⡘⣛⣻⣿⣬⣽⢿⣟⢾⣿⡭⣿⣿
⠀⠀⠀⠀⠀⠘⣣⣿⢿⣮⢻⣿⣓⠡⠟⣡⣿⣿⠟⠻⠮⢛⡌⡀⣾⢸⣿⡜⢸⣿⣿⣿⣏⣸⣿⣏⣿⠇⣽⡻⢯⡟⡻⣿⣿⢿⣾⣷⣷⣯
⠀⠀⠀⠀⠀⢠⣭⣅⢿⣿⡇⣬⢛⣡⣾⣿⣿⠃⢹⢸⣿⡿⣸⡇⣿⡇⣿⣷⢨⣛⢿⣿⣾⣿⣿⣋⣿⣿⢸⣿⣿⡿⣷⣥⣿⣼⢿⣧⣿⣿
⠀⠀⠀⠀⠀⠸⠿⠿⣧⠻⢇⣴⣿⣿⣿⡿⢣⡆⣾⣽⣿⡇⣿⣇⣿⣿⢸⣿⠸⠿⡛⣼⣿⣿⣿⣟⣛⣛⠂⠛⠛⠋⠓⠘⠛⠛⠚⠛⠻⠟
⠀⠀⠀⠀⠀⢸⣿⣿⣆⣴⣿⣿⣿⣿⡿⠱⡇⣇⠏⣇⢿⡇⣿⢸⣿⣿⢸⣿⢰⣿⡇⣿⣿⣿⣿⡿⠟⠥⡎⣴⡝⠿⠿⠿⠿⠿⠿⣛⣫⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣡⠀⠃⣿⢠⣿⠸⢹⣿⢸⣿⡿⣼⣿⢸⣿⡇⣿⣿⣿⣿⢇⡈⠛⠶⠾⠄⠋⠹⠿⠇⣿⣾⡯⠠⠍
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣴⣿⡀⠄⣿⣾⢹⣤⣾⡟⣼⣿⡇⣿⣿⢸⡿⠗⢘⣛⣛⣛⣻⣿⡿⠶⠶⠿⠿⢷⣤⣤⣤⣦⣤⣤⣤
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣨⡄⠀⠈⠙⠿⠿⠙⠿⠿⠿⢿⣿⣟⠿⢃⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⣭⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡿⠀⠰⠿⠿⢷⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠁⠀⢠⣿⠅⠀⠈⠀⠀⠀⠘⠛⠿⢿⣦⡄⠀⠀⠀⠀⡇⡄⣶⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠉⠉⠄⠀⠀⠀⠀⠀⢰⣬⠑⠈⠻⠀⠂⠀⠀⢅⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⢠⡿⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣂⡀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣰⣾⣿⡿⢿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠼⠻⢿⡿⠃
⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⡀⡰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⠠⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⠀⢖⣚⠿⣷⣦⣤⠀⠀⠀⠀⠀⢀⣀⣴⣾⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⣿⣇⣷⡀⠀⠀⠀⣠⣾⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠿⠿⠿⠿⠿⠷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⣾⠿⢛⣩⣴⣶⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣋⣴⣾⣿⣿⠿⠟⢛⣛⠁⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂
⡒⠶⢶⠤⢄⠀⠀⠑⠊⠀⠀⠀⠀⠀⢀⠔⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠠
⠠⢀⠀⡇⠀⠀⠀⡠⢤⣶⣆⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡸
⠀⢀⠆⠀⠀⠀⠀⠀⠉⢄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠙⠋⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠸⠀⠀⠠⠂⠀⠀⠀⠀⠑⠇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠄⠉⠉⠉⢠⠁⠀⠀⠀⠈⠳⣤⣀⣀⢴⢣⠀⠀⠀⠀⠀⠠⠎⠉⠑⡄⠀⠀⠀⠀⠸
⢀⠇⠀⠀⠐⠄⣀⡀⠀⠀⢀⡀⠈⡀⠤⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡼⠶⣄⠀⠰⠋⠙⠳⡄⠀⠀⠈⠧⣀⡴⠁⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢺⡀⢀⡸⠀⠘⢤⣀⠴⠃⠀⠀⠀⠀⠀⡶⠖⠢⡀
⠀⡠⠶⢤⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡞
⠀⣇⠀⣠⡦⣀⣀⢄⡀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠚⠁
⢀⣈⠉⠁⡸⠋⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠁⠈⢳⠄⣇⠀⠀⠀⢠⠆⠀⠀⠀⢀⠄⢤⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠀⠈⠀⠀⠀⠘⠀⠙⢄⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣀⠠
⢤⠴⠋⠀⠈⠲⠤⠖⠃⠀⠀⠀⠀⠹⢄⣀⠇⠀⠀⠀⠀⢀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⠀⠀⠆⠻⠟⠀⠚⠂⣤⠄⠀⠀⠀⠀⠠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠁
⢀⣤⠆⢱⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠠⠉⠐
⠉⠀⠀⠀⢢⠀⠀⠘⢅⣀⡼⠓⠢⢼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠄⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠾⢁⡤⠦⠠⣄⠀⠀⠀⡠⠄⢄⠀⠀⠀⡠⠲⠶⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⢄⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⡧⠀⠘⢅⣀⡼⠀⠀⠀⠈⡂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠢⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠢⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠁
⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⠋⠀⠀⠀⠉⢣⠀⠀⠀⠀⢠⠀⠲⡎⠉
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡄⠀⠀⠘⢄⡀⠀⠀⣠⡎⠀⠀⠀⠀⠸⡀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠃⠀⠀⠀⣸⣙⠉⠉⢱⠼⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⢴⠘⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⢱⠀⢣⡀⠀⣨⠃
⠀⠀⠀⠀⠀⢠⠒⠒⠄⠀⠀⠀⠀⠀⣇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠡⠀⢀⠌⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⡄⠀⠀⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄