Potted plant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠋⠳⠞⠀⢷⡏⣱⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢘⠳⣼⠀⡄⣠⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠻⣄⠀⠁⢸⠄⠒⠣⣄⣀⣤⣾⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠚⠉⠙⢒⣏⠀⣼⣖⡸⠇⠉⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣉⣶⠋⢈⣻⠞⢫⠙⣦⣄⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⣤⢿⡀⠀⡂⣿⢀⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠘⠺⣷⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠳⣄⠀⢀⣿⡇⠀⠀⠀⠀⣀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡵⡈⢧⠀⣿⡇⠀⢀⡴⠋⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠜⡈⢳⣿⡇⡰⠋⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣿⣿⣇⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣿⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣠⣀⣀⢴⣿⣷⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⢰⣋⠿⠽⠯⠯⠯⠼⠽⢽⣽⢀⡎⣈⣸⣵⣧⣠⣀⣄⣄⣠⣀⣀⣀⣈⣉⣉⣉⠽⠿⣹⠆
⠀⠀⠀⠀⠀⠀⠸⡄⠉⠉⠙⠒⠒⠒⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠂⡶⠲⢲⠒⣏⡟
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⢀⠆⡸⢠⠇⡼⣱⢃⠃⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⡀⡀⢠⢀⢄⡄⡜⡰⢁⠎⡜⢡⢏⡜⣰⢡⢏⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢏⡗⡶⣲⢦⠬⡤⢤⢥⡤⡤⣤⠤⡤⢬⠾⣴⢓⡾⣲⠛⡿⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠈⠀⠁⠃⠚⠘⠱⢃⠞⣠⢋⡴⣡⠞⡴⢃⡼⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠜⣡⢎⡴⢡⠞⣁⠎⠐⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠊⡴⠁⡴⢁⠞⡴⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠎⣠⠋⣰⢫⠞⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⣡⢞⡴⢃⠞⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⣡⢋⡴⢫⢾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⣡⢋⡔⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢀⢀⠀⠀⠀⠀⢘⣡⢚⣵⣫⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⠀⠀⠁⠈⠉⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠔⡡⢊⡡⠊⣡⠔⣩⠔⡡⢚⡡⠊⡡⢊⡠⢊⡔⢃⠔⡠⣢⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠉⠀⠉⠀⠉⠀⠋⠐⠁⠊⠐⠁⠁⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣼⣏⣹⠧⣤⣶⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⣾⣿⣿⣿⡃⠙⣿⣿⣿⣿⣿⣍⠁
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣻⣿⣿⣿⡿⠀⠀⠻⣿⣿⣻⣭⣀⣀⣀⣀⣴⣾⣿⣷⣤⡀
⠟⠛⠛⠛⠻⠿⢶⣿⣿⣷⣦⣀⣽⣽⣿⣿⣿⣟⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿⠿⣿⣟⣯⣻⣿⣿⣿⡟⠛⠋⣉⠿⠋⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣍⠘⠛⣿⣟⡅⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⢸⣿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⣠⡤⣠⣷⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⢀⣾⣶⣿⣿⠡⣼⠩⣽⡻⣟⣳⣴⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣾⣿⣿⣿⠛⢻⣇⢰⡇⣱⠋⠙⢿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⡿⠋⠀⢸⠈⢻⡇⡿⢀⣶⣿⣾⣿⣯⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢹⣿⠁⠀⠀⢀⡏⢀⡘⣿⣧⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⣿⡇⠀⠀⣸⣇⣴⣾⣿⣿⣁⡄⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣦⣤⢻⣇⠽⣿⣆⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣵⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⣀⣿⣿⣿⣰⠏⠁⠀⠛⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⠀⠈⠙⢿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠋⢹⣿⣿⣽⣋⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⠀⠀⠀⠈⠻⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣶⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⠯⠻⠉⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣷⣶⣧⣠⣆⣀⣄⣤⣾⣿⣧⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠶⠶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣽⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⡀
⠀⠀⠀⠀⠀⠀⣀⠤⣤⣀⣴⠏⡹⢀⡀⢤⣤⢀⠤⣀⢠⢢⠤⢔⠲⡄⠘⡌⠿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⢀⡠⣷⠊⠱⢩⢒⢁⣐⣸⣇⢫⡟⢁⣎⣁⡄⡧⠤⢼⡂⠑⠠⠬⣉⠄
⠀⠀⠀⠀⢀⡀⣀⠖⡡⠄⠂⠬⣱⣟⣡⡫⠒⠀⠒⠈⢣⡎⢠⠂⢿⣂⣁⣀⣈⣲⣉⣐⣢⣄⣀
⠀⠀⠀⡎⡠⠄⢾⢊⠤⢶⠴⢆⣨⢛⣿⡶⣾⢿⡧⣄⣨⡇⡇⢸⠜⠛⠉⠛⠫⣥⠀⣀⣤⡽⠢⡱⡀
⠀⠀⠀⠑⠒⢲⠬⠽⣄⢀⠉⠑⢬⢻⣧⣙⣧⠞⢋⠭⠍⢹⣴⠃⡠⠂⡉⠉⣀⣼⣁⣀⠈⢙⡃⠀⠃
⠀⠀⠀⠀⡔⢁⠔⠉⠈⡗⠚⣓⢦⢟⠭⠉⠉⠶⣥⣂⣴⢹⣿⣬⣬⠵⢶⣟⡩⠤⠄⠉⢲⠁⠉⠒⠃
⠀⠀⠀⠀⢇⠈⢀⡔⡹⡇⠀⣀⡈⠖⢦⡐⠠⢄⠈⠟⡻⠋⠺⣏⠒⠒⠒⠤⠙⣤⣤⣀⣀⠇
⠀⠀⠀⠀⠈⢉⡩⠒⣨⠽⠛⠲⢶⠞⢋⡩⠵⠢⡍⠰⠁⠜⣰⢿⠓⢦⣍⡀⠀⢸⠦⡈⢢
⠀⠀⠀⠀⢀⠎⠠⠊⠀⠰⣣⣴⢃⠔⢉⡀⠴⢂⣧⣀⣠⣾⡇⠉⡇⠀⡏⠭⣻⠩⡀⢣⠈⡄
⠀⠀⠀⠀⠸⣄⠁⣀⡠⠚⣧⣽⣤⣤⣤⣴⣾⣟⠋⣸⣿⣿⣿⣄⢁⣴⣿⠒⠜⠣⡐⠀⡠⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠰⣉⠉⠉⠉⠉⠉⠉⠉⠉⠈⡉⠉⠉⡉⡉⢉⠉⠉⢍⡵⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠋⠋⠋⠩⠉⠩⠙⠋⠉⢌⠍⠕⡡⡫⡫⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢊⢎⢔⠕⡑⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⡡⢃⢊⠜⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠨⢊⠔⠕⡡⢊⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡀⠀⠀⠀⠀⠀⠀⠀⡡⡢⡪⢒⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠡⠀⠀⠀⠀⠀⠀⠀⡪⢊⢔⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠦⠤⠤⠤⠤⠤⠤⠤⠎⠵⠥⠽⠧⡄
⠀⠀⠀⠀⠀⠠⠠⢄⠠⢀⠠⢀⣘⣦⣀⣀⡀⣀⣀⣀⣐⣂⣂⣓⣑⡳⡇⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠁⠉⠈⠑⠉⠉⠉⠉⠁⠂⠁⠈⠂⠑⠈⠒⠙⠊⠑⠉⠊⠐⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣄⠀⠂
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⡄⠿⢀⡆⠀⠀⠀⠀⠀⠀⠞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠲⠶⠷
⠀⠀⠀⠀⢀⡿⣦⠆⠇⡠⡴⠀⠀⠀⠀⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⡿⣿⠆
⠀⠀⠀⠀⠸⡌⢻⢤⡞⢰⠃⠀⠀⢸⡍⠛⢩⡇⠀⢰⠀⡄⢸⠀⠀⠀⠀⠀⠀⣾⠿⠿⣳⡄
⠀⠀⣢⣀⠀⠀⣼⠘⢠⠎⠀⠀⠀⠀⠧⠀⠼⠁⠀⠈⠀⡇⢸⢰⡀⠀⠀⠀⠀⢿⠛⠁⢸
⠀⠀⠹⡉⢧⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⣿⡮⡇⡆⡀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠙⠬⠃⢐⠃⣄⠊⠙⢦⡀⠀⠀⠀⠀⠀⠀⢦⡀⣷⣻⣿⣿⠀⠃
⠀⠀⠀⣠⠀⠀⣾⠰⠋⠛⠲⢄⡃⠀⠀⠀⠀⠀⠀⢠⡿⣼⣿⣿⣯⣲
⠀⢀⡞⠁⣰⠆⠙⠀⣀⡶⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡿⡏⣿⣿⣿⠀⠀⡂⠆
⠀⣭⢠⡞⠁⠀⠄⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠱⡎⣻⡇⠀⠀⡅⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⠏
⠀⠈⠏⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠈⢿⣼⣧⣿⠁⠀⠀⠙⠂⠜⠀⠀⠀⠀⠀⠀⠀⢳⣴⠂
⠀⠀⠀⠀⢶⣿⠟⠛⢑⡆⠀⠀⠀⠀⣠⣄⠁⠀⠀⠀⠀⠈⢿⢿⡏⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡇⠟⠛⠻⣦⠀⠐⣄
⠀⠀⠀⠀⢸⡏⢁⠈⠀⠀⠀⠀⠀⣶⠘⠛⠳⠦⠀⠀⠀⠀⠀⠀⢀⠄⠀⢰⡾⡾⣶⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠳⠤⠸⠞⠀⠀⠀⠀⠑⢤⣀⠴⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⢧⣧⠿⠀⠀⠀⠀⠀⠀⠻⠤⠤⠔

⠀⠀⠀⠄

⠀⠀⠀⠰⠶⠶⠀⠀⠀⠠⠦⠶⠄⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠛⠚⠓⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⢄⠐⢲⠡⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⢀⠄⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣖⠠⣄⠹⡄⠓⠀⠀⠃⡞⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⡇⠰⠁⠊⣅⠠⡄
⠀⠀⠀⠀⠀⠠⠄⠡⡌⠓⢄⠀⠠⠀⠐⠀⡜⠀⠋⠔⠀⠀⠀⠀⠀⠀⠠⠤⣘⠀⠀⡀⠀⡐⠈⢁⠞⢂⠝
⠀⠀⠀⠀⠀⠐⠟⡂⠂⠄⡀⣱⣶⣿⣿⣶⣀⠠⠒⢀⠜⠀⠀⠀⠀⠰⡐⠦⠈⠣⡀⣴⣶⣤⡔⠁⠀⣉⠤⠮⣤
⠀⠀⠀⠀⠀⠐⢌⡉⠠⠀⠀⠿⣿⣿⡿⣏⣀⣀⣈⣉⠭⠂⠀⠀⠀⠐⠋⣤⠤⢀⣈⣿⣿⣿⣿⡆⠁⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠓⡲⠖⢀⠔⠈⢀⠜⢁⠈⡐⢬⡓⡌⠁⠀⠀⠀⠀⠀⢉⠖⢂⠀⢉⠼⠛⢟⠻⠍⡁⠀⣌⠩⠃
⠀⠀⠀⠀⠀⠀⠘⠐⠚⠓⣋⠄⠋⠰⢆⢢⡉⠂⠃⠀⠀⠀⠀⢀⡔⠀⠈⢀⣮⡔⣡⠀⡆⢀⠡⡀⢈⠑⢦⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣿⡄⠀⠀⠀⢀⠔⡑⠀⢀⣴⡟⠉⠁⠘⠔⠈⢌⠑⢵⢌⢃⠉
⠀⠀⠀⠀⠙⠣⡒⠠⢀⡀⠀⠀⠀⢀⠀⠀⠸⣿⡀⠀⠠⠂⠀⠁⣴⡿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠑⠠⡀⠈⢳⠢⡀⢿⣧⠠⠁⠀⢰⣾⡟⡡⠲⠃⠀⡀⠄⠒⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠒⢄⢂⠈⢺⣿⠃⠀⠀⢸⡿⠋⢠⡡⠒⠁⠀⡠⠊
⠀⠀⠀⠐⠦⡀⠤⠀⢀⡀⠄⠀⠀⠀⠀⠰⡄⠀⠙⡀⠀⠀⠐⠁⠀⡌⠀⠀⠀⠎⣀⠀⠤⠐⡲⠖⠂
⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠙⠢⢄⠀⠀⠀⡇⠀⠀⠰⡀⡐⠀⠀⠀⡁⢀⠠⠚⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠓⠁⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⡀⠀⠀⠀⡆⠀⠀⠀⡬⠀⠀⠀⠀⡀
⠀⣀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢃⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⣠⠊⠀⠀⠀⠀⠀⠀⠉⠐⠠⣀
⠈⠁⠀⠀⠀⠀⠉⠐⠤⣀⠀⠀⠈⠢⡀⠀⠈⡀⠀⠀⢀⠇⠀⠀⠄⡠⠖⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠛⠿⠷⠶⠾⣷⣾⣿⣶⣶⣿⣶⣷⣾⣿⡿⠿⠿⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⣿⣷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⣠⣄⡠⡆⣪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡶⠈⠀⠀⠀⠘⠶⠀⣴⡄⣀⠀⠀⣤⡄⢀⣔⡢
⠀⠈⠀⠀⠀⠀⠀⠀⠈⠆⠛⠱⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠳⠗⠈⠉⠁⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⡝⢦⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣿⡯⣳⣧⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⢰⣿⠀⠀⢀⠀⠀⠀⠴⠓⠀⠸⠟⠛⠟⠿⠂⠀⢠⣆
⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⠀⣄⠀⣠

⠀⠀⠰⠄⠀⠀⠀⣠⣠⣆⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⡀⠀⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠤
⠀⠀⠈⠀⠀⠈⠷⣯⣽⣽⡶⠃⠀⠀⠘⠇⠀⠀⠷⢿⡇⠀⣼⣿⣿⣷⠀⠀⠀⢰⠀⠀⠀⠀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⢀⡔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢉⣠⢉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠇⠠⠃⠀⣶⡶⣯⣶⡆⠀⢠⣦⡴⠀⢰⡦⠛⣤⠀⠀⢀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠀⠀⢘⣃⣀⡛⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⣀⡤⣤⠀⠀⠀⠀⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠴⠂⡄⠀⠀⠀⠀⠀⠀⢠⡈⠃⠁⠠⠀⠀⠉⠛⠉⠀⠠⢄⡀⠉⠀⠀⠀⠀⠚⠀⠀⠀⠀⠨⠗⠖⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢈⠀⠀⠀⠀⠂⠀⠀⠀⠣⠟⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠒⢤⡀⠀⠀⡇⠀⠀⠙⠓⠶⣄⠀⠀⢠⠞⠁⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠉⠉⠀⠀⠈⢳⡀⠀⡇⠀⠀⠀⠀⠀⠘⢃⡰⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠛⢦⡀⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠎⠠⠃
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⠑⢦⣌⠳⡄⠀⠘⣠⡇⠀⠀⠀⠀⢀⣾⡋⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡴⠋
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠳⣌⣂⠀⣿⡃⢀⣠⡴⢚⣉⡼⠋⠉⣧⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⡆⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣏⣻⣿⣟⠊⠉⠉⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⠁⣠⠄⠀⢠⠎⣹
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣠⢾⡿⠉⣿⡏⠀⠈⠛⠳⠶⢶⣦⣞⠁⠀⠀⣀⣀⢀⣸⠦⢤⣀⢀⡾⠃⢹⣀⠔⠃⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠱⣄⠀⠀⠀⢀⠞⣱⠋⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⡄⠀⢻⡈⠉⠀⠀⠀⠉⣿⠁⣰⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠻⡶⢢⣄⠈⠉⠐⠊⠉⣾⠁⠀⠀⠀⣿⠇⢇⠀⠀⠀⠀⠀⣀⣀⣴⠛⠳⡀⢧⠀⠀⠀⠀⢠⡿⠟⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠹⣆⠈⠓⢤⡀⠀⠀⠉⢳⠀⠀⣰⠋⣿⠸⣇⠀⠀⠀⢸⠏⠁⠀⠀⠀⠸⣾⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠙⢦⡀⠀⠈⠓⠚⠁⠀⠇⡇⠘⢳⣤⡴⠋⠀⠀⠀⠀⠀⠀⣿⣦⣄⣴⡧⠤⠔⠒⢳⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⡸⣦⡟⠈⢷⠦⣤⣤⡤⠤⠶⠛⣯⣄⣼⣁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢳⡘⡇⠰⣇⠀⠀⠀⠀⠀⠀⢀⡎⠙⢧⠉⠛⠶⣄⠀⠀⣹⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣠⠶⢚⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⣿⡸⣆⠈⠳⣦⠀⠀⠀⢠⡟⠀⠀⠈⣆⠀⠀⠈⢳⡾⠃⠀⠀⠀⣸⡧⠶⠚⠛⠋⠉⠁⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢠⡟⢃⠻⡀⠀⠛⣦⣤⠴⣟⠀⠀⠀⠀⣿⣄⡴⠓⠚⠁⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣼⠃⠘⣎⢃⠀⠀⡜⠁⢀⢿⣦⠖⠦⣤⠟⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠻⣟⠓⠒⠒⠤⢄⣀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠟⣸⠀⣴⠃⢠⡞⡼⠃⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠈⢣⡀⠀⠀⠀⠉⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⣰⠇⢠⢋⡼⠁⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⣼⠋⢠⢃⡾⠁⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠙⢷⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠏⢰⢃⡞⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡙⢷⣄⠀⠀⠀⡇⠀⠀⠀⣿⠀⢇⡸⠀⢀⡤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣧⡀⠀⢸⠀⠀⠀⡇⢸⠸⠃⡴⠋⡴⠁⢀⡤⠖⠒⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⡀⠀⠀⢣⠀⣇⠺⢀⡾⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠿⠿⠿⠿⣧⣇⠀⠀⣾⠀⢻⡇⡘⠁⡾⠶⠦⠶⠦⠤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠶⠶⠶⢶⣤⣤⣬⣿⣧⣤⣿⣴⣼⣧⣧⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠀⠉⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⠤⠄⠀⠤⠤⠤⠴⠶⠶⠄⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⠶⠦⢤⣄⣀⣀⣀⣀⣤⣤⣤⣤⡤⠶⠶⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⣇
⢀⡤⠤⣀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤
⡎⠀⠀⠈⠑⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀⢀⡴⠋
⡇⠀⠀⠀⠀⠈⠳⡀⢃⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⠞⠉⠉⠳⡋
⢰⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡿⠀⠀⢻⡀⠀⠀⠀⢸⢀⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠
⠈⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⢆⠐⠀⠀⡀⢳⠀⡇⠀⠀⠈⢱⠀⢀⠄⣸⠏⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡞
⠀⢹⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠑⢅⠀⡇⠈⣦⡇⠀⠀⠀⢸⢀⠏⢠⠃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡼⠁
⠀⠀⢳⠀⠀⠰⣄⠠⡀⢸⡄⠀⠀⠀⢸⡸⠀⠀⢻⡆⠀⢠⠀⢸⠃⢠⠏⠀⢀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢰⠃
⠀⠀⠈⢧⠀⠀⠀⠑⠳⣴⠋⠙⢦⣄⠀⡇⠀⠀⠸⡇⠀⠘⡆⣿⠀⡞⠀⠀⠀⡆⡄⠀⠀⢀⠇⢀⠄⢠⠃
⠀⠀⠀⠈⢣⠀⠀⠀⠀⢿⠀⠀⠀⠙⣆⢸⠀⠀⠀⣧⠀⠀⠱⡇⣸⠀⠀⠀⠀⠱⠀⡠⠂⣼⠖⠁⢠⠃
⠀⠀⠀⠀⠀⢳⡀⠀⠢⣽⠀⠀⠀⠀⠙⡇⡇⠀⠀⢸⡆⠀⢰⣇⠇⠀⢀⠀⢀⡧⠚⠁⢰⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⡇⠀⢤⣂⢀⠘⣷⢀⠏⢸⠹⡀⢸⣿⠀⠀⢸⠀⡞⠀⠀⢀⡏⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢹⡄⠀⠉⢾⠃⠹⡏⠀⠀⡀⠁⠈⠁⡀⠀⠀⣼⠁⠀⠀⡞⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⢷⡀⠲⣜⡄⠀⢣⠀⠀⡇⠀⣿⠂⡇⠀⢰⢃⣠⠄⡼⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢳⡀⠈⠹⣠⠊⡆⣠⡇⠀⣿⠀⢸⢀⠏⠉⠀⡜⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣦⣱⣙⣦⣫⣀⣷⣃⣇⣈⣏⣀⣀⣎⣀⣀⣾⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⣘⡄⢠⠀⠀⠀⠀⠀⠀⡄⠛⠀⠰⠀⠀⠀⠀⠀⠀⢀⠑⠾⡀⡶⠊⣁⠀⠀⠀⠰⣄⡀⠀⠀⡞⡇⠀⠀⣀⡄
⠀⠀⠀⠐⢤⡀⢹⣠⢖⠴⠂⠀⠀⠀⣀⠒⢀⡆⠀⠛⣀⠀⠀⠀⠠⣀⠙⡄⢹⢀⡞⢁⠀⠀⠀⠀⠳⡝⢆⠀⡇⡿⢠⢞⡿⠁
⠀⠀⠐⠒⠒⢿⣾⣿⣳⡤⠀⠀⠀⠀⠄⠑⣌⣿⣜⠀⠠⠄⠀⠀⠤⠤⡑⢜⣾⣎⠞⡡⠤⠀⠀⢤⣀⡙⢮⣇⣧⣷⡷⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠐⠢⢌⠢⣿⡯⢊⠴⠒⠀⠀⠀⠙⢯⣓⢽⣿⣏⣴⣒⠿⠋
⠀⠀⠀⢠⣤⣤⣿⣦⣤⡄⠀⠀⠀⠀⢠⣤⣤⣿⣤⣤⣄⠀⠀⠀⠀⢰⣶⣷⣿⣷⣷⣶⠀⠀⠀⠀⠀⢠⣬⣽⣿⣭⣭⣤
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⠀⣰⣷⡀⢠⡆⠀⣠⠀⠀⢀⣤⡜⢛⡰⡄⢐⡾⠆
⠀⢀⡙⢷⣦⡀⣿⡇⢀⣴⠞⠁⠀⢶⣄⠘⣿⣿⣿⣿⡿⣣⡄⠈⣧⡀⢺⣦⢿⣿⢦⣾⠆⣸⠇⠀⢠⣶⡍⠱⡜⣣⣣⡪⢄⣤⡄
⠀⠀⠙⠷⣯⡳⣼⣷⡿⠋⠀⠀⠀⠀⠉⠓⠈⠀⠁⠁⠘⠋⠀⠀⠘⢿⣆⠻⣾⣿⣾⠿⣴⠋⠀⠀⠀⠀⠀⠠⠝⣾⠓⠕⠈⠉
⠀⠀⠀⠀⠀⠉⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠁⠀⠀⠀⠀⠀⠈⠻⠷⣻⣿⣯⠟⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠐⢀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣄⠀⠉⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢫⠀⡤⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⡄⠶⠇⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠋⠚⡃⢀⡀⠈⠃⠀⠀⡀⠀⠐⠃⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠙⢎⠁⣿⠁⡀⠀⠁⠉⠀⠀⡄⠉⣭⡀⠀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠷⠰⠋⠑⢧⡀⠋⠀⠀⠀⠀⢠⣄⢰⣶⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠂⠀⡀⠀⢀⠄⠀⠘⠢⠤⠀⠁⢦⠀⠀⠀⠐⣯⡉⣿⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠦⠈⡃⠀⠸⠃⢠⡓⠀⠀⠆⠀⢀⡃⠀⣻⡄⠈⣧⠉⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢠⡤⠁⠀⠈⣁⠀⡟⠆⠀⠛⠀⠀⢻⠃⠈⠛⢿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣙⠀⠀⠰⠎⠁⠘⠋⠁⠴⢀⡙⠀⠶⠀⢻⠤⣀⡀⢠⡤⠴⠆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠂⠀⠀⠠⠠⠆⠐⢀⠀⠠⠙⠰⠆⣀⣼⠀⠉⠷⠀⠀⠀⠀⡠⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣀⠰⣌⣀⣧⡄⠀⠀⠀⠁⠈⠱⠋⠀⠀⠀⠈⢻⣆⡀⠶⠛⠚
⠀⠀⠀⠀⠀⠀⠈⠁⠋⠙⠿⢁⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡏⠠⠆⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠒⣰⠃⣠⣄⠀⠀⠀⠀⠐⡃⠀⠀⢸⣬⡅⠈⠓⢀⠀⢰⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⢀⡀⠶⣧⣄⣻⠀⠀⢠⡶⠀⠈⠁⠀⠀⣸⠉⠀⢮⠁⣄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡏⠶⠚⡻⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠁⠸⠐⢶⣋
⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠶⢄⠶⣀⠤⢨⠗⠀⠀⠀⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠛⢁⡀
⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃⠒⠀⠀⠟⠀⠀⠀⠹⠥⡶⠄⢀⣖⣠⠟⠛⠁
⠀⠀⠰⣿⡃⠀⠀⠀⠀⠀⠀⢒⡀⠠⡐⠆⠀⡀⣾⠃⠀⠠⠀⠲⠀⠀⠠⠈⢙⣁⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠘⢣⡄⠀⠀⠀⠀⠀⠀⠀⢂⣤⠘⠢⣤⠀⠀⠀⠄⠀⢀⠀⠀⠲⡶⠆⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⢀⣄⠙⠀⠀⠀⠀⠀⠀⠐⣿⣿⢀⣤⠘⣀⠰⠂⡄⠀⣼⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠐⢶⠀⢠⣦⠀⠠⣌⠛⣤⡿⣀⡽⢃⡀⠀⢰⠇⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣅⠀⠀⠙⠻⣿⣾⡏⠀⠁⢄⠀⡜⠀⠘⠀⠀⠀⠀⠀⠀⠀⠰⠀⣴⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣤⣠⡀⠘⡿⠀⠈⠀⠀⠰⡇⢀⠃⠀⠀⠀⣀⣦⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢺⣷⠀⠀⠀⠀⢰⣦⠀⠠⠐⠚⠛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣴⠀⠀⠀⢈⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠘⠻⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠈⢰⡞⠀⠀⠀⠐⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢄⢸⡇⢀⣾⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡆⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢡⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⢾⣋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⣲⢤⡀⠹⣿⣧⣿⣿⢃⣤⡖⣲⣶⣔⣦⣄⡀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣾⣷⣤⣿⣆⣿⡦⡈⠻⠛⢡⣾⣻⣷⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⣿⣧⣤⣴⣶⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠓⢦⣤⣝⠙⡻⣿⣿⣷⠀⠂⢸⣾⡟⣡⠇⠀⠀⠀⠀⠀⠀⠐⡄⢀⡆⢾⣧⣴⠛⠋⠀⠙⠻⠿⠿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠷⠤⠽⢿⠀⡔⠐⡯⠖⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⡴⠏⠓⠀⠀⠀⠀⠀⢀⣠⠆⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⢀⣀⠀⠀⠀⣀⢈⣡⣶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣄⣀⣀⡀⠀⢄⠀⠀⢀⠂⠀⠀⢀⣸⢉⣉⣠⣼⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣲⣦⣽⣦⡐⣤⣄⣠⣤⣄⠀⠀⠀⠈⣷⡿⣿⣿⣿⣷⡶⠦⢱⣦⣼⣿⣍⣶⡾⢿⣿⣿⣿⣗⣾⠗⠲⣤⡀
⠀⠀⠀⠀⠀⢀⢐⣿⠟⠩⠤⠤⠈⣉⡛⢿⣼⣿⣿⣿⣿⣿⣆⡀⠀⣼⣿⠟⠻⣿⣿⣧⡀⡟⠓⡛⢉⣠⣤⣴⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣦⡤⠄
⠀⠀⠀⠠⠖⠋⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡉⠋⢀⣰⣾⣼⠏⠀⠀⠉⢹⣿⣾⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠑⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⠉⠉⠁⠀⠀⠈⢹⣽⠏⠁⠀⠀⠀⠀⠀⢻⡿⠟⠋⠋⠩⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠷⣄⠀⠀⠢⢤⣬⣵⣏⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣄⣀⠉⠉⢉⢉⣁⣀⣹⣧⡀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⠙⠿⡿⢻⡿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⣠⣿⣿⡇⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣱⣶⣿⣿⣿⣿⡇⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡠⠀⣀⢀⣀⠀⣀⣠⠔⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠛⠿⣿⣿⣿⣿⣇⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⡿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⡅⢶⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣇⠀⠀⠟⠁⣸⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣿⣿⣿⠀⣿⠀⣆⣀⡤⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢿⣿⣧⢰⠦⠟⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⠆⢸⣿⣧⠈⣠⠚⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⡟⣋⣨⡽⠿⠛⣿⣿⠗⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣏⣻⠟⣿⠀⠶⠂⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠈⢿⣷⡶⡄⣄⠒⣘⣋⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⣏⣤⣤⢰⣂⣭⣿⣿⣿⣷⠶
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠏⠀⠈⠙⠋⠛⠛⠋⠉⠁
⢀⠙⠉⣠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⡀⠀⣿⣰⣿⠄⠀⠀⢀
⠀⢱⡶⢼⡧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⢙⣟⣁⡤⠂⣠⡎
⠀⠈⠃⡤⠛⠀⠈⠁⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⣿⣿⡿⠛⠁⡤⣨⠏
⠀⠀⠀⠀⠀⣤⡄⢳⢀⡟⠀⠀⠀⠀⠀⠀⢠⡌⢻⣄⠙⣿⣿⣧⡾⠟⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡈⠃⠎⠀⢠⠀⠀⠀⠀⠀⣿⣿⣄⢿⠀⡞⠉⠀⣀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⡞⠀⠀⠀⠀⠘⣿⣿⣿⣧⣷⢁⣶⠈⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠁⠀⢀⡰⣤⡀⣿⡿⠙⢿⡿⠈⣳⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡄⣠⠛⢱⡍⢿⣾⠃⡀⠀⢀⡾⣥⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡆⣿⣀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣯⣄⠀⣤⡈⣿⡀⢲⠀⢸⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣄⠀⠀⢿⡍⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣉⢈⡉⠀⠘⠿⠻⣷⢸⣦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢿⣿⣦⡀⠀⢿⣿⠋⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣧⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡇⢸⠟⣿⣿⠇⠀⡏⣀⢃⡼⠃⠀⠀⠀⠠⣀⠀⠀⠀⠐⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠊⠀⠈⠻⠀⠆⠘⣿⠚⠁⠀⠀⠀⠀⠀⠙⢷⡌⠀⠰⡀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⢠⡇⠀⢺⣇⠀⠉⠀⠀⠀⠀⠀⠀⢀⣿⣤⣹⣦⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠁⠀⠀⣿⡄⠄⠀⠀⠀⠀⠀⠀⠈⢻⡉⣿⣿⣀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢰⠀⢠⡆⢸⣇⠀⠀⠀⠀⠀⢀⡴⠀⢾⣇⣡⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢲⣤⣄⡀⠀⠙⠷⣦⠸⡇⠘⡟⠀⠀⢀⡦⢀⠈⠁⠀⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣌⡳⢦⡄⠀⠘⠇⠀⠀⠀⢐⣈⢰⣷⠐⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠻⢿⣿⣷⡆⢰⡇⠀⠀⣴⠿⣿⠀⢻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⢿⣇⣘⡁⢉⡼⢁⣤⣿⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⢀⠙⢿⠁⢩⡄⢸⣏⢉⢡⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠈⡀⣼⡇⢸⣿⡤⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⢘⣷⠘⡇⢠⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⢀⡟⠀⠀⠀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⣿⡆⠘⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢎⣿⡄⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠛⠛⠛⠛⠛⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⢀⣤⣴⡶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣞⣛⣫⠭⠭⠭⠭⠭⠭⣍⡽
⢀⣤⢞⡝⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢶⣄⣠⣴⣾⡿⠿⠛⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⣀⡴⣡
⣿⣧⢍⣔⣂⣀⣐⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠬⠤⠒⣾⡯⠓⠉⠁⢀⣤⣶⣾⡿⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠋
⢸⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⡿⠛⠉
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⢞⡿⠋
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣾⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠘⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁
⠀⠹⣮⡻⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠈⠙⠷⢧⣴⣂⣤⠩⠭⠍⠀⠀⠀⠀⠀⠀⠅⢀⣀⣠⣤⡶⠟⠋

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⢀⣿⡄⠀⠀⠐⣄
⠀⠀⠀⠄⡀⠀⠀⠂⣤⡀⠘⣿⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠫⢝⣶⣄⠀⠀⠀⠀⠀⡖⠀⢹⣿⠀⢠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⢀⡀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠙⣆⠀⢀⠀⣱⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠖⠀⠀⣠⠀⠀⠀⠀⠁⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⠙⠇⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠁⠀⣀⣤⣤⣀⡀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⠀⠰⡀⠀⠀⠀⠀⠀⣠⢎⡕⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠳⡀⠀⠀⠀⡴⢡⠎⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠻⡲⢄⠀⠀⠀⡠⠜⠀⡿⠀⠀⠀⢱⠖⠑⠋⣰⠏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⠢⡱⣄⠀⡇⠀⠀⣇⠀⠀⠀⢘⠀⠀⣰⠏⢀⣄⠀⣙⠀⠀⠀⠀⣀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⢮⡑⠋⠳⠀⣿⠀⠀⣀⠜⠀⢀⡟⡰⡟⢠⠀⢧⠀⢀⢔⡫⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠳⣄⠀⢇⢹⡀⢸⠀⠀⠀⣸⠏⡜⢀⡜⠀⡰⢟⡵⠋⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢦⣀⠀⠙⣆⠈⠛⠧⡀⣇⠀⢀⡏⡼⠀⡜⡔⠉⣴⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠻⡳⡄⠘⣧⠀⠀⢃⡸⠓⠊⡼⠁⠀⢧⣹⡾⠁⠀⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⡀⠀⠀⠀⠘⢆⠘⢮⢢⣘⣧⠀⢘⡂⠀⣸⠃⠀⠀⣸⡟⠁⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠛⢕⠢⣀⠀⣸⠀⠈⢳⡄⠈⣧⣿⠇⢀⡏⠀⠀⠀⢻⠀⠀⠰⣋⡠⢄⡶⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠙⢮⡉⠉⢄⠀⠀⠹⡄⠸⡉⠀⣸⠀⠀⠀⢀⡼⠄⠒⣋⡵⠚⢁⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠙⢦⡎⠀⠀⠀⠹⡄⠈⠱⡇⠀⠀⣰⠛⢁⡴⠞⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⢻⡖⢤⡀⠀⠹⡄⠀⡄⠀⠀⢱⣴⠋⠀⠀⠀⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⠆⠀⠀⠹⣤⡃⠀⠀⢳⣸⠃⢀⣴⠟⠁⠀⠀⡔⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠖⠒⠀⠛⠘⠒⠀⠘⠛⠚⠃⠛⠂⠐⠒⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡀⠀⠀⠀⢀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠙⢦⠀⡠⠊⠉⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠳⡄⠀⠀⠀⣀⣹⡀⠀⠀⠀⠀⣠⣯⡤⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠉⠓⢿⣦⠾⠛⠉⠉⠉⠛⠶⣤⠞⠋⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⣼⠇⡴⠒⠲⡄⠀⠀⠖⠉⠱⠌⣧⣀⣤⣤⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠁⢹⡄⠀⠠⠀⠀⠀⠀⢀⠆⠀⢠⡏⠉⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠉⠀⠀⣠⠞⠀⠀⢀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡀⠀⣀⣠⢶⡟⠉⠳⠤⣤⣤⣤⠴⠚⠙⢷⣤⣀⠀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⡏⠀⠀⠀⠀⠀⣿⠀⠀⠦⠀⠀⠻⡌⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣰⢿⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣠⡴⡏⠀⢳⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡸⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡰⠁⢀⡠⠖⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢼⣡⠞⠁⢀⡆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠉⠒⠢⢄⡀⠀⡎⠀⡿⠁⣀⠴⠋⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢀⣀⠈⠲⡇⠀⣿⢋⣉⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣈⡉⠓⣇⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢒⣙⠛⠟⠣⣤⣉⣿⣍⣭⣭⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠁⠉⠉⠉⠈⠀⠀⠀⢠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠉


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⢧⢀⡖⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣸⡄⠀⠀⢸⡟⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠙⢦⣤⣾⠀⣀⣤⣾⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣤⣤⠤⢾⡀⣸⡏⠉⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢠⠞⠉⣇⠈⠓⢦⡤⠴⠋⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⣤⣀⡈⠧⠤⢶⠋⠀⠀⣿⡀⠀⠀⢹⠖⠋⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠉⠓⢦⡘⢦⣄⣴⡏⠛⡶⠒⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠙⢦⠀⢠⣇⡞⢁⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠛⠛⠛⠛⠓⠚⠛⠛⠛⠓⠒⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡍⠉⠉⠉⠉⠉⠉⠉⢉⡽⣿⡥⠚⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⣀⡤⠖⠋⣠⣿⢿⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠛⠋⠉⢁⣠⡴⠚⣹⠙⣆⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠒⠒⠋⠉⠀⠀⠀⡏⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⠿⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣍⣉⣉⣉⡉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣴⣿⣶⣤⣰⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠷⢦⣄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢿⣿⠋⠉⢻⡿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠻⣤⣄⢸⡇⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠉⢸⡏⠀⠈⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠗⠒⣤⠤⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡫⠖⠋⠉⠓⠆⡀⠀⠒⠖⠒⢦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡤⠖⠒⠓⠀⠀⠀⠒⠒⠢⢄⡀⠘⡖⠂⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠶⠤⣉⠛⡇⢠⠏⠀⠊⣠⠄⠀⠂⢀⣙⠓⠢⡀⠱⠀⡷⠀⠁⠒⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⢀⠒⠲⢄⠘⠃⣱⡸⠀⠁⡞⠀⢀⠀⠀⠀⠈⠳⡀⠹⠀⣸⠇⠀⢀⠱⡄⠰
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠺⠀⠤⠀⠈⠀⡀⢀⡄⣠⠱⣄⠸⠄⠀⠋⢀⠀⠐⡂⠀⠇⣀⡼⡡⠂⠀⠈⢆⡔⠁
⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⢀⡀⢠⠆⡼⢁⢋⡀⣧⣀⡀⣹⠦⢤⡀⠜⠀⠀⢁⡤⠚⡁⠤⠴⣦⠀⢐⠋⠐⢐
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠋⠀⠇⠘⡥⢊⠁⠀⠀⠠⠄⢱⠀⠀⠈⠳⣴⠞⠁⢰⠁⡜⠀⠞⠁⠐⠀⡄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠁⠠⠀⠀⠒⠀⡠⠊⣈⢉⠳⡄⠈⠀⡆⠸⠀⠁⡀⠤⡤⣔⠈⠐⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠒⢀⠊⠐⠆⠘⡆⠁⡇⠀⠀⠙⣶⠀⠉⠉⠆⠀⠘⣠⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⠀⡀⢠⠇⡠⠃⠀⢀⠀⡙⢠⡀⣀⠤⠶⠋⠐⠉⠥⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠇⠼⠐⠃⣀⠔⠁⠀⠀⡈⡐⠀⢑⡤⢀⡄⠀⡄⠠⡀⠤⡀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠂⠙⠌⠀⠘⠠⣰⠠⢁⠔⠘⢧⣈⠀⠀⢋⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠐⣞⣶⣒⣿⣳⠃⠒⠀⠤⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠘⡛⠛⢛⠛⠛⠛⢛⠛⡉⡉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡏⢰⡁⠘⠈⠀⠀⣀⠀⠸⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⢣⡄⠃⡀⠘⢠⡄⠉⢶⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠨⠠⠄⠁⠠⠀⠀⡄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠸⢄⠀⠶⡀⠐⠇⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⣀⠀⡀⣀⣠⣦⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⢀⣠⣤⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⢹⣇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠟⠛⠛⠛⠛⠛⠛⠛⠻⣶
⣤⣾⠋⢡⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠠⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⢀⣀⣤⣶⡶⠶⠞⣩⡿⠋
⠈⠉⠐⢦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠶⣶⣄⡀⠀⠀⡙⢿⣄⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⣰⣤⣴⣾⠿⠉⠉⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⣀⠀⢻⣆⠀⠀⠀⢿⣷⠀⠀⠀⣰⡿⠋⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⣶⣄⢻⡄⠀⠀⢸⣿⠀⠀⣼⠟⠀⠀⣠⣾⢛⣁⣀⡤⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⢸⣿⠀⣼⠏⠀⣰⣿⠟⠓⠉⠉⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠺⢿⣦⡀⢸⡇⢠⡟⢠⣾⠟⠁⠀⠀⠀⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣸⡇⠘⣷⣿⣃⣤⣴⣶⡶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣰⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⡶⠶⠶⢾⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠟⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢶⣦⣤⣀
⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀
⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢻⡇
⠀⠀⢸⡇⠉⠛⠻⠷⢶⣶⣤⣤⣤⣤⣴⣶⣾⣛⣛⣛⠛⠉⠉⠉⠉⠉⠉⢹⣏⣿⠉⠉⠉⠉⢛⣛⣛⣛⣻⣷⣶⣦⣤⣤⣶⣶⠾⠟⠋⠀⠀⢸⡇
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠻⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠏
⠀⠀⠀⠀⠀⠉⠉⣿⠳⠶⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠶⠶⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢌⣆⣥⣙⣖⣠⡄⡀
⠀⠀⠀⠀⠨⠀⡆⡄⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠛⠟⠛⠻⡛⢟⡄
⠀⠀⠀⠢⡀⢻⡂⠅⢹⢀⠎⠁⠀⠀⢀⠀⡇⠀⠀⢀⠀⠀⠀⠀⣀⣀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⡃⠐⠈⣰⠕⣸⠀⣀
⠀⠀⠀⠀⠙⢮⢧⣾⣧⣃⠀⠀⠀⠀⠀⠁⠄⡀⠈⡈⠀⠠⠄⠀⠉⠉⠀⠀⠈⠀⢀⠀⠀⠀⠠⢰⠆⠀⠢⠀⠀⠀⠤⢖⠀⠀⢀⠏⠩⠞⠂⠇
⠀⠀⠀⠀⠖⠲⡷⠟⠋⢉⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⢀⣨⢀⡀⠂⠀⠈⠇⢻⠆⠰⢀⠀⠈⠘⠒⠶⠨⠄⠐⠻⠄⠂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠈⠆⠀⠈⠄⠢⠊⠁⠀⠀⠀⠈⠀⠀⠉⠁⠀⠎⢃⠂⠀⡀⠈⢰⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⡶⠿⠄⠀⠐⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢹⠄⢀⠁⢀⡀⢘⡇
⠀⠀⠀⠀⢀⡀⠀⠙⡆⠀⠀⠀⠀⠀⠠⠤⠄⠀⡀⡀⠠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠦⠬⠼⡾⠠⡎⠀⠀⠀⠀⠴⠀⡀⠀⠈⠓⣄
⠀⣄⠀⢀⠈⡉⠁⡄⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢲⠇⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠈⠂
⠀⠈⠉⠀⠐⠢⢂⠀⠀⠀⠀⠘⠀⠀⠀⠰⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⣀⡆
⠀⠀⢤⡀⣀⠀⢸⠀⠆⠀⠀⠠⡀⠀⠀⠀⠀⠂⠀⣀⣥⣶⣾⣿⣿⣟⣿⡿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠃⠀⠀⠀⠠⠈⠉⠉⠉⠉⠉⠉⠉⣹⠁
⠀⠀⠀⠀⠀⠨⢍⡂⠰⠄⠀⠀⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠀⠀⠀⠀⡤⠁⠠⠀⠀⠌⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡷⠀⡆⠠⠤⡀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠐⡄⠀⠰⢄⠈⠀⠂⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠳⣄⠀⠘⡄⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠁⠣⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠈⠑⢶⠁⠀⠈⠀⠋⠀⢀⠀⠲
⠀⠀⠀⠀⠀⠀⢓⠘⡍⠀⠀⠀⠀⠀⣀⠴⠂⠀⠀⡄⢢⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠐⠄⠆⠀⠁⠂⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠤⠤⠧⠤⡄⠀⠀⠨⣁⡀⡐⣀⢀⣀⣀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠄⠀⣠⣤⢜⡄⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠃⠀⠀⠀⢉⠉⠉⠉⠉⠉⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⠀⡀⠀⠚⢀⠀⠀⡀⣄⣸⠁⠉⠈
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠑⠀⠀⠀⠔⠋⠀⠄⠀⠀⡀⠀⠀⠠⡄⠀⠀⠀⢀⡀⣁⠀⠀⠠⠀⢰⠀⡇⠀⠀⠀⠀⠀⢀⣠⠶⠒
⠀⠀⠀⠀⣀⠀⠑⠒⠂⠒⠃⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠘⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠠⡑⡀⠀⢀⠎⠀⣷⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠰⢤⠦⠀⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⣿⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠠⠄⡀⢀⡈⢀⠀⢁⢰⣀⣀⡒⣀⠃⣠⣤⢀⣀⠂⠀⣠⢊⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠈⠉⠉⠉⠀⣀⣨⠃
⠀⠀⣀⠀⠀⠐⠉⠙⠉⠉⠀⢈⡿⠿⡉⠉⠉⢿⡏⠉⠋⢻⡟⠉⠉⢿⣿⠁⠀⠈⣷⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣸⡇⠀⠨⠀⣀⣾⡁⠀⠀⢾⣧⢀⡀⢸⣿⠀⠄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣀⣈⣉⣀⣻⣿⣓⣀⣀⣸⣿⣇⣀⣀⣹⣿⣀⣈⣿⣿⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠑⢄⡰⠀⠐⠢⡀
⠀⠀⡀⠔⠐⢄⡠⠊⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠤⠥⢄⠀⠀⠨
⠀⠐⠀⠀⢀⠠⠥⢀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡠⠀⠃⠀⠁⠀⠀⠀⠑⠈⠑⠢⡀⠀⡀⡀
⠀⡈⠶⠠⠁⠀⠀⠀⠃⠀⠓⠒⠄⠀⠀⠀⠀⠄⠀⠀⠀⠱⣀⠀⠀⡠⠀⠀⠀⠜⠁⠀⠈⢂⡔⠈⠐⢄
⡎⠀⠀⠠⡀⠀⠀⡠⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠢⠄⡴⠆⠀⠈⠉⢒⠂⠤⠔⢣⠀⠀⠄⠒⠠⡀⠀⠀⡁
⠰⣀⢀⡠⠌⠀⠉⠀⢐⠦⠀⠊⠀⠀⠀⠀⠀⠀⠀⡔⡐⠡⡀⠀⠀⢈⠀⡐⠈⠉⠁⠈⠀⠀⠀⠈⠂⠚⠤
⠀⢀⠀⠀⡆⠀⠀⠀⠌⠡⡑⣄⠀⠀⠀⠀⡀⢀⢀⢀⣓⠬⡙⠅⠀⠁⠀⠰⡀⠀⠀⠈⠆⡀⠀⣀⠂
⠀⠀⠁⠀⠀⡒⠀⠝⡡⠈⠁⢈⠰⢢⠃⠂⢬⠢⣘⢸⠀⠀⠈⠉⠀⢀⢀⠔⠉⢂⠞⡇⠀⠀⠀⠐⠠⢀⡠
⠀⠀⠀⠀⠀⠈⠺⡋⠀⠀⠀⣨⠔⠁⡘⠢⡀⠙⢬⠘⠠⡈⠀⢄⠔⡡⠀⠀⢠⢁⡊⢡⣀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢈⠢⡀⠀⠁⠀⠀⠀⡐⠉⠄⠈⢰⠀⠈⠢⠂⠐⠐⢄⠢⡄⠈⡑⢠⡹⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠀⣀⣤⠀⢀⠀⠀⠀⡄⠸⣀⡐⠁⡜⡄⠈⢀⠱⢤⠎⠠⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠂⠻⠭⠀⣔⢂⠀⠀⡃⣀⡙⢀⡘⠐⣚⣀⠨⠬⠶⠐⢂
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠈⠉⠀⠀⠐⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢫⣟⢹⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⡏⠘⠉⡇⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇⠀⠀⡇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣏⢿⡆⢀⠀⢳⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⠀⢿⣏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡟⢸⡇⢸⠆⢸⡇⢠⡇⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠙⠀⣿⠆⢸⡟⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢼⠃⠘⠋⠈⣷⠀⠀⠀⣠⣾⣶⣥⣆⡀⠀⠀⡆⢸⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⠈⣶⡷⢀⡿⢻⠃⠀⢀⢛⣹⣿⣿⣿⢣⡄⠀⠁⣼⠙⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⢸⣏⣠⣍⣠⣀⣠⣆⡀⠀⢻⣿⣿⣿⣿⣉⣿⡇⣄⠀⣿⠠⠄⣼⠇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠸⣿⡟⣿⣿⡿⣿⠟⣧⢀⡈⣿⢻⣿⢻⡏⢿⡷⠏⠀⡿⠀⠀⣿⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢼⣠⣿⢻⠉⡟⠀⠏⢠⠉⣾⣿⣿⢸⣿⢻⣷⣼⡇⠀⢠⡆⠀⠀⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⡿⢸⠻⡇⠀⠀⠆⡀⢻⡏⡟⢸⣿⢸⣿⣹⣷⡀⢾⠀⡀⢠⡟⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠸⣿⠇⠀⠰⠇⠘⠀⠀⠁⠘⣿⡇⣻⣿⣾⣿⣦⣤⣤⣿⣤⡃⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣿⠀⠳⠀⡆⠀⠀⢠⠀⠀⢿⡇⣿⣿⣟⢹⡿⢻⣿⣿⠙⢷⣿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⡇⠀⠀⣇⠘⠀⢸⠀⡄⢹⣷⣿⣿⡏⣼⠁⠚⡷⢸⠁⣼⣿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡆⢰⠀⣿⠀⠀⢸⠀⠁⢸⣿⣿⡇⠀⡿⢠⡄⠇⠸⠀⡇⣿⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢨⠀⢹⠀⠃⢸⣆⠀⢸⣼⣿⣷⢠⡅⠀⠉⡆⠀⠀⡁⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⡀⢸⡅⠀⠈⣿⠀⢸⣿⣿⣇⠈⡃⠀⠀⡀⠀⠸⣇⣿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢳⠘⣇⠀⠀⣿⠀⣘⣻⣿⣿⠀⡁⠀⣴⠁⠀⠀⢻⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⡆⢹⠀⠀⣿⠀⢿⣿⣿⡟⠀⠀⠀⠿⠀⢀⡄⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⢳⠀⣷⠀⡿⠀⢸⣿⣿⣷⠀⣀⠀⣿⠀⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠉⠰⣇⠀⣾⣿⣿⣿⠂⣨⠀⣿⡀⢴⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣧⠈⣰⠇⣸⠀⢿⣿⣿⣿⡇⣿⢠⡿⢁⣾⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⣿⣿⣿⣇⠁⡼⢿⣡⣾⣿⣿⣿⣷⣥⣾⣷⣾⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⡾⠷⠞⣋⣉⣩⣛⣿⣟⣛⣋⠛⠛⠛⠛⠛⠿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠛⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢶⣦⣀⣠⡤⢤⣤⢤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⣿⣟⢙⡓⢺⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣿⣿⣇
⠉⠹⠿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢧⠀⠀⠀⠀⠀⠀⠀⠸⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠘⡆⠀⠀⠀⠀⠀⣤⣀⠈⢹⡀⠀⠀⣀⣄⠀⠀⠀⣠⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⣠⠃⠀⠀⠀⠀⠀⠘⣎⠑⣄⣧⠖⠉⣠⠃⠀⠀⢸⢡⢢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⢀⡴⡆⠀⠀⠀⠈⠢⣼⣿⠤⠞⠁⠀⣤⣄⠘⡾⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⠒⠢⢼⣀⠎⢰⠇⠀⠀⢲⠦⡀⢰⠃⣀⣀⣀⡀⠘⣌⣣⡷⠚⢉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣢⣽⡶⠋⠀⣠⡀⠈⢧⣽⣾⣟⣋⡠⠞⢱⢦⡈⡹⠋⠙⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⣄⣀⠀⢳⣠⡞⢹⠃⡺⢆⡟⠉⣉⠀⠀⠀⠸⣀⣷⡟⠩⢉⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠝⣾⣿⠖⠁⠀⠹⣾⢟⡭⠟⢠⣤⠀⢀⡜⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⡇⠀⢿⠲⣄⡏⢀⣠⠀⢸⢘⣧⣎⡤⢤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣒⣚⣲⡇⠀⠘⢦⣸⣷⣩⠞⠀⠈⢻⠿⠤⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣧⠤⠤⠤⠬⣧⠤⠤⠤⠤⡿⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠱⣦⣬⣽⣿⣯⣭⣭⣿⣭⣽⣿⣿⣿⣿⡷⠆⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠛⠙⢒⠒⠒⠒⠒⠒⠒⡒⠚⠛⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡀⠀⠀⠀⡇⠀⡇⠀⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⠀⡇⠀⠃⠀⡇⠀⡇⢸⠀⠸⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢼⣄⣤⣀⣇⣀⣇⣨⣤⠶⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡍⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⡲⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⡇⠀⠀⠀⠀⠀⣠⢊⠜⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⡀⠀⠀⠀⠀⠀⠀⡸⢸⠁⠀⠘⢄⠀⠀⢀⡔⣡⠏⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠫⡲⣄⠀⠀⡠⠚⠁⢸⠀⠀⠀⢸⡏⠉⠁⣰⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢮⡳⣄⢱⡀⠀⢻⠀⠀⠀⠀⡇⠀⢰⠇⣠⡦⡀⡸⠀⠀⠀⣀⣤⠖⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠙⣎⠉⠈⢆⢸⡄⠀⡤⠜⠀⢀⣏⢔⡟⢠⠃⠳⣄⡠⣪⠗⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⢳⡀⠘⣜⡇⠀⡆⠀⠀⣸⢏⡞⢀⠎⣀⠔⣩⠞⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⢶⣄⠀⠹⡄⠈⠙⢢⠱⡀⢀⢏⡞⠀⠘⢎⢀⡾⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠫⡳⡄⠹⣄⠀⠘⡔⠁⠁⡼⠁⠀⢸⣴⠟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠳⢶⢄⡀⠀⠀⠘⡄⠙⢎⠢⠿⣆⢰⡽⠀⣸⠁⠀⠀⣸⠏⠀⠀⡠⠔⠊⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠙⠮⡓⢤⡤⣇⠀⠈⢳⡀⢸⡾⠇⢀⡇⠀⠀⠀⢙⠀⢀⣨⠦⣒⠽⠋⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⣄⢘⠄⠀⠀⢳⡀⠳⢤⣸⠀⠀⠀⣠⠞⠉⣡⠴⠋⠁⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⢾⣄⠀⠀⠀⢳⡀⠀⡇⠀⠀⢸⠁⣠⠞⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣄⠀⠀⢳⡍⢢⠀⠀⢳⠀⡇⠀⢀⣴⠟⠁⠀⢀⣀⣀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢤⣀⡀⣹⡗⣄⡀⢈⣷⣅⡔⣻⡃⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠈⠁

⠀⠀⢠⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢶⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⣤⣤⡤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠩⠖⠂⠀⠀⣚⡧⠄⠀⠀⠀⠀⠈⠀⠲⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣶⠦⢴⠀⠀⠀⠀⠀⠀⠈⢨⣖⡀⠀⠀⠠⠄⢀⠀⠤
⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⡀⠈⠡⠀⠀⠀⠀⠀⠈⠀⠀⡄⡄⣀⡠
⠀⠀⢧⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⢿⠀⢄⢢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠤⡀⠀⠀⠒⢝⠄⠁
⠀⠀⠀⠸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢠⠀⠈⡀⠤⠀⡐⠀⠀⢀⠀⠈⡀⠈⢀⠀⡀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠈⢀⢂⠀⠃
⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠶⠀⣦⠀⠀⠀⠀⠀⠀⠾⣸⡜⣯⣗⢯⠵⡆⠀⠀⠀⠀⠠⠒⠤⡀⠀⠀⠀⠀⠀⠳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠁

⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⡄⣤⠡⣶⣦⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠼⣠⡎⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⢿⣿⣧⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡁⢹⡂⡈⢀⠎⠀⠀⡁⠀⠂⠀⠐⠀⠀⠐⡘⡿⢰⠀⢀⠂⠀⠀⡄
⠀⠐⠲⣄⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠆⠀⡄⠀⠰⠁⠀⠀⠐⠀⠀⠀⢀⡙⢦⣾⡣⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⢳⡁⠀⠀⠀⠀⢈⡗⠈
⠀⠀⠀⠴⠆⠋⠀⠀⠀⠀⠀⠀⠄⠠⠀⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠡⠒⠻⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⢀⡴⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣧⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢈⡿⠯⠭⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣷⣾⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠶⣄⣼⢉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠼⠷⢾⣿⡭⠵⠛⠓⢲⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠛⠛⠓⠚⠓⠒⠛⠛⠋⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⣀⣀⣀⣠⣤⣤⣤⡤⢤⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⣀⣀⣀⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢈⠀⠘⢦⣀⡀⠀⠀⠀⣠⠞⠁⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠔⠋⠉⠻⣆⠀⢸⠀⠀⠀⠈⠙⣦⠀⡼⠁⠀⠀⠀⠀⠙⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠙⡄⢸⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠜⠁
⠀⠀⠀⠀⠀⢀⡶⠋⠉⠛⠦⣙⠢⡀⠀⢱⡘⠀⠀⠀⠀⣠⣿⢁⠀⠀⠀⠀⠀⠀⠀⡇⣰⠏⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⣝⣆⣸⣏⣀⣤⣖⣊⣥⠞⠉⣳⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠃⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⢈⣹⢿⣭⠿⢇⣉⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠚⠀⠀⠀⢸⡠⡖⠀⡴⠋⡷
⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⢀⣔⡽⠋⠨⣿⡀⠀⠈⠉⠛⠛⠻⣤⠀⠀⡶⢦⡴⠛⠒⢦⣴⠋⢠⡴⠊⠀⠀⡇
⠀⠀⠀⠰⣤⡀⠈⠳⠄⣀⠴⢫⠞⠀⠀⢠⣿⠧⠀⠀⠀⠀⠀⠀⢈⡷⣄⢹⡀⠀⠀⠀⢀⣿⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠹⣌⠓⢦⡀⠀⠀⠻⢦⠀⠀⡸⣿⠰⣆⠀⠀⠀⢴⠚⠋⠀⠈⢣⡇⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠙⢢⡀⠀⠘⠷⠾⠁⢀⡷⠙⢦⣤⡴⠃⠀⠀⠀⠀⢘⣧⣀⣠⣎⡀⠴⠖⢆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⣼⢣⡟⠘⡷⢤⣤⣤⡴⠖⠻⣧⣼⣇⡀⠀⠀⠀⢦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⣎⢇⠸⣇⠀⠀⠀⠀⠀⡰⠁⠹⡄⠉⠳⣄⠀⢨⠀⠀⠀⢠⠁⠀⢀⣀⣀⣀⡀⠴⠖⢛
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣹⡞⣄⠀⢹⡀⠀⢀⣼⠁⠀⠀⣾⠀⢀⣈⣿⠁⠀⢀⣠⠞⠂⠉⠁⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⡏⢰⢸⠆⠀⢹⠟⠋⣵⣀⣀⡀⣽⠓⠋⠉⠁⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢶⡶⠤⣤⣄⣀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠸⡀⣼⠁⠀⡏⣦⠀⡞⢀⣼⣳⠋⠀⠙⠁⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜
⠈⠳⣄⠀⠀⠉⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⣷⡏⠀⠀⠀⣿⡼⢁⠞⣼⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠈⠳⣤⡀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢸⠇⠀⠀⣄⣿⢁⠎⡼⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⠀⠙⠳⠤⣀⡀⠙⢦⡀⠀⠀⠀⢸⠀⠀⠀⣿⢁⡞⡜⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣿⣦⡀⠀⢸⡄⠀⠀⡇⣈⢷⠁⣠⠖⡟⠁⢀⣀⡀⢤⡤⠄⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠘⡀⠀⠀⢇⢹⡀⡜⢡⡞⣠⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣽⣦⡉⠀⠀⡼⠘⣷⢀⠋⣸⣧⡄⢀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠦⠤⣤⣤⣄⣈⣿⣧⣀⣧⣤⣿⣸⣰⣅⣀⣀⣀⣀⣀⣭⣭⡶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠦⠦⠤⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠲⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⠴⠖⠛
⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⠿⠿⠿⣿⣿⡿⠿⠿⢿⠿⠿⠿⢿⡿
⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡾⠀⡔⠂⠒⢦⡎⢉⡆⠀⡀⠀⠀⠀⢀⣠⡤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⢰⠃⡠⠜⠲⢦⣼⣳⢏⣀⣀⠜⣠⠔⠋⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡷⠃⠀⠙⢒⠞⠉⢉⡄⠀⢘⠀⡜⢁⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⡾⡆⠪⣄⣠⠞⠙⠖⠁⢀⣴⠶⠚⠉⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠳⣄⣀⣀⠀⠈⡇⢸⢰⠇⠀⠀⣴⡀⠀⣗⢠⠊⠀⣀⡠⠤⢄⣸⠀⢸⣆⠤⠠⡄⠀⣀⣠⠤⠔⠒⠒⠒⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠉⠙⠳⣤⣀⣟⣠⣔⡁⠀⢳⡘⠏⠀⢀⡜⠁⡇⠀⢸⡇⠀⠸⣥⣤⣠⡤⠾⡷⢮⣡⡤⠖⣡⣞⠅⠀⠀⢀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⠶⠚⠛⡶⠚⢧⡈⠉⢢⡈⢧⡀⠀⡞⢀⢠⠇⠀⣼⢀⢿⠀⠀⣔⠁⣠⠾⢤⡼⠅⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠚⠻⠤⠼⠋⠒⠚⠁⠺⣧⠀⠳⣼⠇⠀⠀⡟⠈⢸⠀⢀⡼⠋⡡⠒⢁⠤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠛⠺⠫⣍⣉⠙⠲⡌⢧⠄⠘⠇⠀⠐⠓⢘⠃⡰⠛⠠⠞⣤⠞⡥⢚⣁⣠⡤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠐⠉⠀⠀⣀⣈⠷⣦⢤⣉⣉⠱⠷⢖⠛⢯⡙⢆⠀⢧⠁⡸⢁⡿⠋⠛⠢⡤⣄⠉⠉⢨⡉⠑⠲⠤⣤⣀⣈⣉⠡⠂
⠀⠀⠀⠀⠀⡠⠞⠁⣀⡤⠊⡠⢐⣶⠋⠀⠀⡴⢧⡔⠉⡽⠶⠤⠒⢥⡤⢬⣪⠷⣼⣦⣧⣎⣠⠤⠴⡾⠒⠒⠉⠂⡤⠷⡄
⠀⠀⠀⠰⠚⠐⠛⠉⠁⠀⣼⠀⢡⠇⠀⠀⡼⢡⠄⠙⠒⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣀⡤⠴⠒⠉⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡴⠃⠀⠀⢰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠶⠶⠶⠶⠚⠛⠉⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠙⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛
⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⢀⣰⡤⢮⣤⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⢘⠉⡄⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠚⠞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣤⢄⠖⠀⠀⠀⠀⣤⠀⠐⢀⣀⣠⡤
⠀⠀⠀⠀⠀⠄⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢤⠉⡋⠑⠿⠃⠀⠰⣦⠀⠀⠘⢇⢘⣿⡿⡟⠾⠶⡄⠀⠀⠀⠠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠈⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣠⢛⠊⠉⠀⠀⠀⠀⠀⣀⢠⡤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠈⡁⡬⠀⠀⠀⠀⠀⣿⠀⣸⡋⢀⣤⡄⠀⠀⠸⠏⠛⠿⡢⠾⣥⡄⠀⢐⣴⣷⢾⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⠰⡥⠋⠀⠀⢀⠀⠀⡀⠀⢀⣀⣀⣿⣦⣼⢠⣾⢁⣀⣀⠀⠀⢰⡷⣟⣭⠳⢄⠀⠀⠀⠛⠀⠈⠉⠁⠛
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠈⢁⠉⠃⠀⠸⠁⣠⣿⣿⣿⣼⣍⡉⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠀⠀⣷⣶⢤⣴⠃⠀⠀⠀⠀⠉⠉⠉⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠀⠀⠐⢂⡀⠀⠀⠀⢠⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣾⣤⣤⠀⠀⠀⠀⠀⣀⠀⠐⠣⠛⠈
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠘⠻⠛⠛⠛⠀⠀⠀⣀⠀⠀⠀⠀⣰⠟⡿⣿⠟⢿⣦⠀⠀⠀⠚⠰⠂⠘⠁⠛⠩⠐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠈⠀⠀⠐⠃⠀⠀⠘⠁⠀⠙⠁⠐

⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠿⠻⡿⠛⠟⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡀⠀⢀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⣠⡿⡭⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣤⣤⣴⣶⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢸⡡⠞⠻⠥⠭⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡽⠋⠍⢉⡭⠷⢄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⣒⡻⠮⠭⢖⣒⣚⣿⣒⣒⠒⠦⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⠯⠗⠒⠋⠉⠉⠉⠀⠀⣿⠀⠈⠉⠉⠉⠙⠒⠒⠭⢕⡲⢤⡀
⠀⠀⠀⠀⠀⠀⢰⡇⠸⣁⠀⠀⠀⢀⣀⣀⣤⠤⠤⣿⠤⠤⠤⠤⢤⣀⣀⠀⠀⢀⡽⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣈⠉⠒⠛⠯⠤⣤⣀⣀⣀⣾⣀⣀⣀⣀⣠⡤⠬⠛⢊⣡⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠙⠓⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠖⠛⠋⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠶⠶⠖⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⡈⠀⢀⡤⠀⠀⢀⢀⠛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢈⣄⡇⠔⡠⠀⢠⡀⠈⣦⣠⢊⠁⣠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡾⠵⢮⡀⠀⠀⡐⢍⣻⡟⠉⠄⠊⣄⢀⢈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢴⠀⠀⠀⠀⠀⠀⠠⡶⡅⠋⠍⡧⠀⠐⣦⣰⣆⣼⡃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠄⢠⠄⡤⢐⠋⠘⠓⣄⣠⡦⢀⠃⠀⠀⢀⡀⡔⠀⢻⣟⠁⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠣⣸⣎⡴⠊⢀⡀⠈⢺⠁⠈⣲⢧⣠⠔⡨⠘⠁⠓⠀⢈⢔⠆⣧⡾⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠩⠹⡿⢯⡀⢠⡀⠄⠠⡀⠆⢠⢃⢈⡏⡁⠀⢀⠀⢦⠶⠛⡀⠐⢹⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠃⠀⠁⠀⡁⠈⠐⠈⠺⡃⠀⠌⢰⢹⠀⠇⠀⢸⠖⡁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠲⣼⡄⠀⠋⢕⣀⢀⠈⠔⢁⣌⠄⢸⣠⠷⠾⠲⠶⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡳⣄⠀⠀⠙⠏⠱⡏⠀⡏⠀⣬⠄⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠪⠀⢀⣉⣥⡴⣧⣴⣶⣶⣶⣶⢾⡶⠦⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢷⣥⣀⣹⣸⣇⣚⣏⣿⣸⣀⣤⡤⠖⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠙⠛⠛⠛⠶⠶⠶⠒⠒⠚⠛⠋⠉⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠒⠒⠒⠀⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢔⡉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠃⠀⠀⢾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⣠⡀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⣹⠀⠀⠀⠀⠀⢀⡄⠀⠀⠢⠀⠙⠀⠀⠀⠀⠀⠉⢴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢤⡔⠠⠤
⠀⠀⠻⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⢀⣀⠀⣀⣠⣀⢀⡘⠃⠀⠀⠀⠀⠈⣂⠀⠀⠀⠀⠀⢠⡄⠀⠁⠶⠂
⠀⠀⠸⡀⠀⢠⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⣿⣿⣿⠿⠿⠛⠻⢿⣷⣶⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠃⠠⠈
⣦⠀⠴⠆⠀⠈⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣾⠉⠙⠀⢠⣄⣀⠇⠀⠙⠋⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⣿⠙⠒⢦⠀⡈⠀⠀⣶⠀⠈⠂⠀⠀⠠⠀⠀⠀⣀⠀⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠞⠧⠀⢀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⢜⢀⡔⠀⠆
⠻⢀⠀⠈⠀⠁⠀⠀⣿⠀⣦⡀⠀⠀⠀⠀⠀⠀⠽⣶⣿⣞⠁⠀⠀⠀⠀⠀⡠⠀⠀⠐⠀⠘⠀⠀⡀⠠⠀⠀⡤⠀⠀⠲⠶⢈⠁⡀
⠀⣿⣤⡀⠈⠀⠀⠠⣿⡀⠀⡤⠀⠀⠈⠀⠀⠀⠀⠘⣿⠛⢀⠴⡇⡄⠐⠭⠃⠀⢀⠠⡄⠀⣆⣰⢧⠀⠀⠀⠀⠶⡀⠼⢂⣰⡀⠉
⠉⠁⣀⠘⠆⠰⠅⠀⣻⣄⣽⠀⠀⠀⠀⠀⠀⠀⠦⣄⠙⡧⠃⠎⠁⠛⡀⠀⠀⣰⠛⡠⠓⠃⢸⣝⣤⠀⠀⠀⠀⠀⠘⢦⣌⠀⠀⠠⠦
⠀⣸⠏⢳⡀⠀⠇⢀⡽⠉⣿⣧⢀⡄⠠⠀⠀⠀⣀⠋⢀⠁⠐⠛⢁⣽⠁⣶⢦⣛⢉⣇⠐⡆⢾⡟⠈⠳⡄⠀⠀⠀⠀⠂⠘⠉⡈
⠀⠁⢀⡀⣷⣀⣾⠦⣯⢠⣏⣹⣯⠀⠀⠀⢀⢄⣿⠀⢿⠀⠀⠀⠥⢸⠋⠉⠢⣬⠐⢻⣤⡙⠢⠙⠀⠀⠈⠶⢠⠀⢀⡄⢤⡄⠀⠓⠘
⠼⢆⠀⠛⠚⡉⠖⣂⣞⠒⣉⠙⣟⠳⡄⠠⠀⢸⠏⠀⠎⢓⣦⣇⡄⢠⡀⡀⠀⠀⢰⣷⣾⣾⢤⡄⠐⢃⡤⠖⡴⢖⣘⠢⢂⠉⠀⠀⠰
⠀⢺⡶⣥⠤⡵⡟⠟⣿⠞⠁⠸⣏⠀⢿⠀⣾⢿⡷⢀⡆⠾⠴⢛⡍⢻⠐⠉⣀⡄⠀⢐⣿⡦⣈⠄⠀⣬⣄⢠⣷⣋⠉⡀⠀⠀⠐⢦
⠒⢈⣴⣤⣈⢿⣯⣭⣿⣄⠘⠰⢄⢠⠘⠚⢷⣏⠀⠸⠛⢋⡀⠀⠰⣏⡠⣶⠋⡳⢻⢰⠉⢛⢃⡾⢀⠙⠁⠀⠁⠘⠳⣼⢳⣠⣶⠄⠻
⠻⢧⣟⣿⣱⣮⣦⡜⣿⠫⠀⠀⠹⢀⡿⣿⣿⣿⣿⣷⠶⠆⠠⠰⢾⣋⣾⡛⣼⣯⣣⣬⣃⠉⠡⠇⣼⣀⠄⠀⣴⣀⡰⠏⢀⡗⠙⠺⠃
⣟⠻⣿⠽⠛⠃⢽⣿⢁⣀⣀⠴⠆⣼⡦⣷⠟⠛⣳⡏⠀⠙⠲⠐⢹⣿⠋⡡⠈⣻⣻⣿⠊⢁⣼⠉⣀⠡⣛⣠⣿⡟⣷⢶⣿⣿⣶⡄⢀
⠠⠻⠿⠵⠷⠄⠠⠴⠫⠿⠿⠟⠿⠹⠥⠀⠿⠿⠳⠯⠄⠾⠃⠴⠼⠯⠏⠄⠄⠁⠹⠌⠁⠇⠛⠀⠛⠳⠈⠛⠾⠡⠽⠿⠿⠯⠝⠃⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡞⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠀⠀⠀⢀⠀⠈⠀⡁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠄⠀⡃⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠤⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣢⣆⣀⣐⠈⢠⣇⣠⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣤⣧⣤⣦⣤⣤⡷⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣻⣿⡿⢿⣿⣿⣿⣾⣏⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣿⣷⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠦⠀⣴⠄⠠⠶⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⣿⣿⢛⣿⣿⣉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⣆⠀⣴⡄⢠⡦⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⣿⠿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣀⣀⣀⣀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠖⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠂⠀⠀⠸⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠄⠠⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠘⠠⡀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⢄⣤⡐⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⣀⣡⠠⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠻⠿⠷⠦⠤⠼⠿⠶⠧⠶⠾⠛⠻⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣶⣾⣿⣻⣿⣷⣾⣦⣤⣿⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠀⠤⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠙⢿⠟⠙⢿⠟⠙⢿⡟⠉⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⡿⣿⣼⡿⣿⣴⡿⢿⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠂⠀⠀⠀⠀⠀⠐⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⣤⣿⣄⣠⣿⣄⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉


⡿⢿⠿⠿⠿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⢸⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢣⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠙⢦⠀⢃⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢉⠉⠒⢦⠀⠀⠀⠛⠀⠀⠀⠀⠓⢬⣼⡦⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇⠀⠀⠀⠀⡀⠤⠒⢒⡶⠿⠿⠯⢍⣉⣉⠑⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠃⠀⠀⢀⠌⢀⠜⠀⠀⢀⠔⠉⠀⠀⠔⠁⠀⠀⢡⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠓⠊⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠰⡆⢄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⣼⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠣⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⢿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠲⠤⠀⣀⣀⠀⠒⠠⠄⣀⠀⠀⠑⢄⠱⡄⠀⠀⡄⠀⢀⠅⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⣧⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠛⠶⣄⡈⠢⡘⡄⠀⡇⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⠀⠈⠳⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡓⠸⣷⡀⣃⠇⠀⠀⠀⢠⠀⠀⠀⠀⣀⡤⠔⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠤⠙⠚⣻⣯⠀⠀⠀⠀⣼⠆⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⢣⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠁⢙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠀⠋⠀⢨⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠑⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⣀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠚⠋⠉⠀⠀⠀⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⢲⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⢴⡓⣞⠉⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⡠⢾⠉⢹⡓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⢠⠊⢢⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠒⠢⣼⠁⢰⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣈⡧⣠⠾⢤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡤⠔⠣⣄⣠⡟⣴⣋⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢩⠖⠓⣤⠼⠑⠢⡀⠀⠀⠀⢸⠀⠀⣠⠖⠁⠀⠀⠀⡞⠀⣹⠁⠈⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠉⠤⡠⠆⠀⠀⠀⠈⠢⡀⠀⢸⣄⡔⠁⠀⠀⠀⠀⠀⠙⠚⠁⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠖⠚⢾⠚⣆⣒⡒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣀⡉⠉⠉⠉⠉⠉⠁⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⢹⠏⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠥⠀⢈⣉⣈⣉⡉⠥⠤⠄⢒⡩⠜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠒⠒⠒⠒⠒⠒⠒⢒⣊⣩⠥⠖⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡈⠉⠓⠖⢒⠒⢒⠀⣫⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠛⠉⠉⠁
⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠶⠶⠶⠖⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠲⠶⠶⠶⠤⢤⣤⣤⣀⣀⡀
⠀⠀⠀⢀⣠⣤⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⢶⣤⣄⡀
⢀⡴⢺⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣄⡀
⡞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⣶⣔⣶⣞⠷⣾⡛⠿⣿⡿⢿⣿⣿⣽⣿⣷⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠙
⢷⣀⠳⣄⡀⡀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣾⣷⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⢀⡼
⢸⡍⠓⠌⠙⠳⠾⣯⣾⣿⣿⣿⣿⣯⣿⡿⣯⣿⣷⣿⣷⣿⡻⣿⣟⣷⡿⣿⡾⣿⣿⣻⣟⣿⣽⣿⣯⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢶⣀⣤⠴⢋⡡⢾
⠀⣧⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣧⣿⣽⣿⣽⣿⣿⣿⣿⣛⣿⣿⣻⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣿⣿⣿⡯⠿⠿⠛⠋⠉⠀⠂⠁⠀⡿
⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠚⠛⠚⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⢸⡆⠉⠙⠲⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⡿⠁
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠶⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠴⠶⠒⠛⠉⠉⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢠⠟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢦
⠀⠀⠀⠀⠀⡟⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⢧
⠀⠀⠀⠀⠀⡇⢰⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡆⢸⡆
⠀⠀⠀⠀⠀⢿⡈⢧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇⣸⠁
⠀⠀⠀⠀⠀⠘⣷⠈⠳⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣠⠟⣰⠏
⠀⠀⠀⠀⠀⠀⠹⡆⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠤⠤⢤⣤⣤⣤⣤⡤⠤⠤⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠾⠭⠭⣭⣭⣭⣭⣭⠭⠭⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⣦⣆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠢⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢙⣧⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠰⣅⣩⣥⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠛⠙⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⣴⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡟⣀⢀⣄⣀⣀⠉⠛⠁⠀⣤⠀⠀⠀⣤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠟⠋⠙⠿⣦⠀⠀⠀⢼⣦⠀⣸⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣰⢴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢎⡄⠀⠀⠀⠀⠘⢿⡆⠀⠀⡹⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣄⣤⡿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠈⠁⢀⣠⡴⠟⠀⠀⠓⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠉⣴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⡷⠆⠚⢍⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡤⣾⣷⡦⣶⠶⢿⡾⠿⢿⣦⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣾⠟⠋⠀⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⢦⡀⣀⡄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢈⣁⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠐⠀⠲⠀⠀⠆⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⢇⠀⣩⠀⠉⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⡄⠐⠂⢠⠈⠙⡆⠰⢅⠀⠀⠀⠀⣀⠀⡴⠃⠐⠒⣤⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⢠⡄⠤⠁⠀⠀⠁⠀⠀⠀⠀⡴⠂⠀⢀⡠⠂⠀⠀⠀⠀⡶⠀⣑⠊⢡⡄⠀⠇⠀⡀⢰⠇⢴⠖⠀⢁⡤⣄⠀⠰⠦⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠈⠓⠲⠤⠀⠀⣡⢀⠃⠀⠀⢀⠄⠀⠀⡀⠔⠁⡀⠤⠒⠂⠂⠀⠇⠠⠉⠀⠼⠁⠠⠒⢁⡴⠃⠀⠀⡵⠀⠫⡀⡨⠃⢦⡄⠃
⠀⣀⠤⠖⠊⣀⠄⠠⠤⠤⠄⠀⣀⠀⢠⠤⠶⠊⠻⠦⠶⠦⠀⠐⠒⠀⢠⠔⠀⠀⠀⠀⡠⠄⠀⠉⠉⠒⠂⢤⡘⠁⠴⠶⠦⠀⠀⠘⠧⠤⣤⠀⠀⠄⠀⢁⡈⠁⠢
⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠐⠒⠒⠀⠄⢲⡚⠒⠀⠡⠞⠀⠈⢁
⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠐⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣲⠠⠚⠁⠀⣒⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠃⡜⢀⡄⠀⠀⠀⠀⢤⡀⠀⠀⢸⡄⠀⠀⣠⡾⠏
⠀⠀⠀⠀⠀⣀⠑⢤⠀⢀⡀⠄⠘⢁⠀⠀⠀⢸⡿⣯⣦⣸⣧⠀⠜⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⡤⢒⣦⣴
⠀⠀⠀⠀⠀⠈⠠⢀⡤⢻⡧⠠⠖⠁⠀⠀⠀⠈⣷⡜⢿⡇⢹⣿⠂⣤⢀⣤⠀⣢⡴⠋⢸⠄⠀⠀⡏⠉⡼⢁⣤⣠⣄⣶
⠀⠀⠀⠀⠀⠀⠱⡢⠅⠊⠁⠄⣀⠛⠀⠀⠀⡀⠙⠛⠸⣶⢈⡁⠸⠛⣿⣿⢾⣯⣀⣀⡀⠉⠀⠀⠛⠀⠁⡈⠉⠀⠈⠈
⠀⠀⠀⠀⠀⠀⢰⡿⠛⢻⠚⠋⠁⠀⠀⠀⠀⢟⣃⣰⣆⠀⢸⠀⢶⣧⣡⣴⡿⠿⠟⠛⡋⠉⠁⠀⠀⠀⢸⠁⡠⡄⣰⣆⠤⡄
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⡴⠎⢳⣎⣣⣠⡞⠀⠀⠐⠀⠐⠲⠆⠀⠀⠀⠀⠀⠈⠊⠈⠀⠀⠰⣨⠇
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⡾⠇⠟⠀⠀⠈⠉⠉⠭⠍⡄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⢇⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⣠⡴⢠⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠛⠲⢆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⣤⠒⢆⠘⠆⠀⠀⡄⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⠀⡀⠶⠰⠙⠤⠳⡯⢰⡄⡁⠀⢰⠦⠤⢤⡇
⠀⠀⠀⠀⠀⠺⠷⢮⣅⢀⡀⠀⠀⠀⣐⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢴⠴⠶⠶⠶⠦⡼⠁⠁⠀⠤⠤⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⢤⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠈⠁⠀⠰⠊⠀⡀⠀⠀⠀⠈⠱⠄⠀⠀⠀⠀⠀⠸⢓⣶⠶⠶⢶
⠀⠀⠀⣃⠀⢀⠁⠀⠀⠠⠀⠀⡀⠀⠁⠀⠀⣙⠂⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀
⠀⠀⠀⠛⡐⡀⠀⠀⠂⠀⠠⠀⠁⢠⠀⡰⣧⠀⠀⠀⠴⠤⣠⠀⠀⢀⠏⠄⠀⠀⣀⠀⠀⠀⠀⢴⡋⢱⠦⡀⠃⠀⠀⢃⢤⡔⠀⠈⡀
⠀⠀⠀⠀⠐⠀⠀⡠⠚⠀⠲⠀⠂⢸⢀⡴⠛⠁⠈⠀⠒⠀⠀⠀⠀⠐⠏⠀⠀⢀⣦⢍⠀⠀⢸⠫⡔⠐⠈⠛⡦⠀⢱⡀⡘⠉⠐⢢
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢐⣀⣘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡒⢰⣸⣿⠝⠀⠀⠘⡀⢀⡤⡉⠀⣂⣤⣸⡶⣀⣾⡞⢣⡦
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠖⠚⠻⠄⠀⠀⠀⠀⠀⣠⢠⢾⣛⠿⠧⠤⣹⢄⢨⠇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⠀⠀⠀⠀⠀⢸⠇⠀⢸⣿⠃⠂⢆⣡⢣⣥⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⣄⡈⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣘⡉⠁⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠇⠀⠈⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠑⡄⠀⠀⠀⠀⡜⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⡁⠀⠀⠘⡄⠀⠀⠰⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⡁⠀⠀⠀⠰⡀⠀⡆⠀⠀⠀⠀⡀⠀⡠⠀⢤⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⡆⠀⡀⠀⠀⢡⢀⠀⠀⢆⠀⠀⣡⠊⠀⠀⢸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢰⠀⠈⠢⢀⠈⣼⠀⠀⢸⡰⠠⠁⠀⠀⠀⢸⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠐⠤⣀⡤⢀⠀⠎⠀⢹⠀⢀⠘⢀⠃⠀⠀⠀⠀⡎⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠸⠀⠀⠳⣘⠀⠈⡄⠈⡆⡄⠀⠀⠀⡠⢠⠖⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⡆⢀⡀⠹⡆⡄⢳⠀⣼⠀⢰⢠⠃⢀⠆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢱⡀⠁⡇⢻⠀⠀⢡⡇⡀⢈⠃⠀⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡱⡈⠳⡘⡄⡤⢨⠃⠁⠜⠊⣜⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠱⠲⠑⠇⠚⠒⠸⠀⠘⠀⠺⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⣻⣿⡿⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣧⢹⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠻⣧⡀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠿⠃⢀⣿⠷⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡶⠟⠁⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⣀⣤⡶⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡆
⠀⠀⠀⢠⣾⠋⠁⢾⣿⣿⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣄⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠷⢶⣬⣿⠀⠀⠉⠛⠻⢿⣿⣿⣛⣻⣶⣶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⢛⣋⣭⡶⠟⠋⢹⣇⣉⣉⣉⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⣿⣋⣭⣀⣀⣀⠀⣾⣏⣽⠟⢋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⡉⠉⠉⠙⠛⠛⣋⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⠛⠛⠛⠶⠶⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠉⠁
⠀⢠
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⢫⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢸⡇⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣡⠞⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠈⢷⡄⠀⠙⠛⠶⢶⡄⠀⠀⣴⠋⢀⣴⠃⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣄⣀⣄⣤⣼⠇⣀⣼⣧⣤⣰⡏⢈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡿⠿⠿⣏⠉⠉⣽⠿⠋⠉⠁⠉⠉⠻⢶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠻⢶⣄⠀⢹⡆⣼⠇⢀⣀⣥⣴⣶⣷⣴⣴⣝⡷⣟⠳⢶⣶⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠿⣦⣸⣿⢟⣴⠟⣩⠞⠋⠉⠀⠀⠀⠈⠙⣻⣶⣿⣏⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⡟⢡⡞⠁⠀⠀⠀⠀⠀⠀⣀⡶⢋⣼⢿⠽⣒⣻⣏⡛
⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣠⣤⣤⣄⡀⠀⣿⣯⡿⡇⣷⡟⠀⠀⠀⠀⠀⢀⣠⣶⣫⣴⢿⡿⢁⡾⠉⠁⢀⣉⣻⡶⢶⡶⣄
⠀⠀⣠⣖⣛⣉⣉⡉⠉⢉⣁⠀⠀⠀⠙⠳⣤⣄⡀⣧⢸⠄⠀⠀⣠⣤⣶⣿⣿⣯⣭⣾⣉⣰⠟⣠⡴⠚⠋⠁⠀⣸⠋⠙⠞
⠀⠀⠉⠉⠀⣠⡬⢿⣦⣀⣉⡛⠲⣤⡀⠀⠀⠈⠉⢻⢸⣧⣴⡾⠟⠋⠉⠁⠀⠀⠀⠈⠉⠙⠛⠿⣤⣄⣀⣤⣾⣃⣀⡀
⠀⠀⠀⣴⢋⠥⠶⣺⠏⠉⢉⣽⠇⠘⢷⣄⡀⠀⠀⢸⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⢉⣉⣉⣉⣛⣛⣒⠲⣄
⠀⠀⡼⢁⣃⣠⣴⡟⠀⠀⣸⡿⠷⠾⠛⠉⢉⣽⣗⠸⡇⣿⡴⢦⠀⠀⠀⢀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⣬⣻⣯⣀⢀⣤⠖⠛⠛⠛
⠀⢠⠞⢉⡼⠋⣼⠁⠀⣼⠋⠀⣀⣤⣴⠞⠛⠓⢿⣿⠟⠉⢰⣇⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠉⠁⠉⣹⡟⠁
⠀⢀⠜⢉⡴⠊⡿⢀⡼⢃⡴⠾⠯⢽⣮⣷⣠⠴⣿⣅⠀⠀⢸⡟⠁⠀⠀⠀⠀⢀⣠⣤⠶⠻⠛⠛⠾⢶⣶⠶⠶⠟⠋
⢠⡏⡠⠊⢀⣴⡇⣸⢡⡟⣠⡤⠞⠋⣹⠟⠁⠀⠈⠙⠆⠀⢸⠟⡷⣶⡖⣾⡿⠛⠉⠉⣿⣄⡀⠂⠀⠀⠉⠳⣄
⢸⡗⢁⣾⠟⠉⡇⡇⣿⠟⠁⠀⣠⠞⣁⣀⣀⣠⣤⣤⣤⣠⣟⠀⡇⣿⣰⣫⣤⢤⠤⠄⠻⣍⠙⡳⢦⣀⠀⠀⠙⣆
⣏⡴⢻⡏⠀⠀⣻⣽⠇⠀⠀⠀⠉⣹⡏⢡⡿⠁⠀⠀⠀⢈⢿⣤⣧⣿⢟⣡⣤⣶⣶⣾⣒⣾⣧⣤⣤⣬⣟⠶⣤⡘⣆
⠈⠁⣿⠁⠀⣴⠏⠉⠀⠀⠀⣠⡾⠋⠀⣾⠁⠀⠀⣴⠟⠋⠉⢡⣿⢡⡞⣵⡾⢡⠏⠉⠛⠋⠉⠀⠀⠈⠙⢷⣄⠁⢹⡆
⠀⠀⣿⡀⢠⠏⠀⠀⣀⣴⠞⠋⠀⠀⠀⣿⠤⠶⠚⠁⠀⢀⣰⣾⣿⣼⠟⣿⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡀⣿
⠀⠀⠘⣷⠈⣠⠴⠚⠉⠀⠀⠀⠀⢠⣾⡭⠖⢚⣾⠿⢛⣏⡇⣿⢻⢸⠸⡇⣸⢯⣟⣛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠈⢷⣿
⠀⠀⠀⢹⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣏⣉⠙⠷⣼⠾⣼⠿⣧⠟⠠⡀⢈⣙⣶⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣉⠙⠛⠛⠷⠶⠾⠶⠷⠾⠛⠛⠋⠉⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠛⠒⠲⠶⠶⠶⠶⠶⠒⠒⠛⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣤⣄⣀⣀⣀⣀⣀⣠⣤⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⢄⠀⠀⠀⠀⠀⡰⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⢆⠀⠀⠀⢠⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠑⢄⠀⡇⠀⠀⠀⠈⠆⠀⠀⡂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠊⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠢⣁⠀⠀⠀⠀⠘⡀⢀⠃⠀⡀⠀⠀⢸⢀⠔⠉⠀⢹⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢹⠀⠠⡀⠀⠀⢡⢸⠀⠀⠁⠀⡀⢰⠋⠀⠀⠀⢸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⡄⠀⠈⠁⠰⠈⣮⠀⠀⢀⡐⢡⠃⠀⠀⠀⠀⣬⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠒⢆⡴⠢⣄⠈⡆⠀⢹⠀⢠⢸⢀⠇⠀⠀⠀⠀⠀⠇⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡅⠀⠈⢧⣡⠀⠘⡄⠀⣆⡈⠀⠀⢨⢀⠄⡸⠊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢃⠀⡀⠀⢻⣀⠄⡷⠀⣴⠁⠀⠀⠎⠁⢠⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⠈⢲⠈⠏⠀⡀⢁⡏⠀⠀⡞⠀⢀⡇⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⡄⠓⠆⡸⠀⡿⢰⡇⠁⠰⠕⢂⢏⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣜⣔⣼⣀⣿⣧⣸⣁⣠⣁⣠⣶⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡿⠒⠀⠀⠀⢡⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡀⠊⠀⢀⡤⢴⠕⢀⢀⡆⢠⡖⠊⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡈⠑⢦⠀⠘⢧⣄⠒⠉⠀⣸⣶⣾⣾⢧⡸⢗⣋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣀⠄⠀⠀⠳⡀⠀⡢⠟⠛⠉⠀⢠⣿⣏⢈⡤⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢢⡀⠀⠀⣯⠆⠀⠀⠀⠀⠀⣼⠟⠋⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣺⣟⣢⣴⣯⡀⣀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠛⢿⣯⣤⡦⠦⣠⡀⠀⠚⣁⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣙⡀⠀⠠⡄⢰⠀⠀⠸⡇⢀⢄⣀⠀⢀⠄⠀⠀⠀⡸⠋⠀⠀⠀⠈⠙⠻⢶⢤⣄⣀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣑⠤⣀⣼⣧⣄⡀⢤⡵⠋⢫⠀⠀⡌⠀⠀⠀⠚⠁⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⠀⡀⠀⢠⡀⠤⣼⣒⢿⠙⣯⣿⠋⠙⣿⡟⠁⠀⠠⣠⡚⠀⠀⣰⠇⠀⠀⡀⣶⠂⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠙⡄⠀⢹⠀⠀⠸⠀⠀⢠⣿⠋⠁⠀⢠⠏⠀⠀⣼⠁⢻⡶⢤⠈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠈⠒⠀⠀⣡⡐⣸⠀⠀⣸⣠⡔⠋⠀⠀⠀⠈⡏⠀⠀⠀⣿⢀⡾⡀⠀⠀⢰⡇
⠀⠀⠀⠀⢀⣠⠤⠴⠲⠻⠦⠤⠠⢀⣀⣉⣩⣿⠶⢾⡷⠦⠤⠤⠀⠀⠚⠛⠁⠀⠀⠀⠺⣿⣽⣗⣠⣖⡁⠀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠟⠉⠀⠀⠸⣷⡀⠀⠀⠀⠀⠠⠇⠀⠀⠰⠀⢸⡿⠉⠉⠛⠉⠤⠀⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⡼⠀⠀⠣⠀⢠⡟⢁⠀⣄⠀⠠⠀⢀⡀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⡇⠀⠀⠀⢰⡟⠁⠈⢡⡜⣶⠖⣤⣯⣤⣀⠀⡤⠄⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣼⠁⠄⠈⢠⡟⠀⠐⠠⠖⠾⡌⣽⣛⠋⢉⡀⠀⣄⣤⣄⡀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣆⠘⢦⢛⠀⣠⡅⠀⠀⠀⠀⠀⠉⠙⠦⠠⠀⠀⠀⠀⠉⠑⠢⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢹⡄⣸⠻⣅⡂⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢻⡏⠀⠈⠙⢲⣾⣧⣄⣀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠀⠐⢠⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⣇⠀⠀⠀⡾⠃⠀⠀⠉⠉⠉⠙⠓⠦⠤⢰⣦⣀⣦⡄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠈⡇⢀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⣀⣀⣀⣠⣤⣽⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣏⣥⣤⣴⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⢀⣶⣶⣶⣶⣤⣤⣀⢀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣤⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⣤⡶⠶⠶⠶⠶⡤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⢉⣀⠠⢀⢿⡤⠤⠤⠤⢶⣷⠤⠤⣀⡉⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠫⢂⡤⠒⠉⠀⠀⠐⣇⡀⠙⠢⠤⠒⠁⢀⣱⠀⠀⠀⠁⠒⢄⠰⡝⣷
⠀⠀⠀⠀⠀⢀⡤⠶⢶⣿⣱⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⢡⢹⣼⠋⠛⠓⢦⡀
⠀⠀⠀⠀⢰⠋⠰⣶⠾⣟⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⣿⠟⣻⠖⠀⣧
⠀⠀⠀⠀⠸⣄⠀⠈⠑⠛⠶⡍⠛⠿⠿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠿⠟⠋⢁⡶⠛⠋⠁⢀⣰⠇
⠀⠀⠀⠀⠀⠉⠛⢶⣤⣄⣀⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣷
⠀⠀⠀⠀⣀⣠⣤⣴⠶⠾⠿⠿⠿⠿⠿⠷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠸⣿⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠿⠿⠿⠿⠿⢶⣦⣄
⢀⣠⡶⠟⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠛⢿⣦⣀⠀⠀⠀⠀⢹⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⢀⣠⣄⣤⣤⠶⣶⡾⠟
⠛⠿⢃⡈⠉⠉⠙⠛⠛⠛⠻⠿⠷⠶⢦⣄⣠⡄⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⢀⠐⢀⣠⣤⡶⠿⠛⠛⠉⠀⣠⡾⠋
⠀⠀⠀⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⡀⠀⠆⠙⢿⡄⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢠⣾⣿⠿⠛⠋⠑⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣿⣷⣶⡀⠈⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⣼⡟⠁⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣜⣷⠀⠀⠀⣿⣿⠀⠀⣾⠏⠀⣀⣠⣾⢟⣡⣤⠤⠖⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⣿⡿⠀⣼⡏⠀⣠⣿⠟⠛⠉⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠿⣿⣆⠀⣿⡇⢠⡟⢀⣼⡟⠁⠀⠀⠀⠀⢀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣿⡇⠘⣷⣾⣏⣠⣤⣶⣶⡶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⢠⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⣶⣦⣤⣄⡀
⠀⠀⠀⣠⣴⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⡀
⠀⠀⢰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧
⠀⠀⢸⣿⠻⠿⣶⣦⣤⣀⣀⣀⡀⠀⠀⢀⣀⣠⣤⣶⣶⡶⠶⠿⠿⠿⠿⠿⠿⠿⢿⡿⣿⠿⠿⠿⠿⠷⠶⠶⠶⠶⣦⣤⣀⣀⡀⢀⣀⣀⣠⣤⣾⠿⠛⠁⢠⣿
⠀⠀⠈⣿⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣾⣷⣿⣤⣤⣤⣤⣶⣶⣶⣶⣶⠾⠿⠿⠿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠘⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⠿⠶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣴⡶⠾⠛⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢷⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠂⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠀⠐⠋⠋
⠀⠂⠀⠀⠀⢣⢀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠤⡉⡰⢀
⠀⠀⠀⠈⠀⠀⠸⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⠞⢠
⠀⠀⠀⠀⢤⠂⠀⠆⠨⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠰⠃⢀
⠀⠀⢀⠀⣦⠁⠃⡌⠐⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠠⠄⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⡂⠀⠐⢊⠤
⠀⠀⢳⠂⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠐⠀⠀⠈⠁⢰⠠⠀⠉⠀⠀⠀⠀⠀⡀⠐⠑⠂⠀⠀⠀⡀⠃
⠀⠀⢸⡀⠀⠀⠀⣸⡃⠀⠀⠀⠐⠒⠈⡀⠀⠀⢀⣀⡓⠘⢀⡄⠀⠂⠾⠃⠀⠀⠀⠀⠀⠀⠐⢌⠍
⠀⠀⢸⠀⠀⠠⡐⢕⣀⠀⠀⠐⠛⠆⠂⠀⡀⠀⠀⠀⠠⠄⠋⠀⢦⡀⣤⣄⡀⠈⠀⠀⢀⠈⠀⠤⠂
⠀⠀⡞⠀⠀⢤⣈⣩⠢⠂⠀⠢⣀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠉⠱⡆⢢⠀⡀⠀⠀⠀⠀⠀⠁⠲⠘⠋
⠀⠀⠀⠀⠀⠢⣭⣠⠶⠖⠂⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡎⠀⠀⢇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡄⡘⠀⠀⠀⠘⡀⡜⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⡇⢰⢾⡇⠀⠀⠀⠀⢻⠷⠀⢡⠀⡰⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣄⠃⠘⠈⢣⠀⠀⠀⢀⠏⠀⡇⢸⡜⠀⠇⠀⠀⠀⠀⠀⢠⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠘⡄⡇⠀⠀⢣⠀⠀⡜⠀⠀⡇⡸⠀⠀⣶⡀⠀⣠⣄⢦⡎⠀⠸⣠⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢦⡀⢂⠀⠀⢱⡇⠀⠀⠈⡆⢰⠁⠀⠀⣿⠁⠀⠀⡇⠘⣎⢰⡏⠈⡆⠀⢀⠇⢱⠀⡰⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⣼⠀⠀⠀⣷⠀⠀⠀⢡⡆⠀⠀⠀⡏⠀⠀⢠⡇⠀⢈⣿⠀⠀⢸⠀⡜⠀⠀⢿⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠉⠒⠠⢀⡘⡄⠀⠈⡆⠀⠀⢹⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⡀⡸⠇⠀⡈⠳⡀⠀⢠⠛⡇⠀⢀⠎⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠻⡄⠀⢓⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⢀⠃⠀⡏⠣⣴⠀⡇⠀⠱⡀⠆⠀⢡⢀⠎⠀⢰⠀⣆⠔⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠙⡄⠘⡄⠀⢸⢳⠀⠀⠀⠃⠀⠀⢸⠀⠀⡇⠀⠘⢦⡁⠀⠀⢻⠀⠀⠈⡏⠀⠀⢸⡴⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢌⣆⠸⡀⢸⠸⡆⠀⠀⡀⠀⠀⡘⠀⡠⢡⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠓⠚⠛⠛⠒⠒⠓⠒⠚⠛⠓⢓⡏⢆⠀⠀⢱⠀⠀⡇⠀⠀⠀⡇⠀⠀⡏⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠁⠈⢆⠀⠈⡆⠀⣇⠀⠀⠀⡇⠀⡸⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢢⡀⠘⣄⢸⠀⠀⢰⠀⡰⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠤⠵⠦⠼⠦⠧⠤⠶⠴⠧⠴⠯⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⣀⣀⣤⣤⣤⠜⠀⠀⠀⠀⠀⠀⠘⠯⠭⠭⠭⠭⠤⠭⠭⠽⠁

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