Ham Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣠⣤⣴⠶⠶⠶⠶⠶⠶⣶⣤⣤⣄⡀
⠀⠀⠀⢀⣖⣭⣩⡿⡻⠛⠛⡉⠃⠀⠀⢀⠀⠄⠀⠈⠁
⠀⠀⠀⠈⠛⢿⣿⣧⣤⣎⣤⣴⣿⡾⠂⢀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⡋⠀⠀⢀⡀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⠸⠀⣀⢼⠀⠀⠀⠈⠐⠒⢿⢿⣋⣁⣀⡀⡠⢤⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠈⢭⠀⠁⢼⣋⠁⢬⣤⣤⡀⡀⣁⣷⡾⣟⡻⠅⠒⠊⠑⢀⡴⠋⡱⠀⣰⣠⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠈⠛⠻⠂⢀⣁⠩⠲⠧⠀⠒⠂⢉⣁⣤⡴⠞⠛⠂⣁⣤⠞⠁⢉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⠶⠲⣒⢒⣛⣛⡭⠭⢥⠴⠶⠒⢛⣛⠭⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⣀⠤⠶⠾⣟⠉⠉⠉⢻⣟⠓⠶⢤⣀⡀
⠀⠀⠀⡴⣪⣶⣿⣶⣄⠙⣆⠀⣠⠟⠹⡄⠀⢰⠟⣟⠶⣄
⠀⢀⡞⣼⡿⠉⠉⠙⢿⣆⢹⡾⠋⠀⠀⢻⣤⠏⠀⠘⣆⢨⡿⣦⡀
⠀⡞⣼⡟⠀⠀⠀⠀⠈⢿⡄⣷⡀⠀⠀⣴⢿⡀⠀⠀⠘⣾⠁⠈⠻⣦⡀
⢸⢳⡿⠀⠀⠀⠀⠀⠀⠸⣇⢹⣷⡴⠞⠁⠀⢳⡀⠀⡼⠙⣦⠀⠀⣼⠳⣄
⣿⣸⡇⠀⣠⠶⣦⡀⠀⠀⣿⢸⡏⢳⡀⠀⠀⠀⢳⡞⠁⠀⠈⢧⣼⠃⠀⠘⣷⣤⡀
⣿⣿⠁⢰⠃⠀⢸⣷⠀⠀⢹⠸⡇⠀⢳⡀⠀⣰⠋⢻⡄⠀⠀⣼⢷⡀⠀⣰⠛⣦⠙⢷⣄
⣿⣿⠀⢸⡀⠀⢸⡿⠀⠀⢸⠀⡇⠀⠈⣳⡞⠁⠀⠀⠻⣦⡾⠁⠀⠻⣴⠏⠀⠘⢧⣼⠋⠳⣦⡀
⣿⣿⠀⠈⢷⣶⡿⠃⠀⠀⣾⢸⣇⣠⠞⠉⢳⡄⠀⠀⣠⠟⣦⠀⠀⣰⠟⣆⠀⠀⣸⠿⡄⠀⣼⠛⣶⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠻⡅⠀⠀⠀⠻⣄⡾⠁⠀⠈⢧⡴⠃⠀⠈⢷⣰⠏⠀⠙⣶⠇⠀⠘⢯⣹⠏⢹⣿⣿⠒⠒⠲⠶⠶⠾⠁⠀⢠⡿
⢻⣿⡇⠀⠀⠀⠀⠀⠀⣾⢡⡟⠀⠹⣄⠀⢀⡴⠻⣆⠀⠀⢀⡞⠳⣄⠀⠀⡼⠻⣄⠀⢠⡟⠳⣄⠀⢈⡿⠶⣿⣿⡁⠀⠀⢀⣀⣀⡀⠀⠀⠈⢳
⠸⡟⣧⠀⠀⠀⠀⠀⡼⢃⣾⡅⠀⠀⢙⣶⠋⠀⠀⠘⢧⡴⠋⠀⠀⠙⣦⡞⠁⠀⠘⣧⡟⠀⠀⣙⣷⣾⣥⣤⣿⣿⠟⠉⠉⠉⠉⠙⠛⠳⣤⣀⣀
⠀⢷⡹⣦⡀⠀⣠⠞⣡⡞⠁⢻⣀⡴⠏⠙⢦⡀⠀⣠⠞⠳⣄⠀⠀⣴⠋⢳⣄⣠⣴⡿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠈⢳⣌⠙⠛⣡⡾⠋⠀⢀⣴⢿⣄⣀⣤⣬⣷⣾⣥⣤⣤⣼⡷⠾⠟⠛⠋⠉⠁
⠀⠀⠀⠉⠛⠿⠿⠷⠿⠿⠿⠟⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠶⠒⠒⠒⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠛⣛⡋⠙⠒⠒⠤⣀⣀⣀⠀⠉⠁⠀⠀⠉⠙⠒⠶⠋⠉⠙⢯⡁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣁⠀⢀⡘⠠⡀⠈⠐⢤⠀⠀⠀⠀⠉⢉⠓⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠱⡤⠒
⠀⠀⠀⠀⠀⢀⠞⠁⠠⠊⠀⠀⠀⠈⡆⠘⠄⠠⠐⠀⠀⠀⡀⠤⠄⡑⢄⠑⡌⢆⠀⠀⠀⠀⢀⠤⠴⠃
⠀⠀⠀⠀⢀⡏⠀⠀⠈⠒⠒⠂⠀⠂⢀⡠⢄⠀⠀⠀⢀⠌⠀⠀⠀⠘⡄⢄⡸⢸⠀⠀⠀⡠⠊
⠀⠀⠀⠀⢸⡀⡔⠀⠉⢱⠀⡊⠀⠀⠀⠀⠔⢀⠄⠂⠁⠀⠀⠀⠀⠀⠇⠀⠀⣸⢀⡠⠚⠁
⠀⠀⠀⠀⠀⢧⡈⠂⠤⠤⠀⠙⠒⠤⠀⠊⠀⠘⠤⠤⠄⠐⠒⠂⠒⢊⣀⣀⡴⠟⠋
⠀⠀⠀⠀⣀⠤⠬⠽⠾⣒⣒⣒⣒⣓⣚⣛⣋⣋⣉⡭⠭⠭⠭⠭⠭⠭⠥⢤
⠀⠀⡠⠚⠁⠒⠀⠀⠀⢢⠀⡠⠄⠀⠠⡄⠠⠒⠒⠀⠀⠀⠀⠉⠐⠄⠀⢸⡇
⢠⠎⠀⠀⡠⠅⡀⢀⣀⠁⠈⠦⠀⠀⣀⠈⠊⠄⠒⠠⡀⠀⠀⠀⡠⠃⠀⣾
⢸⡀⠀⠀⢄⠀⠀⠀⠀⠈⠢⢀⡠⠄⠀⠨⡁⠁⠀⠀⠈⣒⢂⡉⢀⠔⣱⠃
⠀⠳⣂⠤⢀⡁⠒⠀⠀⠐⠁⠢⠤⠤⢀⠀⡸⠐⠭⠠⠄⣒⠬⢂⡡⠞⠁
⠀⠀⠈⠉⠒⠲⠤⠤⣄⣀⣒⣒⣒⣒⣒⣒⣒⣂⣀⠬⠥⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⢿⡷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢮⣳⣯⣽⣻⣶⣤⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣞⢿⣿⣿⣾⣿⣿⣶⣤⣀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣵⡿⣿⣿⣽⢷⣮⣽⣿⣶⣤⣀⡀
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣗⣯⡿⣿⢟⣿⣮⠫⣻⣿⣿⢷⣦⣄⣀
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢿⣟⣷⣽⢿⣟⣭⡛⢷⣿⡿⣻⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦
⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⢽⣺⣷⢽⣿⡿⢿⣽⢿⣟⣮⡿⣯⡺⣹⣿⣿⡟⢿⣿⠷⣶⣶⣤⣄⡀⢀⣰⠟⠀⠈⠛⠛
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣳⣷⢿⣙⢿⣜⣻⣵⡟⣿⣟⣮⡿⣯⣷⢟⣷⣿⢝⣿⡯⣻⣾⢿⣿⡏⣀⣠⣤⣦⣤⡾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⣯⢝⣯⣿⣟⣽⢟⣼⢿⣟⡾⣟⣿⣿⣟⣿⣟⢹⣿⣏⣿⢯⣿⠟⠋⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⣿⣻⡮⣿⡷⣟⣷⣿⣻⣾⢿⣽⣷⡿⣥⣿⣟⢹⣯⣿⡿⠃
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢽⣿⣾⣿⣿⢙⣿⡾⡟⣿⢷⠟⣿⣞⣯⣿⣿⣿⡿⠋
⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⢯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⣿⡇⣿⠹⣿⣿⣧⣿⣺⣻⣿⣼⣿⣿⠟⠋
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢸⢸⡀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣇⣿⢸⣿⣿⣿⣻⣿⣿⣿⠿⠋⠁
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⢎⠣⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣭⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣀⣲⠦⢄⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠛⠉⢉⣿⠛⠻⢷⣦⡂⠀⠈⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣾⢿⡋⠀⠀⠀⠠⠾⠁⠀⠀⠀⠈⣻⣧⡠⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⡧⢀⠀⠀⠀⠀⠀⠀⠀⢤⠟⠋⠹⣿⡄⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠏⠀⠀⠀⠀⠘⢻⡄⠀⠀⢀⣤⠶⣾⣃⣢⡀⢠⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⣀⣤⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⠀⠀⠀⠘⣧⡶⠚⢻⣁⣤⣀⡀⢈⣽⠈⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠶⠶⠶⠆⠾⠶⣦⡶⠛⢳⡴⠾⣧⣀⠈⠙⠋⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⠋⢀⣀⣠⣧⠀⣰⠋⠙⢦⣀⠀⢀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡘⣿⣄⠀⠀⣈⣤⠑⠛⠩⠥⠀⣛⢐⠃⠀⠤⠤⠙⠛⣁⠈⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠂⠉⠑⢈⠻⢿⣾⣏⣀⡀⠀⠀⠀⠀⣿⣏⣀⣀⣀⣀⣀⣀⣿⣀⣤⣴⡿⠃⠀⠀⠀⠀⢀⣤⠊⠀⠀⠉⠐⠀⢄
⠀⠀⠀⣷⣤⣀⣀⡀⠀⠈⠐⠪⠍⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣟⣛⣛⣛⠉⠁⠀⠀⣀⡤⠴⠾⠛⠋⠀⠀⣀⣀⣠⣤⣾
⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣭⣭⣭⣭⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⢍⡉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⢉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠈⠁







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

⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠖⠛⠉⠉⠛⠙⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢛⡻⠿⠶⠦⠤⢀⡀
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢄⣀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠶⠀⠈⠀⢄
⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣾⡿⠛⠉⠉⠀⠀⠀⠀⠀⢀⣜⠀⣀
⣿⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠓⠌⠀⠀⢀
⢸⣄⣦⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡀⡰⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣖⠊⠀⠀⠈⠀⠀⠀⢸⡄
⠈⣿⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⣴⡴⠏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣦⠭⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⠶⠏⠛⠉⠀⠀⠀⠀⢀⡀⢤⣔⡆⠉⠙⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠎⠁⠀⠀⠀⠀⣀⡀⡤⡤⠌⠉⠛⠀⠈
⠀⠈⡏⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⢀⢀⠄⠐⠚⠉⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠈⣯⡀⠀⡠⣂⣾⡛⠥⠔⠒⢚⣁⢀⣀⣀⡀⣀⣀⣀⣀⠀⠀⣠⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠙⣿⣞⡯⠏⠥⠤⠤⠒⠓⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠉⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⢄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠐⠒⠈⠉
⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠰⠂⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⢰⢅⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠓⢠⣄⠀⠀⠀⠀⠈⠀⠐⠀⠺⠓⠁⠀⠀⠐⠀⠀⠀⠀⠈⠀⡻
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢀⣠⣰⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠣⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⡄⠀⠀⠀⡠⢸⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡽⠋⢹⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠄⠀⠺⢥⣒⠲⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠠⣶⣏⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳
⠀⠀⠀⠀⠞⠀⣼⠟⠉⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣀⠀⠀⠀⠠⡄⠠⣇
⠀⠀⠀⣡⠰⡴⠁⠧⠀⠀⠀⣠⠀⠀⠀⠀⣀⠀⣤⠖⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠎⠰⠀⠁⠀⠀⠀⠠⠀⠀⠀⠛⢆
⠀⠀⠠⡄⠀⠗⢀⠺⠀⢀⡴⠁⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢀⡀⡂⢀⠀⠀⠀⠀⣵⣿⣿⣤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠐⠠⣰⠾⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢇⠁⡶⠂⠀⠀⠀⡟⠿⠃⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡆⠰⠀⠀⠀⠀⢀⣴⡇⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢈
⠀⠀⠀⠀⠄⢀⣙⠓⠲⠠⠔⠙⠓⠐⢂⠀⠀⣀⠀⠀⠀⠀⢀⣴⣗⣳⣴⣶⣿⠿⠛⢛⣋⠀⠁⠰⠒⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠠⠤⠠⡞⠁⠀⠀⠀⠀⠀⠀⠘⠀⠠⣭⡉⠀⠀⠀⠄⠚⠋⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠓⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠻⢍⠉⠉⠉⠉⠛⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣡⡤⠦⢤⣄⠈⣇⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⠞⠁⠀⠀⠀⠈⢧⢹⡀⠘⠇⠀⠄⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣞⠀⠀⠀⠀⠀⠀⣼⠀⠙⢦⡀⠉⠒⠲⠤⣄⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⡥⠶⠦⣌⠉⠉⢙⣓⠶⢚⣡⠴⠶⢦⡙⢦⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢀⠖⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢡⠋⠀⠀⠀⢸⣀⠀⠫⠼⠃⡏⠀⠀⠀⠀⢻⠈⣷⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⠔⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣇⣀⠀⠀⠀⠀⠉⢳⡀⡴⠞⠁⠀⠀⠀⠀⢸⡇⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣄⡈⠋⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⠽⠿⠿⣿⡷⢦⣤⣤⣼⣇⣷⣄⣀⡀⠀⠀⠀⡼⠀⣾⠀⠀⠀⠀⠀⢀⡴⠛⠛⠋⠀⠈⠙⠛⠉
⠀⠀⠀⠀⢀⣠⡴⢶⣛⣛⣋⡉⠸⣁⣀⣠⠤⠤⠗⡴⠚⠛⠛⠛⠛⠿⢭⡙⢷⣤⠞⠁⣼⠃⠀⠈⣀⣤⠖⠋
⠀⠀⠀⣴⢋⠴⠋⠉⠉⠉⠉⠉⠙⢲⡁⠀⢯⠝⣠⠇⠀⠀⠀⠀⠀⢀⣼⠃⣾⣀⣤⣾⡥⠶⠖⠋⠉
⠀⠀⢸⣇⠸⠤⠤⠒⠒⠲⢄⣀⣠⠜⡵⠚⠉⠉⠀⠀⢀⣠⡤⠶⠚⣋⣤⠞⡿⠉
⠀⠀⠈⢯⡈⠈⠁⠀⠉⠙⠢⣌⠀⠘⢇⣀⠀⠀⢀⡴⢋⡤⠖⣚⣩⡥⠶⠛⠁
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠛⠷⣄⡙⠦⢄⣈⣉⣉⣉⡴⠋⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣄⣀⣀⣀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⠶⠚⠛⠓⠲⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣋⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⣾⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⢰⠏⣿⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣴⣿⢿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿
⠀⠀⢰⡏⣿⠸⣇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉
⠀⢠⣾⣧⠘⣧⠹⣆⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⡟⢿⠹⣇⠈⢷⣌⠻⢦⣄⡉⠙⠓⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⣷⠘⣧⡙⣦⡀⠉⠛⠶⣬⣉⡛⠶⢦⣄⣀⡈⠉⠉⠙⠛⠓⠶⠶⠶⢤⣤⣤⣤⣭⣿⣷⣤⣀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⢰⣿⣇⠈⠳⣬⡛⠶⣄⣀⠀⠈⠉⠛⠓⠾⠿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⠀⠀⠉⠉⠛⠻⠦⣄⣻⡄⠀⠀⠀⣠⡴⠛⠁
⢹⡹⣟⢷⣀⠈⠙⠓⠶⣭⣟⣳⡶⢦⣤⣄⣀⣀⣀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠶⢦⣄⡀⠈⠙⣧⣀⡴⠞⠉
⠘⣧⠘⠷⣝⡳⢦⣄⣀⠀⠈⠉⠙⠛⠳⠶⠿⠭⣭⣿⣿⣿⣿⣿⠶⠶⠶⠶⣦⣤⣤⣀⡀⠀⠀⠈⢻⣦⣤⠟⠋
⠀⠈⠳⣤⡈⠙⠛⠶⢯⣿⣿⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⢙⡿⠶⠾⠋⠈⠁
⠀⠀⠀⠈⠙⠓⠶⢦⣤⣤⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⡭⠼⠛⠉⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣶⠓⢈⢏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢐⡫⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠰⢚⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⣫⣾⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣻⣿⠿⠻⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣾⠏⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⢠⡞⠡⠐⠚⢡⠴⠆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡁⠀⠂⠀⠃⠀⢀⡀⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢈⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢝⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣰⠋⠀⣀⡾⠃⠀⢠⠈⠁⠀⠀⠀⢀⠀⠀⠀⢠⣠⣿⣿⢣⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠙⢳⣿⣟⣻⣄⣀⣂⠀⠀⠀⣀⣂⠀⣠⣴⣯⣼⣿⡟⣡⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣥⣽⣿⣿⣿⣷⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠄⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠻⣿⣿⣍⣩⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣯⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⡿⣽⣿⣿⣿⣿⣿⠿⠛⠋⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠄⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⡶⠶⡿⠋⢉⣉⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠁⠀⢰⠃⠰⠁⠀⠈⠑⢄⡈⠢⡀
⡴⠋⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⡕⢀⡈⠢⡀
⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠀⠀⠀⠀⠀⠀⠀⠸⡆⢳⣀⡀⠀⢀⠜⡠⠊⠈⠢⡘⢆
⠙⣦⠄⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡠⠍⣑⠊⠰⠥⠀⣀⣀⣳⠈⢆
⣼⠁⠀⠀⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢳⡀⠀⠉⠉⠐⠒⠒⠀⠤⡀⠘⡄
⠻⣄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠳⢤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢆⠳⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠳⣦⣀⡀⠀⠀⠀⠈⢧⡙⣄⠀⠀⠀⠀⠀⠀⠀⢁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠀⠀⠀⠀⠀⠱⣌⠳⡀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠈⠳⣌⠲⣄⠀⠀⠀⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠿⢶⣤⣀⣈⠳⣌⠙⠢⠤⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⢿⣦⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⣤⣤⣤⢀⣀⡀⣀⡙⠂⠀⠠⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠗⢮⠙⠉⠈⠀⠀⠈⠀⠙⠉⡓⠲⣦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠊⠀⠀⠁⢀⡄⠀⠐⠀⠀⠁⠈⡹⢶⣀⣀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠠⡀⠈⠀⢀⠀⠀⠄⡈⠀⣠⠞⠃⢸⠋⠈⠙⢿⢦⠙⠶⡌⠑⢄⠀⢸⢃
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠑⢢⡀⠀⣰⠛⠁⠀⡞⠀⠀⠀⠘⡏⢳⠀⠘⢆⠀⠢⠈⠁⢀
⠀⠀⠀⠀⠀⠀⣸⠹⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⣼⠋⠀⠀⣼⠁⠀⠀⠀⢀⡇⠈⠀⠀⠀⢣⠀⠱⠀⡼
⠀⠀⠀⠀⠀⠀⡇⠀⢻⡀⠁⠄⠀⠂⠀⠀⢀⡞⢀⠀⠀⣸⠃⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣇⠀⢱⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠹⣤⠀⠂⠀⠀⠀⡜⠀⠀⢀⡞⡱⠀⠀⠀⠀⢀⡟⠀⠀⢸⠀⠀⠀⡟⣤⣸
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⢦⡌⠀⡜⠁⠀⣠⠎⠰⠁⠀⠀⠀⠀⡼⠀⠀⠀⢸⡶⠟⠛⠁⠀⠘
⠀⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠙⠲⢤⠴⠞⠁⢠⠄⠀⠀⠀⢀⣾⠃⢀⣤⣤⠆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠄⢀⣀⣀⠉⠂⠐⠻⠟⠁⠀⠉⠁⠈⠁⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠀⠤⠤⢀⣀⣀⠀⠀⠈⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⣠⠖⠂⠉⠀⣀⡤⠔⠒⠂⠐⠁⠀⠐⠢⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠊⠀⢀⣴⠊⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⣠⣂⣤⡾⠥⠤⣤⠾⠒⠒⢲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠔⠋⢁⠞⠀⠀⡰⠃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣌⡀⠀⡾⠀⠀⣸⠃⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠉⢹⠛⠒⢻⡟⠒⠲⠶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠁⠀⠈⠉⠣⢄
⠀⠀⠀⡃⠀⠀⡟⠀⠀⢸⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠖⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⡓⠦⢤⡇⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠈⠑⢦
⠀⠀⠀⠱⣄⢸⡍⠛⠓⢾⡤⣀⣸⡄⠀⠀⠀⠀⠀⡠⢋⣀⡄⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⢀⡴⡟
⠀⠀⠀⠀⠈⠂⠓⠄⡀⠘⣧⠀⠀⡄⠀⠀⠀⠀⡰⣡⠟⠁⠀⣀⠌⠁⠘⠛⠶⣦⣤⣤⣤⠶⠎⠂⠁⠀⠀⠀⠀⢀⠔⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⢈⣢⣀⠀⠠⣷⢏⠠⠀⠉⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡒⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠛⠛⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣛⣭⣍⣻⣋⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⠴⠶⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠯⠭⠥⠤⣄⣀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠒⠒⠲⠤⣄⣠⡴⠒⠓⠦⡶⠚⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠠⠒⠒⠠⢄⡀⠀⠀⠙⠶⠴⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢦⡀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢀⡠⠤⠤⠤⡈⠐⢦⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⢠⡀⠭⣙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⠜⠁⠀⠀⠀⠀⠈⡆⠀⠳⢄⡠⠔⠃⠀⠀⠀⢀⡠⠤⢄⡉⠲⡄⠱⡌⢳⡀⠀⠀⠀⠀⠀⠀⡴⠤⠞⠁
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠈⠢⠤⠤⠤⠀⠠⠔⠁⠀⢀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠙⢆⢸⠀⠈⡄⡇⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⡟⠀⢀⠤⠤⠤⣄⠀⣠⠔⠒⠒⠒⠊⠁⣹⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⢸⠀⠑⠊⠀⡇⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⣧⠀⢇⠀⠀⠀⢸⠀⢇⠀⠀⠀⠀⠀⡰⠁⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⢇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠑⠂⠤⠜⠀⠀⠉⠒⠒⠒⠊⠀⠀⠈⠒⠠⠄⠒⠒⠒⠒⠒⠂⠉⣀⣀⣠⡴⠟⠋
⠀⠀⠀⠀⠀⠀⣀⣠⣍⣛⣒⣲⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠛⣛⣛⣛⣛⣛⣋⣉⣩⣭⣭⣥⣀
⠀⠀⠀⢀⡤⠚⢁⡠⠤⠤⠀⢉⡉⠉⠉⠉⢉⣉⣉⠉⠉⢉⣉⣉⣉⡉⠁⠤⠤⠤⠠⠤⡀⠀⠀⢹⡆
⠀⢀⡴⠋⠀⠀⢢⣀⣀⣀⣀⣀⠝⠀⠎⠉⠀⠀⠀⠱⡀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠇
⢀⡞⠀⠀⠀⡴⠒⠤⣄⣀⠤⣄⡀⠀⠑⠢⠤⠤⠤⣀⠈⠑⢆⠈⠉⠢⡀⠀⠀⠀⢀⡴⠃⠀⡔⡿
⠸⡇⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⡠⠤⠤⠤⢌⠉⠁⠀⠀⠀⠈⠑⣒⣈⠁⠀⡠⠊⡼⠁
⠀⢻⡤⣀⡀⠀⠑⠢⢄⣀⣀⣀⠤⠊⢐⠁⢀⡀⠀⠀⠀⡃⠀⣖⠂⢉⣉⡡⠔⣊⠔⢊⣠⠞⠁
⠀⠀⠙⠲⢬⣉⣒⠒⠤⠄⢄⢀⣀⣀⡀⠉⠀⠈⠑⠒⠒⣁⣀⣀⡠⠤⠔⢚⣩⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠶⠤⠤⠤⠬⠭⢭⠭⠭⠤⠤⠤⠶⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⢿⣟⠛⠛⠛⠛⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⣀⣀⣀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠙⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡴⠋⠁⠀⠈⠹⣆⢻⡀⠀⡆⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⡞⠀⠀⠀⠀⠀⠀⢹⠌⠳⣄⠀⠠⠤⢤⣀⡀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣀⣀⠳⠴⠖⠦⢤⣀⡤⠟⣀⣀⣈⠳⣄⠀⠀⠀⠙⠂⠀⠸⣧⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⠞⠉⠀⠉⣧⠀⠀⡞⢳⠄⡴⠋⠉⠀⠈⢷⡘⣧⠀⠀⠀⠀⠀⠀⠘⠳⢶⣤⡀⣀⠞⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠇⠀⠀⠀⠀⠙⠲⣄⠈⢁⣴⠇⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢰⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣾⣶⣶⣤⣀⡀⠀⠀⢸⠄⣏⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⠀⠀⠀⠀⣠⣤⡴⠟⠛⠳⢦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠞⡿⠊⠉⠉⠉⠳⡍⢛⣻⣿⣿⣷⣿⣳⠶⢦⣄⠀⢠⡞⠁⡾⠁⠀⠄⠀⢀⣠⠞⠁
⠀⠀⠀⢀⣤⢞⣫⠭⠷⠶⠶⠦⢤⣕⠢⠖⢚⠭⣍⠑⠋⠀⠀⠀⠀⠀⠉⢙⡆⢹⠞⠉⣠⡾⢁⣀⣠⡴⠞⠋
⠀⠀⠀⡿⢡⠋⠁⢀⣀⣀⠀⠀⠀⠈⡳⢀⣨⠴⠥⠊⠀⠀⠀⠀⢀⣀⡤⠞⣡⣿⠶⠾⠛⠛⠋⠉
⠀⠀⠘⣷⠀⠙⠩⠥⠤⢌⡑⠢⠴⠚⣵⠋⠀⠀⠀⠀⢀⡴⠖⢛⣉⣥⠴⢚⣡⡟
⠀⠀⠀⠻⢦⣄⣀⣠⣤⣤⣈⠓⢤⡀⠙⠶⠤⣤⣤⠴⠋⡴⠊⣩⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠳⣦⣈⠓⠢⠤⠤⠤⠴⠊⣠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣤⣤⠾⠋






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠂⠁⠀⠈⠁⠁⠁⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⣉⣡⣤⣴⣶⣶⣶⣶⣤⣄⡙⠦⡀
⠀⠀⠀⠀⠀⣾⠉⠉⢳⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⠄
⠀⠀⢠⠖⠋⠁⠀⠀⠀⠱⣦⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡄
⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢄
⠀⠀⠀⠿⣄⠀⣀⣤⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠢⡀
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣴⣿⣿⣿⣿⣿⣿⣿⣷⡿⣡⣴⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠰⠿⠿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡷⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣤⣉⠛⠛⠛⠛⠛⠛⣋⣉⣛⠛⠛⠛⠛⢋⣉⡩⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉





⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢛⣛⣛⣉⣉⡛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⣿⣶⡛⠀⠈⢳⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⣿⢻⣽⣿⣿⣷⣟⠀⠀⢸⣏⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⣠⠴⣲⡿⠋⠉⣠⠖⠋⠀⢀⣿⢻⣽⣿⣿⣿⣟⠀⠀⣸⣯⠟⠉⣩⠟⠉⠉⣹⠷⠦⣄⡀
⠀⠀⠀⠀⣾⣡⠞⠁⢀⡴⠛⠁⢀⣠⠞⢉⡇⠻⠿⠿⠿⠷⢟⣠⡾⠛⠁⣠⠞⠁⠀⣠⠞⠁⢀⡴⠋⣷
⠀⣀⣀⣀⣿⠓⠦⣶⣋⡀⣀⡴⠋⠀⣠⠾⠛⠛⠋⠉⠉⢉⡽⠋⠀⣠⠞⠁⠀⢀⡼⠃⢀⣴⣯⠴⠚⣿⣀⣀⣀⡀
⡞⢩⡤⠤⢤⣄⠀⠀⠈⠉⠙⠛⠒⠺⠷⠶⠤⠤⠤⠤⠴⠯⠤⠴⠾⠥⠶⠶⠖⠛⠛⠋⠉⠁⠀⠀⣠⣤⠤⠤⣬⠙⡆
⠹⣌⡛⣋⣩⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣭⣉⡓⣋⡼⠃
⠀⠈⠉⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣉⣓⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣚⣋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢩⡏⠀⠀⠀⠉⠻⡯⠭⣿⠛⠁⠀⠀⠹⡏⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⣏⠀⠀⠀⠀⠀⢷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠸⡆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡷⠦⢤⣀⡀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⢀⣀⣠⠴⠾⡆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠶⢤⣄⣀⠉⠙⠒⠶⢤⣧⡀⣿⠴⠖⠛⠉⢁⣀⣤⠴⢷⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⡽⣿⡤⠴⠖⠋⠉⠁⠀⠀⠸⡆⠘⣇
⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣄⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣨⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⡼⠃
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⠶⠷⠶⠷⠶⠶⠶⠾⢻⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡴⢟⡋⣠⣐⣒⣤⣄⠐⣃⡀⣈⡁⠰⢶⣄⣉⡁⠙⠛⠻⢷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⢀⡄⠈⣴⠏⢉⣉⠀⠴⠀⠉⠁⠋⠉⠰⢶⠀⠀⠁⠖⠸⠳⢦⣀⠬⡉⢿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⢋⡉⡡⢖⡚⠁⣥⡾⢳⡄⢀⠀⠀⣛⡛⠀⠙⢁⡀⢀⡤⠶⠖⢲⡀⠲⠆⣈⠐⠀⣤⠀⡍⢿⣤⡀
⠀⠀⠀⣴⡶⠶⠶⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⣶⡄
⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⣿⣿⣷⣦⣤⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⣤⣤⢴⣿⣿⠋⠈⣷⣯⣛⣿⣷⣤⡈⢿⣿⣿⣿⣿⣿⣿⡶⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠘⢿⣿⣷⣿⣿⣿⣿⣿⡿⣿⠅⠀⣿⣿⣿⣿⢟⠁
⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡉⠉⠘⠿⠿⠿⠮⠃⠉⠀⠀⣿⣿⢿⣷⠎
⠀⠀⠰⠂⠈⠭⠉⠉⠛⠛⠿⢿⡿⠿⠛⠛⣉⣉⠉⣭⠀⠀⢀⡐⠀⠀⠀⠐⢾⣿⣿⣿⡿⠆
⠀⠀⣜⣒⣲⠦⣄⣉⣀⣀⣀⣾⣧⡰⣶⣷⣟⣛⣛⣿⣿⣲⣦⡶⠶⠶⠂⠀⠀⣹⡿⠛⠁
⠀⠀⠂⠐⠒⠂⠐⠒⠒⠒⠒⠊⠉⠉⠻⢽⣽⣿⣿⣿⣿⣿⣿⣖⣓⣀⡤⠖⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠁⣿⣎⠇⠀⠐⠫⠐⠛⠀⠀⢀⠺⠹⠀⠀⠀⠰⠥⠀⠄⠀⠀⣄⣔⠒⠀⠀⠠⠤⠭⠤⠀⠀⠠⠌⡫⠄⠀⠀⠈⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡔⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⡀
⠀⠒⠒⠂⠂⠀⠀⠸⠿⠃⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠯⠽⠃⠀⠀⠀⠾⠥

⠀⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⢄⠀⠀⣀⡀⢄⡀⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢀⠘⠀⠀⠈⠉⠉⠁⠀⠀⠛⠛⠛⠁⠀⠀⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠄
⠀⠒⠒⠒⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠐⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠈⠁⠁

⠀⠠⠠⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⣀⣈⡁⠀⠀⢀⠰⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠐⠐⠂⠀⠀⣀⣀⣢⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⠿⣿⣿⣿⣯⠉⠽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⡉⠉⢻⡏⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡁⠀⠀⠀⠀⡛⠻⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢤⣤⣤⣤⣤⣤⣤⣴⡶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠛⢦⠤⠤⠤⢷⠖⠛⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣽⣭⣹⣛⣛⠿⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⣾⣳⣦⠀⠀⢸⠄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⢭⣭⣛⣛⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠿⣿⠿⠁⠀⠘⣗⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢟⣻⣿⣴⣿⣯⣭⣿⣿⣷⣾⣭⣭⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢠⠶⠾⣧⡀⠀⠀⠠⠀⠀⠀⠠⢿⠄⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠸⣄⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠺⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠟⠻⠛⠿⣿⡿⠛⣏
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠤⠂⠀⠀⢸⠇⣤⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣇⠀⠀⠀⠀⠀⠈⣎⠙⢛⠛⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠽⠷⣤⣄⣀⣀⣀⣨⡤⠾⠗⠻⡅
⠀⠀⠀⠀⢠⡿⢻⡇⠀⠀⠀⠀⢀⣠⡤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⣤⣾⣄⠀⠀⠀⠸⡆⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⣿⣹⠁⠀⠀⠀⣴⣏⣷⣿⣿⣿⣿⣿⣾⣹⢦⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⣯⣿⣿⣧⠀⠀⢀⣷⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⢹⡏⠀⢤⠤⡼⣷⢹⠓⠣⣷⠛⠹⡩⠚⢝⣾⢷⠤⣤⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠚⡿⣿⠿⠃⠂⡀⠈⢽⣃⠔⣀⠈⠀⢳⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⢰⡇⢿⢸⠀⡃⣿⠘⢣⡇⣿⢸⢺⢸⡇⡇⠀⠀⣿⠀⠀⠀⠀⠀⣠⡶⢿⣿⣤⠈⠔⠂⠐⡡⠈⠀⠀⡐⠂⠼⣇⠀⢁⠐⠀⠀⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠸⠄⣧⣿⢸⡀⢃⣿⢘⣣⣇⠋⣘⣸⣸⠇⠧⠀⠀⣿⠀⠀⠀⠀⠐⣏⠀⠄⠘⣷⡇⠐⠁⠀⠠⠈⣀⠀⡀⠂⠠⢯⡴⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢯⡦⣶⣶⣶⣷⣾⣯⣵⢛⣸⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠶⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠯⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣷⣫⠟⠉⠛⢦⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠛⢁⣤⣤⡀⠀⠀⠀⢀⡀⣠⠴⠛⠁⡌⠉⢁⡀⠀⠀⠈⠑⢲⠜⠁⣤⠔
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠟⠉⠀⠙⢶⡄⠄⡉⣟⠡⠀⠊⢀⣄⠀⣸⣷⠀⠀⢀⣴⠇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠀⠀⠀⠀⠀⠉⢶⣄⡤⠀⣠⠄⢈⣿⣀⣿⣿⡖⠊⠀⠁⠀⠠⢇⣼⣿
⠀⠀⠀⢠⣦⣀⡀⢈⡴⠁⠀⠀⠀⠀⠀⢈⣿⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⠄⠀⢀⢡⡶⢋⢉
⠀⠀⠀⠀⠈⠙⠻⣮⣼⠷⢤⣀⠀⠀⣠⣾⠗⠀⣀⠈⠀⢨⣿⣿⣿⣿⣿⣿⣶⣿⢠⣶⣤⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠲⣬⡁⠀⠀⠉⠷⢶⣿⣃⡀⣀⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⢀⣴⠄⠈⠙⢶⡀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣉⣀⡠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠛⠋⠲⠦⣀⡀⠉⠲⢦⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠈⠛⠉⠀⠀⠀⣠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠷⣶⣤⣽⣿⣿⣿⣿⡿⠿⠟⠿⠛⠋⠀⢀⡄⢀⡀⠀⠀⣠⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢁⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠴⠿⠟⠉⠀⠀⠈⠀⠀⠀⠊

⠀⠀⠀⠀⢀⡤⠶⠲⢿⠉⠉⠉⢹⣟⠓⠶⢤⣀
⠀⠀⢀⢖⣵⣿⣿⣦⡈⢧⠀⣠⠏⠹⡄⠀⡼⠹⡟⢦⣄
⠀⢰⢣⣿⠋⠀⠈⠻⣷⡘⣟⠁⠀⠀⢻⡼⠁⠀⠹⡄⡟⢳⣄
⢠⣏⣿⠃⠀⠀⠀⠀⠹⣇⢻⣆⠀⣠⠞⢳⡀⠀⠀⣹⡇⠀⠘⢷⣄
⣼⢸⡏⠀⠀⡀⠀⠀⠀⢿⢸⡿⣞⠁⠀⠀⢳⡀⡼⠃⠹⣄⢀⡾⠙⢷⣄
⡟⣿⠁⢠⠋⠙⣷⠀⠀⢸⡜⡇⠹⣆⠀⠀⢀⡿⡅⠀⠀⢙⣾⠁⠀⢨⣿⡳⣤⡀
⣧⣿⠀⣾⠀⠀⣿⠇⠀⢸⡇⣧⠀⠹⣆⡴⠋⠀⠹⣄⢠⡞⠉⢧⣀⡞⠀⢳⡄⣽⢷⣄
⣿⣿⠀⢹⣄⣴⡿⠀⠀⢸⠇⡏⢀⡴⠻⣆⠀⠀⠀⣹⣏⠀⠀⢈⣿⡀⠀⠀⣹⣇⠀⢈⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀
⣿⣿⠀⠀⠉⠉⠀⠀⠀⣾⢸⣿⡋⠀⠀⠘⣦⢀⡞⠁⠈⢧⣠⠞⠀⠹⣆⣠⠏⠘⢦⣼⠁⠘⣟⢻⡟⢻⣿⣷⠤⠤⣤⣤⣤⠞⠁⠀⣼
⣿⣿⡀⠀⠀⠀⠀⠀⢰⠇⡾⠀⢳⡀⠀⢀⡼⢯⡀⠀⠀⣰⠿⡄⠀⠀⣸⢧⡀⠀⣸⠳⣄⠀⠈⣿⢧⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢧
⢸⡿⣇⠀⠀⠀⠀⢠⠏⣼⡇⠀⠀⢻⣴⠋⠀⠀⠳⣤⠞⠁⠀⠙⣦⡼⠁⠀⠳⣴⠃⠀⠈⣳⣴⣃⣠⣿⣿⠟⠛⠛⠛⠛⠛⠳⣤⣀⣀
⠀⢧⠻⣄⠀⢀⡴⢋⡼⠃⢹⣄⡴⠋⠙⣆⠀⢀⡴⠛⢦⠀⠀⣠⠏⣳⣄⣠⣼⡿⠿⠿⠿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠈⢧⣈⠛⣋⡴⠟⠀⢀⣴⣻⣄⣤⣤⣼⣷⣯⣤⣤⡼⠷⠾⠟⠛⠉⠉
⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢒⣁⡤⣠⣦⣤⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠛⠛⢻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣤⠀⡏
⠀⠀⠀⠀⠀⠀⢠⡲⣿⣿⡆⠀⠀⠀⣠⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣀⢰⣿⡄⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠟⠁⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⡀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣇⠂⠀⠀⠀⠁⡴
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡻⣿⣿⣷⣄⡀⠶⣾⡁
⠀⠀⠀⠀⠀⢀⠖⠛⢢⡀⠙⢮⡛⠿⠿⢿⣿⣿⡻⡢⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠹⡄⠀⠱⡄⠀⢰⣿⣿⣿⣇⢡⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⣄⠀⢹⣿⡿⣿⣿⣇⠀⠀⠀⠀⢾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠈⠉⠈⢿⣷⠘⠿⠸⡄⠀⠀⡰⠛
⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢱⠀⡸⠁⠀⠘⢿⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⠁⠀⣤⠀⢺⡏⠁
⠀⠀⠀⡇⠀⠀⠀⢀⠀⢾⣣⡟⠀⠀⠀⢀⣀⣠⠀⠁⠀⠈⢁⡠⠂⠀⠙⠛⠛⠀⢀
⠀⠀⠀⢡⠀⠀⠀⡡⢖⢛⡷⠒⠘⠉⠉⠁⠀⢰⠀⠀⠀⠀⢸⣽⣇⠤
⠀⠀⠀⠘⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠒⠉⢸⠐⠄⣾⣛⠛⠛⠛⣛⠛⠃⡄
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠏⠀⢀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠲⠆⠶⢶⠒⢚⠋⠍⠅⠤⢨⡧⠷⠶⠶⠾⠶⠶⠞⠣⠶⠀⠀⠀⠀⠀⠠⠀⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢚⡔⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠖⢤⠏⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠾⣤⠎⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠐⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⢄⡔⢲⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢃⠾⣡⠎⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⣠⢐⡖⠁⡀⢡⠴⠾⡧⠖⠓⠀⠀⠘⠉⠉⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠈⢁⣨⠤⠁⢢
⠀⠀⠀⠀⡸⡱⠊⡀⠊⠀⠈⠂⠀⠠⠤⠠⠒⢶⠲⠚⠙⣻⣻⡯⠉⠫⣭⠫⠼⢏⠙⠿⣯⠜⢛⡷⠮
⠀⠀⠀⠐⢻⢠⠊⠀⠀⠀⠐⠀⠁⠊⡁⠀⠀⠀⢳⣤⡴⠏⠁⠛⠻⡹⠊⠁⠠⠼⠷⠈⠤⢿⣛⣽⠤
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣤⣤⣤⣄⣀⣀⣀⠀⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⡷⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢋⡀⠤⠖⠋⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⣀⠔⠊⡡⠒⠉⠀⠀⠀⠀⠀⠀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⠀⣠⣴⣾⣿⣿⠟⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣠⠖⠁⠈⠛⠿⠿⠓⠀⠀⠀⣰⡏⠐⠻⠿⠟⠋⠀⠑⢦⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⡀⢠⣿⡇⠀⠀⣠⠀⠀⠀⠀⠀⠙⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢹⠇⣼⣿⣇⠀⠰⣿⠀⢠⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⡄⢠⣷⡿⠀⠀⠀⣿⣿⣿⡄⠀⠃⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡄
⠀⠀⠀⠀⠀⢀⣴⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣿⣿⡇⢸⣆⢰⣿⣿⣿⣷⢠⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⣄
⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣼⡇⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦
⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠿⢿⣿⡟⢻⣿⠟⣛⡛⣿⢛⣛⠻⡟⣛⣛⣿⢛⡛⢿⠻⣿⡿⡿⠿⠿⣷⣶
⠀⠀⠀⠀⢤⣴⣶⣶⣶⣶⣶⣿⣿⠀⣛⠠⣿⠱⠆⢿⡇⣭⠡⣿⢨⣭⠘⡇⢨⣽⡇⢺⣿⢾⠐⣿⡇⡇⢘⣻⣿⣿⣶⣶⣶⣶⣶⣶⡤⠄
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣀⣛⣥⣧⣿⣿⣼⣷⣿⣷⣿⣶⣶⣾⣷⣶⣶⣿⣦⣵⣾⣦⣭⣼⣧⣘⣛⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠴⠿⠿⠿⠟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠿⠿⠿⠦
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠀⣰⠂⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡇⡠⠉⣀⠄⠤
⠀⠈⠀⠀⠐⠀⠀⠀⢄⠀⠀⠢⠀⠠⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢵⡆⡄⣏⣤⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⢈⡙⠾⣄⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠨⠉⠀⠉⠀⢐⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⣀⠀⠀⡀⠂⠀⠀⠆⢠⠀⠩⠑⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡤⠉⠙⠒⠺⢦⣁⣢⡀⢾⠀⢠⠐⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠖⠋⠁⠘⠂⠈⣃⠈⠠⠀⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⠀⠀⣀⠤⢤⣄⣢⢄⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠉⠀⠒⠠⠀⠐⠂⠀⠀⠙⠒⢛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⠙⠋⠉⠑⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣠⢰⢠⠀⣀⠄⡄⢠⠄⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠉⠘⠘⠐⠙⠐⠁⠘⡘⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣤⡴⢖⣚⣛⣉⣉⣉⣙⡓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⣠⣴⠟⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣴⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡟
⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠟⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢋
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣫⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⣠⡾⠁
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣻⣼⠟⠁⢀⣴⣶⣶⣶⣦⣄⠀⢰⡏⢠⣾⡿⠁⣠⣴⣶⣿⣿⣿⣷⣦
⢀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⣫⣾⠟⠁⠀⢀⣿⣿⡿⠛⠛⠿⣿⣷⡈⢠⡿⠋⣠⣾⣿⣿⣿⠟⠉⠀⠀⠉
⣼⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣵⡿⠋⠁⠀⠀⠀⠈⢿⣿⣧⣠⠀⠀⢹⣿⡇⠘⢁⣾⣿⣿⣿⠟⠁
⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣸⡟⠀⣠⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣀⣾⣿⣿⣿⠟⠁⣀⣤⡴⠶⣒⣀⣀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢟⣯⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣠⣴⣾⣿⡿⠿⠋⣡⣴⣿⠟⠉⠐⠊⠉⠉⢙⣿
⠈⢿⣿⣿⡿⣟⣋⣭⡶⢟⣻⣵⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠩⢭⣤⣴⡾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠈⡿⠿⠿⣛⣯⡵⠞⠛⣉⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠉⠛⢋⡩⣴⣶⡿⠿⠛⠛⣩⣟⠛⢁⣤⠖⠀⣠⡞⠀⢠⡾⠠⠀⣶⠀⠈⢯⡉⠉⢿⡟⠿⠿⢷⣦⣤⡀
⠀⠀⠀⠀⣏⢼⡋⠀⠀⣠⡴⠛⠁⢀⡴⠟⠁⠀⣴⠏⠀⠀⣼⠇⠀⠀⣿⡅⠀⠈⢷⡀⠀⠙⣦⡀⠀⠈⠙⢯⡂
⠀⠀⠀⠀⠹⣾⣿⣴⣿⣁⡀⣠⡼⠋⠁⠀⢠⡾⠋⠀⠀⢰⣿⠀⠀⠀⢹⡇⠀⠀⠘⣷⡄⠀⠈⢻⣦⣠⣴⣿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣦⣤⣾⣧⣤⣤⣤⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⡿⠟⢛⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣭⣽⣛⣛⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⣾⡇⢸⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡾
⠀⠀⠀⠀⠀⠀⠹⣎⢿⣿⣿⡉⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣿⣿⣦⣬⣭⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠈⠉⠉⢹⣿⡏⠉⠉⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣤⣶⣶⣶⣿⣿⣇⣿⣿⣸⣿⣿⣿⣷⣶⣶⣦⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠈⠻⠿⣿⣿⣛⣿⣿⢻⣛⣻⣛⠿⠍⠁⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡶⠒⠒⠒⠒⠒⢲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⣒⡒⠒⠒⠒⠒⠒⠚⠃⣠⠗⠒⠒⠒⠒⠒⠚⢧⡀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⡽⣛⡛⢦⡀⠀⠀⣞⢓⣒⣒⣒⠒⣒⣒⡒⣒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠞⠹⡟⠁⠉⢻⠇⠀⠀⠉⠉⠉⠉⠉⣩⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡶⢶⣏⣀⠀⠀⠀⠀⠀⢯⠀⢸⠆⢸⡄⠀⠀⠒⠒⠲⡖⠒⢲⡖⠒⢶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠉⠀⠈⣷⠀⠀⠀⠀⢘⣀⣤⣄⣘⠁⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠀⠀⡶⢳⢄⣿⡀⠀⣀⣰⠯⠥⠤⠤⠭⢷⣀⡀⠀⠀⠀⡇⠀⣸⣇⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣅⠀⠘⠳⢦⣠⣟⡏⢠⠈⠓⠶⠯⣿⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡞⢹⣆⡏⢹⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡶⠴⣇⣹⠇⢺⠶⠶⠶⠶⢾⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠙⠚⠙⠓⠚⠈⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠳⠶⠶⠶⠶⠞⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣶⠶⠶⣶⣶⡶⠶⢶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣿⠸⠭⠇⠸⠭⠭⠿⠀⠯⠟⢸⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢛⣛⣛⣛⣛⣛⣛⣛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣈⣉⣉⣉⣉⣉⣉⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠐⢀⠠⣄⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠈⠁⠈⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⡀⢠⠄⣠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣼⣱⣿⣆⠫⣆⠀⠀⠀⣰⣿⣿⢦⡀⠀⠀⢀⡾⢡⡀⠀⠀⠀⣠⣾⠆⠀⠀⠀⣠⡾⡀
⠀⠀⠀⠀⢿⡿⣮⡈⡼⢢⢟⡆⠀⠰⣏⡻⣴⡾⡷⠀⠀⢼⠿⣆⣿⠀⠀⠘⢿⣏⣠⠇⠀⠀⢿⡱⢹⠆
⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⢀⡖⣩⣦⣭⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⢀⣹⣆⢾⡄
⠀⠀⠀⠀⠈⢰⣿⣿⣿⣗⠘⠀⠀⠀⠀⠀⢀⣠⣾⣟⣿⣦⣀⠀⠀⠀⠀⠀⠀⢠⣿⢈⡸⢿⢻⢸⣷⣠
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⣰⣿⡿⣿⡿⡿⣿⣿⣷⠀⠀⢀⣀⢀⣟⣻⣎⣻⣆⣾⣾⣹⣟⡁⢀⡀
⠀⠀⠀⠐⣒⠀⠀⠀⠀⠉⣙⣓⠀⠀⠀⣿⣯⡇⢺⡇⢸⢱⢸⣿⡇⠀⠀⠘⠻⡍⢿⢹⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣷⣧⣵⣯⣜⠎⡰⣿⠃⠀⠀⠀⠀⠙⢮⣣⣻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠤⠠⠩⠉⠉⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢈⠟⠉⠉⠉⠛⡃
⠀⠀⠀⠀⠀⢰⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⡜⠒⠒⠲⠶⠒⢳
⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠠⢤⣿⢾⣿⣦⠄⠀⠀⠀⠀⠀⠀⢠⠄⠐⠀⠠⡀⠀⠀⠀⠀⢰⡉⢹⡆⠄⠀⠀⠀⠄⠀⠸⣄
⠀⠀⠀⠀⠀⠈⡿⠿⢿⠁⠀⠀⠀⠀⠀⣠⠔⣡⣶⡶⢶⣦⡈⠢⡀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⡆⠀⠰⢱⣿⡍⠀⠀⢰⠀⠀⢘⠡⣴⣿⣿⣤⣼⣿⣿⣲⠉⠂⠀⠀⠀⠀⠠⡀⢸⣭⢀⣤⡀
⠀⠀⠀⠣⢠⣃⡈⠀⣉⣻⡇⠜⠀⠀⠲⣄⠙⣿⡏⠏⠻⣻⡿⢚⡴⠂⠀⢀⡀⠀⣀⣙⢦⣥⢚⣋⠀⠀⣀
⠀⠀⠀⢰⣰⣮⡅⠄⢸⣅⣦⡦⠀⠀⠀⠈⠀⣈⠛⠛⠛⢋⡠⠊⠀⠀⠀⠈⠉⠉⠉⣩⠞⡟⢺⣍⠉⠉⠉
⠀⠀⠀⠈⠀⠒⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠇⠀⠙⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⡶⢿⡿⠿⠿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠛⠻⡄⠈⠳⡄⠀⠹⡄⠈⠄⣁⠈⠟⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢷⡄⠹⡄⠀⠹⡄⠀⠹⡄⠀⠀⠂⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠈⣿⡄⠹⡄⠀⢹⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⣠⡿⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢀⣤⣄⠀⠀⢸⣧⠀⢳⠀⠈⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⣤⣤⣾⠟⠁⣴⣿⣁
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣾⡟⠻⣷⡄⠀⣿⡀⠈⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇⠀⠀⠈⠈⢙
⠀⠀⠀⠀⠀⣀⣼⡿⠀⢸⣿⠀⠀⢹⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠷⠶⠶⠶⠿
⠀⠀⢀⣴⡾⢛⣿⣧⠀⢸⡇⠀⠀⢸⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⠁
⠀⣠⡿⠋⣰⢛⢺⣿⢔⢸⣧⠀⠀⢸⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡛⢿⣧
⢠⡿⠁⣰⠃⠌⠴⣿⣋⡘⣿⣄⣠⣾⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣴⡿⠃⠀⣷⠈⣿⡇
⣾⡇⢠⡏⠀⠈⠀⢹⡏⠁⠈⠙⠛⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣠⣾⠋⠀⠀⠀⡿⠀⣿⡇
⣿⡇⢸⡇⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⡭⣖⣴⡿⣿⠁⠀⠀⢀⡼⠁⣰⡿⠁
⢻⣇⠀⢷⡀⠀⠀⠀⠸⣷⡀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣀⣀⡬⢶⣺⣿⡿⠟⠩⢋⠁⠂⢀⡠⠚⠀⣴⡿⠃
⠈⢿⣆⠈⢳⣄⠀⠀⠀⠙⢷⣤⣀⣠⣾⣃⣀⣀⣀⣀⣤⣤⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⣠⠴⠋⢀⣠⣾⠟
⠀⠀⠻⣷⣄⠉⠳⣤⣀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⡤⠖⠋⢁⣠⣶⠟⠋
⠀⠀⠀⠀⠙⠻⣶⣤⣉⡛⠳⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠖⠚⢉⣁⣠⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣶⣤⣤⣄⣀⣈⣤⣤⣤⣤⣶⠶⠾⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⢿⡿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⠳⡖⢋⠕⢊⣾⠟⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣿⠃⠀⠉⠉⢠⣿⠇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢧⠀⠀⠀⣾⣿⣀⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣧⣀⣼⡇⢀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣄⠀⣀⣠⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣟⢶⡀⠀⠀⠀⡼⠁⠀⣰⠋⠉⠁⢸⡇⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⢫⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⠿⠀⢹⡆⠀⡰⠁⢀⡜⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣇⢀⣠⠗⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡿⣄⢀⣀⡼⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⢷⡿⡆⣤⠀⢁⠀⡀⢰⠃⠀⠀⠀⠀⠀⣰⠃⣬⣿⡿⠟⠋⠉⠀⠀⣀⣤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡿⣔⣿⡻⠛⢡⡀⠀⠀⠀⠀⡴⢁⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠀⠈⠁⠙⠉⠳⠤⠏⢹⣄⣀⢀⣜⡡⢟⣫⣥⣾⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠀⢀⣺⣷⣤⣦⡀⠀⢀⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣏⠀⠉⣷⢀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⢀⡤⠤⢴⡶⠶⠒⠒⠛⠓⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⢤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠙⠲⠦⣤⣉⣉⠛⠒⠶⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⡆⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠛⠛⠛⣛⣻⣿⠿⠟⠛⢛⣿⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣙⣲⣦⣄⣀⣀⣀⣠⣤⡤⠤⠶⠶⠒⠒⢛⣉⣉⣤⡤⠶⠖⠛⣹⣇⣤⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣠⡄⠙⢯⡉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣉⣁⣠⣤⠴⣒⣋⣽⣟⣩⠿⡟⠁
⠀⠀⠀⠀⠀⣾⣋⠀⠀⠀⠀⠈⠳⠦⠤⠤⠤⠤⢴⣶⣒⣚⣿⣭⣭⣿⣶⣚⣻⠯⠿⠟⠛⠉⠁⠀⣼⠃
⠀⠀⠀⠀⠀⢸⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠛⠻⡶⢦⡀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢃⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⡶⠶⠛⠋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢶⣬⣿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣶⡶⠶⣚⣛⣻⡏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⠈⠉⢹
⠀⠀⠀⠀⠀⠀⠙⡝⠒⠦⠤⠔⠒⠂⠉⠀⠀⠀⠀⠀⢈⡢⠀⠀⡠⠔⠂⠉⣀⠀⢶⠆⢪⠁⠀⢸⡇
⠀⠀⠀⠀⣰⢻⡉⠙⠄⠈⢄⣤⣤⠀⠐⠈⠀⠈⠁⠀⠈⠅⣥⣾⣧⢢⠾⠌⠋⡁⠠⠄⠀⠁⠀⢸⣧
⠀⠀⢠⡶⣯⣨⢳⠀⢰⡀⠘⣿⣿⣇⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⢀⠄⠀⣠⠈⠁⠀⠀⢸⣯⢆
⠀⠀⠀⣧⢹⣼⣎⡆⠈⣧⡀⠙⠙⡻⠀⠀⣀⠀⠠⠰⡄⠀⢹⣿⠟⣩⣇⢀⡀⠀⠀⠀⠠⠀⢠⡈⣿⡆⢆
⠀⠀⠀⢹⡈⢿⣿⡾⡄⢸⣧⠈⢁⡄⠁⢀⡁⠀⠀⠀⠀⠀⠈⣿⣷⠄⢿⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⡼⡀
⠀⠀⠀⠈⣇⠸⣿⢿⣷⠀⢿⣇⠈⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣾⡇⢀⠄⠀⠀⠉⠙⠒⠄⠀⢸⡇⣇
⠀⠀⠀⠀⢸⡇⢻⣏⣿⣄⠈⢹⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣃⣠⣶⣿⣛⣛⣛⡳⠶⢶⣾⣿⣺⢢
⠀⠀⠀⠀⠀⢷⠀⢿⣾⢹⠀⢸⣋⠒⢄⢀⣦⣀⢀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣷⡿⣿⣭⣷⡱⡀
⠀⠀⠀⠀⠀⠘⡃⠈⣧⡘⡀⠀⠀⠁⠈⣺⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣻⡿⠿⠿⣿⣿⣿⠿⢿⣶⣿⣿⣶⣿⠥⣘
⠀⠀⠀⠀⠀⠀⠳⠀⢻⣧⠣⠠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠉⠈⠷⣭⣽⣿⣿⠇⠀⠀⠀⠀⠉⠉⠛⠲⠯⣭⣽⣛⠻⢿⡁
⠀⠀⠀⠀⠀⠀⠀⡆⠘⠽⠿⣿⣿⣻⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠶⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⡿⢿⠙⠶⠖⠀⠀⠈⢛⡄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣌⣀⠠⠀⠀⠀⠀⠈⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠀⠠⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⠆⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⢷⣶⠾⠛⣉⡤⠞⣡⣿⡿⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢡⣾⡟⠁⠀⠿⢤⡼⠥⢤⣴⣿⡿⠁⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⣾⣿⠁⠄⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⡀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠈⢷⡀⠀⠀⠀⣸⡿⠛⢿⣶⣤⣤⣤⣤⣤⣼⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⡀⠀⣠⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣀⣀⣿
⢀⠀⠀⠀⠀⠀⠀⣾⣆⢠⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠞⠿⠷⠛⠉⣿⠃⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣷⣴⠞⠋⠉⠉⠉⠙⣿
⣼⡄⠀⠀⠀⠀⠀⢻⡜⠛⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣻⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⡿⠹⡆⠀⠀⠀⠀⠀⢿
⣿⣧⠀⠀⠀⠀⢠⡜⡇⠀⠸⣷⡇⠀⠀⠀⡼⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡧⠚⠁⠀⠀⠀⠀⠀⣸
⣿⣿⣆⠀⢰⡄⠸⠀⠀⠀⠀⣸⠇⠀⢀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢹⡟⢿⣆⣺⢷⡜⢦⣀⢀⣠⠟⢀⡴⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠈⣧⣈⣿⣯⣠⣿⡆⠈⢉⠁⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠛⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠘⣿⣇⠙⢿⠙⢿⣀⣿⡀⢀⠘⡴⢀⣴⢆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡏
⠀⠀⠈⣿⡄⠀⠀⠘⣿⡿⣇⢸⣷⡙⡟⠼⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣾⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡀
⠀⣧⠀⢹⣷⡀⠀⠀⢻⡇⠹⣾⡏⢿⡆⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⢀⡾⠁⣤⣿⡿⠿⠛⢉⡝⠀⡔⣠⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢳⣾⣿⡇⠀⠀⠀⠀⡀⠈⠀⠀⠙⠳⠛⠋⠀⢹⣧⣀⣀⡀⢠⣞⣡⠶⠋⣁⣤⣶⣿⣿⣤⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡀⠈⠋⠋⠀⠀⠀⢦⣿⣦⡀⢠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠘⣧⠀⠀⠀⠀⠀⣷⣾⣿⡯⠻⢿⣿⣦⠀⠀⠀⢸⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠘⣧⡀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠈⣿⣿⣀⣤⢿⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⣤⣤⣀⠹⠿⠿⠶⣖⣒⣭⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⢻⡉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢾⢉⣤⣴⣷⣶⣶⣶⣤⣀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣭⣽⣥⣄⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⢄⣉⣠⠆⠀⠀⠀⠀⠀⠀⠀⣾⣧⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⢋⡅⢠⡆⢸⣾⠃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⢚⣋⣉⣀⣀⢶⣾⢿⠿⡷⢾⡿⢿⣿⣂⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⢖⡞⣻⠏⡹⠋⡽⢋⡿⢛⡶⢦⣤⡆
⠀⠀⠀⠀⠈⢿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⣿⣒⣷⠾⠷⠾⠴⠾⢶⣟⣺⡏⠙⠃
⠀⠀⠀⠀⠀⠈⢷⣌⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⠿⠿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠙⠛⢛⡛⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠸⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣷⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣸⡿⠉⠉⠉⠉⠉⠉⠉⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡶⢲⢞⡿⢻⣿⡳⢲⠖⣾⣧⡀
⠀⠀⠀⠀⠀⣿⣛⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠶⠧⢮⣴⣥⣿⡴⠧⠾⠖⢿⡁
⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠃

⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⢸⣽⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣶⣤⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣟⣿⣿⡏
⣾⣿⣷⠄⠀⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠀⠘⠻⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⢿⣿⣿⠿⠇⠀⠀⠀⠀⠂⠀⠀⠘⠃⠀⠀⣿⡿⠟⠋
⣁⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠋⠀⣤⡈⢶⡖
⡶⣶⢸⣿⠇⢀
⠿⠃⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⣤⣤⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⠿
⡿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣽⠋⣻
⣇⣸⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣿⣿⣴⣾
⣿⣿⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛
⠀⠀⠀⣀⣀
⢀⣠⣾⣯⣽⣿⢧⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⣿⣯⣭⣿⡿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡤⣄⡀⠀⢐⣯⣿⣷⠄
⣿⣿⣿⣷⡿⠙⣟⢿⡿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣽⡇⠀⠀⠘⠋⠁⠀⠂
⣿⣿⣿⣿⡿⢤⣷⣟⣷⢻⣯⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡷⣿⣧⣄⠀⠀⠀⢘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣻⣿⣿⣝⣿⣿⣿⣿⣳⣥⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⣸⣿⣿⣿⠟⠿⣿⣯⣤⠠⠀⠈⠻⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⡇⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠈⠙⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠀⠀⣸⠀⠀⠀⠀⠟⠀⠀⠳⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠖⢻⡟
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⠛⠉⠉⠁⠀⠀⢀⡎⣠⠏
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⢀⡄⠀⠀⢰⠂⣀⣺⡴⠃
⠀⠀⠀⢀⡾⠃⠀⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⣁⣠⡤⠶⠚⠋⠉⠉⠓⣦⣄
⠀⠀⢠⣏⠰⠂⠀⢀⡤⠀⠀⠈⠁⠀⢀⣀⣀⣤⡤⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠾⢏⡉⠀⠀⢀⡴⠖⢺⡏⠉⠉⠁
⠀⠀⢸⡏⠓⠲⠶⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢴⡶⣿⣭⣭⣤⡤⠤⠤⠴⠶⠖⠚⠋⠑⠀⣠⠷⣤
⠀⠀⠈⡇⣇⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠒⠛⢛⡟⠛⠿⠶⠴⠶⠋⠀⠈⡆⠀⠀⠀⠀⠀⠀⠄⢀⣀⡤⠶⠛⣡⣾⠁
⠀⠀⠀⠳⢦⣤⣬⣁⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠖⠛⠉⠉⣇⠀⠈⠆⠀⢀⡼⠁⠀⠀⡆⠀⠰⠀⠀⠀⠁⠀⠂⣀⣤⡤⠶⠚⠉⣁⣠⠴⠚⠁⠘⣇
⠀⠀⠀⠀⠸⣇⠰⠁⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠶⠶⠾⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠛⣉⣁⣤⡤⠶⠚⠋⠉⠀⠀⢰⠀⠀⣿
⠀⠀⠀⠀⣰⠟⠳⢤⣥⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠴⠶⠶⠒⣒⣚⣛⣋⣭⣭⠥⠴⠖⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⠄⠀⠈⣠⡼⠃
⠀⠀⠀⠀⠷⣤⣤⠤⠶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣤⠶⠛⠁
⠀⠀⠀⠀⠀⡟⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠘⣇⠸⠀⢰⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠈⠛⠒⠶⠷⠶⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠒⠾⣄⠀⠉⠱⣄⣀⣀⡤⠤⠶⠒⠒⠚⢋⣭⣭⡉⠉⠉⠉⠛⠒⠒⡶⣦⠤⢤⣀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣹⣦⡀⠀⠈⠛⠙⣄⣇⠈⢧⣀⠀⠀⠀⠀⣠⡿⣽⢿⡟⢿⣿⠶⣤⠀⢰⢃⡷⣴⢳⢠⠏⣼⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠸⣀⠀⠈⣇⠀⠀⢀⠘⢾⠂⠈⠈⢧⠀⠀⢰⡟⢸⣇⣾⣳⣤⣿⠶⣾⡇⡜⣸⢠⢃⣾⢋⡼⢉⠗⡹⠊⠑⠦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠉⠓⠪⣕⢦⡳⢄⣦⡘⢦⡀⢿⣁⡞⢹⣿⡋⠁⢻⣄⣼⣧⣇⢇⡎⣸⢣⢞⡴⡡⢊⣤⣖⣽⠧⢚⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⣒⠶⣭⡳⣌⠳⡵⡄⠉⢙⠲⣍⢿⣿⡀⡸⢘⡏⠲⣤⠏⢠⣿⡸⣸⢱⣣⢫⢎⣾⣿⣿⢟⡫⠗⠋⢁⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢡⣖⡺⠟⢮⣧⠹⡿⣄⠀⠙⢮⣇⣟⠻⣤⣾⣟⣦⣾⣖⣻⣿⣷⣷⡿⡱⣳⢟⢽⣫⡗⢉⡴⢤⢴⠋⠉⢳⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣰⢫⢮⣻⡻⣦⣀⣳⡳⣝⠮⣗⣶⣪⠽⡷⢚⠽⠀⠀⠀⠀⠀⠉⠛⢿⠿⢵⣵⣟⠵⢫⡏⠈⡹⠧⡤⢦⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⢨⣧⣗⣿⡛⠻⣍⠛⡻⠛⠉⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⠀⠀⠉⠲⣍⢠⠚⢁⡴⢦⡞⠀⢸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠺⣿⡏⠳⡉⢳⠈⣿⡁⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠖⠒⠒⠋⠁⠀⠀⠀⠀⠀⢈⡏⠐⡅⢀⡞⢑⡶⠋⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠙⠢⣌⣹⢀⡟⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠗⢲⣋⠭⠛⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠦⣀⠀⠀⠀⠈⠙⠓⠾⠦⣝⣛⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣺⣽⡿⠭⠖⠚⠉⠀⠀⠀⢀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠙⠒⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠒⠉⠁⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠓⠒⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠋⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⣒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣉⠉⠙⠛⠒⠒⠚⠛⠋⠉⢉⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⣟⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠛⠉⠀⠀⠀⠀⢀⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢀⣀⣀⠤⠔⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡭⢝⣛⣳⣬⣽⣿⣿⣯⣴⣾⣿⣯⣽⣒⣲⡦⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⠽⣗⣾⡿⣿⣷⣾⡿⣿⣷⣺⡽⣿⣷⣺⡿⠽⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣭⣿⣿⣯⣭⣵⣿⣯⣭⣽⣶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⠻⠿⣿⠿⠟⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⣤⣿⣤⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠙⠓⠦⣤⣿⡤⠶⠛⠉⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⡰⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣢⡒⢷⡀⠀⠀⠀⠀⡐⠱⣍⠀⠄⡑⢇⣳⣀⠠⢊⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡊⠉⢲⣀⣀⠹⠁⠑⣄⠴⢾⡽⣿⣣⢟⡠⢡⢄⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠱⠘⠃⠀⣤⣋⢌⣛⢻⣷⣟⠋⢠⠁⡼⡀⠘⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢁⠀⡁⢳⡄⢠⣴⠾⡴⡮⢤⣹⣷⣿⠚⣕⡁⢻⣧⡴⠀⣉⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠁⠀⡡⠉⠠⡜⢁⠰⣦⡀⣋⣿⣼⣄⠑⢾⣟⣾⣫⣭⡽⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠛⡔⠧⠀⠀⡠⠿⣲⣦⣹⣃⣼⠋⣻⣸⣟⢖⠻⣟⢻⣿⣦⡁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⡀⠤⡄⠞⠡⠩⣝⠛⠯⡼⡹⢃⣽⡉⠿⣾⠿⡶⠖⢚⠉⠉⡨⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠶⢄⠧⠰⣴⣤⠐⡟⢗⣼⠏⢷⡀⠛⢻⣒⠶⠲⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⣵⡛⡧⡠⢉⡔⠋⢸⠀⣾⠄⢰⡋⠁⠀⠀⠢⣵⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠠⠀⠀⠠⠜⠿⠆⠰⠯⣱⣤⡼⣶⡅⢩⢸⠗⡠⠐⢈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢻⣠⠿⣷⣿⠈⣟⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠹⠟⣄⣽⣷⠾⠇⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢄⠈⣄⣀⠅⡃⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣤⠾⣧⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠘⠗⢾⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡻⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠇⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⠉⠈⠦⠄⠃⢥⡤⠀⠄⠐⢀⡜⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠀⡁⠖⣀⠰⢍⡳⠀⠀⣀⣀⡀⠠⠤⠒⠃⠀⠀⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣾⣛⣫⠍⠐⠁⠀⠉⠉⠀⠀⠀⠀⠀⠖⣦⣿⠁⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠞⠛⠋⠉⠉⠉⣀⣦⠴⣶⡾⡋⢻⣤⢤⣤⣿⣟⣿⣽⣦⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠛⡟⠛⡃⢀⡠⣤⣿⣉⠉⢋⠁⣐⠛⠈⢁⠈⢿⣟⣩⡜⣟⣥⣶⡻⣻⣷
⠀⠀⠀⠀⠀⢠⠗⠋⢓⡆⠲⠛⠿⠧⠜⠉⠉⡠⠆⠈⠁⢀⡴⠇⠤⣀⠙⠛⢿⠷⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠓⠛⠳⠄⠁⠀⠂⠒⢂⡽⢣⠴⠀⠀⠈⠑⠠⠄⠻⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡤⠔⠀⠉⠉⠉⠉⠉⠁⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⢀⣀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⠀⠀⠀⠠⣄⡀⠀⠀⠤⠄⠒⣩⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢻⠀⠀⠀⠀⠀⢀⠶⢆⡀⣀⠰⠚⠁⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠖⠓⠀⠤⠤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢌⡦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠻⣦⠈⠡⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⠶⠶⠶⠆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠔⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢋⡆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠏⠦⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠰⠀⠳⣄⠀⠀⠀⣀⢠⠔⠒⡝⠁⠈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠈⠷⠐⠊⠁⠀⢀⡠⠟⠲⠦⣤⣀⡀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠱⣤⡜⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⡠⠛⠻⠉⠉⠉⠁⠀⠀⠈⠒⢄⡀⠀⢀⠞⠀⠈⠙⠃⠤⠤⠌⠿⠿⣧⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠙⠓⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⡨⠛⢷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⣳⣤⡚⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠒⣒⣖⡚⠛⣻⣿⡛⢻⣿⣖⠒⠒⠖⠲⠚⠷⠲⣶⣶⡶⠶⣶⣶⡿⢵⣶⣤⢶⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠘⠋⠉⠃⠈⢉⠉⠃⢹⣏⣹⠃⠀⠀⠀⠀⠀⠰⣿⣽⣿⢺⣿⣹⡿⢺⣯⣽⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡦⠤⠴⣦⠤⠤⠤⣤⡤⣥⣤⣤⣤⠤⠤⣤⣤⣤⣬⢭⣥⣤⣭⣭⣥⣬⣭⣉⣠⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢠⣀⣀⣠⣘⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣻⣯⢸⡇
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠐⠒⠚⢦⠔⡄⠤⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⠀⠀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣆⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠍⢹⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⢘⣄⠀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠬⠤⠤⠤⠤⠤⠤⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠓⢤⣤⣇⠀⠱⢦⣄⠀⠠⣄⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠓⠒⠚⠛⠛⠛⠒⠛⠓⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣧⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⣄⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠉⠙⠓⠒⠒⠒⡶⢯⣤⣔⣙⣉⠑⣂⠀⠀⠀⠠⢀⡠⣤⣾⣿⠟⠉⢃⣸⣶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⠊⣷⣕⡒⠋⠀⢠⡶⠒⠋⡡⠞⠉⠀⢀⣀⠽⠟⠛⠛⣶⡶⠶⠗⠓⣿⡹⠄⠊⢀⣾⠏⣿⣧⠁⠘⢿⣒
⠀⠀⠀⠀⢀⣴⣿⣶⣿⣟⣿⣷⠀⢸⣷⣚⣛⣀⠀⠤⠒⠅⡉⢓⢒⡟⢋⣙⠉⢙⣙⣋⣡⣤⣴⣶⣿⣯⣴⣿⣿⡄⠀⠼⠁⣰⣄⢒⡛⠂⣤⢄⡀
⠀⠀⠀⠀⡽⣿⣿⣿⡉⠛⠷⣀⠀⠈⠉⠛⠚⠿⢷⣦⣤⣤⣌⣭⣵⣾⣿⡟⠃⠸⣿⡿⣭⣽⣿⡟⠓⠞⢩⣠⠄⠁⠀⠀⡌⠋⢸⠆⢀⠀⠀⠀⠀⢢⡄
⠀⠠⣄⣀⠀⣬⣿⡇⠙⠓⠲⡦⠀⠐⢀⡀⠀⠀⠀⠈⠉⠛⠛⠋⢉⣠⠟⠀⠀⠀⠀⡠⠋⣤⠈⠹⠃⠀⠈⠀⠀⢀⣴⠋⠀⢠⠓⠠⠞⠉⡀⢀⣴⡿
⠀⠀⠀⠈⠉⠙⣿⣿⠀⠀⠀⠀⠈⠙⣉⠛⠢⠄⠀⣀⠀⠀⠈⠉⠀⣀⣀⠀⢒⣐⣿⡺⣿⣿⣃⡀⠈⠀⢀⣠⠚⠁⡇⠀⠐⠇⣄⢀⠀⡼⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⠒⢛⣋⣉⣥⣽⣿⣷⢶⣿⣿⡏⠉⠀⣠⣴⠎⠋⠀⣰⠷⠃⠀⣷⢐⡴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⡿⠿⣿⣿⠿⡿⠟⠛⠂⢰⡃⠛⣿⡀⠉⠱⠍⣀⣀⣴⠋⠀⠐⠄⠈⢃⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠛⠲⢬⡝⠛⠤⠀⠀⠿⠅⠀⠈⢷⡀⠐⠈⡋⠙⢿⣾⣿⠷⢆⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣛⠓⠂⢤⣄⡀⠀⠀⠙⢦⡀⣼⣶⣴⡿⠓⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠐⠢⠄⠙⠉⠉⠁⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠠⠾⣿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⢢⡀
⠀⠀⠀⠀⠀⣀⣠⣴⡿⢠⣿⠇⠀⠠⢶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠀⠀⢀⠇⠀⠠⢶⠒⠦⢄
⠀⠀⠀⣠⣿⣿⡏⠀⠐⢿⣯⣤⣤⣴⠿⢹⡿⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠋⠀⠀⠀⠰⠯⠤⠤⠐⠉⠀⠀⠘⠄⡀
⢀⣠⣾⣿⣦⣿⣶⣶⣶⣷⡟⣳⣾⣿⣶⣶⣰⣾⣮⠇⣶⣠⣠⡀⢀⣀⢀⠋⠀⠀⠠⠒⠂⠐⠐⠠⠄⠀⠀⠀⠐⠀⢀⠅⠀⣀⣀
⠀⠈⡟⠙⠻⣿⡿⠟⠛⠛⠃⠛⠻⠿⠿⠿⠿⣿⠏⠉⣿⠳⠴⠃⠀⠈⠎⠐⠒⠀⠀⠂⠂⠀⠂⠐⠀⠠⠀⠠⠤⡀⠈⠈⠞⠁⠤
⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⣿⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣤⡀⣿⠀⠀⠀⠀⠀⢐⠀⠀⡤⠆⠨⡁⠀⠀⠐⣂⡉⣭⠙⠃⠐⠠⡀⠅
⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡿⢿⣿⣷⠏⠀⠀⠀⠀⠀⠐⢦⡈⠤⣄⠀⢅⠤⠀⠀⠀⠊⡀⢂⠀⠀⠆⢰
⠀⠀⠈⠙⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠌⠑⠪⠄⠀⣀⣁⣀⣀⣀⡁⠤⠥⠒⡝⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⢀⠄⠀⠀⠀⡀⠀⡠⠊
⠀⠀⠀⠀⠀⢠⣯⡽⠿⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡙⠲⢼⢨⣤⡤⢴⣶⡋
⠀⠀⠀⠀⠀⣾⠋⠛⠛⠾⣿⢿⠟⠛⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠐⠀⠸⢸⠭⠅⠘⠀⠁⣆
⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣿⢸⡆⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢆
⠀⠀⠀⢰⡏⠀⠀⠀⠀⢸⡇⠈⠁⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡆
⠀⠄⠠⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣀⣀⣀⣠⣤⣤⠴⠶⠶⠗⠛⠛⠛⠛⠛⠉⠛⠉⢙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⡿⢛⡉⠩⢥⠀⠀⠉⠁⠐⠂⠀⠒⣂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡠⠊⠄⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢃⣀⡀⠠⠀⠐⠀⠉⠁⢀⣀⠀⠤⠀⠀⠀⠀⠀⠉⠭⠁⠀⣴⣿⣿⣿⠀⠀⠀⠀⢀⠔⠀⢠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠂⠠⠤⠀⠀⠀⠀⠈⠉⠀⢀⡀⠠⠄⠀⠀⠂⠠⠤⠄⠀⠀⠐⢩⣭⣿⠀⠀⠀⡰⠋⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡶⠀⣉⡁⠀⠀⠉⠉⠄⠀⠀⠀⢀⣐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⠀⠀⣀⠠⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣋⢉⡀⠀⠀⠤⠄⠀⠀⠤⣀⠡⠤⠄⠀⠈⠉⠐⠒⠒⠀⠀⢻⣿⣿⡇⢀⠄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠉⠐⠂⣀⠀⠀⠉⠀⠀⠐⠀⠀⠀⣉⣀⣠⣔⣂⠤⠒⠤⢢⣰⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⡮⠉⣀⣀⠀⠀⠀⣐⣂⣐⣤⣄⠔⠲⢭⣶⣬⡳⠯⣔⠊⠀⣩⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣴⣤⣾⣷⣶⣿⣿⡿⠿⠛⠛⠛⠛⠲⢦⣼⡄⠀⢀⢀⣿⣤⣾⡿⢃⣿⣿⣿⣷⣖⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⢾⣿⣿⣿⣭⣿⢶⡶⣿⣿⡿⣽⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣟⢟⣿⣿⡿⣿⣷⣶⠶⡶⣖⣺⣺⣭⣿⣷⣾⣿⣟⢟⡿⣻⣟⣿⡷⣜⡫⠿⠛⠉⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣷⣝⡻⣽⡶⢶⠾⣿⢿⡿⣿⢿⣿⣿⣿⢿⠿⢏⣛⠿⠍⠚⠊⠁⠀⠀⢀⡶⣶⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡇⠇⡏⣿⣮⡙⢾⡑⠮⢷⣙⠯⠏⠝⠉⠐⠃⠈⠀⠀⣀⣶⣶⠀⠘⠃⠀⠘⢷⡿⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣦⢇⡌⡏⡟⣾⡟⠉⣀⣄⣀⠀⣴⣻⡆⠀⠘⠃⠀⠘⠿⠏⢀⠀⠄⠄⢴⣖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠓⠧⣀⢿⡇⠀⣿⣼⣿⠀⠙⠛⠁⢀⣀⠠⠄⢲⣶⠁⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡽⠀⠀⠀⠀⠈⠹⡇⠀⣈⡙⠥⠐⠂⠀⠈⠀⠀⠀⠀⣀⣿⣆⡀⠀⠀⠀⠀⢻⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⣀⡤⠤⠖⠚⠋⠉⢹⣿⠐⠍⠀⢀⠠⢸⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⠀⠀⠀⠀⠀⢀⣀⡄⣷⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢈⠐⢗⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣧⠴⠖⠒⠋⠉⠉⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣃⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠭⣒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠒⠈⠁⠈⣿⡄⠀⠀⠀⠀⠀⠘⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠉⠒⠤⣁⠒⠄⣴⣠⡠⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠤⢢⠤⢀⣄⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠃⠀⠰⠏⣠⣀⣸⣷⣎⣉⣀⡿⣷⣼⣟⠋⣼⣿⡿⣿⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠉⠉⠉⢉⣉⡁⣤⡤⢾⣛⣿⡟⠀⡹⠃⢀⣤⣞⣯⣴⢅⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠿⣧⠀⣠⣴⣾⣿⣿⣿⣷⣿⣿⣽⣿⡿⢿⣶⢁⣾⣿⣿⣏⣿⣁⡀⠘
⠀⠀⠀⠀⠶⣤⣤⣤⣿⡛⠋⠉⣉⣽⣛⣛⣺⡿⠋⢡⣶⣾⣿⣾⣿⣿⢧⣿⣏⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⢛⣩⠙⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⣟⣿⣿⡏⣾⡏⢙⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⡿⣹⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠘⠃⠐⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡷⣿⣿⣿⣿⣿⣷⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣙⣏⣿⣿⣾⡿⣻⣿⣯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⡝⠠⣿⢻⣿⣿⡏⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠋⠀⠘⠚⠯⡼⢻⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠿

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠊⠁⠯⠽⠭⠇⠤⠀⠿⠿⠼⠵⠸⠥⠁⠸⠿⠫⠼⠯⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠁⠀⠀⠀⠀⠈⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠂⠀⠀⠀⠢⣤⣀⣠⣴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠅⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠒⠂⠀⣀⠄⠀⠀⣀⡄⣀⡤⠞⣹⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠈⠉⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⣉⠙⠛⠛⠉⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢅⣀⠤⣤⢤⣤⢤⡤⠼⢑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⡄⠀⠜⣀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠼⡇⠂⠀⠒⠒⠒⠒⠂⠀⠐⡁⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠜⠉⡤⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠢⣀⡠⠆⠀⠀⠀⠀⠀⠀⡠⢶⠁
⠀⠀⡀⠀⠠⠀⠀⠀⠀⠇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⢀⣀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⣀⣀⣤⣤⡲⠯⠖⠋
⡀⢀⡍⠀⠐⠒⠒⠂⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢀⠀⣤⢯⡑⢢⣀⠀⢀⡔⠙⣏⡙⠉⢹⠏⠀⠀⠙⣄⠀⠀⡀
⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⢀⢀⡀⠀⠀⡀⠀⣀⠠⠤⠌⠀⠠⠀⠘⢯⣻⠄⠈⠒⠚⠳⠆⠀⠀⠉⢹⠀⠀⠀⠀⡇
⡇⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠠⠀⢀⠀⢀⡀⠀⢀⠤⢄⠀⠀⢀⡤⠴⠖⠊⠷⠀⠚⠀⠘⠒⠲⠤⢄⣸⠒⠤⣀⡴⠁
⡇⠀⠈⠦⠤⢤⠤⠤⠴⠏⣄⠀⠀⢩⠀⠀⠀⠁⠀⡯⠉⠐⠅⢤⣀⠀⠀⠘⡄⠀⠈⠁⠠⠠⠠⠄⠀⠀⣀⡤⠞⠋⠀⢠⣧⡴⢲
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣟⠀⠀⠀⠐⡬⠤⣈⡤⠼⡆⠁⡀⠀⠀⠀⣺⠌⠉⠀⠀⢀⣠⠔⠉⢹⣤⠶⠥⠤⠤⠤⠤⠤
⡇⠁⠈⠁⠀⠉⠁⠉⠉⠉⠉⠁⠈⠈⠉⠁⠁⠁⠁⠉⠐⡀⠀⡌⠁⠉⠉⠁⠉⠁⠐⠠⠄⢀⣀⠳⣊⣤⠤⠚⠉⠀⠀⠀⠸⡎⡅⠉⠁⠉⠉⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖
⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⢹⠃⠀⠒⠂⠒⠁⢧
⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠧⠤⠤⠤⠤⡌⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡔⠉⠑⠲⠤⢤⡼⠀⠀⠀⠀⠀⠀⠀⢣⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⢀⠷⠤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠐⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣄⠀⠀⠀⠉⠉⠐⣒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠉⠁
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⢤⢤⢤⣐⡐⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠒⠒⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢀⣀
⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠷⢶⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡀
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⢠⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣠⣴⢶⠶⠿⠛⠉⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⢠⠃⠰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠿⠿⠃⠁⠀⠀⠀⠀⠀⠀⢀⡴⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠀⠀⡇⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠷⡙⠃⠀⠀⢀
⡇⠀⠀⣿⣶⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⢀⡄⠀⠀⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠠
⠇⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⣠⣶⡔⢂⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠀⠻⠶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⢠⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣠⠾⠟⠋⠛⠀⠀⠀⠀⢀⣀⣠⠲⢿⣻⡀⠈⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⡆⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠠⠀⣀⡴⠞⠃⠀⠀⠀⠀⣀⣤⡤⠶⣷⠇⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⡄⠀⠸⡟⠀⠀⠀⢀⢠⣤⡴⠞⠋⣀⠀⡤⠰⠖⠚⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠱⡀⠘⣯⡀⣠⣔⣵⣿⠭⠒⠚⢙⣋⣠⣠⣤⣤⡄⣤⢠⣀⢠⠀⠤⠤⠀⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠱⡀⠙⢿⣿⡾⠥⠴⠶⠖⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠘⢄⠀⠈⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠂⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣐⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣖⣒⣊⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠭⣓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢑⡢⠭⣀⠈⠙⠓⢦⣄⠀⠀⠤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⢴⣪⠥⣒⠁⠀⠈⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠬⠿⠶⣥⣀⡀⠀⠀⠀⠀⣼⠀⠀⢀⣀⣠⡤⠶⠶⠿⠯⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⠿⠗⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⣶⢶⣶⠶⠶⠶⠶⠖⠒⢒⣒⣒⣒⣶⣶⠶⠶⠓⠓⠒⠛⠛⡞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠁⢳⣸⡟⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⣀⠀⠀⠀⠀⠐⠊⠙⢦
⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃⣀⣠⣤⣿⣷⣶⣶⣶⣖⣒⡚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⢀⡴⠞⠛⠉⠁⠀⣿⠟⠉⠀⠀⠀⠀⠐⠋⠭⠭⠭⠭⠭⠍⢉⣛⡛⣛⣛⡒⠒⠒⠒⠲⢶⡾⠓
⣰⠋⠀⠀⠤⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣈⠉⠩⠭⠭⠭⠤⠄⠀⠀⠀⣼⠉⠓⠦⣄⡀
⡏⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⣀⣀⣀⣉⣉⣉⡀⠐⠒⠒⠒⠠⠍⠉⠉⠉⠀⠀⠀⠀⠀⢇⠀⠀⣀⣀⣹⡷
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠶⠾⠿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣈⣻⠉⠉⢠⠇
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⣠⠴⠖⠒⠛⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸
⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡙⢷⡠⠀⠀⠀⠀⠤⠤⠶⢖⣒⣛⣯⡭⠭⠶⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀⠀⠀⠀⠀⠀⠀⢿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠀⢬⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⠀⠀⠀⠀⠀⢠⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⣻⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠿⡄⠀⠀⣀⠀⠀⠀⠀⣲⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⣿⣴⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠘⣷⡆⠀⠀⠙⠀⠀⡀⠀⠛⠁⠀⠀⠀⣺⣟⠄⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠂⣙⠂⠀⠀⢼⠁⠀⣤⠀⢺⠃⠀⠀⠀⠿⠁⡀⠀⠀⠀⠘⠿⣁⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣺⣀⠐⠢⠿⠓⠀⠀⢿⠄⠀⢤⠀⣿⠃⠀⠀⠠⣤⣠⡆⠀⠀⠀⢀⣶⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⣤⣤⠄⠔⢠⢼⡄⠘⠇⢉⣠⠄⠀⠀⢻⡿⠇⠀⠀⠐⣿⣇⠀⠀⢿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⠀⢩⣇⠀⠙⡿⣩⠆⢱⣿⡴⠀⠀⠱⣤⣿⠀⠀⠀⠀⢻⡞⠀⢠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣤⡞⢯⡆⠀⠀⣽⠂⢪⣽⣧⠈⠀⠢⣬⡉⠂⠀⠀⢀⣀⠸⢟⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢷⠀⣾⠃⠀⠀⠫⡜⠻⠛⢷⠀⠀⠀⠹⣿⠀⠀⢀⡀⠟⠀⠀⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣷⠉⣶⠀⢿⠆⠻⠦⢙⡟⠀⠀⢳⣤⣈⠃⠀⠘⣵⣏⠀⢀⣿⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣠⠿⠇⠀⠁⣠⣶⣛⠁⢀⠀⣰⣿⡏⠀⠀⠀⢛⣧⡀⢸⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡾⠁⣿⠆⠸⡇⠘⣧⣾⣿⣇⣻⡇⠀⢿⣄⠴⠀⢼⡋⠐⡏⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡀⢈⠀⠳⡆⢁⡌⢻⣩⣟⢀⣹⡇⠤⣼⠋⣤⣈⢈⡡⠤⣘⢯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣾⡃⠂⣩⣾⠀⡌⠱⣿⠗⢹⡏⠁⢿⣦⢆⣡⣬⣦⡐⢾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢜⣷⠄⠶⣁⡖⠀⠛⣴⡶⣿⠀⢁⣸⣇⡿⠘⠛⠛⣷⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡤⢹⡿⠀⠀⢠⡀⢈⠀⠘⡁⠈⣿⣦⠶⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡘⣿⢳⣄⠀⢙⠋⠀⢸⣻⡟⢪⣤⠴⢀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣯⠀⣾⡿⠄⠘⣿⣃⢹⡅⠲⠿⠗⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⢋⡀⠀⠟⣴⣿⣧⣍⠠⠿⠀⣰⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⡀⠛⣽⠋⠈⣤⡀⠆⠈⢿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡌⢷⠀⣀⣾⡀⠛⣶⠀⠱⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣰⡄⢻⡿⡇⢸⠟⣿⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⡏⢹⣷⣀⠀⢀⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⣿⣯⣿⣡⢿⣨⡅⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢿⣿⠃⣶⣿⡅⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⢻⣾⣿⣷⡈⣿⠁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣷⣼⣯⣿⣿⣌⠳⣀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣬⣥⣼⣆⣻⡕⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣾⠿⣿⡗⢈⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢳⡾⣿⣷⡌⠀⣿⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣏⡟⣡⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠇⣼⠘⠃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣟⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢿⠀⡥⠁⠀⠀⠀⠀⠀⠀⠀⢹⡣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣸⠃⠀⠀⠀⠀⠘⠀⠀⡀⡀⡑⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⣶⣶⣶⣶⣤⣶⣶⡴⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠈⢿⠁⠀⠊⠀⠀⠀⠀⠀⠀⠉⡷⠁⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡱⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠁⠀⠀⠐⠀⠀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢹⣣⠞⠂⠊⠀⠀⠀⠀⠈⠉⠀⠺⠿⠿⠿⠿⠿⠿⠛⢛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⢀⠀⢀⠋⠱⡇⢠⠄⡀⠂⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣘⠶⢴⡷⣶⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠐⡌⢡⠀⢀⣹⡇⠰⠁⡈⠀⢀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢠⡆⠂
⠀⠀⠀⠀⠀⠀⠑⢈⣀⠇⠀⡀⢀⠀⢰⡇⠀⢀⠀⡀⢠⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣦⡈⠄⢸⠀⣠⢎⠜⠠⡾⡈⠀⢠⠇⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⢰⡼⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠐⠄⠘⠀⠀⢫⠏⠒⢼⣠⣴⠋⠀⢸⠃⢀⠄⡱⠂⠀⠀⠐⠀⣤⠀⠸⠀⠀⠀⠀⣟⠉⢀⠀⠀⠄⠀⠰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠑⠷⣄⢄⠀⠄⠀⢸⠕⠁⠀⠀⣼⣴⣠⠜⠁⠀⠀⠀⠀⠈⠘⠧⣼⡀⠀⡀⢤⣼⡰⠊⠋⠀⠀⠀⠀⡟⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠈⠀⡙⠀⠀⠀⠀⠷⠋⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⢈⣼⡅⡴⠀⠀⠂⠀⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠠⣯⡠⣄⠀⣠⣐⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠙⠏⢹⡜⠀⠀⠀⢠⠀⠀⠠⠇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄⠀⢱⡀⡏⠉⢳⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⢸⠀⣄⣠⠂⣰⡧⣀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡖⠘⠁⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⡏⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⢘⡠⠛⠳⢦⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡉⠑⠒⠶⠤⠤⣠⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠂⠀⠰⠟⡉
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠉⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠋⠁⠀⠀⢀⣠⠴⢎⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠈⢄⠀⠀⠉⣿⡩⢙⠶⠦⣤⣀⡀⠀⠀⠀⠀⠉⠐⠂⠠⠄⠀⠀⠀⠀⠐⠂⠁⠈⠿⠀⠀⠴⣶⡉⣀⣀⣀⣡⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⣲⣾⣷⣌⣀⠀⠀⠎⠉⠛⠶⢤⣄⣀⠀⠀⡀⠀⠀⠀⣶⠀⠀⠀⣀⣤⣶⠁⠀⣀⣀⢙⠉⢉⣽⡃⠀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢀⡈⠙⠻⢯⣶⣖⣶⣶⣾⠿⣿⣿⡟⠶⠦⣤⣀⣀⣈⡤⠶⠻⠁⢠⡷⠺⠫⢉⡍⣾⡾⠟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠲⣄⠀⠀⢀⣀⠀⠀⠀⢉⣉⣻⣶⡀⠺⠀⠉⠡⢀⡀⠄⣠⣏⡠⠤⠚⠋⠰⠁⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢄⡀⠀⠈⠑⠢⠤⠀⡀⠉⠁⠀⠚⠂⠙⠻⣷⣤⣤⣤⡤⢶⡮⠭⠤⢤⣤⣤⠄⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣁⡀⠈⠐⠠⢄⡀⠀⠀⠀⠙⠢⣄⠀⠀⢀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣯⣿⣿⢷⣜⣿⠞⠛⠳⣤⣀⠀⠀⠈⠷⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡍⠛⠿⣏⣿⣴⠶⠤⣄⣀⠉⠲⢦⣄⡀⠀⠀⠀⣀⠀⠀⣀⣤⡀⠀⠀⠈⠀⢀⡰⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠉⠻⠦⢀⣄⠉⠓⢦⣄⠈⠛⠓⠒⠶⠾⣶⠿⠮⣙⣿⠷⠶⠶⠚⢋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠓⠄⠄⣈⠳⣤⡀⠀⠀⠀⠀⢀⠠⠀⠛⠛⠃⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠀⠀⠀⠀⠉⠘⠛⠂⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠒⠦⢤⣀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⣿⣿⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢿⣿⣦⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⢻⣿⣇⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⢹⣿⡆⠀⠈⣿⣿⠀⠀⠀⣾⡇⠀⣿⣿⠀⢀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠹⣿⣧⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⣿⡇⠀⠀⢹⣿⠀⠀⠘⣿⣧⡀⠹⣿⣧⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠘⣿⣇⠀⠙⣿⣦⠀⠀⠀⠀⢰⣿⠇⠀⢰⣿⠇⠀⠀⣾⡿⠀⠀⠀⠈⠻⣿⡄⠙⣿⣇⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⢸⣿⠀⠀⢹⣿⠀⠀⠀⢠⡿⠃⠀⠀⣾⡏⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⣹⡇⠀⢸⣿⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣸⡏⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⡟⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⣿⠁⠀⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⢠⡿⠁⠀⠼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠟⠛⠛⠛⠉⠉⠉⣉⣉⣉⣁⣁⡠⣤⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⠙⠛⠛⠻⠷⢶⣦⣤⣀⡀
⠀⠀⠀⠀⢀⣠⣤⡶⠟⠛⠉⣉⣁⡤⣴⠶⢂⣶⣾⡿⠛⠻⣿⡿⠛⢉⣩⣿⠟⠁⣉⡼⠛⢿⡉⢉⣭⡯⠟⠉⢀⣿⡾⠷⠢⣤⣤⣌⡉⠛⠿⣦⣄⡀
⠀⠀⣠⡶⠟⢋⣡⠤⠐⠛⣡⣽⡯⠛⢁⣴⡿⠛⠻⣷⣄⢀⡼⣠⣴⠿⢋⣡⡴⠛⢿⣦⡀⢠⣿⠿⠋⠀⣠⡴⠛⠿⣧⡄⢀⡼⠛⠉⡹⢿⣶⡀⠉⠻⣦
⢠⣾⠋⢀⡴⠋⠁⣀⣤⣾⣽⣧⣴⡞⠉⠛⣷⠆⠀⢀⣤⣿⣿⣿⣿⠛⠛⢻⣷⠀⠀⣉⣼⣟⣡⣴⡚⠛⢻⣷⠄⠀⢈⡴⠋⢀⣤⣾⠟⠁⠀⢱⠀⠀⢸
⣾⠇⠀⠸⣄⣠⣾⠿⠋⣹⠁⠀⠹⡿⠂⠀⣁⣤⣾⣿⢿⠟⠁⠈⢻⠷⠀⠈⣁⣤⡾⠋⠝⠁⠉⢹⡿⠀⠀⣁⡤⠞⠉⢀⣴⡿⠛⠁⢀⣀⠴⠃⢀⣠⣾
⣿⣆⡀⠀⠙⠛⠧⣤⣴⠿⢄⣀⣀⠤⠞⢋⣤⡿⠛⠁⠈⣦⣀⣀⣀⠤⣴⣿⠟⠁⢀⣴⡷⣄⣀⣀⣤⡶⠟⠁⠀⢀⣴⣿⡟⠤⠖⠛⠉⣀⣤⣶⣿⣿⣿
⢻⣿⣿⣷⣦⣄⣀⡈⠈⠙⠛⠛⠣⠴⡾⠿⠃⣀⣀⣤⣾⣋⣁⣀⣤⣾⣏⣁⣠⣾⣟⣁⣀⡀⣴⠿⠿⠤⠶⠐⠚⠛⠋⣁⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⣀⣀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠉⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠋⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢠⣿⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⢻⣿⠛⢻⡿⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⣿⠁⣀⣀⣤⡤⠶⠛⠛⠉⠉⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠉⠙⠛⠶⣤⣄⣀⠀⠀⠸⣷⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣿⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠦⣿⡆⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢰⡿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣾⠇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⣇
⠀⠀⠀⠀⠀⢰⡟⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣾⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠸⣧
⠀⠀⠀⠀⢰⡟⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢻⣆
⠀⠀⠀⠀⣿⡃⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⣿⡀
⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠑⠶⠖⢈⣉⡭⠍⠥⠀⠀⠑⠜⣏⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠈⣄⠀⠐⠠⢀⣈⣡⠤⠄⢀⣀⣈⠠⡠⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⢀⣀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣇⠀⡈⢳⣄⠀⢢⠴⠖⠂⠉⠥⠤⠀⢬⠚⡏⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣷⣄⢸⣿⡇⢹⣿⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠃⠘⣦⠈⠳⢦⣀⠉⠉⠁⣀⣀⠙⠆⡜⠁⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡿⢿⣿⣿⡇⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠐⠦⣀⣘⣧⠈⠲⣌⡑⠂⢀⡈⠙⢃⣳⠂⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⣿⡇⠈⠻⣿⠇⢸⣿⠀⠹⣿⡆⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠉⠉⠀⢠⣼⠟⠀⠈⠀⠈⡰⣃⣴⠟⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⢠⣴⠤⢠⣴⡄⣤⠀⣤⢦⡄⣤⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠦⣤⣤⠀⠀⠀⠀⡐⣿⠿⠋⣠⡴⢀⠤⣱
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡿⢸⣟⣃⣸⣻⡦⣿⡽⣧⣰⣶⣿⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠶⠶⢤⠤⠤⠖⠈⠁⣈⣤⠶⣿⠟⠀⣠⠾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠈⠉⠀⠈⠀⠈⠉⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣁⠀⠀⠀⠀⠀⠀⠈⠉⢀⡴⠞⠁⢀⠜⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣀⣀⣀⡀⠠⠄⠂⠁⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⢄⣢⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠙⠛⠉





⠀⠀⠀⠀⠀⠀⠠⣶




⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠉⠛⠫⠿⢶⣦⣄⣑⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣬⣛⠷⣤⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠴⣀⠀⠨⡙⠻⣾⣿⣷⣦⡀
⠀⠀⣤⣤⣤⣀⡉⠙⠲⣤⣀⢕⡻⢔⡢⣕⠢⣙⢿⣿⣿⣶⣄
⠀⠀⢻⣿⡛⠋⠛⠛⠲⠄⠉⠻⢿⣦⣝⠶⣝⠦⣕⠩⠻⣍⠻⣿⣦⡀
⢦⣄⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⢄⡙⠻⣷⢌⠳⣌⠳⣍⠎⡳⣝⢿⣿⣄
⣤⣀⡉⠀⠈⠻⣷⣄⠀⠠⣤⣄⡀⠙⢦⣈⠻⣄⠈⠳⣌⠳⡌⠻⠬⢻⣿⣷⡄
⣤⣤⣬⣁⡀⠄⡀⠙⢷⣄⠙⣿⣿⣷⣦⣙⢷⣌⠣⠀⠌⢣⡘⢄⡔⠀⠹⣷⡙⢆
⣀⣤⣤⣭⣙⡂⢌⠀⠄⠙⢷⡈⢷⡄⠉⠛⢷⡝⢧⡀⠈⢢⠹⣌⠌⢦⡀⠹⣇⠈⢆
⠉⠀⣀⣠⣤⣄⣀⠀⠀⠐⡄⠙⣆⢻⡄⠀⠀⠹⣦⠹⡄⠀⢳⡘⡾⡜⣷⠀⢿⡆⠈⠆
⠞⠛⣉⣁⣀⣀⣉⠛⢦⡈⣚⠄⡈⢂⢳⠀⠀⠀⠘⣧⠐⠀⠈⣧⢰⢧⠸⣇⠈⣿
⠖⠛⠉⠉⠀⢀⣉⠙⢦⡹⡼⣏⠠⠀⠈⡆⠀⣴⡄⠘⡇⠀⠀⢹⡆⣿⡀⣿⠀⢹⡇
⠤⠴⠶⠖⠛⠉⠙⠻⣆⢱⢰⠏⠀⠀⠀⡇⢠⣿⣿⡄⢹⠀⠀⠸⡇⣿⡇⢹⠀⠈⣇
⠶⠤⠶⠒⠒⠲⢶⡄⠙⣼⠀⠀⠀⡆⠀⠇⣼⣿⣿⡇⠈⢠⠀⠀⡇⡿⡇⠘⠀⠀⢻
⣤⣤⣤⣤⣤⡀⠀⡏⢠⡟⠀⠀⠈⠁⢠⣸⡿⠁⢹⡇⠀⢸⣦⡇⡇⢿
⡀⠀⠀⠀⢹⠇⣸⢇⢮⡁⠀⠀⠀⣠⣿⠟⠀⠀⢸⠇⠀⣼⣼⡇⠀⠸⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣋⣉⣤⡤⠶⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣋⣛⡫⠿⣧⣀⣤⠶⣛⣥⠶⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢃⣎⣋⠒⠄⠴⣈⡼⠁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⣂⣵⠤⠬⠒⢊⣡⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢶⠖⠚⢛⠛⠓⠒⢚⠙⠶⠶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢛⠉⣂⡖⠶⠚⣃⠐⠂⠴⠦⣩⡓⠒⢄⡀⣭⡉⢙⠶⣶⡀
⠀⠀⠀⠀⠀⢀⣀⡶⣛⠛⠵⡞⢁⡼⢦⡈⡁⠀⣖⠂⠐⢂⠀⡠⠤⠴⡄⠠⢍⡃⠍⣌⢹⢻⣄
⠀⠀⠰⡶⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠲⠲⠶⠶⠶⠾⠷⢶⡆
⠀⠀⠀⠹⣦⡒⠐⠒⠐⠒⠀⠂⠐⠂⠒⠂⠐⠂⠐⠂⠐⠒⠐⠒⠂⠒⠀⠐⠂⠐⠂⠐⠂⠒⠀⢲⡞
⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠒⠂⠀⠀⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⢀⡶⠖⠈⠁⠀⠀⣀⡤⠶⠒⠋⠉⠉⠀⠀⠀⠀⠉⠖⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡴⠋⠀⠀⢀⡴⠋⠀⠀⠀⢀⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣰⣟⣀⣀⣀⣴⣯⣤⣤⣤⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇
⠀⠀⠀⠀⠀⠀⠀⣸⠷⠚⣻⠏⠉⠁⢡⡟⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠎⠁⠀⣰⠃⠀⠀⣠⡟⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⣮⣀⠀⢠⡏⠀⠀⢰⡟⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⠀⠀⡸⠈⠉⠛⣿⠓⠒⠚⡿⠳⠶⠶⣾⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠤⠒⠌⠉⠁⠀⠉⠉⠛⠧⡀
⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⢀⡇⠀⢀⣠⡞⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⣐⠂⠀⢀⢀⣠⣶⠯⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⣄
⠀⠀⠀⠠⣇⠀⠀⢸⠁⠀⠀⢈⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⣷⠒⠒⠀⠠⢤⣀
⠀⠀⠀⠸⡈⠙⠳⣾⣄⣀⠀⠘⡇⠀⠀⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠋⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠱⢄⠀⣷⠈⠉⠙⠻⡷⠤⣤⣨⡎⠀⠀⠀⠀⠀⠀⠀⡜⢁⣠⣄⣒⡒⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⠼⠋⠀⠀⠀⠀⠀⠀⣨⢞⠏
⠀⠀⠀⠀⠀⠀⠑⠼⠦⣀⠀⠈⢿⡄⠀⠀⡅⠀⠀⠀⠀⠀⢀⡎⣴⡟⠁⠀⠀⢀⠌⠉⠐⠻⠗⣶⡤⣤⣤⣤⣤⣴⠮⠕⠊⠁⠀⠀⠀⠀⠀⠀⡠⢊⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠚⠓⢄⣀⠙⢶⣀⠀⠀⠀⣾⣼⠟⢀⡠⠖⠊⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⣂⠔⣫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠓⠷⣤⣤⡿⠯⠒⠁⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣵⡮⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⣀⠀⠀⠀⣀⣠⢴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⡤⠤⢤⡀⠀⠀⠀⠙⠆⣰⠿⠃⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢱⠀⠀⢀⡀⠀⠀⢠⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢸⣧⠀⢰⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢧⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠚⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠲⠤⠞⠋⠛⠿⠿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⢀⣤⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⡂⠀⠀⢸⣧⣤⣤⣤⣄⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠛⠻⠛⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⣽⣿⣿⣿⡇⠀⣀⣀⣀⢀⣀⣀⠀⠨⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡿⠁⠀⢨⡟⣱⣿⡇⠀⢿⣿⣿⣿⣿⣿⠁⠈⣿⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠙⢿⡇⠀⠀⠛⠻⠿⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⡇⠀⢀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⢈⠀⢁⠀⠆⠀⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⢠⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠙⠛⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⡻⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠟⠑⡧⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⠀⠈⣙⠁⡖⣸⡅⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢤⠀⠀⡧⠀⣛⣵⣯⣏⢤⣀⡃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡤⣲⢶⣷⣿⣿⣿⣿⣌⡹⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠌⠀⠀⢸⡠⢾⡟⠉⣿⣯⢻⣿⣿⣷⢴⣃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠥⣃⠘⣽⣾⣧⡀⠘⢿⣿⣿⣿⣿⣳⡗⠂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠚⠑⠂⡄⠀⠰⢿⢒⣭⣽⣬⣿⠟⠁⠀⠈⠫⣿⣿⣿⣿⣷⡆⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⠀⢀⣀⡁⠐⡿⠘⢷⣿⣿⠿⠛⠀⠀⠔⠀⠠⢹⣿⣿⣿⣷⣴⠆⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⡀⢸⣤⠯⣯⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⢨⣿⣿⣿⣧⣿⠄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⣷⣦⡿⣧⡟⠀⠀⢀⠀⣀⡀⠀⠀⠄⠀⠀⠈⣹⡖⢸⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⣽⣭⣾⣿⣷⣿⣿⡿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⢀⠀⢺⡯⣿⣿⡿⢿⣏⣿
⠀⠀⠀⠀⠀⡀⣾⣿⣿⣯⣼⣿⠞⠁⣀⣴⣤⠡⡀⠄⠐⠀⠠⢀⠀⠸⣀⡸⡷⣿⠿⢳⣦⣽⣿
⠀⠀⠀⠀⠀⣡⣾⣿⣿⢿⠿⠃⠀⢰⣿⣿⢾⣆⠀⠃⠄⡀⠀⠂⢀⣊⣼⡯⣰⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠈⠋⠹⠼⠟⠾⣿⣿⠿⣿⢻⣿⣿⣯⣿⣧⣈⣠⣤⣨⣤⣿⣿⣿⣿⣿⣿⡙⣿⢼⠛⠓⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠲⠏⠋⣿⣾⣟⠻⣿⣿⠟⠻⠿⠟⠋⠉⠃⠈⠓⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠏⠉⠹⠟⣀⠐⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠃

⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣤⡸⠋⠿⢳⣾⣀⡄⠀⠀⠀⠀⠀⣀⠸⣿⣆⢲⡄⠀⠀⠀⠀⢄⠙⢦⡀⠀⠀⠀⢰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢠⡴⢼⣦⣤⣤⣤⣤⣿⣤⣤⠀⠀⠀⠀⢿⣦⣿⣿⣿⡿⠀⠀⠀⠀⠈⠳⠞⢇⠀⠀⢀⡼⠿⠿⠋
⠀⠀⠀⠉⠈⣧⢸⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢠⣆⣸⣿⣿⡟⢹⣧⣼⡀⠀⠀⠀⠀⠀⠀⢑⣴⠋
⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⣿⡟⠻⠀⠁⠀⠹⡿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣸⠁⠉⠉⠉⠁⢱⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡢
⠀⠀⠀⠀⣠⣮⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣼⣄⠀⢀⣾⡀
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣰⣿⠟⠋⠁⠈⠙⢻⡿⣄⠀⠀⠀⠀⢸⣿⣿⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡆⢰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⡄⢴⠀⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⢀⠞⣤⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠗⠸⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠃⠚⠀⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠛⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡦⣄⣀⣀⣠⢼⡿⠋⠀⠀⠀⠀⠘⠛⠛⠀⠛⠛⠛
⠀⠀⠸⡏⣿⣿⡿⠋⠀⢂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠋
⠀⠀⠀⢻⣌⡟⠁⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣀⣻⡶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣿⣿⡿⠏
⠀⠀⠀⠀⠀⢷⡸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⡏⠉⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⠁⠀⠸⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠧⠤⠤⠤⠤⠤⠤⢷⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢌⣷⣷⣾⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣬⣿⣿⣿⣿⣷⡿⠿⢿⢷⣧⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣾⣿⣿⡿⠛⠉⠐⠚⢣⠀⠘⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⢠⣶⠁⠈⠲⢾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣾⣿⣿⣿⠶⠛⠁⠀⠀⠀⠀⡾⣾⡀⠀⠑⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⣀⣀⣈⣭⡿⠋⠀⢠⡀⠀⠀⠀⠀⠀⣾⠏⠙⠲⣟⣄⠄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡎⣧⠀⢀⡔⠀⢸⣿⠀⠀⠀⠈⣷⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⣤⣅⠀⢀⠀⣼⣿⡄⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣿⣟⡿⠋⣇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⠀⠈⠉⠸⣿⢀⡟⠘⣧
⠀⢀⣾⣥⢾⡿⠿⣿⣻⡿⠋⠀⠀⠀⢿⡄⠀⠸⣄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠰⠊⠀⠛⠘⠀⢸⡏
⠀⡜⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣖⠀⠙⣷⣤⣀⣀⠀⣸⡇⠀⠀⣠⠔⡾⠆⠀⡀⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣄⣻⣿⣿⣿⣿⣿⣿⣄⡈⢑⠓⢄⢦⡴⣴⣾⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠙⣿⣿⡟⠀⠀⠙⠓⠢⠼⡅⡄⡟⢦⡀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠹⡄⢻⣿⡅⠀⠀⠀⠀⠀⠀⣰⣷⠇⠀⠀⢦⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣘⢾⣿⣷⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⣸⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠻⣦⡀⣴⣷⣦⣱⡏⢀⡀⠀⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠸⣿⣿⡋⠉⠉⢾⣿⣷⣎⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣟⢷⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⡈⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠐⠦⢳⡋⠀⠀⠀⠂⠀⢠⠁⠀⠀⢆⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠈⠈⠲⠡⠏⠀⠀⣀⡎⢀⠄⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⡘⠀⢐⢤⠁⠋⠘⢨⡅⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠰⣤⣘⠅⢰⡞⢃⠃⠉⠰⣿⠊⠳⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠤⠀⠋⢛⣸⠐⠀⡁⣻⢜⠘⡋⣠⢆⠎⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣆⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡏⢩⠄⠈⠁⡯⠈⢸⡏⣭⠜⢱⣫⡴⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠃⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠰⠸⣇⠃⠀⢠⡄⠀⣖⢳⡀⣼⡇⡾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣧⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠄⠌⢲⢸⡎⢰⡦⠛⠛⠙⠋⣰⠤⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⣠⢼⡖⢋⡔⢙⡐⠁⠀⠀⠀⠀⠀⢀⣤⡶⢀⠀⠀⠀⠀⣆⡃⠀⡀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣾⣾⡿⢾⣤⣿⡁⠀⠀⠀⠀⠀⢰⠟⠋⠀⠈⠀⠀⠀⠀⣈⣳⠿⠡⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢺⠛⣙⣴⣿⠸⢻⡵⠂⠀⠀⠀⠀⢸⡲⠆⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣹⣸⣿⡀⠛⠀⠀⡀⠀⠈⡅⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠃⠀⠀⠀⠀⢀⡴⠗⢺⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠄⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠋⠀⠠⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⣠⡖⠁⢀⣀⡀
⠀⠀⠀⠀⠀⣷⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋
⠀⠀⠀⠀⠘⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⣠
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠔⠂⠀⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢻⣌⣀⠾⠁
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠
⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀
⠀⠀⠀⢀⡴⠻⢛⡳⢤⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⠃⠐
⠀⠀⠜⢡⣤⠶⠦⠁⠨⣿⡇⠀⠹⡆⠀⠀⣀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⡙⡄⢀
⠀⠀⠀⠀⠀⢠⣤⣠⣄⣀⠉⠉⠙⢿⡟⠛⠛⠦⣍⠙⠓⠒⠀⠀⠀⢐⣶⠂⠀⠉⠉⠉⢛⣓⠺⠛⠉⠝⠓⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣰⡀⠰⠻⡍⠻⣍⠑⠦⠷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⣀⣀⣐⣚⡋⠂⠀⠀⠀⠀⠠⠄⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠻⣷⡶⠂⠈⠲⣤⣌⣑⡖⣶⣄⠀⠀⠀⠀⠀⠀⢀⠴⠺⠿⢿⣯⣭⠬⣬⣟⠛⣛⡶
⠀⠀⠀⠀⠀⠀⠙⢅⡾⣷⠆⠠⠞⠋⠭⠉⠛⠳⣄⠀⠀⢀⣴⠧⠀⠀⢴⡀⠀⢀⡀⠀⡀⠀⠀⣀⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠁⠀⠈⠁⠀⠈⠂⠰⠧⠀⠀⠀⠀⠀⠈⠧⠀⠀⠠⠷⠗⠂⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣄⣠⣀⣄⣀⣀⣀⠀⣠⣤⡦⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⡾⢷⣤⣾⣶⣿⣸⠭⢹⠛⣻⣿⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⠭⢵⣜⣯⡷⠿⣏⢵⣿⡿⣋⡙⡀⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⢶⡦⠨⠗⠂⠀⠩⣍⣉⣉⣈⣉⠉⠀⠀⠈⠀⢈⣷⡑⠀⠀⠠⠤⠴⠦⠒⠲⠆
⠀⠀⠀⠀⠀⠀⢲⣤⠖⠀⣿⣖⠚⠑⠶⡄⠁⠀⠀⠈⠛⠝⠢⣀⣀⠀⠠⡀⣶⣥⣹⣿⣤⣀⣀⣀⠀⢀⣼⠀⠀⠀⡀⠀⠻⠦⣄
⠀⠀⠀⠀⠀⠀⠛⢻⣵⡿⣄⠀⠱⠆⢄⡀⠈⠳⡤⢀⠀⠈⡓⢹⣶⡟⠞⠀⡎⠁⠁⠹⣿⣿⡟⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢠⣤⣕⠤⣈⡻⢿⣞⣿⠆⡬⢉⣠⣶⢤⠈⣥⡜⢿⣼⣿⣇⢄⠘⢀⠀⣂⠀⣿⡏⠙⠄⠀⠀⠀⠀⠰⠤⠄⠀⠀⠀⠀⡼⡐
⠀⠀⠀⠀⠉⠋⠻⢿⣶⣭⣍⣛⡛⠿⠷⠚⠻⣯⣉⡃⠿⠛⠂⠈⠻⢿⣯⣑⠢⢤⣈⣠⣼⣧⣴⣦⣄⠀⠀⠀⠀⣤⣀⠀⠁⢐⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣯⣤⠀⠤⠄⢒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠬⠉⢛⠛⠛⠛⠛⠛⠒⠛⠛⠒⠒⠊⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡽⠾⠯


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣈⠣⣰⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⣄⠀⠀⢱⡀⠠⠋⡀⢹⠛⢢
⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⢱⠀⠃⠀⢳⠀⠂⠁⠀⠸⢀⠈⡘⡜⠐⠀⢀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢠⠿⡇⠀⢠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢢⣆⠀⢠⠈⢷⠃⡎⣠⢆⠌⢰⡇⠀⠀⡶⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⡏⢀⠂⢡⣳⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⣇⠀⢡⠘⣴⠷⢁⡜⠥⢼⠁⠎⠀⡆⣴⠀⣠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡀⠀⠀⠀⢸⠀⠈⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠈⢢⡀⣶⠛⢦⠜⢣⡕⠚⡄⡀⠘⣡⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆⠘⡆⡿⢀⡆⢠⡿⠃⠀⣀⡤⠖⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠶⡛⡇⢐⠈⠒⢸⠀⡀⠜⠁⡄⢀⠀⡀⢺⠁
⠀⠀⣤⠠⠤⠤⠄⣀⣀⠘⣆⣿⣤⠃⣿⣠⡇⢸⠅⢀⠞⠁⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠱⡀⢀⣰⡇⡞⡟⢀⠜⣠⠏⠐⢀⡜
⠀⠀⠈⠓⠦⣤⣀⡀⠀⣉⢪⣉⠣⣀⢺⣿⣥⠂⢠⣏⢀⡀⠔⢃⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⣾⢿⡏⠀⣷⣥⣶⠿⠒⠒⠉
⠀⠀⠀⠀⠀⠀⢈⠝⠛⠉⢁⣈⣈⣻⣧⡽⠟⠁⣸⣞⣉⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⠹⣿⠁⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢴⣶⠞⢿⡀⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢻⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠀⠀⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⢞⡛⠛⠛⠛⠛⠿⣟⡒⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⠉⠉⠛⢦⣌⠙⠶⣄⠀⢀⠀⠙⠶⣄⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠳⣾⠀⠀⠀⠈⢷⣄⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⡿⢷⡀⠀⠀⠀⢹⣦⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡇⠈⢷⡀⠀⠀⣸⠘⣧⠀⠀⠀⠈⢿⡻⣦⡀
⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣧⠀⢀⡏⠀⠘⣇⢠⠀⠀⠀⢣⠀⠙⣧
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢸⡄⣼⠃⡄⠀⠘⡾⠀⠀⠀⠈⠀⠀⣼
⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣤⠶⣤⡀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣷⠏⠀⠸⡆⢰⠇⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⡇⠀⠀⠀⢀⡟⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⠏⠀⠀⠀⣿⡟⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⢿⠀⠀⠀⠀⢷⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⣿⣴⠋⠀⠀⠀⣠⣿⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢀⡾⣿⠁⠀⠀⢀⡴⠋⣈⣴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⡟⠀⣠⣴⣯⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣤⣤⣤⣴⣾⣥⠤⠶⠶⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁