Maple sugar Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⡀⡀⠀⠀⠐⢼⡆⠀⡶⡄⠀⢀⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠇⠘⠃⢸⣦⣼⠂⠘⢻⣯⡄⠘⠂⣸⡇⣰⣿⣃⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠄⠀⠀⠀⠐⠀⡙⣿⣿⣿⡄⠀⣽⣇⠝⠓⣿⣿⣿⣿⣿⣿⣦⠟⠁
⠀⠀⠀⠀⠀⣠⣄⡀⠀⠤⢀⣀⠀⠀⠀⠀⠀⣁⡿⢻⠯⣁⣰⢿⠓⠰⣿⣻⣿⣿⣿⣿⣿⣷⡿⣂⣀⣀⡰
⠀⠀⠀⠀⠐⣿⣿⠟⠶⠜⢿⠃⠀⡀⠀⠀⣀⣶⡊⠀⠀⠤⠘⠋⠀⠩⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣹⣾⣶⣦⡄
⠀⠀⠀⡄⢀⢸⣿⣶⠀⣦⣠⣾⣿⣿⣆⠔⠻⠻⠟⢀⡀⣠⣶⡀⠀⠀⠀⢠⣴⣿⣿⠿⠿⠻⣿⣿⣿⣿⣟⣟⡃
⠀⠀⠈⢗⡊⠛⢻⡏⢙⡓⣿⣿⣿⠻⠓⠀⠀⠒⠀⢀⠘⠁⠀⠁⠠⣠⡀⣠⣼⣟⣙⠶⠛⠓⣏⡰⡾⢷⢿⣿⣦
⠀⠀⠀⢘⣷⣿⣿⣿⠿⠉⠀⠀⠁⠂⢤⠠⣮⣿⣷⣦⡌⠈⣢⠀⠀⣩⣯⣿⣽⣿⣿⣿⣟⣩⡀⣰⣶⣾⣷⣿⡛
⠀⠀⠀⠀⠤⠖⢉⡙⠂⠀⠀⡀⢀⣶⣀⢀⣉⠫⣍⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⣿⣏⡉⣥⣼⣿⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠍⢀⠘⣴⢴⣿⣾⡟⠻⢋⣉⣰⣾⣿⣿⣿⣿⣿⣿⢿⣿⠟⢿⡿⠾⠛⣙⣽⣿⣿⡾⣿⣿⣿⣿⠁
⠀⠀⠘⢛⢻⣿⣇⣰⡤⠖⠛⠋⠀⠠⣠⣿⡿⠟⠛⠻⡿⠿⡿⢋⠘⢦⣭⡾⠶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⣅⢄⢀⡈⢣⠀⠰⣶⡂⠹⠁⠉⠁⠀⢀⣘⣤⣄⣶⡷⣄⡐⡻⣖⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⣯⡅⣈⠁⠀⠀⡉⠀⠀⣤⢀⠣⢼⣿⣿⣿⣿⣷⣶⣶⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⣠⢾⣿⠟⠁⠷⠠⣾⣾⣦⣏⣸⣿⣾⡏⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠏
⠀⠀⠀⠀⠁⠘⢁⣴⣆⠙⢻⣿⣿⣿⣿⡿⢿⡟⠹⠇⠈⢿⣿⡏⣼⠛⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⠻⡃
⠀⠀⠀⠀⠀⢰⣾⢿⠟⠱⣾⣿⣿⠟⠿⠀⠈⠁⣀⡀⠐⢸⣿⡇⠀⠀⠁⠀⠁⠀⠋⠀⠉⢿⡏⠁
⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠈⢸⠋⠀⠀⠀⠀⠈⠉⠀⠈⢸⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢸⣿⣇⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⡶⣦⣽⣆⣳⣤⣿⡞⣸⣿⣯⣥⣗⣶⣶⣘⣮⣷⣦⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣁⣙⣉⣛⣙⣙⣋⣋⢻⣿⣿⣿⣿⣯⣛⣻⡛⣛⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⡿⣿⣿⣅⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠉⠉⠉⠁⠙⠉⠩⠿⠋⣢⠙⠿⣿⣭⣧⠭⡭⠭⠭⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣀⣐⣀⡀⠀⠀⢂⠀⠁⠐⠚⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠀⠉⠈⠉⠛⠛⠻⠹⠏⠽⠛⠀⠀⠀⣀⠈⣕⡸⠀⢦⣠⣦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠆⠀⠰⢿⡴⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡤⠀⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⠛⠀⠀⠀⠀⢀⣀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⡄⠀⠀⠈⠙⠋⠈⠁⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⡇⡆⠀⠀⠀⠀⠀⡄⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢭⠧⣈⣀⣨⠤⠥⠤⢟⣀⣠⣤⠄⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠩⠋⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣀⣤⣄⣀⣤⣤⣄⣠⡀⣳⡶⠞⠛⠲⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣉⣏⢀⣀⢀⣉⡈⠭⣿⣿⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⢀⡞⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⠞⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡠⠂⠁⣀⡤⠔⠲⠖⠶⠢⡤⣄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠀⠀⠊⠀⡴⢛⣧⡶⠞⢃⠐⠉⠃⠄⡈⠓⣄⠀⠀⠀⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⠈⠀⢠⡞⠁⢪⡟⠀⠐⣵⠶⡄⢀⠄⠁⡀⠘⢷⡄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⠀⢠⡟⢀⡴⢃⠀⠀⣰⠃⠀⠉⣠⡄⠀⠀⢂⠈⣶⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⣴⢠⡄⣀⢀⣾⡗⠋⠀⢀⠀⢈⠷⣈⣀⣤⣔⣸⡇⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⣿⣿⡇⠀⠉⠙⠷⠀⠀⠋⠀⠘⠛⠉⠀⣸⡟⣭⢿⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠈⠀⡿⠉⣿⠀⠀⣤⠀⠀⠰⡄⠀⠀⡄⠀⠀⣼⠃⣥⡾⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠠⠀⠀⠀⢿⠠⣾⠃⠀⠀⠀⠀⢀⡄⠀⠈⠁⠀⣺⡿⠊⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⣀⠋⠛⢻⠄⠀⠀⣸⡇⠀⠀⠀⠻⣿⠁⢠⣻⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠧⠀⠰⣧⣴⡴⠶⢿⣿⠶⠶⠲⠞⡋⢀⣀⣾⠟⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠸⣄⠐⠈⠠⠀⠤⠘⠿⠀⠀⠂⠀⠀⣿⢡⡟⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠀⠀⠀⢻⠤⢚⠤⠴⠶⠶⠶⠒⠒⠛⠋⠠⠟⡿⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠰⡀⠈⢧⣤⠐⠶⠢⡄⠀⠐⠄⡠⠘⢡⣼⠃⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⠀⠀⠁⢀⠈⠛⠲⠷⠦⢿⣼⠧⠴⠷⠾⠞⠁⠀⠀⢀⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠳⣦⣄⢀⡀⠀⠀⠀⢀⠀⡀⠀⣠⠄⢀⣾⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣀⣀⣤⡤⠀⡤⠄⠀⠀⠤⠀⢠⣤⣤⣀⣉⡛⠛⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢏⣛⠛⠛⠻⠷⢤⣠⣤⣄⣀⣠⣮⣵⡿⠿⠟⣋⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠉



⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣻⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡟⠛⠛⣿⠟⣟⣂⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⣷⣤⣤⣴⣀⣿⠋⠉⠛⣴⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⣦⣤⠤⠦⣴⣿⡘⣄⣀⣼⣁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⣿⣿⣓⣒⣞⣿⡷⣨⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣯⣿⣶⣻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢉⣠⣽⣿⣿⣿⣿⣿⣿⣶⣀⡈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⣾⣿⣿⣿⡿⠛⠛⠉⠉⠉⠉⠙⠛⠿⣿⣿⡻⣦⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣾⣿⣿⡿⠋⠀⠠⠂⠀⠀⠉⠉⠒⠦⣄⠈⢻⡄⠙⣧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⡿⠁⢀⠂⠀⠀⢀⠘⠧⡄⠀⠀⠈⢣⠀⢹⠀⢿⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⡇⠀⡇⠀⢰⡄⠲⠂⣴⠳⠆⣴⠀⠘⠃⠈⡇⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⡇⠀⠰⢿⣲⣄⣿⣔⣢⠟⠀⠀⡄⠀⡇⢸⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⡇⠀⣇⠀⠠⠾⠑⠺⠟⠿⡼⠒⠀⢠⡇⢀⡇⣼⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣸⠀⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣽⣇⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁⣰⠇⢰⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣛⣛⡛⠒⠒⠒⠒⠛⠛⢻⣛⣛⣋⠠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣉⡁⣀⠀⠀⠀⢠⣀⣀⣈⡹⠿⢟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣟⣿⣶⡖⣶⣶⣶⡶⢶⣶⣶⣶⠒⣶⣾⣛⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣷⢿⣶⣥⣿⡀⠤⣷⢾⠠⠄⣼⣴⣀⡟⣾⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠯⢿⣽⣿⣛⣋⣘⣿⣛⣁⠽⠯⠴⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⢀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⠻⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣿⣶⠘⢋⣥⡄⠀⠀⠀⠀⠀⠀⠐⣄⢃⠈⠊⠀⡎⡰
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣮⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⠿⠿⠛⠏⠱⡄⠀⠀⠀⠀⠀⠐⠚⠀⠳⣄⢼⡗⡓⠠⠂
⠀⠀⠀⠀⠀⣼⣿⢿⣿⣸⣿⣟⣟⣻⠛⢻⡆⠀⠀⠀⠀⠒⠚⣏⢹⢿⣛⠀⢀⡤⣤⣶⣿⠆⠀⠀⠀⠈⢻⣀⣈⡱⢾⡿⢯⠒
⠀⠀⠀⠀⢀⣿⣾⣿⡻⣿⣿⣿⣿⣵⣷⢄⡀⠀⠀⠀⠀⠀⠞⠓⢁⣰⣷⡶⠉⠀⣈⠋⠻⣦⠀⠀⠀⠀⠀⠀⢸⠶⠠⠂⠀⠁
⠀⠀⠀⠀⢸⣿⣾⡳⣿⡹⣿⣿⣽⠻⣹⢿⢶⡄⠀⠀⠒⢸⡤⡤⣤⠉⣉⣑⣲⠚⠛⡰⣦⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴
⠀⠀⠀⠀⣜⣟⣿⣿⣿⣷⣿⣟⣶⡻⣳⣷⡈⠇⠀⠀⢰⡚⠓⠿⣀⣈⣿⡿⡿⢤⣀⣀⣀⣹⡇⠀⠀⠀⠀⠀⠀⢀⣏⠰⣠⢣⡞⠀⠇
⠀⠀⠀⠀⣱⣿⠿⢿⣟⡘⣿⣼⣫⡾⡿⣿⣿⡄⠀⠀⠀⢰⡶⣶⣛⣿⣿⣉⣁⡀⣰⣿⣻⢿⡁⠀⠀⠀⣀⠀⠀⠀⢯⣤⣠⠇⠐⠀⠀⠄
⠀⠀⠀⠀⢿⡗⠾⢄⣍⡟⣿⣿⢹⡤⠒⠿⣾⠃⠀⠀⠉⣉⣴⣾⣿⣋⣀⣠⣿⡯⠀⢋⣁⣦⡃⠀⢀⣸⡏⠰⠋⠀⠙⢻⠿⡄⢠⡄
⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⢻⣧⠞⠁⠉⠁⠉⠀⠀⠀⠀⠙⠯⠥⠛⠛⢻⢻⡽⠣⣴⠿⠙⠋⠁⠀⠈⢣⣹⣤⡠⠂⢀⠞⣦⢽⡏⠧⠚⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢣⢀⡊⠄⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣙⠛⣟⢟⣿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢾⡿⣿⣿⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⣦
⠀⠀⠀⣾⣿⣟⢈⠀⠀⠀⠀⠀⢀⡓⠒⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣿⣿⡇⠈⡇⠀⠀⠀⠀⠀⣷⡥⡁⠀⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⡾⣿⣘⡇⠘⠈⡇⠀⠀⠻⣄⣠⠋
⠀⠀⠀⡿⣿⣧⠞⢁⠀⠀⠀⠀⢀⡆⠤⠤⠀⠒⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣿⣷⢼⠀⠀⠀⡇⠀⠀⠀⢱⡋
⠀⠀⠀⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠠⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣾⡲⠀⠀⡟⠛⠀⠀⠸⠃
⠀⠀⠀⣿⣿⣿⡆⣠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠁⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠱⠷⢱⠸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢳⠛⢆⡀⣀⠀⠀⠓⠂⠰⡇⠀⢈⢇⠀⠂⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡀⢦⠀⠀⠀⠀⠀⠀⠘⠁⢢⡌⠀⠘⠀⠋⠀⠀⠀⠀⠀⡄⠀⡰⠀⢴⠄⠀⡃⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⡶⠇⠠⠇⠀⠀⠀⠐
⠀⠀⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣑⠈⠱⡀⠀⠀⠠⠀⠀⢀⢀⠊⠀⠀⠣⠀⠀⠀⠄⢀⡤⠀⠀⠀⠀⠀⠘⠿⠩⠥⠀⠀⠀⠓⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣀⠘⠢⡀⠀⠀⠀⠸⠀⠀⢀⠔⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠄⠀⠤⠐⠁⠀⠀⠀⠈⠃⢄⡀⠀⠀⣠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⠀⠉⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢉⣲⡾⠅⠀⠀⠀⠠⡀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠀⠀⠀⢤⣴⣹⢿⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠂⠀⠒⠤⠀⠀⡀⠙⢃⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⡇⠀⠀⢠⣙⡿⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠖⠀⠀⠰⠃⠀⠀⡇⠀⠀⠁⠀⠀⢀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣦⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⡈⠀⠀⢈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧
⠀⠀⠀⢿⡷⠀⠀⠀⢰⡇⠉⠄⠀⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⣠⣤⣶⣶⢶⣦⣤⣷⣶⣷⠟⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢇⠀⠀⠀⢁⠀⡿⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⡇⠀⠀⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠁⠀⠀⠰⠀⠀⠜⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠄⠐⠡⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠠⠄⠀⠀⠠⠄⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣾⣓⠲⠶⢤⣌⠁⠀⠀⠀⠀⣀⣠⠤⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠒⠤⠀⢀⠀⠀⠤⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣯⣍⣛⣓⠶⠤⠍⠓⠺⠋⠡⠤⠄⢀⡅
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢆⠀⢹⣶⠭⣭⡙⠒⠤⠤⠤⠄⠒⠒⠋⢙⠀⡃
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢄⡙⠓⠲⠤⠤⢙⣷⡶⠄⠰⠞⠛⣉⠔⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⣀⡀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⠤⠀⠀⠤⠀⠀⠐⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⢹⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠶⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠁⠀⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠻⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠁⠀⠀⠀⡀⠳⡀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠘⢃⠠⠚⠁⠀⠀⠀⢉⠗
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠃⠀⠀⠀⡄⠰⠴⠁⠈⠂⡘⠀⠀⠀⡠⠁⠀⢳⠀⠀⠆⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⣀⠄⣠⠎
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡄⠀⠰⠀⠀⠀⠀⠉⠁⡀⠀⠀⠀⠀⣀⠂⠀⠀⢀⡀⠎⠁⡴⠁
⠀⠀⠀⠀⠀⢠⣼⣧⣠⡾⣧⣴⡿⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⡀⠃⠀⠀⠀⠘⠀⠰⠀⠀⠀⠀⡤⠁⠀⠀⠊⠁⠀⢠⡞
⠀⠀⠀⠀⠀⡼⢡⡟⢩⠀⢀⠘⠧⡀⠀⠀⠀⠐⠀⠈⠂⠀⠰⠃⠀⠀⠀⡄⠁⠀⠀⠆⠀⠀⢀⠇⠈⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠠⠀⠀⢀⡀⠦⣾⠆
⠀⠀⠀⢠⣴⣿⢆⡇⠈⡄⣺⠠⣄⣹⠇⠀⠀⠀⣆⠀⠀⠀⠀⡐⠀⠀⠈⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⡠⠐⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⡰⠋
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠛⠉⠀⠈⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠄⠈⠁⠀⠀⠌⠀⠀⠀⡘⠀⡀⠐⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠈⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⡀⡼⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⡠⠖⠊⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢄⡀⠰⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣀⠀⡀⠠⠄⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡠⢀⠉⠋⠦⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⢀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣿⣿⣿⠇⠻⡃⠀⢀⣈⢠⣄⠀⠀⠁⠙⡄⠀⣀⣀⡛⠀⢀⠀⠀⣤⣤⣉⣀⠀⠀⠀⠠⠀⠈⢀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢟⣴⣿⣿⡏⠀⠃⠴⣿⠌⠠⡀⠀⠈⠳⣆⠀⠈⠃⠀⠀⡌⠁⠄⢀⠄⠘⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⢠⣿⠊⡤⣿⣼⡇⠀⠸⠄⢸⡏⣤⠈⠢⡀⠀⠈⠿⡀⢸⠀⠸⠃⡀⠘⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢀⣾⠃⢠⡇⣿⢻⡄⠀⠀⠂⠇⠈⠿⢢⡀⠈⠒⠀⠀⠐⢢⣴⣇⠀⣀⠀⠀⠀⠠⣤⣄⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣼⠻⠀⠺⢰⡇⠸⡇⠀⠀⠘⠒⢶⠲⣤⠀⠀⠀⠀⠀⣀⡼⠋⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⠤⡀⢤⠒⠛⠛⠁
⠀⠀⠀⠀⣸⠃⢿⠀⡇⢿⡇⠀⣿⠀⠀⠀⠀⠈⠃⠘⡄⠀⠀⢀⡴⠋⠀⠀⠀⢠⠐⠀⠄⣀⠞⠉⠁⠀⠡⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⡏⠀⢸⠀⡇⣿⣴⠀⢻⡀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠳⠀⠈⠁⠀⠀⢀⡘⠀⠀⠀⢼⠀⠀⡀⠀⠐⠂⠀⠁⠄⠀⠄⠠⠀⢰⡾⠃
⠀⠀⠀⣸⠁⠀⢸⠸⡇⡇⢻⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣠⠋
⠀⠀⠀⣿⠀⠀⢸⢠⡇⢧⠘⡇⠀⣿⠀⠀⠀⠀⠀⠀⣴⣿⣶⣦⠤⣀⠀⠀⠀⢨⠀⠀⠀⠁⠀⣰⠎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⢰⠁
⠀⠀⠀⣿⠀⠀⢸⠀⡇⢠⡀⢹⠀⠛⠀⠀⠀⠀⠀⣰⡏⢻⠙⠿⣦⠈⢿⠀⠀⠘⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠌⠀⠀⠀⣀⠰⠊⠁⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⣿⠀⠀⢸⡀⢱⠸⡇⠘⣇⠂⠚⠀⠀⠀⣼⢣⡇⠀⠈⠀⠘⣧⠀⠀⠀⠀⠃⠀⠀⣼⠀⠀⠀⠀⠀⠈⣀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠎⠁
⠀⠀⠀⣿⠀⠀⠊⠁⣾⡁⣀⡠⠙⠆⠀⠀⠀⣰⠃⠀⢷⡈⡇⠀⠀⢻⡄⠀⠀⠀⡘⠀⡴⠃⠀⠀⢀⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉
⠀⠀⠀⣿⠀⠀⠻⠟⠛⡋⠉⠀⣶⡖⠀⠀⣰⠇⠀⠀⠈⡄⠃⠀⠀⠀⢷⡀⠀⠀⢁⣘⠁⠄⠒⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠂⠀⠀⠘⢀
⠀⠀⡰⠉⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡀⢾⡄⠀⠀⠀⠈⠓⠤⠿⣿⠉⠤⡀⠀⣀⡀
⠀⠀⢿⣶⠇⠀⠀⠀⠀⠛⢀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠈⠉⠉⠙⠛⠁⠀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡤⢤⣄⡀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠌⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⣤⣤⣤⣀⠀⠀⠁⠄⡀⠀⠀⠈⠠⡀⠀⡀⠀⢩⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢡⣄⠀⠀⠉⠛⠢⣀⠀⠀⠀⠀⠀⠐⣈⠂⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠈⢉⣏⠉⠳⢷⣄⠀⠀⠀⠀⠀⠀⡇⠀⢈⡟⠙⠳⠶⠖⠙⠋⠛⠳⣦⠀⠀⠀⠀⣨⠗⠚⠋⣻⡛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⡟⠉⠦⠀⠀⠙⢆⠀⠀⠀⠀⠀⢇⠀⡼⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⡼⠀⢀⠞⠁⠀⣀⣴⠎⠱⢦⣀⠀⠘⠓
⠀⠀⠀⠀⠀⢀⡠⡄⠰⠶⠎⠁⠀⠀⠀⠱⠆⢤⣤⢳⣀⠀⠀⠀⠘⢀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⢀⠴⠒⠿⠋⠁⠀⠀⠈⠙⠋⠛⠓⠶⢆
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣄⠀⡈⠙⢷⡄⠀⠀⢈⡕⠀⠀⠀⢀⠀⠀⠀⠈⢂⣴⠎⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⢀
⠀⠀⠀⣴⠁⠀⠀⠀⢀⠁⠀⠀⠀⣸⡄⠀⠀⠨⠀⠀⠀⠀⢹⠀⠀⠀⢡⠀⠀⠀⠈⠀⠀⠀⢀⡜⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦
⠀⠀⡸⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⣃⠀⠀⠘⣄⠀⠀⠈⠀⠀⠀⠎⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⡇⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠁⠀⠀⠀⠉⠂⣀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠟
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⡷⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠀⠀⢸⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣀⠤⠓⠲⠶⠖⠚⠤⣀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢺⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣧⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⠀⠀⣼⠀⠀⠀⠀⢸⡋⠀⢙⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣽⣤⣤⡀⠀⠒⠃⠀⠘⠋⠙⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⣸⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡬⡇⠀⢤⠀⠀⠀⡤⠖⠚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠋⣟⠙⠃⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢾⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣋⣀⣀⣀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⣉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢉⣵⣋⣉⣀⣀⣀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⣿⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⡀⢾⢀⣞⢧⣀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠤⡤⢾⠀⠁⢸⣾⠊⡾⠋⢁⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣄⠀⠀⠑⢄⠀⣏⡉⠀⢘⠠⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣘⠦⣀⠀⠀⠈⣿⣀⡴⠋⠄⣧⢻⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡌⠳⠤⢤⡀⢰⡏⢦⡀⠈⢿⡦⠀⠑⠢⣀⠨⠉⠀⠀⣤⢥⡟⠀⢠⣾⠟⢧⣀⡤⢤⣤⢔⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⣶⠀⢠⠉⠉⠀⠄⠻⣄⣸⠀⠢⠀⠀⠈⠈⢆⣠⡾⠁⢈⢧⡴⠋⡎⠈⠀⠀⠀⠀⣴⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢗⡿⣦⣾⠀⠀⠀⠠⠀⠈⠁⠃⠀⠈⠒⢔⡆⣾⡁⠀⡀⠀⠰⠀⢰⠃⠀⠀⢀⣈⠿⣛⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡄⣈⡉⠛⢆⡀⠀⠀⡇⠀⠸⡄⠀⠠⡀⠀⠉⣿⣔⠞⡀⠁⠁⠀⡸⠀⣀⣀⡘⠛⣉⣭⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠉⠛⠋⠙⢶⣄⡇⠀⠀⡇⠀⢀⠈⢢⣐⣿⠗⣦⠁⠀⢀⠀⠰⡄⠉⠈⠉⠀⠀⢨⡽⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣋⡢⠈⠙⠒⠉⠉⠈⣑⣦⣴⡇⠀⣼⠀⠐⠈⣻⣼⠋⠀⠀⣻⢠⢞⠐⠉⢀⣈⣉⣀⣂⣴⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣝⣓⢘⡒⠒⠒⠛⢉⠁⠙⣷⡄⣺⠄⠀⠀⣿⣧⠊⡄⢀⡿⠃⠀⠀⠀⢉⡉⢩⣭⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣍⢒⢐⠲⡖⠛⢛⣻⣿⠀⠀⢠⣿⣍⠰⣡⣾⣡⡂⣀⢡⣶⣤⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣮⣬⣁⠁⠀⢄⠹⠾⢷⣵⢲⡿⢃⣶⠟⣞⣿⠟⠉⠋⠁⢘⡷⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠥⣀⠀⣀⣨⣵⡦⠴⠦⣴⣦⣿⣿⣿⣿⣥⣿⣏⠀⢀⡤⠂⠀⡠⠾⠻⡿⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣯⣤⣴⡶⠚⠋⠁⠴⠉⠀⢈⠝⠁⣠⢾⣿⣉⡟⠓⢦⣉⡉⠙⠒⠲⣞⠛⠚⠛⣛⣿⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠶⣥⣤⠵⠶⣦⣤⣥⠶⠛⠁⣾⠃⠉⠳⣌⢀⣈⠳⣄⠀⣠⡬⠽⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠈⠙⠺⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⢿⣇⠀⠀⠀⢀⣯⡉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠄⠀⡏⠉⠉⠉⠉⠉⡇⠀⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⢠⠞⠁⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢻⠀⢸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⡄⠸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢡⠀⡇⠀⠀⢿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡷⠖⠛⠋⠛⠛⠶⣄⡀
⠀⣼⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⢰⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢤⡀⠀⠀⠀⢻
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢳⢀⡠⠶⠒⠒⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢢⠀⠀⠈
⡇⠀⠀⠀⠄⠀⠀⠠⡴⠒⠚⠛⠓⠺⠇⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇
⣧⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠃
⢹⠀⠀⠀⠐⠀⠀⠀⠀⠱⢄⣀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠏
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⣀⠴⠋⠀⠀⠀⣸
⠀⢹⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣠⠄⠀⡤⠤⠤⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⡴⠃
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠓⠋⠉⠉⠉⠉⠀⢧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡟⠀⠉⠛⠲⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠃
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠤⠖⠒⠒⠛⠉⠉⢧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠓⠀⠉⢍⡉⠉⠉⡩⠙⡆
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠸⢀⣠⠚⠙⡅
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣅⠆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠉⠂⡤⠒⠘⠋⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠂⠀⠀⠇⠀⠀⠑⠂⠤⢄⣀
⠀⠀⠀⠀⠀⢀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠢⠄⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠣⡀
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠲⡘⠁⠈⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠹⡄
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠠⠠⢤⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⡀
⢸⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠤⠀⠄⠠⣀⢄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣇
⡇⠀⠀⠀⠀⠈⠡⠆⠀⠀⠀⠂⠀⡈⣁⠞⠨⣀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⡲⣈⠁⠬⠗⠋⠂⠓⠂⠐⠀⠚⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⠀⠀⠈⡀⡀⢀⠄⡠⢄⠔⠒⠄⡠⢀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠘⠀⠀⣼
⠀⠀⠀⠀⠀⠨⢀⠘⠀⢠⠀⠀⠀⡃⠶⡅⠉⢈⠂⣈⡠⠂⠀⠀⠀⠀⠀⠀⠀⡃
⠈⣆⠀⠀⠀⢐⡉⠠⠂⠅⠌⠀⠄⠍⠒⠋⠂⠊⠒⠀⠀⠀⠀⠀⠀⠀⠆⠀⣸
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⠃
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⠀⠉⠀⠀⠀⠀⡰⠁⠀⣏
⠀⠀⠀⠀⠈⠒⣤⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠁⠀⠁⠀⢀⠔⣀⡤⠔⠉⠉⠉⠉⠙⢢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠒⠒⠶⢦⠤⠀⠤⠤⠤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢤⣀⠀⠀⣀⣀⠤⠤⠤⠤⠤⣀⣀⡀⣀⣀⠤
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡄⠂⠐⠢⡀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠁⠀⠼⡀⠀⠀⠀⠈⢣⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣁⡘⢹⣆⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠃⠘⢆⡈⠉⠓⠢⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣛⠗⠣⠀⠠⠂⠀⢁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣄⠀⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊⠉⠚⠦⠦⢄⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⡆⠀⠀⣀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⣤⠀⠀⠀⠀⠀⠰⡆⠈⠐⠓⠀⠀⠉⠉⠁⡜⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠁⠀⠀⡔⠀⠀⠀⠀⠀⠀⣰
⠀⣀⠤⠐⠐⠦⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠠⠬⠃⠀⠀⠀⠀⡴⠁
⡴⠁⠀⠀⢐⠂⢸⠀⢀⣠⠴⣊⣡⡄⠴⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢼⡀⢀⡠⢄⠀⢠⠃⠀⠀⠀⠀⢀⡜⠁
⡇⠀⠀⠀⠀⠀⠉⠉⢁⣠⣤⠞⠁⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⡾
⠘⢦⣀⡀⣀⣀⠤⠖⣩⠟⢁⡔⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠁
⠀⠀⡼⠋⠀⠀⢀⡼⠁⠀⢾⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠤⠤⠤⠒⠋⠉⠋
⠀⢸⠁⠀⠀⡀⠈⢱⡀⠀⠀⠉⠉
⠀⠘⣄⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠏⠲⠊⠁⠀⠀⠀⠠⢀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠈⠄⠐⠀⠄⠀⢀⠘⠀⠠⠚⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡀⠶⣄⣦⠀⠀⠛⠇⠀⣴⠱⠈⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠐⠑⠢⠼⠀⠀⠀⠠⣹⣆⡀⡀⢼⡠⢃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⢀⡀⠰⠀⠀⠀⠀⠈⣿⡁⠀⠸⠏⠀⠀⠀⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠁⢀⣀⠀⣄⠀⠀⠀⠀⢿⡇⠐⠆⠂⠀⢀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠼⡇⠀⢺⡃⠀⠀⠀⠀⢀⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠰⠋⠁⢻⠣⠆⢉⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⠲⡀⠀⠀⠐⠒⠋⢾⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡆⠄⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠇⠉⠀⠀⠈⠀⠈⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣎⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡄⣻⣖⢞⡢⡀
⠀⠀⠀⠀⠀⠀⡰⣿⣨⣼⣿⡷⠒⠂⠀⠀⠀⠀⠀⠀⠏⠇⠿⠾⣶⣶⢾⣰⡲⠀⠀⠀⠀⣀⣿⠿⡿⠀⠀⢀⠀⠀⣗⠀⢀⡀⠹⣴⡛⢿⣿⡟⣢⡀
⠀⠀⠀⠀⢀⣼⣁⡁⠈⠋⠹⣿⡶⣦⡄⡀⠀⠀⠀⠀⠰⢯⣀⢀⣘⣁⣀⣀⡀⠀⠀⠀⠸⣤⣿⣿⣷⡀⠀⢸⠛⠛⠟⠿⣿⠇⠀⠘⢷⡟⠋⣽⡿⠇
⠀⠀⠀⠀⢀⡿⢿⠋⠓⢠⣰⡎⠱⠿⣄⠀⠀⠀⠀⠀⠛⠋⢙⣿⠙⠉⢻⡟⠁⠀⠀⠀⠀⣨⣿⣿⣿⣇⠀⠀⠙⠒⠒⠚⠋⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⣿⣥⡜⠿⢤⣤⡛⠛⣅⣠⣠⠢⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠉⠉⠉⠻⣷⡄⠀⠀⢀⣀⢤⣄⣤⣴⣶⣶⣆
⠀⠀⠀⢰⣟⣁⣀⣀⠬⡿⣿⡉⣉⠿⠛⢦⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣟⡤⢀⢹⡇⠀⠀⢻⣸⠿⡟⢛⣟⠿⢯⣏⣦
⠀⠀⠀⠀⡿⢿⣿⣄⣀⣉⣿⣿⣛⡶⣶⡀⠀⠀⠀⠀⣞⣻⣿⣿⣭⣉⣳⣶⡄⠀⠀⢸⡷⣆⠙⠋⣁⣄⣾⡇⠀⠀⠀⠿⣿⠋⠽⣿⣶⣾⣿⡍⣱⡄
⠀⠀⠀⠈⣷⣤⣄⠀⣿⣧⣠⣬⣿⢿⣦⡌⠁⠀⠀⢀⣿⣿⣿⣿⠭⣽⡾⣊⠅⠀⠀⠨⣿⢿⣖⢒⣲⣿⣿⠅⠀⠀⠀⠀⠈⠛⠻⢤⣀⣿⡛⣫⡟
⠀⠀⠀⠀⠀⠈⠛⠓⠙⢺⠛⠉⠉⠒⠛⠀⠀⠀⠀⠸⣿⣿⣛⣿⣷⣿⣿⢟⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣯⣽⡷⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣶⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⣺⣿⣿⣶⣤⣬⣼⣟⡿⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣋⠙⠫⠻⡯⣿⣿⠟⠡⡄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣻⣿⣿⣿⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣽⣍⣻⣷⢤⣾⣿⣿⣵⣤⠄
⠀⠀⠀⠀⠀⠀⠙⢏⢦⣠⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠙⢛⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠽⠟⠋⠁
⠀⠀⠀⠀⢀⠀⠴⡌⢧⣁⣼⠏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡄⣰⢿⠟⠋⠨⠳⠈⣿⣠⠀⠀⢠⡀⡀⢠⢤⢴⠀⠀⠀⠀⠀⠀⡠⠚⣮⣼⠿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠤⠲⣼⢹⣿⣤⠢⡀⠒⢤⢾⣴⠃⠀⠀⣞⠁⢑⣫⠀⡤⠂⠀⠀⠀⠀⠠⠛⣻⠄⠀⠰⢤⣿⣿⣿⣙⠀⠀⠀⢀⡀⣄⣢⣼⣏⢡⡗⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠠⢵⣄⠂⠀⠀⠀⠀⢶⡞⣾⣼⣃⣀⣉⣵⠆⠀⠀⠀⠸⣄⠙⠛⠶⠾⢿⣏⣴⣿⡿⠀⠀⠀⣩⣵⣿⣿⣿⣿⠛⣦⡛⣠⡀
⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠒⠙⠟⡉⠓⠒⠂⠀⠀⠀⠑⢀⠈⠻⣷⣶⣶⣾⣿⣿⠏⡀⠀⠀⠀⣰⣿⠻⣿⢛⣿⣶⣾⡱⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⢿⣿⣯⣬⣍⣹⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠾⠹⠹⠴⣶⣶⡶⣟⣴⡢⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣾⠵⣋⠀⠀⠀⠀⠀⠀⠀⢀⠞⢲⣭⡽⠿⢶⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠾⣅⡀⣀⡛⣀⣀⡀⠀⠀⠀⠀⠀⠀⢼⣟⢿⠿⣿⣷⣮⣽⡷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠛⢷⡇⠄⠐⢒⠤⡾⣿⣾⡃⣣
⠀⠀⠀⠀⠀⠀⠐⠞⠛⢳⡏⠛⠛⢻⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣛⣻⡯⣁⡎⠀⠀⠀⠀⠀⠀⠸⣆⠘⠷⠶⣴⣾⣶⡿⢉⣼⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠏⢙⡛⢻⣏⣹⣆⡀⠀⠀⠀⠀⢀⠀⠙⢷⡤⢤⢄⣀⣸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣷⣟⣻⣯⡾⢻⣝⡆⠀⠀⠀⠀⠑⠢⢀⠘⠻⠿⠿⠿⠿⠟⡉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣯⣿⣿⣽⣿⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠠⢇⡉⢚⣿⣰⠂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠉⠛⠙⣛⡉⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢫⢖⣩⣶⣿⣿⣿⣿⣧⣞⡛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⣧⠞⡹⢖⠇⠀⠀⠀⠘⣿⢻⣧⢤⡀
⠀⠀⠀⠀⠸⣿⣔⢿⣋⣀⣽⣿⣯⣽⣏⣿⡛⠄⠀⠀⠀⠀⡰⣿⡤⡾⡂⢄⠀⠀⠀⠀⠀⠹⣖⢣⡼⣠⡶⠃⡠⠔⠀⠀⠀⠀⣸⣿⣿⣧⡴⠃
⠀⠀⠀⠀⠀⠉⠛⢶⣿⣿⣿⣥⣹⣿⣘⠟⠧⠀⠀⠀⠀⢻⣴⢋⡿⢾⣿⣾⡗⠢⣄⠀⠀⠐⠒⠻⣿⣥⣦⣤⣈⣩⡤⠀⠀⣀⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣵⢈⣿⢷⢺⣟⣽⠇⠀⠀⠀⠈⠹⠁⡙⠒⠶⠉⠀⠀⣴⣿⠛⠉⠉⢙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣀⢠⣄⡠⣤⣠⣴⣤⣤⡀⠈⠻⣇⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⠁⠀⣴⣷⡄⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢿⢉⣷⣿⠿⢿⣿⣿⡿⡧⢣⠀⠀⠈⠉⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⡀⠀⠀⠀⣿⡄⡀⠛⠛⠃⡠⣼⡇
⠀⠀⠀⠀⣴⣤⣤⣾⣦⣤⣴⡆⠀⠸⣟⣥⡿⠤⢾⣶⣉⢙⣗⠶⢇⠀⠀⠀⠀⠸⢷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣥⣇⠀⠀⣿⣷⣿⡭⠤⣴⣿⣾⠁
⠀⠀⠀⠀⠹⡉⠉⠉⠉⢉⣿⠃⠀⠀⠉⢿⣄⣈⡹⠿⠿⣿⣿⣇⣀⣽⠀⠀⠀⠤⣄⢟⠉⠙⠹⠿⣫⠽⣿⣿⠟⠃⠀⠀⢹⣿⣿⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠓⢦⣬⣟⠛⢫⣾⠃⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⡴⠞⠿⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⡷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣿⣏⣾⣿⣿⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣽⣿⡿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⡇⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣟⣿⣷⣤⣀⣀⣀⣀⣀⡀⠠⢤⣤⣼⡿⠿⢿⠿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⣤⣬⣽⣧⣝⢿⣯⣩⣭⣭⣷⣶⣶⢶⣶⣶⡦⠶⣶⣾⠋⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⣡⣴⣿⣿⣿⣻⣿⣿⣎⢻⣿⣯⣿⣵⣯⣵⣯⣥⣾⣥⣶⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⣿⢿⣿⠋⠉⠉⠉⠉⠉⠹⣇⢻⡍⠉⠉⠀⠀⠀⢹⣿⣿⣿⣿⡿⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⣼⠏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢰⡏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣷⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⢻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡆⠀⠀⠈⢿⣿⣿⣿⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡀⠀⠀⣿⣿⣿⠏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⡇⠀⢸⣿⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣷⠀⠈⣿⣿⣿⡈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⡆⠀⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣁⣀⣀⣀⣀⣤⣀⣠⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⡿⣿
⢀⣤⣤⡶⠾⠿⠟⠛⠛⢛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⡇⢿⡶⢾⣿⣿⣿⣿⣿⣷⣿
⢿⣯⣀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⣶⣾⣿⠘⣿⣀⣀⣀⣩⣿⣿⣼⣿
⠀⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⡄⠃⣿⡿⠟⣿⣿⣿⣿⣿⣿
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣷⣶⣾⣿⣿⣿⣟⣛⢁⣿⣿⣿⣿⣿⣿
⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣙⣛⣛⣿⣿⣿⣿⣿⠛⣸⣿⣿⣿⣿⣿⣿
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡈⣩⣽⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⢿⣿⣿⣿⠟⠒⡆⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣾⣿⣿⣿⡛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣬⣭⣽⣿⣿⣧⡖⠂⣸⣿⡟⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⣾⣶⣿⣿⣿⣷⣶⡯⢀⣿⣿⣿⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣿⡏⣼⣿⣿⣿⣿⣻⣿⣿⣧⢿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⡿⢠⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣭⣭⣿⣿⣿⣿⣿⠆⣼⡏⠀⣿⡿⣧⣻⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣒⣲⣿⣿⣿⣿⡏⢰⣿⠁⠀⣹⣷⡈⢿⣿⣿⡜⣿
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣭⣹⣿⣿⣿⠟⠀⣾⡏⠀⢰⣿⣿⠿⣼⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣽⣿⣿⣿⣶⡆⣸⣿⠁⠀⠘⢿⣿⣦⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣀⠀⠀⢉⣩⣭⣭⣿⣿⣛⣛⣳⣤⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣛⣛⣛⣛⣉⣙⣛⣛⣛⣛⣛⣛⣩⣭⣭⣭⣭⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉
⠀⠈⠁⠉⠈⠃⠀⠀⠁⠀⠀⠀⠘⠀⠁⠀⠈⠀⠈⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⢀⡠⠤⠤⠤⠤⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠣⢤⠀⠀⠠⡇⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢠⢇⣤⠞⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢇⠸⠀⡇⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠤⠒⠐⠂⠠⠔⠒⢻⠙⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠐⠵⠀⠀⠐⠀⠀⠀⠳⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⣀⡀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣀⡌⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠢⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⠤⠀⡄⠀⠀⡠⢄⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠁⡬⠀⠀⠀⠀⠆⠀⡀⢃⣠⠇⣀⡀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⡄⠚⢀⣸⠦⠗⠀⠿⠼⠀⠀⠤⠯⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠂⢉⡆⠪⡑⠁⡙⠁⠄⢀⡰⠁⠖⢰⡋⢠⠉⠂⠀⠀⠀⠀⠀⢠⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢈⡂⠄⢀⣀⠜⡰⠀⠀⢰⡈⢙⡄⠀⣸⠀⠒⠐⠃⠀⠀⠀⠀⠀⠸⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⠤⠐⠊⠘⠒⠁⠀⠓⠊⠈⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠖⠀⢠⠀⠀⠀⠀⠀⠀⡰⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠈⠁⠀⠀⠀⠀⡴⠁⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠉⠀⠀⢀⠎⢀⣀⠤⠊⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠶⠶⠤⠤⠤⠤⣤⡤⠄⠀⣀⣀⡸⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠶⠒⠊⠉⠁⠀⠀⠀⠉⠉⠛⠓⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠒⠛⠛⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⣇⣀⣀⣠⣄⣠⣥⣤⣿⣟⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠈⠀⢠⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⢠⠖⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⠤⡾⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣄⡀⠀⠀⠀⠀⢀⡴⠶⢦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠙⣦⠀⠀⠀⣸⠁⠀⠀⠷⡴⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠲⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠖⠒⠊⠛⠛⠛⠛⠛⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣀⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢸
⢰⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣼⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⡤⠤⣀⣀⡀⠀⠀⠉⠀⠀⠀⠙⣆⢀⣠⣤⢶⠶⢶⣤⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⠙⠳⠶⠇⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠸⠏⠀⠀⠀⠀⢸⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢠⡀⠀⠀⢰⡇⠀⠀⣠⠄⠀⢀⡴⠃⠀⠀⠀⠀⠀⠸⡇
⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣯⡀⠀⠀⠀⠀⠀⠀⢀⡇
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠞⠁⠀⠀⠀⠳⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢰
⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⣀⣤⣆⠀⢠⣄⣀⣀⣀⣀⣠⣽⠄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠛⠒⠛⠛⠋⠉⠀⣿⠀⢸⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠋⠀⠀⠀⠀⠀⡤⠈⠂⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⠁⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢺⣍⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⠄⠀⠴⡮⢀⡀⠀⠀⠀⠀⠈⠁
⠠⢴⣆⠀⠀⠀⠐⠀⠀⠀⠀⢰⡄⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠸⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠠⠀⠁⠀⠉⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀⠀⠀⠐⠀⠂
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣠⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡃⡀⠀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠷⡴⠶⠶⡾⠮⠷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⠿⠿⣿⣿⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⣿⣿⠶⢶⣿⣿⣮⡣⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣿⣿⠀⢸⣿⣿⡏⢻⣿⣶⣮⣵⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣿⠀⣿⣿⠿⡟⠁⠀⠉⢢⡉⣦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⠀⣿⣿⢸⡇⠀⠀⠀⠀⣧⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⣿⢸⡇⠀⠀⠀⠀⡘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⣿⣇⢿⣿⡜⡇⠀⠀⠀⠀⡇⣸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣧⢿⠀⠀⠀⢰⢁⡏⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡎⣿⣿⡼⡆⠀⠀⡎⠘⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣄⣼⡆⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣫⣶⣶⣦⣝⢿⣿⣿⣿⡟⢿⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢋⣾⣿⣿⠿⣿⣿⣧⠻⣿⣿⣿⣸⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢣⣿⠛⢿⡍⢘⠨⡿⣿⣧⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢃⣿⣿⣌⣇⠠⡅⣈⠜⢙⣿⣇⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⣼⣿⣿⣿⡥⢰⣆⣉⣰⣿⣿⣿⡄⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢠⡟⠛⣟⠻⢿⠛⡛⠟⡟⢻⠛⡛⣧⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣯⣥⡜⢂⣾⣤⣿⣧⣤⣼⠀⣥⣿⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣧⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢠⣿⣯⣼⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣿⣿⠿⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡿⣿⣿⣿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⠻⠿⣷⣶⣮⣭⣭⣭⣭⣭⣭⣭⣽⣶⣶⣿⣿⡿⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠤⠤⠤⠤⠤⠤⠬⠤⠤⠤⠬⠭⠿⠯⠥⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠿⠿⠿⠿⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠛⠛⠛⠛⠛⠛⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣶⠶⢶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⣤⣀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠉⠙⠻⣷⡀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⣻⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣿⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣀⣴⣶⠿⠿⠟⠻⠿⢷⣶⣤⡀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⠁⠀⠀⠀⠀⣠⣾⠟⠻⣷⣄⠀⠀⠀⠀⠘⣿⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡏⠀⢀⣤⣤⣤⣿⡇⠀⠀⣼⣿⣤⣤⣤⡀⠀⣿⡇⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢸⣷⠀⢸⣿⠉⠙⣿⣿⠀⢀⣿⡿⠋⠉⣿⡇⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠘⠻⣷⣄⠈⠉⠀⠀⠉⢀⣤⣾⠟⠁⠀⣿⠃⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣿⠀⠀⠀⠈⣿⣧⣶⣿⣷⣦⣼⣿⠀⠀⠀⠀⠉⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡇⠀⠀⠀⠛⠋⠁⣿⡇⠈⠙⠋⠀⠀⠀⢠⣄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠈⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡾⠟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢦⡞⣏⠰⣶⣶⣮⣴⢞⣤⣤⠰⣦⣀⠐⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣾⣿⠖⢤⢀⣀⡨⣀⣀⣦⣗⢰
⢐⡻⡄⠋⢙⠿⣟⣡⠈⢨⢸⡗⣫⠩⡟⠊⡩⡼⢀⣀⣀⢀⣄⠀⣀⣠⣠⠟⣤⢝⡎⢼⠨⣏⣮⠹⣿⠫⡐⢓⢻⠤⢳⠾⣇
⠈⠇⢑⠦⡋⠏⢹⡼⢎⣽⢨⠶⣨⡷⠚⣶⢑⣯⣘⣿⠹⣏⠋⣿⣿⢿⣟⣿⢍⣜⣄⡼⡔⠿⢆⠓⢿⡧⠙⢠⠙⡏⣸⢳⡟
⠐⠀⠾⡖⣩⠓⢞⠋⠂⠶⢊⢌⡽⠋⢔⣠⠋⡐⣬⡱⢏⢀⣀⠈⠗⠞⠣⠊⢄⣿⡸⢆⡲⢌⣆⠛⠶⢦⢘⠀⢅⠱⢗⠊⢍
⠀⠀⣰⠀⡌⡙⠂⣀⠀⠀⠀⠀⠀⠋⠀⠓⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀⣆⠁⢲⠌⢺⡷⠄⠈⠀⠁⠙⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡏⠉⠉⠉⢹⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠙⡧⠤⠤⠤⠼⢦⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⡇⠀⠀⠀⢀⡼⠀⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠱⠤⢄⠀⡏⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⢸⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⢸⠀⠀⢸⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠈⠙⠳⡄
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠹⡆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠹⡀⢀⣠⡤⠤⢶⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠈⠑⢄⠀⠀⢹⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠤⠶⠶⠶⢼⠇⠀⠀⠀⠀⠗⠉⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡄⠀⠘⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⠁⠀⠀⡇
⠀⠀⠀⠘⡇⠀⠀⠐⠀⠀⠀⠈⠢⣄⠀⠀⠀⠁⠀⠀⠈⠁⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢠⠏⠀⠀⢰⠇
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠧⣄⣀⡠⠔⠋⠀⠀⢀⡞
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣤⠤⢶⠀⣰⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⢤⣀⣀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠄⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⣻⣤⡲⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠀⠀⠠⡼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⡆⠀⠀⢠⠟⠞⢃⡾⣹⢧⡹⡏⡜⠛⠁⠀⠀⠀⠀⣀⡤⠒⠋⠘⠁⠠⣶⡀⠀⢸⡞⢻⣀⡀⠀⠀⢠⣷⡄⠀⠀⠀⡩⡀⣥⣾⡀⣠⣿⣄⣾
⢀⣄⢠⣿⠀⣰⡰⡚⠛⣸⣦⣴⣃⣶⣤⣴⣏⠀⠙⠿⠀⠘⠁⢀⡠⢔⣾⡏⠀⠀⠀⠀⠀⢴⣿⣆⠀⠼⣇⣾⡍⠁⠀⠀⣦⢷⣰⢀⠀⢰⡟⢻⣠⡏⢳⣿⣸⣇⢿
⢸⣿⣫⣭⣷⣿⢉⣿⢉⣻⡿⢩⠇⢸⣧⠁⣾⡆⣸⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣎⣻⢸⡤⣀⣽⣏⠹⠶⠀⣠⣤⣿⡉⢼⠁⠼⣷⣚⣡⣇⣸⣧⣹⠙⡛
⢸⣿⣽⡉⣿⠟⠁⣈⢈⡉⢹⣿⣠⣾⣧⡖⢁⣿⣏⠈⡝⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⢿⣌⣥⠈⠾⡟⠳⠇⠀⢈⣡⣯⡛⠆⣉⠰⣾⡿⢋⣍⠁⢹⡻⡦⣿
⢸⣯⣴⣿⡝⠛⠋⠈⣿⡛⠛⣿⣿⣿⡿⣥⣿⢿⣿⣆⣻⣿⣾⣧⣦⣷⣶⣴⣄⣤⣄⡤⠚⣇⣼⣮⣙⣥⡀⡇⠀⣀⣴⡌⢀⣧⢥⠔⢣⡴⢤⣿⣯⣿⣷⣼⣿⣁⣿
⢸⣿⣿⣿⠧⠾⣀⣼⠞⢷⣶⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣯⣛⣧⣿⣿⠖⣉⣿⠈⣧⡙⢯⢻⣿⣟⡣⠾⣙⣿⠅⠞⡔⠢⠗⢤⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡄⣠⠏⠈⣄⠀⢳⣀⣻⡇⠿⠛⢿⠈⠟⠻⡿⣿⠟⠙⠛⠙⠿⠿⣿⣿⡿⢛⣡⣻⠆⠁⣹⡚⠻⡿⢓⠦⠓⠆⣹⢇⡠⠃⡤⠧⡘⠾⢿⡿⡿⡻⠻⠻⣿
⠈⠋⠻⢯⣀⡴⠦⠤⠊⠓⠛⢿⣄⣀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣡⠀⣥⠀⢈⣍⠠⡬⠃⠈⠋⠸⡀⠤⣹⠇⡴⢳⠀⡉⠙⡈⢃⠁⠀⠀⠀⠁
⠀⠀⠦⠴⠁⠀⠦⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠀⠀⠀⢀⠀⢐⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣝⡀⠀⢀⠁⡊⠀⠀⠈⢻⢦⠀⠴⢂⡿⡄⠀⠀⠹⡦⡐⠐
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠈⠓⢍⠓⢤⣁⠀⠀⠀⠀⡟⢀⠀⢀⠞⠀⡟⠀⠀⢠⠀⠹⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⢧⠀⠈⠳⡀⠐⣦⡙⢮⠢⢸⠁⢠⠃⠀⡠⠋⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢖⠈⣀⣀⡀⠀⠀⢸⡤⠀⠀⢧⢠⣇⠹⡌⢳⠘⣆⡿⢀⡞⠁⠀⠀⢀⠆⢀⠎⢣⠀⡀
⠀⠀⠀⠀⠀⠈⠀⣈⠉⢳⡎⢢⡀⢸⠀⠶⡀⠈⠻⠂⠀⢱⠀⠀⡿⢽⣼⠀⢠⠀⢀⡌⢀⠠⡀⡏⠐⠁
⠀⠀⠀⠀⠀⠀⠈⢹⠙⠸⡇⢀⠱⣾⡄⢁⠈⠢⡀⢠⡄⡞⠀⢀⠇⡄⠋⡠⢁⢣⠏⠀⢸⢣⢰⠇⢀⢦
⠀⠀⠀⠀⠀⢀⣆⢺⡊⠀⠹⣇⠰⠠⢄⠀⠂⠀⠰⠂⢠⠃⢀⡞⡐⢸⠐⠀⢠⠃⠀⡰⠃⣸⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⡏⢦⣀⠀⠀⠈⠳⣝⢤⡈⠲⠀⠀⡄⢸⢠⠟⠐⠀⢾⠀⠂⡇⣠⠏⠀⣀⡎⠀⣠⢀⡸
⠀⠀⠀⠀⠀⠀⠱⣄⠈⠑⠢⢤⡀⠘⡄⠱⠀⠀⠀⠆⠈⠿⠀⠀⠀⠀⠀⡆⢹⠇⡄⢠⠎⢀⡰⣻
⠀⠀⠀⠀⠈⢻⠆⠈⠲⢄⠀⣄⡙⠶⣗⠀⠁⠀⠀⠘⢄⠈⠂⠰⠀⠀⠀⠐⡤⠊⢄⣮⠖⢋⡜⠁⣦⡀
⠀⠀⠀⠀⠀⠘⠒⠠⠱⠀⠱⡀⠂⠑⠄⠀⡄⠀⠀⠀⠀⠉⠂⣤⠀⠀⠀⠀⠄⠐⠎⠥⢈⠏⡀⠀⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⡀⡇⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢐⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠓⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠀⡀⠁⠀⠔⠀⡀⠀⡀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠀⠈⠈⠀⠀⠁⠀⠈⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣿⡄⣸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠞⠁⠟⠹⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠞⠀⠀⠂⠀⠀⠀⠀⠃⠉⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⢦⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠶⡡⢿⡞⡏⠀⠀⠀⠀⢰⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⢀⠟⡉⠀⠁⣘⢳⢿⡄⢸⠀⠀⢨⠻⠻⣤⣇⢀⣖⠦
⠀⠀⠀⠀⠀⠀⣴⣥⠄⡀⠀⣹⡗⣡⣾⣿⠃⣰⡇⡸⠀⣿⠿⣄⣠⣿⢣⡀⠈⠹⣾⠁⠀⠈
⠀⠀⠀⠀⠀⠠⠋⠉⠛⠳⢾⣯⣾⣻⢳⠃⢠⣿⠇⡇⠀⢿⣾⡘⡈⢻⣇⢻⣤⠬⢶⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠉⠭⠙⠒⠋⠛⢻⣿⡄⠚⠛⠓⠓⠘⠻⡏⢁⡤⠔⠈⣷⣀⠄
⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠘⠇⠀⠀⠀⠀⠀⠀⢸⢸⡇⠖⠂⠀⠀⠀⠀⣹⣀⠀⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠤⠷⠞⢀⣀⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⢀⠌⠀⢠⠋⠱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠉⠀⠉⠉⢉⡉⠉⢩⡀⠴⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠒⠒⠚⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠣⢄⠀⠀⣇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡜⡠⠎⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠓⣁⢤⠤⠬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡂⠀⠈⠀⠀⠸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠂⠠⠄⢀⠀⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠰⡒⠃⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⢆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠅⠢⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢀⠄⠀⡠⠀⠠⢒⠀⡤⠄⠤⢄⠀⠀⠀⠀⠀⠈⡀⠀⢹
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠒⣀⠀⡄⢁⠀⡌⠖⠃⠢⡄⢿⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠤⠡⠀⠐⠉⠁⠀⡁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠐⡔⢆⠊⠑⠁⠄⡱⠀⠖⡖⠡⠀⡀⠀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠘⡄⠀⠀⠀⡡⠂⡠⡔⡡⠀⡀⡦⡨⠆⠀⠇⠈⠈⠀⠀⠀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⡰⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠌⣀⠤⠊⠉⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠙⠒⠒⠒⠒⡶⠒⠀⠠⠔⠓⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠢⢄⣀⡀⠤⠄⠒⠒⠒⠢⠤⠤⠤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠈⠀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠐⡀⢀⣠⠀⠀⠀⠰⡷⡄⠀⡀⢦⡀⠆⠠⠆⢈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠘⠃⢤⠍⢧⣿⣧⠉⢻⡄⠀⠶⣿⡿⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠒⠲⢛⡃⠒⠠⣄⠀⣺⡿⠂⠘⢧⣼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠈⠙⣿⣧⠱⣄⠈⣿⣀⠀⢠
⠀⠀⠀⠀⢀⣤⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⢈⠁⠀⣀⡀⠈⠂⠂⠖⠈⠉⠑⢻⣿⣄⣿⡀⢹⡶⢠⡯
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣌⣑⣈⣃⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡙⢷⣈⣿⣼⣧⠖
⠀⠀⠀⢹⣿⡿⠟⠁⠐⠿⢷⣮⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⢀⡽⠛⣶⡶⠾⣿⣿⣄⣿⣿⠁⢀⣿⣿⣿⠗⠂
⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⢠⣿⣷⡀⢸⣽⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⡄⡩⠴⡞⠋⡀⠀⡀⠀⠈⢹⣿⣧⠈⣿⣿⡟
⠀⠀⠀⠿⠶⠒⣿⣧⣾⣿⣿⣿⠿⠇⠜⠻⡄⠀⠿⣿⠟⢿⡿⠿⣿⠿⢛⠛⠻⠋⠊⠟⠀⠂⠒⢿⡐⠛⣺⡟⢿⢀⡏⠑
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⣬⢀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠚⠛⠛⠛⠉⠋⠉⠁⠀⠀⠀⢀⣸⣿⣿⣿⡧⠀⢻⠶
⠀⠀⠀⠀⠀⣀⣄⣤⠛⢉⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣠⣄⣀⣶⣿⣿⣿⠿⠟⣿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⣉⢉⢛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⡀⢠⠄⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠈⡀⠀⠀⢀⡀⢹⢦⣘⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠄⠄⠀⠀⡁⠤⠘⣁⠠⠐⠂⢢⣁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠀⠰⠤⠐⠞⢀⣀⡀⠀⠀⠠⠉⠱⠒
⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠶⠵⢆⡠⠀⠠⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⡠⠐⠀⠀⠀⠀⠒⢄⠀⠀⠀⠐⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⠴⠀⠔⢄⡀⠀⡠⢁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡀⠘⠀⢰⡆⠀⠰⡦⢠⠁⢘⠅⠕⣨⣀⠀⢀⡄⠀⡇
⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⡀⠀⢨⠀⠂⠀⣤⠀⠀⣀⠁⠁⠀⢀⡔⠁⠈⠑⢀
⠀⠀⠀⣠⠀⠀⠪⡜⠒⠒⡄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠤⠈⠃⠀⡄⡠⢚⠀⠀⠀⡀⣶⢓
⠀⠀⠀⠁⠀⠀⠁⠉⣉⣩⢇⡀⠀⠀⠀⠀⠀⡀⠆⠤⠌⢠⠄⠊⢰⠀⢐⠦⢈⠀⠈⠃
⠀⠀⠀⠀⠀⠄⡀⠤⢤⣤⠺⠂⠀⠀⠀⠀⡀⡘⠉⠁⠐⠉⢄⣧⢀⠓⠂⠉⠁⠒⢘⠀⠀⡄⡀⡌
⠀⠀⠠⡏⠈⠁⢀⠀⠮⠘⠈⢀⠀⠀⠀⠀⠳⡃⠠⠬⠉⠐⠀⢙⠃⠀⠨⠀⣍⡍⢩⠑⠉⠉⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⣴⠊⠁⠀⠀⠀⠀⠑⡒⢒⠒⠊⠀⢠⠀⠀⠀⠐⠈⣣⣼
⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸⣃⢇⠀⠀⠢⢀⠀⠀⠀⠉⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠇⠀⠀⠀⠀⠀⣩⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢁⠀⠄⠀⠒⠒⠓⠛⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡼⢠⢠⠀⠀⠀⠀⠀⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣷⣾⣈⠀⠂⣇⣀⣸⣼⡏⠀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠁⠈⠉⠉⠉⠀⠀⢈⡟⡻⠛⠉⠀⠈⠀⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⣀⡀⠀⠀⠀⠀⠀⢻⣄⣤⠴⠤⣤⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠻⡿⠉⠉⠙⠿⠛⣿⣿⣶⡟⠁⠀⠀⠈⣇⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠛⠛⠘⠛⠐⠒⠀⠉⢽⣿⡇⠀⠀⠀⠀⡿⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⠀⢀⡾⠁⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⡠⠖⠈⠁⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠳⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠁⠀⠀⡤⠋⢁⣤⣶⣋⣡⡭⢉⣹⣍⡹⠛⢦⡄⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠰⠈⠀⣰⠏⣰⣿⠟⢋⡴⣊⡠⠈⠙⠶⣄⠙⣧⡀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠀⡄⠀⠀⣼⠏⢐⡽⠛⠀⢈⣾⠉⢷⣠⡞⠃⡼⢡⠈⢿⡄⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⠁⠀⣸⠃⠰⠏⡔⣀⣄⣿⠋⠀⠀⠶⣿⡀⡠⠊⠦⠘⣿⡀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠀⠀⠀⣿⣴⡗⠦⢤⣽⣿⠁⠐⣤⠀⠀⣿⣵⠶⠾⣿⣿⣿⣧⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⠀⠴⢸⣿⣿⣧⠀⠀⠀⠙⠃⡀⠁⠀⠀⠉⠀⠀⠠⣿⣿⠻⡟⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⠉⢿⡄⠀⠻⢄⠀⠈⡷⠁⠀⣴⠆⠀⣰⣿⣾⣼⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠂⠀⠀⠀⢿⣸⣿⣁⣀⠀⠀⠀⢠⣇⠀⠈⠀⢀⣨⣿⠟⢵⣿⠃⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢹⣌⠛⠉⣽⠇⠀⠀⣠⣯⡀⠀⠀⠈⣿⡏⠁⠼⣿⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⡟⠂⠘⣷⠶⠾⢿⢿⣿⣿⠿⠛⠛⠭⢄⣷⣿⡿⠋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⠀⢀⠀⠀⢹⣦⠘⠁⠘⠀⠛⠀⠛⠃⠂⠃⢀⠀⢸⣿⣿⠁⠀⠀⢠⣜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢿⡷⢃⠶⠶⠖⠒⠛⠛⠛⠛⠋⠁⠾⢹⡇⠀⠀⠀⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⢢⡀⠘⢷⣤⠶⡶⠒⡴⠂⠐⠲⢠⠟⠉⣶⡟⠀⠀⠀⢠⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢄⡀⠙⠲⠿⠶⠾⣿⠷⠶⠿⠿⠛⠋⠀⠀⠀⢠⡞⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠹⣦⣄⣀⣄⢀⢀⣀⣀⡀⢀⣀⣀⣴⠀⣠⣿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⣠⣬⣄⣤⠀⣤⢦⠀⠄⠤⠄⠠⣤⣤⣤⣄⣙⠛⠃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⡻⠿⠛⠿⠿⢤⣤⣤⣄⣀⣀⣴⣿⣿⡿⠿⢟⣣⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠶⠆⠤⠌⠀⠀⠴⠖⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠭⠭⠭⠭⡽⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢫⠥⠴⠤⡉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⡒⠒⠶⠶⠚⢆⠀⠀⢸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠈⠀⠀⠀⢸⠀⣠⠞⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠈⠻⣥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⡠⠔⠒⠒⠢⣄⠀⠈⢌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠊⠀⠀⡀⣀⠀⠈⠳⡄⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡰⠁⠀⠒⠀⠀⠐⣒⠀⠀⠘⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣸⠁⣀⠀⠄⢀⡀⣀⠀⠀⢠⣄⡸⡄⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢡⠇⠀⠒⠀⠁⠈⡍⠉⢦⣀⠎⠀⠀⠹⡐⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠰⠀⡸⢀⠑⠠⣀⠀⠻⡀⠀⡀⢀⠀⠰⡸⠀⢇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡆⠀⡇⠀⠈⠐⠀⠈⢡⡇⢀⠰⡌⠀⢀⠇⠀⢸⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠄⠀⠀⠀⠈⡋⠁⠀⣀⠓⠇⠀⡜⠉⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠈⠢⣀⠈⠁⠒⠂⠤⡁⢦⡜⠤⠆⠀⢸⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠸⣄⠀⠀⠈⠀⠒⠒⠒⣇⡠⠤⠤⣀⣠⠇⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠒⠒⠶⠶⠤⠤⠎⠴⠖⠒⠊⠁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠶⠶⠒⠚⠛⠛⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣂⣀⣀⡀⠤⠤⠤⠤⢼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠁⠀⠀⠸⣄⣀⠀⠀⠀⡔⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠂⠀⠁⠀⢸⠆⢀⡠⠛⠉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡋⠸⠉⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⢀⣠⣀⠀⠓⢁⣀⣡⡤⣤⠤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠉⠁⠀⠀⠨⠉⠉⠀⠘⡀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠑⠊⠀⠀⠀⡇⠀⠀⠀⠛⠲⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⣄⡀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⡀
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠪⡉⠉⠀⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠹⡄
⠀⢠⠏⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⣃⣨⡀⡠⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢃⠀⠀⠀⢻⡀
⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠈⣧
⢸⠁⠀⠀⡀⠀⠀⣀⡀⢠⠲⠀⠀⠖⠉⠑⠐⠍⣉⠁⣶⠓⠂⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹
⡟⠀⠀⠀⠁⠀⠀⠇⠀⠆⢀⠀⠄⠀⠘⡃⠀⡀⢩⠤⠟⠸⢄⡄⢨⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⢲⡀⡏⢀⣀⡧⠴⠑⠆⠻⠞⠀⠐⠀⠴⠧⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⣇⠀⠀⠂⠀⠀⠀⠓⠃⠉⠁⠀⠀⠀⡀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⢻⠀⠀⠀⠀⠀⠀⡤⠒⢒⡆⢮⡁⠚⢉⠎⠁⣄⠀⣡⡎⢦⠖⢲⠋⢉⠑⢂⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠺⠃
⠸⡄⠀⠀⠀⠀⠀⠢⢄⡈⠑⠀⢹⠆⡌⠀⠀⢠⠘⠣⡇⠀⠀⣼⠀⡬⠤⠞⠀⠀⠐⠂⠀⠀⢰⠂⠀⠀⡶
⠀⢷⠀⠀⠀⠀⠀⢘⢉⣀⠴⠣⣅⡼⠁⠸⣀⡄⠑⠖⠉⠒⠒⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠃
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢠⠏
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠀⢸⠄⠀⠀⠀⠀⠀⢀⡎⠀⢀⡞
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡤⢤⠀⠀⢀⠀⠀⠀⠀⢠⠎⠀⠀⠘⣧⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠳⣦⠄⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⢀⡴⠁⣀⡤⠔⠊⠀⠀⠀⠀⠈⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠶⠤⠤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣰⡯⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⣀⣀⠤⠴⠒⠚⠛⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠖⠚

⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⣇⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠰⠋⡇⣦⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠰⡆⣨⢛⢥⡶⠀⠀⠀⠀⠀⠀⢸⢸⣄⣧⣠⠀⠀⠀⠀⠀⢀⠀⣲⠛⡏⠀⠀⠀⠀⠀⠀⡾⡿⠜⡄
⠀⠀⠀⣷⣼⢀⡾⣤⠦⡼⠀⠀⠀⠀⢸⣾⠈⡟⠙⢻⠀⠀⠀⠀⠀⠘⢟⢫⣿⣀⡀⠀⠀⠀⢀⠠⢇⠠⣤⢷⡄
⠀⠀⠀⠘⠦⠾⠇⠘⠃⠁⠀⠀⠀⠀⠀⠁⠰⠛⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⠐⢯⠃⠀⠀⠀⠘⣷⠛⠘⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀
⠀⠀⠀⠀⠘⡿⡏⡅⠀⠀⠀⠀⠀⢀⢀⠀⣿⢣⣀⡀⠀⠀⠀⠀⠀⠀⠎⣼⣿⢰⡀⠀⠀⠀⠀⠀⡄⣾⡼⣃⡋
⠀⠀⠀⠀⠸⣧⠛⣇⠀⠀⠀⠀⠀⠈⠉⢷⠾⡌⠛⢛⡁⠀⠀⠀⠀⢰⣜⣇⢹⡾⣧⡀⠀⠀⠀⠀⡁⢏⢁⢹⠠⠇
⠀⠀⠀⠸⣆⣿⢶⣼⠀⠀⠀⠀⠀⠀⣻⡛⠀⡿⣆⠛⠇⠀⠀⠀⠀⠸⣿⠹⢰⡀⠻⠀⠀⠀⠀⠠⣼⡾⢿⡘⢾
⠀⠀⠀⠀⠀⠰⠏⠋⠀⠀⠀⠀⠀⠀⠈⠃⠻⠅⠙⠋⠀⠀⠀⠀⠀⠀⠙⠘⠋⠃⠀⠀⠀⠀⠀⠀⠈⠃⡎⠻⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠘⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⢺⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠻⣿⡄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⡀⣰⣿⡿⠃⠀⢠⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡼⣿⠁⠀⠀⠸⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⣿⣷⠈⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣦⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠀⢀⣿⣷⡀⠀⠀⣸⣿⣿⡟⠀⢤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⡇⠀⠀⠀⢱
⠀⠀⠀⢤⡀⠀⣴⡿⠀⡀⠙⣿⣿⣿⣿⡆⠀⠀⢸⣷⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠈⣿⣷⡄⠀⠀⠙⠻⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣷⣤⣀⣤⣿
⠀⠀⠀⠈⣿⣶⠟⠀⠀⣿⣦⣾⣿⣿⣿⠇⢀⣴⣿⠟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠉⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣇⠀⢀⣿⣿⠀⡀⠀⠘⢿⣿⣿⣿⢟⣴⣿⣿⠋⠀⢠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⠀⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣇⣀⣽⣷⡀⠈⠙⠿⢋⢸⣿⣿⣿⣷⣤⣾⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⣿⣌⣿⣿⣿⣿⣿⡿⢡⣾⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢠⠀⠙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⡟⠀⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣶⣿⣿⣿⣿⡟⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⡟⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠖⠒⠚⠛⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠦⠔⠒⣖⠀⠀⠀⠀⡛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠈⠙⡆⠀⢀⠧⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢐⢡⠚⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⢀⠤⣀⠘⢊⣀⣣⠤⠤⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠬⠁⠀⠈⡀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠀⠀⠀⣇⡀⠀⠈⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⡀⠀⠀⠉⠲⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠱⡄
⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠲⡙⠁⠈⢩⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⣆
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢰⡡⢤⣀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢂⠀⠀⠸⡄
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠤⢀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢷
⡜⠀⠀⠀⠀⠀⠖⢀⠋⠁⠀⠁⢤⠀⠀⠲⢀⡇⡈⠈⠀⡼⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⡄⠰⢆⠐⣆⡰⢄⠸⣬⠍⢄⢈⣿⣀⣱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠖⠁⠚⠀⠉⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⢧⠀⠀⠀⠀⠀⠔⠒⣢⠲⡁⠊⠱⠋⢠⠀⣡⠊⠴⢲⡎⢉⠑⡄⠀⠀⠀⠀⠀⠸⠀⠀⢸⠃
⠸⡀⠀⠀⠀⠀⢓⡤⠈⠂⡸⢂⠀⡀⠠⡌⠑⡆⠀⣸⠃⡖⠐⠃⠀⠀⠁⠀⠀⡏⠀⠀⡏
⠀⢳⠀⠀⠀⠀⠠⠐⠒⠁⠓⠊⠀⠓⠒⠈⠉⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣸⠁
⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⢠⠃
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⣀⡀⠈⢁⠀⠀⠀⠀⠜⠀⠀⢯⣀⣀
⠀⠀⠀⠀⠀⠙⠲⡤⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⡠⠊⣀⡠⠔⠉⠀⠉⠉⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠶⠦⠤⠤⣤⠤⠤⠤⠤⠤⠼⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠿⠓⡢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣦⣴⣇⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⡰⠛⡝⠀⠶⠆⠀⠀⠀⢀⠀⠀⢸⡆⠀⠈⡖
⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠟⢨⣿⠀⠁⠀⠀⣢⠀⠀⠀⢢⡠⣼⠇⠀⢀⣿⡀⣷⣆⡄
⠀⠀⠈⠁⠐⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣐⡿⠿⠂⠀⠀⣴⣿⠂⡄⠀⠸⣿⠃⣠⢤⣼⣿⣶⣯⣿
⠀⠀⠀⠀⠀⢀⡟⠛⠻⠷⣶⡶⢤⠄⣠⢤⠘⣆⣤⣴⠰⠟⠿⠉⠁⣐⣾⣿⣿⡯⠀⠀⣶⢲⡆⢠⣌⣵⣾⣿⣷⣿⡿⠇
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠸⢿⣀⣄⠊⠲⣠⡶⠄⣿⣩⣷⣿⡿⠟⠿⠛⠟⠉⠉⢍⣙⠻⠃⠀⢀⠈⠩⣙⣿⡇⢮⠑
⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠲⢿⣿⡇⣰⣿⡀⠀⠀⠀⠉⢻⠀⠠⡠⣦⣵⣤⣶⣾⠁⠀⢨⣁⣈⣠⣴⣿⡿
⠀⠀⠀⠀⠀⠙⠷⠖⠒⠒⠒⠿⢣⠏⣼⣿⣿⣿⣤⣄⠀⠀⢸⣧⣤⣤⣼⣿⣿⣿⣿⣦⠀⠈⢿⣛⣻⣿⣿⣇⡾⣸⡄
⠀⠀⠀⣴⠿⠶⣤⣶⣶⣿⣿⣿⣏⣸⡿⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣅⠄⣦
⠀⠀⠀⢋⢾⣽⠟⠉⠡⠀⠉⢋⣾⡟⣷⡘⣿⣿⡍⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠟⢻⣞
⠀⠀⠀⣿⣽⠁⠀⠀⠘⣄⢂⣼⢿⣿⠙⣿⢻⣿⡟⣻⡦⣾⠟⢾⣷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⠟⠁⠐⡛⣿⡀
⠀⠀⣶⣿⡃⠀⢸⡁⢀⣳⡞⡃⠸⠸⠃⣿⢸⣿⡆⣿⣷⡿⢶⢾⣿⣿⣿⣿⠀⣻⣟⣿⣿⣿⣿⣿⣿⣽⡆⢀⠆⠀⡥⠏⠉
⠀⠀⢿⣿⣧⡀⠀⠳⢾⠟⠣⠈⡝⠂⢢⣯⡘⠿⣷⡻⢿⣿⣿⣿⣿⣿⣻⣿⣶⣿⠷⠿⠿⠯⠫⠁⠉⢾⣥⣡⡤⣰⠅
⠀⠀⠈⢻⣷⣍⠀⠀⡀⠀⠀⠊⢀⡴⠋⠉⠉⠀⠀⠉⠻⣟⣾⡿⣿⣿⣿⠿⡿⠋⠉⠉⠻⣿⣿⣻⠿⠯⠟⠛⣿⣏⡀
⠀⠀⠀⠠⣬⣿⣿⣷⣷⣶⣶⣿⣿⣶⣶⣶⣶⡶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⡒⢲⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣉⣉⣉⣉⣁⣉⣉⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠛⠻⠿⠿⠿⠿⠿⠷⠾⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠦⠀⠀⠐⠶⠶⠶⠶⠶⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣧⡀⠀⣀⣤⡄⠀⣤⣼⢀⣴⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⢹⣿⡇⠀⣿⣿⠸⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠇⢰⠀⢸⣿⡇⠀⣿⣿⡄⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⣿⠀⢸⠀⣿⣿⡇⠀⢸⣿⣿⢨⡉⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⣾⣿⠀⡄⢀⣿⣿⡇⠀⢸⣿⣿⡼⣇⠀⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣼⣿⣿⠀⠇⢸⣿⣿⡇⠀⢸⣿⣿⡇⢿⡄⠀⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣰⣿⣿⠇⡆⠀⠈⠛⢿⡇⠀⠸⣿⣿⣿⡘⣿⣄⠰⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠃⢀⠃⠀⠀⠀⢸⡇⠀⠀⠙⢿⣿⡇⠻⣿⡷⠆⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣤⣤⣤⣿⣤⣀⣀⣀⣤⣶⣄⣀⣀⣀⣀⣿⣦⣤⠠⡶⠿⠿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣛⣛⣛⣋⣩⣿⣿⣿⡿⠯⣍⣹⡛⠉⠩⣭⣽⠟⢿⣿⣿⣿⡿⠟⠓⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⠟⠋⣉⣿⣿⣋⣴⣤⣴⡶⠊⠀⠙⣿⠗⠈⠳⣦⣬⣿⣿⢿⣿⣿⠿⠛⠺⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠟⠛⣹⡿⢁⣴⡟⢁⣈⠉⠁⢾⣿⣋⣀⡹⠷⠂⠙⣅⡀⢱⣦⣸⣿⣿⣿⠶⠾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⢛⣿⢿⠟⢉⡽⠃⣹⣿⣾⡿⠿⠛⠛⠛⠿⢿⣷⣦⡙⣷⡞⣭⡉⢉⡹⣿⣿⠦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⣩⡟⣥⣿⡷⠻⣷⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⢿⡿⢺⣷⠾⣿⣶⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⢛⡟⠁⢻⣾⣀⣾⡟⠁⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣿⣧⡜⢿⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⣿⣸⣷⠚⠙⢿⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⣴⣿⣿⡷⠀⠀⠀⠀⢽⣿⣿⠿⠟⢿⣿⣧⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⡟⠁⣼⡄⠹⠀⠀⠀⠀⠀⣀⡀⢀⣻⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠻⣿⡔⢷⣼⠙⣿⡉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⡟⣧⡰⠿⠻⡆⠀⠀⠀⠀⣼⣿⡇⠘⢿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠙⣷⢠⡟⢳⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⡇⠙⡇⠸⣇⠀⠀⠀⠐⣶⣿⣿⣿⡖⠈⢻⡿⣿⡿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠸⢻⣿⢧⣦⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⢇⠀⣿⡆⠉⠀⠀⠀⠀⠙⣿⣿⡿⠇⠀⡸⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣀⢻⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢾⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⢿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣷⡈⢡⣄⢻⠀⠀⣤⣤⣤⣄⣤⣄⠀⣤⣤⡄⠀⢠⣤⣴⣤⠰⣿⠆⣠⣤⣤⡀⠀⢸⣿⡇⣿⣇⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣿⠃⢼⠋⢸⠀⠀⣿⡏⢸⡿⢸⣿⢠⣶⣿⣷⣤⢸⣯⣸⣿⠀⣿⠆⣿⡷⢻⡇⠀⢸⣿⣿⠏⣿⣿⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⣇⣼⠉⠳⠀⠀⠈⠁⠈⠃⠈⠋⠀⠙⠋⠙⠉⠸⠿⠉⠀⠀⠿⠆⠙⠛⠛⠁⠀⣾⣿⠉⣼⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⢻⡿⠁⢸⡆⣿⠀⢰⣿⣛⠂⠺⣷⣀⡾⢰⣿⠾⣷⢴⣿⠀⣾⡆⢰⣿⠿⣷⡄⠀⣿⣿⡾⣛⣿⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠻⣿⣀⡇⠠⠀⡆⢠⣍⣿⡿⠀⢻⣿⠃⢸⣿⡇⠁⠘⣿⣦⣿⡇⢸⣿⣤⣿⠃⣸⣿⣅⣴⢿⣿⠛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⣯⣝⠿⣤⣤⠁⡄⠀⠀⠐⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⢰⣿⣿⢿⡏⣼⡿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣣⣼⣿⣄⣽⡉⣆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⡁⣼⣷⣿⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⢿⣏⢻⡷⢿⣦⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣩⡿⠿⠏⢡⣿⠋⣡⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣝⣛⣿⣿⡿⣶⡤⢶⣌⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⣴⡟⣠⣾⣷⣿⠷⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣯⡉⠻⣷⣈⣣⣈⣽⠂⣨⡐⠂⣀⠀⠀⠀⠀⠀⢠⡔⢒⣩⡶⠿⣿⠗⣭⣽⡿⣡⣴⠾⣫⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣍⣀⣈⣿⣿⡟⠻⣷⣬⣿⡿⠒⢶⣦⣬⡵⠶⣶⣾⣻⣥⣤⣾⡿⢾⣿⠏⠘⠛⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠻⠍⠉⠛⢿⣄⣹⣏⡈⠻⣷⡦⣉⣭⣿⣿⣿⡿⣫⣽⣷⣿⣶⣟⣥⣤⣶⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣶⣶⠀⠀⢈⣿⣿⣿⣷⣉⣲⣿⣿⣷⡛⢛⣾⣿⣿⠟⠋⣀⣩⣽⡿⠿⠛⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡜⠛⢻⣶⣾⣿⣟⣙⣻⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣿⣏⣉⣠⣤⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⣯⣍⠉⠯⠛⠛⠛⠛⠛⠛⠛⠛⠛⢯⣭⣭⣟⣛⣿⣯⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠶⠲⠶⠖⠲⠶⠖⠲⠒⠚⠋⠉⠉⠉

⠀⠀⣸
⡇⣠⠿⠀⡀⣤⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣿⡉⠀⠺⣳⠀⢸⡟⠀⡄⣸⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⣾⣥⣌⠉⣠⡼⠂⠸⢁⣘⢻⣯⢀⣼⣴⡯⠤⣾⣠⠀⠀⡀⠁⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢿⡶⠂⠠⠤⠀⢀⣬⡍⠼⣥⠀⣿⣿⠛⠂⢹⣿⣄⣼⢁⡀⢀⠁⡀⠀⣰⠀⡀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⡀⣀⠀⢠
⡷⠨⣙⣟⡳⠒⠀⢸⡟⣀⣘⠟⡯⣿⠛⡘⣋⡀⣽⣿⠟⣛⣦⣿⣼⡇⢰⡿⢻⣧⣶⡾⠇⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⣶⣿⣡⡏⣾⣿⣵
⠀⠀⠀⠀⠈⠈⠀⠘⠛⣷⠍⠂⣼⡻⠂⠠⠤⠀⢐⣿⣧⠆⠰⣿⡗⠭⢿⡥⠄⢿⣿⡷⠼⣿⡿⢲⣾⣆⡀⢀⣄⣤⣿⣿⣿⣿⣿⣿⡿⠥⠽⠿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢯⡃⢦⣤⠄⠀⠉⢻⣇⠐⠈⢻⡿⢠⢽⣏⣀⣋⣿⡥⠀⢹⣇⣈⣿⡿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠾⠿⣯⣘⡛⣷⣀⠊⢿⡧⢴⢺⣄⣐⠈⣷⡆⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠚⠛⠶⠿⠿⠿⠒⠛⠉⠉⠁





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠓⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠄⠀⠠⢄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠛⠃⠀⢰⡁⠀⠀⠀⠀⠱⡄⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠋⠹⠲⡆⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢉⠏⠱⡀⠑⠒⠦⢄⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠴⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⣤⡎⠀⠀⡈⡐⠠⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⠵⢮⣤⠈⡀⠈⠀⠀⠁⠀⠨⠱⠄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⠀⠀⠉⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣋⠀⠀⠸⠀⠠⠐⡆⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠠⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⢀⡞
⠀⡠⠖⠉⠉⠙⠲⡀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⠒⠊⠀⠀⠀⠀⢠⠎
⡞⠀⠀⠀⠰⠉⢀⣇⣀⣠⠴⠚⢅⡠⣆⠐⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠧⠄⠠⠔⢢⠀⢀⠇⠀⠀⠀⠀⠀⣠⠏
⣇⠀⠀⠀⠀⠀⠀⠁⠀⣀⢴⡴⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⢠⠏
⠈⢦⣀⣀⣀⣀⠤⠔⢊⡵⠋⢠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠏
⠀⠀⡠⠋⠁⠀⠀⢠⠟⠀⠀⣏⠘⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠤⠤⠤⠤⠖⠚⠉⠙⠁
⠀⢰⠇⠀⠀⠐⠀⠙⢆⠀⠀⠈⠉⠉
⠀⠘⡇⠀⠀⠈⠀⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢪⣵⠖⠒⠛⣩⠭⡄⢐⣒⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣪⠋⠁⠀⠀⠀⠀⠐⠻⠈⢠⠚⣡⡾⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⠙⠅⠉⠉⠉⠛⠽⢶⣄⠀⠀⢈⣴⣿⢿⣫⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣿⣿⣿⣯⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠔⠉⠀⢢⠀⠀⠉⠭⡻⢒⠶⣤⣄⡀⠀⠄⡌⣾⣿⣿⣿⡟⢗⢀⣴⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣫⠕⡾⠅⠀⠀⠀⠀⠀⠙⠢⠤⠤⠴⠔⢊⢟⣥⣿⠈⢞⣼⢿⣿⠿⠗⣠⡾⣿⡿⡿⡧
⠀⠀⠀⠀⠀⠀⣺⣅⠀⠲⠋⢡⠀⠀⠬⠄⠀⠀⠀⠀⠀⠀⠀⢀⠤⣪⣵⣽⣿⣿⠄⣽⣿⡿⠿⠥⠾⣿⢾⣝⣝⡴⠋
⠀⠀⠀⠀⠀⠀⣿⠪⣍⣙⠳⠶⣭⣑⠢⢌⣀⠔⢒⣲⡖⠐⣪⢵⣺⣿⣿⣿⣿⣟⣨⡾⠭⠁⠀⠀⡄⣿⣫⣫⣾⠣⣄⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠩⢝⡳⢶⠬⢿⣶⠤⣒⣫⢴⣾⣽⣾⣿⣿⣿⣿⠿⠿⢎⣁⣀⣀⠀⡄⣶⡃⣾⣿⠿⠧⣭⠁⠘⠿⠓⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⡒⠬⢅⡋⠃⠊⢹⠒⠾⢵⣟⣻⣿⢻⠿⠻⠉⠉⢁⣀⠤⣞⡽⡷⣽⢧⠻⣟⡿⠶⠒⢙⡧⢠⡁⠞⢚⣠⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣶⠬⣝⡛⠴⡬⠍⣽⣿⣿⠛⠫⠏⠀⠈⠉⠁⡠⢮⣾⣾⡇⡎⢦⣞⠁⠀⠀⡘⠀⠈⠒⠭⢗⣿⣿⣯⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠿⠓⡡⢍⣉⠛⠴⢼⠿⠭⠅⠈⠉⠀⠀⠀⢀⢔⣔⣟⣽⣿⡇⣦⠏⠀⣀⠤⠊⠀⠀⠀⠀⠀⠒⠀⠉⡏⠉⡓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣶⠥⠤⠪⠁⠀⢃⡀⠤⠬⠷⣒⠂⠀⢀⠤⠄⢲⠖⢒⣵⡷⣳⣫⣿⣿⠛⠍⠁⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢀⠘⣄⠀⠣⢋⡤⢞⣥
⠀⠀⠀⠀⠀⠀⠀⣯⠍⣉⣀⣒⠒⠂⠠⠬⠍⢉⣙⣒⠊⠥⠤⠬⠥⢒⡽⣫⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠤⡺⠴⣚⡥⢖⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣒⣒⠒⠈⠭⠭⠭⠀⢒⣒⣒⣶⣚⣒⣟⣤⣥⣾⢾⣿⣿⣷⣴⡤⠐⠶⣶⠠⢄⡀⠀⣀⡠⠄⣂⡨⠱⣐⣭⣶⣿⣷⣾⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢱⠶⡰⢬⠭⣭⣩⣀⣐⣒⣒⡒⣲⢒⡒⣒⢒⣚⣺⡿⢕⠅⠀⠉⠺⢗⡦⢭⡙⣂⣨⠭⣔⣲⡯⢷⣿⣿⣿⣟⠿⠒⣉⠤⢖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡓⠉⠢⠕⠦⣑⠂⠊⠴⠩⢚⡕⣨⠌⡁⢩⢌⠄⡹⣷⣵⠀⠀⠀⠈⠛⡗⠪⣻⣿⣯⣼⣾⣿⠿⠟⣋⠡⢔⣚⣭⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠂⠀⠀⠀⠀⠈⠑⠺⢦⡤⠤⠔⠐⣤⣄⣠⢔⣾⣶⣟⣽⣷⣄⡀⠀⠀⠅⠈⡿⠿⣟⡫⣭⣖⣾⣍⡘⠭⠓⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠒⣽⣦⣜⣛⣩⣤⡾⣻⣿⣿⣟⢿⠭⠊⠉⠒⠤⣀⠀⣿⡽⡼⠾⠛⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠢⡢⠄⠑⣯⣿⢿⣯⡷⠗⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⢀⡘⠀⠸⣿⠗⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠠⡠⢔⠀⡀⠐⡨⢀⠁⢊⠔⠁⢔⠀⢂⠔⢁⠄⡀⢂⠔⡀⠀⠠⢀⠔⠠⢂⠄⠀⡠⢒⠔⢀⠄⡠⢂⠔⡠⢈⠔⡡⢂⠔⡀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠡⢊⠤⢂⠤⡢⠐⡡⢊⠥⢊⠔⡈⢐⡥⠊⠔⡠⠀⡡⢂⠔⡠⡪⢊⠔⠁⠐⡡⢊⠔⡡⢊⠔⢡⠎⡔⠡⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠐⠁⠐⠁⠊⠀⠉⠐⠡⠂⠠⠊⠄⠁⠊⠎⠀⠀⠘⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢇⣤⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⢠⠟⠙⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⡀⢠⡆⠀⠀⠀⠈⣧⠄⠐⠸⠀⡤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⡰⠉⠷⠀⠐⠑⠀⠃⠀⣤⡠⠞⡷⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠸⢤⡇⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠐⡁⠘⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠈⠁⡐⠂⡰⠁⠀⠀⠀⠤⠂⡳⠀⠇⠆⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣦⡱⡄⠲⠇⠘⠀⠀⠀⠀⠀⠀⢀⠀⠞⠀⠔⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠌⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠊⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠈⡤⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢥⡀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠮⠴⠖⠖⢤⣼⢶⡿⣷⣾⣷⠋⢻⣿⣷⡖⠦⢤⡄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣤⣤⣴⠞⠋⠀⣸⠁⢀⣿⢻⣆⠀⠙⢯⣟⠉⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣁⣀⣠⣶⡇⠀⠸⣿⠄⣻⡆⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠈⣿⠷⠏⠛⠉⠘⠶⠶⠞

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣠⡇⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠋⠀⢀⣾⠟⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣴⣿⡏⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⢳⣿⢀⠠⠾⢻⣿⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⣿⡿⣱⣿⡿⠃⠀⠀⣼⣿⣼⠠⠄⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣽⣿⣿⣿⣿⣆⣠⣾⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⡿⣿⣿⣿⣿⣿⢣⣼⣿⡎⢷⣇⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⢏⣾⡟⣸⣿⣿⣿⣿⡇⡾⣿⣿⢻⡌⠻⣆⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢠⠁⣿⠟⣿⡿⣰⣿⣿⣿⣿⣿⡘⣇⢸⣿⣿⣿⠀⠙⣷⣄⠠⡱⣄
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣾⣿⡇⣿⢸⣿⣿⣿⡿⠧⠀⣼⡈⣿⣿⡇⢢⠘⣿⣧⠙⣿⣦
⠀⠀⠀⠀⠀⠀⢸⡀⣼⢿⣿⣿⠀⣿⣼⠳⠏⢠⣷⢀⣼⣿⠃⣸⢹⡇⣸⡄⠸⣿⡇⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠘⣧⢹⡜⣿⣿⡄⢹⣿⠀⠀⢸⣾⡈⠻⣿⢀⡟⣹⠇⣿⣥⠀⣿⣷⠀⢻⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⣿⣿⣿⣦⡿⣷⣄⡈⠻⠏⠀⡹⣾⣱⠏⣼⣿⣧⠀⣿⣿⠀⢸⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣻⣯⣛⣿⣿⡝⢷⣂⠠⣼⣷⣿⢏⠼⠁⢸⡇⢰⣿⡟⠀⣸⢄
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠈⠋⣉⣿⣿⣿⣷⡙⠿⠿⠯⠁⠀⢀⠴⠋⣴⣿⠟⠁⣰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣷⣦⣤⣤⣤⣷⣼⣿⣿⠗⢀⡴⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⠴⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣧⣴⣿⡭⠤⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠿⠟⢻⠟⢿⠿⢻⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠞⠛⠛⠛⠛⠶⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⢀⣀⣴⠟⠋⠉⠻⠋⠀⠀⠈⢻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠙⠛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⠉⠉⠉⠉⠻⡶⠛⠛⠛⠷⣦⣰⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠷⣦⡀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣽⣿⢭⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢤⡆⠀⠀⠀⠀⠀⠀⠀⠈⠾⠽⠶⠁⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⣺⣗⢺⠂⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣻⣿⣻⡟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠀⠀⠀⠀⠀⢾⡷⣽⠆⠀⠀⠀⠀⣴⡖⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠸⣗⡿⣗⡟⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⢲⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠙⠀⠀⠀⠈⠩⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣺⢿⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⡆⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣤⣿⣿⣤⣶⣶⣶⣯⣴⣷⣭⣿⡆⠀⠛⢲⡀⢛⣒⣶
⠀⠀⢀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⡏⢿⣿⣿⠀⢀⢀⡐⢾⢈⣦⣠⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣰⣶⠟⣤⢿⡏⢈⡷
⠀⢀⣾⣿⣿⣧⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠋⠀⢀⡌⣦⣠⢷⣏⣿⣯⣯⣧⡐⠀⠀⠉⢈⣍⣉⣩⣍⣭⣥⣤⡄⠀⣜⣿⣶⣼⠟⢹⣏⣸⡅
⠀⣼⣿⠏⠀⢿⣿⣇⠀⠀⠸⣿⣿⢿⢿⣿⣿⠃⠀⠀⢀⣜⣾⣷⣿⣿⣿⣛⣿⣿⣼⣿⣿⣷⣦⡰⣼⣿⣍⠓⢺⣟⡋⠉⠉⠀⠘⠿⠞⢿⣶⣿⠿⠛⠁
⠀⠻⢧⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⣁⣸⣿⣿⡟⠛⠈⠑⠀⠀⠀⠀⡀⠀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡀⣴⢠⡀⠀⠀⠀⠀⠀⠀⠆⡐⠂⡆⠐⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⣸⢼⣠⢧⣟⣳⢼⡰⣅⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⠁⡄⣑⣘⣄⠀⣀⣙⣦⡴⣃⠀⠀⠀⢠⡀
⠀⠀⠀⢸⡆⠀⠀⣯⣻⣾⣾⣿⣿⣿⣾⣷⣿⣷⣿⡄⠀⠀⠀⠀⠀⢀⣼⣧⣶⡤⣄⠀⠀⠀⠀⢀⠙⠐⠀⠑⠿⠟⠀⢠⣞⣿⡻⣞⡽⠁⠀⢠⣤⣽⠆
⠀⣰⢠⡿⢁⡀⠀⠈⠛⠛⢉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⢠⣼⣽⣿⣿⣿⣿⣿⣤⠀⠀⣀⡴⠛⢦⡞⠀⠀⠀⠀⠀⣹⣟⣿⣏⠀⠀⢰⣛⣦⣹⣦
⠀⢿⡈⢷⣼⣄⠀⠀⠀⣠⢿⣆⣤⠀⠀⠀⠀⣦⣷⡄⢣⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣞⠀⡄⡟⢷⡜⣮⣷⣴⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⢈⣽⣿⠁
⠀⢸⡿⢸⣿⣿⠇⠀⣰⣯⢾⣿⣏⣦⠀⠀⠲⣬⡟⣷⣦⡙⣷⠀⠁⢸⣿⣿⣿⣿⡟⠃⠸⣧⣿⣿⣵⣿⣟⣿⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⣿⡟⠋
⠀⣾⣷⣾⣿⣿⠀⠀⣿⡇⠀⠋⢹⡿⠀⠈⣧⣿⣷⣿⣼⣷⣡⣧⠀⠻⣿⡟⢽⣿⡅⠀⠀⣽⣯⣿⣿⣿⣿⣻⡇⠀⠀⣀⣤⣴⣆⡀⠀⠀⠀⠉⢻⣿⣦
⠀⠈⠛⠛⠛⠋⠀⠀⠈⠛⠀⠐⠋⠁⠀⠀⠙⠛⠉⠋⠋⠙⠛⠋⠀⠀⠘⠀⠘⠋⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠃⠀⠾⠿⠿⠿⠿⠟⠛⠗⠀⠚⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠚⠉⠉⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⠤⠤⠤⢼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠐⡄⢀⡠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⡰⠩⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠐⠈⠋⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⢀⡀⠉⠓⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠈⠑⢄
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢤⠐⠁⢂⠆⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⢣
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠄⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⡆⠀⠀⠀⢀⠀⠄⠀⠄⠂⠐⡀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠀⡉⠄⠀⣌⠅⢠⠐⠋⢐⡆⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡄⠀⠀⠀⠒⠁⠀⡉⢀⢀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠊⢠⠁⠁⢐⠠⡃⠉⡩⢐⠠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠸⡀⠀⠀⠠⠅⠒⠢⠀⠐⠈⠐⠉⠀⠁⠂⠀⠀⠀⠀⠀⠂⠀⠎
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⡐⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠔⠀⡀⠓⠒⠂⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠤⠤⠤⠤⣤⠤⠀⠀⠰⠖⠂⠁⠀⠀⠀⠀⠀⠑⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠤⣀⣀⣀⠠⠄⠀⠀⠤⢄⣀⣀⠠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣦⢲⣿⣇⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⣖⣀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣷⠚⣩⣿⢿⣿⣥⡿⠁⡆⡙⠆⠀⠑⠈⢀⡼⠞⠀⠷⣦⠈⣷⣇⠀⢀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠉⡙⠌⣿⣻⣟⣡⡴⢳⣷⠆⢹⣄⣀⣠⠀⠀⠀⠀⠀⠀⠈⣧⢸⠃⢱⡆⠀⠀⢸⢋
⠀⠀⠀⠀⠀⠆⢠⣿⣿⣾⡌⣿⢩⠁⣴⣾⣿⢻⡾⠟⠉⠙⡄⠀⠀⠀⠀⠀⢀⣿⠿⠀⠀⠀⣞⣀⢸⣆⠀⠐⠂
⠀⠀⠀⠀⢀⡴⠀⣀⡠⣤⣭⠻⢦⣄⠀⠀⢢⡽⣀⢀⡀⠀⠘⣦⣀⣠⣶⣴⠏⠀⠀⠀⠀⠀⠉⢁⠿⡉⠿⠷⠶⠁
⠀⠀⠀⠀⢾⠀⠀⠿⠀⠸⣿⡥⢌⣽⣏⣡⡛⣴⡇⠀⠈⢢⣄⣼⡿⣏⠍⢻⣿⣷⡲⢦⡤⢀⠔⠁⠐⠁⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠘⠀⠀⠀⠀⢾⣻⣶⠋⢁⣿⠙⣢⠀⡁⠀⠀⠀⠹⣿⣯⠓⢀⣸⠿⠄⠀⠀⠈⣴⠀⠠⣿⣶⡆⠀⢈⠀⣠
⠀⠀⠀⠀⠉⠙⠇⠦⢤⠈⣿⣿⣤⣾⣿⠀⠉⡤⠀⠀⣤⣀⣀⡼⠙⠛⠏⠀⠀⠀⢐⣶⡏⠁⢲⣀⣈⡍⠳⢆⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⡾⠋⠉⠁⠀⠙⠳⠀⠀⠀⠘⠛⠛⠋⠀⢆⣀⠀⠀⠀⠃⣘⠉⠀⣤⡀⣉⡿⡤⣤⠘⢿⠖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠋⠓⠶⣦⣄⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠙⣿⡄⠀⠁⢉⠀⠂⡜⠀⠈⠉⡀⠀⣀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣿⠀⠀⢀⡈⢉⣭⣤⣄⡀⠀⠁⡟⠁⠤⠐⠾⢦⡀⠘⠁⠀⢡⡼⢦⠉⢰⣅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠿⠿⠛⢻⠀⠀⠾⢡⡟⢻⣿⣿⣿⡆⠀⣿⣄⠀⠳⢦⡀⠙⣷⣦⣴⡀⠀⠄⠀⠾⠏⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⣸⣿⣿⠰⠀⠸⡇⠀⠌⠠⠍⠋⠉⠋⠀⣰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢧⠀⡀⣖⠀⠀⢦⣤⣤⠶⢤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡷⠀⠦⢘⡧⠀⠀⠀⠀⠀⣼⡏⢿⡿⠁⠀⣀⢻⣿⡷⠶⣿⢁⢈⣠⣤⣾⣖
⠀⠀⠀⠀⠀⠀⠠⠀⠦⢻⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣧⣿⡃⣤⣾⠇⣾⣻⣧⣐⠁⢿⣯⡄⣠⠻⢸⠇⠁
⠀⠀⠀⠀⠀⠀⠣⠀⠀⠄⣧⠀⣾⣏⣉⡀⣦⣄⠀⠀⠀⠀⠈⢧⠀⢻⣿⣿⢽⡀⠸⠿⣿⠛⠉⢠⠙⢮⣉⣞⣫⣖⡄
⠀⠀⠀⠀⠄⠀⠀⡄⠈⠀⠙⡄⠈⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠿⠋⡬⠁⠂⡀⠧⢐⠈⢀⡀⣄⠈⠛⡁⠨⠄
⠀⠀⠀⠀⣈⠀⠀⡁⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠳⠖⠀⠀⠁⠀⡁⠈⠀⠱⠚⣅⠀⠉⠁⠀⡠⢀
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⢿⢻⡿⢢⣤⣤⣴⢶⠿⠛⠛⣽⡟⢧⡤⠀⠀⠂⠀⠀⠁⠀⢀⣠⣄⠟⠉⠂⠚⠏
⠀⠀⠀⠀⠀⠖⠂⠀⠘⠆⠀⢈⠦⣷⣿⢿⡇⠀⠀⠀⠀⠀⢸⡖⠹⠁⣿⣄⡠⣔⠔⠀⣴⣷⠿⠻⣿⡀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠰⠠⠐⡄⠀⠈⣀⠉⢿⣿⡿⢦⠀⠀⠀⢠⣏⣶⢸⣿⣿⠿⢣⣿⠀⠀⠈⠁⠀⠀⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠢⣌⣼⣇⣸⠀⠀⠀⠸⣿⡟⠋⠉⠀⣠⡻⠿⠓⠒⣻⡇⠀⠈⠉⠳⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣠⣤⢶⠞⠃⠙⠟⠀⠀⠀⠀⣿⢷⣄⡀⠀⠀⠀⠀⠀⣠⠀⠀⢠⣤⣴⠖⢀⣤⠀⡆
⠀⠀⠀⢀⣠⣶⡶⠀⠐⣛⣀⣿⡅⢂⠀⠀⣸⡇⠀⠀⠀⠀⠈⢧⠈⠻⠀⠀⠀⢀⠀⢘⣦⣀⣼⣿⡃⣶⠠⡂⠀⣀
⠀⢀⣤⣿⣷⣶⣅⣤⣾⣿⣿⣿⣿⣿⡧⣀⠋⠹⡖⠀⠀⠀⠀⠀⢣⡰⠇⠀⠀⣾⠀⠸⠋⠻⣿⣧⠀⠀⡄⠆⠘⠷⠂
⠀⠙⠉⢿⠠⣿⠻⢟⢿⡄⠀⠈⠙⣿⡷⢍⠀⠀⠀⣀⠀⠂⠀⠀⠋⠀⠀⠀⠀⢀⠴⠀⠀⠠⠿⠈⠉⡲⠀⢡⣄
⠀⠀⠀⠀⠀⢻⡁⢠⠀⢁⡳⣦⣮⣤⡟⠀⠀⠀⠀⠉⠀⠓⢦⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠒⠀⠀⠇⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠁⠂⡀⣤⠙⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠂⠤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠶⠖⠒⠛⠛⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⣈⣠⢤⡤⠤⠤⠤⠤⠴⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⢀⠣⢤⡀⠀⠀⠜⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠈⠀⠀⠀⢀⠇⣀⡴⠋⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡌⢸⠁⢰⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⣀⠤⠦⢄⣈⣁⠤⢼⡖⠶⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠢⠀⠀⠀⡄⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⢁⠀⠀⠀⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⢀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢀⡤⠤⠇⠐⠤⢠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠱⡄
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢣⠀⠀⠀⢹⡀
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⠲⠴⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢷
⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡠⠤⠀⡤⠖⠠⣀⡤⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢸⡆
⡼⠀⠀⠀⠂⠀⠀⠚⢠⡋⠀⠀⠈⠠⡦⠀⡀⠰⠀⣸⢀⡁⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⣧
⡇⠀⠀⠀⠀⠀⠀⠀⡄⢠⠦⠈⢢⣀⡶⣀⣹⣀⡏⢠⣈⢉⡇⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠠⠤⠋⠼⠀⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀⠀⠀⣿
⢷⠀⠀⠀⠀⠀⠀⣠⠤⢄⢠⡴⢤⠔⢦⠒⢉⠉⠂⡤⢀⡤⣤⠴⠒⠦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡿
⢸⡀⠀⠀⠀⠀⠸⣁⠀⠚⢄⠑⣄⢀⠃⠀⠘⠀⢞⡇⠈⠁⢸⠀⣘⣀⡼⠀⠀⠠⠀⠀⠀⡴⠀⠀⢰⠆
⠈⣇⠀⠀⠀⠀⠀⠴⠚⢀⡴⣐⢁⡎⠀⡀⢈⠳⣠⠟⠤⠤⠻⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾
⠀⠘⣆⠀⠀⠀⠀⠁⠉⠁⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠃
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠀⢰⡀⠀⠀⠀⠀⠀⢠⠇⠀⢠⠇
⠀⠀⠀⠈⠳⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⠀⠀⢀⠀⠀⠀⠀⢠⠏⠀⠀⢺⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠓⢦⣤⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠑⠐⠉⠀⠀⢀⡴⠁⢀⡠⠔⠋⠉⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠶⠶⠦⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣰⡯⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣠⠤⠶⠒⠚⠋⠉⠉⠓⠒⠶⠦⠤⠴⠶⠖⠚

⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⢰⣷⣿⠇⠀⢻⣷⡆⠀⠀⢰⣷⣿⠿⣿⣿⣆⡄⠀⠀⠀⠀⢻⣿⣿⣿⣶⣇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣶⠀⠀⠀⠀⡄⣿⣿⠏⢿⣿⡆
⠀⠀⠸⣿⠁⣰⣦⠈⣿⡇⠀⠀⢸⣿⠿⠀⠘⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣶⡿⠁⡀⠛⣿⠀⠀⠀⠀⣿⡿⠁⠀⢸⢿⡿
⠀⠀⠀⠙⠦⡙⢛⠴⠋⠀⠀⠀⠀⠻⠄⠀⠀⠠⠟⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠹⠄⢾⡿⠀⠋⠀⠀⠀⠀⠙⠧⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣆⢸⣿⡄⡄⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⢠⡄⣾⣿⢿⣿⣀⡄⠀⠀⠀⠀⣶⣻⣿⣷⢀⡄
⠀⠀⠀⢸⣿⣿⣿⣇⣷⠀⠀⠀⢈⣿⣿⠏⠻⣿⣿⣶⠀⠀⠀⣼⣿⣿⠋⢻⣿⣧⠀⠀⠀⣿⣿⣿⠟⠈⣿⣿⣿⠀⠀⢰⣦⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇⢀⣦⠀⣿⠇⠀⠀⠀⢻⣿⠁⠀⣼⢿⡟⠀⠀⠀⠸⣿⠉⢀⣆⠉⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠈⠁⠘⠟⠁⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠛⠟⠀⠉⠀⠀⠀⠀⠈⠙⠚⠛⠛⠋

⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⢀⢀⣼⣿⣷⡄⠀⠀⠀⠀⡀⠈⣿⣧⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠀⡀
⠀⠀⢀⣿⣿⣿⢿⣿⣿⡄⠀⠀⢀⣿⣄⣽⣿⡟⢀⡀⠀⠀⠀⡀⢻⣿⠛⢿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⣿⣿⣿⣾⣿
⠀⠀⠸⣿⡟⠉⠀⠹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⣿⣾⠋⢠⡀⢻⣿⠀⠀⠀⢠⣸⣿⡏⠿⣷⣾⡆⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿
⠀⠀⠀⠻⣧⡀⠀⣰⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⢿⣄⣿⣧⡼⠃⠀⠀⠀⠀⠻⡏⠁⠐⢻⡟⠀⠀⠀⠈⢿⡿⠷⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡙⢿⣿⣿⣿⣿⣿⠟⣩⣶⡇⠀⠀⠀⠈⡇⠉⠳⣄⡀⠀⠀⠀⠀⢀⡴⠚⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠈⠻⠿⠋⠰⣾⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⢙⣦⣀⣠⣾⡋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣴⣾⣿⣶⣿⣷⣌⠻⣿⡇⠀⠀⠀⠀⡇⠀⣠⠞⠉⠀⠈⠁⠀⠙⢦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⠿⠿⠿⠿⠿⠿⠿⠿⠷⠎⠁⠀⠀⠀⠀⣷⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣉⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⢸⣿⡇⠀⠀⣶⣖⠒⠒⠒⠒⠒⠒⠒⠒⠒⢾⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣙⠿⣿⣿⣿⣿⡿⠟⣹⣿⡿⠟⠁⠀⠀⡇⠈⠳⣤⡀⠀⠀⠀⠀⣀⡴⠛⠳⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⢈⡛⠿⣋⠰⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⣹⠦⣄⣠⢾⡉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣴⣿⣿⣾⣿⣷⣌⠻⢿⡇⠀⠀⠀⠀⡇⠀⣠⠞⠁⠀⠈⠀⠀⠙⢦⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠁⠀⠀⠀⠀⣷⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⡷⡿


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⡀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣽⣿⢢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠷⠟⣤⠭⣭⠩⡛⡆⠐⢲⡟⠿⠩⠖⢾⣿⠿⢿⣇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡆⠀⠈⠀⠠⠀⠀⠀⠀⢸⣧⡀⠀⠀⠉⠋⡀⣰⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⣴⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠜⠠⠤⠄⢴⠷⠖⠀⠀⢀⣾⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢰⡀⣠⣴⣿⣷⣶⣾⣿⣷⣶⣆⢸⡇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣧⣿⠟⠛⠛⠛⠛⠛⠛⠛⢻⣾⡇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣀⠀⣾⣿⣿⣷⠀⣀⣮⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣧⣀⣘⣭⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠈⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⢀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠰⠳⣄⡎⠀⠀⠁⠠⠀⡜⢆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠈⠆⠀⠀⢀⠀⠰⠁⢸⠈⠰⠃⢰⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡏⠲⢦⠀⠀⠀⠀⠀⠈⢄⠁⠀⢸⠀⠀⠀⡌⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⡘⠘⡐⢚⡇⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⡀⠀⠳⠉⠀⠌⡰⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣄⡀⠀⠀⠀⠀⠂⠄⠐⠂⠀⠀⠁⠄⠂⠀⠀⠤⠊⠉⠈
⠀⠀⠀⠀⠀⣼⠹⣭⢍⣠⢴⠚⢠⣀⣤⡤⡖⠢⣤⢼⣐⠒⣦⠀⢲⢢⡀⠘⠛⣻⣻⡄⢠
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠻⠼⠛⠛⠊⠳⣾⡴⠃⠰⣌⣠⡼⠷⣤⣸⡖⠲⠮⠯⠟⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢰⠏⠂
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠂⠀⠀⠠⠒⠀⠚⠀⠀⢀⡠⠀⠂⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢸⡆⣰⣧⣆⠒
⣴⣧⣿⣇⡆⠀⠀⠘⣯⠐⠂⠀⠀⢲⡄⠀⠀⠂⠻⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⢷⠀⢠⣾⢷⣭⠌⠛⢶⠒⢠⡆
⣻⡟⢫⣿⣧⣷⣏⡠⠀⠔⠐⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡔⢯⡀⢘⡁⢂⠪⡦⠴⡘⢦⣝⢳
⠚⣯⡶⢹⣿⣿⠋⠂⠀⠂⠐⡈⢺⣶⣆⣤⣀⣤⢀⠀⠀⠀⢀⡀⣤⢀⣠⡊⠃⣴⠞⠃⢜⡺⠤⠉⠱⣿⠀⠈⠀⠙⢿
⢈⠁⠖⢸⣉⡤⠎⣠⠆⠀⠀⠐⠲⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠈⠈⠺⣂⠘⣯⡤⠒⣀⡠⣜⡀⠀⠈⠶⢾
⠸⠄⢠⣟⡉⠠⠠⠶⢀⣰⢿⠑⢠⣙⣯⢓⣹⣭⠟⣋⡁⠀⠀⠀⠙⢿⠀⠈⠙⠳⣎⢢⡟⠒⠉⠈⠣⠌⡂⠀⠠⡀
⠀⠀⢠⡏⠠⢰⠂⢠⠊⠙⢄⣯⡀⠀⠉⠁⠀⢄⣪⣷⣻⣓⣦⣴⡶⠂⠀⡀⠁⣌⠚⢿⣗⠄⣇⠀⢰⡆⠈⠲⡀⡀⠑
⠀⡰⠋⠀⢀⡬⣟⠀⠀⠀⢣⣀⠧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⡋⠀⠀⠉⠐⠉⠄⠀⠁⢿⡁⣀
⠀⠀⠀⠈⠀⠀⠀⠙⠊⠀⠊⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠘⠉⠀⠄⠐⠤⠦⠀⠽⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠲⢦⣄⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣀⣀⣀
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⣻⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡴⢾⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠿⢫⡟⠛⠛⠻⣤⣞⡃
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠙⢦⣤⣀⣀⣠⣤⡞⠉⢳⣦⣤⣀⣀⡀⠀⢀⣀⣤⣏⡿⣠⣭⡗⠀⠀⠀⣿⠉⢿⠄⢀⣄
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⠹⣤⣤⣤⣽⡜⢯⣩⣟⢻⣍⣧⠙⣴⣧⣴⠟⣦⣤⡾⠡⣿⡭⠤⠟⠼⠧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣶⢂⡶⢶⣲⡶⣠⠶⠶⣦⡴⢶⡶⣀⠰⡖⢶⣔⡶⠒⣆⢲⡒⠒⠓⢶⣘⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢾⡉⢰⡇⠀⠀⢸⣗⠛⢰⠋⣷⠙⣻⡏⠀⠀⠘⣧⠛⢶⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢧⣤⣤⣤⠟⡴⠞⠛⠳⢷⡙⣦⣀⣀⡴⣷⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡴⠒⢲⢆⡘⣇⠀⠀⠀⣰⢃⡄⢶⠶⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⣷⠙⢲⣶⠚⢡⡏⠹⣎⢧⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⢁⢺⡄⠙⠶⠛⠹⠷⠖⠋⠀⣸⠂⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠟⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⢿⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⢦⣌⢷⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⣆⠙⠷⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⡓⠦⡀⠈⢷⡀⠀⠀⠀⣿⠀⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡄⠀⠻⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⣠⠟⠀⠀⠀⠹⣄⡀⢻⠀⠸⣇⠀⠀⠀⠀⠀⢰⡇⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠟⢰⡏⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠘⢷⣄⠀⠀⠀⠀⠻⣄⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⡉⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠳⢦⣄⠀⠀⠈⠳⡄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠈⠉⢻⠓⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠀⠀⢠⣸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⡞⠀⠀⠀⢀⣤⠟⣿⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠀⠀⢹⡆⢀⡤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⡖⠉⠀⣀⡴⠞⠋⠀⣰⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠘⡇⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠘⢧⣠⠞⠁⠀⠀⠀⠘⠁⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⠇⢸⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⢠⢀⠞⠁⠀⣰⠋⣠⡾⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠃⢀⣠⠄⣀⣴⠆⢀⠀⠀⠀⠞⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠰⣶⣤⣛⠀⠈⢁⣾⣿⣷⣿⣿⠃⠀⠀⣀⠀⠖⢀⣀⡀⠀⠀⠀⠀⠀⣰⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣍⣻⣦⣄⡀⠀⣀⠐⣀⣈⠛⠻⣟⣻⣿⣿⡿⠟⣋⠀⠀⣠⣤⣤⣤⡶⠿⠛⠁⠀⠀⠀⣀⡼⠯⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⠶⠛⠻⢶⣤⣄⣈⣁⣰⣿⡿⣯⣥⣤⣀⡛⣿⣿⣶⣬⣍⠀⠻⠷⠶⢶⣆⣤⣴⣾⣿⣶⣶⣶⠤⠴⠶⠖⣶
⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣤⡤⠤⠶⠶⠚⠋⠉⠉⠉⠉⠁⣀⡤⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⠲⠶⣿⣿⣭⢤⣭⣍⣛⡛⠛⠶⠦⢤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠋⢑⣻⡿⠟⠋⢁⣀⡈⠉⠉⠉⠋⠉⠛⠒⠾⠭⣅⣀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣯⣉⣀⠤⠖⠚⠉⠉⠀⠠⠖⠛⢉⣀⡙⠚⠙⠛⠶⠶⢦⣄⣠⣤⡴⠶⠯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣫⠄
⠀⠀⠀⠀⢠⣄⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣩⢧⠶⠂
⠀⠀⠀⠀⣄⣈⣱⣆⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⣩⣿⣦⣶⠛
⠀⠀⠀⢠⡌⠉⢡⣎⣁⣀⡄⠀⣠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣤⣾⣥⡼⠳⠶⠾⠃⢀⠀⣠⠄
⠀⠀⠀⠀⠓⠚⣯⠉⢉⢁⣠⠀⠋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⡞⠀⠀⠀⢰⠃⠁⢺⣤⠿⢶⣧⡾⢿⣶⠶⠾⠋⠊⠀⠟
⠀⠦⠐⠶⡴⠾⢛⡓⠟⠉⠁⠀⠀⣧⠀⡀⢀⡀⠀⠈⢧⡄⠠⢠⠆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣟⣫⡿⠶⢟⡿⠶⠶⠂
⠀⠀⠶⣦⣀⣴⠞⠛⣶⣄⣼⠻⠇⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣳⣫⣿⣭⣿⣟⣻⡷⢶⡾⠇
⠀⢀⣤⣬⣡⣂⣴⣾⣇⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣽⠶⠖⠺⢛⣿⣷⣤⣤⣶⠄
⠀⠉⠉⠉⠙⡉⠉⣹⡋⠛⠋⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠶⠼⠿⠿⣿⣧⣤⣤⡤⠆
⢀⡝⠛⢿⣍⣠⠾⠻⡿⢷⠆⣦⠆
⠈⣿⠏⣉⣈⠈⣀⢾⣧⣀⠀⡾⠟
⠀⠀⠀⠀⠿⠋⠏⠈⠙⠛⠋⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠓⢓⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠈⠀⠠⠀⣶⡶⠀⠀⠀⠠⠀⠀⠀⠀⠐⠖⠓⠶⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣭⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠚⠓⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⠛⠙⠚⠓⠓⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠀⢠⠖⠀⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠚⠐⠳⠖⠤⠂
⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠌⣠⠖⠈⠈⣧⣽⠋⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡐⠧⠢⠔⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡯⠀⠈⠐⠉⠈⠒⠚⠀⠙⢆⢀⡠⢀⢀⠀⢠⡄⠤⠒⢲⣴⣧⣶⡜⢚⣒⠘⢀⠀⡀
⠀⠀⠀⠀⠀⡠⠐⡐⠒⠊⠉⠁⢡⣹⣷⢰⠀⣰⣶⡆⠀⡄⣯⡴⣄⢅⠠⡌⡛⣿⣏⣴⠀⠌⠁⢉⡁⡀⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣌⠄⠈⠉⢅⣐⣋⠏⡁⢹⠀⢀⡇⠀⣠⠤⠼⠂⠂⡁⠀⠈⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⢀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠋⠉⠁⠉⠐⠄⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣷⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⣿⡦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣴⣿⣿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⣟⢾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⡿⢡⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣷⣿⣿⣿⢉⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣯⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⡀⣐⣶⡾⠿⠿⠿⠿⠿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣀⣤⣤⣽⣷⣍⢿⣯⣥⣤⣤⣤⣤⣾⣭⢭⣥⣶⣶⠶⢶⣶⡿⢉⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣈⣤⣞⢿⣿⣟⣙⣿⣿⣆⢻⣿⣿⣯⣯⣽⣫⣵⣯⣥⣾⣧⣴⣾⣿⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⣿⡿⣿⡟⠛⠛⠛⠛⠛⠛⠻⣦⢹⣟⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⢇⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⡿⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣼⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢀⡿⢡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⡄⠀⠀⠀⠀⠈⣿⣾⣿⣿⣷⠘⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⣼⢃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢷⡀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣧⠹⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡘⣧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢹⡆⠀⠀⠀⣹⣿⣿⣿⡇⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⣿⡀⠀⠀⣿⣿⣿⡏⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢹⡇⠀⠰⣿⣿⣿⡃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣧⠀⠀⢻⣿⣿⣧⢹⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⡄⠀⣼⣿⣿⣿⡜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠸⣇⢸⡇⠀⢻⣿⣿⣿⣿⣿⣿⡟⣿
⠀⣀⣀⣤⣴⣶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠶⠾⣿⡈⣿⣤⣼⣿⣿⣿⣿⣿⣿⣦⣿
⣾⣟⠉⠁⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣽⣧⢸⣷⡄⠉⠉⠛⢻⣿⣏⢿⣿
⠉⢻⣿⠿⣷⣶⣶⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⠉⠆⢿⣷⣿⡿⣿⣿⣿⣿⣾⣿
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣈⣙⢻⣿⣶⣴⣿⣭⠄⣏⣿⣿⣿⣿⡿⣿
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢬⣭⣽⣻⣿⣿⣿⣿⣥⣴⢄⣻⣿⣿⣿⣿⣗⣿
⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣤⣽⣯⣭⣿⣿⣿⣿⣯⠅⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢠⣾⣯⣿⣿⣿⡿⠶⠶⠂⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⣶⣿⣿⣿⣋⣉⡁⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢉⣿⣿⣿⣿⠿⠏⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣽⣿⣿⢿⡶⠦⠀⣸⣿⣿⢿⣿⣿⣿⣿⠉⣿
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⣶⢾⣿⣿⣿⣿⣶⠶⢀⣿⣿⣿⣾⣿⣿⣿⡏⢸⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⡿⣿⣿⣷⣏⣿
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣧⣿⡿⢡⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣾
⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⣶⣿⣿⣿⣟⣛⡀⣼⡿⠀⣿⣿⣏⠹⣯⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣻⣻⣿⣿⣿⣿⠯⢠⣿⠃⠀⢻⣿⠙⣷⣿⣿⣷⢻⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤⢴⣶⣿⣿⣿⣾⣛⠁⣾⡏⠀⢀⣼⣿⣷⡘⣿⣿⣿⡞⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣶⣿⣿⣿⠛⠁⣰⣿⠁⠀⢸⣿⣿⢏⣿⣿⣿⣯⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣻⣿⣿⣶⣶⣟⢀⣿⡏⠀⠀⠀⢻⣿⢾⣿⣿⣿⣻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣭⣭⣽⣿⣯⣭⣤⣶⣼⣿⠁⠀⠀⠀⣿⣿⣾⣿⣿⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣛⣉⣉⣉⣉⣉⣭⣭⣭⣭⣍⣉⣩⣭⣭⣭⣥⣥⣼⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⣄⡄⣠⠶⠶⠶⠶⠶⠶⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⠛⠛⠉⠉⠁⢠⣬⣥⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⡤⢤⣤⣴⣶⠶⠶⠶⠾⠿⠃⠀⠀⠀⢠⣽⣿⣿⣿⣇
⣤⣴⣶⡶⠶⠿⠛⠛⠋⠉⣈⣧⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣮⡻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⢍⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣼⣿⣿⣷⡶
⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⣭⣷⣾⣿⣿⣩⢻⡟⣽⣿⣟⡝⣿⢫⡿⡿⣫⢻⣿⣿⣿⣿⡿⠋
⠀⠀⠀⢀⣴⣾⣿⣏⣷⣿⡸⣿⣿⣿⣿⣶⣿⣷⣶⣿⣷⣶⣿⣷⣾⣿⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠙⠻⠿⣻⣿⣿⣿⣶⣶⢰⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢰⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠛⠛⠉⠉⠉⠉⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠀⠀⠀⢀⣀⡤⠤⠒⠒⠲⡄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢠⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣳⣹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠜⢯⣷⣷⣿⣿⡗⠛⠛⠳⢦⣀⠀⠀⠀⡇⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠠⠃⢠⢁⠎⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣌⣀⣘
⠀⠀⢰⡯⣉⣩⣉⣉⣍⡭⢿⠂⠀⠀⣀⣤⣤⣤⣤⣤⡄
⠀⠀⢸⡗⠲⢚⠲⢼⣄⣀⣾⠀⠀⠀⣿⠉⠛⠛⠉⠉⡿
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⣄⣠⣤⣀⣴⠇
⠀⠀⠀⢹⣤⣀⣄⣀⣀⣴⡇⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠋⠉⠉⠉⠙⠛⠻⢿⣿⡛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⢀⣀⣀⣀⣿⠷⣄⡀⠀⠈⠙⠳⣦⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⢠⣟⣉⣉⣉⣩⡄⠈⣻⠂⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢻⣴⠏⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣤⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣄⠀⣷⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⢿⠀⣿⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⢠⡴⠶⠾⠀⠈⠉⣇⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⣴⢶⣄⠀⣾⠋⡇⢠⡶⠛⡆⠀⠀⡾⠫⠦⢹⡇⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⠁⠉⠁⠀⢻⡆⣨⣿⣥⠈⡇⢸⣇⣀⣼⡇⠀⠚⢻⡄⠀⠀⠀⠀⠀⢸⣿⡇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⡇⠀⠀⢸⡄⢰⣦⣶⣌⣇⢿⠀⢸⡄⣧⠈⠉⠀⠈⣿⣦⣄⣸⡇⠀⠀⠀⠀⠀⢸⣿⡿⠛⣷
⠀⠀⠀⠀⠀⠀⢸⡏⠙⢻⣇⠀⠀⠸⠷⠟⠀⠈⠉⠋⠸⠶⠾⠃⠹⣦⣤⡤⠶⠇⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡤⠶⣆⠀⢀⡴⠟⢻⡄⠀⣴⠋⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⣧⡀⣰⠏⠉⢷⡀⢀⡼⠋⠀⠀⠸⣦⡏⠀⠀⠀⣧⣼⠃⠀⠀⠀⠀⠀⣼⣃⣤⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⢷⠏⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣾⡿⣶⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠘⣷⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣴⣶⣶⡶⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⣿⡏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿