Public health Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣤⣬⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⡴⠖⠛⠉⠉⠉⠛⡇⠀⠀⠀⠀⠀⣴⠶⠶⣦⠀⠀⠀⠀⠀⢸⠛⠉⠉⠉⠛⠲⢦⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣿⠀⠀⣿⣀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠓⠒⣶⠀⠀⣶⠒⠚⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣤⣤⡿⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣬⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣠⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠹⡾⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢠⡇⠙⢦⡀⠀⠀⠀⠸⣇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠶⠖⠻⢦⣤⡴⠛⠛⢶⣤⠴⠛⠳⠶⠚⠷⢤⡴⠚⠛⠳⣤⡤⠾⠓⠶⠖⠻⠶⣯⠖⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠤⢤⣀⠀⣘⣦⣀⣀⣴⡃⠀⣀⡤⠤⣄⠀⢈⣷⣄⣀⣠⣟⠀⢀⣤⠤⣤⡀⠀⣹⣦⣀⣀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠁⠀⠀⠙⡏⠉⠀⠈⠁⠀⠉⢻⠋⠀⠀⠈⢿⠉⠁⠈⠉⠀⠈⢹⡏⠀⠀⠀⢹⡋⠉⠀⠉⠁⠀⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢿⡀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠲⠚⠻⠦⣄⡀⠀⠀⢀⣤⠴⠛⠓⠒⠛⠶⢤⣀⠀⠀⢀⣠⡴⠞⠓⠒⠚⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢠⣶⡆
⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣇⡀⢀⠀⠀⠿⣿⣀⣩⣷⡄
⠀⠀⠀⠀⢀⣟⠃⡀⠀⠀⠀⣸⣷⡰⠂⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣗⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠻⠛⠀⠀⠐⣿⡉⠉⣿⡇
⠀⠀⠀⠀⣿⣿⣿⡟⠀⣾⢷⠋⣉⠳⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⣿⣿⣷⢽⣿⣿⣷⠤⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⣿⠿⠷⢰⡟
⠀⠀⠀⠀⣹⣿⣿⡅⠸⢏⡸⣌⣛⡸⠃⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣾⣿⣿⡿⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠉⣿⣇⠘⠁⠀⠀⢿⡦⠤⣼⣿



⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⣤⡄⠀⠀⢴⣶
⠀⠀⠀⠀⠀⢠⣿⣟⡀⠀⠀⠀⠠⣶⡄⣘⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠃⠀⠀⠀⣠⣶⣌⠉⠀⠀⠀⠀⠀⢠⣶⡍⠀⢰⣯⣥⡀⠀⠀⢹⣦
⠀⠀⠀⣴⣦⣼⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⣿⣤⣤⣦⡀⠀⠀⠀⢸⣿⣟⣛⡉⠀⣼⣻⣿⣟⣧⠀⠀⠀⠀⠀⢸⣿⡓⠒⢋⣿⠟⣷⠀⠀⢸⣿
⠀⠀⠀⠉⣿⠛⠻⣿⣟⠛⠛⠛⢻⠿⣿⢿⣿⡟⠛⣿⡋⠀⠀⠀⠀⡸⢿⣿⡇⠀⠀⠸⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣷⡆⢸⡏⣷⠉⠀⠀⣽⡇
⠀⠀⠀⠀⠿⠿⣾⠿⠿⠿⠿⠷⠿⠷⠿⠾⢿⠷⠾⠿⠃⠀⠀⠀⠀⠥⠴⠿⣷⠀⠀⠀⠿⠄⠿⠀⠀⠀⠀⠀⠀⠀⣼⡏⠁⢸⠃⢸⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢋⢀⡈⠓
⠀⠂⠀⠀⠀⠀⣴⣦⠀⠀⠀⣴⡆⠀⠀⠀⣶⡆⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⠐⠒⠛⠛⠃⠡⠂
⠀⡀⠀⠀⠀⣴⣿⣥⣤⠄⢰⣿⣧⡀⠀⣴⣾⣶⡄⠀⠈⢵⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⠂⠀⠀⠀⢀⣀⠀⠀⠀⢠⣤⡆
⠀⠀⠀⠀⠀⣿⣿⣶⠒⠀⢻⣿⣿⡃⠀⣿⣿⣿⡇⠠⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⢴⡟⢰⣤⣹⣟⡀⠀⣶⠈⣿⣤⡀
⠀⠀⠀⠀⢰⠉⣿⣿⠀⠀⠰⢉⡿⢷⡀⢸⣿⣿⠁⠀⣿⡛⠙⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⢻⣿⠶⣶⠀⠈⠛⢛⣿⡇⢼⡗⠒⣿⣿⣧⣠⣄⣀⣠⡀
⠀⠀⠀⠀⠈⠉⠉⠹⠃⠀⠈⠻⠉⠀⠀⠸⠟⠿⠀⠀⠟⠉⠉⠃⠀⠀⠀⠀⠿⠿⠿⠇⠰⠶⠿⠀⠿⠀⠀⠻⠿⠿⠃⠸⠁⠿⠿⠿⠛⠛⠻⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣒⢊⣭⠉⢭⡭⣭⠉⠉⣉⡑⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⠁⠀⠈⣿⠒⣿⡀⣸⣏⣣⢄⡜⢹⣇⠀⣸⠖⠈⣙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡎⠉⢠⠀⠀⢋⣁⡭⠤⢶⢶⠶⠶⠤⠬⣍⣐⠻⠤⠆⣠⡟⠦⠙⢦⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠐⢷⣌⡛⠒⣋⠴⠚⠉⠀⣠⡔⡡⡪⡇⠀⢀⠀⠀⠈⠙⠲⢌⡛⢀⣤⢟⢃⡙⢦
⠀⠀⠀⠀⢠⠞⢠⣆⡀⢰⠙⡡⠊⠁⠀⢀⢔⣾⡺⡧⡊⡞⠀⡀⢀⣇⠀⠀⠀⠀⠀⠙⠦⡁⢴⠟⠉⠀⠳⡄
⠀⠀⠀⢠⠏⣠⣤⣈⠻⢣⠞⠀⠀⠈⢲⣤⡿⠿⣬⢻⡼⠀⠀⠈⠉⠀⠑⢤⡐⠂⣁⠰⠀⠙⢦⠀⢀⢠⣤⡹⡄
⠀⠀⢀⡏⠰⠷⣯⡼⢡⠃⠀⠀⣀⣠⡄⠙⢦⡕⢉⠁⠇⠀⠀⠀⠀⠀⠈⠀⠙⠀⡾⠀⠀⠀⠈⢣⢹⣸⡇⠃⢹⡀
⠀⠀⡼⠀⠓⠦⣌⢡⠇⠀⢀⠾⣾⣿⣘⠔⠂⠈⠺⣠⠁⠀⠒⠀⠀⠀⢀⡤⠴⠞⠙⢦⡀⠀⠀⠈⢇⢰⡶⡾⡇⣇
⠀⠀⡇⠸⠷⠶⠏⡼⠀⡠⢳⢶⢶⢬⣽⢂⣉⡡⠂⡈⠲⡊⢱⣇⢀⡴⠋⠀⠀⠨⡟⡦⠙⢦⠀⠀⢸⡈⠦⠉⠛⢸
⠀⢸⡇⢸⢳⠀⡀⡇⣔⢕⡑⣡⡦⠟⠂⠂⠀⠀⠠⠆⠀⡌⠿⣻⣾⣤⡀⠀⠀⠀⡻⡇⠀⠈⢣⠀⠈⡇⠗⡶⢾⢸⡂
⠀⢸⡇⠘⠛⠛⠃⡇⠀⠀⢸⡁⠀⠀⢀⠁⠀⣈⣻⠿⠟⣷⣿⠍⠫⣍⢓⠀⠀⠠⡳⡇⠐⠤⠞⠀⢀⡇⠞⠙⠟⢸⠇
⠀⠀⡇⠀⠀⠀⣀⢳⠀⠀⠀⢳⣄⠀⠐⠀⢈⡬⠻⣺⡿⡏⠋⠈⠡⣾⠻⣟⠀⢀⣛⠆⠀⠀⠀⠀⢸⢡⣴⠶⠞⢸
⠀⠀⢳⠀⢀⢠⡤⡘⣆⠀⠀⢸⠈⠓⠁⠀⠀⢀⣴⠿⡻⡇⠀⠀⠀⠙⠓⠈⡰⣯⡿⠀⠀⠀⠀⢀⡏⣄⠈⠳⠆⡏
⠀⠀⠈⣇⠸⣼⡇⠗⠘⣄⠀⠀⠑⠀⠀⢀⡴⢟⣽⡀⡿⡧⠀⠀⠀⠀⠀⠀⣙⢮⡻⣄⠀⠀⢀⡞⣈⣉⠛⠟⣸⠁
⠀⠀⠀⠘⣆⠀⠀⠀⢁⣈⢦⡱⡀⠀⠀⢿⢁⡞⠻⠇⠚⠛⠒⢖⡄⠀⠀⢀⣭⡟⠀⠉⠄⣠⠏⢸⠉⠙⡇⣰⠃
⠀⠀⠀⠀⠘⢆⠀⠞⠁⣸⠇⠙⢮⡢⣄⡀⢑⣳⠀⠀⠀⠀⣀⡇⣀⣀⡴⣧⠝⠁⠀⣠⠞⡡⢺⣦⡀⠋⡴⠃
⠀⠀⠀⠀⠀⠀⠳⣄⠙⠁⠀⠀⠀⠈⠓⠭⣜⡑⠀⠁⠀⠀⠉⠲⠿⠼⠟⣋⡤⠖⠋⠀⠀⠃⢽⠜⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠲⠂⠀⠀⠠⣍⠙⣒⠒⠒⠒⠒⠒⣋⣉⡁⠀⠀⠰⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠀⣴⡇⠀⢉⡽⠃⢯⣹⡇⣿⠚⡧⠀⠀⠀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣉⣀⣀⣘⣚⣁⣈⣩⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠛⠻⠿⢿⠟⠛⠻⣿⠟⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠟⠛⠋⠛⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣿⣿⣿⣤⣤⣤⣤⣤⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆
⠀⠀⠀⢠⣿⣿⡿⠟⠿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠟⠉⠁⠀⠀⠀⠉⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠻⢿⣿⣿⣿
⠀⠀⠀⢸⣿⠟⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣄⣀⢀⣴⣿⠁⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⣼⡟⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⢠⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠻⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣄⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠈⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣟⠻⣿⣿⣿⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠛⣠⣙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣀⣀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⢀⣠⣴⣿⣿⣿⠃⠀⠀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣟⡁⠀⢀⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⡶⠾⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣼⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣧⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⣉⣉⣉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⠉⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⣀⣴⡾⠟⠛⠛⠛⢻⡇⠀⠀⠀⠀⣾⡿⢿⣷⠀⠀⠀⠀⢸⡟⠛⠛⠛⠻⢷⣦⣀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣼⠟⠁⠀⠀⠀⠀⠀⢸⡇⠀⢰⣶⣶⣿⡇⢸⣿⣶⣶⡆⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣧⡈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣤⣤⡀⢀⣤⣤⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⣿⣇⣸⣿⠉⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣄⣠⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⣠⣾⠟⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠈⣿⣷⣄⠀⠀⠀⠀⣿⠏⠀⠈⣿⡇⠀⠀⠀⠀⠀⣿⠋⠀⠈⣿⡟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⣀⣠⣿⡋⣻⣷⣤⣀⢀⣿⣧⣀⣠⣿⡃⣀⣤⣤⣀⠀⣿⣦⣀⣠⣿⣷⣿⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠋⠙⠛⠛⠛⣿⡟⠉⠉⢻⣿⠛⠉⠛⠋⠛⣿⡟⠉⠉⢻⣿⠛⠉⠛⠋⠛⢿⡿⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣀⣀⣀⠀⢻⣧⡀⢀⣼⡟⠀⣀⣀⣀⠀⢻⣧⡀⢀⣼⡟⠀⣀⣀⣀⠀⢹⣧⡀⢀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣾⠟⠉⠻⣷⡿⠟⠻⠟⠛⢿⣾⠟⠉⠻⣷⡿⠛⠻⠟⠻⢿⣾⠟⠉⠻⣷⡿⠟⠻⠟⠛⠿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠘⣿⡀⠀⢀⣿⠇⠀⠀⠀⠀⠸⣿⡀⠀⢀⣿⠃⠀⠀⠀⠀⠸⣿⡀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⠶⠿⢿⣦⣄⡀⢀⣠⣴⡿⠿⠶⠿⢿⣦⣄⡀⢀⣠⣴⡿⠿⠾⠿⢿⣦⣄⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠙⢿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠙⣿⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣴⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⣿⣿⣿⠃⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⢻⣿⣿
⣿⣿⣿⠀⠸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠀⢸⣿⣿
⢹⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿
⠀⠻⣿⣿⣿⣷⡀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠈⢿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⢛⣉⡙⠀⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⠀⢋⣉⡛⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢁⣴⣿⣿⣿⣿⠀⣿⡿⠛⠃⢸⡇⠘⠛⢿⣿⠀⣿⣿⣿⣿⣦⡈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⣿⣿⣿⣿⣿⣿⠀⣿⡇⠘⠛⢻⡟⠛⠃⢸⣿⠀⣿⣿⣿⣿⣿⣿⡄⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠘⠃⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⡿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⢿⣿⣿⣿⣿⣿⣿⣦⣤⣉⠛⠿⠿⠛⣉⣤⣴⣿⣿⣿⣿⣿⣿⡿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡈⠻⣿⣿⣿⣿⠏⣡⣤⡙⢿⣿⣿⣿⣿⢋⣤⣌⠛⢡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⢠⡈⠻⢿⣿⡀⢿⣿⠇⣸⡿⠿⣿⣧⠸⣿⡿⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣤⡌⢡⣶⣦⠀⣤⣦⣤⣤⠈⣰⣶⡄⢡⣤⣤⣤⣤⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠻⠧⠘⠿⠟⠠⠿⠛⠛⠿⠆⠹⠿⠃⠼⠟⠛⠻⡿⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⣼⣿⡆⢰⣾⣶⣾⣶⠀⣿⣿⠄⣶⣷⣶⣷⡆⢰⣿⣷⠀⣶⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⡁⠺⠿⣿⡿⠟⠀⡙⢋⠀⠻⢿⣿⠿⠗⢈⡛⣁⠘⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⡈⣠⣾⣿⣿⣿⣿⣷⣆⠁⣴⣾⣿⣿⣿⣿⣶⡌⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠃⠻⠿⠿⠿⠿⠿⠿⠟⠀⠿⠿⠿⠿⠿⠿⠿⠇



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⢿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⣿⣿⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⢀⣀⣠⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣤⣤⣤⣀⣀⡀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⣰⣿⠟⠁⢀⣤⣾⡿⠟⠛⠛⠉⠙⠛⣿⡇⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠻⢿⣷⣤⡀⠉⠻⣿⣆
⠀⢀⣼⣿⠋⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣤⣤⣼⣿⠀⠀⣿⣧⣤⣤⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠙⣿⣧⡀
⠀⣾⣿⠁⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠛⠛⠛⠀⠀⠛⠛⠛⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠈⣿⣷
⢸⣿⠃⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣶⣶⣶⠀⠀⣶⣶⣶⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠘⣿
⣿⣿⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⠉⢹⣿⠀⠀⣿⡏⠉⠉⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿
⣿⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢺
⣿⣷⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣿
⢸⣿⡄⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢠⣿
⠀⢿⣷⡀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣦⣄⣠⣴⣾⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢀⣾⡿
⠀⠈⢿⣷⡀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⣾⡿⠁
⠀⠀⠈⠻⣿⣦⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣾⡿⠋⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠈⢻⣷⣿⠿⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⢿⣷⣤⣾⡿⠋⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠈⣿⣿⣦⡀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢹⣿⡟⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⢠⣿⡏⠻⣿⣦⣀⡀⠀⠀⢻⣿⡄⠀⠀⣠⣿⡇⠀⠀⣀⣀⠀⠀⠀⣿⣧⡀⠀⠀⣸⣿⣣⣾⣿⣋⣀
⠀⠀⣀⣤⣶⣾⡿⢿⣷⣾⣿⣿⣷⣴⣿⡿⠿⢿⣷⣴⣾⣿⢿⣷⣾⣿⣿⣶⣴⣿⠿⠿⣿⣦⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⠿⣿⣦
⢠⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⢹⣿⠏⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⣽⣿⠁⠀⠀⠈⣿⣯⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⡇
⣿⣟⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠘⣿⣇⡀⠀⢀⣾⡿⠀⠀⣀⣀⣀⡀⠀⢹⣿⣄⠀⠀⣠⣿⡏⠀⢀⣀⣀⣀⠀⠀⢻⣿⡀⠀⠀⣰⣿⠇
⣿⣿⠀⠀⠀⢀⣾⡿⠛⠛⢿⣷⣶⣿⠿⢿⣿⡿⢿⣷⣶⣾⠿⠛⠻⣿⣶⣾⣿⠿⣿⣿⠿⣿⣷⣶⣿⠟⠛⢿⣷⣶⣾⡿⢿⣿⣿⠿⣿⣶⣦⣄⡀
⣿⡏⠀⠀⠀⣼⣿⠀⠀⠀⠈⣿⣯⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿
⠛⠃⠀⠀⠀⠸⣿⣆⡀⢀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣠⣤⣶⣿⠿⠿⠿⠿⠿⣿⣶⣦⣄⡀⠀⢀⣤⣶⣾⠿⠿⠿⠿⠿⣿⣶⣤⣀⠀⠀⣠⣴⣶⣿⠿⠿⠿⠿⢿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢹
⣠⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⠀⠀⠀⠀⠀⠀⢸
⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣃⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠉⠙⠻⣿⣷⣾⣿⠟⠋⠉⠀⠀⠀⠀⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⣦⣿⣇⠀⠀⣸⣿⣴⡶⢶⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣀⣀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣿⠋⠛⠿⠿⠛⠙⣿⣄⣠⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⣀⣀
⠀⠀⣴⣿⠿⠿⣿⣦⠀⢿⣿⣄⠀⠀⠀⠀⠀⢀⣨⣭⣭⣵⡾⠛⠛⠛⠛⢷⣬⣭⣭⣄⡀⠀⠀⠀⠀⠀⢠⣿⡿⠀⣴⣿⠿⠿⣿⣦
⠀⣸⣿⣧⣄⡀⠘⣿⣇⠈⢻⣿⣦⡀⠀⠀⠀⣿⠋⠉⠉⣿⡇⠀⠀⠀⠀⢸⣿⠉⠉⠙⣿⠀⠀⠀⢀⣴⣿⡟⠁⣸⣿⠃⢀⣠⣼⣿⣇
⣼⣿⠛⠛⠻⣿⡆⢹⣿⡄⠀⠙⢿⣿⣦⡀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⢀⣴⣿⡿⠋⠀⢠⣿⡏⢰⣿⠟⠋⠛⣿
⣿⣷⠀⠀⠀⢻⣿⡀⢿⣷⡀⠀⠀⠙⢿⣿⣦⡻⠶⠶⠶⠿⠷⠶⠶⠶⠶⠾⠿⠶⠶⠶⢟⣴⣿⡿⠋⠀⠀⠀⣾⡿⢀⣿⡟⠀⠀⠀⣾
⢸⣿⡆⠀⠀⠈⣿⣧⠘⣿⣧⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⣼⣿⠃⣼⣿⠁⠀⠀⢰⣿
⠀⣿⣷⠀⠀⠀⠸⣿⡆⠹⣿⡆⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⢰⣿⠏⢰⣿⠇⠀⠀⠀⣾⣿
⠀⠸⣿⡆⠀⠀⠀⢻⣿⣶⣿⣿⣤⡀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⢀⣤⣿⣿⣶⣿⡟⠀⠀⠀⢰⣿⠇
⠀⠀⢿⣷⠀⠀⠀⣼⣿⠋⠀⠉⠛⢿⣷⣦⣀⠀⠀⠀⠀⠙⢿⣿⣦⣴⣿⡿⠋⠀⠀⠀⠀⣀⣴⣾⡿⠟⠉⠀⠉⣿⣷⠀⠀⠀⣾⡿
⠀⠀⠸⣿⡇⠀⠀⢻⣿⣄⡀⠀⠀⠀⠈⠙⠿⣿⣶⣄⡀⠀⠀⠙⠿⠿⠋⠀⠀⢀⣠⣶⣿⠿⠋⠁⠀⠀⠀⢀⣠⣿⡟⠀⠀⢸⣿⠇
⠀⠀⠀⢻⣿⡀⠀⠀⠉⠻⢿⣷⣦⣀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠀⠀⠀⠀⣀⣴⣾⡿⠟⠉⠀⠀⢀⣿⡟
⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠈⠙⠿⠗⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠺⠿⠋⠁⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⠀⠀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠘⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⡄⣠⠀⢀
⢀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠐⣠⡸⢇⣸⡇⠁⣙⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀
⠈⠭⠛⣒⣿⠠⠀⢠⡀⢠⠀⡀⢀⣓⡛⠂⢿⡇⢴⣿⢀⠀⢀⠀⢀⠀⣀⠀⠀⠀⠀⠠⠀⠀⢄⡀⠀⡆⣩⢤⣽⢄⢺
⡤⠂⠉⠐⣷⠀⣤⡶⠏⢉⣶⠸⣿⣿⣷⠐⠋⠁⠹⠧⣼⡆⣸⡆⠁⠈⠉⢀⡱⣮⠆⣤⣤⣷⠄⠀⠸⠇⠇⢸⣿⡅⠁
⡀⢀⣀⠠⢾⣯⢻⣷⣦⣼⣿⣤⢿⣯⣿⡿⠀⠀⣄⣶⣦⣤⣄⣅⠀⢀⠦⣤⣀⠉⠀⠉⠈⠉⠀⠀⣠⣶⡀⣾⣿⡄
⠁⣾⣼⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⡈⢑⢮⡉⠀⠀⣟⢻⣿⠊⠀⠽⣿⣤⣀⠀⠀⣿⡇⢠⣿⣿⠃⠀⠀⠈⣶
⠀⠹⣿⡿⠛⣿⣿⣿⣿⣿⣿⣻⡇⣿⣿⣿⣙⣿⣾⡿⡄⠀⠀⢛⣿⣿⣿⣿⣿⣗⠀⠀⠠⣿⣿⠞⠻⣿⣷⣀⣀⣴⢿
⠀⠀⠉⢸⣶⣿⣿⣿⣿⡟⢻⠿⢿⣿⣽⣾⣾⡟⣿⡿⣷⠶⢶⡿⠟⣛⠋⠀⣹⠿⡷⣶⢺⣿⡿⣤⣠⡿⠿⠯⠽⠐⠿
⣀⣈⣀⣈⣛⣛⣋⣙⣻⣃⣨⣛⣼⣉⣈⣷⣈⣙⣛⣓⣃⣀⣈⣀⣰⣛⣀⣉⣉⣀⣀⣀⣈⣀⣀⣘⣉⣁⣀⣀⣁⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣿⣧
⠀⠀⢀⣠⣴⣶⣶⣆⣀⠀⠀⠀⠈⠀⠛⢶⢾⣿⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣿⣿⣷⣄⠐⣤⣷⣄⡀
⠀⠀⠈⠉⠉⠙⠉⠵⡤⠀⣀⣀⣀⣀⣀⠐⢛⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⣆⣼⣿⣧⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⡇⢰⣿⢹⣟⠀⠀⠀⠀⠀⠈⣿⣿⡏⢹⣿⡟⠁⠀⠹⣿⡀⠀⠀⠀⠄⠂⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⣤⣩⠛
⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠸⣀⡀⢀⣁⢸⡟⠀⢻⡆⠀⠀⠀⠈⠁⠉⠉⠁⠈⠉⠁⠐⠀⢀⣿⢿⡆⠀⠀⠀⠘⠛⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠈⠉⠻
⠀⠀⠀⠀⢀⣻⣟⢈⣿⣇⢘⣿⣃⣘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠘⣷⠀⠀⠀⠀⠀⠰⠟⠛⢹⡇⠀⠀⣸⡿⠉⢿⡆⠀⢠⣶⡄
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⠆⠉⠀⠀⠚⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⢀⣀⣠⡦⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⡟
⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡆⠀⣿⣷⠀⠀⠛⢣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣆⣠⠄⠀⢠
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣷⣀⡿⠟⢻⣿⡀⠀⠀⠀⠀⣀⣶⣶⣷⣶⣤⣜⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠉⢀⣀⣀⣲⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠀⢻⣿⣿⣹⡅⠀⣴⡾⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠇⠀⠀⠀⠀⠀⠀⠀⣽⡇⣿⠀⠀⢿⣿⠟⠻⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⠀⠉⠉⢉⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⡄⠀⡄⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣶⣶⣤⡂⢠⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣼⣿⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠁⠀⢩⣤⣤⡙⠁
⠀⠀⠀⠀⢰⣿⢻⣿⠉⠉⡉⠁⣀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠈⠿⠇⣴⣤⡀⢸⣿⣿⣏⠀⢠⣶⡆⠀⠀⠀⠀⠀⢀⡀⠀⣶⣾⣿⡄⢀⣘⠛⠛⠛⠁
⠀⠀⠀⠀⢸⣿⣴⣿⠀⣿⠓⢸⡙⢰⡟⠂⣿⠃⠀⠀⠀⠀⠀⣰⠄⠀⠈⣿⣿⠄⢿⣿⡏⠀⣿⣿⣿⠆⠀⠀⠀⢀⡿⢿⣤⣿⣒⣾⣧⣿⣻⡇⣀⢀
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠐⣿⡋⣁⣀⣼⣿⡇⠀⢸⡿⣇⠀⠀⠀⠀⠋⢁⣽⣿⡿⠉⠙⠋⠛⠿⠟⠋⠛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⠷⣶⣤⣾⣷⣿⣿⣿⣿⣿⣶⣾⠃⣿⠀⠀⠀⠀⠀⣨⣿⣿⠃⠀⠀⠈⠉⢀⣀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠸⣧⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠹⠇

⣶⣶⣶⣶⣾⣿⢿⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⣶⠶⣾⠶⡾⣶⣶⡶⠶⢾

⠀⠀⠀⠀⠀⠀⠀⠀⣉⠂⠀⣉⡃⠀⣇⡇⠀⠀⠀⠀⠀⠀⢠⠐⠈⠉⠉⠁⢂⠜⠃⠀⠀⠀⠀⠀⠀⠀⣸⢀⢒⣯⡇
⠀⠀⠀⠀⠀⠀⠀⡎⠤⠁⠈⠤⠸⠘⠠⠈⠀⠀⠀⠀⠀⢠⠁⠊⢈⠑⢊⠜⠑⠈⡄⠀⠀⠀⠀⠀⠀⠀⠩⡉⠉⢉⠋
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠎⠘⢤⠞⠘⣤⡜⠀⠀⠀⠀⠀⠸⢀⠵⡁⠙⠁⢀⠌⠀⡇⠀⠀⠀⠀⠀⠀⡀⠤⠿⣈⠧⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣧⢅⣠⡽⣄⣀⢯⣇⠀⠀⠀⠀⠀⠀⠡⣀⠈⠢⠔⠁⢀⠜⠀⠀⠀⠀⠀⠀⡘⠀⡔⢑⠉⣤⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠑⠓⠚⠚⠒⠓⠓⠚⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠓⠒⠃⠒⠒⠒⠚⠒⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡖⣄⣰⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⢈⡁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⣈⣀⠀⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠔⠀⡷⢿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠠⡄⠀⠀⠭⡀⠀⠀⠀⠀⠀⠀⠗⠘⡓⠼⡀⠀⢺⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢲⠟⠿⠧⣼⠐⠶⠀⠀⠀⠀⠀⠀⠒⡄⠀⠐⠆⠀⢰⠀⠃⠀⠀⠀⠀⠀⠈⢄⠺⡹⠲⡹⢀⡔
⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤⢀⡐⣂⠽⡆⠈⠀⠀⠀⠀⠀⢠⢣⢹⡀⢘⡃⢀⠋⡜⡄⠀⠀⠀⠀⠀⠲⠊⠁⣰⢆⠱⢎⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠉⠉⠑⠜⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠣⠤⠤⠇⠀⠱⠁⠀⠀⠀⠀⠀⠒⠒⠤⠤⠄⠊⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡢⣔⡆⠠⡲⠀⠀⠀⠀⠀⠀⠀⠠⠒⣒⢒⡒⢒⣒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⢔⡲⠁⠀⡧⣇⠀⠀⠀⠀⠀⢰⢁⣈⣋⣀⢑⡠⣲⣄⠀⠀⠀⠀⠀⠀⢘⠰⢦⣥⠄⢐
⠀⠀⠀⠀⠀⠀⠀⡜⠓⠄⠉⠙⡆⣸⠀⠀⠀⠀⠀⠀⠀⢸⣸⣤⣤⣼⣨⣀⣍⢸⠀⠀⠀⠀⠀⠀⠘⠄⠀⢁⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢣⢠⠂⢢⢰⠋⢹⢢⡎⠀⠀⠀⠀⠀⢸⣠⠤⠠⡄⡇⢈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠐⡄⠊⠉⣵
⠀⠀⠀⠀⠀⠀⠀⠸⠼⠀⠸⠼⠀⠸⠥⠇⠀⠀⠀⠀⠀⠸⠘⠤⠠⠇⠱⠬⠭⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠃⠤⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠐

⠀⠀⠀⠀⢠⡄⠀⣀⠀⠀⠀⢰⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠘⠁⠋⠄⠀⠀⠛⠈⠀⠚⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡆⠀⠀⠀⠁⠐⠀⠀⠁⠀⠀⣴⣶⣿⣿⣿⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣶⣄⠀⢀⠀⣠⣶⡄
⠀⠀⢠⠂⠀⠀⠘⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠀⠀⠀⢀⠠⠀⠀⡀⢀⠀⠀⢿⣿⡿⢿⡟⠛⣿⡛⢿⣿⡄⠀⠀⠀⠀⠀⠙⢟⢀⡁⡀⠸⠋
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⢀⣿⣛⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣦⢑⠀⣦⣀
⠀⠀⠑⠦⠌⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠸⣿⣿⣿⣿⡄⣿⣿⢿⣿⡇⠀⠀⠀⠀⠺⣿⠟⠉⠀⠀⠙⠿⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂⠄⠐⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠸⠗⡀⢀⠀⠀⢿⣿⣶⣿⣧⣽⣷⣿⣿⡇⠠⠤⠄⠀⡀⠀⠀⠂⡠⠂⠐
⠀⠀⢡⠃⠐⡀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠈⡔⢈⠄⠀⢀⣁⠨⡄⠂⠀⠀⠀⠀⡅⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠉⠉⠀⠐⡴⠖⢶⠷⠶⠲⠶⡷⠶⠹⠶
⠀⢀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠍⢁⠀⠀⠈⠉⠱⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠈⠂⠀⠀⠀⠀⠀⠓⠀⠂
⠀⠂⠀⠘⠀⠌⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⣤⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠠⠃⠼⡁⠀⠘⠀⢊⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐
⠀⡀⠀⠠⠀⠀⠈⡀⠀⠀⠀⠀⣆⠀⠀⠁⠀⣼⣿⣿⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⠀⠙⠁⠈⢀⡀
⠀⠀⠀⠀⠔⠢⠔⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠉⠉⠉⠈⢠⣅⠰⠆⠀⡀⠀⠐⠗⠀⡖⠄⠀⠀⠀⠀⣶⣤⠀⣀⣀⣀⣴⡆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣐⠀⠀⢀⡄⠀⠀⠀⢨⡄⠀⠈⠀⠀⣄⠀⠀⠀⠀⢈⡀⠀⠄⠠⠀⠠⠀⠀⠔⠀⠀⠀⠀⠀⠀⠙⢶⣤⡴⠟⠋⠀⠀⠀⠀⡠⠠⡀⠀⠀⠀⠀⠀⠐
⠀⠛⠂⠉⠀⠀⠈⠀⠀⠀⠀⢘⠀⠀⠁⠀⠀⣿⡀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠤⠒⠄⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⢻⠇
⠀⠀⠡⠀⠀⠀⠀⠀⠀⡀⠀⠈⡁⠅⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠙⠒⠋⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⠀⠃
⠀⠀⠀⣣⣬⠀⠀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⢸⣻⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⣀⡀⠀⠀⠉⢉⣻⣯⡉⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⣀⠀⢠⡀⢄⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⠀⠒⠀⠁⠀⠸⠿⠇⠀⠀⣦⣬⣹⣋⣡⡆⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠉⠁⠒⠂⠀⢀⠊⡉⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠿⠿⠿⠟⠃⠀⠀⠀⠔⠏⡦
⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⠀⠀⠀⠀⠀⠈⡄⠀⢀⠀⠀⠀⠠⠀⠒⠒⠂⠐⢤⠀⠀⠀⠀⠀⠀⠘⢃⠀⡀⠀⠓⢀⠀⠀⣾⣷⠎⠀⢀⡀⠀⡀⠢⡤⠆⠘⡀
⠀⠀⠸⠿⠿⠟⠛⢛⠉⠁⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠘⠁⠂⠀⠀⠉⠉⠀⠀⠘⠀⠀⠙⠀⠀⢠⡃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⢠⢄⠀⠀⠈⣀⢀⣀⡁⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠤⢀⠀⠀⠀⣠⣶⡄⠀⡀⠃⠀⠈⢈⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⢉⠌⠀⠁⠀⠀⠠⢚⠀⠀⢀⠉⠀⠛⢁⠜⠀⠀⣠⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠙⠁⣀⣾⠀⠀⠀⣿⣿⣿⢀⡀⠰⢦
⠀⢠⠀⡄⠀⠨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠁⠀⠈⠀⢄⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢡⣀⠀⠀⡀⣀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠐⠀⠐⡀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠰⠀⠀⠆⠀⠀⠂⠈⠀⠀⠀⠀⠀⠉⠈⠘⡆⠉⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⢤⣤⣶⣦⡀⠀⠀⢰⠘⣀⡀⠀⠀⠤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠛⠂⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠂⡤⠄⠀⠀⠀⠀⠄⠀⠀⡂⢠⠀⢀⠀⢠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢠⠞⠀⠀⢀⠀⠀⢀⣶⡶⡀⠈⠀⠚⠁⠉⠀⠁
⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠊⠀⠀⠀⠀⠀⠀⠣⠰⠜⣤⠀⠀⠀⠀⠤
⡌⠀⠁⠐⡊⠉⠁⢠⣦⣆⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠻⠿⠀⠔⠀⠀⠀⠀⠀⠀⢀⠐⠐⠈⢠⡠⠀⠀⠀⠘⣧⡀⢃⢙⡀⠃⠀⠀⢀⡀⢀⡠⡀
⠀⠁⠲⡀⠁⢀⠀⠈⣿⣿⠀⠈⠂⠀⡀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠂⠀⠡⠅⠉⢁⠁⠀⠂
⣤⣴⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣻⣏⣹⢉⣻⣋⣽⡟⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⡀⠐⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⠀⠀⠀⡈⣿⠤⠄
⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⣿⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠊⠀⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠢⠀⡀⠔⠈⠓

⠀⢀⣄⣸⣿⣗⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠄⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠻⢿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⢺⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣬⣫⡀⢸⡇⠀⠀⣠⣤⣤⣄⠀⠀⠀⠈⢻⡀
⠀⠀⠁⠸⠿⠟⠀⠁⠀⠀⠀⠀⠸⣿⠟⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⢿⣿⡇⠀⠀⠻⢿⠿⠟⠁⠀⠀⠀⠸⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⣰⡿⠂⠀⠀⣠⠞⠳⣄
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⣿⣿⠋⣠⡈⢿⣿⡇⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣠⡞⠁⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣈⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⢠⡄
⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣉⣁⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣁⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀
⣿⣿⢛⠻⠟⡻⢻⠟⣿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⣿⣿⡇⢤⠄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀⠀⠀⠀⠘⠃⠀⠀⠀⡤⠤⣀⣶⣶⡦⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⣿⣿⡇⠼⠄⠀⠀⠀⠸⢢⠆⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠩⢹⡇⠀⣿⠿⠿⠟⠛⠋⠀⠣⣰⣾⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⡷⠤⠴⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⢠⣶⣾⢸⡀⠀⠀⢠⡎⠉⠉⠉⠉⠉⠀⠀⠀⢀⠄⢠⢰⡆⣿⡇
⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣼⡇⠀⢬⣿⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠛⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣀⣀⣀⣀⣘⣃⣿⡇
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠒⠒⠀⠀⠀⠀⣶⣦⣤⠤⣤⣤⢤⣤⣤⣤⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡓⣿⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠚⠛⠛⠛⠀⠀⠀⠀⣿⣿⣶⡇⠀⠀⢀⣀⣠⣤⠀⠀⠛⠉⠀⠁⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⡶⠆
⠀⠀⠀⠀⠀⢀⣀⠀⣠⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⢠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⠻⢯⣀⠀⠀⠀⢸⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣀⡊⠓⠲⢻⠀⠀⠀⢸⣷⣿⣾⣿⣿
⠀⠀⠀⠀⢈⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠀⠀⠀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠛⠛⠒⠀⢸⠤⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⢫⠀⠀⠀⠀⠀⢶⣦⣤⣴⡾⠉⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⠻⠟⠿⠟⢃⡀⠀⠀⠀⠛⠘⠳⠁⠠⢸⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠤⠴⠦⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠤⢊⠀⠂⠒⠒⠬⡑⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⢀⠔⡨⠄⠒⠈⠉⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠐⡀⠇⠀⠀⡀⠖⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⢊⠔⡩⠂⠡⠀⠀⣠⠖⠄⠀⢹⠀⡄⠀⠀⠠⡀⠀⠀⠈⠀⠀⠱⡀⢢⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡐⠁⠠⠊⠀⠀⠀⠀⠀⠣⠀⠀⠴⠉⠐⠇⠀⠀⠐⡄⠀⢁⠂⠀⠀⠀⠀⠀⠁⠡⡀⢆⢀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡈⠀⠁⠀⠀⠀⠐⠀⠘⢇⠐⠈⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢀⠀⠶⠀⠀⠀⠀⠙⠂⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠇⠘⠀⠀⡛⢉⡖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢰⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡹⡷⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⡁⠀⠰⢠⠆⠀⠀⠀⠀⠕⠀⠁⠀⠀⠄⠠⠀⡀⢢⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⡀
⠀⠀⠰⢣⠀⠀⠀⠀⠀⠀⠀⠉⣀⠠⠾⡦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠄⠉⠀⢀⠀⠀⠂⠀⠀⠀⠀⣷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠐⡀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⡈⠠⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠑⠂⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠂⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠂⠂⠀⠂⠀⠄⠐⠀⣤⠀⡆⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⢀⡀⡄⠀⢰⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠊⠀⠀⠀⠉⠣⡀⠀⠡⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠶⠛⠋⠛⠋⠀⢏⠉⢣⡢⡀
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⡣⠈
⠀⠀⠠⠈⠀⠁⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⢜⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡢⢀⠀⣀⡀⠀⠀⠉⠢⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⣴⠛⡏⠉⠷⡀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⣤⢴⠆⠈⠁⠒⡭⠄⠀⠀⠚⠉⠀⠀⡀⠀⢀⡡⠀⠦⠌⢛⠡⠂⠀⠘⣄⢀⠾⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡗⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠊
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢄⠀⡀⠄⡧⠀⠀⠀⠠⠀⠀⢸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⢀⠔⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠑⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡜⠃⠀⠀⣀⠄⠈⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠂⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠚⠀⡠⠁⠀⠰⠇⠐⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⡄⠀⠀⠀⡀⠀⠄⠀⠀⢠⠀⠀⡠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢠⠀⠠
⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠁⠀⠈⠀⠀⠆⠀⠃⠀⢸⠀⠠⠀⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄⢀⡴⣇⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣴⣾⡀⣆⣠⣦⠖⠀⢸⠀⢠⡄⢒⢫⣴⣷⣿⣅⠀⠀⠀⠀⠀⡀⢦⢎⠃
⠀⠀⢀⣼⢉⣼⣿⠟⠞⢁⣼⣾⡾⢰⠇⠀⠙⢾⠯⡽⣿⡷⢀⢴⢐⣆⡘⣿⣿⡟⡳⠇⠀⠀⠀⠀⡀⡄⠠⠤⠬⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠉⣁⠀⣸⡿⠇⣀⣒⠀⢲⡈⣩⣆⣄⣾⣴⢎⠲⢑⣠⣃⠈⠠⣤⣒⠊⠀⠆⠀⠐⠇
⠀⠀⠀⠀⠀⠀⡂⠀⡀⢡⡄⡠⠨⣱⣏⣯⠁⠀⠀⠀⣀⣶⣿⠦⢅⠀⠄⠋⢩⢤⡯⢤⠀⢉⣀⠆⠤⢤⢲⠆⠂⢀⣴⠂
⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠙⢿⡅⢌⠀⠀⠳⠀⠀⢉⠁⡆⠈⠁⠀⠘⠉⣉⠁⠀⠀⠈⠉⠁⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠓⠘⠑⡞⠒⠓⠻⠘⠛⠐⡶⠀⡟⠉⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⢖⢀⣀⡂⣟⠂⡐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠉⠡⠌⡁⠀⣐⠂⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢁⣀⣀⠀⠀⠀⡀⢄⠀⠈⠊⠀⠐⠂⠐⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠈⡱⠊⠓⠠⠀⠤⠂⠁⠀⢎⠀⡠⠔⠀⢀⠀⡀⡀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⡀⡨⠂⠢⠄⠀⠁⠀⠀⠁⠑⠄⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠘⢅⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠐⠠⢄⣁⠀⢬⡄
⠀⠀⠀⠀⠀⠀⣤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⠉⠁⠐⠐⠃⠂⠤⢀⢁⡀⢀⠀⠀⠀⠀⠀⠀⢁⠄⠘⠒⡀⠀⢢⡀⠠⠤⡀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠐⠂⢁⣀⡀⠸⡀⠀⠀⠐⠀⠀⠠⠂⠀⠀⠡⠌⠀⠁⠐⠃⠀⠠
⠀⠀⠀⠀⠀⢠⠈⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠲⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠁⡅
⠀⠀⠀⠀⠀⠀⡀⠠⡈⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡄⠀⠀⠀⠀⠀⡀⠤⡾⠃⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⢄⠐⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⣐⠣⡀⢀⣀⠐⠒⠊⡘⠁⠀⠸⠄⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠔⠁⠔⠍⠀⠈⠉⢀⠡⠞⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢈⠙⠋⠒⠒⠲⠖⠀⣀⣀⣀⣀⡒⠈⠅⠀⠒⠈⡠⠴⠁⠀⠦⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠀⠤⠤⠤⠤⠤⠀⠐⠂⠀⠁

⠀⢹⡀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠐⠒⣀⡀⠀⠀⡐⠀⢸⡃⠀⠗⠀⠀⣱⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠸⠀⠀⢰⠂⠸⠤⡀⠉⠩⠚⠁⠐⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢺⠸
⠀⢸⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠧⠈⢀⠀⡄⠀⠀⠀⠀⠀⠀⠠⡄⠀⠁⠁⠀⠀⠀⠀⠀⢣
⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡈⠀⠀⠀⠀⣼
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣀⡀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⡀⣠⣧⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢲⣺⠀⠀⠃⠀⣠
⠁⠈⠹⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠄⠛⠚⠛⠉⠀⠀⠉⢆⠀⠀⠀⠀⢀⡠⠔⠁⠀⢀⠠⠋⠀⢠⠖⠘⠓
⢠⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠔⠊⠁⠀⠀⠀⠀⣱⠁⠀⠀⡇
⡉⠀⠀⠀⡟⠀⠀⢄⠠⠀⢀⢀⠀⠄⠈⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠄⡙⠀⢘⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢱⠠⡀
⣀⣀⣜⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣀⣀⡠⠬⠔⠊⠀⠀⠈⢆⡃⠀⢀⣀⠴⠁⠀⠀⠀⠀⠀⠳⣵⣄
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠐⠒⠂⠠⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀
⠀⠀⠀⠀⠈⡆⠀⠈⠌⠂⡲⠄⠠⠔⢀⠀⠀⠀⠀⠐⠴⠋⠀⠀⠈⢳⡀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠐⠒⠋⠑⠒⠃⡀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠀⠈⠀⠀⡇⠀⠀⡠⠊⢀⡃⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠐⠁⠀⢀⠃
⠀⠀⠀⠀⡠⠊⠀⢀⢀⡀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠈⢠⠄⡄⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠂⠐⠐⠈⠀⠀⠀⠈⠿⢏⠀⠜⠓⠀⡀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀
⠆⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠎⠁⣀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠂⠀⠀⠀⠀⠀⡔⠈⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣄⣹⣥⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢢⠀⠀⠀⠀⡌⠁
⠀⠀⠀⣠⠁⠀⠀⠈⣀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠘⡨⠼⣫⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠱
⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠻⠆⠄⠐⣀⠞⠀⠀⠀⢇⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠱⡀
⠐⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠁⠀⠀⠀⠀⠀⠀⠉⠒⠛⠒⠚⠁
⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡡⠄⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⣀⣁⢱⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⢿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⠇⠀⠀⠀⢀⠄⠀⠀⠉⠙⠒⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⢀⣤⡀⢀⠀⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢮⠀⠀⠀⠀⠀⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⠖⠒⢦⡀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⢹⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⠈⠓⠚⠉⢀⣠⣿⣿⣿⣿⡿⠿⠛⣩⠟⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠙⠤⠤⡤⠟⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢿⠉⠉⠉⠉⠉⠉⠁⠀⠀⡠⠞⠁⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⢁⡏⠀⠀⠀⠳⣄⣀⣀⣀⣀⣤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⠉⢹⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⢛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⡤⠃⠀⠀⠀⠀⢰⠃⠀⢠⠀⢀⣴⠟⣩⢞⡹⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠁⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⡇⠀⠀⠀⠩⢞⡽⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⡤⣼⠖⠃⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠊⠀⠀⣇⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⡤⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀
⠀⠀⠀⠀⠀⢀⡠⢔⠂⠀⠄⠀⠀⠀⠂⠀⠀⠉⠢⠑⡀⠀⠀⠀⣠⡤⠀⠀⠀⠤⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠄⢁⠪⢀⠀⠠⡀⠉⠑⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡩⣫⣵⣤⣀⣠⣄⡀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠐⠁⠐⠁⠀⠀⠀⠸⠀⠀⠔⠃⢆⠀⠀⢂⠀⢃⠀⠀⢈⢨⠀⠁⠊⢡⢄⣐⠟⠋⠀⠀⠀⡤⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠘⠀⠙⢄⠂⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠘⢃⠀⡀⠀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠠⠤⠀⠀⠀⡠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠆⠀⠀⠀⠘⣿⣇⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢠⢀⡄⠀⡀⠁⠢⢐⠀⠀⠀⠀⠀⠀⠒⠒⠰⠦⠤⠤⣄⡀⠀⠀⠓⠀⠀⠀⠄
⠀⢠⢣⠀⠀⠀⠀⠀⠈⢁⠤⢾⡧⣄⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠉⠀⠀⠀⠀⠀⠀⠀⡐⠐⠏⠃⠀⢹⠁⢰⠋⢢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⣀⣀⠠⠄⠀⠀⠀⠀⠀⠀⣤⠀⠀⣄⡀⠀⢸⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⢰⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢣⡀⠀⡄⠀⠀⠀⠀⠀⠀⢰⣂⣀⠀⢰⠀⢠⡀⡘⠀⠀⠀⠀⢀⠀⠤⠄⠄⠀⠀⠀⠈⠀⠀⠀⠀⢈
⠀⠀⢀⠔⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⡉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠮⠁⠀⡐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠸⡀
⠀⠀⢀⠀⠀⠂⢄⢐⣋⠀⠘⠢⡀⠀⠀⢠⡤⠂⠀⠐⡄⠘⠒⡄⠀⠀⢸⠉⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢸⡄⠀⠀⠂⠋⣨⢇⣂⡀⠀⠢⡀⢤⠀⠀⣴⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⢠⠑⠂⠀⠤⠴⠇⠀⠀⠈⠐⠄⠈⢀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⢸⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠑⢄⠒⠐⠚⡇⠀⠀⣀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠂⠢⠄⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠈⠓⠤⠀⢀⠺⡤⡤⠟⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⡓⠀⠀⢀⠀⠒⠉⠉⠉⠛⠃⢦⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⡀⠀⠀⠘⠛⠁⠀⣠⡦⠀⠀⠀⠀⢀⠉⠀⠀⠙⣇
⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⢠⣿⣾⡀⢀⠀⠀⠀⠀⠠⢀⠄⣿
⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠊⠁⠀⠈⣷⠊⢡⡄⠁⠀⠀⠀⠀⠄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠲⠟⠀⠠⠈⠃⠀⠀⠀⠀⠀⠙⢉⣄⣐⠂⠀⠀⠀⠈⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠶⣝⠟⣵⡿⣱⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣵⢛⣷⣬⣥⣾⣮⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣜⠿⠿⠿⠿⠿⣣⣿⣿⣿⣿⡿⢟⣠⣤⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣶⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣝⣋⣴⣿⣿⣛⣛⣛⣛⣛⣛⣻⡟⣱⣿⣿⣿⠏⠁⠺⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣝⣫⣾⣿⣿⣛⣛⣛⣻⡿⣣⣿⣿⣿⣿⠏⠀⣀⣤⣶⣶⣾⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣱⣿⡟⣛⣭⣷⣶⣶⣶⣭⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣝⣫⣾⣿⣿⣛⣛⣿⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠉⠉

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⣧⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢹⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣼⠁⠐⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦
⡀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣀⠠⡁⠢⣉⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠦⡤⠷⠬⠷⠜⠓⠛⠁
⢀⢀⢀⢀⡀⡀⡀⡀⡀⡀⡀⢀⢀⢀⢀⢀⠀⠀⡀⡀⡀⡀⡀⢀⢀⢀⢀⢀⢀⠀⡀⡀⡀⡀⡀⡀⢀⢀⢀⢀⢀⠀⠀⡀⡀⡀⡀⡀⠀⢀⢀
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠔⢢⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣠⠒⣀⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢦⣴⣠⠄
⠀⠀⠀⠀⠀⣠⢄⡸⠀⡞⠀⠀⠀⠀⠹⣶⢸⣿⠁⠀⢠⠾⠉⢓⡔⠃⠀⠀⠠⠀⠀⠀⢠⣾⡻⢟⡾⡱⠏⠀⠟⣢⠀⢀⡴⣫⠀⠂⠀⡬⢋
⠀⠀⠀⠀⠀⢣⠀⢷⣤⠖⢰⠀⠀⠀⠀⣇⣰⡶⠃⠀⢻⠐⠡⠀⠀⠠⠀⠀⢀⠇⠀⡔⠋⠂⠁⠈⠀⠀⠀⠀⡸⠁⠀⣸⠃⢀⡀⠐⠂⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠳⢾⣿⠒⠁⠀⠀⢀⣾⡇⠀⣱⠀⠀⠈⠣⢀⠈⠀⠀⢀⣢⠎⠀⠀⠁⠉⠂⠄⠀⣀⣀⡠⠞⠁⠀⠀⢻⠋⠈⢁⡄⠒⢀⠜
⠀⠀⠀⠀⢀⡴⠒⠚⠓⠒⠒⢄⠀⢸⣏⠀⠀⡿⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⣄⠀⠀⠀⠀⠘⢘⣋⣈⡴⠛⠁
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡐⠀⢸⣴⠇⣼⠃⠀⠀⠀⠀⣠⠄⡶⣠⣫⠦⠤⠀⠀⠀⢠⣿⣯⠻⠾⠟⠋⣧⠀⠀⠀⠀⠀⠉⣁
⠀⠀⠀⠀⠈⠓⠂⢤⣀⠔⠈⠀⠀⢸⡟⢠⠃⠀⠀⠀⠀⣜⡕⡠⠁⠈⠡⢜⠀⠈⡆⠀⢹⠃⠾⡷⢘⡿⠫⡇⠀⠀⠀⠀⣀⠤⣿⠇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠯⠃⠀⠀⠀⠀⢰⡿⢠⡖⣣⠀⠀⣸⠇⢰⠇⠀⠀⠁⠀⠠⠤⠀⠀⠇⠀⠀⡴⣻⠀⠀⠻⠄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠀⠀⡀⢤⡠⢀⠀⠀⢸⡇⢸⣷⡇⠀⢠⡟⢀⡜⠀⠀⠀⠀⡀⠤⠂⠉⢲⣄⠀⢸⡫⣿⢣⢆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠟⢋⣴⠏⠐⣍⣽⡛⠛⡞⣁⠄⠘⢧⣿⡻⣧⣴⣿⣧⠞⠀⠀⠀⡴⢋⡤⣂⣦⠀⢸⢇⠀⠘⣿⠡⠢⠂⠉⠂⠀⠀⢠⠟
⠀⠀⠀⠀⠀⡠⢾⠂⣍⠉⠁⠀⠀⠳⡼⢿⣀⣸⣴⠀⠀⠀⠀⠙⠛⠘⠛⠁⠀⠀⠀⢸⡁⠸⣿⣇⠟⠀⡿⡸⠀⠀⠈⠑⠦⢤⣄⣤⠞⠖⠉
⠀⠀⠀⠀⣼⠁⠈⠀⢸⡀⠀⠀⠀⠀⣗⣻⡟⡾⠀⠀⠀⢀⣀⣤⡆⠀⠀⠀⠀⢀⣤⠘⡧⠀⢀⣀⣠⠞⡑⠁⠀⢀⣀⣤⣤⣌⡉⠁
⠀⠀⠀⢀⣿⠆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣛⡝⣋⣀⣀⠀⣀⣴⠏⡟⠀⠈⠁⠀⠀⠀⠁⠀⢠⣞⢁⠀⠀⠀⠀⠈⡆
⠀⠀⢀⣾⣿⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⣀⣀⣙⣷⣾⠿⠟⠛⠋⢁⢰⡿⠋⡸⠁⠀⠀⠀⠀⠀⢀⡀⠀⢻⡿⠂⡀⣀⣴⠊⠁⠂
⠀⠀⢸⢟⠟⣰⠀⠀⠀⠀⢸⠀⠀⢀⣶⠉⣸⠁⠀⠀⠀⠑⠄⠀⠀⢙⢻⡁⠈⠀⠀⠀⠀⠀⠀⣀⢸⡇⠠⡀⠙⠒⠀⣿⠰⣝⠔⣀⠀⣀⠀⢸
⠀⠀⠘⢯⡐⣥⠏⡆⣀⣠⠏⠀⢀⡏⢪⠀⡗⢨⠄⠀⠀⠀⢸⠀⠀⠘⠀⠉⠢⣀⠀⢀⠀⠀⣰⡇⣸⡇⠀⠱⠀⠀⠀⠈⠂⠨⠧⣀⣠⣡⠴⠋
⠀⠀⠀⠀⠉⠛⣾⡞⠋⠀⠀⠀⠘⡇⠁⢄⣧⠀⡤⠀⠀⠀⡼⠀⠀⢴⠠⣄⢼⢉⣁⣀⠇⠀⣿⡅⢿⣩⠀⠀⡇⠀⢀⡀⠀⠀⣤⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⣹⣌⠐⢀⣠⠞⠁⠀⡇⣬⠀⡼⠈⠛⠚⠋⠀⠀⠸⡖⢸⣏⠆⣠⠁⠀⠀⢳⣯⠘⣯⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠀⠀⠀⠀⠀⠀⠉⠁⠉⣉⡁⠀⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⠞⠁⠀⠀⠲⡸⢛⣛⡻⠋⡷
⠀⠀⠀⠀⠀⣴⣏⣿⠏⢻⣇⠀⠀⠀⠀⡠⠒⢸⠏⠉⢀⡶⡉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠙⢢⣠⠅⠠⡀
⠀⠀⠀⠀⡔⢻⣹⠟⢳⣸⢾⡀⠀⢀⡾⣡⠀⠈⢹⢀⡼⢁⠵⠄⠈⠋⡆⠀⣠⣾⣏⠷⠚⠁⢰⣆⠀⠀⠀⠀⢀⣾⠗⢱⣂⠾⠬⡁⣋⠸⡀
⠀⠀⠀⠘⣧⣧⣿⢄⢸⠁⠀⡇⠀⢸⢡⡟⣀⠀⢻⠋⠀⠀⢡⠀⢸⠀⡵⠀⢿⣡⠀⠀⠀⠀⠀⠒⡘⠀⠀⠀⣼⣿⣡⣼⡣⢀⣠⠍⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠿⡴⠞⠀⠴⠁⠀⠸⡏⢿⡏⠀⡞⠘⠀⠆⠈⢀⡏⢠⠇⠀⢿⠁⠁⠀⠰⢆⠀⠀⡀⠠⠀⠀⣯⠑⣶⡏⢌⢦⡄⢠⢀⠤⡇
⠀⠀⠀⠀⠀⢀⠀⠿⠀⠀⠀⠀⠀⠀⠳⣌⢷⣸⢧⢀⡼⢀⠴⢋⡴⠃⠀⠀⠀⠁⠈⢱⠘⡣⠉⠀⠁⠀⠀⠀⠹⡶⢣⡮⢯⣹⣶⣇⢎⡼
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠏⠁⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠪⠷⣞⠿⢽⣿⠟⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣷⣶⣤⣾⣿⣿⣿⣿⣷⣾⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢻⣽⠗⠿⠋⠹⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⣫⡟⠁⠊⠀⠀⠠⠄⠀⢫⣿⠝⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠛⠻⢿⣷⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣇⠃⠆⠀⡔⠸⣫⣰⠀⠆⠠⡜⢇⣿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⣀⠀⠀⠨⢝⡻⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⢈⣅⢈⠋⠏⠀⠀⣠⠀⢸⣏⣯⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠇⠀⠈⠉⠐⠟⣂⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣯⡠⣄⠐⣧⡄⣁⠀⠂⢀⣩⠄⡾⣸⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣮⠐⠀⠏⠉⠀⠈⠭⠋⣸⠖⣻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⢀⣼⣿⣿⡀⠀⠀⠀⠀⠙⠛⢹⣿⣿⣿⣿⣿⣿⣳⣶⣶⣶⣶⣿⣷⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠃⠀⠀⠠⣾⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠈⠛⣻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠁⠀⠀⠹⢿⡿⠟⠻⠿⠟⠁⠈⠉

⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣐⠤⣀⠀⠀⠀⠘⠁⡤⠞⠓⠄⢀⠠⠂⠀⠀⢀⣘⣷⣻⢆
⠀⠈⠒⠦⠘⠄⠀⢀⡰⠀⠀⠘⡆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⠀⠀⠘⠛⠮⠻⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠈⠐⠃⠀⠡⠖⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢠⠀⢄⡀⠀⠀⠙⠄⠀⠀⠀⠀⠒⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⠈⡀⢁⠀⠑⠀⠀⠸⣄⠴⠋⠱⡀⠀⠀⠂⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢁⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠤⠙⠂
⠀⠉⠃⠀⠈⠉⠒⠠⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠴⠒⠂⠀⠀⠀⠠⠀⡠⠃⠂

⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣀⡀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠉⠁⢉⠀⠈⢸⢳⠂⠀⢀⠴⠋⢠⠄⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠡⡀⠀⠀⠀⠀⠀⠀⠀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣱⠄⡀⢀⠠⠤⢐⡪⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠿⡺⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⢀⢃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣪⠀⠀⠀⠀⠀⠒⠏⣜⠠⢀
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠉⠉⠁⠢⠤⢒⢋⠎⠁⠉⠢⣄⠀⠀⡘⡘⠀⠉⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠌⠌⠀⠀⠀⠀⠈⠆⠰⠰⠁⠀⠀⠀⠈⡌⡀
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢸⢡⠃⠀⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡐⢄⠀⠀⢀⠴⡡⠃⠀⠀⠀⠀⠀⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠒⠈⡠⠔⠊⠀⠀⠀⠀⠀⠀⡰⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢀⠤⠊⣾⣿⣿⣦⠀⠀⠀⣀⠔⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡠⠔⠁⠀⠀⠻⣿⡿⠟⠈⠭⠁⠒⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡞⢐⣆⣤⡸⢦⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡖⠐⠒⠾⢤⡈⡹⠖⠋⠀⠀⠀⠁⠈⠈⠀⠉⢓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠚⡲⡄⢈⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣹⠁⠀⠀⠀⠐⢉⠤⠀⡀⠔⠒⠠⠀⠀⣠⠀⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠁⠀⠀⠀⠈⠑⢤⡀⠀⠀⢰⣲⠋⠀⠀⠀⣠⠖⢀⠂⠀⡀⠸⠧⠤⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⣀⣠⠚⠁⠀⠀⢁⣴⠋⠂⢨⡗⢚⠦⠄⠀⡀⡀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡟⠷⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣿⢿⣿⣷⣦⣀⡾⠛⠉⠀⠉⠉⠉⠀⠐⠠⣄⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠠⠀⢸⠐⡀⠀⠀⠀⠀⣼⡿⣧⡘⣧⣞⣩⣤⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⠀⢀⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡀⠊⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⣿⣀⣡⢽⣴⢯⡐⢆⣻⡃⠀⠀⠀⠀⠀⠀⠰⡄⢸⢄⢀⠁⠀⡀
⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠊⠀⢀⡴⠀⢀⡏⢠⣀⣀⡤⠔⠚⠉⠉⣹⣿⢛⡄⠋⠀⠀⠈⢢⠀⠀⠀⢀⡀⠶⠛⢪⢀⠏⡠⣚⠁⡀
⠀⠀⠀⠈⡢⠄⠀⠒⠒⠀⠀⠁⠀⡀⠤⠚⠕⠀⢀⠞⡠⢚⠍⠉⠉⠁⠂⢀⡞⢡⣿⠋⠀⠀⣀⣠⠄⡪⠓⢏⠁⠘⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠠⢋⡎⠀⠂⠀⠀⠀⢀⢀⡎⢀⢀⠃⠀⢀⣞⡿⣮⡟⠀⠀⠀⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠖⠈⠀⠀⠀⠀⠀⢸⡄⠀⠂⣀⡀⠀⠀⡸⢀⠀⠸⡀⢀⡊⠐⠛⠉⠀⠀⠀⡐⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⡀⠀⠂⠀⠻⣦⣀⣀⣀⣀⠴⠣⠂⠀⠀⠙⢯⡀⠀⢀⡀⠠⠐⡈⠔⠁⠀⠀⠐⠠⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠈⠀⠀⠀⠀⠀⠀⠁⠀⠒⠂

⠀⠀⢀⠠⠒⠀⠀⠀⠢⢀⠀⠀⠀⡠⠆⠤⣢⡀⠀⠀⡢⠄⣠⠄⠀⠀⠀⠏⠃⠡⠤⠈⡠⡄⢠⡀⢠⡀⠘⠑⠀⠀⠀⠠⠂⠛⠓⡆⠀⠀⠀⠀⠀⢀⣻⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡼⠁⣶⢐⡅⠁⠀⠀⢩⠋⠉⠐⠄⠀⠀⠈⢌⠀⠠⠅⢨⡆⠐⡂⢀⠔⡡⠀⠀⠀⠀⢢⡁⠀⠁⠇⠀⠀⠀⢠⡾⠥⠤⠔⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡣⠀⢀⠞⡡⠂⠀⠀⡄⠀⠀⠀⠨⡀⠀⠀⠀⠑⠨⢐⠒⠒⠒⡚⠅⠊⠀⠀⠀⠀⠀⡠⠀⠤⠄⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠐⠒⠒⠈⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⡈⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⡀⠀⠀⢠⠄⠲⠀⢄⠀⠈⠢⡀⠄⡰⠁
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠄⠀⠠⢀⠀⠀⠀⠀⠐⢄⠀⠀⠀⣠⠂⠀⠀⢀⠠⢀⣀⠠⢀⠀⠀⠀⠸⣀⡙⠦⣀⠀⠈⠀⠀⠉⡀⠀⠀⡠⠀⠀⠀⠈⠈⡀
⠀⠀⠀⠐⣧⡜⠀⠀⠀⠈⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠲⢦⣠⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⡪⡃
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠠⢔⣲⠒⢂⡢⠌⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢽⠿⠴⢅⡀
⠀⠀⠀⢀⠋⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡒⠊⣉⡉⠃⠂⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠐⠀⠂⢀⠀⠀⠀⢀⠊⠁⠢⠄⠀⠁⠀⠀⠐⠄⡀⠀⠀⠀⡀⠄⠀⠀⢧⡠⢀⢋⣁⡤⠸⠀⢀⠍⠡⡀⠀⢆⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠃⠙⠢⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠍⠉⠀⠔⠁⠀⡣⢲⠣⣿⡆⠈⠢⡀⢀⠀⢀⠔⠁
⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠦⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⢀⠤⠒⣾⡈⣴⠦⡀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠰⢲⢑⡐⠆⠀⠀⠀⠀⡈⠀⠀⣀⠁⠀⠀⠀⠀⣀⠀⠀⢻⡷⠤⠀⠀⠂⠐⢻⠗⠒⢯⠳⠘⡀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⠃⠀⠀⢰⣄⣰⠻⢎⡜
⠀⠀⢀⠄⠊⠉⠑⠠⡀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⣠⠊⢀⠀⡲⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠃⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠸⢍⣸⠠⠤⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠺⠀⠀⢌⡤⠀⠘⠁⠀⠀⠀⠀⢀⡀⠈⠂⠄⣀⣀⠠⠔⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⡠⠒⠉⠒⢄
⠀⠀⠢⢀⠀⠀⠀⡀⠊⠀⠀⠀⠊⠁⣀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢹⡇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠁⢀⠊⠀⠀⠀⠀⠀⠘⠄⠉⠀⠀⣄⠀⠀⠰⡚⠘⠳⢤⡤⢞⣰⠃⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠙⠢⠤⠤⠒⠉⢀⣠⡤⠒⡇⠀⠀⠈⢣⢀⠖⠁
⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠈⠒⠬⠶⠖⠋⠁⠀⠀⡀⣤⣲⢒⢝⣧⠼⡎⠉⠁⠀⣀⣤⣲⢪⢏⣹⡰⠚⠁⠀⠀⠀⠀⣻
⠀⠀⡤⠀⢀⣀⣀⣀⣀⡠⠄⠊⠁⠙⢯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠎⠯⣱⡣⠶⠊⠁⠀⠀⠀⢰⡦⠚⣵⡰⠧⠛⢉⡀⢀⢀
⠀⠀⠈⠒⠠⢀⡀⠀⠀⠀⢀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠉⠁⠀⠀⠀⠀⠀⠀⠠⠓⠘⠇⠀⠀⠀⠀⠇⠼⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⢻⣿⣿⣿⣿⣿⣿⣇⡴⣆⠹⡿⠋⠉⠁⠀⠀⠠⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠈⠋⠀⠀⠀⠀⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠛⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣦⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋⠉⠁⠉⠛⠃⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠈⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣶⣤⡀⢀⣠
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠉⠙⠛⠿⣷⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠦⣄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⣀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡄
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠒
⣿⣿⣿⣿⣿⠟⠁
⠘⣿⣿⠋
⠀⠘⢿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⡶⠾⠟⠛⠛⠛⠛⠛⠷⠶⣤⣤⣤⣤⣤⣤⠤⠶⠒⠊⠉⠉⠉⠙⠳⢦⣤⣀⣠⠆

⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠑⠀⠀⠶⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠢⡙⢆⡀⠉⣉⡀⡀⠩⠀⠰⠂⠙⠀⡰⣰⠀⠠
⠔⠠⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢄⡀⠀⠀⡆⠀⠀⠀⠀⠠⢈⠉⠀⠀⢨⡁⠀⠀⡙⠢⡀⠀⠀⠀⢀⡔⠔⣠⢮⡼⠁
⠐⠂⣄⠀⠀⠊⠂⡀⠀⡧⠐⢁⡠⡄⡀⠀⠀⠸⣀⣀⠀⠀⠄⠀⠡⠀⡄⢀⠁⠂⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠖⠋⠑
⠀⢀⠈⠀⠃⠈⢀⢐⠀⠀⠠⠍⠀⡀⢀⠐⠀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠰⠆⠀⢀⠠⠔⠀⠁⠀⠤⠠⠏⠀⡁⠀⠀⠌⠀⠆⠠
⠀⠀⠀⠐⠈⠀⠁⠨⠀⠀⠀⠀⠀⠶⠅⠠⡨⠀⠀⠀⠀⠀⠠⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠁⠀⠁
⠒⠂⠀⡀⢈⡁⠀⠀⡠⠂⠢⡀⠀⢀⣔⣽⠣⠁⡠⠒⠀⣈⡀⠄⠀⠀⠈⠀⠊⠁⠀⠐⠀⠀⢀⠀⠀⠤⠀⠔⠁⡇⠀⠀⠀⣀⡘
⠀⠀⡀⣉⢠⢀⠀⠐⠀⠀⠀⠃⢠⡵⠋⠄⠁⠀⠁⠆⠣⠀⠈⠁⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⡋⠀⠀⠀⠉
⠈⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠱⣞⡖⠀⡀⡀⠐⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⡀⠄⢀⠄⠀⠄⠄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣒⠒⠂⠀⠀⠀⠀⠀⠌⡀⡟⡁⠀⠀⢈⠆⠀⡀⢁⠁⡀⠀⠀⠀⠐⠊⠀⡀⠀⡀⠀⠐⠂⠜
⠀⠌⠂⡀⠀⠡⠀⠈⠁⠀⠀⠀⠀⠀⠀⠴⠃⡇⠹⠀⠀⠀⠀⠀⠀⢁⠀⡤⢨⠀⠀⠠⣀⠀⠀⣷⡄⠀⠈⠀⠁⠀⠀⠀⠀⠀⣤
⠄⠘⢀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡔⢇⠀⣃⣤⠁⠈⠠⣀⠄⠀⠀⠀⠶⠂⠀⠀⢀⠠⠄⡀⠀⠄⠀⠀⠀⠀⠈⠛⠀⠒⠒⠊⢀⠤
⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠌⠀⠀⠰⠀⣠⠀⠀⠀⠀⠸⠐⠂⠀⠀⠰⠅⡀⡂⢀⢔⠀⠰⠴⠃⡄⠠⠀⠀⠀⠀⠀⢀⠂
⠠⠀⠠⠄⠒⠂⢄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠌⠋⠀⠘⠁⠄⠐⠘⠂⠁⠂⠀⠀⠀⠐⠒⠅⣀⠄⠢⡀⠀⠄⢀⠈⢖⡰⠀⣀⣄
⠀⠅⠰⡂⠢⠄⠀⠅⠀⠀⠰⠀⢀⠔⠁⠀⠀⠤⠤⡞⠁⡀⠀⠀⠀⠀⠀⢃⠁⡄⠀⠠⠊⠀⠀⠀⡗⠀⢀⡌⠀⠉⠀⡀⢀⠀⠂
⠈⠀⠀⠏⠡⠂⠀⠂⠀⣄⡀⠤⠁⠠⢊⡡⡁⠐⠄⠀⠠⣧⠀⠀⠀⠀⢁⡀⢠⠀⠀⠅⠀⠀⢈⠈⠀⠀⢉⠀⠀⠀⠀⡀⠀⠐
⠀⠉⠈⠐⣀⠀⠀⠈⠀⠐⢀⠀⠀⠁⠠⠀⠈⡠⠂⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠑⠊⢀⡎⢀⡀⠃⠀⠐⠀⠒⠀⠀⠀⢀
⠄⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠉⠀⡁⠀⠀⠂⠀⠀⠀⠧⠔⠂⠀⠀⠀⠑⡀⠀⠂⠈⠈⠠⠀⡁⠀⡁⡀⠀⠀⡙⢈⠁⠀⠀⣠⣁
⢉⠂⡄⢊⠐⠁⠀⠀⠀⠀⠀⣀⠊⢀⡀⠀⢠⡠⡠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠙⡄⢁⠒⠀⠂⠈⢻⣿⠀⠀⠀⠀⠈⠐⠀⠀⠀⠒
⢀⠄⡉⠠⢎⠶⠀⠀⠀⢀⠆⠀⠐⠀⠐⠔⠐⠒⠀⢂⢀⡀⠀⠀⠒⠀⠀⣀⠀⠁⠄⠁⠀⠠⢤⠀⠇⠀⢀⠤
⢈⠀⠆⠀⠆⢺⣡⠧⠔⣸⠀⢀⠀⡀⠆⠀⠀⠀⠀⠸⠀⠉⠀⠀⠒⠉⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠈⠤⠈⢁⢆⡸
⠀⠀⠂⠂⠀⠡⠗⠆⠀⣆⠔⢠⣠⢀⠈⠂⠤⠠⠐⠁⢄⠒⢬⡀⠀⠀⣂⠀⠀⢀⢂⠀⡀⠀⠐⠒⠒⡄⠈⢀⡉⠈⠋⠀⠀⠀⢀
⠂⠄⢀⠆⠀⠀⢀⠀⠀⢀⡴⣲⢏⠂⣠⢠⡄⠐⠀⢤⡠⢀⠀⢈⠓⢊⠰⠁⠂⠡⠈⠈⠀⠀⠀⠀⢸⠀⠀⢉
⠘⠄⠋⠠⠐⠂⠀⠂⠀⠠⠟⠁⠂⠀⠀⠣⡕⣠⠊⠒⢝⡷⡒⠀⠀⠀⡀⠲⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠂⠀⠤⠀⠀⡠
⠀⠀⠁⠀⠀⠀⢀⠐⡀⠀⠂⠄⠀⠀⠀⢐⢻⣅⠅⠀⠀⠙⠙⠂⠀⠀⠁⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛⠊⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢃⠀⠀⠡⣰⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠃⠀⢿⢲⡦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠸⡷⠤⢀⡒⠲⢽⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠢⡀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠉⠀⠀⠈⠀⣄⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡗⠲⡄⠈⠀⠀⠠⠌⢀⣦⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣏⡄⠀⠀⠀⠀⠀⠀⠈⡄⢰⠀⠀⠀⠀⠀⣼⡇⡀⠘⠅⠙⠤⠤⢄⠤⠌⠂⢄⣉⣿⡋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠄⠀⠀⠀⠀⠀⠰⠧⠄⢷⣄⡀⣠⡖⢠⠀⠐⢃⡀⢊⣉⢐⡘⢒⡞⣓⣉⣍⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⢀⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣯⣀⣰⠟⠙⣏⣲⢐⡶⠒⡯⢭⣯⣽⣧⣴⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⠶⢾⣶⣤⣤⣤⣄⣐⣂⣤⣦⣼⣿⡁⠀⣹⣶⡶⠟⠉⠉⠙⠋⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⡶⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⢀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⡀⠀⠀⠀⠶⣀⣐⣪⠴⡈⡆⠀⠀⡠⠔⠊⠉⠉⠉⠀⠒⠒⠒⡺
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢤⣄⡀⠀⠀⡇⡇⣠⠊⢀⡠⠄⣒⣂⣤⡀⠤⠄⠊
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⢌⢢⠀⡇⡷⠁⣤⠏⢂⡩⠤⠤⣀⠬⠷⠦⣀
⠀⠀⠀⠀⠀⡧⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠀⠀⠀⠀⠀⠈⢆⢳⣷⢁⣺⠵⠾⡅⠀⡠⠊⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⢐⢀⡠⠔⡖⢻⠿⠿⣼⠿⣫⠔⠚⡇⡅⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⠉⢆⠀⠀⠀⠀⡇⢰⠋⠀⠀⠣⣈⠒⠤⣳⣊⣹⣆⠀⠳⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢠⠃⠀⠘⡄⠀⠀⠀⣷⡇⠀⠀⠈⠐⠤⡉⠒⠒⠒⠒⠉⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⡇⠀⠀⠀⠰⡀⠀⠀⣇⡥⠔⢄⠢⢄⠀⠀⠉⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠸⠀⠀⠀⠀⠀⣧⠀⢀⠏⣤⡞⠊⡀⠀⠀⡡⠊⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⢡⠀⠀⠀⠀⠀⠀⢣⣌⠮⠴⢥⣀⡀⠈⡞⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡎⢠⠁
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢑⢢⣤⡤⢊⢣⣼⡟⠊⠉⣀⣉⡡⠽⡃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡸⠀⡎
⠀⠀⠀⠀⠀⡧⠼⠤⠤⠤⠍⠲⢲⡶⡶⢋⡟⢫⡙⠃⢌⡀⠀⠀⠹⡄⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡰⠁⡜
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠋⡠⠊⡇⠈⡍⠳⢄⡙⢆⠀⠀⡇⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⠜⢁⠜
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠚⢰⠉⠀⠀⢡⠀⡇⠀⠀⠉⠚⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡠⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠐⠐⢧⡀⠀⠈⠶⠀⠀⠀⠀⠀⢀⡔⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⠉⠳⠦⣆⠀⠀⠶⠒⣉⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠠⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠋⠉⠉⠈⠁⠀⠀⣀⠈⠠⠀⠰⢦⣴⣿⣦⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⢀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠠⢷⣽⡿⠃⠀⢀⠠⣿⣽⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⢸⣿⣿⠛⠿⠿⠟⠻⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⠄⢒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠀⣀⢻⠀⠀⠀⠀⠠⠰⠐⠀⠀⠀⠈⠐⠒⢲⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠉⠛⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠊⠄⠆⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢻⣄⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⣼⣆⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⠉⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⣾⣿⣿⣟⢶⣦⣼⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⠆⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠂⠀⠀⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⢸⡿⣛⣥⠀⠀⠀⠀⠀⠿⠿⠛⠻⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠙⢄⣠⣶⠞⢹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡶⢻⣿⣿⣿⣿⣿⣇⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⣔⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡰⡩⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢑⠢⡀⠀⡁⠰⡐⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠎⠑⢌⢢⡇⢸⢃⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣁⡀⠀⣀⠱⡱⠸⡞⡐⠪⡓⠄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠬⡙⣷⢡⡁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠬⣠⠤⠄⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⠳⣄⠀⣀⣠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠙⡯⠗⣚⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⢀⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⣀⣤⣀⡠⠐⠂⢄⠔⠚⠚⠟⠋⠤⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⣶⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢑⡖⠋⠀⠀⠀⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⡿⠋⠹⣓⠦⢖⣤⡭⣭⠶⣄⢄⣀⠼⡸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⡩⢮⡺⠟⢸⡏⠑⠲⡮⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⢀⠤⢊⠴⠋⠈⠀⡀⣇⠀⠀⠱⡴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠤⠍⠔⠊⠁⠀⠀⠸⠴⠡⠜⠀⠀⠀⠈⠢⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⢤⠄⢤⡄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⠷⠓⣿⣿⣿⡿⣿⡞⠷⢷⣖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠁⠀⠀⢸⣿⣿⣿⣷⣿⣿⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢕⡢⢤⣀⠸⣿⣿⣿⣿⣏⡟⠀⢀⣠⠴⣚⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠡⠦⣭⣉⡛⠛⠛⣛⡛⡉⠭⠖⠪⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠉⠓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠉⠉⠉⠉⠉⠉⠉⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣦⣤⣥⣤⣴⢤⣀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⣠⡤⣦⣥⣤⣭⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠸⣿⣿⣿⠇⠀⠈⠁⠀⠀⠂⠀⠀⠠⠀⠀⠈⠃⠀⢹⣿⣿⣿⠃⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⠄⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠐⠀⠠⠤⠂⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠠⢄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠐⠂⠀⠈⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⢀⡠⠤⢄⠀⠀⠀⠀⡇⠠⠄⠀⠈⠁⢀⡠⠈⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣳⣤⣞⠀⠀⠀⢳⠀⠀⠀⠘⢦⣀⠀⠄⠀⠀⢀⡼⠁⠀⠀⠀⢀⡴⠋⣉⣀⣠⣤⣤⣤⣭⣭⣉⡓⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⠀⠈⢳⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠁⠀⠀⠀⠀⢀⡾⠞⠛⠉⠁⠈⠀⠀⠀⣀⠤⢬⣉⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡇⠀⠀⠀⢨⣧⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⢤⣤⣤⣄⣀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴
⠀⠀⠀⣰⡿⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡫⠉⠐⠒⠈⠐⠒⠂⠈⢍⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠜⣅⢀⠀⡀⢀⢀⠀⡀⣀⢂⡡⣰⠌⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣭⣥⣿⣿⣿⡿
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢁⣤⡔⢕⢁⣬⡀⠗⣩⣍⠦⢗⣴⡁⡘⠄⢿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⣷⣾⣿⣿⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣟⡵⠋⠀⢙⣒⠋⠈⠓⠞⠁⠉⠛⣋⡈⠙⢶⣔⢸⠀⠀⠀⠀⠀⢀⣴⣿⣖⣋⣩⣯⣿⣷⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⣧⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⢻⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠻⠟⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠀⠀⠀⠀⢠⠚⡇⠀⠀⠀⣾⣷⠀⠀⠀⣤⠀⠀⠀⣾⡆⠀⠀⠀⣼⠓⡀
⠀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢠⠶⣬⣦⢷⠀⠀⣤⠈⠁⣠⣤⡤⠤⢤⣤⣄⠀⠠⡤⠀⢀⣯⣞⡵⢦⠀⠀⠀⠀⠀⣠⣤⣤⣴⣧⠤⣤⡀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣴⠉⠸⠥⢈⡏⢧⡀⠀⠀⠀⠳⣄⡀⠀⣀⣠⠏⠀⠀⠀⣠⠎⣟⠀⡽⠊⢱⡄⠀⠀⢸⠁⠀⠙⠛⠋⠁⠀⢻
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠦⣤⣠⠾⢦⡀⠉⠲⢤⣄⣀⣀⠉⠉⢉⣀⣀⣤⠴⠚⠁⢀⠼⢦⣀⣤⠞⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸
⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⠒⠛⠉⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠓⠒⠉⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠉⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡴⠚⡉⢱⠀⠀⢀⠜⠁⣸⠁⠀⠀⠀⠀⠀⠀⢧⣤⣤⣀⣀⣀⣀⣠⣤⣤⡿⠀⠀⠀⠀⠀⢀⣠⡤⠴⢶⣶⡯⣍⠉⠓⠦⣌⠉⠓⢦⡀
⠀⠀⠀⠀⠀⡜⠘⡆⠱⠀⣡⠖⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠉⣮⡇⠀⠀⠈⡧⠀⠀⣹
⠀⠀⠀⠀⠰⡇⠀⣀⡤⠚⠡⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣠⡾⣄⣀⣄⣠⠇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢰⢯⠀⠀⢠⡖⠁⢀⡟⠁
⠀⠀⠀⠀⠠⡏⠉⠁⢄⠙⠆⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⣒⣺⠀⣿⣒⣲⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⣿⠀⠀⡼⠀⠀⡼
⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⢀⣸⠆⣏⡀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣸⡿⢤⡼⠧⠤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣬⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠰⠂⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⢰⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄
⠀⠀⠀⠁⠀⠀⠀⠀⢠⢰⢇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠠⡈⡞⣞⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠧⠀⠀⠀⢲⠰⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠆⠅
⠀⠀⠔⣉⡒⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠐⡋⠁⠉⠂⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⡀⠎⠠⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠐⡠⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⡂⠀⠀⠀⠀⠠⠀⠀⡀⠆
⠀⠀⠐⠦⠴⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⡀⠀⠢⠄⠀⠀⣀⣀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⢀⡄⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⡾⡴⢬⢱⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢠⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣴⢀⡤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠤⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠰⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠛⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠆⠀⠀⠒⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠅⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠄⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢦⣀⣀⡄⠤⠋⠀⠀⠀⢠⠠⠤⡤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠌⢀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠑⠠⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⡾⠀⠀⠀⠀⢁⡀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠐⠘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⢠⠀⠀⠀⠀⠃⢠⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠆⠀⠀⠀⠠⠄⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠄⠀⠀⠂⡀
⠀⠀⠀⢀⠠⢶⠀⠀⠀⠀⢀⠐⣦⡀⠀⠀⠘⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⢀⣶⣦⣤⣤⠀⠄
⠀⠀⠀⠀⠑⣌⠃⠀⠀⠀⠐⠃⠈⠀⠀⠀⠈⠉⠀⠀⠀⠰⡦⠀⠂⠀⠀⠀⠠⠂⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠿⣛⣷⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠾⠉⠹⠁⣀⢴⡟⠓⣆⠀⠀⠀⠀⠀⣀⡠⠔⠒⠒⠒⠒⠒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣐⣛⣒⣒⣲⠯⠓⢉⡶⠚⠁⠀⠀⠀⡴⠋⠁⠛⠓⠒⠒⠂⠀⠀⠀⢀⢨⡂
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠶⠖⠙⢏⠙⢶⡁⠀⢨⠗⣒⣲⢾⣟⣛⣻⣍⡹⢦⠀⠀⢧⡄⠂⠰⠀⠄⠐⠰⠀⠀⠀⡠⠔⠁
⠀⢀⡤⢒⡉⣉⢀⠀⢀⣀⠀⣀⡈⠁⢀⠯⠍⠭⢭⣓⣍⣩⢤⠤⢦⡈⡙⢾⠀⠀⠀⠈⠉⠒⠒⠒⡎⠙⣇⠈
⠈⠓⠫⠿⠾⠯⠯⠽⠿⠟⠛⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⠀⠀⠀⠀⠀⠀⠀⢰⡤⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢿⣲⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠇
⠀⠀⠀⢀⡤⠒⢲⠾⡷⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢸⣼⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢀⠀⡠⡀⢀
⠀⢠⡖⢙⠀⢠⠊⣠⠃⠀⠘⡝⠢⡀⠀⠀⠀⠀⢰⠋⠀⠐⠗⠀⠈⡆⠀⠀⠀⠀⢀⠴⠊⠉⠉⠙⢠⢩⠄⠛⢠⡉⠉⠢⡀
⠰⠁⢘⠌⢢⠀⠑⢜⢦⡀⠸⣔⡅⢳⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠎⠀⠈⠁⣘⠡⠐⣠⠄⠭⠀⠀⠀⠀⢱
⡇⣴⢣⠞⠁⢀⡠⠊⣀⠇⠀⠈⡟⣾⠀⠀⠀⣠⢃⣀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡆⡀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸
⢣⠈⣺⢦⡀⠸⣀⠸⣅⠀⠀⣎⢸⡝⠀⠀⣰⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⠘⢼⣦⠎⠑⠒⠒⠀⠀⠀⢀⣀⣠⠔⠁
⠀⠳⣧⣼⠁⠀⡨⠇⡼⠀⢀⣼⠟⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠙⠓⠼⠤⡸⠤⠤⠛⠁⠀⠀⠀⠀⠘⢦⡀⡀⡀⠂⠀⠀⣀⡀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⡆
⠀⠀⣴⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠡⠠⠠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣰⢧⠇
⠀⠀⠹⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡻⠉⠁⠙⠋⢻⡇
⠀⠀⠀⠱⡀⢢⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡾⠿⢦⠩⠿⣶⢦⡀⠀⠀⠀⠀⠀⠀⡴⠃⠈⠋⠰⠓⠀⠶⠄⠙⡶
⠀⠀⠀⠀⠱⠈⢇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡮⣀⠀⠸⠀⠀⢀⡱⠻⡀⡄⠀⠀⠠⣔⠃⠘⠁⠔⠀⠀⠤⠀⢠⠀⢵
⠀⢀⡤⠖⠲⢆⠘⠄⢱⣤⣀⣀⣀⠀⠀⠀⢀⣇⠁⠉⠪⡳⡇⣄⢔⠡⠐⠆⢧⠸⡄⠀⢀⡇⠀⡀⠀⠀⠤⠄⢀⡀⠀⠀⢘
⢠⠋⠀⡴⣲⡶⠷⣠⠞⣵⣲⣦⠈⠳⡄⠀⢸⣿⡀⠤⣰⠾⢀⠲⡀⠀⠀⡄⡞⠀⡇⠀⠈⡂⠀⠉⠀⠂⢀⡀⠀⠀⠚⠀⡞
⡞⠀⠀⡾⠉⢾⣠⡇⣸⠋⡇⠘⣆⠀⢹⠀⠀⢇⢎⠉⠀⠀⠂⠐⢌⠢⡔⡱⠁⡜⠀⠀⠀⡧⠐⠂⠀⠀⠀⠀⠀⠖⠀⡸⠇
⢣⠀⠀⣧⠀⠀⢳⣷⠉⣆⡇⠀⣿⡀⢸⠀⠀⠈⠣⣑⠦⠧⣀⣀⠤⣣⢞⡤⠊⠀⠀⠀⠐⠓⢄⡀⠘⠁⠀⠉⢀⣀⡖⠁
⠈⠣⣤⠗⠀⠀⠠⡼⠀⠀⠀⠀⠘⠶⠋⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠚⠁⠈⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠄⣀⡈⠁⠀⠀⠑⠀⠐⠂⠂⠐⠀⠠
⠀⠀⢀⠀⠀⠸⡄⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⢀⡀⠉⠀⠀⠀⠚⠐⠆
⠀⠀⠀⠀⠀⡀⢁⠈⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠓⠀⢠⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠠⠀⠄⠀⠀⠀⠈⠀⠀⠀⣠⠀⠀⠀⠌⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠁⠀⠂⠀⠀⠀⠄⠀⠈⠁⠄⠚⣦⣮⠀⠰⠀⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠥⠟⢀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡅⠀⠀⠀⠈
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⣔⡉⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠦⢄⡀⠀⠐⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡀⠀⠀⠀⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠋⠀⠀⣀⠀⡀⠘⠀⡄⠉⠂⡀⠀⠀⠀⡠⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢀⣀⡜⠉⠀⠑⠀⡀⠔⠀⢄⠀⡸⠀⠀⠀⠀⠈⠀⠀⠙⠃⠀⠀⠀⠀⠁⠀⢠⠔⠁
⠀⢀⡈⠆⠀⠀⢠⡀⠢⠀⠀⠀⠀⠈⠒⢹⡆⢀⠃⠀⠋⡀⠀⢀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡀⠀⡀⠲⠀⡄⠀⡀⠳⠀⠀⠀⠠⠀⠘⠃⠈⡃⠠⠈⠁⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢈⠐⠄⠐⠀⡇⠢⠀⠀⠀⠀⠀⠀⠑⠆⠀⡈⠁⠆⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠂
⠀⠐⠁⠄⠂⠀⢂⢡⠄⠄⠀⠀⠀⠀⠈⠐⠆⢱⢢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠇⠁⠆⠀⠸⠁⠠⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢀⠀⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⢡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠠⠀⡖⠀⠊⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢦⠀⠀⠀⠱⡁⠀⠈⠂⠀⠄⠀⠈⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠰⠀⢀⡵⠀⠍⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢨⢡⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠢⠀⠀⠀⠀⠀⠀⠒⠘⠃⠀⠀⠈⠁⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠈
⠀⠀⠰⠄⠀⠰⠆⠀⠀⠀⠀⠀⠠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢴⠀⠀⢈⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠄⠄⠀⠈⠳⠀⠀⠀⢀⡄⢠⡀⠢⠀⠀⡎⠀⠀⣀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠷⠀⠂⠀⠀⢀⠀⢠⠤⠄⠐⠀⠀⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢯⡥⠀⢀⠆⠀⠑⠀⠠⡀⠈⢢⡁⣶
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⣎⠁⠀⠠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠔⠁⠀⠀⠀⠀⡀⠠⣤⡀⢳⣿
⠀⠀⠀⠀⠀⣀⣈⣀⠒⠒⠁⠀⠀⢀⡄⠠⢀⠀⠀⠲⣚⠀⠇⠀⠀⠘⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⡄
⠀⠀⠀⠐⠁⣤⣀⠈⢣⠀⠀⡉⠀⠛⠹⠄⠀⢁⠀⠀⠉⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠉
⠀⠀⠀⠀⠠⣿⣧⠆⢀⠀⠀⠃⣀⠀⠀⠀⠀⠌⠀⠐⠙⢄⠀⠀⠀⠀⠀⠣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠈⠀⠀⠀⠔⠃⠀⠀⠀⠙⠀⠀⡠⠊⠀⠀⣠⣸⠆⠖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠠⠀⠀⠀⠐⠀⠀⢱⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠚
⠀⠀⠀⠀⠀⠀⠈⠀⠒⢤⣄⡀⠀⠀⠐⠀⠀⠀⠈⠢⣤⣤⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⡄⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢤⣀⡇
⠀⠀⠀⠀⠀⠐⠲⣤⡄⠐⠶⠦⠤⣤⣀⡍⠈⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣘⣦⠀⠀⠀⠀⡆⠀⠀⢰⠀⢙⠁⠀⠀⠄⠘⠀⠀⡦⠀⠂⠀⠈⠃⠀⠠⣀⣠⡶⠀⠀⠄⠁⠀⠀⠁⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣍⡳⡄⠀⠀⡇⠀⠀⠈⠀⢘⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⢀⡀⡀⢸⠀⠀⠀⠀⠈⠀⢠⢀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⡀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠀⠀⠀⠁⠈⠈⠀⠀⠘⠀⠀⠂⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠉⠀⠈⠁⠀⠉⢢⠀⠀⠀⠀⠀⡄⡰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀
⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⣇⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⣂⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⡀⠀⢸⠀⠀⠆⠀⠀⠈⠺⠏⠁⠄⠀⠀⣠⠤
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁
⠀⠀⠀⠀⡰⠁⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢐⡀⠀⢰⠂⠀⢀⡀⠀⡄⠀⣀⠀⢀⠌⠀⠀⠀⠀⠐⠀⣠⠊⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠠⠀⠈⠁⠀⠀⣵⠊⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠈⠃⠀⡰⠁⠀⠈⢀⠀⠀⠀⠀⠀⠠⠀⠂⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠒⠹⢆⠀⢀⡤⢀⠀⠀⡠
⠀⠀⠀⠀⠻⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠤⡀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠂⠉⠀⠈⡆⠸⢇⡀⠤⠊⠀⢰⣄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠄⠀⠈⠐⠀⢈⠀⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⣀⣀⣠⣴⠄⠀⠀⠀⠀⠀⢴⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣁⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⠇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⣠⡴⠶⠛⢛⣉⣉⠛⠛⠛⠶⢦⣄⡈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣀⣠⣾⣍⣀⣀⣴⠏⠉⣉⣿⢶⣞⠛⣦⠈⠙⢶⡄⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣰⠞⠉⣿⠀⠀⠉⢹⡟⢳⣾⣏⡀⢀⣹⣷⣿⣤⣄⡀⠹⣆⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢰⡏⠀⠀⣿⣀⣀⣀⣾⡁⣼⠃⢈⡿⣯⠁⣼⢻⡄⠈⠙⢶⣿⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠸⣇⠀⣠⠿⣯⡉⠉⣿⢻⡟⠶⣾⢥⣬⣿⣁⡀⣿⢀⣀⡼⢿⡄⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⣦⣿⠀⠈⠙⢻⡷⣾⣥⣸⣧⣴⡋⣻⡉⠉⢻⡏⠉⠀⢨⡇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠈⣿⠶⢦⣤⣼⣧⣿⠾⢿⡋⠉⠉⣿⠛⢷⡀⠻⢦⣤⡾⠃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠘⢧⣄⣴⠏⠀⢻⡄⠘⢧⣤⣴⠏⢀⣼⠃⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⢦⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠙⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣤⣤⣤⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣦⣤⣀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣷⣶⡆
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀
⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠉⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣿⣿⣷⡆
⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠰⠁⠀⢴⠆⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠈⣿⣿⣿⣿⣿⣅⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠹⣿⣿⣿⣿⣿⣷⣤⣈⠀⠘⠛⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⢿⣿⡿⠿⠛⠁
⠀⠀⠈⠉⠛⠻⣿⣿⠛⠛⠉⠀⠲⢶⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠈⢿⣿⠟⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣦⣴⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂⠄⠀⠀⣀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⢦⣀⠸⠀⠀⠀⣀⠰⠠⠒⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⡀⠻⠏⢀⠂⠈⢂⠠⠈⢢⣰⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠓⢄⠌⢀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠪⣿⡀
⠀⠀⠀⢨⣈⠑⠀⢰⠂⠚⠧⠀⠀⠀⠑⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁
⠀⠀⠀⠘⠛⢁⠂⠈⢰⡤⠀⠠⠀⠀⣩⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⢡⠀⠀⠄⠀⠤⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠃
⠀⠀⠀⠀⠀⠀⠲⠤⣀⠀⠠⠀⠀⠑⠶⠦⠋⠀⠀⠀⢀⠀⢀⠁⠀⠀⠀⠀⠀⠒⠐⠓⠀⠄⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⢄⣀⠀⣤⣀⣙⠒⠠⢦⠀⠀⠀⠀⠀⠀⠀⠘⠄⠘⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠉⠳⠦⣧⡀⠀⠰⡄⠀⡆⠐⠀⠀⠀⠂⠀⡆⠀⠀⠑⠀⠤⠴⠆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠈⠈⠈⠀⡀⠐⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠈⠈⠁⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⢀⠆⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠷⠗⠀⠀⢀⠄⠀⠀⢀
⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀
⠀⠀⠀⠁⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠄⠀⠓⠀⢩⡤⠰⠀⠁⠐⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⡠⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠀⠂⠃
⠀⠀⠁⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢴⡀⠀⡀⠀⠀⡀
⠀⠀⠈⢇⢠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠒⠈⢳⠸⠁⠀⠈⢠⡤⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠄⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣴⠶⠋⠀⠀⠀⠀⢇⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠛⠉⠛⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠉⠛⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣠⣤⠤⠤⠤⠤⣄⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠤⠖⡶⠚⠓⠦⠤⡄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣿⠀⠀⠀⠀⠈⣳⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢸⣁⣀⣴⠃⠀⠀⠀⠀⠙⡦⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠻⠾⠶⠦⠶⠶⠶⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠨⠍⠉⣻⣛⠛⠛⡛⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠂⠘⠀⠈⠋⠈⠁⣀⣀⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣤⢤⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠤⣄⣀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠘⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠲⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢁⠴⢦⣲⠿⣶⣦⡤⢍⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠠⡶⢶⡄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⡎⢻⣶⡾⣿⣾⣻⠷⣿⣞⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠞⣻⠆⠀⡾⠃⠚⣻⡆⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣙⢿⣿⣿⡟⣽⠷⣏⡛⠊⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢛⡀⠀⡥⠀⢸⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢍⣳⠟⠳⢚⠑⠒⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣀⣀⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡏⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠀⠀⠀⠀⠀⠹⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀