Decorated Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⠖⣶⠃⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣦⣄⣥⣾⣽⣦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠈⠉⠉⠱⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⢀
⠀⠀⢠⣄⣨⣗⣦⣾⠂⣾⣶⠶⡾⢷⠀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠄
⠀⠀⠈⢙⣿⣿⣯⣥⠀⠋⠰⡶⠀⠛⠿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⢠
⠀⣻⣲⡶⠟⠁⢀⠀⠀⡎⠁⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡻
⠈⠉⠉⠀⡄⠀⠀⠀⣼⡀⢦⡀⠘⢇⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠀⠐⡆⢉⡇⢮⣵⡀⡾⠴⠀⠀⠀⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⣴
⠀⠀⠀⠀⠀⠀⣶⣴⡟⠉⠃⢈⡟⠀⠀⠈⠁⠠⢿⣦⠀⢃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⠐⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣤⠴⠋⠀⠈⣹⣶⣟⠁⢠⣄⠀⠀⣠⣤⣿⡆⠀⢇⠀⠀⠀⠄⠀⣞⠀⠀⠀⠀⠀⠀⠀⢲⡇⠀⠘⠣⠶⣗⣀⢸⠿⠂⠀⠀⠘⠒
⠀⠀⠀⠀⠀⢤⠼⠷⣶⠉⣿⢻⣷⣿⡻⢷⠟⠁⠀⢻⣿⠀⢀⣁⠀⠂⢀⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠷⠀⠀⠈⣵⡒⠒
⠀⠀⠀⠀⠀⣤⠄⠈⠙⣤⣨⣼⣿⣇⠀⠀⠀⠀⠈⠩⢹⣷⢾⣇⢀⣠⠟⠛⠒⠂⠀⠀⣀⠀⠈⠑⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣭⡥⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠛⣿⡝⢫⡔⠀⠀⢠⡀⠀⠛⠀⠂⣿⡿⠁⢶⢃⣀⠀⠈⠉⢻⢠⡇⣰⠖⠛⠉⠁⣡⠄⢺⡇⠀⠀⠀⠀⠻⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⣿⣿⣷⣆⠀⠀⠀⠀⠁⠀⠀⠀⢸⠿⣶⢦⡞⠻⠿⣿⠷⣤⣴⣾⣿⠣⠀⠀⠁⣾⣿⠀⢿⡆⠁⢀⣴⠂⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣉⠛⡄⠀⠠⠦⠼⠀⠀⠀⠉⣰⣧⣀⠥⠤⢄⣠⡼⠉⠛⣿⡌⠷⠁⣠⡚⠁⢀⡀⠀⣀⣀⠀⠋⠐⠶⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⡀⠀⠀⢠⡇⠀⠀⠀⠀⣿⡏⡄⠐⠐⣎⠹⣿⣷⣄⡀⢐⣘⣁⠉⠈⠛⠃⠀⢸⢇⡈⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄⣠⣤⣦⢻⣶⣶⣄⠐⠙⠳⠄⠢⡄⠙⢢⣿⣾⠁⡀⠀⠘⢏⢢⣶⣦⣠⡀⠘⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠋⠻⣿⢎⣿⣿⡏⠃⣀⠴⣷⡦⢀⢶⠟⣙⠁⠛⠁⠀⢠⢤⣾⣟⣂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠘⠛⣠⠀⠀⠈⠻⡀⠈⠃⢠⠆⠀⠀⡨⢟⣿⠛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠉⠉⠒⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣄⠀⣤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠢⣹⣤⣧⠛⠉⢛⠑⢄
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠐⢶⡤⣸⠀⢸⠁⠀⠀⠱⠀⠀⠀⢠⠖⠲⢤⢄⣠⠄⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠰⡀⢑⣦⢀⢵⣤⣷⣾⡆⢀⠤⡀⠀⠶⢶⣇⠀⢀⣥⣬⣿⣾⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡿⠋⠀⢸⠋⢁⡸⣿⠀⠈⠲⡶⣄⣿⣿⡁⢀⣀⣸⣇⠤⠞⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠎⠉⠛⡆⢀⡘⠀⠊⢀⡜⠓⣧⣯⣉⢃⠀⠀⠹⠋⠀⠙⢓⣶⣮⠉⡽⠋
⠀⠀⠀⠀⠰⠾⢩⡇⠀⢀⣀⡀⠠⠤⢄⡖⠉⢑⡴⣇⣀⡀⣇⣧⣠⣞⠀⠈⠀⠀⠀⣹⠊
⠀⠀⢀⣠⣤⣊⡹⠿⠛⢧⢈⠝⠉⠉⠁⠀⣠⠎⠀⠯⣤⠍⠛⠡⣭⡿⡗⠒⠉⠉⢻⣿⣉⠉⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠊⠉⠉⠁⠀⠀⠀⠘⠒⢶⣖⡀⣤⠗⠀⠤⡄⠀⢸⣿⣿⣁⣉⡙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢤⣏⣀⣼⣿⣗⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⢯⠒⠂⠬⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡑⣎⠍⠉⠓⢦⡀⢀⡴⠚⠉⠩⣱⢊⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⢁⣀⠀⠀⠀⢹⡏⠀⠀⠀⣀⡈⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡴⠖⠒⠲⢤⡇⠀⠀⡰⡽⠓⢶⣀⡦⣴⣦⢴⣀⡶⠚⢮⢄⠀⠀⢸⡤⠖⠒⠒⢦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡔⣭⠀⠀⠀⠀⣀⢱⣴⡿⠲⣧⣽⢾⣇⠒⣸⣇⠒⣸⣷⣯⣼⠖⢿⣦⡎⣀⠀⠀⠀⠈⣭⢢⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠠⣦⣵⣎⡿⢉⢻⣬⣅⣿⣅⣀⣿⡿⠋⠙⢿⣿⣀⣨⣿⣨⣥⡟⡉⢿⣱⣮⣴⠄⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡱⢿⢐⣤⠷⣦⣾⠏⠉⠉⠙⠛⠁⣠⡤⢤⡄⠈⠛⠋⠉⠉⠹⣷⣴⠾⣤⢂⡿⢎⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠷⢄⣘⡟⢉⠹⣧⣀⣼⡟⠀⡴⣚⠓⣦⣤⣧⣮⣵⣼⣤⣴⠚⣓⢦⠀⢻⣧⣀⣼⠏⡙⢻⣃⡠⠾⠤⠤⣀
⠀⠀⠀⠀⠀⠀⣠⢞⠁⠀⠀⠀⣴⡿⡛⣶⡾⠟⠛⠉⠀⠀⣧⣴⡿⠋⠀⠀⣉⡉⠀⠠⠙⢿⣦⣼⠀⠀⠉⠛⠻⢷⣶⢛⢿⣆⠀⠀⠀⠈⡳⣄
⠀⠀⠀⠀⠀⢮⡱⢼⠆⢀⢔⡮⠼⣦⣥⣽⡇⠀⣰⢫⢉⣿⢁⠀⢰⣬⢾⣝⢟⡺⣫⠶⣧⡆⠀⠈⣿⡉⡝⣆⠀⢸⣯⣬⣴⠧⢵⡠⡀⠰⡯⢎⡵
⠀⠀⠀⠀⠀⠈⡇⠁⠀⠘⢹⣄⣳⣿⠁⢹⣷⠀⠹⣤⡾⠋⣐⣶⠯⣣⡿⠾⡞⠳⠷⢷⣼⠽⣖⣂⠹⢿⣤⠏⠀⣿⡏⠈⣿⣞⣠⡏⠃⠀⠈⢸⠁
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⡼⢩⠙⣿⡿⠁⣠⣤⣿⠀⠀⣜⢷⣾⡏⣯⣺⢼⡣⣟⣽⢹⣟⡾⣣⠀⠀⣿⢤⣀⠈⢿⣿⠋⡍⣧⠄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠲⣿⠶⢾⣏⠀⠀⣏⢎⣿⡇⢸⣽⡱⢾⡉⠾⡷⣏⣹⣿⠶⢘⡷⢎⣿⡁⢸⣿⡱⣹⠀⠀⣹⡷⠶⣿⠖⠶⢾⡁
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠐⢻⣘⣠⣿⣷⡀⠙⠒⣿⠀⠀⢫⡞⢿⣇⣟⣽⢺⡟⢯⣿⣸⣯⢷⡝⠀⠀⣿⠚⠉⢀⣾⣿⣄⣃⡞⠂⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⡇⡀⠀⢀⣹⠋⡽⣿⡀⣸⡿⠀⣰⠛⣷⣄⠩⠾⣖⡟⣷⢶⢧⡾⡶⡾⢫⣲⠿⠍⣠⡾⠛⣆⠀⢿⣇⢀⣽⢯⠙⣏⡄⠀⢀⢸⡀
⠀⠀⠀⠀⠀⢞⡱⣚⠆⠀⠊⢗⢲⠟⡛⣻⡇⠀⠹⣜⣈⣿⡀⠀⠸⢛⠾⣯⣮⣵⣝⠷⡟⠇⠀⢀⣿⣁⣣⠏⠀⢸⣟⢛⠻⡖⡺⠙⠀⠰⣓⢎⡳
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠻⣷⣥⠿⢷⣦⣤⣀⠀⠀⡟⠻⣷⣄⠂⠀⣁⣉⠀⠀⣰⡾⠟⢻⠀⠀⣀⣤⣴⡾⠿⣬⣾⠟⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⡶⠊⢩⣧⣌⣰⡟⠉⢻⣧⠀⠳⢭⡤⠟⠛⣟⢟⡻⣻⠛⠻⢤⡭⠞⠀⣼⡟⠉⢻⣆⣁⣼⡍⠑⢶⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡱⣞⠨⠻⡶⠟⢿⣆⣀⣀⣠⣤⡀⠙⠓⠚⠋⢀⣤⣄⣀⣀⣰⡿⠻⢶⠛⠅⣷⢎⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠐⠟⡻⢏⣧⣈⣼⢛⡋⣿⡋⠉⣿⣷⣄⣠⣾⣿⠉⢙⣿⢙⡛⣧⣁⣾⡙⢟⠻⠂⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠣⣛⡀⠀⠀⠀⠉⡸⠻⣷⠴⡟⣻⢿⡏⠤⢹⡏⠤⢹⡿⣟⢻⠦⣾⠟⢇⠉⠀⠀⠀⠀⣛⠜⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠳⠤⠤⠴⠚⡇⠀⠀⠑⣳⡤⢾⠉⠗⠻⡟⠺⠉⠷⢤⣞⠊⠀⠀⢸⠓⠦⠤⠴⠞⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢀⡈⠉⠀⠀⠀⣸⣇⠀⠀⠀⠈⢀⡀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡫⢏⣂⣀⡤⠞⠁⠈⠳⢤⣀⣐⡹⢌⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠒⠒⠒⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠂⠀⣲⠶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⠔⠊⠀⠀⠀⢀⡞⡡⡾⠉⠀⠀⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠔⠛⠉⠉⠑⠐⠦⢄⡀⠀⠀⢀⢠⣖⡽⠎⠁⠀⠀⠈⠒⢒⣶⠣⠥⠊⡰⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡔⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾⡿⠛⠛⣻⢥⠤⣤⠞⡀⢀⡠⠚⢀⡀⠠⠖⠀⠀⡠⠀⠀⠀⠠⠀⣀⠠⡀⣤⡖
⠀⠀⠀⠀⠀⠀⠀⢜⣴⠟⠋⠀⠀⠀⠀⠀⠙⣛⣿⡿⠛⠛⠛⠛⠉⠉⠀⢀⡠⠴⣄⠉⣀⡠⠒⠁⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠘⠻⣿⣷⡟
⠀⠀⠀⠀⢠⣴⣴⣾⡧⠌⠀⢀⣀⣀⣴⠾⠟⠋⠀⠀⠈⠁⠂⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠶⢜⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⡤⠶⠒⠀⠐⠐⠛⢛⠖⠀⠀⠀⠀⢤⠀⢀⡀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⡞⠁⢀⣤⠾⠛⠁⢀⠤⠔⠒⠀⠀⠀⠀⠀⠄⠘⡀⠀⠀⠈⢀⠈⡀⠘⠁
⠀⠀⠀⠀⠀⠀⢀⢞⡡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⡀⠀⠃⠠⡅⠀⠖
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⣀⡤⠖⠒⠀⠄⠀⠃⠀⠀⠀⢠⠔⠉⠹⢃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠐⠃⢀⠖⠃⢄⠉⠀⠉⠰⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡀⣄⡀⠀⠀⠀⢠⣋⡤⠔⢈⡀⠀⠀⠘⠃⠀⠀⠀⣠⣿⢶⡀⠀⠀⠀⠄⢀⡿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⢻⣿⣦⣂⡤⠯⠀⠐⠂⠰⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢤⡀⢸⣼⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠙⡿⠁⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣱⣌⣿⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢈⡂⢀⡀⠀⠶⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡐⠁⠀⠸⣧⣀⣀⡴⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣻⡄⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⣁⠤⠌⠷⠿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⠇⠁⠀⠀⢸⣡⣞⣡⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⡰⠋⠀⠀⠀⠀⠀⡈⠣⠖⢒⡉⠀⠓⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢀⡿⠁⢹⠿⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠓⠲⣧⣽⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⠀⢸⣆⡆⡜⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠤⠶⣿⣿⣿⡇⠀⠀⠃⠀⢰⠃⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣠⠞⠛⠛⠇⠙⠀⠀⠈⢩⡠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣿⡟⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠑⡾⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠂⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⢸⡿⣍⠻⢍⠛⠟⠲⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠚⠟⢋⠝⢋⡿⣿
⠀⠸⣷⢄⢱⠴⣓⣚⣳⣶⣦⣙⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡛⣡⣞⣶⣛⣒⡳⢔⢁⢴⡟
⠀⠀⠹⡦⢹⣎⡕⢊⣁⣀⣋⡝⢻⣾⣯⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣫⣗⡮⠛⣉⣃⣀⣁⠲⣝⣾⠠⡾⠁
⠀⠀⠀⠹⡦⢻⣰⡏⢡⣤⡄⠭⣙⣛⠾⣾⣷⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣻⡾⠞⣺⡩⠅⣤⡤⠉⣧⣽⠣⡾⠁
⠀⠀⠀⠀⠹⡆⢧⠳⣄⡙⠦⣀⠐⠈⠁⡃⢝⡻⢽⢿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣿⠷⣛⠅⡃⠁⠐⢀⡠⠞⢁⡴⢣⠃⡾⠁
⠀⠀⠀⠀⠀⢻⡀⢷⡀⠉⡒⠠⠬⢕⣂⠤⢀⠈⠚⢹⣿⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢟⢿⠙⠊⢀⠠⢄⣒⠭⠤⠖⡊⢁⣴⠇⣸⠃
⠀⠀⠀⠀⠀⠸⡧⢸⣏⠳⠥⠔⠣⡀⠆⠉⣑⠺⢤⣄⡘⢻⠿⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣷⠟⣀⣤⠼⢒⡉⠁⠆⡰⠓⠤⠵⢋⣿⠠⡟
⠀⠀⠀⠀⠀⠀⣟⠐⣿⡷⠶⠂⠀⠈⠉⠉⠈⢦⡂⠈⡙⠧⣿⣬⢾⣷⡄⠀⠀⠀⠀⠀⠀⣴⡗⣯⣼⡤⠟⡉⠐⣠⠎⠈⠉⠉⠀⠐⠲⠶⣿⡗⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠤⡏⣴⠚⠋⡙⡉⠐⠲⠠⢄⡉⠉⠈⢄⡈⠻⢷⡽⡿⡄⢀⣶⣦⠀⡼⡗⣽⠿⠉⣀⠌⠈⠉⣀⠤⠲⠚⠈⠙⡉⠛⢲⡈⡇⢾⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣑⣬⡳⠷⠷⠧⠤⠾⠤⠾⠤⢽⣂⣨⠕⠊⠂⠻⣟⣿⡼⣿⡟⣼⣿⡾⠁⠃⠒⣥⣀⣺⠤⠼⠦⠼⠦⠤⠷⠷⢶⣫⣜⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⣶⣤⣄⠀⠀⠄⠠⢄⠀⠀⣉⠙⠳⢦⣄⡈⢿⣿⡏⣿⣿⠋⣀⣤⠶⠛⢉⡁⠀⢀⠤⠀⠄⠀⢀⣤⣴⡾⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⡿⣲⠷⣶⣤⢶⣧⣤⣴⣾⡿⣛⣿⣧⣿⡟⠻⣿⣶⣤⣴⣷⢦⣴⡶⢷⠹⠿⣿⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡔⠸⠠⣽⠀⡇⠙⡎⠁⠀⠿⣿⣷⣾⡿⣿⡿⣏⣶⣿⡿⠇⠀⠉⡞⠁⡇⠸⡥⢸⠐⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠌⠀⠐⣿⠀⢧⠸⣅⠃⠀⠀⠛⢻⣿⠁⣿⡇⢹⣿⠛⠃⠀⠀⢃⡽⢠⠇⢸⠗⠀⠈⠄⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣼⢣⠈⣹⡀⠘⡆⠈⣇⠘⠀⢀⠀⡎⠸⣿⡧⠈⡆⢀⠀⠘⢀⡇⢀⡞⠀⣼⡉⢠⢙⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⢠⠓⡀⠐⢳⡀⠘⢦⡈⠉⢦⣈⡼⠁⠈⣿⡏⠀⠹⣌⣠⠋⠉⣠⠞⠀⣰⠓⠀⡐⢃⠠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⢘⠒⡄⠉⠽⢆⡀⠙⠲⠤⡿⠁⠀⠀⣿⡇⠀⠀⠹⡤⠴⠚⠁⣀⠾⠍⠁⡄⣚⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠈⣌⣢⡀⠉⠽⠲⣶⠞⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⢶⡶⠺⠉⢃⣠⣊⡌⠀⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠲⡔⠂⢁⣲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣊⠁⠒⡴⠲⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠀⡀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠂⠑⠀⠀⠂⠀⠀⠀⠀⠁⠐⠒⠀⠄⠠⠁⠄⠁⠠⠡⠀⠐⠃⠀⢀⠀⠀⠝⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢎⡀⠆⠇⠀⠀⠀⠶⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⣀⠀⠈⠀⠀⢀⠀⠈⠵⢂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⢀⡀⡠⠀⠀⡀⠀⠀⠠⠂⠂⠁⡀⠀⠀⠰⠀⠀⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⣠⠀⠨⠤⠍⠀⢠⠀⠀⠀⠈⠐⠩⠊⠀⢀⠀⢈⠀⠀⢢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⢷⠁⡿⠘⠎⠈⡇⠱⠇⠈⠀⠀⠀⠈⡄⠰⠂⣤⠀⢈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⣄
⠀⠠⠄⠤⠀⠀⠀⠀⢈⢇⣉⣀⢉⣙⠃⠀⠁⠁⠉⠈⠈⠈⠁⠁⠀⠀⠒⠀⢐⠀⡆⢰⡆⡠⡀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⡆⠈⠛
⠀⠀⠀⠀⠀⠀⠠⠀⢘⡛⡛⣛⣛⣻⡃⢜⡇⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠀⠗⠀⠇⠸⠃⠈⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣀⣀⣀⡀
⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠁⢁⠠⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠩⠀⢤⠄⢀⢠⠋⡉⢲⠀⠀⢀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⢠⠄⠀⢀⠠⠄⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢤⠤
⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡄⠀⠀⠀⠈⠀⡄⠀⠀⠈⠁⠈⠁⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⣀⠠⠀⠀⠀⠀⠀⠀⠀⠽⠃
⠀⠘⠘⢈⠈⠁⠀⠀⠀⠀⣀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠐⠀⢀⣄⠀⠄⠀⠀⢽⡦
⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠉⠈⠀⠀⠉⠈⠁⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣄⣶⡄⢿⠇⣦⡄⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠗⠢⢄⣿⠋⠿⡏⠣⡆⠀⠘⢻⠛⠁⣶⠟⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠻⢿⣆⣻⠀⣰⡜⣦⢱⡀⣰⠿⠒⠚⠒⠤⢞⣵⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣦⡈⢻⠀⣿⡄⠐⣶⡄⠈⣇⢸⠃⢸⢸⡿⢁⢀⣴⠀⢰⡆⠀⣤⡴⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡌⢻⠃⠀⠑⠾⢦⣄⡈⠙⡄⠙⣿⡄⣿⣿⠀⣿⠎⠟⠀⣜⡡⠔⠉⠁⠘⠟⢡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡄⠀⠈⣉⣒⢷⡀⠀⣤⣤⣌⣻⣦⣿⠀⠘⣿⣿⣿⠀⢨⡶⢁⡴⠇⣤⣤⡄⢠⡼⢓⣭⠀⠀⢀⣤⡶
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣉⠙⣦⠤⣙⣿⠓⠙⠳⣤⡉⠀⠀⠈⢿⣄⠀⣿⣿⡿⣧⣞⡴⠋⠀⠀⢈⣡⠔⠋⠀⣟⣃⣠⣤⣜⣫⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠱⣶⣦⠀⠉⠳⢤⡄⠈⠿⣄⠀⠀⠀⠙⢿⢿⣿⣿⡟⠉⠁⠀⠀⣠⠾⠁⢀⣴⠞⠉⣴⡿⠀⣀⡬⢉⣥⣤⣄⡀
⠀⠀⠠⣴⣶⡦⢤⡤⣶⠒⢚⣉⡚⢷⣄⡀⠀⠙⣦⡀⠈⢻⣦⣀⠀⢸⣿⣿⣿⡇⠀⣀⣴⠞⠁⠀⣰⠋⠀⢀⣠⣗⣊⣉⠉⠓⣖⡪⢭⡉⠁
⠀⠀⠀⠀⣀⡤⠊⣾⠿⠀⠛⠛⠋⠀⠈⠙⢷⠀⠈⠛⠓⠾⠿⣿⣷⣯⣿⣿⣻⣲⣾⣿⠿⠓⠛⠛⠁⠀⣼⠋⠀⠈⠛⠿⠓⠀⠹⢿⡄⢹⣦⡀
⠀⠀⠀⣼⣿⠀⠀⠀⠰⣷⣶⡀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣾⡿⠟⠀⠀⠘⢿⡇
⠀⠀⠀⠉⠀⣠⣤⡤⢤⣤⡴⠿⢶⣟⣷⣶⣶⣽⠿⢶⣶⣆⣀⡀⠀⣰⡿⣫⣾⣷⠀⢀⣀⣀⣤⣴⡾⣿⣶⣷⣾⣿⡿⠿⠶⢶⡒⠲⣶⣶⡀⠁
⠀⠀⠀⠀⠐⠛⣋⡴⠋⠁⠀⣴⠉⠀⠀⠀⠁⠈⠉⠉⠙⢭⣿⣿⣶⣼⡻⣿⣿⣿⢟⣿⠿⠟⠛⠉⠉⠉⠈⠀⠀⠀⢙⣦⠀⠀⠉⢳⣌⠙⠃
⠀⠀⠀⠀⠀⡰⢡⣿⡀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⡿⣷⣌⢻⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣾⡎⢣
⠀⠀⠀⠀⢀⣧⡀⠻⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢿⣶⣿⣷⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠁⣸⡆
⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣽⣟⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣿⢿⣿⢿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⢟⣼⣫⡿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣩⢴⣫⡵⢋⣼⢯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣤⣤⣄⠀⠀⣠⣾⣿⣿⠿⣻⣿⡾⣿⣧⢿⣧⡻⣦⣀⠀⠀⣠⣤⣤⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠾⢿⣧⢛⣫⣾⢫⣶⡿⢟⣭⢖⢮⣝⠳⣮⣟⢶⣭⡝⣳⡯⠷⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⢿⣎⢿⣿⣺⣿⡱⣿⢱⡏⣳⢹⡷⣹⣿⢾⡿⣣⡿⣱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣷⣭⣓⣝⠳⢿⣿⣭⢷⣫⣶⡿⣋⣬⣾⡿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣍⠳⣻⣽⣾⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⠀⣴⡆⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⠀⣶⡄⣠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⣿⡇⢻⡆⠛⢀⢴⡗⠀⠀⠀⠀⠀⠀⠀⠸⣶⢄⠸⢃⣾⠃⣿⣷⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠂⢿⠀⠀⠉⢻⣧⡾⡇⠀⢀⣠⡤⣄⣀⠀⠀⡿⣆⠿⠊⠁⠀⢸⠉⠐⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠘⢇⣰⣀⠴⠋⠺⡶⠺⠿⠷⠀⠰⠿⠷⠶⡿⠚⠳⣄⣡⣠⠟⠀⠀⢀⡴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠐⠂⣠⣽⣿⣩⣇⡀⠀⠀⠴⠒⠛⣛⠛⠛⡛⠒⠲⡄⠀⠀⣈⣯⣹⣾⣥⡀⠒⠲⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣏⠀⠈⡶⠙⠈⠉⠓⠶⡆⡰⠣⠘⢄⠐⢈⠳⡠⡴⠖⠚⠉⠘⢱⡌⠀⢈⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠁⡹⣩⢛⠀⢠⡀⠀⠀⣧⣤⣁⠱⠋⠐⠈⠐⠈⠷⢁⣡⣤⡇⠀⠀⣤⠁⢚⢯⡹⡁⠉⠛⠶⣤⣀⡀
⠀⠀⠀⢀⣠⢴⡶⠛⠉⠀⢀⡄⢀⣴⡶⠗⠁⠞⠱⢆⠀⠞⢱⣆⠙⠃⠀⠀⠀⠀⠀⠀⠛⢁⣶⠹⠆⢀⠆⠹⠆⠑⠷⣷⡀⠀⡀⠀⠈⠙⠳⣦⣄⣀
⠀⢰⢾⣿⡓⢁⡀⠀⣤⣤⠞⣰⡞⠁⠀⠀⠀⡀⠐⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠀⠀⠀⠐⠀⠀⠀⠀⠈⠻⣦⠩⣄⣀⣀⠀⠈⠂⢽⣿⣦
⠀⢸⡇⠻⣧⡉⠉⠐⠚⠦⣸⠏⠀⠀⠀⠀⠀⢋⡓⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳⡉⠃⠀⠀⠀⠀⠙⣧⢀⠾⠇⠒⠛⣡⣿⠏⣿
⠀⢸⡇⠀⠈⠃⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠟⠁⠀⣿
⠀⢸⣧⣴⣇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣦⣄⣿
⡴⢯⢏⡅⠹⣄⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⠋⡛⣿⣦
⠀⢸⡏⢱⠀⠈⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠚⠁⢰⠻⣿
⠀⢸⡿⢺⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⢾⣟
⠀⢸⠂⡇⠗⠦⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⠤⡏⡆⣿
⠀⢸⠄⠁⠛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠰⠆⠃⣿
⠀⢸⠆⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠙⠒⢦⣄⡀⠀⠀⢀⢄⣿⢹⣷⠤⡀⠀⠀⠀⠠⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡆⠀⠀⠀⢀⡠⣴⣏⢹⡆⠄⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣬⣤⠙⠿⡷⣾⣅⣀⠀⠀⠠⢿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢿⠆⠀⠀⢄⣠⢿⡾⡿⠛⣀⣭⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢙⠳⢶⣌⣈⡟⠶⣆⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⣠⡶⠛⣁⣨⣼⠖⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠀⠀⠀⠉⢻⠶⢬⣝⡳⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠞⣋⣥⠶⣺⠋⠁⠀⠀⠈⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢭⣶⠀⠄⣤⠖⠳⡈⠙⠛⢷⠶⣬⣉⠛⠙⠛⠛⠛⠋⠉⣉⣡⡴⢾⠟⠛⠁⡰⠓⢤⡄⠀⣶⣎⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠿⡶⣼⠁⠀⠀⠈⠂⠀⠀⠐⠀⠉⠙⠲⣦⣤⣤⠶⠛⠉⠀⠂⠀⡀⠀⠊⠀⠀⠀⢳⢴⡿⢟⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠙⠢⡀⠀⠀⡀⠛⠋⠀⠀⠀⠈⠛⠁⠀⠀⠀⡠⠚⠁⠀⠀⠀⠸⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠐⠀⠜⠀⢀⡄⠢⠀⡀⠂⡄⠀⠑⠀⠀⠀⠀⠘⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠀⠀⠠⠐⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣀⣀⣀⣀⣀⣠⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⡄
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠿⠿⡿⠿⠿⠋⠀⠀⠀⠀⠀⣤⣼⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⢰⣶⣄⣤⣤⣤⣤⣄⣤⣾⠀⠀⠀⠀⠀⠀⠻⡿⠿⠿⠿
⠀⠀⠀⠀⠈⠻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⠀⠀⠀⠀⢘⣿⣿⣷⡽⠿⠿⠿⢿⣿⠀⢀⣀⡀⠀⣀⣾⣿⡀⠀⠠
⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣀⣀⣙⣿⣁⣀⣀⡀⠀⢸⣿⣿⣿⣿⣽⣛⣿⣿⣟⠀⢘⣿⣟⣟⣻⣻⣿⡿⠀⢀
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣭⠀⢸⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠀⠀⠆⠀⠀⠀⠀⣩⣄⣀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⣤⠀⠀⠀⠀⢰⡶⢴⣶⣀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣯⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣠⡄⠀⠿⢶⡆⠀⡀⠀⠀⠀⠀⠀⢸⢺⡇⣻⣿⣦⣴⣦⣴⣾⡏⢻⡿⢬⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⣴⢾⡄⠀⠀⠀⠀⠀⢛⣀⣾⣷⣻⣹⣴⣷⢠⠐⠇⠀⠀⠀⠀⠀⠀⠀⢸⠼⠗⢸⡿⠿⣿⣿⣿⣿⣧⣼⡇⢸⣿⣧⣰⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⣷⢺⠇⠀⠐⠒⠂⣠⣬⣿⣿⣿⣥⣿⡿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⣿⣿⣭⣭⣽⣿⢿⣿⡇⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠋⠘⠀⠀⠈⠉⠁⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣹⣿⡿⠼⠿⠷⠾⠿⢿⣿⣾⣧⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠁⠸⡿⠷⠀⠀⢠⣶⠶⣶⢈⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⠛
⠀⣿⣁⢤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣽⣿⣿⣿⣿⠀⠀⠂⡀⠀⠀⠀⢻⣶⠀⠀⠈⠷⠿⠋⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠟⡋⠻⠴⢶
⠀⢿⣿⢷⡧⣨⡇⠀⠀⠀⠀⠀⠀⢀⠁⠒⠄⣿⣿⣿⠿⠟⣿⣿⠀⠀⠀⠀⠀⢀⣤⣼⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠹⡇⠄⠛
⠀⣾⣿⣾⣿⢻⡇⠀⠀⠀⠀⠀⣴⢷⢀⠀⠀⠻⠛⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠒⠒⠋⠙⢛⠳⠀⠘⣫⠟⣴
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢨⢶⣁⣷⣆⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣰⠲⠉⢱⣤
⠀⡟⠛⡯⣻⡛⣿⣿⣿⣿⣿⣿⣿⣦⣊⡉⠙⠃⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠠⠄⠸⠿
⠀⠛⣁⡛⠻⠍⣿⣿⣿⣿⣿⣿⠟⠛⢛⠛⠛⠃⠀⠀⢸⣿⣿⣿⢤⣠⣰⣀⡀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢿⣷⣼⣥⣿⣿⣿⣿⣿⣿⢉⠲⠍⠓⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⣷⠀⠘⢿⣿⡿⠃⢀⠘⠛⢛⣻⣿⡀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠀⢀⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠉⢀⠀⠈⠀⣰⣿⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠇
⠀⣦⣤⣤⣮⣾⣤⠀⣀⠀⠸⠄⣄⠀⠾⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡜⠁⢠⣄⡈⠙⠋⠉⠉⣩⣭⠀⢀⣠⣤⣤⣀⣿⣾⣿⣷⣶⡇
⠀⣿⠋⠀⠀⠙⣿⠀⠡⠀⠐⠀⢈⣧⣀⣀⣤⣡⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢿⡇⢀⣿⣿⣿⣶⠀⠀⠀⢘⣿⠐⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣷
⠀⣿⣶⣦⠀⢀⣸⠀⠐⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⡇⠚⠛⠛⠛⠛⠀⠀⣴⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⢀⡀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣤⣤⣤⣀⣀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⣾⣿⣿⣿⣿⣿⠻⣿⣿⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣅⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣕⡸⠿⠿⠿⠿⠿⠇⠀⠀⢀⠀⣿⣿⣯⣉⣻⣿⡀⢻⣿⣿⡇⠈⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣡⣴⣾⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣦⣮⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⣿⣿⣿⣿⡷⠋⠙⢻⣟⠀⠀⠠⠀⠀⠘⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⣿⡿⠃⣠⣾⡧⠀⠀⠀⢀⣤⡀⠸⠿⠋⠋⣻⡇⠀⠳⠈⠀⠀⢀⣀⠀⠁⠀⣼⣿⣿⣿⣿⣿⡏⠀⠠⣀⣽⣧⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠰⣿⣶⣿⣾⣿⡇⣠⡄⠀⢘⣛⠁⢠⡀⠀⢠⣿⡇⠀⠈⠉⠈⠀⠈⠙⢘⡖⠁⡿⠛⠛⠛⠛⠛⡣⠄⢴⣄⠀⠉⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠁⠈⢗⠀⢘⠛⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⢸⣾⣶⣷⣶⡖⠛⠁⠀⠀⠀⣠⣴⡆⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⡄⣾⣁⣀⣽⣓⡾⣿⣧⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⢑⣠⡄⠀⠀⠛⠛⠀⠘⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠛⠛⠛⢻⣿⣿⣻⣷⣶⡅⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣘⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠐⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⢯⣤⠈⣿⣧⣴⠉⠙⠲⢤⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡴⠚⠉⢉⣦⣾⡟⠁⣬⡿
⠀⠀⠀⠀⣤⣿⣧⣙⢻⢦⠍⢣⡹⡳⣄⠀⠈⠂⠀⠀⠀⠀⠘⠁⢀⣤⣞⢋⡎⢭⡴⢿⣩⣿⣷⣤
⠀⠀⠀⠀⠙⢿⣿⣆⢙⠾⠷⣄⢁⠹⠈⢳⣄⠀⠀⠀⠀⠀⠀⣴⡟⢁⠃⡌⡠⠿⠶⡋⣰⣿⡟⠋
⠀⠀⠀⠀⠀⣼⣿⣧⣹⣰⡉⠙⢪⡓⢧⣠⠘⢷⡀⣾⣧⢠⡾⠁⣅⠜⢊⠜⠉⢹⣦⣋⣿⣿⡦
⠀⠀⠀⠀⠀⠈⢛⣿⣯⣍⣳⣴⣈⢙⠢⢝⡢⣬⣿⣿⣿⣿⣥⢜⠡⢒⡉⣠⣦⣚⣩⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣤⣤⠿⢿⠿⠻⠛⣹⣿⣿⡍⠻⢿⢿⡿⢿⣤⣤⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢋⠝⡀⠐⠁⠰⢀⡴⣿⣟⣿⣿⣄⡀⡗⡉⠂⢀⠫⡛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣡⡾⡴⠒⡱⡻⠋⣰⡿⣿⣿⢿⣌⠙⠟⢞⠒⢦⢧⣈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣴⠀⡐⢠⡠⠚⢁⡇⢿⡟⢰⠈⡓⢌⠀⢀⠀⣦⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣴⡁⣼⠀⡊⣸⠃⠀⠀⠘⡆⡇⠈⣧⢸⣦⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢻⣿⣿⣧⣾⡷⠃⠀⠀⠀⠀⠙⢿⣷⣿⣿⣿⡟⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣛⣀⣼⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣧⣀⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⠗⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡿⢛⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⢢⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢉⡁⠀⠀⠀⠀⠉⠑⢄⠀⢻⡿⠃⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠿⠅⠊⠀⠀⣄⡀⠹⡀⠀⣆⠎⡰⠉⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣿⠩⠃⠀⠀⣿⣿⣦⠈⠲⣿⠔⠉⠀⠁⠀⠀⠀⣀⡤⠐⠂⠀⣀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⣠⡀⠀⠀⠀⠀⠋⣿⢊⠇⠀⠀⠈⠻⣿⠀⢠⢁⣴⣿⡟⠀⢀⡤⠊⠀⢇⡠⠊⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠒⢄⠈⠡⡀⠀⠀⠀⢘⢻⡕⡲⠀⠀⢰⠒⢌⠣⡌⣾⣿⡿⠁⢀⠂⠸⠀⢠⡫⠔⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠐⠂⢵⣄⢡⠀⢿⠗⢀⢹⣯⢓⠀⠀⠀⠢⣈⡅⠗⣋⡁⠀⠀⡌⠀⢀⡴⠋⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠈⠳⡀⠈⠀⢀⣁⣿⡪⢢⠀⢀⠔⠁⠀⠀⠀⠀⠉⠙⠢⣀⡼⠑⠂⠉⡸⠃⠀⡠⠒⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠄⢠⢡⣄⠀⠙⡛⠊⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠊⠀⠀⠘⠀⣠⠎⢀⡠⠄⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠀⠀⠀⠀⠹⡄⢀⠖⠋⠀⠇⠀⠀⠀⠀⠀⠀⢠⠔⠒⠂⢄⡀⠀⡇⠀⠑⠢⢤⣶⠞⠐⠒⠮⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠤⢄⡉⠲⠤⠄⢀⡽⠃⠀⠀⠀⣀⠠⠤⠤⠀⣀⣠⠁⠀⠀⠀⠀⠈⢶⠀⠀⠀⠀⠀⠙⡝⢏⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠌⢑⣤⡠⠊⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⡉⠠⠊⠉⠑⢄⠀⠀⢃⡀⠀⠀⠀⠀⢡⡈⠑⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢠⣤⠸⡃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠔⠛⠓⢄⠀⠀⠀⡀⠀⡘⠀⠉⠢⡀⠀⣠⢀⠹⣉⠙⢆
⠀⠀⠀⠀⣀⠤⡒⠈⠁⠈⢄⠀⠉⠒⠡⢀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢺⠀⠀⢀⣠⠇⠀⢀⣇⠔⠳⠀⠀⠀⠈⢶⠳⡀⠱⠀⠈⠉
⠀⢀⡴⠋⠀⢀⣈⣢⣄⣀⡀⠑⢄⠀⠀⠀⠱⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⣀⠊⠀⠀⠀⠇⠀⠀⠀⠈⣀⠈⠙⠁
⢀⢎⠄⠂⠉⠀⣀⡤⠴⠒⠛⠉⠉⢛⡶⠶⠄⠳⡀⠀⠀⠀⠡⣀⠀⠀⣠⡖⠉⠑⠄⠤⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠏⠀⠀⣤
⠾⠒⠂⠀⠒⠚⠠⢀⡀⠀⢀⠤⠊⠁⠀⠀⣀⠤⢛⠦⣀⣀⠠⠊⠈⠉⠁⠘⢄⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡈⠀⠴⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠒⠒⠒⠒⠉⠠⣖⣶⠟⣛⣆⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠤⠰⠎⠁⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⡽⠏⠥⠂⠈⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠒⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡽⠛⡔⠊⠀⢀⡠⠂⠁⠙⢦⣀⠀⠀⣀⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⠏⡂⠁⠁⠀⣠⠋⢀⡀⠤⣲⠋⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠁⠀⠀⡐⠉⠁⠀⢀⠜⡇⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣾⢢⠈⠁⠀⠀⢀⠁⠀⣀⢴⠃⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⢚⣿⢊⠒⠀⠀⠀⠀⢸⠃⠉⠀⠏⠀⠀⡀⡠⠊
⠀⠀⠀⠀⠀⠀⢀⣘⣿⢻⠚⠀⠀⠀⠀⠀⠘⠀⠀⠸⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡝⠋⠙⠀⠀⠀⠀⠀⠀⠀⢃⠀⡆⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣧⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣞⠉⠂⣤⣤⣐⣒⣒⣠⣤⡄⠈⢙⡆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢦⠁⡀
⠀⠀⠀⠀⢀⣀⡀⢀⡔⢻⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢹⠓⣄⠀⣀⣀
⠀⠀⠀⣀⣤⠌⣹⠟⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠘⢿⡉⢥⣄⡀
⠀⠀⠀⠉⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠈⠁
⠀⠐⠲⢶⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣖⢚⡋
⠶⠟⠉⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⠓
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⢰⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢱
⠀⠈⢆⡆⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣆⠎
⠀⠀⠀⢣⠀⠀⠀⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠈⣧⠀⠘⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠆⠀⢠⡟
⠀⠀⠀⠀⠰⡱⡴⠆⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠁⠆⡰⡱⠁
⠀⠀⠀⠀⠀⠐⢕⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠕
⠀⠀⠀⠀⠀⠀⠈⣻⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣏⣃⡀⠀⠀⢦⡀⢀⠀⠈⠁⢀⢌⡆⠀⠄⢀⠰⣫⢷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠯⠩⡗⠅⠘⢣⡨⢃⠚⠱⠦⠥⢘⠨⠀⡨⢾⡯⠹⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⠘⣭⣡⠒⢀⠀⠃⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠚⠙⠉⠙⠙⠒⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠶⠾⠁⠀⠀⠀⢤⡠⠤⠤⡠⠄⠀⠀⠀⠹⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡄
⠀⠀⠀⠀⢠⣶⠟⠇⠀⠐⠊⠑⠒⠢⠀⠀⠀⠀⠀⠔⠒⠒⠉⠒⠀⠘⠟⢷⣄⠀⠀⠀⠀⠀⢰⢻⢸⣷
⠀⠀⢀⡤⣾⠷⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣦⡀⠀⠀⠀⢸⣾⢸⣿⡀
⠀⠀⠸⣿⣿⣄⣀⣀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢀⣾⣀⣀⣠⣾⣷⡟⠀⠀⠀⢸⢿⢸⣿⡇
⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⠋⠀⢀⣠⣶⣿⢸⣿⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠙⠻⣯⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣯⡿⠋⠛⠉⠁⠀⠀⠸⠟⠛⢻⠈⣿⠀⡟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠖⠛⠛⠛⠛⠛⠉⠉⠉⠹⠛⠛⠛⠛⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠤⠶⣷⣤⣴⣤⣤⣤⣴⡷⠦⠤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡇⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢿⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢸⡇⢀⣿⡇⢸⣇⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡏⡟⠏⠉⠉
⠀⠀⠀⠀⠀⢀⡤⠔⠉⡩⡤⠖⠂⢸⡇⢸⣿⣧⢸⣿⠀⠒⢤⢌⡉⠳⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣀⣤⣤⣿⣇⡾⣿⠿⣌⣿⣤⣤⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⢸⠀⢸⢸
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠉⠀⠈⠛⠀⠀⠀⠘⠁⠀⠉⢻⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢿⠘⣦⠏⣸
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢶⡤⢷⣤⣴⢦⡴⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣀⣀⢀⣀⣀
⠀⠠⠀⠋⠋⠛⠚⠛⠛⠓⠠⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠒⠉⠓⠀⠉⠀⠉⠒⠘⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⣙⠇⠀⢀⠢⡤⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⢀⡀⣀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠡⠀⠀⠈⠉⠀⠁⠁⣤⠈
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⡄⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠠⠌⠀⠠⡀⠀⠀⠀⠀⠦
⠀⠀⠀⣤⣀⣤⡀⣀⣀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡹⠟⠚⠛⠛⡦⠆⠀⠀⠠⠉⠀⠀⠀⠀⣴⣼⣳⣿⡶⣤⡄⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⠂
⠀⠀⠀⠀⠘⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⡞⠀⠈⠀⠀⠀⣀⠁⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢁⠻⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⡀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠀⠀⠀⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠢⢄⠀⠀⠀⠠⣀⢀⡀⡀⠀⢂⠤⣀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠻⠟⠶⠓
⠀⠀⠀⠑⠒⠂⠀⠀⠀⠈⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠬⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠈⠀⠀⠹⡀⠹⠋⣳⡍⣿⡴⢿⣟⠉⡝⠀⠜⡩⠊⠰⢁⠞⠙⠁⡠⠞⠁
⢤⣄⠀⠀⠀⠀⠀⠁⠈⢢⣴⠦⠤⣤⣄⡀⠀⠀⠀⠀⢠⢖⠛⣧⣄⢸⢱⠟⠋⠀⠀⣻⡜⣁⣤⣀⣁⣀⣀⢄⣀⣤⡈⠀⠀⠀⠀⣠⣔
⣒⠠⠀⠒⠄⠀⠀⠀⠀⣟⡀⠠⢀⠤⣼⠋⠗⠓⢀⢴⢟⡀⠀⠈⠀⠚⠓⡶⠀⠀⠈⠋⠉⠉⠀⠁⠠⠏⠀⢀⠃⠀⢻⡆⡠⠐⠉
⡒⠀⠠⠤⣀⠀⠀⠀⠀⣽⠂⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⠀⢠
⠉⠛⠂⠀⠀⠀⠀⠀⠀⠈⢲⡆⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠠⢿⠉⠉⡧⠀⠀⠀⢘⡆⠀⠀⠀⠀⠑⠉
⠤⠄⠀⠀⠀⠀⠀⢀⡠⠤⣴⢳⡤⠀⠀⠀⠀⠀⠁⠰⠐⠀⣀⠀⠀⢢⠈⡄⠊⠁⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠚⣫⠄
⠴⠒⠦⠤⠀⢀⡜⠉⠛⠁⠘⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠛⠉⠉⠷⣶⢦⡄⢀
⡒⠖⠂⠀⠀⣸⡏⠁⣀⠔⠚⠀⠈⠒⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⠟⣙
⢛⢉⡴⠎⠉⠃⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⡀⠶
⠈⣿⣀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠒⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤
⡒⡚⠻⠷⢶⣟⠀⠈⠳⢴⣎⡠⠀⠀⠀⠀⠀⠈⠀⢠⠀⠄⠆⠀⠀⠀⢀⠀⠠⠄⠈⠈⠀⠀⠀⠀⠀⠁⠀⠄⢰⡄⠀⠀⣀⣀
⢀⣀⡀⠀⠀⠘⠳⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠄⠀⠀⠀⠀⠀⢴⢼⠁⢤⠚⠋⠉⠂⢉⣉
⠿⠁⠀⠀⠀⠀⢀⠀⠍⠁⣻⠀⠀⠀⠀⠈⠙⠉⡉⠀⡀⠀⢀⣀⡁⠀⢆⠀⠀⠈⠁⠀⠈⠉⠀⡠⠶⣤⡤⠞⠋⢀⡖⠀⠈⠐⠒⠄⠠
⠈⠀⠀⠀⡠⠂⠁⠀⢀⣴⠿⣄⣄⣡⠴⡄⠀⣠⡷⢚⠂⠀⠀⣹⡍⠂⢢⣄⣀⣤⠟⠦⠴⢧⣀⣀⣶⠏⠓⠲⠞⠋⠁⠀⠈⠀⢄⠐⠠
⣖⠔⠊⠀⠀⡠⠔⠋⠙⠁⠀⠀⠀⠀⠀⠉⠋⣱⠃⠸⣏⣠⣴⠋⢷⡄⠀⠀⢡⠇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠁⠀⢀⡴⢋⡤⠊⢁⣀⣠⢂⡖⢠⢈⡠⠀⢰⢃⣴⣤⡌⢷⡱⢳⣧⣙⡃⢟⢉⠀⠀⠀⠁⠀⢰⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠋⠀⠈⡥⣄⠐⠄⠀⠂
⠀⠀⠀⠀⠐⠄⣰⡾⠃⢠⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠂⠀⠀⠀⠄⢠⣀⣀⡠⠊⢐⡄⠀⣀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣄⣷⢄⠀⠀⠀⠆⡯⠀⡰⠋⠠⢀⠀⠀⢃⢠⣶⣮
⠀⠀⡈⠀⠀⠀⢀⡇⡘⠀⠐⣿⡾⠖⣢⣾⡽⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⡄⢈⢁⠄⠀⠀⡏⠖⣀⡁⣽⣋⣵⠞⠋⢀⣀⡀⠄⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠡
⠀⣨⠃⠀⡔⣼⢷⣯⠊⡸⢫⡟⠁⠀⣴⠋⠁⠙⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡸
⢰⡇⠀⠈⣰⠃⠀⢀⡼⢡⡏⠀⠀⠀⣇⠀⣾⠟⠁⡀⠂⠘⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⠃⠠⣏
⡞⠀⠀⣰⡅⡀⠀⣼⡇⢹⠀⠀⠀⠀⠙⣄⠀⠉⠁⣀⡄⠀⠀⠀⠀⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡠⠐⠛⠓⢦⣔
⡇⠀⠀⠁⠔⠁⠀⡅⠑⠘⡇⠀⠀⠀⠀⠀⠀⠀⠋⠹⠙⠀⠐⢀⡀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠤⡰⢀⣤⣀⡞⠃⠈⠉⠀⣠⣴⡤⠀⢉
⡃⢊⠄⢸⠁⠀⠠⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡚⠉⠉⡐⢄⠀⡨⠛⠉⠉⠁⠰⢄⡀⠀⢻⡥⠐⠁
⡿⠌⡆⡔⠀⠀⢰⡆⠀⠀⠀⠛⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢩⣢⡴⠟⠲⢄⡔⠂⠈⡷⠀⠀⠀⠀⠀⣀⠀⢱⡄⠄⠀⠀⠉⠣
⣇⠀⠘⠀⠀⡀⠀⢟⠠⡀⠠⠐⠤⠙⠦⢀⡀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠒⠉⠀⠀⠀⠀⠈⢓⡈⣕⣷⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠂
⣧⠀⠀⠀⠀⠀⠀⡼⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠞⠉⠁⠀⠀⠀⠀⠀⢂⡨⠤⢀⡈⠻⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢻⡴⠁⠀⠀⡃⠀⠀⠘⣦⡐⠢⠄⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠤⣄⠙⣄⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠁⠆⠀⠀⠆⢁⠀⠘⠀⠈⠝⢯⣍⢐⠸⡀⠤⠠⠄⢀⠝⠃⠀⠀⢀⠔⡪⠀⠀⠀⠀⠀⠸⣇⣾⠀⠀⠀⠑⣄⠀⠀⠀⠤⠐⣋⠉⠁⠀⠢⢀
⡀⠀⣄⠘⠀⠀⡆⢀⠀⠈⢄⠀⠌⠙⠷⣦⣤⣤⣈⣁⡠⣤⠴⠊⠡⠈⠀⠀⠀⠀⢀⡀⠀⠸⢿⡆⠀⠐⠀⠀⠙⠂⠀⠀⣀⣀⣈⢀⡀
⠀⠈⠸⣦⠀⠀⠀⠀⠃⠀⠀⠁⠀⠠⡀⠀⠀⠈⡀⠁⡸⢁⠔⠀⠒⠂⠀⠀⠀⠈⠁⢀⡀⠤⠷⢵⡀⢀⠈⠀⠀⠂⣲⣆⠠⠒⠒⠒⠤⣀
⠀⠀⠀⠙⣦⡐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠀⠐⠡⠈⠀⠀⠀⠀⠀⠀⣀⠀⠂⠁⣀⠀⠀⠀⠀⠠⡀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠈⢻⣄⠀⠀⢡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⣠⣤⡶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠙⡖⠶⠀⠴⠴⠆⠀⠒⠐⢄
⠒⠒⠀⢄⠀⠀⠉⠳⣄⠀⠳⡔⠈⠂⠀⡀⠄⣀⠀⠀⠀⢀⡠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣂⠀⠀⠀⠠⢄⠀⠀⢸⠄
⠀⠀⠀⠀⠡⡐⢄⣀⠈⣙⣶⣿⣶⣤⣬⣭⡢⠶⠎⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠈⠰⢿⠃⠀⠊
⠀⣀⣀⠀⢀⣈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠊⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⡀⡀⡀⢀⣀⣀⡀⢀⡀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄⢀⣴⡆⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⣶⣄⠀⢼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠘⠛⠁⣾⡿⠠⣿⡆⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣾⡗⠸⣿⡆⠙⠛⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢁⡀⠄⣀⣤⣿⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⢿⣧⣄⡀⠀⣀⠁⠈⠛⠁
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠴⠿⣿⠞⣽⡿⠟⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠿⣿⣝⢾⡿⠷⠄⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠈⠀⡨⠇⠀⠀⠀⣀⡴⠋⠀⠁⠀⠀⠀⠢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠁⠈⠳⣄⡀⠀⠀⠀⠯⡀⢈
⠀⠀⠀⣠⣬⡲⠤⢤⠤⠖⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠓⠦⢤⠤⠴⣪⣤⡀
⠀⠀⢘⣛⡋⢁⣴⣶⡤⠁⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⡇⠱⣴⣶⣄⠉⣛⣛
⠀⠠⠾⠿⠃⠾⠿⠟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⠿⠿⠆⠻⠿⠧
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐⢶⣶⡄⢶⣶⣦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣶⣶⠆⣴⣶⠖
⠀⠀⢨⣭⣅⡈⠻⠿⠓⡀⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⡰⠻⠿⠋⣀⣭⣭
⠀⠀⠀⠙⢛⠵⠒⠚⠒⠦⣬⡂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣢⡤⠖⠒⠒⠲⠝⠛⠁
⠀⠀⠀⠀⢈⠀⢑⡆⠀⠀⠀⠉⠳⣄⠀⡀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣖⠁⢈
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠲⣶⣿⢦⣻⣷⣦⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣶⣿⣫⢾⣷⡶⠂⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⡈⠁⠂⠉⠛⣿⣶⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⡟⠋⠁⠂⠉⡀⢀⣤⡀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢠⣤⡀⢿⣷⠀⣿⠇⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢿⡇⢰⣿⠇⣠⣤⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⠈⠻⠇⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠿⠋⠀⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠻⠏⠉⠀⠀⠀⠀⢀⠲⣿⣷⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⡠⣆⡄⠀⠁⠀⢦⡄⠈⠙⠛⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣀⠠⠤⢂⡰⣣⣮⢷⣩⡥⠤⠄⠈⠁⠒⠰⠶⠆⢉⢆⡀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⢖⣯⣵⣏⣇⣿⣾⢿⡟⣢⠁⡔⠀⠠⠐⠀⠀⡄⠘⠬⢵⢋⡴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠖⢀⣤⣄⣁⡉⢋⢽⣿⣿⣟⣫⣿⠻⣧⠀⠓⡠⢉⠧⢦⣧⠀⠠⣀⣤⠋⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠯⡷⡿⣿⡇⣹⣺⡯⣬⡯⢿⣿⡦⠍⣰⡆⢣⣈⠙⠂⠁⠅⢀⠜⠉⠡⠄⢠⡴⠶⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢷⣾⣿⣿⣿⢿⢉⣿⡞⠕⢡⣧⠴⠊⠹⡙⠀⢹⡖⢲⣔⣶⡂⠀⠀⠐⣦⠛⣃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡽⣷⣯⣿⣽⣐⣿⠛⡢⠺⠋⣉⣁⡀⡙⢤⣹⠘⡉⢦⣼⣯⡶⠈⢆⣼⠋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⣻⣹⣿⣿⣟⣷⡿⣴⢏⣠⠖⠋⠉⠀⠈⠉⢷⣟⢀⡷⠳⣼⠟⡉⣓⣾⡋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⡫⢷⡧⣯⡝⣿⣯⣿⣿⣿⠀⢀⠀⠀⠀⠀⠈⣿⡿⡻⢄⣹⠞⣱⣼⠷⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣻⣿⣭⣗⣯⣏⣷⡫⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣿⢰⡴⣌⢹⡼⣤⣏⡱⠊⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣿⡿⢯⣻⡟⣯⡝⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣦⠙⣾⣉⢻⡤⠆⢸⣶⡒⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⠚⠋⣳⣿⡐⣿⠁⠀⠀⠀⠀⠀⠀⠶⠟⠋⣰⢋⣴⣇⠛⣾⡅⡂⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣦⣀⢸⢸⣿⠀⠀⠀⠀⠀⢑⠄⠀⢠⣾⣿⣦⣹⢯⢟⢻⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⠌⠛⣾⢿⡄⠀⠀⠀⠠⠀⠀⠀⠀⢰⣽⣿⣿⣧⣃⢜⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢾⠑⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢻⢏⡴⢊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡂⢻⡿⣦⡀⠀⠀⠀⠀⢀⣆⠀⢈⡠⢻⣟⣉⠭⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⡜⠄⣿⠛⠲⣶⠲⣺⠟⢳⣿⣠⣂⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣱⠋⢉⠽⣿⣗⡉⠙⢣⡤⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢰⠋⠀⣜⠀⠉⢣⡀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠐⠊⠉⠓⠰⠖⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠢⣄⡈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⠤⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠙⠳⡂⢌⡛⢶⠤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠳⡃⠀⡤⠚⠉⠉⠲⣄⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠲⢌⠉⠓⠊⠙⠳⡴⠚⠓⠶⠉⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡇⠀⣀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡽⠄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠗⢋⣵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢿⠄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠦⡼⠘⢤⠃⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⡆⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⠀⠀⠉⢹⣃⣀⣤⣤⠶⠚⠉⠀⠀⠀⠀⠰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢈⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣁⣀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠅⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠆⠀⠀⠐⠒⠛⠻⠶⡄⠀⠀⠀⠀⠀⠀⠀⡤⢝⣷⣌⡉⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠉⠓⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠔⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⣴⣴⡀⣶⣾⡁⠚⠆⠀⠀⠀⠀⠀⠀⠀⢺⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠘⠇⢷⡏⠃⠙⠀⠀⠀⠀⡔⠢⠤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⣞⠉⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠙⠢⢤⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠰⣕⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣖⠚⠁⠀⠀⠀⠀⠀⠀⠁⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡏⠹⡄⠀⠀⠀⢀⡄⠀⠀⠀⡇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡘⠀⠀⠉⠓⠒⠚⠁⠘⠦⠤⠞⠁⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠦⠀⠀⠀⢀⠄⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡤⣄⠈⠢⡀⠃⠀⢀⣀⠀⠈⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢹⣶⣿⣇⠀⠙⠀⠀⣿⣽⣇⠀⠈⠀⠄⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠉⠛⣠⠀⠇⠀⠙⢿⡗⠈⠀⢸⠀⣀⣴⣲⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡔⠀⠘⠀⡘⠂⠀⠀⠅⠀⠀⠒⠀⠸⣿⣿⠇⠀⠸⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⢀⡘⠀⢀⣂⠀⠀⠀⠀⠦⠀⠀⠘⠋⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠙⠀⣿⣹⡇⠀⠠⠀⠀⠀⢀⠀⠖⠁⠐⠀⠀⣴⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢄⠙⢿⠇⠀⠀⢀⣤⡀⠀⠀⠀⠀⠂⠀⢰⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠨⡀⠉⡠⠠⠂⢾⣷⡇⠀⡂⠀⠀⠀⠀⠈⣿⠟⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠄⠛⠀⠁⠘⠟⠀⢐⢇⣤⣄⠀⢀⢈⠅⠀⠀⠴⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠙⠀⠀⡁⢀⡌⢸⣿⠟⠀⠈⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢠⣶⣦⠀⠀⠀⠀⢸⡀⢈⠁⠀⣀⠀⠄⠈⠀⣰⣯⡽⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠐⠉⠀⢡⠔⠀⣠⡤⡄⠀⠢⠿⠛⠁⠠
⠀⠀⠀⠀⠀⠰⣧⣀⡓⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣴⠚⠒⠐⠁⠀⣰⣶⠀⢠⠀⢸⣿⡿⠃⠘⠁⠀⢀⠌⣀
⠀⠀⠀⠀⢾⣄⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠐⠈⠁⠀⣾⠆⢀⡠⠛⠉⠀⠈⠈⠀⠀⠀⡰⠃⢀⣠⣄⡀⠈⢁
⠀⠀⠀⣀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠸⠃⠀⠂⠀⠀⠒⠋⣂⠀⢈⠁⢠⣴⣦⠀⣤⢠⣿⣿⡾⠃⢀⠌
⠀⠀⠀⠾⢷⣦⣤⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣝⠛⡧⣄⠁⠠⠶⣸⠁⠘⠟⠃⠹⡶⠿⠟⢛⣼⣿⣷⢵⣾⢛⠟⠳⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⡡⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⠾⣻⡟⢽⣫⣷⡠⠒⣻⡀⣀⠈⣙⣉⡉⣠⠈⢋⣉⣉⣨⣾⣿⣻⣯⡚⣸⡇
⠀⠀⠀⠂⠀⠐⠒⠊⢉⣠⡾⠷⠒⣒⠢⠄⡄⣀⣀⡠⠴⣞⠩⠔⣺⢇⡤⢃⠹⣍⡇⠀⣩⠔⠁⠈⠛⠋⣠⡁⣀⣤⡀⠁⠩⠙⠛⢫⢁⡀⠊
⠀⠀⠀⠀⣄⠄⠰⠒⠱⠣⠀⣀⠀⠀⠀⠂⡀⠀⠄⢀⡹⠅⣊⣤⡏⡁⠘⠘⠄⣝⢻⠀⠰⢀⠑⠂⠀⠒⠠⠀⠈⠉⠀⡐⠠⣤⣶⣶⣄⠀⠢
⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⠀⠄⠠⠀⠀⠐⢀⡊⢥⠖⣪⠞⡋⣿⠌⡹⣋⢺⠝⡏⠄⣬⠙⠆⠀⠛⠛⡠⠈⠑⠋⠉⢐⠂⠀⠉⢍⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠙⠦⣰⡄⠈⢀⣀⠠⠘⠠⠰⠴⣰⣯⠷⠋⣠⣡⠉⠖⠒⠙⠋⠙⠁⠀⠀⠉⠁⠁⠈⠁⠐⠒⠶⢶⡌⣧⠀⢠⣤⣤⡈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⢤⡀⢀⣀⠤⠴⠿⠋⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢉⠛⠃⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠁⠀⠀⠈⠀⠉⠀⠀⠀⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠰⣄⣀⠀⠀⢀⣠⣶⠾⠼⢶⣤⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢄⣽⣷⣶⣾⣿⣟⣥⣄⠀⠀⠈⠛⠻⢷⣄⡀⢤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣷⣽⠏⠁⡦⠊⠀⠀⠀⠀⠀⠀⠈⢲⣾⣿⣏⣴⡙⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡄⠀⠀⠀⡠⠔⠚⠓⠒⠄⠀⠈⠙⠍⠙⢿⣧⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠁⠉⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⡀⢠⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣧⡑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣾⣷⣄⢀⡀⢤⣠⢤⡀⠀⠀⠀⡠⠀⠀⠐⢺⣿⠁⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠈⢦⣙⠿⠿⣿⡛⣆⣈⣉⣙⣳⣶⣍⣂⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⢈⠛⠻⠿⠛⡋⠉⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠚⡛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⣙⡇⠀⠀⢀⠺⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠙⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠹⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⢀⠀⢀⣘⣾⡷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢴⣂⠀⡀
⠀⠀⠀⠀⠙⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠦⢶⡥⠀⠀⠸⣥⣎⣁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣇⡴⣻⣄⠀⣺⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠉⠁⠀⢠⠄
⠀⠀⠀⠀⢰⡄⣿⡏⢙⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡐⠻⢶⡄⠀⠰⣅⠠⠦
⠀⣈⣙⣿⣾⢃⠈⠀⠛⠀⢻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠜⠀⠀⣧⡈⠛⠀⣀⡀⠀⡀
⠀⠙⢛⣿⡟⠋⠀⢰⠀⣤⡄⠑⣆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣆⣸⠀⠀⠀⡌⠀⠠⠀⢧⠤
⠀⠲⣶⠟⠁⠀⠀⠈⢷⡾⣷⣶⡏⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⠂⠄⠰⠂⠒⠁⣀⣈⠐⠂
⠀⠈⠉⠀⠈⢃⠀⠉⣠⡟⠋⠀⠹⠀⢶⣤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⣶⣋⢑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠏⣤⣄⠦⣀⠃⣄⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠘⢿⡷⢖⠀⣰⢒⣄⢿⣾⡿⣋⣁
⠀⠀⠀⠀⠀⠀⠀⠊⢠⠏⠱⠒⡉⠀⠀⠦⣠⣾⣿⡟⠀⣛⡲⢵⣦⠀⢠⣴⣾⡯⠅⠀⢸⣷⠈⢀⠂⢿⡧⠚⠂⡘⠉⠐⣌⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡌⣻⣧⡅⢸⣿⣷⣶⣯⣽⣿⣿⠶⣿⣿⢿⣶⣶⣷⣾⢿⡗⠀⠀⢺⠉⠓⠀⠙⢎⠃⡈
⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠐⠛⠻⠿⢷⠈⠛⠛⠛⠛⣿⠟⣼⠀⢻⡛⠇⠈⠛⠛⠛⠻⡶⠓⠀⠀⠉⠀⠀⠀⠠⠏
⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠛⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠙⠁⠀⠀⠀⢀⡾
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⡀⠀⠀⠀⠀⠈⣿⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⢲⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠧⡀⠀⠀⠀⠀⢹⢿⣻⣿⡇⡀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣠⠶⠋⠁
⠀⠀⢿⣿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣘⣿⣿⡏⠴⠠⡄⠀⠀⠙⢿⣿⣿⣿⣛⠅
⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣉⣩⡽⢯⣶⣍⣲⠆⠐⠶⢄⣹⣿⣿⠇
⠀⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣾⣏⡓⣶⣾⣿⣿⡍⣴⠄
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣽⣿⠿⢙⣙⣿⣻⣿⣿⣽⣋⣽⣛⢻⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣙⣉⣿⠉⠀⢻⡉⠻⣿⣿⣿⣿⡭⠉⠉⠀⢀⣄
⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠸⡟⡿⢿⣯⣽⣿⣷⣄⠀⠙⣿⣿⣿⣿⣿⣷⣿⡆⢀⣾⣿⣿⣶⣤⡀
⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣭⣀⡸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠻⣮⡛⣿⣷⣄
⠀⠀⢀⣿⠟⠋⠀⠀⠀⣠⣾⣿⣿⣿⠟⢑⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠐⣩⡿⠟⠋⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡖⠀⠀⠀⠀⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠆⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣮⢳⡐⡄⠀⠀⠀⠀⠀⠀⡄⣾⠈⢁⡀
⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⣧⢳⡀⢀⣤⣤⣤⣀⣷⡸⢀⣾⡇⠀⠀⢀⣶⣮
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣸⣿⣟⣷⣿⣿⢟⣛⣿⣿⣷⣼⣿⣷⣶⣷⣿⣿⣃⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢹⣶⣾⣿⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣭⣿⡿⣹⣿⡟⠁⠀⢀⠍⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⣤⣄⠀⠄⢘⢓⣏⠀⣠⣿⣎⣻⣿⣿⣿⣿⣯⣭⣻⡿⣿⣿⣿⡿⠉⢰⣿⣏⣤⠀⠀⠈⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢿⣷⣷⡦⣈⠁⠀⣾⡟⣛⢛⣿⡿⡿⣿⣟⣭⣽⣷⣶⣾⣿⣡⠀⠈⢿⡿⣿⣾⣶⣶⣀⣀⠈⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠺⡦⠀⠀⠀⠀⠀⠀⠉⠳⢶⣦⣝⣲⣿⣿⣁⣿⣿⣿⣿⣯⣹⣿⣿⣽⠛⠛⢿⣧⣎⣴⣿⣷⣹⣿⣟⣿⣿⣿⣿⣾⣵⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣽⣿⣿⣭⣿⠏⠀⢿⡛⠩⠀⠀⠘⠃⣸⣷⣍⢻⣟⣮⢻⣼⣿⠿⠛⢋⣉⣤⣴⠂
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣿⣿⣿⣿⣿⣿⠎⠋⢐⡂⠈⠐⢶⣶⠄⠘⣧⣽⣭⠛⢻⡟⢛⣉⠭⠔⢒⡈⠉⣉⠡⠤⠴⠶⡂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⣉⣿⣿⡿⡿⠆⣐⣿⠀⠀⠀⠀⠁⠀⢀⡿⢿⣿⠀⣠⢫⣧⣶⣾⣿⣯⣭⣶⣶⠖⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣤⣾⢠⣿⢧⢸⣿⣿⣟⢷⣿⠀⠙⠁⠀⠀⢠⣾⣧⡤⠉⣠⣾⣷⣦⣭⡾⢿⡿⣿⣟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠁⢼⣿⣿⣎⣻⣿⣿⣾⣿⣦⡀⣀⠴⠆⣼⣿⣿⡠⠐⠋⠻⠻⢿⣟⣱⡏⣶⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣽⣿⡿⠻⠛⠛⢉⣨⣿⢇⠈⠉⠁⣩⣿⣿⠿⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣦⣤⣠⣶⡿⣿⣿⣟⡷⣶⣿⣿⣏⡀⠀⠀⠓⠘⢿⣿⡿⠁⣸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠟⠉⡈⣩⣴⢿⣿⣧⣽⢷⣼⡿⣿⣿⣤⣬⣽⣻⣿⣎⡓⡄⠀⢈⡻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠹⠿⢷⣽⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡿⣆⠢⡹⣿⣧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠟⠀⠀⠀⠀⡈⠀⠀⠀⠙⣧⢻⣎⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⣆⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣠⣤⣤⢤⣤⣤⣙⢳⣄⠀⢀⣴⠟⣉⣀⣀⡀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⣠⡾⠟⠉⠀⠀⠀⠀⠈⠙⠷⣿⣧⣿⣵⠟⠋⠉⠉⠛⢷⣄⠀⠈⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⢁⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠉⠛⠛⠲⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⣤⣄⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠏⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⢀⣤⣤⡀⠀⠀⠀⣿⠁⠀⠀⣀⣀⣀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠙⢷⡄⢘⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⣿⠉⣿⡗⠀⠀⠀⣿⠀⠀⢰⣿⠋⠙⣧⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⣀⣀⣀⣘⣿⡇⠀⠀⠀⠀⠀⢀⣴⠶⢶⣤⡀⠀⢻⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠁⠀⣿⠀⠀⣠⡶⢷⣦⡀⠀⠀⠀⠀⢀⣿⡿
⠀⢠⣴⠟⠋⣉⣉⣙⣻⣿⡄⠀⠀⠀⠀⢸⣷⣤⠀⠈⠻⣦⠈⣿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡟⢀⣼⠏⠀⢶⡿⠃⠀⠀⠀⢀⣼⣿⣤⣤⣄⣀⡀
⢰⡟⢀⣴⠟⠋⠉⠉⠉⠉⠛⠻⠶⣦⣄⡀⠈⠁⠀⠀⠀⠙⣷⡘⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⢡⡾⠃⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⠛⠻⣯⣍⠻⣦⡀
⣿⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⠀⠀⠀⠈⢻⣿⣦⣄⡀⠀⣿⡄⢀⣤⣤⣼⣷⡟⠁⠀⠀⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠹⣆⠈⣿
⢿⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⣼⠋⠁⠉⠙⣷⣼⣷⠟⠁⠀⠙⣿⡀⠀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼
⠸⣧⠈⣷⠀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⡀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⣾⣷⠟⠉⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⢠⡿⢠⡿
⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣤⡀⢀⣠⣿⣇⠀⠀⣠⣾⣏⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣿⠇⠀⠀⠀⢠⡟⢁⣿⠁
⠀⣿⠀⢸⡇⠀⠀⣠⣤⠀⠀⠉⠛⠛⠿⠶⠶⣦⣤⣤⡾⠋⠉⠉⠙⠛⢿⣿⣿⣿⣿⣷⡿⠛⠉⠉⠉⠙⢷⣄⣠⣤⣴⡶⠶⠟⠋⠁⠀⣠⣤⡀⣿⠁⢸⡇
⠀⣿⠀⢸⡇⠀⠈⠿⠿⠃⢀⣠⣴⠶⠶⠶⠾⠟⠛⢻⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣼⠿⢿⣶⣶⣦⣤⣤⣀⠀⠀⢿⡿⠃⢹⡇⠸⣷
⢰⡿⠀⠘⣿⠀⠀⠀⠀⢠⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣶⣶⣶⡿⠟⠉⠙⣿⠋⠈⠙⠻⣶⣶⣶⡞⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠈⣷⠀⢻⡇
⠸⣷⠀⠀⢿⡀⠀⠀⠀⠈⠿⣶⡿⠁⠀⠀⠀⠀⠀⢀⣠⣴⠞⢻⡏⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⣿⠉⠛⠛⠶⢦⣤⣀⠀⠀⣷⣦⡾⠃⠀⠀⠀⠀⣿⠆⢸⣿
⠀⢿⡄⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⢻⡄⠀⠀⠀⣸⣿⣷⣄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⠙⠛⢶⣄⠁⠀⠀⠀⠀⢀⣴⡟⠀⣸⡇
⠀⠈⢿⣄⠀⠀⠛⠷⣤⣤⣤⣤⡶⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣼⣿⢶⡶⠾⠋⢸⡏⠙⠛⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣿⣟⣥⣤⡾⠟
⠀⠀⠀⠙⠻⠶⠶⡶⢶⣿⡟⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⢟⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⠻⣦⠀⠠⣶⣄⠀⠀⠀⠀⠀⢻⡌⠙⣯⡉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡇⠀⠀⠀⠀⠀⣾⡛⣃⣴⠟⢁⣾⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣇⠙⠷⣦⣼⠟⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⢻⣄⡀⠀⠀⠀⠈⠛⠋⠁⠀⣸⡇⢀⣀⠀⠀⠀⢰⡟⠀⠀⠀⢰⣿⣼⡿⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠈⠛⠳⠶⣤⣄⠀⣴⣶⠀⠹⣷⣾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠋⠁⠀⠙⠟⢁⣀⣀⣀⣀⣠⣾⠋⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠙⢿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⣉⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠀⣠⡾⠃⠀⣠⣴⡶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠻⣦⡀⠀⠀⠀⠀⣠⡾⣿⠟⣿⠻⢦⣤⣴⠾⠋⢀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠈⠛⠷⠶⠶⠛⢋⣴⠏⠀⠘⢷⣦⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣤⣴⠶⠟⠁⠀⠀⠀⠀⠈⠉⠉⠁

⠂⠀⣀⡀⠀⠐⠀⢀⣀⠀⠀⠘⣷⣤⡴⡿⠀⠀⢀⠀⠄⡀⠘⠂⠀⣀⡀⠀⠐⠀⠁⣀⠀⠀⠘⣷⣤⡴⡿⠀⠀⢀⠀⠄⡀
⠀⢸⠉⠀⠘⠀⠀⡴⠪⣥⠆⠀⠀⠉⡁⠀⠀⢰⠦⣴⡟⢡⠂⠀⢸⠋⠀⠘⠀⠀⡴⠪⣅⠆⠄⠀⠈⡁⠀⠀⢰⠦⣴⡞⢡
⠀⠀⠀⣀⠀⠀⡏⠁⠃⠀⠀⠀⠀⠀⠠⠺⠀⡹⢟⣿⢹⠆⠀⠀⠘⠀⢀⠀⠀⡎⠀⠂⠐⠀⠀⠀⠀⠠⠺⠂⡹⢟⣿⢹⠆
⠀⠰⠆⠈⠋⠀⠈⠠⠀⠀⠀⡴⠈⠀⡠⠾⠁⣤⡶⠤⠀⠀⢠⠀⠰⠆⠈⠋⠀⠈⠠⠀⠀⠀⡴⠈⠀⡠⠾⠁⣤⡶⢤⠀⡀
⡶⠂⠀⠀⠀⠺⠃⠀⠀⠂⠀⡀⠀⢄⠀⠀⠈⢟⠓⠚⢀⣿⣿⡶⠂⠀⠀⠀⠺⠃⠀⠀⠂⠀⡀⠀⢄⠀⠀⠈⢟⠓⠚⢀⣿
⠙⠀⠀⠀⠀⠀⡠⠀⣀⡀⠀⠉⠀⠀⡀⠄⠀⠘⠃⠀⣀⡘⠋⠙⠀⠀⠀⠀⠀⠠⠀⣀⡀⠀⠉⠀⠀⠀⠄⠀⠘⠃⠀⣀⡘
⠀⠀⠀⠂⢡⣂⠀⠀⠈⠁⠀⠀⡄⠀⢀⠀⠐⠦⠀⠈⠛⠃⠀⠀⠀⠂⠢⢤⣂⠀⠀⠈⠁⠀⠀⡄⠀⢀⠀⠰⠤⠀⠀⠛⠃
⠈⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡛⠑⣀⠀⠀⠀⠀⠈⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡟⠃⣀
⣢⣀⡀⠀⠀⠀⠀⣅⠀⠀⠀⠀⣈⣀⠱⣶⣇⡀⠉⠀⠀⠀⠰⣢⣀⡀⠀⠀⠀⠀⣍⠀⠀⠀⠀⣘⣀⠱⣴⣆⡀⠁
⢀⠁⠀⢸⣧⠀⠀⢻⣷⡶⠾⠛⠁⠀⠀⠈⠉⠀⣠⣶⣶⣄⠀⢀⠁⠀⢸⣧⠀⠀⢻⣶⡶⠾⠛⠁⠀⠀⠉⠉⠁⣠⣶⣶⣤
⠘⣄⣦⣼⠟⠀⠀⠘⠉⠀⣤⠀⣀⠤⠴⣿⠀⢠⠘⠋⠑⡿⠀⠘⣄⣦⡼⠟⠀⠀⠘⠁⠀⣤⠀⣀⠤⠴⡟⠀⢠⠙⠋⠑⡿
⡀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢸⣅⠀⢀⣬⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⢸⣄⠀⣀⣼
⠀⢠⡖⠒⢠⠀⠀⢐⡲⠀⡀⠀⠛⠿⠯⠉⠀⢀⡀⢀⣡⠆⡀⠀⢠⡶⠂⢠⠀⠀⢀⡲⠀⡀⠀⠛⠿⠏⠉⠀⢀⡀⢀⣡⠆
⠀⢘⠀⠀⠀⠀⡠⠋⠈⢛⠁⠁⠀⠀⠂⣠⡀⢼⣭⣿⢧⡘⠀⠀⢘⠀⠀⠀⠀⡠⠋⠈⢛⠁⠀⠀⠀⠂⣠⡀⢼⣭⣿⢧⡘
⠀⢀⡀⠰⡤⠀⠣⠀⠀⠀⠐⢀⠀⠀⠉⣨⠄⠊⣑⠛⠘⠁⠀⠀⢀⡀⠰⡤⠀⠡⠀⠀⠀⠐⢀⠠⠀⠈⣨⠄⠊⣑⠛⠘⠁
⣀⡈⠁⠀⠀⣠⡄⠈⠀⡀⠀⠋⠀⠀⠊⠉⠠⣿⣏⣩⠀⣦⣸⣀⡈⠁⠀⠀⣠⡄⠈⠀⡀⠀⠊⠀⠀⠊⠉⠠⣿⣏⣩⠀⣦
⢯⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠦⠀⠐⠈⠀⠀⢱⡄⠀⠐⢻⡿⢯⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠦⠀⠑⠀⠀⠀⢱⡤⠀⠐⢻
⠀⠀⠀⡀⠀⠀⠈⠀⠲⠆⠀⠀⠀⠀⠂⠁⢀⣀⠀⠠⣶⡆⠀⠀⠀⠀⡀⠀⠀⠈⠀⠲⠆⠀⠀⠀⠀⠂⠁⢀⣀⠀⠠⣶⡆
⠠⠀⢀⠄⠉⠒⠀⠀⠀⠀⠀⠀⠃⠀⢰⢤⣤⢍⠀⠀⠀⠀⠀⠠⠀⢀⠄⠉⠒⠀⠀⠀⠀⠀⠀⠃⠀⢰⢤⣤⢁
⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢆⣀⡆⠀⠦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢆⣀⡃⠀⠶
⠚⠖⠂⢠⡄⠀⠀⣷⣀⣀⣤⣤⠖⠒⠈⠿⠷⠂⠀⣀⣀⠀⠈⠚⠒⠂⢠⡄⠀⠀⣷⣄⣀⣤⣤⠖⠒⠈⠿⠿⠂⠀⣀⣀
⢰⠀⡀⢸⡿⠀⠀⢸⠿⠋⠉⠀⠀⠀⢀⣤⠀⠀⢺⡿⢻⣿⠀⢰⠀⡀⢸⡿⠀⠀⢸⠟⠋⠁⠀⠀⠀⢀⣤⠀⠀⢺⡿⠻⣿
⠀⠓⠻⠛⠁⠀⠀⠀⠀⠀⠛⢠⠖⠁⠉⠫⠀⠘⠀⠀⠀⠋⠀⠀⠓⠻⠛⠁⠀⠀⠀⠀⠀⠛⢠⠖⠉⠉⠻⠀⠘⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡀⡀⠀⠀⢀⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠉⠉⠉⡽⠉⠋⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠁⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠱⠀⠀⠀⠀⢀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢀⡴⠋⠁⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⢀⡴⠋⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣰⠏⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⡴⠋⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣴⠃⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⡠⠋⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣰⠇⠀⣀⣤⠞⠛⠙⠉⠓⠲⣄⡀⠀⠀⠀⠀⣀⠀⠀⢰⠋⢻⣤⠞⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢠⡏⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣄⡠⢴⡏⣩⠗⢠⠏⢀⡔⠻⣧⡀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢻⡄⢺⣍⣁⡴⠋⢠⠎⠀⠀⠘⣷⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠⡇⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⢸⡇⠀⠉⠀⠀⢠⡏⠀⠀⠀⠀⢸⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢈⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣸⠇⠀⠀⢿⡄⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠈⢿⠇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⣀⡴⠋⠀⠀⠀⠈⠻⠤⡀⠴⠚⠁
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠉⠈
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠛⢮⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠂⠀⠀⠀⢀⣿⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⢰⡏⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⣿⠀⠀⠀⠀⢠⠔⠁⡟⠀⠀⠀⠀⠹⡄⠀⠀⠰⠆⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡴⠛⠁⠀⢀⣴⠖⢲⡄⠀⠀⢠⡾⠉⠻⣦⣀⡤⠖⠂⠉⠉⠉⠓
⠻⣄⠠⠴⠚⠁⠀⢠⡇⠀⠀⠀⠀⠀⢱⠀⠀⣤⡀⠀⠀⠀⠈⠻⣦⣀⣠⠤⠆⠀⢺⣿⢁⡀⠀⠀⠀⣾⣧⠰⠚⢀⣠⠶⠋⠀⢀⡴⠊⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⡇⠀⣿⡇⠀⠀⠀⢀⡤⠚⠙⢷⣄⠀⠀⢸⣿⠋⠙⠦⡠⠞⠉⠛⠒⠚⠋⠁⠀⠀⡰⠋⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⠀⠛⠁⠀⠀⡴⠋⠀⠀⠀⠀⠙⣷⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⢀⡠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣦⣤⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⣄⣀
⠀⠀⠀⠻⣝⠮⣝⡲⢤⣀
⠀⠀⠀⠀⠈⠳⣄⠙⠲⢬⣙⠦⣄
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠓⠦⣝⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⠲⢭⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠉⠓⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠐⠂⠀⠈⠙⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠈⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡇⠀⠉⠙⠒⠦⠤⠤⠤⠴⠒⠋⢀⡠⠖⠚⠛⠓⠲⣄⠐⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡤⠤⠒⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡞⠀⠀⠀⠀⠀⠀⠈⢳⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⠛⢷⣤⡀⠀⠡⠘⣇⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠻⣷⢤⡀⠈⠳⢤⣀⣀⣀⠴⠚⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡓⠦⣤⣀⣀⣀⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠴⠒⠛⠓⠲⢤⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠱⡄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⡀⢷⡀⠀⠀⠀⠀⠀⠀⣰⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠑⠦⣄⣀⣀⡤⠖⠁⢐⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⡿⠿⣿⣿⣿⣿⠿⣻⣿⣯⣵⣾⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣯⣝⣻⠿⠏⠀⠀⠀⠉⠀⠈⠐⣦⠀⠹⣯⣶⠿⢟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢲⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢲⣀⣀⣀⣀⣰⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⡼⠿⢷⣶⣶⣿⣿⠛⢻⣟⣋⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⠿⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠃⠀⡀⢸⣾⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣶⣿⣿⣾⣿⣿⣷⣀⣀⣀⡀
⠤⠤⠤⢤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤⠤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⣛⣛⡿⣻⣿⡛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⢈⣠⡶⠿⠿⣿⣿⠛⠛⢿⣿⣿⠟⠳⠦⣀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⠾⠋⠀⠀⠀⢰⡟⠁⠀⠀⠈⢻⣟⠂⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⡔⠟⣠⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢻⣦⠄⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡾⢫⣾⣟⣻⣄⠀⢠⣯⡀⠀⠀⠀⠀⠀⠈⣿⡐⣶⣿⣦⡀⠀⢷⡀⠀⠀⠀⠀⠈⢻⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣷⡛⠀⢺⣾⣿⣷⣼⣿⠁⠀⠀⠀⠀⠀⠀⣸⣹⡿⠟⢛⣿⣦⠈⣷⠄⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠇⠀⠀⠀⠀⠀⣠⡿⢟⣃⣄⡻⣿⠁⣨⣿⣿⡃⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⢴⣿⡿⠑⢸⡶⠀⠀⠀⠀⠀⠀⣿
⣿⡿⠀⠀⠀⠀⠀⠀⢸⠉⡁⠉⠉⠉⠉⠀⢨⣿⡏⡇⠀⠀⠀⠀⠀⠛⠛⣿⡊⠋⠉⠘⠛⠓⠛⣿⣧⠀⠀⠀⠀⠈⢿
⣿⢃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣼⣿⡛⠀⢀⣾⣿⣶⡆⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸
⣿⠸⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⢠⣿⣿⡟⣿⣷⠀⠀⢿⡯⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸
⣿⡰⠀⠀⠀⠀⠘⢠⣼⣿⣶⠀⠀⠀⠀⢀⣿⣿⣵⣿⣿⣿⣄⣼⣿⣧⠀⣼⣿⡇⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⢸
⣿⡄⣆⠀⠀⠀⠐⢾⣿⣟⢻⣶⣄⣄⠀⠸⢿⣟⠷⣦⠀⠉⠀⠀⠀⠀⠐⣿⣿⠷⠁⢠⣄⣸⣾⡏⣽⡇⠀⠀⠀⠀⢸
⣿⣧⢙⡄⠀⠀⠀⠻⠇⣀⣏⣩⢼⢿⣿⣶⢿⣿⠿⣦⣴⣠⣤⣀⣄⣀⣜⣿⣿⣶⣼⣿⡿⢻⣿⣿⣿⡇⠀⠀⠀⠀⣾
⣿⣿⣧⣧⠀⠀⠀⠀⠓⢛⣿⣷⣞⠀⢸⣿⡯⠛⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⠏⠈⣿⣿⣤⣼⣿⣿⡏⡴⠀⠀⠀⣸⣿
⣿⣿⣿⣯⡀⠀⠀⠀⠀⠘⣯⡽⢿⣶⣿⣿⣧⠀⣿⣿⡄⢠⣿⣿⡀⣰⣿⡿⣧⣴⡿⢿⡟⢹⣿⣿⡤⠉⠀⠀⣴⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣆⠀⠋⠉⠳⠻⣷⠶⣧⡿⣾⡽⣿⡼⣴⣞⣿⡜⠙⠃⠀⢠⣿⡟⡾⢀⠃⢀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠻⣷⣄⠀⠀⠀⢸⡇⠁⠀⠈⠀⠉⠀⣈⣿⠀⠀⠀⠀⣰⣿⣿⣿⣾⣞⣤⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡠⣤⣈⡻⠧⣀⣀⡛⣿⣤⣀⠀⠀⢀⣸⣿⡿⣧⣤⣢⣾⡿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄
⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣠⡆
⠀⠀⠀⠀⠉⠻⠟⠀⠀⠀⠀⠀⠘⠓⢀⠐⠓⢀⠀⠀⠀⢤⣦⣤⡄⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠳⠶⠖⠞⠋⠀⠀⠀⠘⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⡀⠀⠀⠀⢰⣬⣤⠀⠀⠀⠀⠠⠶⠶⠶⠄⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⡆⢠⠇⣀⠗⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⣸⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠄
⠀⠀⠀⢀⡧⣾⡽⢁⣶⡄⠀⠀⠀⢠⣿⣿⣿⣿⡅⠛⢸⣿⠿⠋⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢿⣿⣿⡿
⠀⠀⠀⣼⣔⣟⣡⣷⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⢀⣴⡂⢸⡟⠀⠀⠀⠀⣠⡀⢸⡃⠀⠀⠀⠈⠛⠻⠿⠿⠇
⠀⠀⣴⣧⠾⠉⠻⣨⠁⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣠⡴⠯⢶⣬⡇⠀⠀⠀⠈⠉⠃⠸⡄
⠀⠀⢿⡇⠀⣠⣞⡷⠣⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡆⣿⠀⣀⢸⣇⣶⣿⣟⡁⢸⠎⠃⠀⠠⠄⠠⠤⠴⠶⣿⣤⠤⠤
⠀⠀⢸⣷⠞⠛⣃⣠⠯⠀⠀⠀⠀⣾⢰⡿⢀⣠⠀⣧⣿⣀⣏⣠⠟⠁⠀⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⣀⣄
⠀⠀⠠⣿⠀⣼⠋⠀⠀⠀⠀⠀⠀⣿⠛⣿⣼⢿⠟⣷⠌⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⣿⡿⠁⠀⠀⠠⣶⡄⠀⠀⣿⠀⠻⠋⠀⠀⠁⠀⠀⠀⠀⠂⠈⠴⠈⠀⠀⠀⠀⠀⢄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢸⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⡌⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⣈⠛⡇⠀⠀⠀⢰⠀⠀⣴⠀⠀⠶⠀⠀⢾⣿⡀
⠀⢀⣿⣿⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢧⡶⢶⠾⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⣤⣄⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⡈⠀⠂⠀⠀⠀⠀⢿⡿
⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀⠀⠀⢉⠹⠶⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠡⡁⢀⣈⣾⢥⣄⠀⠈⠁
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⢈⠣⡄⢉⡉⡩⠙⠶⡟⠲⣆
⠀⠀⠀⠹⣿⣻⠏⣠⠾⠋⠉⠙⣷⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠂⠀⠀⠁⠼⣄⣁⠀⠐⢢⡷⠴⣇
⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣘⣷⡀⠈⣳⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⣄⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠿⠷⠿⠿⠗⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣿⣿⣿⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠂⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠉⠋⠹⠟⠛⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⣠⠔⠋⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⠀⢀⡤⠊⠁⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡇⢀⡴⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡷⠋⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠖⢉⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠴⠶⠞⠋⢸⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢁⡤⠶⠒⠲⣤⡀⠀⢸⡶⡏⠈⡇
⠀⠀⠀⠀⠀⠀⢠⡟⠀⣰⠋⠀⠀⠀⠀⠀⢿⠀⡟⠀⡗⠚⢣⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⢀⡟⢸⠃⠀⡟⠀⣈⣉⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠈⠣⡀⠀⢀⣀⡴⠋⣰⠏⠀⢰⢠⡞⠉⠉⠙⢷⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⣉⣉⣡⠴⠛⠁⠀⠀⡎⢸⡇⠀⠀⠀⠀⢷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⡇⠘⣧⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠙⣦⡀⠀⣀⡾⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠙⠛⠉⢀⣾⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣲⣒⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡾⢶⡄⠀⢴⡀⠀⠀⠀⠻⣟⣛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⡁⢈⡁⢀⠄⠀⠀⣀⣰⣶⣚⣿⣏⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⣮⣇⣠⡄⠀⠰⠟⠈⢹⣿⠿⣿⣿⣿⣿⣿⣦⣶⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣏⣙⣿⣷⣶⣶⣿⣿⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣟⣈⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡲⣴⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣣⠟⢻⡏⠂⠹⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣍⣿⣿⣿⣿⣿⣏⡉⠻⠛⡿⠛⠻⡂⠠⠈⠉⠉⡿⠀⠘⣷⣄⡀⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣿⣿⣿⡿⠋⣤⡄⣰⣦⡅⠀⡀⠉⠀⠀⠀⠀⢠⣆⠀⣿⣾⣇⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⣃⡠⢠⣾⡟⠛⠩⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⣾⣿⢷⣤⣤⣦⣀⢠⠄⠀⠀⠀⠀⠀⢸⣿⡁⢾⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢿⡉⠋⠉⣿⣟⡋⠀⠀⠀⣴⣶⣆⠀⢸⣿⣦⡼⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⢹⣿⣾⣿⣿⣿⣿⠟⢿⣷⣾⣿⣿⡇⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⣹⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣘⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⣿⡏⠈⣿⣿⠏⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣷⣿⣿⡦⠈⠻⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠟⣿⣿⣯⣄⣾⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⡻⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠿⡀⠒⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣶⣿⣿⡏⠀⢀⣴⣦⡀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠦⠄⠀⡼⠋⠉⠥⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠈⠹⣆⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠃⠀⠀⢦⠈⢿⣤⣤⣇⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⠇⠀⠀⠘⣺⣷⣾⠁⠀⢨⡗⠋⣉⡁⠀⠀⠸⣆⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢈⡇⠀⠀⠀⠘⣁⣴⣇⡀⠀⡾⢿⡿⠭⠀⠀⢠⡾⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⠶⠶⠒⠛⣩⠏⡏⠉⢻⣷⡀⠃⠀⠀⢀⣼⠋⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⢀⡇⠀⠸⡏⢳⡄⠀⠀⢨⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⣻⣗⣀⡴⠋⢻⡀⢀⣹⡄⠙⠳⠶⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⠳⣾⡏⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡑⢢⣷⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⢠⡏⠒⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡆⠀⠀⠀⠀⠀⣰⡣⢌⣇⠀⠀⠀⠀⠀⣼⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠡⢸⡇⠀⠀⠀⠀⠀⣿⠁⠀⢿⡀⠀⠀⠀⠀⣿⢠⠉⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣡⡀⣼⠃⠀⠀⠀⠀⢸⡇⠰⢂⢸⡇⠀⠀⠀⠀⢹⣄⣄⢡⡏
⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⣟⣁⣀⣀⡀⠀⠀⠈⣇⢁⠀⣸⠃⠀⠀⣀⣀⣀⣙⣿⣋⣀⣀⣀⡀
⠀⠀⠀⠸⠁⠘⠿⠿⠭⠭⠿⠭⠽⠿⠟⠂⠙⠀⠙⠻⡷⠋⠀⠋⠐⠻⠿⠿⠯⠿⠯⠿⠿⠿⠃⠘⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠸⣿⣿⣟⣻⣿⣛⣿⣿⡷⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣠⠖⠒⠒⠦⣴⠋⢳⣀⣀⣤
⠀⠀⠀⠀⠀⡏⠉⠉⣿⡄⠀⠘⢦⡀⣴⠛⠓⢦⢸⠁⠀⣤⠉⢻⠀⠘⠋⠀⡽⢧⠀⠉⣀⡬⠇
⠀⠀⠀⠀⠀⢻⠀⠀⠈⠁⠀⠀⠈⡇⡏⠀⠆⠈⢿⡄⠀⢀⣠⠾⡇⠀⢰⠊⠁⣼⠀⡞⠁
⠀⠀⠀⠀⠀⠈⣇⠀⠀⣤⡄⠀⠀⢷⡇⢠⠶⡄⢘⣧⣤⣼⣤⣀⡙⢚⡭⠤⢤⣨⠟⢧⡀⣀⣤⣄⡤⠤⢤⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⡀⠀⢹⠻⣤⣤⣼⣉⠉⢠⠼⠟⠚⢻⡇⠀⣄⠙⣾⠀⢀⠀⢿⢦⡀⠙⠁⣠⣿⡀⠀⠤⣞⠀⠀⠀⢠⡟⠉⠙⣇
⠀⠀⠀⢀⡤⢦⡀⠓⢚⡯⠤⣄⣿⠉⠙⡇⠘⢲⡄⢰⢿⡇⠀⠿⠃⣿⠀⣈⡀⠈⣇⣷⠀⡏⠁⣏⠉⠃⠀⢈⡇⣤⠶⣼⡇⠀⠀⣿⣠⣄⡀
⣾⠛⠉⣿⡀⠀⠛⣶⠏⠀⣤⡄⢻⡀⠀⠷⠶⡞⠃⠘⢻⣧⣤⡤⠞⠳⠤⠏⠹⠴⠞⠛⠚⠃⠀⠙⠲⠤⠴⠚⢸⡇⠀⠈⠃⠀⠀⠟⠁⠀⣿
⢹⡄⠀⠈⠁⠀⠀⢸⣆⠀⠹⠃⢸⣇⣀⣤⠴⠟⠛⠋⠉⠀⠀⠀⣴⠛⠶⣄⠀⣠⠖⠛⣦⠀⠀⠀⢠⡴⠶⠶⠶⠛⠒⡂⠈⠀⠈⠉⠒⢛⠛⠛⠛
⠀⢿⡀⠀⢶⣆⠀⠈⣿⠲⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣏⣀⣀⡭⠉⢅⣀⣀⣻⣤⣤⡀⢸⡇⠀⠂⠀⠀⠊⢆⠀⠀⠀⠀⠄⠁⠀⠀⡀
⠀⠈⣧⣀⣸⠟⠖⠒⢋⣤⣀⡴⣆⢀⣄⡀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣧⠈⡗⠀⠀⠀⠀⠠⠚
⠀⠀⠈⠉⠁⠀⡴⠦⣾⠀⣿⠁⣿⠋⣸⣃⠀⠀⠀⠀⢺⠥⠭⠬⠤⠤⢬⠀⣄⠀⠇⠒⠒⠒⠒⣿⠀⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⢠⣷⣄⠘⣇⢸⢠⠏⡰⢋⣽⣃⣀⣠⣤⠸⡇⠀⠀⠀⠀⢲⠀⠉⢀⢸⣄⠀⠀⠀⣿⠀⣿⠀⠄⠁⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⢀⣤⣬⡷⠾⠷⠾⠛⠈⠉⠋⠉⠉⠉⠁⠀⢸⠀⣧⠀⠀⠀⠀⠁⠀⠀⠀⠙⠃⠀⠀⠀⣿⠀⢻⠂⠀⡀⠈⠀⠀⠄⠀⠀⠰⠂⠀⢀
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣿⠀⢸⡄⠂⠀⡠⠀⠀⠀⠀⠀⠸⢀⠐⠁
⠀⠀⠀⠸⡗⠂⠈⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⠀⡀⢒⠀⠀⠘⠁⠀⠠
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠈⠀⢸⠀⠀⢀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⡀⠀⠀⣿⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⡇⠀⠈⣇⣀⣊⣀⣀⠀⢀⡀⢀⣈⢀⣀⡐⠁⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠴⣄⢀⡴⠀⠀⠀⠀⠀⠀⡔⣛⠲⣤⠒⣑⣦⠀⠀⠀⠀⠀⠀⡠⠊⣙⢦⠀⠀⠀⣠⠔⠒⠚⠓⠲⡄
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡀⠈⡇⠀⣀⠀⠀⠀⠀⢦⣙⠋⠀⢇⠀⢛⣣⠆⠀⠀⠀⢰⠀⢃⠀⠙⠁⠀⠀⠜⠁⠈⡧⠀⠀⠀⡼
⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠠⠤⢞⢙⠦⠌⠀⠀⠀⢀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠠⠀⠀⠄⣉⠀⠀⢘⣇⠀⠀⠀⢀⣋⠅⠀⠀⠈⠄
⠀⠀⠀⣤⠸⡆⣄⠀⠀⠀⠀⠐⠀⠈⡏⠀⠚⠀⠀⠀⠀⠴⣊⣄⠈⡖⠀⣠⡐⠆⠀⠀⠀⢸⠁⡌⠀⣠⡀⠠⠀⢢⡀⢀⡷⠀⠀⠈⢳
⠀⠀⠀⢸⡇⠇⣈⣒⠀⠀⠀⠀⠴⠞⠙⠶⠀⠀⠀⠀⠀⠀⢧⣋⡠⠛⢄⣉⠝⠀⠀⠀⠀⠀⠀⠱⣌⣋⠝⠀⠀⠀⠙⠥⢄⣀⣠⠴⠋
⠀⠀⠀⠸⠧⠤⢤⣌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠳⣦⠀⠀⠀⠀⠀⠀⣄⢰⢀⡞⠋⣡⠤⢤⣄⡀⠀⠀⢠⡀⡦⠀⣰⠀⠀⢸⡃⠈⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣥⣸⡇⠀⠀⠀⠀⠤⠬⠈⢸⢀⡞⠁⠀⠀⠀⢳⠀⠀⠀⣣⣣⡼⠃⠀⠀⠀⢇⠀⠀⢰⠗⢲⡄
⠀⠀⠀⠀⢠⢄⢀⣶⠀⠀⠀⠀⢴⡋⠝⠻⣿⡷⠃⠀⠀⢀⡴⠒⠒⠀⠘⡇⠀⠀⠒⠒⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢼⣦⣤⣯⣠⠞
⠀⠀⠀⠀⣀⣿⠝⢿⣴⣢⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠈⠀⣴⠞⠉⠙⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠈⠛⢻⣳⢾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢦⣤⠤⠴⠾⠃⠀⠀⠀⠀⠀⠀⣈⣁
⠀⠀⠀⠀⠀⠘⠋⠀⠉⠁⠀⠀⢰⣶⣄⣴⡆⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢶⡤⠤⡤⠔⠁⠀⠀⠀⢬⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠋⣿⣥⡀⠀⠀⠀⠀⢀⡔⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢻⢢⠀⠀⠀⠀⠀⢀⠢⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡏⠛⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠉⠀⢀⠞⠀⢣⠀⠀⠀⠀⢠⡑⢊⡅
⠀⠀⠀⡇⠞⣠⡖⠀⣀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⢌⡡⠆
⠀⠀⠀⠇⢰⢋⣴⠛⠁⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⠀⠀⠀⠢⠔
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠁⣸⠃⠀⠀⠀⢀⣀⠀⢠⣇⠔⠂⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡇⠀⠀⣙⣊
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠈⠑⣼⡏⢀⣤⡤⠄⠀⠀⢀⣀⡀⠉⢀⣀⠀⠀⠀⠀⡨⠒⠑⢦⡈⠁⠀⠀⢬⡥
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢀⣠⣤⣤⣼⣧⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠁⠄⠀⠠⠃
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠰⠋⠉⠓⡤⠚⠉⠙⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡶⠚⠲⢄⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⡀⣦⠀⠀⣠⠖⠒⠀⠀⠒⠲⣄⠀⠀⣴⢀⣠⡤⠶⠶⢤⡀⠀⠀⠀⠀⡠⠖⠛⢶⡀
⠀⠀⠀⢸⡀⣎⠀⠀⠀⠀⠀⠀⠿⠀⠀⣀⣀⠀⠙⢮⡃⠀⢿⡀⠀⠀⠀⠀⢀⡿⠀⢘⡵⠋⠀⣀⡀⠀⠀⠟⠀⠀⠀⠀⠀⠀⣱⢀⡇
⠀⠀⠀⠈⠻⠮⣥⣤⣤⡤⠤⠖⠒⠛⠉⠁⠀⠤⠤⠀⠈⠑⠊⠙⠲⠤⠤⠖⠋⠑⠊⠁⠀⠤⠤⠀⠀⠉⠓⠒⠶⠤⢤⣤⣤⣬⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢸⣆⡤⣤⠀⢀⣤⡀⠀⢀⡀⠀⠀⠀⢀⡀⡤⣄⠀⣴⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠛⠀⡿⢀⣏⣀⡷⠀⢸⢇⠞⢹⡦⣾⠏⢀⣾⠻⡇⠀⣸⡇⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠓⠊⠈⠉⠧⠄⢹⡟⣴⡽⠃⣿⠀⠷⠏⠀⣉⡁⢼⠧⠖⠉
⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡽⠀⠀⠀⠀⢀⡴⡄⠀⢸⠇⠀⠀⠀⠛⠀⠀⡴⠋⠀⠀⡾
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠉⠀⣀⣀⠀⢀⣞⠜⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠳⠄⠤⠞⠁
⠀⠀⠀⠀⠀⡔⢹⡇⣠⣄⠘⣧⣄⣷⣾⠁⠀⠶⠀⣠⢤⣾⠁⢀⠴⣄⠀⢠⡄⠀⡀⢰⡋⠿⠀⣸⠂
⠀⠀⠀⠀⠀⠛⠀⡷⢀⡟⠀⣏⢀⠏⣿⠀⣰⠇⢰⣇⣰⡇⠀⣿⣠⡏⠀⣿⠀⣰⠏⡘⢷⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠜⠉⠉⠀⠈⠉⠘⠂⠊⠉⠘⢧⡴⠋⠀⠓⠊⠈⣹⠏⢾⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⣤⣤⣀⡀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠉⠙⠛⢶⣴⣿⣒⣉⣉⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠖⠒⠉⢠⠋⣬⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⢠⠷⠀⠀⠀⠀⢨⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢺⡗⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⢀⣀⡠⠀⠀⠀⣡⣿⡍⠀⠀⠀⠀⢠⡀⠀⠀⠀⢽⠅⠀⠠⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠠⣼⣷⠄
⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠘⣡⣿⣌⠢⠀⠀⢠⣿⣷⡀⠀⠀⢺⡒⠀⢠⣿⣿⡄⠀⠀⢠⣆⠀⠀⠀⠴⣿⣿⠶⠆
⠀⠀⠀⠀⠀⠖⠒⠂⠀⠀⠔⣩⣿⡝⠢⠀⢀⣿⣿⣿⣧⠀⢐⠱⣝⠀⢠⣾⣿⣄⠀⠀⣾⣹⡀⠀⠀⠾⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣱⣿⡝⠢⠀⣼⣿⣿⣿⣿⣇⢁⡼⣌⠁⠉⣽⣯⠉⠀⣸⣷⢺⣇⠠⠴⠾⣿⣿⣟⣉⣀
⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠚⠁⢺⠈⠂⠸⠿⠿⢿⠿⠿⠿⠀⢸⠀⠀⣾⣿⡿⠷⢠⣿⣷⣼⣿⡄⣠⡾⢿⡿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠉⢮⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⠤⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣰⠁⠀⠹⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠇⠀⠀⠀⠱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⡜⠙⡆⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⠀⠀⠸⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⢀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣇⢸⡇⠀⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣀⣀⠺⣍⣡⣴⣒⣒⣚⣀⣀⣿⣇⣀⣐⣒⣒⣲⣤⣨⣽⢂⣀⡨⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⠖⠲⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣄⣠⣿⣴⣶⣼⣤⣴⣦⣷⣤⣴⣾⣤⣥⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣶⣶⣾⣿⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⢠⡆⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡆⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⠇⠷⢈⡤⣺⠀⠀⠀⠀⠀⠀⣷⡠⣉⠾⠙⣿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⠁⠹⡆⡀⢨⠿⣭⡤⣶⠏⠹⢶⣤⣭⠷⡅⢀⢠⠏⠈⢉⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⣀⠤⢾⣽⣁⠀⠀⠒⠒⠒⠒⠒⠲⠆⠀⢀⣯⣷⠦⣀⠂⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⢧⡀⠊⠀⠈⡅⠳⠜⡁⡐⢄⢨⡃⠞⢪⠁⠈⠰⢀⡬⡿⠦⣀⡀
⠀⠀⠀⠀⣀⣤⠖⠚⠉⠀⢀⣦⠟⢣⠎⠀⢰⢹⡑⠆⠀⠀⠀⠀⠰⢊⡟⣆⠀⡑⡌⠹⣦⡀⠀⠉⠓⠦⣤⣀
⠀⠀⡾⣿⢀⣀⠠⡤⠌⣴⠋⠁⠀⢀⡀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠀⡀⠀⠀⠙⣦⢡⣄⡀⢈⡋⣿⣶
⠀⠀⡇⠙⢧⠀⠈⠉⡼⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠈⣧⠚⠁⠉⣡⠟⢸
⠀⠀⣇⣤⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣄⣸
⠀⠾⣏⡍⢣⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡨⢉⣫⠦
⠀⠀⣷⣤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⣈⣻
⠀⠀⡏⡘⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡠⠟⢹
⠀⠀⡇⠁⠃⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠐⠈⢸
⠀⠀⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠉⠓⠦⢤⣀⠀⠤⣏⣿⢶⠄⠀⠀⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡇⠀⠀⠠⡴⣿⣹⠤⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠬⣍⡛⠳⣄⡀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⢀⣴⠞⢙⣉⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠁⠀⠉⠛⡦⢭⣓⠤⣄⣀⡀⠀⠀⠀⢀⣀⣀⡠⠴⣚⡭⢴⠛⠉⠀⠈⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣽⣖⢀⠖⠙⠀⠉⠛⠒⠮⣍⡉⠉⠉⢉⣩⠵⠒⠛⠉⠀⠋⠲⡀⣲⣯⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⠀⠀⠀⠄⠀⠀⠀⠠⠍⠛⠛⠩⠄⠀⠀⠀⠠⠀⠀⠀⠻⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢃⢠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠤⠤⢥⡴⢄⡀⠀⢀⡥⠬⠦⢤⡤⠀⣬⣤⣐⣀⠐⢄⠡⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⡀⠀⠴⠊⡁⢠⠄⠀⠀⠀⠀⠈⠉⠀⣀⠈⠙⠃⠀⠀⣉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠛⠛⠀⠈⡄⠀⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠈⡀⠈⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠍⠀⠐⠁⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠈⠁⠈⢛⠂⠀⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠁⢰⣠⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠈⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠿⡀⠇⢘⠀⣀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⡀⢲⡀⠅
⠀⡀⠀⢤⡀⠔⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⡎⠁
⠀⠉⢡⠟⠀⠣⠀⠃⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠂⠸⠄
⠠⠈⢠⠀⡀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢉
⠋⠀⢀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⢠⠈⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈
⠀⠀⠀⠀⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡁⠘
⠀⠀⠀⠀⢀⠈⢡⠙⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠠⢴⡋⠦⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠰⠢⠀⠁⠐⢃⡠
⠀⠰⠖⠈⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠑⡆⣰⠜⡈
⠀⠀⠀⠘⠀⠂⠸⣇⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠘⠈⠙⠀⠈⠁
⠀⠀⠀⠰⠆⠀⠐⢈⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢶⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠤⣀⠀⠤⡈⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠂⠀⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⣀⣠⠀⠝⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡏⡤⠀⣈⠀⠠⠶⠶⠃⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⠀⠀⠲⣦⣄⠀⡀⠀⣠⣄⣠⡈⠀⠤⣘⣃⡀⠀⠴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠈⢡⠘⠂⠀⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⢍⢈⠁⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠁⠀⠉⠐⠀⠀⠋⠆⠀⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢠⠂⠀⠐⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠈⠀⠂⠀⠀⠀⠀⡀⠀⠀⢀⠞⠀⡠⠈⠀⠀⠀⠀⠀⠀⢉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⢠⠀⢘⢠⠀⠳⠁⠰⠀⠠⠀⠈⠀⠀⠂⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠀⠀⠆⠀⠄⠀⠀⠀⣂⠡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠎⠀⠀⠀⠐⠀⠀⠀⡐⡀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⠀⠀⠀⣀⡀⠀⠀⢁⡀⠁⠀⠁⠀⠑⢌⠁⠀⠉⠀⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠆⠐⣄⠀⠀⠀⢀⠀⠁⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⢀⠜⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠂⠀⠀⢃⠀⠐
⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠠⠀⠀⠀⢀⠀⠀⠢⠀⠀⠀⠀⠀⡠⠄⠠⠙⠤⡐⠠⡐⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠄⠀⠂⠀⠡⢒⠀⠂⠀⠀⢂⠄⠀⠀⠀⠠⠂⠐⣶⡤⢤⡀⡀⠀⠀⠀⠀⠨⠆⠀⠀⠤⣄⣠⠀⠄⠀⠀⠀⠠⠀⡈⣤
⠀⠀⠆⠈⠄⠤⡤⠔⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⢤⡗⠁⣛⠘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠶⠤⠤⠀⠄⠀⠉⠀⢀⡄⡗⢨⠷⠆
⠀⢀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠂⠀⡈⠀⡀⠀⠀⠀⡠⠋⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠲⠐⠀⠒⠒⠂⠉⠘⠁⠪⢂
⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠀⣌⠉⢉⠁⠀⠀⠀⡠⠀⠀⠀⠠⠔⠀⠀⠀⠀⢀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠀⠈⠦⡀⠀⠀⠀⠈⠑⠤⣀⡀⢀⣀⣀⢔⡈⠤⠒⢉⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠂⠄
⠀⠀⠀⠀⠀⢄⠈⠂⠀⢈⠀⠁⠐⠒⠒⠒⠒⠒⠈⠉⠉⠀⠠⠀⠀⠁⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠈⠀⠈⠁⠀⢈⣁⡀⠤⠄⠒⠒⠉

⠀⠀⠀⠐⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⠀⢰⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠄⠤⢤⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢰⠃⠀⠀⠈⡇⠑⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣄⠐⠈⢀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⢿⣿⡆⠤⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠘⢄⡐⣄⢀⢀⡠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠠⠄⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠈⠉⠹⡏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠠⠀⠠⠄⠂⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶
⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠄⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠐⠠⠀⠀⠀⢀⠀⣃⣤⠀⠀⠈⠀⠀⣿⠀⢸⡇⠀⠀⠘⣇⠰⡀⡀⠀⠀⣸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠚⢿⡟⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠨⡷⣬⡿⢶⠛⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⣠⠀⠸⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⢠⣄⡴⠀⢱⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿
⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟

⠱⠄⠈⢁⣀⣵⡙⠳⡿⠄⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⢀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢕⣤⠀⠀⣠⠊
⢀⣴⣕⠄⠛⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠉⠀⠛⠀⢀⡀⠀⠀⠀⡔⢠⠀⠀⠀⠘⠁⠀⠜⠁⠸⣆
⣝⠂⠙⢀⣴⠄⠓⠀⠀⠀⣠⠰⠲⠲⠆⠁⠀⠀⠴⠀⠒⠠⠀⠀⠈⠀⠀⠀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠠⠀⠀⠈
⡙⠂⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡚⠶⠄⠀⠀⢀⠥⠒⢄⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠘⠉⠁⢢⠀⠀⠀⠈⠀⠀⢸⠒⠒⢀⡀⠀⠀⠀⠁⠀⠔⠀⠀⠀⡠⠚⠁
⠀⠀⢠⠀⠤⠰⠇⠀⠀⠀⢰⠃⠚⠁⠠⡄⠀⠀⢁⠇⠰⠀⠀⠀⢰⠤⠐⣀⠸⠂⠒⢀⠰⡄⠀⢀⡀⠀⠀⠀⠠
⡰⠈⠙⠂⠀⠈⡱⠔⠶⠤⠌⢠⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠜⠀⠸⡀⠀⠉⣠
⠳⠦⠀⠀⠀⠀⣁⠀⡤⠬⠗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⠄⠀⠠⠅⠀⠠⠒
⣦⠀⠀⠀⢰⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢈⠂⠀⠀⠉⠉
⠀⠈⡁⠀⠘⠠⠂⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣤⡤⠤⠄
⣤⡦⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣴⡶⠖⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣼⡷⠖⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⢴⡶⠟⣋⠄⠀⠀⣠⠔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠢⣌⠙⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠐⠺⣻⣿⠿⣿⣾⣿⣿⣷⣾⣿⣦⠸⣿⣿⡶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠸⠇⠘⢲⣶⡇⠀⡰⣿⣿⣦⣈⣿⣿⣿⣛⡛⢻⣯⣰⣟⠿⠷⡟⠀⠀⢀⣀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣺⣿⣯⣠⠀⠀⠿⢺⣿⣯⡲⢶⣿⣿⢿⣿⡿⠉⢻⣿⣿⠟⠀⠋⠘⢧⡐⢠⡾⠗⠛⡁⢡⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣿⣿⣿⣥⢤⣀⡄⠘⠛⢿⣿⣧⠈⢠⣾⣿⠃⠀⠀⠙⢿⣿⣶⣤⣀⣀⠙⢆⠈⢢⡜⣡⣿⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣾⠟⢫⢿⡻⣿⣶⣆⠀⡈⢙⡀⠙⢿⡿⠀⠀⠀⠀⠀⣿⢟⡿⠉⠙⠃⠘⣄⠀⣴⣿⠓⣤⠀⠱⡄⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣱⣎⠁⣰⢷⣺⠟⠹⣿⣷⣞⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡟⠿⣿⣿⣷⠤⣄⣀⢠⣾⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣠⡿⠀⠉⣠⣿⣆⡬⣳⣏⠘⠅⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣎⠛⠛⢺⡆⢸⣿⣿⣿⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⢠⣬⠀⠰⣿⡏⣿⣀⣰⠟⠈⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢼⡧⣶⣾⣷⡈⢩⣿⣿⣭⡈
⠀⠀⠀⠀⠀⠀⠀⣤⠚⠉⠙⠿⠀⠈⣙⣿⣷⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣻⣼⣿⡷⠘⠇⢀
⠀⠀⠀⠀⠀⠀⢈⡃⠀⣠⣤⣄⡀⠈⢡⢻⣋⠀⠀⣩⡀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡏⠀⢻⡿⣟⠃⠐⠀⠈⢈⠛
⠀⠀⠀⠀⠀⠀⠈⠁⠁⢸⡴⣻⣿⢀⣂⣽⣿⠟⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⣻⣰⣤⣀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢟⡏⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡋⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠶⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣮⡅⠀⠀⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠀⠀⠃⠀⠀⠀⢶⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠹⣿⠿⣧⣴⡐⢎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣠⣀⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠀⢉⣙⣀⣿⣷⣀⠈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⡟⠁⠈⣳⣁⣼⡷⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⠻⢿⣿⣿⡿⢿⠿⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠰⠟⣏⣹⣿⡿⠀⢂⣿⡏⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡸⢿⣿⡆⠈⠈⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡉⠋⠁⠁⣨⣿⠿⡦⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⡀⣛⣯⡄⠐⠋⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠉⠈⡖⠀⢸⡿⢬⡀⠁⠀⠀⠀⠀⠀⠀⣴⣦⣀⣰⣦⠀⠀⢸⡏⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠋⠹⡿⠯⠠⠰⢿⡗⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠐⠈⠉⠉⠑⠢⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠙⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠂⠀⠀⠤⠄⠀⠀⡄⠀⠀⠀⠑⠖⠖⢀⣀⠄⠀⠀⢀⣄⣀⠄⠀⠀⠈⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠒⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⢀⡉⢣⠀⠀⠀⠀⠐⠦⠤⠄⢀⣀⡀⠀⠢⠤⠔⠊⠒⠃⠀⣠⢀⠄⠀⠀⢠⠀⠀⠀⠈⢢
⠀⠀⠀⠰⠊⠁⠀⢀⠀⠀⣈⣧⣀⠉⡉⠀⠙⠓⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡜⣠⠀⠀⠀⠀⠁⢳
⠀⢀⡤⠂⠀⠐⠊⠹⣄⡀⢀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⡀⠀⢀⡜⠀⠀⡀⠈⠹⠄⠀⠀⠀⠀⠀⠒⠉⠈⠀⠀⠀⡴⠀⠀⠈⠀⢤
⠀⠊⠀⠀⠒⣆⠀⠀⣀⡍⠀⠀⠀⠑⢪⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠀⠠⣄⡀⠐⠆⠀⠒⠁⠒⠒⠋⠀⢀⠦⠔⠄⠈⠇
⡀⠀⠀⠀⢤⡈⠁⠀⠰⡁⠀⠸⣄⠀⡀⠑⠂⢄⠀⠰⣄⡀⠄⠀⠀⣀⠀⠀⠣⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⣰⠤⠂⠈⠋⠁⢀⠄⠀⠀⡀
⢇⠱⠄⠀⠀⣉⠁⣠⠀⠉⠀⠀⢀⠉⡀⠀⠀⠀⠉⠁⠀⢀⠀⣉⡉⢀⣀⡠⢄⣈⠉⣉⣁⡀⠠⣄⣠⡄⠀⠀⢤⡀⠀⠀⠈⠉⠁⠠⠖⢊⡁
⠈⠢⠀⡄⣄⠈⠀⠻⠀⠀⠙⠤⠈⠉⣁⡜⠐⠋⠈⡐⠊⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⣀⣜⠃⠀⠀⠀⠠⠴⠒⠊⠀⠄⠈⡄⠊
⠀⠀⠀⠈⠢⡁⠀⠤⡀⠄⠐⠂⠀⠀⠀⠈⠋⠉⠉⠀⣿⠀⠀⠀⢰⠀⡇⠰⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠀⠉⠒⠂⠐⠤⡍⠉⢀⣐⡊⡐⠒⠀⠀⠖⡿⠀⠀⠀⢸⠀⢇⡇⠀⡈⠠⢸⠃⠒⠓⠒⠂⠀⠀⠉⡈⣁⣀⡠⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠑⠄⠀⢺⡀⢈⠸⠈⡇⠸⠀⢃⠇⡆⡿⠖⠤⠒⠐⠊⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡆⡀⡇⡄⠠⣸⢰⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⡇⠁⠀⡇⡏⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡼⢇⡠⠴⢧⣇⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠌⠉⠁⠀⠀⠀⠀⠀⠁⠘⠋⠳⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⢠⣴⠦⣴⠠⢤⣤⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠲⠄⠠⣿⡇⣿⠀⢸⠀⢸⢣⠔⠢⠤⠆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⡿⠀⡇⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⡇⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢳⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠴⢦⠀⠀⢈⠤⢤⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠣⠀⠀⠀⠀⠋⠑⡀⠀⠀⠉⠀⠀⠁⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠀⠀⠔⢢⡤⡈⠂⢀⡀⢩⠤⠒⢤⢤⡀⠙⠀⠐⠳⡄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠀⠠⠄⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠑⠲⠀⠈⠓⠀⠈⠈⠋⠂
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣧⠀⠀⠀⠀⠀⠀⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣇⠀⠀⠀⠀⣰⠇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠸⣆⠀⠀⢠⠏⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠹⡄⢠⡏⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢻⡟⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡾⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣼⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣠⣄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠛⠋⢰⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡾⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡴⣿⡁⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠁⠀⢀⡴⠋⠀⠈⠻⣆⠀⠀⢙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠛⢦⠟⠁⠀⠀⠀⠀⠈⢳⡴⠋⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⣤⢞⣩⠤⠤⢤⣀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣀⣤⣤⣬⣛⢦⡀
⠀⠀⠀⠀⢠⡞⡵⠋⠀⠀⠀⠀⠈⢷⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⡞⠁⠀⠀⠀⠉⢳⡝⣦
⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⣼⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⠀⣿⢸⡆
⠀⠀⠀⠀⠸⡆⢳⣄⠀⠀⠀⠀⢠⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⠀⠀⣠⠏⣼
⠀⠀⠀⠀⠀⠹⣦⡙⠳⢤⣤⠴⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⣤⡤⠞⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠴⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⢰⣀⣀⣀⣴⣇
⠀⡆⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰
⠀⢦⡄⢠⠀⣍⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃
⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⠄
⠀⠀⠀⠀⠂⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⢿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠠⡠⣿⣤
⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⡄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣥⠀⠀⠟⢷⢲⡄⠀⠀⠀⠀⠀⠰⣀⣨⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘
⣬⠹⣿⣓⣒⣒⣾⣯⣧⠀⠀⠀⠀⠀⠃⢼⠀⡧⠄⠧⠃⠀⠀⠀⠀⠀⠀⠸⢻⡄
⠀⠉⠓⠒⢃⡖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠨⠀⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⡄⠀⠀⠀⠀⠀⠀⠇⠀⠐⠄
⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⢄
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⡠⣄⠘⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⡤⢴⣴⠦⠼⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠒⠈⠩⡿⣭⠿⠞⠃⠀⠀⠀⠀⠸⠤⠄⢀⣧⣾⣿⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⢠⡤⣴⡧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⡿⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⢸⠇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠿⠀⠀⠀⠀⡆⢸⠇⠀⠀⢠⡀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠀⠀⠀⢰⠃⠉⠀⡼⠀⠀⣇⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠁⠀⢠⡏⠀⠙⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⣶⠀⠀⢰⡀⠈⠁⢠⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⡟⠀⠀⠈⣷⠀⠀⢸⡄⠀⠇⠀⠀⣀⢠⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠸⠇⢄⠀⡄⠀⠀⠀⠈⠁⠀⠀⢠⠀⠛⠈⠀⣧⣰⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⢀⠈⠀⠁⡀⠀⠀⠚⠀⠀⣆⠛⠀⠀⡇⢸⢿⠋⠀⡀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⠋⢸⠃⠀⠀⠃⠀⢰⣆⠑⡆⣼⠘⠀⠀⠙⠀⠀⠄⢠⠀⠈⠀⠠⡇⠸⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠈⣷⢈⡁⡀⠀⠀⢀⠘⠛⠀⠁⠻⠀⠀⢠⡀⠀⠀⣄⠀⠰⠀⠀⠀⠃⡿⠀⣆⠸⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⠀⠐⡋⢻⠃⣷⠀⠀⠚⡀⠀⠀⠀⠀⠀⢰⡌⡅⠏⢠⠟⡄⠀⠄⡀⠀⠀⣀⠠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡸⠇⠑⠴⡄⢡⣲⠐⣄⡇⠀⢀⠀⡄⢈⠀⡀⠿⠀⡾⠠⣠⡇⠸⠇⢀⡜⠃⠀⠀⢰⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⠂⠓⡆⣠⡄⠀⢧⣴⣾⡿⣶⡔⡌⠇⠀⠘⢠⡇⠀⠀⠀⠀⠋⡠⡖⣠⣸⣧⡘⠁⠀⠈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡦⠘⣄⠀⠈⠛⠈⠃⠙⢟⠃⣿⠿⣦⠀⠶⠀⠈⠓⣦⠀⠀⠐⠈⣷⠏⣻⢁⣼⡿⠋⢀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣌⠀⡮⡄⢈⣗⣦⡼⢆⢠⡄⠻⠃⠀⠀⠊⡰⣿⠄⠈⠀⠰⢷⠠⠉⠈⠈⣴⢒⡊⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢈⣛⣠⠤⣿⣄⡧⢴⣾⣿⡹⠇⢸⣧⢱⣄⡶⠀⠆⠁⠁⠁⢠⣄⠀⢁⣈⡀⢻⣧⢀⣿⡌⠃⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠁⠀⠀⠀⢹⣿⣆⡈⠯⠀⣀⣀⠀⠈⠛⢡⣿⣧⠤⠓⠠⢾⣿⣦⡈⠿⠃⢘⠡⢜⣿⡛⠁⠀⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⣀⣠⣾⡾⠁⠀⠀⠀⣨⡿⠂⠒⠒⢿⠏⠀⠀⠀⠀⠀⠙⢿⡟⠈⠁⠙⣄⠀⠈⠙⢿⣯⡭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⡽⠯⠽⠿⣵⣠⢤⣄⣾⡿⣇⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⣠⣿⣷⣤⣠⢔⣿⡆⠀⣠⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠐⠾⠶⠛⠿⠧⢯⡥⠿⣿⣓⠠⠄⠂⠾⠛⣋⠿⠷⠿⠿⠳⢿⠶⠾⠾⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣄⣀⠉⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣠⣰⣷⣶⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡏⠛⣯⠽⠷⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠼⠟⠋⠀⢀⣏⣀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢌⣿⣿⣴⠿⢀⢰⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠛⢸⣴⠃⣄⠀⢈⣿⡄⠂⠀⢀⣠⣤⠀⠀⠀⠀⣤⠀⢤⣤⣀⣶⠆⠀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢳⡮⢿⣿⠟⢻⠉⣽⣯⣨⠄⢂⣾⣇⠄⠀⠀⠄⠀⠀⠂⢀⣙⠃⠀⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣽⣿⡟⠄⠀⢀⠀⠛⢹⣷⠫⣦⣬⡃⢺⣰⣠⡶⡒⣲⢿⣏⠀⠀⠻⠯⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⡆⠀⣀⣄⠀⠘⣿⠛⣏⢛⣻⠿⣿⣿⣃⣼⢛⡙⠣⠀⠟⣄⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⡇⠀⢰⡁⠀⢠⣿⠍⡒⣍⣿⡧⠉⢿⣻⣝⢋⠰⠯⠁⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⣿⣿⣿⠆⣨⣧⡟⡴⣿⠳⠂⢀⣽⣿⣟⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠄⠈⠃⠈⠐⠃⠀⡟⠿⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠛⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠉⢣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⡐⠀⠙⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡅⠁⠀⠈⠃⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠰⢆⠀⠠⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣨⠔⠚⣁⢐⡉⠀⠀⢼⢯⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠲⠊⠀⠀⢀⠀⠠⠀⣡⣿⣀⠃⠱⢦⠄⠀⠰⡦⢠⣀⠶⠘⠃⠀⠀⠀⠀⠀⠀⢱⠈⡅⠐⣪⠴⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⣠⠿⠁⠀⠈⡧⠀⠀⠁⠀⠀⠀⢈⠀⠀⠀⠐⢀⠄⢁⠀⠄⠀⠀⢁⠐⢁⠑⠄⢠⡀⡠⢎
⠀⠀⠀⠀⡀⠶⡄⠀⠀⡀⠄⠒⠛⠀⠰⣶⠦⠕⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠠⣈⠀⣁⠀⠀⠄⠀⠊⠀⠈⢡⠌⠠⠁
⠀⠠⡤⠤⣤⠄⠀⠀⣠⢤⣠⠇⠉⣡⠀⢀⣥⠃⠀⠀⠀⠀⠀⠀⠆⠄⠁⠀⠥⠀⠂⠀⠀⠀⠄⠀⠀⠠⠈⠁⠀⠀⠁
⠀⠁⡀⠀⠀⢠⡄⡈⠂⠌⢄⠀⠈⠉⠀⠉⠙⠂⠀⠀⢤⣠⠤⠔⠀⠀⠀⠀⠀⠑⠂⡄⢀⠀⢐⠄⠀⠀⠄
⠀⠀⠒⠠⠍⠂⠀⠀⠀⠀⠁⠀⣀⠄⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣶⡎⢲⣿⣷⣮⠭⢗⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣖⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠈⣀⠤⠀⠀⠀⠀⠈⠛⣷⠖⢚⡹⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠒⠲⡞⠀⠀⠀⠀⠀⠀⠉⢧⣄⣀⣠⠀⠀⠂⠸⢆⣀⠚⢉⠉⡀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠓⠣⠤⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠭⠛⢋⠁⢠⡡⢀⠀⠀⠀⠤⢁⡲⠄⠠⠰⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⡀⠀⠙⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡑⠂⠐⠈⢣⠊⠒⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠾⢶⣦⣤⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠻⣦⡀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠉⠀⠀⠄⠀⢉⡙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠄⠳⠛⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢭⠀⠀⢀⠲⠀⠠⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢠⡀⠈⠄⠄⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣇⠀⠆⠀⠁⠉⠰⣤⠀⡱⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⡎⠀⠀⠀⠸⣤⠀⠀⢠⠀⠀⢀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⣋⡤⠴⠋⠈⠎⠉⠀⠀⢠⣼⣿⠁⠈⠰
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠜⠣⠁⠀⠀⠀⠀⢁⠩⠂⣴⠀⢶⠙⣦⡀⢠⠉⠀⢀⣔⠀⠀⠀⣠⢤⣦⠚⠋⠠⠀⠈⠁⠀⠀⢻⣑⠚⠂⢀⣱⢒⣩⡾⠉
⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⡠⠒⠁⠈⢀⣴⠟⠛⠲⢶⠂⠀⠸⢯⠀⠀⠈⠟⠑⠿⠊⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢣⡀⠃⠤⢰⠋⠉⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⣰⠯⠃⠀⠀⠀⢸⠂⠀⠀⠀⠑⠄⠀⠈⠀⠤⡀⠀⠀⠀⠁⣤⠃⣰⠄⠰⠀⠀⠀⢂⢤⠉⢠⡌⠕⢀⣰⡄⡠⠚⠢
⠀⠀⠀⠀⠀⡀⠰⢷⡆⠀⠀⡀⡢⠄⠚⠻⠂⠈⠫⣿⠷⣴⠞⠀⠀⠀⠀⠂⠐⢄⠀⠀⠢⠀⢠⠀⠆⣂⠉⢁⡠⡄⠀⠄⠠⠔⠁⠀⠀⠁⡤⠤⠠
⠀⠀⣔⣨⣤⣉⣆⠀⠀⠀⢐⣁⣀⣠⠞⠘⠛⣀⠀⠀⣙⡚⢄⠀⠀⠀⠀⠀⠀⠀⢒⢠⡖⡣⠈⠌⡥⡉⠄⠈⠀⠀⠈⡄⠄⠠⠀⣀⠒⠛⠁⠀⠀⢡
⠀⠒⣈⠁⠀⠉⠈⡁⣀⠰⡈⠁⠋⠁⠀⠀⠾⠟⠀⠺⢛⣇⠚⠀⠀⠀⠀⠀⠀⢀⡀⠂⠁⠀⠀⠀⠑⢄⡀⠢⠀⠀⠀⢠⡁⠀⠠⠀⠀⠀⠀⠀⠀⢠
⢐⣀⠂⠄⠀⠤⠄⡛⠑⠂⠈⠉⠨⠕⠄⡀⠀⠀⢂⠠⠂⠀⠀⠀⠠⠽⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠲⠀⠰⠋⠀⣔⠒⡡⠤⣀⠠⠠⢆
⢃⠀⣈⠋⠒⢒⡨⠄⠀⠀⠀⠔⠀⠀⠀⣤⣟⣀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠅⠀⢨⡈⡿⠓⠦⠒⠂⡄
⠐⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠀⠝⠉⣷⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠢⠄⠀⠀⠀⠀⠀⠀⠉⢵⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠦⢦⡶⡇⠀⠀⠀⠉⠁⠀⠉⠙⣮⣈⠀⠒⣄⠀⠀⡠⠊⢱⣆⠀⠰⠒⠋⠙⠁⠀⠠⡀⠀⠀⠀⠀⠀⢈⠉⠀⠈
⠀⠀⠈⠢⠀⠀⠀⠀⠠⣎⡃⠁⠀⠆⠓⠂⠐⠀⠀⠀⠀⠀⠀⠀⡀⠻⠿⠯⠯⠦⢀⡢⠄⠀⠈⠛⠁⠀⠈⠓⢫⡄⠀⠙⠀⡀⢠⡀⠂
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡐⠁⠈⠧⣜⠠⠔⠀⠀⠀⠛⠉⡶⠉⠁⠘⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠒⠄⠠⠄⢀⡉⢤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⢀⡉⠘⠃⡀⢒⡈⢡⡚⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣖⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣖⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣖⡀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⡀⠙⣆⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⡀⠈⢧⠀⠀⠀⠀⣠⡿⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⣂⠈⢳⡀⠀⣴⡟⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣔⣂⠀⠳⣾⠏⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡔⣂⠀⠙⣆⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⣂⠀⠘⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠹⣷⣂⣀⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⢦⡄⢹⡍⢀⡴⢬⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⠿⡭⢿⠏⠹⡜⢯⡿⠃⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢠⠋⠀⠀⠙⡄⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣀⣰⠃⠀⠀⠀⠀⠘⣆⣀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⡴⡞⠉⢩⠇⠀⠀⠀⠀⠀⠀⠸⡏⠙⢳⢦⣀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣠⠞⠁⢀⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡆⠈⠳⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⠁⠀⠀⢸⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⣇⠀⠀⠈⠳⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⡞⠁⠀⠀⠀⢀⡟⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⡀⠀⠀⠀⠈⢳⡈⠳⢤⡀
⠀⠀⠀⠀⠀⢀⡤⢖⣛⣛⡛⠉⠀⢠⠏⠀⠀⠀⠀⠀⡼⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⠀⠀⠀⠙⡄⠀⠉⢛⣛⣓⡲⢤⡀
⠀⠀⠀⠀⡴⣫⡾⠋⠉⠉⠙⣧⠠⡏⠀⠀⠀⠀⠀⡼⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢧⠀⠀⠀⠀⠀⢹⡄⣴⠋⠉⠉⠙⢷⣝⢦
⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢸⠆⡇⠀⠀⠀⣀⡼⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⢷⣀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠹⣯⣧
⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⢀⡾⣸⡃⢀⡴⣫⣥⣤⣤⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⣤⣤⣬⣝⢦⡀⢘⣇⢷⡀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢿⢻⣄⠀⠀⢀⣠⠞⣹⣅⣹⣫⡾⠋⠀⠀⠀⠹⣆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠏⠀⠀⠀⠙⢷⣝⢏⣨⣏⠳⣄⡀⠀⠀⣠⡿⡿
⠀⠀⢀⡜⣳⢭⣟⣛⣭⠵⠋⠁⢸⣷⡟⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡀⠀⠀⠀⠀⠀⢻⣿⡇⠈⠑⠮⣽⣛⣛⡭⣞⢣⡀
⢀⡴⢋⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢧⡀⠀⠀⠀⠀⢸⣟⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡙⢦
⠻⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢿⣄⣀⣀⣴⢞⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⢦⣀⣀⣠⡾⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣮⣭⣵⣖⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣲⣮⣭⣵⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠀⡄⠂⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠠⣰⠀⠀⠀⠔⠉⣀⣀⠅⠁⠀⠀⠀⠀⠀⠀⠀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⢀⣧⡠⠟⠛⠉⠀⠀⠀⠀⠀⢠⠀⡀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠙⢯⣦⣾⠞⠀⠀⠀⠀⢀⡤⠆⠀⡀⠘⠁⠉⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⣿⣷⣄⡀⠀⠙⢯⢦⣀⠀⢀⡴⡥⠀⢨⣡⣴⡿⢿⣇⣤⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠠⣿⣿⣷⡀⣀⠙⠎⢻⣟⡈⠄⣠⣾⣟⣆⢸⠏⠂⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⠂⠓⣀⢹⣿⣼⠦⢆⠺⠿⣿⣾⣿⠿⠷⠉⣼⣧⢤⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⢫⡰⣽⠁⠀⡠⣻⢈⢻⠿⣏⣥⠤⢞⠫⢌⢿⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣵⠟⣦⢠⠀⡿⣮⣿⣿⡟⠀⠬⡄⢠⣖⣦⢰⠏⠙⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣽⡟⡏⠉⠀⠈⠙⣀⡈⠁⠘⣴⢀⠀⠒⠳⢄⠁⡁⠀⠈⡀⢄⢍⣡⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠅⠉⠏⢳⣿⣵⡞⠛⢲⣦⡉⢳⣀⢀⣿⠪⢧⣴⡀⠚⣅⠚⠶⢮⡷⢊⣄⡀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡻⠧⣾⠞⠉⢠⠼⢻⣿⣿⡔⣿⣿⣿⣶⣦⢤⣒⡡⠥⠐⠉⠙⠟⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣯⣲⠞⢫⣾⣾⣿⣿⣿⣿⣯⡿⣿⡿⢺⣀⣀⡀⠤⠐⠂⠤⢡⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣶⡗⢹⣿⣿⣿⣿⢧⡟⡼⣿⠁⢠⠒⣂⣐⡀⢐⠁⠦⡄⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⣷⣿⡆⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⢱⡖⠁⠐⠊⢴⣞⣁⣽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠘⢳⢻⣯⣿⣶⣟⣿⣿⠥⠚⣩⠂⢠⠏⢈⡷⠐⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠈⣿⣿⡿⣿⡿⣿⣏⢐⡄⣇⠀⠈⠂⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠻⠮⠽⠛⠀⠈⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠶⠶⢶⠶⠶⠶⢶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢟⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢍⠉⠃⠀⠀⠀⢀⠄⠒⠒⠂⢀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣺⣯⣶⠄⢀⠤⠄⠂⠀⣀⠀⠀⠔⠃⠀⠐⠤⡀⠐⠄⠀⢀⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡝⠟⠉⡀⠎⠉⣶⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⢀⡈⢹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣫⡞⠀⢼⠀⢀⡀⣷⡀⠀⢄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⡇⠊⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⣿⣾⣦⣼⣶⣤⣽⣿⣿⣶⣾⣷⣤⣿⣿⣦⣄⣀⣀⣤⣄⡀⢀⣀⣁⡀⠀⠀⠁⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣝⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⡿⠿⠶⣶⣦⣴⢀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠳⣭⣿⣥⣝⣿⣷⣶⣿⣿⣿⣿⣁⡀⠀⣀⡀⢠⣿⣿⣿⣾⣿⡿⠿⣿⣫⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠉⠀⠀⢸⠿⢿⣿⣷⣿⣏⠉⢻⡟⣿⣇⠉⠋⠀⠀⡟⠃⣼⠟⠉⣹⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣤⣤⣤⣤⣬⡉⢿⡙⢿⣆⠀⠁⣿⣿⠀⠀⠀⢠⡇⢰⠏⢀⣾⣿⠟⣡⣾⣿⠁⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠲⣝⠆⠙⢧⠀⣿⣿⠀⠀⠀⠈⡇⠀⣠⡿⢋⡴⡚⠱⠂⠀⠀⠀⠀⠘⠻⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣭⣙⡛⠂⠁⠀⠀⢰⣿⣿⠀⠀⠀⠀⢱⡐⠋⠀⠑⠊⠁⠔⢛⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣭⣽⣛⣛⠟⠃⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠴⠒⢛⣛⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣾⣿⣿⣿⡄⠔⠒⢂⣀⠜⠆⡀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠁⡀⠀⠀⠈⠺⣿⠟⠛⠻⣿⣦⣴⣈⡀⠀⢀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣖⣁⣀⣀⣀⣈⣙⢿⠶⣶⣀⣀⣠⡤⠈⠛⠉⠙⠛⢿⣿⣁⣙⣒⣲⣷⣶⣶⣀⣾⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣛⣟⣹⢛⣟⣻⡿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠁⠐⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠈⠙⠂⠄⣀⡀⠀⠀⠀⠀⠀⡠⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⡁⠢⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⣿⣌⡀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡃⢈⠢⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡈⠢⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⡈⠢⡠⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠠⢄⡐⡠⠀⠠⠄⣈⣀⢀⡱⡌⠆⠙⢦⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠉⠓⠦⢌⣲⡀⡀⠱⡊⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⣈⣁⠀⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠢⢧⣌⢂⠀⠀⠀⠀⠀⠐⡀⢠⠋⠀⠈⠉⠑⠒⠢⢌⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠩⢘⠀⠀⠀⠀⡉⡑⠂⠀⠄⢂⣀⣙⠀⠁⢀⠀⠀⠀⠀⠀⠈⠆⢀⠇
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠀⠂⢤⣙⡓⠂⣀⠔⠁⠀⠀⠉⠑⠢⠤⣀⣐⠒⠂⣁⣀⡠⠂
⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⢉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠠⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠝⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠠⠄⡉⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡞⠉⠙⠢⣌⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⢄⠀⠀⠈⠙⢆⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢤⡑⠠⠀⠀⠤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠶⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⢀⣦⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠀⠀⠀⢀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⡄⢀⠀⣶⡧⠀⠀⢀⣿⣿⠟⢳⣄
⠀⠀⠀⠀⠀⠀⠐⡾⢁⠀⠀⠀⠀⠀⠀⢰⢋⠉⠀⠀⠀⢰⡀⡀⠀⠀⣤⠏⠓⡂⠀⠀⠀⠠⣗⢚⡄⢉⠃⡀⠐⢩⣿⣷⡖⠁⠛⢃
⠀⠀⠀⠀⠀⠀⢀⡷⢻⠀⠀⠀⠀⠀⣰⠿⠟⠀⠀⠀⠀⠤⠓⠃⡀⠀⢠⡄⠘⠟⢀⡄⠀⠀⣻⢼⡃⠀⠰⠀⡘⣿⡟⠉⠀⣀⡴⣿⡀⢀⡄
⠀⠀⠀⢀⢀⣰⣿⣃⣀⠁⢠⡄⠀⢀⣁⡄⠀⠀⠐⢶⠀⢼⠃⣿⠁⣶⠈⠁⢀⣀⠀⢳⡴⠞⠓⠐⠛⠦⣄⠀⠈⠛⣡⡶⠛⠁⠠⠸⠃⢀⡧⡀
⠀⠀⡰⠀⢼⣿⡿⢅⣠⡀⡨⢦⡀⠸⡿⠃⣀⡀⣿⡿⠀⣾⠶⣿⠀⠉⠠⣦⣾⡟⢲⣿⣤⣤⣤⡤⠤⠶⠞⣛⡀⢞⠙⡾⠀⣠⠶⠁⢀⣼⠄⢷⡀
⠀⠀⢧⠸⣿⣀⢶⡎⠀⢈⠃⠄⡇⡆⠈⠐⠿⠷⠈⠁⠸⠁⠀⠸⣧⠀⠠⠃⠘⠃⣾⣤⣤⣠⣤⣀⣤⢠⡶⣿⡧⠈⢢⡿⠋⢀⠄⠀⢀⣅⠀⢠⣅
⠀⠀⠘⡇⣾⣽⣔⢑⣄⣡⢈⣤⡠⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢻⣄⠀⠀⠀⠀⠹⣿⣼⡷⣦⡿⠴⠌⠿⣾⠃⠀⠀⠁⢴⠉⠀⠀⣸⣄⣀⣀⣸⣆
⠀⠀⠀⠈⠻⢿⣿⠿⠤⠀⠉⠞⠁⠀⠀⢀⣼⣤⣀⣀⡄⠀⠀⠀⢸⡟⢀⠀⠀⢀⠄⠙⠳⣶⠶⠶⠖⣲⡞⠋⠀⠀⠀⠀⠀⠀⣀⣼⣯⣥⣤⣤⣤⣽⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠉⢡⡀⠀⠀⣼⠁⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠟⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠋⠙⠒⠀⢿⡀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⢐⠃⠀⢀⠠⡀⠄⡀⡀⠀⢠⠀⠀⡄⡄⡀⢀⠀⡄⠠⢀⣠⣀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠰⠸⠁⠘⠀⠃⠘⢘⠁⠀⠠⠀⠀⠁⠀⠁⠈⠀⠅⠆⠘⠈⠀⠐⠸⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⡀⣶⢰⡾⢇⠋⠹⣦⠟⣠⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠶⣎⣧⢠⡕⡌⡄⣠⠷⠖⠫⠤⣻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣶⡌⢃⢺⠆⠸⣦⠘⣄⡃⣷⡿⣡⢰⡆⢰⠆⣰⠖⢠⡆⢀⡀
⠀⠀⠀⠀⠀⠀⣤⡀⠘⠻⠌⣅⠀⣉⣙⠲⣄⡇⠘⣷⣿⡇⠙⡨⢀⡖⣊⡀⢀⡨⢕⠛⠁⢀⣀
⠀⠀⠀⠀⠀⣤⣌⡙⡤⢜⣿⠎⠓⢬⡉⠉⠙⢧⣀⣾⣿⢷⣼⡔⠉⠀⢉⡥⠊⢰⣟⣀⠤⣻⣥⣄
⠀⠀⠀⣀⠀⠈⢉⣐⣿⣆⠀⠙⠲⡀⠛⢤⡀⠀⠙⣿⣿⣿⠉⠀⢀⡴⠋⣠⠖⠋⢰⣟⣤⣄⡉⢶⣶⠄
⠀⠀⠙⠛⡡⢫⡏⠠⠶⠎⠛⠶⡄⠙⠦⢤⣿⣶⣴⣻⣿⣿⣤⣾⡯⠤⠴⠁⢠⠖⠛⢶⡦⠀⢿⣍⠢⡀
⠀⠀⢰⡿⠀⠈⠲⣶⡄⠀⠀⠀⢹⣄⠀⠀⠀⠀⠹⣿⣿⣿⠋⠁⠀⠀⠀⢠⡏⠀⠀⠀⡰⠶⠖⠉⠈⢿⠄
⠀⠀⠈⢠⣶⢖⡴⠖⢛⠿⠿⠿⠷⠟⢿⣷⣤⣄⡰⣿⣿⣿⣀⣤⣤⣶⠾⡿⠿⠿⠻⢟⠛⠚⢦⡻⢷⡄
⠀⠀⠀⠀⠔⣯⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣮⡻⣿⣷⠋⠉⠀⠀⠀⠀⠀⠀⢸⣷⠀⢀⣿⢂
⠀⠀⠀⢸⣄⠛⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⣠⡆
⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣹⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣾⣵⣮⣿⣷⣿⣧⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⣄⣤⣾⡿⣻⣽⠿⣋⡿⣿⡷⣝⡦⣤⣴⣶⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣻⡼⣿⣽⣿⢵⢫⠖⡝⡮⣿⡎⣿⣳⣏⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣽⣝⣻⢿⣿⣿⣷⣟⣥⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣭⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉