Confused crazy text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢠⣤⡀⢰⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⡟⠃⢳⣼⠀⢹⡾⠈⢧⡤⠤⣦⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⢦⣤⡦⣼⡈⠁⠀⠀⢻⡄⠀⠃⠀⠀⠀⠀⣷⠞⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠙⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠈⠛⠉⣼⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠯⠛⠀⠀⠀⠀⢀⣴⡶⠶⠆⠀⠈⢛⡫⠥⣍⡻⡆⠀⠀⠀⠀⠀⠀⢠⣞⡁
⠀⢠⣤⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⢰⠟⣡⠶⠶⢦⣄⡔⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃
⠀⠀⠉⠹⣷⣤⣀⣀⣀⣀⠀⠀⠀⠈⢸⡇⠀⢀⣠⣼⡆⣀⢀⠀⠀⡸⠀⠀⠀⠀⠠⠚⡉⢢⠀⢛⣦
⠀⠀⠀⠲⢯⣍⠁⠀⠏⢠⡁⠀⠀⠈⠄⠳⣿⣿⣿⡿⠛⠿⠾⠤⣞⡵⠶⠦⣄⠀⠀⣼⡇⠀⠈⠙⢦⡀
⠀⠀⠀⠀⣠⠗⠀⠀⠀⢺⣷⠀⠀⠀⠀⠀⠈⢉⡥⠤⡠⠴⠦⣴⠋⠀⠀⠀⠈⣷⢾⢡⡇⠀⠰⣶⣶⡟
⠀⠀⢀⣼⣃⠀⠀⠀⠀⠸⡇⠙⡖⠲⣄⠀⠀⠁⣠⡤⡤⠤⣤⡏⠀⠀⢀⠀⢀⡏⣸⡞⠀⠀⠀⠀⠉⢷⡄
⠀⠀⣠⣟⣥⠄⠀⠀⠀⠀⢻⣶⣇⣀⠀⡟⠛⠋⠁⠀⡇⠀⢠⠇⠀⣠⢎⣠⡾⢻⠟⠁⠀⠀⠀⣀⠀⠠⣝⣦⡀
⠀⠈⠋⢻⡇⠀⠀⠀⠀⠀⠀⠻⣄⡏⢙⡟⠒⡶⠶⠶⡷⠞⢿⠚⢻⠋⢹⣡⡾⠋⠀⠀⠀⠀⠀⢿⣿⠦⣼⡏⠁
⠀⠀⠀⢿⣤⣶⠀⠀⠀⠀⠀⠀⠈⠛⠺⠧⣤⣧⣤⣴⣧⣤⡼⠴⠾⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⢄⠹⡄
⠀⠀⠀⢠⢞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢐⣄⠀⠀⡈⣷⠿
⠀⠀⠐⠿⠋⢙⡖⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠒⠒⠚⠉⠀⠀⠀⡀⣄⠀⠀⠠⡌⢿⠳⣷⡟⠛
⠀⠀⠀⠀⠀⠻⠟⢻⡷⣿⡄⢠⡆⣀⣶⣶⣠⣿⣇⣤⠀⣤⣠⠀⠀⠀⣷⣹⠛⣆⠀⣻⣮⣧⠉⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⠴⠛⠋⠉⠘⠋⠉⠉⠉⠸⡴⠋⠙⠛⢦⣸⠃⠻⠃⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀⣠⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⣷⣦⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡿⠟⢉⣡⣤⠶⠶⠛⠛⠛⠛⠛⠛⠶⠶⣤⣌⡙⠻⢷⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⠟⢁⣴⠞⠋⢁⠀⠀⢠⢖⣲⡞⣫⡙⣶⣒⢦⢀⠈⠙⠳⣦⡉⠻⣷⣶⡆
⠀⠀⠀⠀⠀⠀⣸⣿⠏⣠⡾⠋⢀⡤⠤⡏⡇⠀⠸⣝⡻⣧⠇⢹⡱⠆⣼⠿⢙⣶⣄⠀⠙⢷⣌⠻⣷⣤⡄
⠀⠀⠀⠀⢰⣿⡿⢁⣴⠋⢀⣔⡉⣯⣷⠄⡇⠀⣀⣠⣤⣤⣤⣤⣤⣉⠓⢬⣽⡼⠹⠤⣤⠀⠙⣦⡘⢿⣇
⠀⠀⠀⣠⣼⡟⢠⡞⢁⢞⡝⠻⣇⣵⣫⣿⣷⣿⣿⣥⣤⡀⠀⠀⢈⣭⣿⣶⣷⣶⡒⠉⠁⢀⠀⠈⢷⡈⢿⣿⡆
⠀⠀⠀⢻⡿⢀⡾⠁⢞⣻⣜⣳⣿⣿⡿⠛⠉⠁⠀⠀⠉⠙⢷⣶⡿⠋⠉⠀⠈⠉⠻⣷⡞⡭⡝⡆⠈⢷⡈⢿⣦⡀
⠀⠀⣴⣿⠃⣸⠃⢸⣬⣑⣲⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡦⠀⠀⠀⠀⠀⢹⣿⡞⣛⡻⡆⠘⣇⠸⣿⠃
⠀⠀⣼⣿⠀⣿⠀⣇⠮⢏⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢸⡿⣡⠾⣥⣆⠀⣿⠀⣿⣷
⠀⠐⣿⣿⠀⡟⠀⠈⠁⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣴⣿⡇⣗⠛⣘⡸⠀⢹⠀⣿⣿⡀
⠀⠀⣿⣿⠀⣷⠀⢾⣓⠢⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠿⠿⠿⠛⠉⣾⠃⡏⡙⠏⡇⠀⣿⠀⣿⡿
⠀⠀⢈⣿⡄⢻⡀⢰⣡⢾⠶⡿⣿⣿⣦⣄⡀⠀⠀⠀⢀⣠⣴⡿⠁⠀⣠⣴⣶⣿⡻⢿⡛⣷⣉⣶⠃⢀⡟⢀⣿⡷
⠀⠀⠘⢿⣧⠘⣧⠀⢯⢉⣃⣹⡈⠻⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⡴⠟⠛⢦⡀⠀⠻⡄⠻⣆⢖⠉⠀⣼⠃⣸⡏
⠀⠀⠀⢠⣿⣧⠘⣧⠈⢻⢋⡱⠝⡄⠈⠳⣦⣀⠀⠀⠀⠀⠘⠉⠀⠀⣀⣴⣿⠀⠀⢻⡀⢹⡏⠀⣴⠇⣰⡿⠟
⠀⠀⠀⠀⠉⢻⣧⡘⢷⡈⠪⣿⢺⡠⢲⠦⣄⠉⠛⠳⠶⣶⠶⠶⠞⠛⣉⡀⢿⡀⠀⠈⠁⢠⣯⡾⠃⣴⣿⡇
⠀⠀⠀⠀⠀⠸⠿⣷⣄⠻⣦⡈⠲⠴⣟⠽⣸⠆⠀⣠⠊⡼⣗⡒⢺⡉⠷⣹⡺⢷⣦⣤⣶⣿⠟⢠⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣌⠙⢶⣄⡈⠉⠁⠀⢸⡵⢦⣱⣼⣁⡻⠷⠭⠝⠉⢁⣠⡶⠋⣡⣾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣌⡙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⠞⠋⣡⣴⡾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⣿⠷⣶⣤⣤⣍⣉⣉⣉⣉⣩⣤⣤⣶⣾⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠿⠟⠛⠻⠿⠋⠉⠉⠁


⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣶⣴⡆⢀⣤⡄⠀⠀⢸⡇⢸⡇⢠⡞⣷⠀⢻⣇⠀⣰⡆⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠁⣿⡟⢹⡇⠀⠀⠸⣇⣸⡇⣿⡶⠏⡀⢠⡟⣠⣿⣀⣼⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠿⠶⠦⠀⠀⠿⠀⠿⠃⠘⠇⠀⠀⠀⠙⠟⠀⠈⠳⠟⠃⠘⠟⠋⠈⢻⡟⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⢀⣤⠀⠀⠀⠰⠶⠟⠁⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⠀⣠⣄⣀⣠⣶⠀⣀⣄⠀⣾⡇⢠⣦⠀⣀⠀⣾⡇⠀⢠⣶⣦⠀⣠⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠀⣿⠻⣿⠙⣿⣾⢻⣿⢀⣿⣡⣾⣿⢰⣿⠀⣿⡇⢀⣿⡿⠋⢰⡿⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣴⡖⢿⣾⡿⠀⣿⠃⠸⣿⠘⣿⡋⠹⣿⡿⣿⠀⢹⣷⡿⢻⣧⣶⠾⣷⡾⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠀⠀⠉⠀⠀⠁⠀⣿⡇⠀⠉⠀⠀⢀⣾⣿⡄⠀⠉⠁⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠹⣧⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⣤⡀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣤⣀⡀⠀⠀⣀⣤⣾⣿⡁⠀⠀⠀⠀⣻⣿⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⣻⡿⠿⠿⠿⣿⡟⠉⠻⠿⠀⠀⠀⢼⡿⠙⠻⢿⣷⣶⣶⣿⣿⣟⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠘⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⣀⣴⣆⠀⠀⠀⣀⣤⣤⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣤⣤⣤⣾⠃⠈⠻⠶⠞⠋⠀⢻⣶⠾⠛⠉⣡⣿⣧⡶⠶⢶⣶⡶⠃
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣹⣦⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡷⠶⠶⠶⠶⠶⣿⡿⠟
⠀⠀⠀⠀⠰⣾⠋⠉⠀⠈⠉⠁⠀⠀⠀⢀⣠⡶⠾⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣋
⠀⠀⠀⠀⣀⣼⡧⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⢶⣦⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣤⡀
⠀⠀⠀⠙⣻⡆⠀⠀⠀⠀⠀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⢤⣴⠶⠞⠛⠁
⠀⠀⢀⣾⢋⣀⣀⡀⠀⠀⠈⠁⠀⢀⣠⡤⠶⠶⠶⠦⢤⡀⠀⠀⠀⠀⢠⣴⣖⣒⣒⣒⠲⢤⣄⠀⠁⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠈⠉⢉⡿⠋⠀⠀⠀⢀⣠⣼⣭⣴⣾⣿⣿⣿⣿⣿⣷⣤⣀⣀⣴⣿⣭⣭⡭⠿⠿⠿⠷⢶⣷⣶⡆⠀⠀⠀⢷⡾⠿
⠀⠀⠀⣰⣯⣀⣀⠀⠀⠀⢸⣿⡟⠉⠀⠀⠀⠀⠀⠸⣿⠇⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⢿⡿⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⣿⣦⣶⣄⣀⣀⣀⣀⣠⣼⢩⣿⠀⠀⠀⣤⣤⣼⡇
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⣇⠉⠛⠛⠛⠛⠛⣛⣩⣽⡟⠀⠀⠸⣿⣭⣉⣉⣉⣉⣉⡉⠀⢸⡇⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠘⠷⡶⠀⠀⠀⠀⠀⢻⣦⣤⣭⣭⣭⣭⣭⣿⠿⠁⠀⠀⠀⠻⠿⠶⠤⣦⣴⣶⠶⠶⠟⠁⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢸⠃⢀⣀⠀⠀⠀⠀⠠⠄⠀⢿⡛⠷⠶⢶⣦⣤⣤⣤⣤⣴⡶⠶⠟⣛⣩⡟⠀⠒⠀⠦⠀⠀⠠⣶⠾⠆
⠀⠀⠀⠀⠀⠛⠋⢩⡏⠀⠀⠀⡛⠀⣀⠉⠘⣷⠲⠆⢤⡤⠤⣤⠀⢠⡤⢴⡶⠾⠿⠍⠁⠒⠮⣄⠀⠖⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠸⡇⣠⡄⠀⠡⡄⠁⠘⠃⠸⣿⠶⠤⢤⣤⠀⠀⠀⠰⠯⠰⣄⠀⠀⠀⠀⠀⠈⢿⡀⠀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢧⣴⣇⠀⠀⠀⠀⠀⢻⣟⠒⠲⠆⢴⠄⠴⠖⠺⠃⢉⣷⣄⠀⠀⠀⠀⠈⣧⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡄⠀⠀⠀⠀⠀⠙⠷⢶⣶⣴⣶⣶⡶⠶⠟⠛⠁⠈⠛⢦⣀⣀⡴⠛⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠷⢤⡤⠶⠲⠦⡀⠀⠀⢄⠀⠀⠀⠀⣠⠶⣤⠄⠀⠀⠒⠛⣹⣃⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡤⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣧⣤⡀⠀⠀⠀⠀⢀⣠⠎⠉⠀⠀⠀⠀⠈⠳⣤⣄⠀⣀⠀⠀⠀⠀⠀⢀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡴⠛⠒⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠓⠦⣤⡟⠑⠾⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⣶⣦⣄⡀⠀⠞⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡝⠓⣀⣤⣶⣶⣷⣶⣦⣄⡀
⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠙⠻⣷⡀⠸⣿⣿⢶⣄⠀⠀⠐⠊⠉⠉⠚⠉⠙⠒⠀⠀⢀⣠⠾⣿⡿⢀⣾⠟⠁⠀⠿⡿⠟⠈⠙⣿⣆
⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢿⡇⠀⡿⢷⡶⢶⠿⠛⠳⣶⠛⠛⢷⠶⢶⠟⡇⠀⣿⠇⣾⡏⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⡄
⠀⠀⣿⡇⣰⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⡷⠸⣧⣼⠀⣸⠀⠀⠀⡇⠀⠀⢸⡀⢸⡤⡿⠒⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⢮⣊⣿⣇⡀
⠀⠀⣿⣏⠻⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢻⣴⣇⣨⡇⠙⡷⠒⠒⡷⠒⠒⡞⠁⣯⣀⣷⣼⠃⠀⠹⣷⣀⣀⡀⢠⢤⡮⣳⠟⣱⣿⣿⠁
⠀⠀⠘⣿⣍⠒⠌⡁⣐⡒⠀⠀⣒⢀⣽⣿⠷⢶⣶⣿⣿⣿⣷⣴⣇⣀⣠⣧⣀⣀⣿⣶⣿⣿⣿⣷⣶⣶⣾⠿⢿⣶⣬⣽⣲⣎⣥⣾⠟⢹⡟
⠀⠀⠀⢸⣿⣧⣗⡀⠪⠄⣉⣰⣴⣾⠟⠁⠀⠀⠀⠀⠈⠙⠛⢿⡟⠉⠉⠉⠉⠙⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⡏⠛⠛⣿⣿⠀⠀⣿⠃
⠀⠀⠀⢸⡇⠈⠙⠛⠿⠿⠿⠛⠋⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠃⠀⢰⡟
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⢰⣿⣿⣿⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣿⣇⣀⣤⣤⣤⡀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣛⠋⠁⠀⢀⣴⠟⠁⠀⠀⣰⣇⠀⠀⣿⣿⣿⣿⠟⠁⠀⣠⣾⠟⠙⣧⠀⠀⠀⠀⢠⡿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣧⣀⠀⣼⡟⣿⡄⠀⠸⣿⣀⡀⠀⠀⠿⠿⠀⣠⣾⡿⠋⠁⠀⢴⣾⣿⣥⣀⡀⢸⡆⠀⠀⠀⣸⡇
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⠃⠸⣿⣀⣀⣈⣽⣧⣤⣼⠛⢻⣦⣿⣧⣤⣄⣀⣀⣀⣉⠉⠉⢻⣿⢸⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⣷⣤⣤⣤⣴⣶⡾⠿⠟⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠸⣷⣤⣄⣀⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠁







⠀⠠
⠀⢀
⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⢦⣄⣰⠏⠁⠈⢙⣦⣀⣀⣴⣯⣥⣤⣬⣿⣤⣤⣾⣛⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠛⠁⠀⠀⢀⣠⣬⡿⠶⠞⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠳⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⢀⣴⠞⠋⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⡟⠁⠀⠀⢠⣿⠀⠀⢀⣀⣀⢀⣤⠖⠛⠉⠙⠓⢦⣄⠘⠁⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⠀⠀⠀⠀⠘⢋⡴⠚⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⣴⣿⡷⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣤⣀⣿⠀⠀⠀⠀⣰⠋⠀⠀⣀⣤⣤⠤⣬⣷⣤⠶⠶⢦⣄⡀⠈⢿⡄⠀⠀⠀⣸⢃⡴⣦⠸⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⠉⢻⡄⡀⠀⢰⡇⢀⣴⠟⠉⠀⠀⠀⠀⠈⣇⠀⠀⡾⣽⣿⢷⣼⣧⠀⠀⢹⡿⠿⠿⣤⣸⡇
⠀⠀⠀⠀⠀⠀⣼⠁⢀⡾⠋⠻⣌⣿⠇⠀⣾⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣇⠻⢃⡼⠙⣿⠀⠀⢸⡇⠀⠀⠈⠙⠛⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⢿⡀⠘⠑⠛⣙⣿⣿⠀⠀⢹⡿⠀⢀⣀⡀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠉⠉⠀⢀⡿⠀⢀⣾⠃⢀⣀⣀⢄⣀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢀⣤⠾⠷⠶⠶⠟⠉⠉⣷⠀⠀⠘⢷⣼⢩⣤⠈⡇⠀⠀⣰⠟⣦⣀⠀⠀⠀⢀⣠⡿⠁⣠⠞⠁⠀⠈⠀⠀⠀⠈⠻⡆⠀⠀⠀⢹⡆
⠀⠀⠀⣴⠏⠁⢀⣤⠶⠶⠄⠀⠀⠙⣧⡀⠀⠀⠙⠿⢿⣴⣧⣶⠿⠷⡄⠀⠙⠻⣿⣿⣿⣁⣀⣈⡁⠀⠀⢠⡴⠶⢶⡄⠀⢀⡇⠀⠀⠀⣸⠇
⠀⠀⣸⠃⠀⢰⡏⠀⠀⢀⣤⣀⠀⠀⠈⠙⠁⠀⠀⢀⣤⠞⠹⣇⠀⠀⠉⠀⠀⠀⠀⠉⠛⠿⣍⠉⠁⠀⠀⠀⠀⠀⣸⠇⠀⠚⠀⠀⠀⣰⠏
⠀⠀⢿⡀⠀⠈⠃⠀⠀⣿⠀⠉⠓⠀⠀⠀⡤⠴⠚⠉⠀⠀⠀⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠈⢻⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣠⡴⠋⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠙⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⢀⣤⠟⠀⠀⣰⠟⢻⡄⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠙⠳⣤⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣋⣠⣤⠴⠛⠁⠀⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⣤⣤⣀⣀⣸⡀⠉⠛⠶⣤⣤⣴⣶⣦⣤⣤⣤⣴⣾⣿⣿⣧⡀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⠶⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⠿⠿⣿⠋⠉⠉⠉⠻⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⡄⠸⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠀⣧⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠃⠀⠀⢘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⠛⠚⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⡀⣀⣀⣠⣤⡴⠶⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠠
⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⢀⣀⣀⣀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠉⣿⣶⡿⠛⠛⢿⣷⣴⡿⠟⠛⠿⣿⡾⢷⣦⣠⡶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡄⠀⣿⡟⠀⣠⣄⠀⢻⣿⠁⣀⣤⡀⢹⣧⣀⣿⡿⠁⢀⣾⠃⠀⠀⠀⠀⣀⡀⢰⣿⠟⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢸⣿⣿⡆⢸⣿⠀⣿⣿⣷⠀⣿⣿⣿⠃⢠⣿⣧⣤⣶⣶⡾⠟⠿⣷⢸⡟⠀⠀⣿
⠀⠀⠀⣴⣿⠿⣿⣷⣶⣤⣤⣀⠀⠀⢀⣴⡿⠇⠀⣿⣇⠘⣿⣿⠃⢸⣿⠀⢿⣿⡟⢀⣿⣿⠃⢀⣾⡿⢿⣏⠀⣿⣧⠀⠀⢹⣿⡇⠀⢰⣿
⠀⠀⢸⡿⠁⠀⠀⠀⠀⠉⠉⠙⣿⠛⠻⢿⣦⣤⣤⣈⣿⣆⡀⢀⣠⣿⣿⣆⡀⠁⢀⣼⣿⡃⢀⣾⢿⣧⣴⠟⠀⢹⣿⠀⠀⠀⠛⠃⠀⢸⡏
⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠋⠛⠿⢿⣿⠁⠈⠻⠿⠿⣿⡏⠛⠿⠟⠉⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⣿⣀⣠⣤⣴⣦⡄⠀⠀⣠⣾⠿⣇⠀⠀⠀⠀⠀⣾⠃
⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⡇⠀⠀⢾⣟⣹⡿⠀⠀⠀⣸⡟⠀⠀⠀⣴⠀⠀⠹⣯⣉⣴⡿⠋⠀⢀⣴⡿⠃⠀⢹⣆⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⡿⣿⡇⠀⠀⠘⢛⡉⠀⠀⠀⣾⡏⠀⠀⠀⢸⣿⡧⠀⢀⣿⡿⠋⠀⠀⠰⣿⣿⣶⣶⣦⡈⣿⡄⠀⠀⠀⣿
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠹⣧⣿⣇⣀⠀⢰⡟⢻⣦⠀⠀⠻⣧⣤⡄⠀⣠⣤⣤⣄⣿⣏⣀⣀⣀⣀⣀⣄⣀⣀⣀⣿⡇⢻⣇⠀⠀⠀⣿⡆
⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣤⣼⡟⠀⢻⣧⣤⣤⣶⡿⠿⠶⠟⠀⠈⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠘⠿⠿⣿⣿⣿⡇
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢀⣠⣤⣾⡿⠋⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠘⢿⣿⣶⣶⣶⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠉⠉⠁












⠀⠠
⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀
⠀⠀⢠⣴⠶⠿⠿⠷⣾⡟⠻⠋⢉⠉⢻⣿⠛⣉⣉⣉⠛⣷⡴⠶⠶⠶⠿⢷⣦⡶⠿⣦⡀⠀⣤⡶⢶⣄
⠀⢠⣿⠁⣴⡶⠶⣶⣿⡇⠀⣾⢿⣇⢀⣿⣿⠿⠿⠿⠀⢿⣷⣶⡶⠀⢀⣾⠛⢿⣄⠈⠻⣾⠏⠀⣸⡟
⠀⠸⣿⠀⠻⣷⣶⠶⣿⡇⠀⣿⠈⠛⢻⡿⠀⣴⣶⣶⠀⢸⣿⠋⢀⣴⣿⣥⣤⡀⠻⣷⡀⠉⢀⣼⠏
⠀⠀⠙⢷⣦⣤⣤⣤⣾⣧⣠⣿⠀⠀⠘⣷⣄⣉⣉⣡⣀⣸⣇⣀⣀⣁⣀⣀⣼⣗⣴⡟⠁⣠⡾⠃
⠀⠀⠀⣀⣀⣀⣁⠈⠀⠉⠉⢁⣀⠀⠀⠀⠉⢉⣉⣉⡉⠉⠙⣛⣛⣛⣛⣛⠉⣾⡏⠀⣴⡟⠁⢀⣀
⠀⠀⠿⣿⣿⠛⢿⣷⡄⠀⣰⣿⣿⡄⠀⣶⣿⣿⠿⢿⣿⣦⠺⠿⢿⣿⡿⣿⡿⢻⣿⣿⡏⠀⣠⣿⣿⠃
⠀⠀⠀⣿⣿⠀⣸⣿⡇⣰⣿⡿⣿⣧⠀⠀⣿⣿⣀⣠⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠙⠿⣿⣶⣿⡟⠁
⠀⠀⠀⣿⣿⣿⠿⠋⣰⣿⣿⣿⣿⣿⣿⠆⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⣿⡟⠀⠀⢠⣿⡿⠁⠀⠘⣿⣿⠀⣿⣿⠈⢿⣿⣦⡀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⠏
⠀⠀⠀⠛⠃⠀⠀⠈⠛⠁⠀⠀⠀⠙⠛⠀⠛⠋⠀⠀⠙⠛⠃⠀⠈⠛⠁⠀⠀⠀⠀⠛⠋
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿
⠀⠀⠛⠛⣿⣿⣿⡟⠛⠃⢸⣿⣿⣿⠛⠛⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣀⣀⠀⢠⣿⣿⣿⢻⣿⣿⡄⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⡇⠀⣿⣿⣿⢻⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣾⣿⣿⣷⣾⣿⣿⣷⠀⣿⣿⣿⠸⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣤⣤⡄⣿⣿⣿⡟⢻⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠷⠿⠿⠿⠇⠈⠿⠿⠿⠇⠿⠿⠿⠀⠻⠿⠏⠸⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⣻⠿⡿⠀⠀⠀⠙⢷⡀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡀⠀⣤⣟⠀⠀⠀⠀⠀⠀⠈⣧⠀⡴⠋⠀⠀⠀⣹⣷⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⠿⣷⣾⢿⣄⣀⡀⠀⠀⣀⣰⠇⢸⡇⠀⠀⠀⠀⠈⠉⡇⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠿⠟⠻⢦⡴⢷⣦⣄⣀⣀⣀⣼⣿⣂⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠙⠲⠦⣤⣄⣀⣀⣀⣀⣤⣴⠀⣾⢠⣄⠉⠛⠛⠛⠋⠉⠛⠛⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⣦⣤⣤⣤⡶⠛⣹⣿⣿⣿⠏⠀⣿⢸⣿⣷⣶⣤⣤⣄⣀⣀⣀⣤⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠐⠛⢄⡀⠙⠺⣿⣿⡿⠋⠀⠀⢸⠈⣿⣿⣿⣌⠳⣤⣀⣀⠀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⢤⡀⠈⠓⠶⠛⠋⠀⠀⠀⠀⡿⠀⠈⠻⣟⣉⣀⡀⠼⣏⠫⡁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠶⢤⣷⠀⠙⠒⠒⠂⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢈⡉⠀⣀⣠⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣠⡬⠷⣤⡶⠶⠶⠲⣦⡶⠒⠚⢿⣤⣤⣤⣤⣤⣭⢭⣁⣼⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣼⢁⣶⠲⢾⡇⢠⣟⣇⣼⡿⢛⡛⠘⣷⡶⠂⣠⠟⠳⣄⠹⡿⢁⡼⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣙⣛⣹⣇⢸⡏⠉⢿⡐⠻⠛⢀⣿⠀⠚⠛⢛⣦⣽⠆⢠⣾⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣉⠉⠉⢉⣀⠀⠈⣉⣉⣉⡛⢛⣛⣛⣛⣋⣽⣃⣰⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢹⣷⢀⣾⣿⡇⠘⣿⡟⢙⣿⡎⠛⣿⡟⠛⠙⢿⣧⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠿⢋⣾⣿⣿⣷⡆⣹⣿⣿⡟⠀⠀⣿⡇⠀⠀⠀⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⡟⠀⠈⢿⡇⢿⠇⠙⢿⡆⠀⢿⠇⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⢴⣶⣶⣶⡄⢠⣶⣶⣶⡄⠀⣶⣶⣶⡄⣰⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡏⠁⣾⣿⡟⠉⠁⢸⣿⣿⣿⣇⠀⣿⣿⣿⣇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣿⣶⠀⣼⣿⡏⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡏⠀⠀⣿⣿⣶⣿⣿⡆⣿⣿⠛⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢿⣿⣿⣿⣷⣿⣿⠉⣿⣿⡇⣿⣿⠄⣿⡿⢸⣿⡇


⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠟⠀⠀⠀⠀⠰⠘⠿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⢁⣤⢤⡀⠀⠀⢀⣀⡀⠈⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⢠⡀⠙⠀⢠⢋⣌⠙⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠻⠟⠀⠁⠀⠘⠿⠃⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⡀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⡤⠾⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢢⠀⠀⠉⠓⠖⠚⠀⠀⠀⠀⠐⠶⠚⢁⡴⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠤⣴⣶⣦⣤⡀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠞⢙⣴⣿⡟⠉⠓⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⣦⣤⣿⣿⠟⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠿⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⢹⣿⡇
⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣦⠀⠀⠀⠤⠄⠒⠒⠒⠒⠀⠸⣿⣿
⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠁⠀⠀⠀⠀⢀⣤⡀⠀⠀⣴⡆⠀⠀⠰⠿⠀⠀⠀⠛⠃⠀⠀⠈⠉⠀⠀⠀⢀⣠⣄⠀⣤⣴⡆⠀⠉⠁
⠀⠀⢸⣿⣿⠀⠀⣀⣀⣀⠤⠤⠤⠀⠀⠀⠻⠏⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄⠀⠀⠀⠀⣶⣾⣿⣿⣧⠀⠀⠈⣿⣿⡄⣿⣿⠃
⠀⠀⠀⣿⣿⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠉⢉⣿⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠉⠁⠀⠀⢠⣾⣿⠿⣿⣿⣆⠀⠀⠀⢹⣿⣿⠉⣿⣿⡇⠀⠀⠀⢸⣿⡟⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⢻⣿⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⡁⠀⠀⠀⢸⣿⣇⢸⣿⣿⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⣀⣀⡀⠀⠀⠈⣿⣿⡏⢹⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠘⣿⣿⡇⠀⠀⠀⣿⣿⣿⢸⣿⣿⡀⠀⠀⢸⣿⡿⠀⠻⠿⠟⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠿⠁⠀⠀⠀⠙⠛⠛⠀⠉⠉⠀⠀⠀⢀⡀⠀⠀⢠⣤⠀⠀⠀⣶⡆⠀⠀⠸⠟⠀⠀⠀⠉⠉⢁⣀⣀⣀⣠⣼⣿⣿
⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠛⡀⣀⣀⣙⣁⣀⣀⣈⣉⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡆⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠒⠒⠚⠋⠉⠉⠁⠀⢸⣿⣿⣿⠿⣿⣿⣿⠟⠛⠛⢿⣿⡿⠛⣉⠛⢿⡟⢉⡉⢻⡿⢩⣿⣿⣷⠀⠈
⠀⠀⠀⠀⠀⣿⣿⣦⣶⣶⣶⣶⣿⣿⣿⣿⠀⢸⣿⡋⣁⠀⢹⣿⡏⢰⣿⣷⠀⢿⠀⣾⣿⡇⠈⣇⠘⠃⡘⢡⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠻⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⡇⠸⣿⣿⠀⣸⠀⢻⣿⡇⠀⣿⣿⡟⣰⡇⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠀⠈⠉⣿⣄⣉⣉⣰⣿⣷⣄⣉⣤⣾⣿⣿⣴⣿⣿⣦⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⡿⢿⡿⠿⣿⠿⢿⠟⢿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠟⠀⠰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠘
⠀⠈


⠀⠈
⠀⠐

⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⢸⣿⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣾⣿⠋
⠀⢸⣿⡇⠀⠿⣷⠸⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣶⣾⣿⣧⣼⡿⠁
⠀⠸⣿⣇⣀⣤⣀⠀⣿⣿⣭⣽⣿⡆⠀⠀⢰⣶⣶⣶⣶⠀⠀⠾⠿⢛⣿⣿⠟⠀⠀⠈⠙⣿⣿⡀
⠀⠀⠉⠛⠻⠿⠟⢰⣿⣿⡍⢹⣿⣇⠀⢠⣾⣿⣯⣿⣿⣦⠀⠀⣠⣿⡿⣁⣤⡀⠀⠀⢰⡿⠿⠇⢀⣀
⠀⢠⣾⣿⣿⣶⣶⣦⣬⣍⠁⠘⠛⠛⠘⠿⠿⠟⠀⠘⠿⠿⠗⠺⠟⠛⠛⣛⣋⣡⣤⣤⣴⣶⣾⣿⣿⣿
⠀⢸⣿⣿⣿⠛⠛⢿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⡟⠻⠿⠛
⠀⢸⣿⣿⣿⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⣴⣿⣿⣿⢿⣿⣿⣷⡄⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⡇
⠀⢸⣿⣿⣿⠀⠀⢀⣀⣀⣀⡀⠀⢀⣼⣿⣿⣿⣷⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣤⣤⣼⣿⣿⣿⠇⢰⣾⣿⣿⣿⡯⠉⠉⠉⣿⣿⣿⣿⣶⡄⠀⠀⠀⣤⣿⣿⣿⣧⡀
⠀⠘⢿⣿⣿⣿⠿⠿⠿⠛⠁⣀⣘⣛⣉⣉⡍⠁⠀⢠⣤⣭⣭⣭⣍⣙⡁⠀⣀⣀⠻⠿⠿⠿⣿⡇
⠀⢀⣠⣤⣴⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣇⠀⠀⠈⣿⣿⣿⠉⢻⣿⣿⡆⠻⢿⣿⣿⡇⠀⣶⣦⣤⣄⡀
⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⣰⣿⣿⣧⣿⣿⣿⣦⠀⠀⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠙⢿⣷⣤⣿⣿⣿⡿⠇
⠀⠀⣿⣿⡇⠀⠀⣀⡀⣰⣿⣿⡏⠁⠀⠿⠿⠿⠟⠸⠿⠿⠿⠿⠿⣿⠿⠃⠀⠀⠀⠀⣿⣿⡿⠛⠁
⠀⠀⣿⣿⣇⣤⣿⣿⠏⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀
⠀⢠⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃
⠀⠚⠋



⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⣐⣾⠡⠼⠒⠚⠓⠚⠗⠻⢍⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡰⠋⢠⠇⢀⣀⡠⠄⠠⢄⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⡇⠀⢠⠊⣁⡈⢱⡤⢤⣀⠱⡄⠀⣛⣈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⢢⣷⠀⣧⠎⠁⠀⠀⡇⠀⠿⠛⣇⠀⡏⠙⠲⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠤⠞⢻⠀⢫⣤⡀⠀⡰⢧⣀⢀⡠⢃⠞⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠊⢉⣄⠈⠃⠀⣈⠝⢏⡙⠀⠈⠛⠒⡂⠀⠈⢩⠂⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠨⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⠄⢀⡤⠃⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡈⠑⠦⢤⢄⡀⠀⡀⠑⠒⣒⣭⠔⠃⡸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⢄⠈⣩⣿⣿⣿⣿⣿⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡿⠻⠛⠉⠻⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⣄⣀⣀⠠⠴⠃⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢠⠤⠐⠂⠘⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠑⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⠁⡜⠀⠀⠀⠀⠀⠀⠈⠅⠉⠓⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⡎⠀⠀⠐⠤⣤⣤⣠⡤⠤⠊⠀⠀⠀⡇⠀⠙⢦
⠀⠀⠀⣀⡤⠤⣤⣀⡀⠀⢠⠎⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⠀⠀⠀⠀⢣⠀⢀⣀⣤⠤⢄⡀
⠀⠀⡼⢡⠖⡣⠖⢀⡭⠿⢏⠒⠒⢤⣀⠀⠀⠈⠉⠉⠉⠁⠬⠩⠭⠭⠥⠤⠤⢤⡤⠒⠒⡺⠿⢭⡀⠲⣌⠲⡌⢢
⠀⢸⡀⡏⠰⣁⠀⡇⠀⠀⠀⢣⡘⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡈⢂⡞⠀⠀⠀⢸⠀⣘⠄⢹⢀⡇
⠀⠈⠓⢧⠄⢳⡥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢬⡞⠠⡴⠚
⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠶⠒⠲⣄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⡀⠀⢷⠀⢹⣄⡀⠀⢘⡇⢙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠙⢦⣜⣇⠹⣤⡽⠓⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⢷⠀⡴⠋⢳⡀⠀⢹⡄⠀⠈⠛
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠸⡌⠑⢾⡇⠙⠶⠞⠁
⠀⠀⠀⠀⢸⠦⣸⡀⣇⡹⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⠖⠉⠒⠲⠤⡤⡄
⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠋⠉⠀⠀⢐⠀⠀⠀⡄⠀⠉⠲⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠐⠀⠀⠈⠀⠀⠀⣀⠤⠤⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠠⡄⠀⣖⠚⠁⢖⠉⠱⠴⢦⣀⡤⠴⠒⠛⠁⠀⢀⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⣀⢸⠀⢀⠞⢀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠳⡀⠒⠀⠙⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢪⠁⠀⠀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⢀⠀⠀⢱⠀⠀⠘⢣⡄⠸⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⢀⠀⠀⠀⠤⠔⠀⠰⣀⢆⠀⠑⠋⠀⠀⡰⠀⠀⠀⡽⠀⠀⠀⡴⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠳⣄⠀⠀⠀⠀⠑⠒⠫⠇⢀⣀⡤⠊⠑⠀⠄⠰⡃⠀⡤⡪⠚⢿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠔⠈⡜⠉⠁⡒⠶⠶⠶⠚⢻⠅⠀⡈⢠⠀⠀⠀⣤⠋⠀⠙⡞⣤⡪⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢤⢸⠀⠲⠤⡵⠀⠐⢳⠀⠘⢶⠋⠀⠀⡄⣀⡼⠁⠀⠀⠀⠸⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣉⠉⢆⠉⢦⡀⠀⣱⠀⠀⢸⠀⠀⢸⡤⠤⠚⢩⠥⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠸⠀⠈⢆⠀⠈⠉⠹⣀⡠⠬⠤⠤⠞⠀⠀⠀⠂⠀⣰⠈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⢒⣊⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣂⠂⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠛⡌⢹⠐⢠⢒⡄⡇⠀⡔⠂⡔⣢⠐⢰⠀⢸⠀⢰⢐⠧⡂⡆⠡⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⡁⣸⢰⣿⢯⣓⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⡑⣻⣣⡿⠃⠀⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡞⣡⠶⠯⠿⠟⠁⠀⠀⠀⢸⣹⠁⠀⠀⠀⣠⣤⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠳⣿⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⣈⣥⣤⣤⣤⣞⣽⣿⣿⡿⣿⣟⠿⢯⣍⡓⠂
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⠏⠀⠀⣠⡤⠶⠚⠛⠉⠉⠠⠚⠉⠿⡦⠀⠀⢉⣭⠭⢟⡓⠶⢿⣷⣤⣉⠑⠂
⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠃⣀⡴⠛⠁⠀⠀⠀⠀⣤⠶⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀⠘⢻⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⣰⣿⣿⣿⣿⣿⡿⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠙⠻⣷⡀
⠀⠘⢿⢿⣿⣿⣿⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠈⢻⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠶⠛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠴⠚⣋⣭⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣳⠦⠈⠙⠚⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣂⡀
⠀⠀⠀⠀⠀⠘⠚⠉⡽⠁⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠙⣆⠀⢻⠉⠳⠬⣷⠲⢤⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣸⠀⠀⠀⠀⠠⢔⣀⡉⠙⠒⠤⠤⣘⣯⡉⠙⢲⠒⠦⠬⣷⣦⡀⠈⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟⠀⠀⠀⢀⡞⠉⠈⠉⠓⢄⠀⠀⠀⣀⣰⣤⠈⢧
⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡏⡼⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⢷⣰⠋⠀⠀⠈⡆⠈⢧⣀⡀
⠀⠀⠀⠀⡞⢉⣀⣉⠑⢾⡼⠁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣷⠀⠳⠆⠺⡄
⠀⠀⠀⠀⢇⠀⠈⠳⠻⠄⠁⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⣠⣀⣸⢠⢴⣄⠀⢀⡇⠀⠘⢯⡍⡣
⠀⠀⠀⠀⠀⠑⠲⠤⠴⢶⡀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣳⣿⠋⠻⠿⠯⠤⠚⣠⠖⠒⡄⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠒⠲⠖⠛⠁⠀⠀⠀⠀⠀⠀⠁⢀⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠄⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⡠⢀⡴⠒⣒⡧⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡸⢀⠆⠀⠀⠀⢸⠉⣉⣹⠭⠼⠧⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⢱⠓⢺⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢖⡓⠄⠛⠀⡞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠤⠤⠴⠃⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⡖⠒⠒⠒⢻⢹⡉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠼⢾⠷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⣀⣠⣤⢾⠒⠲⣍⣹⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣢⠤⠤⠾⠷⢓⣚⡪⠽⠛⠉⠀⠀⠀⢀⣠⣤⣤⣤⠄⠍⠉⠉⠉⠛⠛⠳⠶⠶⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠿⠯⠭⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠟⠻⠎⠙⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠠⠐⠀⠁⠀⠀⠀⠈⠉⠒⠦⢀⣠⠞⠀⠀⠀⠀⠀⠒⠈⢷⣄⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠳⢤⣀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣀⣠⡤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠀⠀⠀⠈⣇⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⢉⡥⠤⠄⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇⠀⠀⠀⠀⠀⢰⠋⠀⣠⣴⡆⠈⢳⠀⠀⠀⠀⡴⢉⣤⣤⠀⠈⢢⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⡶⢸⡇⠀⠀⢰⠀⣿⣿⣷⣶⠀⠀⡇⠀⠀⠀⠀⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⠀⠀⠘⠲⠤⢌⢛⠋⣁⠜⠀⠀⠀⠀⠣⠙⠛⣛⢋⢀⡼⠁⠀⠀⠀⢀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣄⡀
⠀⠀⠀⠀⠈⢧⡈⠙⠦⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡤⠖⠋⣠⠟
⠀⣠⠤⠤⠶⠶⠞⠓⠀⠈⠙⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠙⠂⠀⠀⠀⠀⣠⢞⡟⠉⠀⡀⠛⠷⠶⠤⢤⢤⡀
⣾⣃⣈⠭⠅⠀⠀⠈⠉⠙⡆⣜⠀⠀⠉⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⢘⡇⡔⠉⠉⠀⠀⠀⢭⣭⣁⣙
⢯⠁⣀⣀⣀⣀⣀⣠⣤⠴⠃⢹⡀⠀⠀⠀⠀⡽⠓⣶⢤⣤⣄⣀⣀⣀⣤⣤⡴⠶⣏⠁⠀⠀⠀⣸⠃⠳⢤⣤⣄⣀⣀⣀⣀⡀⢨
⠈⠉⠉⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⣀⣀⣠⠞⠁⠀⣿⢢⡀⠴⣿⣿⡷⢄⡌⣿⠀⠙⢦⣄⣀⣠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠀⠀⣠⠞⣯⠀⠀⠀⢨⣽⡀⠀⠀⢸⣦⡀⠀⠀⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠤⠖⠚⠁⠀⡃⠀⠀⠀⠈⠛⣇⠀⠀⠈⡇⠉⠓⠦⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡿⠃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠒⢲⡆⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢰⠀⢸⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡴⠋⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢯⡀⠀⠀⠀⠀⡹⠂⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣦⣤⣤⣷⣄⣀⣠⣾⣥⣤⣤⣴⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⢸⡏⠀⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⣴⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⢾⠏⠉⢻⣷⡄
⠀⠀⠀⠀⣿⡁⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠙⠋⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠑⠦⣄⠀⠀⠈⢯⠳⢄⡀⠀⢀⡀⠀⠀⠀⠀⣀⡛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣴⣶⠀⠀⠀⠠⣤⣤⣤⠼⠀⠀⠀⠉⠒⠒⠋⠀⠀⠙⠦⠼⠏⠲⣄⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣈⣢⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⡤⠤⢤⣀⠀⠀⠀⠉⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡏⠀⠀⠀⠈⢳⡀⢠⠒⠒⢢⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⡇⠀⠀⢸⡀⠀⠀⠀⠀⣸⡇⢻⠉⠀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣬⡓⠋⠀⠀⠀⠈⢇⠀⠀⠀⠀⣹⠁⠈⠳⠤⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠖⣆⠀⠀⠀⠀⠈⠣⣄⣀⡴⠃⠀⠀⠀⠐⢦⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠒⠐⠋⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠦⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠈⠙⠒⣦⢤⣄⣀⣁⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠦⡴⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠺⠟⠀⢰⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠭⠀⣀⣯⣀⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠀⢨⡭⠉⣹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠉⠙⡟⢒⣶⣶⡾⠖⢺⠟⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⠭⠭⠟⠋⠉⠑⠛⠭⠿⠯⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠀⠀⣠⠄⠀⣀⠤⣦⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡠⠀⢼⣤⣾⢟⡦⠄⠤⠜⠻⢷⠛⣷⣶⣄⠀⢲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⡯⠐⡚⠛⣻⢖⠈⠁⠂⠒⠦⠐⣎⡁⠾⡖⢩⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⠶⢗⠀⠠⡎⠉⠀⢀⣀⣤⣄⣀⠀⠁⠠⠓⣷⣀⡹⠶⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⠀⣑⠀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋⡰⠂⠀⣀⣁⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢄⡶⣿⣼⠃⠀⠀⠸⠿⠿⠟⠀⠀⢹⣿⣿⠀⠸⣀⠄⠸⡄⠈⠉⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⡿⣃⡀⠀⢤⠀⠀⠤⢀⡔⠀⣠⣿⣿⡟⠀⠐⠋⢓⠸⣀⣀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡅⠀⣦⠀⡰⠋⠠⡟⠍⢀⣾⣿⣿⠟⠀⠀⡀⢠⡎⠈⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⢁⣀⡭⣦⣳⠸⣏⠀⠀⣾⣿⣿⠋⠀⠀⠰⠛⢻⠷⡄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⠂⠀⠻⣼⣋⣀⠀⠉⠉⢉⠤⣠⡒⠒⢢⠁⠹⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⡄⠊⣱⣿⣿⡁⠀⣿⣿⣿⠀⠈⣕⣦⠬⠀⠀⠈⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⢀⡧⢰⡟⣷⡿⢷⠀⠉⠉⢉⣠⢼⡥⢤⠵⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⠞⠛⠀⠤⠉⠌⢉⡀⠀⠀⠰⠄⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠉⠛⠛⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠤⠄⠀⡤⠤⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠿⠂⠀⠀⠷⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⣴⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢲⢰⠃⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢵⣏⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⣤⣶⣦⡄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡟⠋⠉⠻⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣾⡿⠋⢿⣿⣿⠏⠻⣿⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⢀⣴⣄⠀⠀⢀⣦⡀⠈⠻⣿⣿⣿
⠀⠀⠀⠻⠿⣿⣷⣶⣤⣭⣥⣴⣶⣿⡿⠿⠃⠀⠀⠀⣿⣿⣿⣧⣀⡀⠈⠉⠛⠓⠚⠛⠋⠁⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⡀⢉⣿⣿⣿⣿⣿⣏⠁⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡼⠉⠉⠀⠀⢸⠀⠀⠈⠉⠹⡄⠀⠀⠀⠀⣿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣾⣿⣿⣿⣷⡹⣿⣿⣿
⠀⠀⠀⣼⣧⣤⣒⣒⣒⣼⣔⣒⣒⣢⣤⣿⡄⠀⠀⠀⣿⣿⣿⡟⠸⠿⠿⠭⠭⠟⠹⠭⠭⠿⠿⡇⢹⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠞⠉⠉⠉⠉⠛⠛⠒⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠂⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⣿⣦⠀⠀⠀⠀⠀⠹⠿⠿⠛⠻⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣠⡤⠴⠶⠶⠦⠤⠤⠄⣀⣀⣀⡀⠀⠀⠀⢉⣠⠾⠁⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠙⣦⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠒⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠴⣞⣽⣃⣶⠀⠀⠀⠀⠰⣟⣛⣻⣿⣿⡑⡄⠀⠀⠀⣿⣉⠀⢊⠁⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠊⠉⠉⠉⠈⠀⠙⡄⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⣿⣀⠄⠉⣰⣇⡀⠀⠀⠀⢰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⠠⣤⣤⣄⠀⢸⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⠀⠈⢷⡀⣸⠋⠈⢳⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠂⠀⠀⠀⠈⠉⠉⠀⡌⠀⠀⠀⠑⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣧⠃⡴⠀⢘⠀⠀⠀⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⡀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠐⠀⡟⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠋⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⠶⠀⠀⠀⠒⠒⠻⢧⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠸⠤⠔⠒⠒⠒⠒⠂⢐⠂⠘⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢰⠲⣄⠀⠀⠀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣠⣤⣤⣤⡬⣷⡌⠳⣄⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡼⠁⢀⠀⡀
⠀⠀⣾⠿⠶⠾⠀⠀⠀⠴⢤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⣾⠛⢛⠛⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡙⠁⠉⠿⠽⣟⣷⡀
⠀⠀⠳⠤⠤⢤⣤⣀⣀⣀⣠⠷⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠏⣠⣎⠁⠀⢀⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣘⠁⠀⠀⠀⢀⣁⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡅⠀⢀⡽⣄⠀⠀⠀⠀⢀⡴⢿⠀⠃⠘⢻⣿⡿⠆⠴⠋⠀⠀⠉⡿⢦⠀⠀⠀⠀⠀⠀⣠⠋⠀⠉⠳⠚⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡁⠀⠈⠳⣄⠀⣠⠞⠁⢹⠀⡀⢠⣾⣿⡇⠔⠀⠀⠀⠀⣸⠃⠈⢳⡄⠀⠀⠀⠴⠉⠑⢢⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢹⠋⠀⠀⢰⢀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣰⢦⡀⠀⠀⠙⢦⡞⠁⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣾⠀⣀⡴⢻⡆⠄⢸⣿⠃⠀⠀⠀⠀⢰⠏⠀⠙⢦⡀⠀⢸⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠚⠉⠀⠘⡇⠀⢠⠁⡠⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠦⣌⣁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⡅⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⠻⣄⣀⣀⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠲⡍⠉⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠄⠘⣷⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢤⣀⠀⣷⣶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠁⠀⣀⡈⣻⠋⠠⠀⢹⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡠⡏⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⣀⠀⠀⣀⣀⣠⠤⠴⠼⠮⣍⠒⠃⠋⠁⠚⠐⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠼⠦⠬⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣛⠂
⠀⠀⠀⠀⠀⠀⠶⣶⠦⠴⠞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣤⣤⣤⣤⣀⠈⠙⣆
⠀⠀⠀⠀⣠⠤⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡘⢾⡜⣡⠖⠋⠁⠀⠀⠀⠀⠈⠳⡄⠀⠑⢄
⠀⠀⠀⠙⠓⠒⣦⠖⠁⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠙⢾⡟⠁⢀⣄⣀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢳⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⠳⣤⠀⠀⠀⠀⡇⠀⠀⢻⠁
⠀⠀⠀⢠⣣⢴⠆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠉⠳⣎⠁⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠋⠁⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⣄⣀⡀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⡋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢍⡁⢀⡇
⠀⠀⠀⠀⠀⢸⠈⠩⠭⣷⠀⠒⢶⠶⠶⠾⠟⠛⠋⠉⠀⠘⠿⠂⠀⠘⠗⠀⠀⠀⠀⠀⢠⡿⠀⢠⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣾⠀⠀⠀⡾
⠀⠀⠀⠀⢀⣀⣸⡄⠀⠈⡆⠀⠀⠈⠛⢦⣤⣀⣀⣤⣤⡶⠂⠀⠀⣀⠀⠀⠀⠴⢾⡯⠀⠀⠀⣇⠀⣀⠴⠗⢒⢶⡄
⠀⠀⠀⣴⠋⠉⢀⠈⠓⠊⠁⠀⠀⠀⠀⠀⠀⠠⠴⠿⠋⠀⠀⠀⠘⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⢾⡉⠀⢹⡄
⠀⠀⠀⣇⠀⠞⢩⡿⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢻⠇⠀⢸⡇
⠀⠀⠀⠹⣄⠀⠘⠀⠹⠀⣧⠀⠀⠀⠀⢀⣤⣖⡋⠉⠉⠉⠉⠀⠀⠈⠉⠉⢙⣶⣄⠀⠀⠀⠀⢀⣷⣄⠀⠉⠀⣀⡾⠁
⠀⠀⠀⠀⠈⠳⠦⣤⡤⠞⠹⡆⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣶⣶⣿⣿⣿⣇⠀⠀⠀⣼⠃⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢟⣿⠿⠿⠭⢌⣙⣉⣩⠿⠿⠟⠻⣿⣿⠏⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠒⠦⠤⠤⣄⣀⣠⣤⣤⠤⠖⠋⠁⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠉⠉⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⣀⠜⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡬⠂⠀⠀⠀⠀⠀⠀⠀⡃⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠉⠁⠒⠒⡆⠀⠀⠀⠀⠀⡝⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡨⠀⠀⠀⠀⢀⣤⣄⡅⠀⠀⠀⠀⠀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠹⠀⠀⠀⢀⠨⣀⠨⡄⠀⠀⠀⠀⠀⡀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠢⡀⠀⠀⠀⢀⣀⢀⡞⠉⡗⠀⠀⡁⠀⠀⠀⠀⠸⡶⠅⢪
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠠⠉⠐⠐⠶⣚⠁⠀⠀⠀⠈⠉⠉⠀⠈⠛⢻⣻⠃⠀⠀⠀⠀⠀⣫⣁⡯⣀
⠀⠀⠀⠀⠀⠀⠀⠅⡠⡍⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠣⠄⠀⠠⠔⣊⢙⣯⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠒⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠉⠘⣼⣻⠀⠀⣷⠘
⠀⠀⠀⠀⠀⠀⠀⡘⠶⣤⡞⢉⡱⠈⠉⣽⡄⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠜⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠘⢄⢠⠄⠀⠈⠓⠒⠦⠏⠢⡜⠗⠊⠙⡀⠀⡔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠚⠈⠉⠀⠀⢁⠀⢠⠐⠉⠀⠀⠀⠀⠈⢱⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢉⠉⠉⣤⣹
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠖⠛⠀⠈⢄⡤⠶⡄⢀⣀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⠀⡟⠋
⠀⠀⠀⠎⠉⢒⣁⠀⠀⣠⣬⡓⠈⢁⠀⠈⢡⠐⠁⢺⠀⣥⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⡅
⠀⠀⠀⠣⠤⠏⠉⠀⠘⣇⡀⣹⣤⠼⠀⠀⠈⢄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣘⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠒⠒⠒⠂⠐⠚⠛⠛⠓⠂⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⠀⢀⡠⠐⠈⠉⠁⠀⠉⠉⠛⠢⣀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢻⣁⣠⣔⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠶⠛⠉⠉⠀⠀⠀⠈⠉⠉⠓⠦⣀⠀⠀⠀⢸⠄⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣼⡄⢠⡀⣾⣦⣿⡘⢧⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣃⡀⠴⢋⣧⠞⢳⡟⠀⠈⢳⠘⡆⠀⠀⠀⠀⢀⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠞⠀⠀⠀⠠⣦⣤⣀⡈⠁⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠘⠛⣛⣛⣉⡉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠀⠀⠀⣷⢸⡆⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡴⠋⠀⠀⠀⠀⡴⠋⠁⣀⣀⡉⠳⡄⠀⠀⠀⠀⢀⠔⠊⡉⠉⠓⢦⡀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⠀⠀⠀⠀⢸⠁⠀⣼⣿⣿⣤⡄⢹⠀⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⢳⠀⠀⠀⠀⢹⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⠀⠀⠀⠀⠀⠘⣀⠀⠘⠿⣿⠿⠁⣘⠀⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡸⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠶⠞⠁⠀⠀⠀⠀⠘⠦⠤⠶⠶⠒⠚⠁⠀⠀⠀⢀⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢠⠴⢄⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⢦⣀⠙⠲⣄⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠒⠒⠲⠦⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠖⠋⣙⡆
⢀⣤⣀⣒⣒⠂⠒⠉⢁⣀⠀⠘⣆⠈⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡔⠉⠁⠀⠴⣮⣉⣀
⣾⣩⡭⠭⠤⠀⠀⠀⠈⠉⢹⡄⡟⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠁⠀⠀⠀⢸⢄⡶⠛⠛⠀⠀⠀⠩⠭⣽⣶⡄
⢻⣀⣀⣀⣀⣀⣀⣀⣠⡤⠾⠁⢿⠀⠀⠀⠀⠀⣠⠏⡿⠙⠛⢶⣖⠒⠒⣒⡿⠉⠹⡎⣧⠀⠀⠀⠀⢀⡟⠘⣧⣀⠀⠀⠀⠀⠘⠓⠶⢬⣿
⠈⠉⠉⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⣆⠀⠀⣀⡴⠃⢀⡇⠀⠀⠀⠈⣉⣉⡉⠀⠀⠀⢷⠈⠳⣄⣀⣠⠞⠀⠀⢀⡟⠉⠛⠓⠒⠶⢤⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠋⠁⠀⠀⣼⠃⠀⠀⠀⠈⠛⢻⣿⡆⠀⠀⢸⡆⠀⠀⠉⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣤⠴⠋⢹⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⣿⠲⠤⣤⣤⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⠤⠶⠶⠶⠶⠶⠒⠒⠒⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠰⣶⠂⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⠐⠒⠂⠂⠀⣻⠒⠲⠖⠦⠴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⡀⠀⣿⣀⣀⣀⣀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠼⣯⡉⠉⠉⠉⠙⣧⡽⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢻⠀⠀⠀⣾⠁⠀⠀⠙⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠄⠒⠒⠒⠒⠚⡗⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⣄⣀⣀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠤⠒⠉⠉⠹⡀⠀⠈⠑⣄⣎⡠⠤⢄⣀⣀⣠⡤⣖⠉⠉⡇⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠁⠀⠀⠀⠀⠀⠙⠢⢤⡶⡿⠛⠈⠉⠀⡠⠊⠁⠉⠉⠳⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠱⡀
⠀⠀⠀⠀⠀⢀⡎⠀⢰⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⠎⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠼⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⡘⠀⠀⠀⢣⠀⠀⠀⢀⡿⠁⠀⣠⠧⠴⠒⠒⠒⠒⠢⣄⠉⠒⠊⢁⣸⠴⠆⠦⣖⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠣⡀⠀⢸⢃⣴⠟⠁⠀⠀⠀⢀⠔⠉⠁⢸⠉⢢⡔⢩⠃⠀⠀⠀⡼⢢⢀⠤⠒⠉⠉⠑⢾⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣾⠉⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡸⢀⠏⣳⠃⣀⠤⠒⠢⡆⡼⠁⠀⠀⠀⠀⠀⡇⠙⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⢠⢃⣸⢖⡷⠊⠀⠀⠀⣸⣿⡿⠀⠤⢄⠀⠀⢠⠃⠀⢰
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠉⠁⠚⡖⠒⢲⠋⣡⠼⣡⠃⠀⠀⠀⡰⠋⡿⢆⠀⠀⠀⡇⢀⡇⠀⠀⠰
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠃⢡⠀⠀⠀⠀⠀⠀⠀⠈⡲⣁⠞⠁⢠⢇⠀⠀⡠⡾⢁⢼⠃⠈⠳⢄⠀⠇⡜⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⢢⠀⠀⠀⠀⠀⣠⠎⡰⠋⠁⡲⠃⠜⢖⠈⠀⡧⠋⠸⠀⠀⠀⠀⢹⠟⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⠀⠀⠀⠱⣄⠀⡠⠚⠁⡐⠁⢀⠔⠁⠀⠀⢀⡱⢞⡇⠀⡇⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⡆⢀⣀⠤⠚⠛⢄⡀⣰⡡⠔⠁⠀⢀⡠⠖⠉⠀⠀⠟⠲⠂⠒⠒⠉⡸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⠤⠄⠒⠒⠃⠉⠉⡛⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠢⡀⢀⠆⠀⠀⠀⢀⡠⠊
⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢈⠟⠒⠒⠒⠊⠁
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠎
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣈⣢⣀⡠⠤⠒⠁⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⡠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣲⣮⣽⡭⣤⣶⣤⣤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣵⣿⣿⣻⣦⢀⢸⣇⠀⢉⢳⣦⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⣺⡟⡻⠿⠿⠋⣨⣼⠋⢧⣀⢾⣧⣹⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⢟⡯⠟⡏⡗⢀⣤⢴⣚⣩⣭⠉⣉⠛⠷⣭⠥⣷⢹⣻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣵⣫⢾⡉⢆⠀⣧⣷⣿⠟⢹⣿⣿⣿⣤⣤⣈⠐⣬⡓⣼⣾⣿⣯⡿⣎⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣾⢿⣿⣮⠇⢸⢠⡿⡏⠈⡄⢸⡍⣉⣟⠉⢻⣿⣇⡾⠈⡮⣯⢻⣍⣀⣸⣎⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣾⠟⢀⡉⣁⣤⠿⠟⠰⠾⣦⣌⣦⡙⠿⡿⣿⠿⡿⢑⣠⣾⡴⠾⠧⠍⢧⣄⢹⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⠋⣟⣄⣤⡴⣉⣴⣶⣖⠶⠶⢶⣶⣭⣻⣷⣶⣶⣛⣻⣿⣛⣡⣴⢶⣶⣿⡛⡿⢻⢿⣿⡂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢉⣴⣟⡵⠾⠛⠋⢍⡾⡟⢌⠻⠟⣣⣆⣄⣴⢭⣍⣝⣿⣟⣻⣿⣉⠋⠀⠘⢎⣳⣿⣿⣷⣗⣩⣄⣀⣉⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢎⡴⣶⢏⡾⠛⠻⢟⣰⣿⣿⠷⠾⣶⣿⣿⣛⡫⠾⠻⠙⠐⠒⡖⢻⠋⢋⢙⠛⠛⣻⠿⠿⣿⣟⡋⠋⢹⣯⣭⣿⠟⣷⣿⡄
⠀⠀⠀⠀⠀⠀⢰⡏⢰⢡⡞⢀⣤⠬⣟⣫⠵⢚⠩⠅⠀⠦⣍⠢⡐⠐⠀⠁⠀⠀⠇⠋⡠⡈⣡⡴⡫⠄⠀⠀⠨⠍⡙⠿⣷⣿⣿⣷⣿⠶⢾⢟⣢
⠀⠀⠀⠀⠀⠀⠀⣇⠘⡙⣽⣥⠖⠩⠤⠀⠈⢠⡶⣚⣻⣷⣚⣧⠐⡀⠆⠐⠀⠀⠀⢠⠣⢥⣿⠟⢉⡁⠌⠉⢁⠲⠚⠛⠒⢄⣠⣬⣡⠴⣦⣮⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣶⣌⣂⣉⡛⠿⢶⢆⣀⣍⢊⣁⠏⡙⠉⠉⡇⠁⠀⠀⣶⠀⡀⢸⡄⣼⠟⠟⢿⠯⣀⠤⠄⠀⡀⣀⠴⠊⣤⣲⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠮⣉⠢⠭⠉⣉⣉⡙⠻⢦⣤⣴⡇⠀⠀⠠⡟⠀⡇⢘⠃⣿⠀⠘⣌⣳⡤⠐⠚⣉⠭⢤⠴⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠀⠛⠻⠶⣊⣩⠇⠂⠃⢆⡇⠀⠀⠘⡄⣹⣭⣭⣉⡀⠉⣐⠭⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠎⠀⠘⠈⠀⢸⡀⠄⡘⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡐⢀⠤⠀⠀⠘⡇⠠⠰⠘⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠁⡌⡄⠀⠀⠀⡟⡀⠁⢡⠀⡈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣧⠀⠀⠀⠰⠁⠁⠀⠆⠃⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢃⠀⠇⡆⠀⡀⠀⠀⠘⠀⢠⠀⢈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⡄⠈⢷⡀⠀⢠⠀⠀⠀⢸⠀⡄⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡂⠨⣷⡱⡀⠀⠃⠀⡌⡼⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⣧⣽⣶⣦⣶⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⠶⠟⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣀⣤⠾⢿⣄⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠖⠒⠛⠉⠉⠀⠀⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣦⣀⣤⣤⡶⠾⠛⢋⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢀⣤⣶⣿⠿⠟⠛⠛⠛⣻⣿⠟⠛⠛⢛⣿⣿⣿⠿⠿⢿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⣿⡎⢻⣇⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠉⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⣹⡇⠀⠀⠀⠀⢰⣿⡇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠙⠛⠛⠀⠀⠀⠀⠀⢸⣿⠀⠺⣿⣽⣻⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⠦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠰⢾⣯⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⢰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⢿⣿⣷⣄⡀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⢀⣠⣴⡾⠟⢉⣿⡇⠀⠀⠀⠀⣰⠏⠀⢸⡟⡀⠀⣼⢿⡄⠀⠀⠀⡿⣧⠀⠀⣼⡇⠘⣿⣇⠙⢿⣦⣄⣀⠀⠀⢹⣷
⢀⣴⡾⠟⠋⠁⠀⠀⣸⣿⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠳⣴⡇⠈⢿⣄⠀⣼⠇⢸⣂⡴⢉⡇⠀⢹⣿⡄⠀⠈⠙⠻⢿⣶⣾⠟
⠛⠿⣶⣤⣀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⡀⠀⠀⢸⡇⠀⠙⠁⠀⠀⣹⣿⣇⠀⠈⠋⠀⢸⡇⠠⢴⣿⣧
⠀⠀⠀⠉⠻⣷⡄⢸⣿⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠏⠀⠙⣦⠀⠀⠀⢸⡇⠀⢰⢿⣿⡀
⠀⢀⡀⡀⠀⣼⡏⣼⡟⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⣼⠏⠀⠀⠀⠘⣷⡀⠀⢸⡇⢠⠟⠈⣿⡇
⠀⣼⣿⣿⣿⠏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠘⣷⠀⢸⣷⠏⠀⠀⢻⣿
⠀⠀⠉⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⢿⣦⣤⣀⣀⣀⣠⣴⠿⠃⢸⠃⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠸⠿⣿⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣸⣆⣀⣀⣀⣉⠙⠛⠛⢉⣀⣀⣀⣿⣀⣀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⢻⣿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⢤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⡶⠶⢶⠶⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⡆⠀⠀⢀⣀⠙⣷⡀⠀⠀⠀⠀⠀⠀⣴⠟⢉⣁⡀⠀⠀⠆⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠷⠾⠛⠋⣿⣄⣼⡷⠀⠀⠀⠀⠀⠘⢷⣤⣾⠏⠛⠛⠛⠛⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣴⣆⢀⠠⠀⠑⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡉⠋⣹⢭⣿⣤⣦⠴⣦⡤⠬⢧⣄⣠⠄⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⠊⠀⠼⣦⣶⣿⣋⣿⣾⠭⠶⣿⣹⠲⢊⠛⠩⣹⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠻⠌⠄⢰⠿⠟⢢⣶⣿⣿⣷⣽⣿⢷⣿⣿⡿⢷⣿⠛⣤⣤⡘⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣰⣾⣿⣉⢉⣽⣿⣿⣾⣚⣾⡿⣷⣶⣍⣯⠉⣼⣿⣯⡰⣤⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣸⡥⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠹⠭⣛⡛⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢃⠛⠀⣿⣥⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⢿⣶⠛⡟⣍⢻⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⢴⣿⣿⣿⠟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣿⣤⠇⣙⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠶⠀⠳⡌⢧⡹⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣁⡨⡝⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⢁⠀⠃⢈⣷⡘⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⢧⡿⣍⡴⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⢐⡊⠙⣿⣇⣲⣮⡿⣿⣿⣿⣿⣻⣯⣿⠟⠉⣱⣸⠿⠘⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⢷⣄⡈⣹⠟⠓⠂⠻⠿⠟⠛⠻⠛⣧⢚⣥⡿⠉⠐⡀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠛⢭⡋⠑⠒⢻⣥⢤⡤⠉⠀⠀⣨⠿⡨⠧⠤⣤⣥⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠾⠀⡾⢯⠋⠛⠯⠀⠬⠁⠆⠀⡛⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⢀⠓⠀⠀⠀⠄⠛⠳⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠤⠤⠤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠖⠊⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⣀⡀⣀⡀⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠘⠞⣻⡟⢭⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠸⣤⣄⢀⡛⡁⠀⢸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⡃⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀⠀⠠⠖⠀⠀⠘⠦⣀⣀⣀⣀⠀⠀⠠⠤⠤⠄⠠⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠤


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢯⠿⠷⠶⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡁⠔⠓⠀⠀⠀⠀⠀⠀⠰⡛⠛⠿⣿⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⡀⢀⣠⣄⠈⠁⠚⠦⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⡟⠉⠁⠀⠀⠀⢀⣾⣿⣧⡆⣼⣿⣿⣿⢿⣿⣿⡃⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢴⠃⠀⠀⢰⣾⣿⣿⢙⡉⠀⠈⣭⣭⣷⡄⠉⠉⣵⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠆⠀⣀⢀⡸⣿⡟⣣⣿⣷⣷⣾⣿⣿⢿⣿⣤⣤⣭⠿⣿⣿⣦⣄⡀⠀⡞⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢾⣿⣿⡇⠀⠈⣿⣻⡟⠌⠉⠉⠈⠄⠸⠷⣿⣿⣿⠆⢻⣿⠿⠇⠀⠡⡈⣻⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣯⣠⣶⣿⡏⠉⠁⠀⠄⢀⠁⠠⠀⠈⢀⣻⣏⡀⢀⣭⣁⠀⠀⠀⠋⢸⡿⠁
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⢺⣿⣿⡇⣿⣿⣿⡅⠀⠤⠀⠒⠄⠀⠀⠀⢘⣿⣿⣿⢼⣿⣿⡇⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⢀⣾⡇⣦⠀⠀⠀⢉⣛⠁⠈⣹⣯⠁⡀⠀⠂⢀⠁⠐⠀⢀⣀⣸⣿⠿⠇⣻⣿⡁
⠀⠀⠀⠀⠀⠸⣷⣯⡈⢂⠀⢰⣶⣿⣧⠰⣿⣿⣿⢶⡆⠐⡀⣀⣀⡑⣼⣯⣿⡀⠀⢸⣿⣿⡷⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠀⠈⠛⠻⣿⣿⣶⣛⠟⠛⣷⣷⣿⣿⡿⢿⢿⣿⢻⣼⣿⡎⠁⠉⠀⠰⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢟⣀⣀⠘⢿⣛⣛⡀⠀⣈⣅⣿⣿⣿⠇⠀⠀⢠⠗⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢨⣿⣿⣷⣿⣿⣿⡟⠸⢻⣿⡿⠁⠀⠀⠀⢀⣀⣼⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠲⡤⢀⡀⠙⠋⠁⠈⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣶⣤⣬⠆⠀⠀⠀⠀⠀⠀⢤⠴⢈⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣶⣳⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣀⣀⣀⡠⠶⠦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠰⠶⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠠⣾⡟⠉⠛⠙⠛⢧⣄⠀⠀⠀⠉⠙⠛⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠤⣤⣤⡤⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⠛⠃⠀⠉⠁⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⣀⣀⠽⣷⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠟⢠⣄
⠠⣾⣿⠛⠶⠶⠀⠒⠀⠀⣀⣉⣀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠰⠆⠈⠙⢿⡀⠀⠀⠀⠀⠀⠈⠛⣏⠀⠀⠀⠺⠷⣀⠀⠀⣀⡀⠰⠂⠀⠀⠀⠀⠁⠰⠆
⠀⠈⠉⠀⠀⠀⠠⠄⠀⠈⠙⠛⠉⠁⢰⡿⢷⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠙⣀⡀⠀⠀⠀⠿⣿⡆⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢦⣄⠀⠀⠀⠀⠀⠀⠈⣶⣄⣠⣤⣤⠀⠘⢿⠟⠙⠁⠀⠀⠀⣼⡆
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⠀⠀⠀⠈⠃⠀⠀⠉⢷⣤⣀⠐⠛⠓⠂⠈⠙⢧⡀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⢣⣄⠀⠀⠀⠀⠀⠀⢾⡏⠀⠀⠀⣰⡶⠶⠖⠀⣶⠟⠻⣿⣷⠶⢄⣀⠀⠀⠈⠹⢶⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠈⣳⡤⠈⠉⠛⠁⠀⠀⣤⠀⠀⠀⠘⢃⣀⠈⠻⣷⣤⠠⣤⡴⠿⣶⣤⣀⣹⡿⠂⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣧⠀⠸⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⡿⠃⠀⠉⠁⠀⠀⠀⠀⣀⠛⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣽⡇⠀⠀⠀⠀⠀⢿⣄⠀⠐⠀⠈⠁⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢉⣹⠶⠶⠖⠂⠀⠀⣠⡄⠐⠒⠖⠊⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠉⢿⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⡀⢀⣶⡆⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠁⠀⢶⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡄
⠀⢀⣴⠀⠀⠚⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠿⠿⠲⠂⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⢀⣀⣀⡠⠶⠶⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢷⣦⠄⠠⠾⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣤⣤⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⠀⠀⠀⢀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠂⣀⣤⣀⡀⠀⠀⢀⣀⣀⡀⠘⠛⠃⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢻⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢄⣀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⢀⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⡄⠀⠀⠈⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣀⠈⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠾⣿⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⢀⠀⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣠⣤⣄⣠⣤⣀⣤⣤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⡏⠸⡏⠉⣿⣿⣟⠛⠋⡙⠻⣷⠾⡝⡁⠀⠀⠀⡀⢄⠉⠀⠀⠀⠀⠊⠀⠄⠀⠀⠀⠀⠀⠛⠙⢟⠉⠘⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠐⢺⡗⠺⡗⠒⣿⣿⡿⡤⣾⠳⣶⠌⠷⡤⠀⠀⠀⠠⠏⢪⣷⠖⠂⠀⡇⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣀⣺⠿⢟⣽⣿⣿⣿⣽
⠀⢘⡇⢠⡇⠀⠟⠛⠻⠿⣿⣷⡇⠀⠸⣧⠀⠀⠀⢈⡇⢛⡃⢠⣄⠀⢻⣧⣶⡏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠛⣽⣿⣿⣿⢷
⠀⠈⠁⠀⠁⠀⠀⠀⠀⢀⡉⢺⣇⠀⠀⠱⠄⠀⠀⠘⣥⡸⢏⡀⢇⡀⠀⢉⣸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⢟⣷⠿
⠀⠀⠀⠀⠂⠀⣦⣴⡟⢎⡁⣻⣿⣇⠀⠀⠀⠀⠀⠀⠈⠁⠸⡧⠀⠁⣀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠿⣿⣿⣶
⠀⠀⠀⠀⢂⠙⡀⠆⠠⣈⠉⠀⠸⣿⣤⣀⡀⠙⠀⠀⠃⠀⠀⠳⢶⣿⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠫⢽
⣶⣶⠶⠀⠈⣰⣟⠀⠀⠋⠀⠀⠀⢻⣿⡟⠛⢠⣄⣰⠄⠀⠠⡟⣿⣿⡦⣄⠀⢀⡀⢀⠀⠀⠀⡀⠠⢤⠄⠀⠀⠀⣀⣠⣀⡠⠄⠀⠚⢀⣴⡄
⣿⣿⣦⣶⣾⣿⣿⣿⣦⡀⣠⣤⣶⣿⣿⣿⠀⢼⠏⠙⣢⠜⠢⠀⢂⠀⠀⠈⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢙⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠹⠿⢿⣿⠿⠀⠀⠀⠀⠡⠐⠏⣿⣜⠂⢐⠀⡀⠀⠻⠷⣾⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⢚⣽⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠐⠀⢸⠉⠄⠤⢣⡀⠠⠀⠀⠀⣿⡿⢢⠈⠠⡀⢴⡄⠂⠌⠁⢤⠀⠀⠀⠀⠀⡠⠐⠠⠀⠀⡅⠀⠆⠀⠬⠔
⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⣿⣿⣤⣴⣤⠀⠉⠀⠀⠀⠀⡿⠁⢀⢰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠃⠠⠀⠀⠁⠐⠂⠀⠀⠀⡀
⡦⣿⣿⣿⣻⣿⣿⣻⣿⣷⣿⣷⣿⣿⣯⣁⣹⣦⠀⠀⠀⠰⣴⣧⠀⣊⣨⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢁⡀⢠⠞⠁
⣷⡾⢿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡄⠀⠀⢀⢿⠟⣴⢐⢿⠀⡃⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠦⠄⠄⠀⠀⠉⠀⠁⠂
⡏⣡⣘⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣯⣿⣻⣞⣿⠀⠀⠀⠘⠃⠁⣸⣾⠀⡇⠤⡌⠂⡙⢴⠆⠀⠀⢀⠀⠀⠀⠀⠐⠚⠀⡀
⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣾⣿⣿⢷⡀⠀⣀⣠⣾⢀⢐⢧⡇⠀⠁⠆⠻⡈⠰⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣤⠞⢢⣴⠀⡠⠋
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠉⠹⡟⠈⠙⠠⠩⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⢀⠀⠰⠆
⠈⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣍⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠢⡀⣧⠀⠀⠀⠀⠒⠠⣄⠀⠀⠐
⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⠓⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣯⡄⠀⠀⢆⡀⠀⠈⠿⢢⣀⣀⠀⠀⠈⡀⠴
⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣇⡞⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠁⣼⣧⡀⠀⠈⠷⠀⠀⢀⣀⠉⠙⠐⠀⠀⠉⠶
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⠘⢿⡇⠀⠀⠀⢀⠆⠐⠁⠀⠀⢀⣿⡆⣀⢻⣿⠀⠀⣦⠀⠀⠘⡿⠋⠀⠀⠀⠠⠂
⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣶⣟⡁⠰⠚⠆⠈⠀⠀⠀⠀⠀⢸⣿⠁⠈⠻⢻⡆⠀⠈⠀⠀⠀⠀⠺⠀⠀⠀⠳⠀⠀⡀
⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢿⣷⡁⢀⡿⣿⡀⠀⠀⠣⢩⠀⠀⠂⡀⢀⠙⠀⠀⠑⠷
⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⠀⠀⠀⣠⠀⣸⡇⢸⡏⠉⠀⠀⠉⡀⠈⠀⠀⠀⠻⡄⠀⠀⡀⠀⠁
⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠀⠀⠀⠀⠀⢠⠃⢀⣿⠀⣿⠀⢻⡇⠀⠀⠀⠘⠇⠀⠀⠀⠀⠄⠀⠁⡄⠀⠀⠀⠀⠐⢀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡠⠄⠀⠀⠸⡆⠘⢻⢠⡝⠀⠈⠇⠀⠀⣠⣠⡄⠀⠀⠀⠀⣤⠀⠠⡀⠀⠀⠀⠄⠠⠋
⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠳⠚⠠⠖⠃⠀⠀⠀⣾⡞⢰⣟⠀⠀⠺⠀⠀⢈⣇⡑⣴⣦⠀⢀⣸⠙⠂⣀⡠⠀⡙⠃⣐⣶
⠀⢿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⡟⠆⢀⣼⠀⠀⣸⣿⡁⠟⢻⡀⠀⠉⢃⠀⠈⠀⠀⢦⠀⠸⣾
⠞⢋⣤⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡄⢀⠀⠀⡀⠀⠠⣿⣿⠄⠐⣷⣾⣿⡆⠀⣿⣿⡀⣀⣈⠀⠀⢀⣈⣁⣠⣦⠄⣶⢿⢿⢳
⠐⣉⣀⢺⣾⡟⣼⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣶⣶⣾⣧⠀⠁⠀⠀⣿⣿⣶⣠⣿⣿⣿⡀⠘⠉⠛⣟⣿⢿⣶⣶⣿⣿⣿⣿⡟⣼⢻⡎⡋⢂
⠀⠁⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⠟⣿⣿⣿⣿⣿⡟⠀⠀⣤⡾⢿⡟⡿⢿⡇⢿⡿⣾⠟⢿⡰⠋⠏⢱⣼
⠀⠀⠠⣬⡿⣿⡿⣿⣿⣿⣿⣿⡇⣹⣿⣿⣫⡿⠿⣿⣿⣿⡿⠻⢾⣷⠶⡿⠋⠙⢿⣿⣇⠀⢴⡟⢡⣾⠛⠇⠘⠓⠈⣷⠁⠀⠀⠁⠀⠈⠀⠉
⠀⠀⢰⣿⡿⣿⣷⣿⣿⣿⣿⣿⡿⠟⣻⣿⣿⡛⠉⠞⠋⠉⠀⠐⠉⠉⠀⠁⠂⠠⠎⠙⣿⠀⠸⠛⠂⢹⠀⠘⠀⠀⠀⠈
⠀⠀⣾⣿⢿⣍⣭⣿⣿⣿⣻⣿⣿⣿⡶⢐⠋⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠘
⣴⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣦⣦⣴⣦⣶⣴⣴⣦⣦⣤⣤⣦⣦⣶⣶⣶⣶⣦⣶⣴⣴⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⢁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⣦⡄⠀⠀⠀⠀⠀⠘⢡⣿⠆⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⢀⣻⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⣿⣿⣀⣠⠤⠆⠀⣀⡤⠶⠚⠋⠉⣀⣤⠤⠶⠒⠛⠉⠉⠉⠙⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢁⣀⠤⠒⠉⣀⣀⣤⣶⣚⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣩⣭⡠⠖⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡟⣰⣾⣶⣦⡀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⢀⡠⠟⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣀⠀⠹⣏⡙⢿⣿⣿⡄⢋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢸⣿⡿⠟⣿⣿⡟⠁⠀⣀⣉⡙⠛⣩⡤⠂⠀⠉⠁⠀⣿⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡠⠚⣁⣀⠀⠘⣿⡅⢠⣿⠏⠀⠀⠉⢁⣈⠉⠛⠁⢀⣴⣶⡄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠀⠘⢛⣿⡷⠀⢻⡇⠘⠿⠀⠀⣴⣾⠿⠻⣿⠀⢰⠟⠋⠹⠇⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⠀⠀⢨⣥⠀⠀⠘⣷⠀⠀⠀⠸⠋⠁⠀⠀⠁⢠⡀⠀⢀⡀⠀⠀⢸⣿⣭⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠀⠀⠀⣠⠶⠦⣿⡄⠀⠀⠀⠀⢠⣶⡆⠀⠀⢷⠀⠻⡿⠀⠀⣾⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀⠀⢰⣿⠀⠛⢻⣷⠀⠀⠀⠀⠀⠙⢡⠆⠀⠸⣇⠐⢦⡀⠀⣿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣇⠀⠀⠀⠀⠴⠋⠀⣀⠀⢻⡀⠀⠁⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣹⡟⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠺⢿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠠⠿⠶⣦⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣀⣴⡧⠾⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣦⣤⣍⣩⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠻⠿⠟⠛⠻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡉⢛⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⠛⠿⣿⠀⢙⠻⠋⡿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⢬⡉⣼⣦⣶⡴⠿⠶⠾⢷⣿⣦⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⠿⢛⣫⣭⣴⡶⠶⠞⠛⠶⠶⣦⡌⠙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⡾⠛⠩⣤⣴⣷⣷⣶⣾⣤⠴⣿⠟⢀⣼⢷⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣥⠀⠀⠘⠢⠔⠾⠛⠿⢿⣿⣯⠵⠖⠋⢑⡾⢫⡧⣼⡨⢝⠪⣙⢳⣟⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣻⣿⣏⣷⣆⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠈⠁⢧⣱⠙⣉⣬⣷⡌⢿⣭⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠽⢷⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⠿⠞⠗⠻⣏⡁⣉⡈⢻⣷⣿
⠀⠀⠀⠀⢠⢪⣶⣶⣾⣷⡘⢢⢠⣦⣶⣤⣄⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠰⢒⢠⣿⣽⠯⠦⣿⠻⡆
⠀⠀⠀⠀⠰⣿⡦⢷⣷⠾⣧⠀⢰⣯⣷⣿⣿⣆⡴⣠⣾⣿⡿⠃⠀⠀⠀⠀⡤⠀⠀⠊⣼⠏⠹⡙⣶⡇⣿
⠀⠀⠀⠀⠈⠈⠉⠉⠼⠛⠋⠀⠀⠟⠾⠿⣾⡿⠙⠻⠟⢻⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⠃⣀⡀⠻⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⣜⡄⠀⠀⠀⣰⣄⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠛⠛⠓⠀⠀⣴⣦⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣶⠀⠀⠋⠻⢠⣤⠃⣤⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢾⣤⣾⣿⣿⣻⢧⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠍⠀⡁⠀⠀⢸⡿⣏⣭⣿⣭⣶⣧⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠄⠰⠀⠀⠀⢿⣿⣿⣽⣿⡿⣿⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⡀⣀⡀⠀⡀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿