Cure Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣷⣄⣀⣴⣿⣿⣿⠟⠁⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠙⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢷⣄⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠹⠗⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠙⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⠦⣤⣤⣤⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⣠⡾⠋
⠀⣠⡾⠋
⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣄⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠈⡟⡆⠀⠀⠀⢀⠇⡼⢀⡠⠔⡺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠜⣿⠀⠀⠀⠀⠀⢘⡄⢱⢹⡠⠖⠂⠺⣀⡟⢁⡴⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⢸⢱⡘⡸⡝⠀⠀⠀⠀⡸⠉⠙⢾⣾⠁⠀⠀⠀⠈⠉⢹⢀⠜⠁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠲⣯⣾⣣⣣⠗⠂⠑⢾⡉⠀⡀⢠⠌⢿⠀⡞⠁⢀⡀⢀⠾⢛⣉⠥⠔⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⡿⠁⠀⠀⠀⠀⠀⢹⣄⡹⡘⢄⡈⣷⡤⢊⣡⣴⣗⣊⣩⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣒⡈⠙⢣⠀⠀⢰⡷⠀⣀⢸⣀⠨⣿⠷⠞⠳⣟⠳⣦⠶⠄⠀⠈⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠭⣙⡚⢧⡀⠸⡀⡞⠉⣟⡵⠊⠀⠀⠀⠀⢿⡳⣜⠂⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠛⠳⣄⠱⣹⣼⢏⡴⠊⠉⠛⠃⠀⠀⠉⣎⢳⠀⠒⢩⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⢤⠞⠉⢉⣁⠾⣷⡿⣿⣯⠒⠒⢲⡆⠀⠀⠀⡠⠃⡼⠒⠐⠲⣇
⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠁⠠⠖⢁⣤⠞⣫⣿⡟⣧⠿⢹⠮⠕⣶⣎⣿⡯⠭⠔⠃⠀⠀⢸
⠀⠀⠀⠀⣠⢔⡪⠭⢒⡤⠤⣤⠶⣺⠏⢠⠎⡜⠈⣧⠘⡗⢤⣉⠻⢴⠁⢟⢯⡒⠒⠛⠀⠀⢹⡀
⠀⠀⣠⣞⣋⠥⠖⢪⢏⠤⢊⡥⡾⠁⢔⠇⢰⠃⠀⣿⠴⠇⠀⠈⠁⠀⠑⢌⠃⠹⡶⣤⡀⡠⠎
⠀⠀⠉⠀⠀⠀⣰⠿⢵⠎⣡⡞⠁⠀⠀⠀⠾⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⡟⢮⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠙⣇⣀⣀⡀⠀⠀⢀⡴⠁⠑⠤⣀⠤⠒⠒⢞⣁⡤⡖⡗⢄⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣧⠃⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⣴⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣰⡆⠀⢠⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⢤⡇⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢠⡘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⡀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠂⡴⠚⠒⡄⠀⠂⠀⠀⠀⢀⣠⣪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⠀⠀⠀⠀⡇⠀⠀⢰⣠⡄⠤⠐⠋⣇⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣯⡄⠹⠁⠀⠀⠈⣆⠀⠀⢸⣠⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠌⠁⠀⠈⡍⠂⠐⠁⢡⠐⣧⣞⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠻⠛⠁⠀⡔⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⣆⣀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣼⠀⠀⠀⣤⣦⡶⢀⢎⠀⠀⠀⠀⠀⠀⠈⡀⠀⢳⣴⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢄⣷⠀⠀⠙⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⢲⣌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣒⣼⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣈⡍⠻⣀⠀⡐⠃⠀⠠⢂⡀⣀⢤⣋⡠⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠒⠁⠉⠁⠙⠙⠁⠈⠋⠀⠈⠉⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣶⡀⠶⠶⠆⡆⠃⠘⠶⠖⠏⠷⠀⠟⠴⠘⠒⠃⠀⠓⠲⠆⠠⠰⠶⠲⠄⠺⠰⠀⢴⠆⠴⠄⠆⡗⠶
⠀⠀⠀⠀⠀⠴⠦⠆⠆⠲⠺⠇⠐⠖⠶⠲⠀⠖⠚⠒⠚⠲⠖⠓⠈⠋⠶⠦⠐⠲⠖⠲⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⢩⣴⡶⠾⠟⠀⠀⠀⠀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣄⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⣾⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠛⠋⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠻⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⠀⠀⠀⠀⢿⣿⣷⣦⣀⠀⠀⣀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣿⠀⠀⠀⡠⠐⠛⠻⢿⠿⣣⣌⠿⡿⠟⠋⠒⢄⠀⢀⣾⣷⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠉⠀⣦⢰⠁⠀⠀⠀⠈⡆⣿⣿⠰⠁⠀⢀⠀⠀⡇⢸⣿⠏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠁⠀⠣⣀⢛⣁⡼⠀⠈⠉⠀⢧⣀⣛⣀⠔⠀⠈⠉⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠉⠁⠁⠠⠎⠙⠆⠈⠈⠉⠁⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⡀⠀⠀⠀⣙⣛⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢁⢈⡿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠀⠀⢸⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⠀⠀⠀⢸⡀⠀⣔⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⡅⠩⠭⠭⠽⣿⣟⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣬⣿⡞⢣⡏⠛⢛⣛⣉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠣⢶⡶⣶⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠛⠛⠛⠛⠒⠲⠒⠒⠲⠛⠃⢸⡈⣷⠒⠂⠘⠋⠙⠒⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⣈⣧⣼⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⢉⣹⠦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠛⠀⠀⠀⠀⠀⠀⠐⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡏⠉⠉⠉⠉⢹⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠟⠃⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣠⣤⣤⣼⣿⣿⠀⠀⣿⣿⣧⣤⣤⣄⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡿⠿⠿⠟⠀⠀⠻⠿⠿⢿⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡄⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠉⠉⢹⣿⣿⣀⣀⣿⣿⡏⠉⠉⠁⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠰⢊⡥⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⡐⠠⠋⠀⢀⠀⠀⠀⠀⠀⡠⠔⠊⠭⠭⠔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⡼⠲⣶⡀⢀⠎⣠⡂⠀⢀⠀⠀⠀⢭⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠁⠀⠃⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⡄⠄⠀⠘⠁⠌⠀⠘⡡⢊⠁⠀⠀⠀⠠⢀⠃⠀⠀⠀⠀⣢⠔⠒⠠⣄⠀⠀⠀⠀⣶⣦⠀⣈⠀⢀⠄⠊⠑⠑⠱
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣢⣈⢪⣆⢢⢸⡆⡀⢀⠔⠛⡡⠄⠐⢀⡠⠂⠀⠀⠀⠀⣮⡃⠀⡀⠠⢀⡑⠄⢠⠈⠸⣏⡴⠋⠔⣁⠴⡪⠂⠀⠌
⠀⠀⠀⢀⡴⠉⠀⡀⠄⣠⠞⠙⠿⢭⣿⢷⣷⠥⠖⠀⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⡌⢆⠈⠢⢬⠓⠄⠻⣬⣷⡿⢃⢵⠌⣐⠡⠀⠂⡀⠔⠁
⠀⠀⠀⠸⢁⢅⠀⠀⠄⠛⡠⢐⣂⣨⣿⣮⠿⢄⠲⠆⠀⡀⠒⡒⠒⠄⠀⠀⠀⠀⠀⠀⠑⠓⠦⠤⢉⢒⡨⣽⣿⣶⣭⠈⠁⠀⠒⠈⠁
⠀⠀⠀⠘⣌⠢⡅⠀⠀⠸⢗⠕⡘⠡⢹⠃⢳⣄⣈⡨⢓⠂⠀⠀⣠⠆⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠁⣿⡇⢹⠀⡀
⠀⠀⠀⠀⠈⠑⢦⣶⠶⠔⠁⡜⠀⠸⣮⠀⣄⠙⢯⡃⠤⠈⠁⠀⢱⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⢔⠀⠀⠘⣿⠈⠀⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠤⣀⠙⠒⠤⣐⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡰⢡⢂⠂⠀⠀⠃⡄⠄⠀⠡⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠀⡠⠬⠕⠒⠠⢅⡨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠁⡎⢀⢸⠀⠀⠄⠈⠌⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡊⣀⠤⠤⠠⠤⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⢦⣄⠀⠠⠃⠀⠀⠈⠲⠒⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⠄⡂
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂⠕⠠⣄⠑⡄⠀⠀⠀⡠⠀⢄⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⡀⢈⠀⠘⠀⠀⠐⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢤⠄⠉⠀⠀⠈⠃⠖⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠁⠀⣤⡁⠀⠀⠀⠀⢶⡂⠀⠄⠌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⣆⡀⡈⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠰⠦⣄⠀⠀⢴⠞⠑⡹⢀⠔⡠⠒⠐⠐⠂⠑⡆⠀⠠⠀⠀⢀⡀⠤⢐⠒⣈⣷⣼⣿⣾⣥⡄⠀⣠⠀⠈
⠀⠀⠐⠐⠂⠐⠀⠐⢠⡶⠆⠑⢦⣤⣿⣾⣅⣡⣄⣤⢖⢣⡤⠶⠀⠀⠀⠜⣠⠇⠄⠈⠀⠀⠈⠄⠘⠁⡀⡠⣾⠟⢻⣫⡅⠀⠀⠐⠃⠨
⠀⠀⠐⢴⡄⠀⣈⠉⠉⠀⢾⣣⠖⠿⠛⢍⢿⠿⣿⠿⣿⡟⠁⡀⠠⠤⢐⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⢉⠀⠉⠉⠀⡎⠁⠼⠀⠀⠐⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠐⠂⠀⠀⡉⠉⠀⠞⠀⣀⠸⠞⠀⣰⡄⠀⠂⡁⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠠⢐⠀⠀⡉⢀⡤⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣁⣂⠈⠁⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠈⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠏
⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⠉⢿⣿⣿⣅⡙⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢠⡟⠋⠋⠋⠈⠙⠛⢿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄⣈⡀⠀⠀⢰⡀⠀⠀⠈⣱⣾⣿⣿⣿⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠁⣀⡴⢡⣿⣿⣿⣿⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠠⠀⣀⣤⣤⣶⡚⠛⠙⠛⠋⠙⢻⣿⣶⣄⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡄⠴⣦⡿⣿⣿⣿⣿⢷⣶⣔⠻⣷⣿⣿⣿⣷⢄⠀⢹⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣽⣿⣷⣶⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣇⣠⣴⢾⣷⡀⠀⠘⠁⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⣺⣿⣿⣿⣿⣾⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣷⣶⡿⠛⠉⠁
⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠀⠊
⠀⠀⠀⢀⣠⡞⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣼⠄⠰⠒⠒
⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣥⣤⡶⠖
⠀⠀⢀⣠⣴⣶⣦⣬⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⡿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠤
⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉
⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠶⣤⡀
⠀⠀⠀⢀⣀⡀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣴⣱⣾⣽⣝⣭⣟⣏⣼⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠈⠙
⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠊⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠉⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣿⠏⣰⣟⡮⠀⣰⣿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠛⠛⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠿⣽⡿⢋⣿⣋⠴⣻⣿⣿⡏⣰⣿⣿⠁⠀⢉⠀⠀⠀⠋⢻⣿⣿⣿⡟⣿⣿⣿⣿⡟⣿⣿⣿⣿⣤⣶⠛⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠒⠏⠙⠻⠗⠊⢁⡟⠃⢸⣿⣏⣼⢈⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⡿⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠂⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣄⡀⠀⠀⠠⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⠟⣛⠁⣽⡏⠉⠇⠙⠁⠀⠀⠀⠉⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⣼⠘⠛⢝⡛⣿⣿⣦⠀⠀⠀⠀⠀⢰⠋⣼⠟⣿⠏⠁⢠⠃⠀⣿⠂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⢀⡆⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣤⣤⣇⣠⣿⣼⠏⠀⠀⠃⠀⣸⡟⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢽⣫⠻⣿⠟⠀⠀⠂⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠘⢦⡀⠀⠀⠀⢀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠙⠦⣄⡘⠃⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠡⣄⣀⣀⣐⣆⠐⣨⣦⣦⡶⣄⠀⡌⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡰⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠚⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡻⠿⠛⡿⢧⡀⠀⠀⠾⣏⢹⡿⠉⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣟⠛⠛⠁⡌⠇⠀⠀⠀⠈⠛⠛⠛⠋⠑⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⣿⡏⣿⣿⡋⠙⣿⠱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣷⢿⣿⣿⣿⡟⢻⡆⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣟⡦⠋⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⢿⣿⣿⠀⣿⣿⣿⣿⢀⡿⣦⡶⣆⠘⠿⣿⣦⡴⠂⠀⠀⡄⠀⠀⢀⡀⣾⣿⣿⢏⡇⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⣹⣷⣿⣿⣿⣿⠟⣷⡟⠁⣸⣷⣀⣜⣹⣦⣤⣶⡞⠃⠀⠀⡇⠀⠻⣿⣿⣿⠀⠼⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⠏⣰⠟⠀⣾⠃⢸⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠉⠀⠀⢿⣿⣻⡟⠉⠁
⠀⢀⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⠏⢀⣾⠇⠀⡟⠛⢿⣿⣿⣧⣿⣿⡄⠀⠀⠀⠀⠀⠈⡝⣿⣿⣶⣶⣤⣄⣀⠀⠀⠤
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⡏⠀⢠⣷⣦⣾⣿⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠋⠀⠀⣿⣿⣿⡯⣽⡀⠈⢿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⢸⣿⡿⠃⢠⣿⣧⠀⠈⢿⣧⣀⣤⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠇⢿⠀⠀⣿⡟⠃⠀⣼⣿⣿⡇⠀⠈⠉⣵⡅⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠀⠀⣯⠀⢀⣼⣿⣿⣿⡇⢐⣠⣤⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆⡀⠀⠀⠈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⠇
⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠖⠋⠁⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠃⠁⠀⠀⠀⠀⠈⠀⠿⢀⠀⠀⠀⠀⠀⠀⠀⢐⣶⠀⠛⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠆⠘⠗⠔⠄⢠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢨⣄⡄⠠⠖⠀⠀⠀⠀⠀⠈⡲⠳⠈
⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⢀⢀⠂⢉⠠⠒⠇⠀⠀⠀⠀⠀⠀⠉⠲⠄⢲⠂
⠀⠀⠀⠀⡔⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠛⠈⠀⠨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⣣⡔⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢄⡌⠀⢈⠶⡀⠀⠀⢁⡀
⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠄⠸⠃⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⡟⡂⠙⠃⠀⠻⡎⠁⠀⠈⠁
⠀⠀⠀⢀⡀⡀⠠⣴⠀⢀⣠⡄⠁⣀⠶⠀⠠⠀⠀⠀⢬⢱⡖⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠘⠉⠇⠐⢉⠄⠄⠀⠀⠠⠍⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⡈⠁⠈⣄
⠀⠀⠀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡁⠀⠈⠇
⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣁⠠⠂⠀⠳⠀⠐⠉⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡩⠀⠠⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢀⡠⠀⠤⡄
⠀⠀⠀⠘⠀⠀⠂⠂⠀⠀⠀⣀⠜⠃⠐⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠂⠀⠀⠀⠀⣿⠁⠁⢨⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⡋⠀⠀⠀⢀⣦⡄⠀⠀⢀⢀⡆⢐⡶⠀⠀⠀⠀⠀⠘⡀⠀⠈⠔⠒⠀⢠⣤⠁⢄⢐⣳⡀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⡀⢀⣐⠾⠫⠎⠠⣀⠀⡀⡞⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⣾⠸⠇⠀⢹⣶⠟⠀⣀⡠⠠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⡘⢷⠀⠀⣍⣱⢾⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢗⠙⢆⠀⠀⠀⢀⠀⠈⡏⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢈⢿⠀⠤⠀⠉⠁⠴⠎⠆⠇⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠹⣀⠀⠀⠈⠀⠃⣀⡤⠌⠸⠁⠀⠀⠀⡅
⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⡡⠀⢁⡵⡄⠀⠀⢠⠔⢘⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡠⠟⠀⠀⠀⡸
⠀⠀⠀⠋⠀⠀⠈⠀⠀⠘⢀⠘⠋⠄⠀⢀⡐⢀⠄⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠄⠀⢠⡄⠀⠀⠁⠀⠀⠀⢀⣀⠤⠁
⠀⠐⡄⠀⠀⠀⠀⠀⢀⠀⡈⠀⠀⠮⠇⠘⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠃⠀⠀⠀⠀⣼⠀⠀⠐⠃⠀⠀⠐⠀⠀⠀⠀⣀⠌
⠀⡀⠉⢃⢀⡄⠀⠀⢸⡗⠀⠀⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡨⠅⠂⠐⠀⠀⢀⣠⠀⡴⠃
⠐⠅⠀⠀⢸⠃⠀⠀⠘⡟⠊⣠⠎⠀⠀⠀⢠⠂⣸⠂⠀⠔⢠⠈⠂⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠋⠥⡎⠀⠀⠀⠀⠤⠄⠠⢄⠤⠠⠄
⠀⠀⠀⠚⠁⡆⠀⡔⠢⠃⠀⠀⡄⠀⠀⠀⢈⡜⢡⡔⠁⠼⠁⠀⣀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂
⠀⡤⠀⣐⢞⣇⣼⡔⠞⠂⡀⣾⠅⠀⠀⠀⠘⠀⠀⠑⡄⠀⢂⠀⠁
⠈⠧⣇⠀⢋⣹⣳⣇⡀⠠⢬⠪⠰⣆⠄⠀⠀⠀⠒⠋⡆⠀⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠈⠀⡇⠒⡑⢌⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣠
⠀⠀⠀⠀⠀⠀⠃⠀⠀⣰⠘⡁⠻⠀⡀⠀⣀⠀⠀⢀⣠⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠀⠉⠀⠀⢀⠄⠀⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠰⠖⠲⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⣰⠧⡴⠋⠀⠀⠁⠀⠀⠡⠄⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠂⠁⠀⠀⢀⠀⠐⠉⠀⠉⠀⠀⠄⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠶⠶⠶⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠿⠗⠒⠒⠒⠒⠒⠲⠶⠿⠿⠿⣿⣶⣄⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠈⠹⣷⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠉⠉⣿⣿⣿⣆⠀⠀⣿⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠀⠀⠿⠿⠿⣿⡇⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⡀⠀⠀⠀⠀⢀⣿⡿⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠃⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⣿⣿⠟⠁⠀⠀⣿⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡄⣴⣶⣦⢠⣶⣶⡄⣼⣿⠟⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠛⠛⢻⣺⠛⠛⠓⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠁


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

⠐⠟⠻⢻⠻⣹⠗⠀⠃⢀⣢⣤⣤⡠⢦⢤⣀⠉⠉⠁⠈⠁⠈⠁⡏
⠈⠃⠉⠃⢠⠍⡁⠀⠀⠈⠻⢿⣿⣿⣾⣶⠿⠧⠐⠒⠛⠲⠖⠦⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⡀⠈⢀⠰⢾⡅⡄
⠀⠘⠀⠀⡀⠀⢃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣩⠇⣙
⢀⣴⣾⠿⠛⠃⠈⠀⡀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢺⡍⡷⠋⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣾⣡⡄⢀⠀⠠⡄⠀⠉⠉⠉⣃⣴⠋⠄⠀⡠⠲⠆⣀⡀⠀⣀⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⠀⠀⠀⠀⢀
⣬⣛⡛⠤⣁⠀⠀⠠⠶⠦⣀⠈⣡⣄⡔⠟⢤⣤⣸⣯⡇⠉⢏⡛⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠩⠎⡂⢀⣀
⡉⠛⠙⠶⠁⠀⠀⠀⠀⠀⢆⣮⠉⠩⣯⣄⠲⣱⠟⠉⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⣤⠀⠐⠀⠰⠀⠀⢀⡄⢿⡄⠀⠀⠉⠀⠀⠀⠍⡣⣤⠄⠀⠴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢩⡿⢷⣶⣦⣀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁
⠀⠀⠠⡘⠒⠒⠀⠀⠰⢸⣶⣿⣿⠀⡀⣤⠀⠀⠀⠴⢁⠀⠀⠀⣸⡀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠙⢿⣷⣦⣄⣀
⢀⡐⠤⣅⠈⠂⠀⡀⢱⣟⣿⣿⠇⠀⠀⠊⢤⣬⣴⠶⢊⣤⡀⣶⠅⠁⠀⡯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⣼⡿⠻⠿⢿⡿⣿⣿⣿⣿
⠀⠀⠁⢸⣷⡆⠁⠀⣿⣿⣿⡏⠀⢠⣴⠀⠀⠁⡠⠚⠉⠹⠃⠀⠀⠀⣰⡟⠓⠶⠀⠀⠀⠀⠀⠀⠴⠆⠌⠏⠓⠰⢿⣦⣶⡾⠷⢿⡿⠿⢿
⠀⠀⠀⣰⡷⠀⢄⣾⣿⣿⢟⠁⠀⠀⠀⠀⢦⡤⠤⠀⠊⢄⠀⠀⣠⣴⣿⣧⡄⠀⠀⠀⠀⠀⠀⠁⠠⠖⠒⠃⢀⠄⢠⡄⡀⣣⣠⣴⠆⠖⠚
⠀⠀⢠⣿⠧⣼⣾⣿⠟⠑⠊⠉⢀⠆⡀⠀⢸⣁⠀⠀⠀⠸⡿⢿⣿⣧⣤⡘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠋⠁
⠆⠀⠈⢱⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⢉⣀⣠⠴⣦⣴⣿⢻⣿⣿⣵⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠠⣾⣿⣿⠀⠀⠀⣀⠶⠀⣀⡤⠀⣀⠀⠀⠀⠀⢐⡛⠹⢌⣿⣿⣿⣏⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⣤⣀⡀⠀⠉⠤⠄⢀⠉⢠⠞⠧⣠⣾⡇⠀⠁⢰⡄⢾⢛⠄⠘⢡⠓⠟⣽⣿⣿⢟⠷⡄⢀⣤⣄⣀⠀⢤⣞⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⡿⠟⢻⢿⣷⣦⣄⣁⠀⠐⠛⠻⠇⠙⠉⠀⠀⡀⠀⠘⠃⠻⢁⡄⢸⣿⣾⣿⡿⠿⠻⣟⡟⢸⣿⣿⣿⣴⣈⢁⣀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿
⠁⠀⠑⣼⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠠⢰⠃⠈⠀⠀⣵⣞⠀⠀⢻⣷⣿⠀⠀⠰⡿⡿⠿⡿⠟⠿⣿⠇⠀⠀⠠⢀⣬⡛⣒⢋⣾⣾⣿⠋
⠀⠠⠐⢄⣀⣻⣿⣿⣿⠛⣃⣀⠀⠀⠀⠀⠺⣃⡀⠘⢀⢡⣿⠁⠀⢸⣿⣿⣿⣶⠀⠀⠀⠉⠑⠛⣢⠴⠆⠀⠀⣄⣠⡤⠄⠉⠻⠾⠿⠇⠠
⢦⣷⡀⢀⣉⠻⣿⡿⣷⣾⡿⢛⡶⠀⠀⠀⠊⠉⣙⡄⠘⠀⣯⠀⠀⡀⠷⠚⣾⣿⣶⣾⣿⣷⣤⣀⣀⣤⣤⣤⡌⠛⠿⠷⠢⠀⠂⣶⠶⢶⣶
⣻⣆⢹⠯⡼⣦⡁⣿⠟⠿⠉⠀⠀⠀⠀⠀⠀⠀⠍⢠⢈⡿⡿⢢⠼⠁⠀⠀⠈⢛⣋⠉⠁⠈⠙⠛⠛⠷⠶⠂⠁⢰⣶⣷⡶⠖⠲⣤⣶⣾⣛
⠛⠋⠒⠈⠹⠛⠿⢙⠀⢀⣴⠀⠖⠝⠀⠀⠁⠀⠻⠢⠀⠠⠮⠀⠀⡄⢀⡀⠀⠙⠿⣷⣦⣶⣠⣽⡶⡒⢾⣧⣥⣌⣹⠓⠰⣶⠿⣉⣉⣀⣩
⠀⠀⠀⠀⢸⣀⠀⠀⠀⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⢻⣷⢻⣿⣿⠟⢸⣿⣿⣾⠓⠤⣤⣤⣠⣤⣿⠿⠟
⠄⠀⠀⠀⠨⢿⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠙⠓⣦⣄⣀⣀⣀⣠⣀⡉⠙⠟⠫⣶⣾⠿
⠠⠀⠀⠀⠀⠌⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠛⠛⠉⠀⢴⡀⡰⠏
⡄⠃⠀⠀⠀⠀⠹⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣺⡇⠘⣠⠖⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⢠⢀⣠
⣿⡲⢀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⣀⠀⠀⢿⣝⡛⣛⣿⡇⢸⣿⡃⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠊⠋
⣿⣇⠚⠳⣄⡀⢸⣿⣿⠛⡄⠀⠀⠀⠀⠉⠀⠀⣾⠻⠟⣿⣿⣿⢸⣿⣿⣷⣀⠈⣿⠀⠀⠀⠈⠃⠀⢠⡀⠀⣠⡶⢶⠶⢦⡀⠀⠀⠀⠀⠛
⣿⣿⣷⡆⠉⠉⣾⣿⣿⣮⣹⡆⠀⠀⢶⠁⠀⠀⢿⡿⠾⠛⠛⠁⢸⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⢰⣦⡧⡼⠁⠚⠁⢀⡠⢽⡖
⣶⣿⡿⢁⠐⣀⣿⣿⣿⡏⡿⠿⣄⣀⣼⣷⣦⣄⣀⣠⣴⡶⠾⣿⣯⣿⣿⣿⣿⢿⣽⣿⣦⡀⠀⠀⠈⠋⠀⣵⠀⠀⢦⣀⢀⠠⠀⠈
⠁⠉⠀⠀⠀⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⢿⡟⠿⣟⣩⣯⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠀⠐⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠛⠛⠛⠛⠻⣶⣠⣤⠶⠶⠶⠶⢶⣦⣤⣀
⠀⠀⠀⠀⢀⡤⠶⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣄⡀
⠀⠀⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇
⠀⠹⣦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠈⠙⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⣀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⢶⣶⠶⠟⠳⠦⣤⣤⣄⣀⣀⣀⣀⣤⡶⠟⠋⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢶⣤⣄⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣦⣀⣄⢀⣀⠀⠀⠀⢀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠿⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣻⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⢸⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡀⠀⠀⠹⣿⡇⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⣿⣶⡄⠀⢠⣾⣿⣿⣿⣿⢿⣁⠀⠀⠀⣿⣧⠀⠀⢰⣁⠀⠈⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⡜⢁⡤⠚⢛⢿⡿⠋⠀⠈⠻⠿⢻⡛⣦⡀⢙⡆⠀⠈⢁⣮⣽⣖⣉⣄⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠙⣦⣀⣀⣜⣉⣭⡙⠆⠀⠀⢣⠘⣄⣳⣿⠞⡇⠀⠀⠀⢸⣄⠘⠻⠟⠁⣠⡇⠀⠀⠈⢃⡰⠃⠀⠈⠓⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⢀⡠⠔⣎⠹⠀⢃⡀⠀⠀⠀⠓⠶⠿⠶⠞⠀⠀⣀⣀⡀⠙⠧⢤⠖⠓⠋⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣄⠀⣈⡗⠀⠈⠓⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠠⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠁⠐⠒⠒⠀⠨⠛⠛⢦⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⣀⡀⣀⣀⡀⣀⣀⣀⡀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣛⣛⣛⣛⣛⣓⣒⣒⠒⢒⣒⣚⣋⣉⣁⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⣴⣿⣿⡟⠁⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⢿⣿⣿⣷⣆⢸⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⢠⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠻⢿⣿⣿⣤⣶⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⠀⠀⣨⠟⠉⠀⠀⠀⠀⠀⠀⠀⠒⠌⠙⢿⣿⣿⣿⣿⣿⠿⢿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠙⠒⢶⠀⠀⠀⠀⠀⢰⣾⣶⠈⠀⠀⠙⣿⡿⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠻⠇⢠⠇⠀⠀⠀⠀⠈⠈⠛⠋⠀⠀⣀⡠⡼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⢀⡤⠋⠀⡀⢀⣀⣀⠀⣀⠀⠉⠉⠁⠀⠀⢸⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⢠⣤⠚⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠹⠿⠇⠙⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠐⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠉⠉⠛⢿⣿⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⣾⣿⡿⣯⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣼⣿⣿⠿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⢛⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣭⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣚⣉⣉⣛⣯⡍⠉⢭⣴⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣶⣟⢶⣤⡾⢷⣤⣶⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣟⠙⣿⠉⠉⠉⡿⠇⢸⣿⠉⠉⠉⣿⠋⣻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣏⠀⠀⣿⠖⠀⠙⢦⡴⠊⠀⠲⢿⠃⠀⣹⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⡆⢀⡴⠒⠿⠿⠶⢦⡄⢸⡀⠀⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣿⣿⣇⠀⠀⣇⠋⠀⠀⠀⠀⠀⠀⠙⣸⠁⠀⣸⣿⣿⣿⡷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢯⣿⣿⣿⣿⡀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⣿⣿⣿⣿⡷⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣿⣿⣇⢪⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣵⣸⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣞⡀⡆⠀⠀⠀⠁⠀⠀⢸⣀⣧⣿⣿⡟⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠄⠐⠀⠀⠀⣼⣿⣿⡿⠋⠡⢀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⠛⢷⡈⣆⣠⡇⡼⠛⢿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠃

⠀⠀⠀⠀⣠⣴⣦⣤⣤⣤⣤⣾⣻⣶⣤⣤⣤⣤⣴⣦⡄
⠀⠀⠀⠘⣿⡀⠀⣀⣀⣉⣩⣭⣭⣩⣉⣉⣀⡀⠀⢀⣿
⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⢹⣿⠉⣿⠉⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠾⠿⠿⠾⠿⠿⠷⢶⣤⡀
⠀⠀⣠⣤⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣀⣀
⠀⢸⣿⠉⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠛⠷⣦⣀
⠀⢸⣿⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠈⠛⠛⠛⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠷⢶⣄⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠶⠶⠶⠾⠟⠋⠀⠀⠀⠀⠙⣷⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⠿⠿⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⢶⣶⣶⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠹⠘⠃⠛⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢙⠙⠋⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⢛⠚⡛⢛⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠹⠙⠋⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠛⠙⠙⠋⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠻⣧⠀⠀⠀⢀⣠⣤⣄⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣴⠟⠀⢀⣰⠟⠋⠈⢻⣷⠟⠋⠻⣧⠀⠀⠀⣴⠟⠉⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣄⠀⠀⠀⠀⢀⣴⢟⣡⣤⣤⣴⣿⡁⠀⢀⣴⣯⡀⠀⢸⣏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣿⡄⠀⣠⡾⠛⠻⠟⣉⣀⡀⠀⠉⠻⠿⠛⠿⣯⣿⡆⠀⠻⣦⣄⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⢠⣴⢿⣤⢶⣤⣿⠋⠉⠻⣦⣀⣴⠶⢶⣄⠹⠿⢷⣤⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣸⣿⣿⠁⣾⡇⠀⠈⠻⣦⡀⠀⠈⠻⣧⡀⠀⠙⢷⣄⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢿⣅⣿⠆⢈⣿⣦⡀⠀⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠙⢷⣄⠉⢻⣆
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠈⣿⠁⢰⣿⠁⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠙⢷⣤⣿
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢀⣿⡀⠀⠻⣦⡀⠀⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠺⠋⠻⢶⣤⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠈⠁⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠈⠻⣦⡀⠀⠈⠻⣦⡀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⡈⠻⣦⡀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⣋⣿⣦⣌⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⠟⠋⣾⠋⠉⠉⠉⠛⠻⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠈⠻⣦⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠟⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣈⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢠⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢷⡒⠒⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⠟⠀⠀⠀⠀⠀⠠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢻⠿⠶⠒⠀⠀⠃⢀⠦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡆⠀⠀⠀⠂⣆⣠⠤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⢀⠞⠉⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠁⠉⠁⣴⠋⠶⠀⠀⠀⢀⡇⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡆⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠱⠄⣀⠀⣙⣼⣄⠀⠀⣀⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠉⠀⠸⢿⠋⠗⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⠶⢤⡀⠀⡰⠁⡀⠀⢆⡀⠀⡀⠀⠀⠙⢦⠀⠈⢧⠀⠀⢀⡤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠘⢥⡮⠏⠑⡾⢍⡢⡀⠉⠛⠓⠒⠒⠚⣫⣤⢤⠈⢣⡜⡡⠾⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠀⠒⠑⠘⣳⡆⠲⠖⢺⠥⢐⠉⠚⠒⣆⠒⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠦⠤⠄⠀⢡⠀⠀⣰⠚⠉⠀⠀⠉⠢⣀⠀⠘⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠘⠓⠳⠤⠄⠀⢤⣄⣧⠀⢸⣀⠀⠀⠀⠀⠀⣈⣠⡇⠀⠀⠔⠉⠀⠀⡠⠛⢧⣤⠤⠖⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢶⣖⡖⢒⣒⣲⠖⠒⠒⠐⠾⠙⢯⡉⠉⡩⠛⠤⣸⠀⢀⣞⣒⣒⣒⣛⣃⣉⣁⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢁⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠀⠀⠙⠉⠉⠉⠉⣦⠼⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⢀⠀⡀⠀⢀⠘⢆⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠉⠉⠙⠒⢢⠠⡶⠶⠀⠖⠒⠚⠋⠉⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠤⢄⣀⣀⡇⠠⠇⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠐⢛⣿⠛⠯⢀⡀⠀⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢾⣗⣶⠶⠤⢵⣦⣬⣽⣷⣶⣶⣊⣀⣀⣀⣹⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠲⠀⠀⠐⠰⠐⠐⠀⠀⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠂⠂⠀⠈⠀⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣀⠘⠈⠁⠀⡀⠀⠀⢸⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡠⠤⠴⠧⠄⣀⡎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠞⡡⠔⠀⠘⣟⠀⢢⣍⠺⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠔⢀⣁⢀⣉⣛⡑⠠⢀⠀⠐⡑⡼⠁⡷⢌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠒⠲⠀⠀⠐⠡⡊⠀⠀⠀⡄⡁⠉⠑⠢⣄⠀⢬⡃⢠⡧⠜⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠒⠀⠀⠃⠀⠀⠀⠀⠀⢡⠡⠀⠀⠀⠀⠙⣦⡑⢏⠈⠈⠀⠀⠖⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢃⢣⡀⠄⠂⡜⠁⡟⢢⠑⡀⢀⡙⢢⠔⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣓⣋⣀⣐⡂⠤⣄⡀⠑⡑⢄⠜⢀⡜⠀⠀⢱⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⠊⠉⠈⢆⠀⠉⠁⠂⢍⡓⠾⡛⢤⡾⣀⠀⠀⠀⡇⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠈⢌⣦⣠⡴⠒⠚⠳⢶⡈⠺⡏⠢⠍⣁⡉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡄⠀⢀⡼⠓⠢⢍⡓⢤⡀⠀⢹⡑⢌⠢⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣘⡾⠖⠋⠀⠀⠀⠀⠈⠲⣝⢦⣸⠇⠀⠣⡘⡄⢀⡆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡋⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢦⢹⡀⠀⠀⠐⠘⡄⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⢾⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⠀⡀⠐⡡⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠙⢦⡀⠀⣠⠞⠁⠀⠀⡰⠃⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠙⠺⣯⢋⠄⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣳⠴⠋⠀⠐⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⡠⠤⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⣉⡁⠀⢠⠞⠙⣇⠈⠑⠒⢹⠉⠉⠀⠀⠀⠠⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡢⣄⠀⢀⡴⠋⠀⢀⣹⣠⠏⠀⡖⠉⠐⣦⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢩⣷⣤⠎⠀⠀⠀⠙⡟⠁⠀⣼⡴⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⠳⠤⢀⣀⣠⢭⣟⠀⠀⠀⣠⠞⠁⠀⠰⣻⡥⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠙⠟⡛⠋⠁⠀⠀⠀⠈⠡⠒⠛⠛⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣐⣠⣂⣤⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠍⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡽⡬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠸⡇⠀⠀⡇⠀⠀⡏⠉⢱⡖⠤⣄⠀⠀⠀⠀⣠⠔⢉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢘⣉⠦⠔⣉⡤⠚⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢏⠉⠑⠒⠳⣤⣤⣧⠠⠼⠒⠈⠉⣠⠔⠊⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢛⢿⡖⠊⠋⢍⠁⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀
⠀⠀⠀⠀⢠⠎⡴⢳⡌⣵⠦⣀⠀⠀⠀⢀⣠⠤⣦⣀⣜⠸⡿⠀⠀⠀⠙⠲⢤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠄⡀
⠀⠀⠀⠀⣾⣸⣃⡷⣼⢣⡟⠊⡗⢰⣹⠹⣇⢉⠔⠋⢁⣠⠒⡄⠀⠀⣀⣠⣄⣀⣀⣀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣴⠃
⠄⠀⠀⠀⠈⠛⠨⢽⣇⣾⣠⠦⠽⢆⢀⠀⠀⢧⢀⡜⠁⣀⠙⠠⡔⠚⢦⠸⣸⠈⣆⠁⡀⠀⣀⠔⠉⠁⠀⣀⡤⠴⠋⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠘⠓⣿⠏⠀⠐⠄⠐⡋⢸⡦⢉⠀⢸⠀⣷⣊⣠⡤⠶⠚⠉⠁⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠤⠜⠛⠛⠯⠽⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡴⠤⢄⣸⡇⢴⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠑⢿⣄⢀⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣙⣻⣄⡴⠶⠻⣉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡉⢉⣳⣶⡀⢤⣤⣤⣤⣤⠤⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇⠀⠀⠀⢠⠤⠖⠒⠛⠉⠉⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⡏⠉⠉⠀⠀⠀⣤⡀⠀⣿⣿⠀⠀⢀⣤⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⢸⣇⠀⣿⣇⠀⣿⣿⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⠀⣿⣿⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣫⣵⣾⣿⣿⣦⣶⣿⠟⠉⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠶⠶⠒⠚⠋⠁⠀⠹⣜⣻⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣤⠀⣄⡄⡄⢶⢠⣄⢰⠆⣄⡴⢄⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠃⠉⠃⠃⠘⠘⠙⠘⠀⠋⠓⠋⠋⠙


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠠⠤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⢟⡀⠀⠀⠀⠠⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡛⡞⠉⠉⣇⡸⠞⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⢹⠷⠚⠳⡅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠓⠲⢄⡴⣥⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡞⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⣀⣀⣿⢧⡀⢀⣠⢴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢐⠋⠁⠀⠻⣁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⡵⣦⣤⣃⡴⣄⠳⢦⣤⣀⣄⣬⡷⠀⠘⡆⢠⢔⣮⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⢯⠁⢹⢩⢿⠷⣤⣠⣬⣥⣖⡹⢯⡧⣌⡥⣉⣀⠞⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⣤⣄⣀⣇⠀⢸⠜⠊⠉⠙⠣⣸⠀⡽⠀⠀⢋⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠙⠛⠛⠧⠤⠤⠤⠬⠆⠈⣆⣀⣀⣀⣀⣈⣱⠇⠀⡰⠋⠉⣩⠟⢻⡤⠴⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠺⣿⡫⢭⠵⠂⠉⠉⠘⠋⠳⣄⣠⠋⠓⢼⡀⠼⢭⡭⢭⢭⠤⠤⠤⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠠⠀⠀⠀⠀⢾⠟⠀⠀⠀⠀⠀⠀⠹⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠉⠓⠒⠒⢤⢤⠤⠤⠤⠴⠒⠒⠋⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠂⠤⣤⣇⣸⣀⡀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣀⣀⣀⣀⡠⣤⣗⣉⣑⠆⠀⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠺⠿⠏⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠋⠉⠉⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢨⠢⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠃⠀⠈⠒⠄⣹⡢⣄⠸⢄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣴⠁⠀⠀⠀⠀⠀⠀⠁⠀⠉⣃⡳⣄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡤⠒⠉⢹⣮⣷⠂⠀⠀⠀⠀⠰⣖⣷⡏⠀⠈⢻⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢣⠀⠀⠈⠛⠋⠀⠀⡖⠀⠀⠀⠙⠋⠁⠀⠀⡜⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⡄⠀⠀⠀⠀⣠⣶⣦⣶⣶⣄⠀⠀⠀⠀⣰⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠙⣦⡀⠀⠀⠓⠒⠂⠒⠒⠚⠀⠀⢀⡴⠃⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⢻⣕⣤⣀⡀⣀⡀⣀⣀⣤⣾⡏⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⣯⣽⡇⠀⠀⠀⠀⢸⣯⣽⠃⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢫⠁⡇⠀⠀⠀⠀⣸⠈⡍⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠡⠀⠀⠀⠀⡆⠈⠑⠢⠔⠊⠀⢰⠀⠀⠀⢀⠎⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡜⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢠⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢰⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⡄⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡁⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢘⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣷⣶⣤⣤⣤⡤⠆⠘⢆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⠀⠀⠄
⠀⠀⠀⠙⣾⣷⣿⣽⣯⣤⣶⠶⠋⠐⠀⠀⠀⠀⠀⠀⢨⣿⣿⡅⢀⣀⣠⣤⣤⣄⠀⠀⠀⠀⣼⢟⣽⣿⣿⣭⣥⡴⠆
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡶⠦⡄⠢⠀⠀⠀⢸⣿⣿⡿⠛⠋⠉⠉⠹⠿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⡿⢯⣝⡓⠆⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣟⠲⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠙⠳⠈⠉⡠⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠌⠙⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⣶⠶⢶⣤⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠒⣀⣀⣀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣹⣷⡀⠀⠀⠀⠀⠀⠀⡀⣠⠊⠁⠀⠀⠀⠀⠀⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⡇⡀⠶⠿⠿⠿⠿⠷⠄⠀⠀⠀⠴⠁⡇⠀⠁⠀⠀⠀⠀⠀⢰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⣤⢠⡄⣤⢠⡄⡌⠀⠀⠀⠄⠀⢣⡀⠂⠀⢀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⠇⠀⠉⠈⠁⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⢙⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄
⠀⠀⠀⢀⣴⣤⣤⣤⣴⠶⠖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣂⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⣤⣤⣤⣤⠆
⠀⠀⠀⠾⣳⣿⣷⣶⣶⣿⣛⠁⠀⠀⠄⠀⠈⠀⠀⠀⠀⢠⣿⠟⠛⠛⢿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⣧⣤⣄⣀
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣟⡓⠶⠄⢀⠀⠀⠀⠀⠀⢸⡿⢠⣴⣤⠘⣿⡇⠀⠀⠀⠀⠀⠀⠙⣻⡻⣿⣿⣿⡿⢯⣍⡛⠂
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡻⢮⣍⡓⠂⠀⠀⠀⠀⠀⠀⣼⡇⠀⠘⠁⠀⣿⡇⠀⠀⠀⠀⣤⣶⠟⠋⠀⠘⠻⢯⡙⠷⣌⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠁⠀⠁⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠙⠃⠈⠉⠉⠉⢉⠖⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠖⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⠤⠤⠒⠒⠉⠁⠀⠀⢡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠑⢄⡲⠉⠀⢀⣐⠲⠒⠀⠀⠀⠘⢋⡤⠤⠤⠈⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⡙⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣤⣄⣀⠀⠀⠀⣀⣀⣤⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⣈⠒⠀⠐⠁⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⣋⣉⣉⣭⣉⣉⣉⣛⣻⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠧⢤⡤⢄⠀⠀⢀⠀⣀⡨⠗⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣄⣸⣀⡾⠃⠀⢷⣂⣠⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠐⠀⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⢹⠉⢩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣓⣢⡼⣤⣜⣢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠌⠉⠉⠉⠪⢢⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠌⠀⠀⠀⠀⠀⠡⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠸⢁⠀⡠⡄⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⣠⠀⢤⠲⡏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠂⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⠸⠖⠒⠒⠒⠒⠒⠒⠶⠞⠀⠀⠀⠈⣥⡛⡟⡛
⠀⠀⠀⠀⠀⠀⠰⡟⢢⠤⢄⠀⠛⢤⡀⣀⣀⣀⣀⡠⠂⠀⢸⠁⠀⠀⠈⡇⡗⠲⠶⢶⢠⣤⣤⣄⣀⣀⣤⣶⠘⠓⠒⠒⠒⣤⠾⠿⣏⡛
⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⠜⠁⠂⣤⡀⢁⡅⠀⢠⡀⠀⢀⠸⠶⠶⠶⠶⠇⡇⠀⠀⣾⡌⣿⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠐⣴⠁⠀⢀⣀⣀⡀⠀⠘⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣈⠉⠈⣅
⠀⠀⠀⢠⠀⠀⠚⠁⠀⠀⠈⠉⠈⠙⠉⠂⠐⠂⠂⠀⠓⠐⠓⠀⠀⠀⠀⠘⠃⠛⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⡀⢸⡇⠀⠀⢹⠄
⠀⠀⠀⠀⢹⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⢻⡟⠛⡟⠛⣟⠛⣿⠛⣻⠛⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡄⢀⡖⠓⠒⠒⠚⢲
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⠀⡇⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⢁⠀⡀⠀⠀⠈⢀⠀⣲
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⡇⠀⢸⠀⡇⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⡀⢸⠉⢰⡖⠘⣿⠒⣶⠂⡒⡎⢳⠀⢸⡇⠀⣧⠀⣸⣠⣧⣤⣷⣄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠄⠀⠠⠦⠀⠀⠠⠄⠀⠶⠇
⠀⠀⠀⠀⠀⡃⠨⠄⠸⡇⠀⠷⠀⢿⠀⠅⠇⠸⠀⠸⢧⡤⠿⠠⠼⡿⠓⠂⠛⢻⡿⠶⠤⣤⠠⠤⠤⠤⠤⠠⠄⠐⠒
⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡃⠀⠀⠀⠀⠀⠀⠀⣺⢴⣶⣶⠿⢶⣿⣷⣶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠐⠦⠾⠤⠤⠴⠴⣏⠀⠀⠉⠉⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠴⠤⠶⠖⠚⠋⠉

⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⣆⢿⣿⢰⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢠⢹⣷⣶⣿⢠⢸⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣝⣥⣾⢸⣿⣿⣿⢸⣮⣫⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡇⡄⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣝⣥⡇⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⢀⣴⠣⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣼⣿⣿⣿⣼⣿⣿⣿⡇⢀⣴⣿⣿⣷⣭⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁
⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⣿⣏⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡃⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⡃
⠀⠀⢸⣿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣄⣄⣠⣤⣤⣿⣧⠀⠀⠀⠀⠀⠀⠉⣈⠙⣿⡥⠔⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁
⠀⠀⢸⣿⢫⡍⣭⠉⠉⣍⣤⢀⣤⢠⣤⡄⠘⠟⠘⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⢆⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⣻⡆
⠀⠀⢸⣿⣀⣁⣀⣀⣠⣏⣫⡬⠯⠬⠥⠧⠤⠤⠤⠤⢼⣿⠀⠀⠀⠀⠀⣀⠐⢸⠇⣣⢺⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣘⡙⡇⢠⡄⠸
⠀⠀⢸⣿⢬⣤⣤⣤⣤⣤⣶⣶⣶⠶⢶⣶⣶⣲⣶⣶⠛⣿⠀⠀⠀⠀⠀⠺⠇⠀⢀⠭⠻⠧⠒⠋⠀⠀⠀⠀⠀⠀⠠⢺⠋⠁⠔⢿
⠀⠀⠸⣿⢸⣋⣉⣉⣉⣁⣨⣭⣿⡄⢈⣭⡭⠭⢹⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣷⠀⠀⠀⠀⠠⠂⢀⣾⠀⠀⢀⠘⠁
⠀⠀⠀⣿⣼⣶⣤⣤⣤⣤⣴⣶⣦⣴⢱⠠⡔⢶⣾⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠉⠀⠠⠀⠀⣤⡴⠿⠃⠀⠀⠼⠲
⠀⠀⠀⣿⣿⡿⠿⠻⠛⠿⠿⠿⠿⠿⠀⠀⢰⠈⠻⣿⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠸
⠀⠀⠀⡿⠿⠇⠀⠀⠀⠀⠠⠞⢣⡐⣠⣦⡜⢁⣤⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡤⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⡇⢸⣀⣀⣘⣋⠁⠀⠀⠀⠳⢉⡾⠞⠉⢅⣽⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡋⠉⢁⠈⠁
⠀⠀⠀⣿⣈⣿⣹⣯⣉⣱⡀⠀⠀⠀⠸⡥⠘⣇⠀⢿⣈⣼⠇⠀⠀⠀⠀⠀⠀⢰⡆⠤⠬⠭⢱⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠘⢦⡀⠀⢀⡙⠀⠙⣦⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⠨⡎⠁⠀⠀⠀⠀⠀⠀⠁⢴
⠀⠀⠀⠀⠿⣿⣿⠇⠀⠀⠀⠀⠑⠂⢸⠁⠀⠀⠿⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡿⣀⠀⢤⡄⠀⠀⠀⠀⠀⠀⢧⠈⠀⡠⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠇⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣠⠘⣁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡹⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⢣
⠀⠀⠀⠀⠀⢰⣿⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡀⢡⠀⠀⠀⠀⠀⠀⠀⡈⠀⢨⠏⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠐⠋⠀⠘⠃
⠀⠀⠀⠀⢀⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣈⡡⠤⠄⠀⠀⠀⠀⠀⠀⢰⣼⣷⣤⣼⠂
⠀⠀⠀⠀⠸⣿⣿⡏⠻⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣖⠓⠾⣿⢿⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀⡿⠟⣽⠖⢪⡿⣿⡂⠀⠀⠀⠀⠘⠀⠀⠈⠁⠀⠀⡉⠘⠃
⠀⠀⠀⠀⢠⠃⢸⢁⠀⠀⣄⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠂⠀⡈⠁⠀⠀⣸⠃⠀⠀⣰⡟⠁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠐⠏⠀⠈⠋⠀⠀⠿⠆⠀⠘⠁⠀⠀⠀⠀⠀⠘⠒⠀⠉⠀⠀⠀⢏⡀⠀⣰⣿⠁⢠⠓⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠳⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠙⠛⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣠⣤⡌⠀⠀⠀⠈⠛⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠈⠉⠙⠂⣤⡄⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠚⢲⣤⣴⣿⣿⣿⣷⣤⡄⠂⢀⡀⠁⠚⠓⠒⠲⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠏⠉⠉⠀⠀⠀⠈⠉⠙⠿⣯⣤⡔⠒⠂⠀⠘⠟⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⢶⣤⣄⡀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣉⡉⠙⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠙⢳⣄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣸⡏⠙⣦⡀⠀⠈⠛⠛⠛⠛⠓⠀⠀⣠⣿⣿⣿⣶⣤⠛⠃⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠻⣿⣆⠈⠻⣄⠀⠀⢤⡤⢤⡄⢠⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠈⠻⣷⣤⡈⠷⡀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣿⣄⠀⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠙⢿⡉⠉⠉⠉⠙⣿⣿⣭⢋⣽⡿⠋⣿⡉⠉⠉⠉⠹⣿⣿⣯⠉⣻⡏⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⠻⣦⣤⣀⣀⣀⣉⣹⣿⠋⠀⠀⠈⠿⢦⣤⣄⣀⢈⣩⣭⡿⠟⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⣹⡿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⡶⠶⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀
⠀⠀⠀⠀⠀⢴⡋⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⢹⣶
⠀⠀⠀⠀⠀⠘⣥⣀⣀⣽⡇⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣦⣤⣴⣶⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣴⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠶⣶⣶⣦⣤⣤⣤⣀⣠⣤⣤⣤⣤⣤⣴⢶⣶⢶⣶⡾⠿⠿⠿⠿⠛⠛⠉⠉⠉⢹⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡟⢫⡄⠀⠀⠀⢨⡏⠁⠀⠀⠀⠈⡿⠉⠀⢘⣿⠁⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣷
⠀⠀⠀⠀⠀⠀⣠⡟⠀⢸⠇⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⡿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⣿
⠀⠀⠀⠀⠀⢀⠿⠁⢠⡎⠀⠀⠀⢸⡗⠀⢀⡀⠀⠀⠀⢿⠄⢠⣿⠀⠀⠀⠀⢀⣀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⢿⠆⠀⢼⡇⠀⠀⠀⢸⣷⣶⡟⠁⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⢙⡿⠷⠿⠃⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣿
⠀⠀⠀⠀⣠⠀⠀⣀⡈⠁⠀⠀⠀⠘⠁⠸⣿⡀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⢸⣿
⠀⠀⠀⠤⣿⣶⡶⠛⢛⣠⣤⡀⠀⠀⠀⠀⠸⢿⡀⠀⠀⢸⣿⡏⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⣙⣿⡇⠀⠀⢸⣿
⠀⣾⣃⣤⠟⠁⠀⣰⡿⠛⠋⣷⡆⠀⠀⠀⠀⠘⢿⡄⠀⢸⣿⠀⠀⠀⣀⣿⡁⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠻⣿⡇⠀⠀⠀⣿⣦⠀⠤⠄
⠀⣸⠟⠃⠀⢀⡾⠋⠀⢠⡾⢿⣧⡀⠀⠀⠀⢀⣴⣿⣦⣾⡿⠦⠶⠚⠿⠛⠛⠛⠛⠛⠛⢻⣿⣷⣤⣤⣤⣤⣿⡇⠀⠀⠀⣾⣷⣤⣤⣴⣆
⣤⠛⠀⠀⣤⡟⠁⠀⢰⠏⠁⢀⣽⡿⠘⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⢸⣿⢀⣀⠀⠘⠿
⠻⣤⣀⣾⡏⠀⠀⡺⠃⠀⢀⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠈⠛⢻⣷⡀
⠀⠈⣿⠋⠐⣤⡾⠃⠀⣠⣾⣧⣤⣤⣤⣤⣤⣤⡶⠿⠿⠿⣿⠋⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣶⣤⣦⣾⣿⠀⠃⣤⡀⠈⡷
⠀⠐⣿⡄⠀⢿⣧⣤⣼⡟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⣄⣈⣿⠿⠃
⠀⠀⠉⠿⢷⣾⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⠋
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⠰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢿⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣤⣤⣴⣶⣶⣾⣿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⠿⣿⡿⠿⠛⠛⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⣄⠼⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠶⠂⠉⠹⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⠋⠙⠁⠀⢀⣰⣶⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣿⣦⣀⡀⠀⠀⠀⠉⠉⠛⠷⠶⣦⣀⣀⡀
⠀⠀⣀⣀⠀⠶⠖⠉⠉⠀⢀⣀⣠⣴⣶⠟⠋⢹⣷⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⠷⠀⠈⠛⠳⢶⣶⣦⣄⣀⣀⣀⣀⣀⠹⢿⡿
⣀⣈⣻⣿⣷⣶⣶⣶⣶⣾⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠉⠁⠹⠋⠙⠋⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣖⠤⣀⣀⠀⣀⡠⢂⣦⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣠⣾⡿⢛⢛⣛⣛⠚⢻⣿⣿⢋⢭⣭⠭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡠⠬⢍⠛⢿⣿⣧⣀⣈⣛⣀⣁⣼⣿⣿⣄⣬⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠊⠈⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⡛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⠀⠀⠊⠈⠒⠁⠈⠒⠁⠈⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣤⣀⣀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣀⣀⣀⣀⡀⠤⠃

⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⣀⣰⣾⠛⣷⣀⣀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⢸⡟⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⣿
⠀⠀⠈⢿⣤⣤⣤⡶⠶⠶⠾⢿⡟⠛⢿⡿⠶⠶⠶⣦⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⣦⡀
⢀⣀⣀⣀⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⣿⠋⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⠛⠻⠶⢶⣤⣀
⣿⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠳⣦
⣿⡀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠛⠛⠛⠛⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠻⠶⣦⡀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠙⠳⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠶⠟⠁⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⣀⣀⣀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠉⠉⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡶⢶⡶⢶⠶⣶⠶⡶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠷⣦⡘⠟⠘⠇⠸⠃⠻⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠘⣿⡶⠰⡆⢸⠆⢶⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⣀⣴⢿⣤⢠⡄⢠⡄⣤⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⡁⢈⡁⢈⠁⣉⠀⣉⠀⠀⠀⣠⡶⠛⠷⣦
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣾⣧⣜⡁⠛⠀⠛⠀⠀⠀⣿⡀⠀⠀⣿⠇
⠀⠀⠀⠀⣼⠏⠁⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠷⣶⡾⠋⠀⠀⠀⠀⠉⠻⣿⠿⠿⢶⣄⠀⠈⠻⠶⠟⠋
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⣠⡿⠀⠀⢠⡾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠙⠻⠷⠾⠟⠋⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢿⣄⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢾⣿⣥⣀⡀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⣶⣾⠋⠉⠙⢷⣄⠀⠀⠀⠀⠈⠻⠶⢶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠈⠻⣦⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠻⣦⡀⠀⠀⠙⢷⣄⠀⠀⠀⣠⡶⠶⠶⠟⠋⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠻⣦⡀⠀⠀⠙⢷⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠻⣦⡀⠀⠀⠙⢶⣤⣤⣤⣤⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⢷⣦⠀⣿⡿⠿⠿⠀⢸⡿⠿⢿⣦⠀⣴⡾⠛⠻⠇⠀⣴⡾⠛⢿⣦⡀⢰⣿⣧⡀⢸⣷⠀⠀⣴⣿⣧⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣾⠟⠀⣿⡿⠿⠗⠀⢹⣿⣶⣾⠋⠀⠙⠿⢷⣶⣤⢸⣿⠀⠀⠀⣿⡇⢸⣿⠹⣷⣼⣿⠀⢰⣿⣉⣿⣆⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⣷⣴⡦⠀⢺⡿⠀⠻⣷⡄⢶⣦⣤⡾⠟⠀⠻⢷⣤⣾⠟⠁⠸⣿⠀⠘⢿⡿⠀⣿⠏⠉⠹⣿⠄⢿⣿⣦⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⣀⡀⠀⢀⣀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀⢀⣀⣀⡀⠀⣀⡀⠀⠀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣿⣏⠀⠻⣷⣠⣿⠋⢀⣾⡟⠉⠉⠻⠀⣿⣟⣉⣉⠁⠈⢻⣿⠁⠀⣿⣿⣦⠘⣿⠀⢸⣿⣋⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠙⣿⡿⠀⠀⢹⣿⠃⠀⠘⣿⡄⠘⢿⣿⠀⣿⡟⠛⠋⠀⠀⢸⣿⠀⠀⣿⡇⢻⣿⣿⠀⢸⣿⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠛⠋⠀⠀⠘⠛⠀⠀⠀⠙⠻⠿⠿⠛⠀⠛⠛⠛⠛⠂⠘⠟⠻⠓⠀⠛⠃⠀⠙⠛⠀⠘⠻⠛⠛⠃




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⣤⣤⣶⡶⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣿⠀⠈⣙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⣤⣾⠋⠀⣾⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢹⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠐⢿⡅⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠀⣿⠀⣿⠀⠀⠀⠀⢸⣿⠀⢀⡿⠐⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠁⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⣿⡶⠟⠁⠀⠀⠈⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠀⣀⠀⠀⠀⠀⣿⠀⣿⠛⠛⠛⠛⠿⠟⠀⠀⠀⠀⠀⢰⡄⠀⠈⠙⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⣠⡾⣿⡟⠀⠀⠀⠀⢿⣄⠙⢷⡀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢸⡇⠀⠀⢀⣴⠄⠉⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⠀⣰⠟⢠⡟⠀⠀⠀⠀⠀⠀⠹⣧⠀⠻⣦⠀⠀⠀⠀⠙⠷⠄⣀⣬⣄⡀⠰⠟⠁⠀⠀⠀⠀⠈⠙⠷⣦⣀
⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡆⢀⣀⣀⣀⠀⣼⠏⠉⠉⠻⣆⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⡀
⠀⠀⠀⠀⢾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⡀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⡇⠈⠛⠛⠋⠀⢿⣄⠀⠀⣰⡟⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⢷⣄⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⢀⣴⠄⠙⠛⠛⠋⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⣀⣤⡶⠟⠛⠛⠛⠛⠛⠛⢻⣦⠀⠀⠀⠀⠀⠈⠛⠷⣦⣽⣷⣶⡄⠀⣼⡇⠀⠀⣿⡇⠀⠀⠰⠟⠁⠀⠀⢸⡇⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠘⢿⣥⣤⡾⠛⠻⣿⠛⠻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠈⠁⠀⠀⢀⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠛⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠛⠷⢦⣄
⠀⠀⠀⣨⣿⣀⣀⣀⣀⣀⣀⣀⣠⣿⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠙⣷
⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠈⣿⡟⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣤⣄⠀⠀⢹⡇
⠀⣿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢸⣷⠀⠀⣀⣤⣤⡾⠛⠛⠛⠛⠳⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⢸⡏⠀⢹⡇⠀⢸⣇
⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⣼⡏⠁⠀⠀⢀⣤⣤⣄⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⡇⠀⢸⡇⠀⢸⡇⠀⢸⡟⠻⣄
⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⣶⡶⢿⡅⢀⣿⠶⣶⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡾⠛⢷⡄⠀⣿⠀⢸⡇⢠⡿⠁⠀⠘⣷⠀⢸⡇⢠⣿
⠀⣿⠀⠀⠀⠀⢰⡟⠉⠙⢷⡄⠀⠀⠀⢸⣿⠀⣿⡇⠀⣿⡄⠈⠙⠛⠁⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⣀⣼⡇⠀⣿⠀⢸⡇⢸⡇⠀⠀⠀⣹⡇⢸⡇⢸⣿
⠀⣿⠀⠀⠀⣤⣼⣧⣤⣤⣾⣥⡄⠀⠀⢸⣿⠀⣿⡇⠀⣿⡄⠛⠛⠛⠛⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡟⠋⣹⡇⠀⣿⠀⢸⡇⠘⣷⡀⠀⢠⡿⠁⢸⡇⠘⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⣿⡁⠈⠛⠛⠋⠀⣿⠁⠀⣿⠀⠀⠀⠀⠀⣀⢸⡿⠟⢹⡇⠀⠻⣦⣼⡇⠀⢸⡇⠀⢸⡇⠀⢸⣧⣼⠟
⠀⣿⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⣿⡇⠀⠙⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿⠀⠀⠀⢀⡾⠋⢸⣷⠶⢻⡇⠀⠀⠈⢹⡇⠀⢸⣇⠀⣸⡇⠀⢸⡏
⠀⣿⠀⠀⠀⠀⠛⠛⠁⠘⠛⠛⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⠁⠀⠸⠿⣶⠾⠇⠀⠀⠀⢸⡇⠀⠈⠛⠛⠋⠀⠀⣸⡇
⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠀⣿⡇⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠾⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⣠⡿
⠀⢻⣦⣤⣤⣤⣶⣤⣤⣶⣤⣤⣤⣤⣤⣾⡏⠀⠘⢷⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣾⠋⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣦⣶⠞⠋
⣿⣿⣿⡿⠿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⠎⠁⠒⢀⣨⠳⡀⠀⠀⠀⠀⣀⠾⠧⡚⠀⠀⠀⠀⢰⠁⠀⠀⢸⠋⡍⡆⠀⠀⠀⡣⠟⣤⢴⡖⠒⡄
⠀⢸⣀⣠⣧⣊⠋⠁⡇⠀⠀⠀⠰⣇⡀⠀⣡⡄⠀⠀⠀⢸⠀⠀⠀⢸⣦⡡⠃⠀⠀⠈⢣⠚⠩⢄⣦⣾⠇
⠀⠈⢦⡋⠏⠀⢀⡰⠁⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡿⠟⠁
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠟⠉⠉⠻⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠠⢤⣶⡡⠤⣬⣷⡀⠀⠀⠀⢰⡲⠒⢢⣀
⠀⠀⠀⢸⠘⠃⡇⠀⠀⠀⠀⠀⠀⢘⠙⠿⡇⠀⠀⠀⠀⠀⢨⠛⡄⠀⣿⣿⡇⠀⠀⠀⣦⣤⣶⣎⣸⣶
⠀⠀⠀⠘⣤⣤⠃⠀⠀⠀⠀⠀⠰⣀⠁⠈⣀⠆⠀⠀⠀⠀⠀⠀⠑⢄⣿⠟⠀⠀⠀⠀⠻⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠰⠆⣁⠀⠀⠀⠀⠀⠀⢰⠒⠒⡂⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⢸⣁⡤⣤⣤⣤⣤⡀
⠀⢰⣩⣵⣶⣾⣿⣿⡆⠀⠀⠀⠀⢸⣶⣤⡇⠀⠀⠀⠀⢰⣈⣉⡀⢀⣉⣑⡆⠀⠀⠀⠉⡇⣿⣿⣿⣿⠁
⠀⢸⣿⣿⣿⣿⠿⠿⡇⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠈⠍⠉⠉⠉⠁⠀⠀⠀⠀⠀⡇⠻⠿⠿⡿
⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⢿⠞⠃⠙⠀⠀⠀⠀⠀⠀⠀⡔⢦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣟⠀⠈⢇
⠀⠠⣤⣤⡤⢤⣤⣤⠄⠀⠀⠀⣀⣰⢓⢢⢠⠔⠀⠀⠀⠀⠀⢨⠟⠛⡅⠀⠀⠀⠀⠀⠉⠙⠒⠼⣆⣀
⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠹⠤⠤⠥⠎⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⣍⠁
⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣴⠿⠛⠙⠳⣤⣤⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣠⠎⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠖⠂⠀⢀⡜⠀⢀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠒⡆⠀⠘⢧⡶⠟⠉⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠘⠗⠁⠀⠀⠀⠀⠀⣤⠀⠊⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡿⠀⠀⠀⠀⠀⠀⢊⡨⠐⠒⢦⠀⠀⠀⠀⠀⠀⡰⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠴⢒⢿⣄⠘⡄⠀⣠⣾⣾⣿⣷⣤⢔⢾⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣉⡉⠀⠀⣼⣿⣿⣿⣟⢯⠎⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⠟⡧⠰⠯⢄⡀⠀⢀⣠⠤⢠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢣⠞⠑⣧⠀⠀⠙⢾⡋⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣿⠟⣵⣋⡤⠶⠛⠳⣤⣀⣠⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⢢⡼⠋⠉⠉⡹⢫⣞⡠⢿⣶⡒⠒⠒⠀⠩⢩⡤⢀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⠞⠀⠀⢀⡞⡵⠁⠙⡄⠀⠉⠻⣷⣄⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣧⠀⠹⣆⡠⣴⣫⠞⠀⠀⠀⡇⠀⢀⣤⣾⣿⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢀⣠⠴⠛⠉⠁⠀⠀⠀⠀⠈⠳⣤⠏⡐⢸⡃⠀⠀⢀⡞⠀⠀⢻⣿⣿⠟⠙⠋
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢔⣵⠏⠁⠀⢠⠏⠀⢠⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠋⠁⠀⠀⡴⠃⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠞⠁⠀⠀⢀⣼⠁⠀⠀⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡤⠤⢤⣤⣏⠟⠀⠀⠀⠀⠰⠿⠛⠛⡟⠉⠉⣿⡏⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠇⠀⠀⠀⢀⠔⡁⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢻⠰⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠢⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠀⢷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⡠⠊⡀⠀⠈⠢⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡿⠀⠸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠤⠴⠚⢁⡠⠀⣈⠔⠊⠀⡤⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢒⣉⡥⢔⡉⠄⣀⠔⣉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢸⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠤⣚⣩⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠄⠀⠀⠘⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢐⠂
⠀⠀⠀⠀⠀⡀⠐⡀⣀⡼⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡲⠂
⠀⠀⠀⠀⠀⠙⠷⣿⡿⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⣧⢀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⢀⣿⢷⣪⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸


⠀⠀⠀⣀
⠀⠰⡀⠟⠚⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠳⣠
⠀⠀⢳⡆⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⢀⠠⢷⡔⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⡁
⠀⠀⠂⡹⣗⡀⣠⣞⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠂
⠀⠀⠀⠓⠀⡙⢧⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⣹⠏⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠁⠀⠉⠀⠀⠈⠁⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠄⢀⠀⠈⠀⠈⠄⠀⠀⠀⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⢤⢀⡌⠀⠐⣊⠀⠀⠰⠄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⡀⠀⠋⠀⠁⠠⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⢃⠀⠀⠀⠐⠄⠀⠀⠀⡀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠴⣀⠀⣠⡀⠠⠄⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢯⣤⠧⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⡀⠀⠀⠀⠀⠀⢀⡀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣁⠈⠀⠐⠀⠀⠀⠀⠀⠊⠈⠰⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡜⠀⠡⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⣀⣀⣤⠶⠶⠞⠛⠛⠛⠛⠛⠻⠷⠶⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⡏⠹⣷⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡠⠶⣄⣠⣶⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⣀⠶⢦⣀⣠⡼⠛⢦⣴⠟⠁⠈⣉⣀⣠⣼⡏⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠛⢶⡶⠉⠉⠙⠛⠁⠀⠀⠘⠋⠀⠀⢠⡇⠀⠀⠀⠀⠹⣿⣿⠇⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢀⣀⣰⣿⣋⣁⡠⠶⠶⢶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⣀⣀⣀⡀⠾⠋⠀⠀⠘⢿⡀
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣅⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢠
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠋⠑⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡾
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠠⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣦⣀⢠
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⣍⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⢿⣤⡟⠃⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠘⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⢀⣤⢶⣆⠀⣠⡀⠙⢷⣤⣄⠀⠀⠀⠀⠀⡖⠋⠙⠉⡀⠉⣷⡄⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠻⠿⠉⠻⠿⠟⠉⠙⠷⣦⣀⠀⠀⠘⡇⠀⠻⠟⢀⡘⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⣼⣧⣤⣠⣤⠞⠁⠀⢾⡋
⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣀⣀⣠⠾⢷⣄⣠⣴⣶⣶⣶⣤⣀⣀
⣿⣏⠉⠉⠙⠛⠻⠷⢾⡏⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠾⠿⠷⢶⣷⣶⣶⣶⣿⣧⠀⠉⠉⠁⠀⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠷⣤⡀
⠀⠛⣷⡶⣴⡞⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⢈⣿⢿⣄⣠⣶⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠈⢿⣤⡿⢃⣽⠋⢿⡶⠶⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣼⠇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣼⠋⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⢂⡀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣈⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠓⠂⠀⠀⠠⠀⠀⠀⠀⠀⠒⠒⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠒⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⣿⠆⠘⠓⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠟⠀⠸⠀⠀⠀⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⢻⣇
⢀⣀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣘⣿⠛⠛⠛⠛⠛⠛⠛⢻⣂⣤⣤⣤⣾⡟⠀⣀⠀⠀⣀⠀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠅⠀⠨⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⠷⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣦⡀⢠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⢠⣴⣶⣶⣼⣿⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡈⠙⠃⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣦⡀
⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⣿⠀⠀⢰⡆⠀⠀⢹⣷
⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⣿
⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢰⡇⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⠀⠀⢸⡿⣆⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⡇⠀⠀⢸⡇⢹⡄⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⣹⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⣼⠁⠀⠀⣾⠁⠀⣷
⢿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡄⠀⢀⡴⠋⢸⡇⠀⠀⠀⣰⠟⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⡾⠁⠀⠀⠀⢠⠿⣄⣠⡼⠃⠀⠀⢸⡄⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠛⠋⠀⠀⠘⢧⣤⡴⠟⠁⠀⢷⣤⣤⡴⢿⡀⠀⠀⠀⣠⢿⡇⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡅⣼
⠈⣿⡆⠀⣠⣤⣤⣆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠛⠶⠶⠛⠁⠈⠳⣤⡴⠾⠋⠀⢀⣀⣀⠀⠀⠀⠀⠘⠁⣿
⠀⢻⣷⠘⣇⠀⢠⣉⠳⣤⣼⠇⠀⠀⠀⠀⠀⠀⢀⣉⣙⣲⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣏⣉⣉⣀⣀⡀⠀⠀⠀⣾⡿
⠀⠘⣿⡀⠙⢶⣄⣹⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⣉⣭⠿⠛⠁⠀⢀⡤⣤⡶⢶⣴⠶⣤⡶⣤⠀⠀⠈⠻⢦⣉⠉⠉⠉⠁⠀⠀⠀⢻⡇
⠀⠀⣿⡇⠀⠀⠈⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⣸⡏
⠀⢀⣿⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⣾⡟⠀⠀⢀⡀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⢸⣿⠁⠀⣰⠟⠀⠀⠀⣶⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋
⠈⠛⠷⠿⠻⣧⣤⣤⣴⣿⣤⣀⣀⣷⣄⣀⡀⠉⠙⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠙⠛⠛⠿⠾⣷⣤⣤⣍⣉⣿⠷⣦⡀⠀⠀⠤⢤⣤⣤⣤⣤⣤⡶⠶⠟⠛⣩⡁⢀⣶⣄⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⠿⢷⡀⠈⠛⢦⣄⣀⣀⣤⠞⠁⠙⢷⣤⣴⣿⡾⠛⠻⠟⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢻⡏⠀⠀⠀⠀⠙⣦⡀⣠⠞⠻⣯⡀⢀⣠⡶⠋⠉⠙⣿⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢻⡄⢀⣤⠀⠀⠈⠛⠉⠀⠀⠈⠛⠋⠁⠴⢶⣄⢠⡟⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⡀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⣿⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⢻⣧⢠⣄⡀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠈⣿⠧⣀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⣾⣋⡄⢹⣇⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢀⣰⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠙⠷⠾⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⠛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣈⣉⣉⣿⠟⠉⠉⠉⠉⠉⠉⠉⣿⣭⣭⣤⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠉⢉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣶⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣦⣴⡾⠇

⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠻⢳⣤⡿⠟⠟⠻⠛⠛⠛⠛⠻⠛⠛⠻⠛⠛⠛⠛⠛⠻⠻⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠨⠀⣤⠭⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⢄
⠀⢠⠄⠀⠀⠀⠤⠊⠉⠑⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡁⠀⠐⠠⠤⠐⠀⣀⠤⠐⠀⠈
⠈⠘⠀⠀⠀⠀⠢⣀⣀⡠⠓⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠐⢖⢒⠒⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠀⠀⠀⠀⠀⠀⠀⡀⠂⠄⠀⠀⠀⠰⡇⠀⠀⠀⠀⠘⡇⠀⠀⢀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠄⠀⠀⠀⠀⠙⠲⠤⣤⣀⣸⣠⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⠄⠀⢀⠄⠀⠐⠀⠈⠓⠎⣀⡀⠀⠈⠀⣠⣈⠀⠀⡀
⠀⠀⠀⢀⠀⠆⠀⠐⠂⠀⠀⠀⠈⠀⠀⠉⠀⡀⠂⠀⠀⠘⠁⢄⣰⠁⠀⠉⠒⠤⡁⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠐⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠤⠂⠀⠀⠀⠀⠀⠀⢀⣀⡠⢄⡀⠉⠒⠂⠍⣙⠒⠲⠤⠤⣄
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠆⠀⢀⡀⠤⠀⠒⠂⠁⠀⠀⡀⠈⠁⠒⠤⡀⠀⠈⠉⠐⠂⠊
⠀⠀⠀⠀⠀⠘⠊⠁⡀⢀⠀⢀⡠⠄⠠⠤⠄⠁⠀⠀⡅⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⡆
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⢢⠒⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠔⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠑⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡔⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⠉⡀
⠀⡤⠄⠤⠒⢪⠡⠉⡠⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁
⠀⠀⠂⣀⡹⠁⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡰⠀⠂⠰⠀⠀⠰⠀⠚⠀⠂⠰⠀⠆⠰⢀⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⣧⣶⣴⣶⣾⣴⣧⣼⣶⣷⣴⢳⣿⣶⣧⣾⢿⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢟⡻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣋⣵⣾⣿⣿⣷⣮⣙⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢟⣩⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣍⡻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣭⣻⣿⣿⣿⣿⣿⢸⡟⣭⣭⡝⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣃⣛⣛⣛⣛⣛⣛⣛⢸⡇⣿⣿⡇⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣭⣭⣭⣭⣭⣭⣭⣭⢸⡇⣿⡿⠷⠭⠭⠭⡍⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⡿⠿⠿⠿⢛⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣝⣛⣛⣛⣛⡛⢸⣇⣛⣛⣃⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⣙⣻⣿⣿⣿⣿⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠉⢉⣿⣿⣿⣿⣿⣯⠉⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣛⣯⣭⣷⣶⣿⣶⣶⣮⣭⣛⣻⣷⣦⣤⡀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠟⠈⠟⠟⠛⣿⣿⢿⣿⣿⣿⣿⣿⡾⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠈⠉⠉⢙⣿⣿⣿⣿⡤⠞⢓⣶⡛⠳⢤⣿⣧⡁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣠⣤⣤⣀⠀⠀⠀⢈⣿⣅⡼⠛⣠⠾⠋⠛⠛⢷⣆⠙⠎⢁⠀⠐⢌⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⡟⠛⢻⣿⣷⠀⣴⣋⣼⢁⡶⠞⠁⠀⢀⠀⠀⠀⠈⠓⢶⡌⣷⣔⣤⡱⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠹⣧⣀⣨⣿⣿⠤⣾⡏⣥⡎⠀⠀⠀⠀⠼⡄⠀⠀⠀⠀⢦⢱⡝⣿⣿⣷⣄⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡸⠿⠿⠿⡃⣠⣿⣿⣿⢡⠄⠀⠀⠀⡇⠀⠀⡄⢐⠀⠘⡏⣷⣿⣿⣿⣯⡃⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢯⣁⣒⠉⢿⣿⣿⣿⣧⢸⠀⡏⠀⢠⢧⠀⠀⡇⢸⠀⣰⣇⣿⣿⣿⣿⣿⣿⡀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣹⣦⠄⣒⣽⣿⣿⣿⣿⣿⣸⡇⠀⣾⣾⠠⢠⡇⢸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢷⡀⢸⡏⠂⢸⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣷⢸⡇⣦⢀⡟⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⣿⣿⣿⣿⢹⣿⡇⣿⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣾⣿⣷⣿⢸⣟⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠾⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠂⠈⠉⠉⠉⠁⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠄⠂⠀⠀⠀⠀⠀⠀⠀⠒⠠⡤⠂⠈⠁⠀⠐⠢⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡤⠄⢐⡒⠒⠒⠂⠀⠤⠬⢄⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠋⠀⠀⠀⠤⢀⡀⠈⠁⠒⠀⠄⡀⠀⠀⠁⠒⠠⣀⠀⢃⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠉⠂⢄⡀⠀⠀⠉⠚⢄⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⢘⢻⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⡀⠈⠑⠤⡀⠀⠀⠈⠒⠄⡀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⢣⡀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⢈⡑⠠⣀⠀⠀⠈⠢⢄⠈⡄
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⡃⠀⠀⠑⣄⠀⠀⠈⠑⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠭⠒⣤⣀⣀⡑⠜⡀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡐⠀⠀⠀⠀⡌⠛⢦⣀⠀⠀⠀⠈⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠼⠛⢳⠑⡀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⠜⠀⠀⠀⢀⠜⠀⠀⠀⠉⠛⢔⡢⠄⣀⡀⠀⠀⠉⠁⠒⠠⠤⠄⢀⣀⡀⣀⣀⣠⠤⠄⠒⣛⡴⡢⠔⠃⡆⠑⢄
⠀⠀⠀⡰⠁⠀⠀⢀⠔⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠌⢁⣐⠒⠂⠀⠀⠀⠒⠒⢈⣁⡠⠤⠤⠂⣉⣁⠀⠤⠄⠪⢄⠀⠀⠁⠂⠉⠉
⢀⠔⠊⠀⢀⠠⠒⠁⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⢀⠤⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠁⠒⠂⠤⠄⠀⢠⠤⢤⠒⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠙⠯⠥⡤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡦⣀⠀⠀⢀⡠⠔⠁
⠀⠀⢀⠌⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠⠀⠉⠉
⠀⠀⠊⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡
⠀⠀⠣⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠊
⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠠⠀⢀⣀⣒⣀⣀⣂⡁⠀⠠⠤⠀⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠉⠉⠁⠈⠉⠁⠰⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠠⠀⠀⠀⢂⠀⢀⠀⠳⣦⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠚⠃⠙⠃⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠈⡷
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠲⡄⠀⠀⠀⠀⡄⠀⠀⠀⢠⠁⠀⠀⢀⠀⠀⡀⠀⢠⠐⠺⡀⠀⠀⠆⢀
⠀⠀⠠⠁⠀⠀⣤⠠⠴⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⢋⣭⠉⠋⠀⢾⣃⡀⠄⠀⠀⠒⠂
⠀⠀⠧⠄⠁⠘⠃⠀⢀⠀⡔⢻⠀⠀⠙⠀⠀⠀⡄⠀⠀⠀⠀⠀⣶⠀⠀⠸⡇⠀⠀⠀⠦⣀⠠⠃⠀⠠⡄
⠀⢸⡀⣤⣄⠀⠀⠘⢤⣌⠓⠂⠀⠀⠀⠡⣤⠐⠁⢠⠀⠀⠀⠀⣿⠐⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠐⠀⠀⠀⠟
⠀⠈⡏⠀⠛⠱⠤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⢦⠀⡇⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⡜
⠀⠀⡇⠀⠀⣀⠀⠄⠀⠛⠀⠀⠀⠀⡘⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠁⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠘⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢦⡄⠠⡖⠒⠈⠁
⠀⠀⠀⠈⠳⠤⢀⣀⣀⣀⡀⢠⠄⠒⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠀⠇⠐⠒⠖⠀⠁⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⡄⠀⣰⠀⠀⢀⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠦⣤⣤⣤⠸⠀⠀⠀⠀⡀⠀⠈⠙⢠
⠀⠀⠀⠀⢀⠀⠀⠻⠀⠁⠐⠁⠀⠐⢦⡀⠀⠁⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢈⠳⡄
⠀⠀⢀⠂⠉⠒⢄⡺⠄⠂⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠠⠀⠀⢀⠉⠀⠀⠀⠠⠀⠉⠉⠀⠉⠀⠈
⠀⣰⡇⠀⠀⣀⠀⠈⠢⢤⡀⠀⠆⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠘⠁⠀⠤⠤⠄⢀⣀⣀
⠀⠈⠀⠀⠀⠀⠈⢢⣄⠀⠈⠒⢄⠀⠈⠁⢦⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡰⣠⠓⠚⠀⠀⢀⠀⠀⠀⠀⠀⢰
⣇⠀⠠⠄⠒⠂⠈⠁⠈⠢⡀⠀⠀⠀⣀⡀⠸⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠛⢻⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⠛⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠀⠀⢠⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠇⠸
⠀⠀⠀⠀⠘⠓⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢸
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠆
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡀⠁
⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⢇⠸⣷⠐⡆⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢻⡄⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⣧⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠧⢹⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢀⣧⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣀⣀⠀⠠⠟⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣀⠀⠀⠈⠛⠉⠳⡛⢃⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄⢄⡀⠀⠐⢄⠀⢆⠀⠀⠀⠀⠀⠀⡄⠀⢦⠰⢄⠰⠀⡆⠆⡀⠄⠠⡀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣄⣀⡀
⠀⠀⡠⣾⣷⡀⠀⠀⢠⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠐⢋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡿⠓⣀⠀⠀⣬⣇
⠀⠀⢈⣼⣷⣄⣿⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⣽⡇⠀⣼⣿⠀⡀
⠀⠀⣼⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣽⣅⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⡇⠉⠉⠉⠉⠉⠉⠁
⠀⠸⢧⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠖⣩⣿⣿⠀⠀⠀⠀⠀⠀⠐⢣⣿⣿⣿⡄
⠀⠠⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⣿⡿⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⡿⠿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠻⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠃⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⢠⣾⣦⣄⣀⡠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣯⣀⣀⡀⠀⠀⠀⠀⡐
⡇⢸⣿⣇⣉⡉⠉⠉⣿⡋⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⡍⠻⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⠐⠚⠛⠓⢺⡟⠛⠓⠒
⠥⠬⢿⠿⠿⣿⣆⢰⠃⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⠆⠇⣠⣶⣇⠐⣶⣶⣶⡶⠀⠀⠀⢸⣀⣻⣿⣿⣿⣆⠀⡏⢱
⠀⢀⠎⢂⠀⠈⢿⡏⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢸⠘⣧⠀⢸⣍⠛⠛⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠠⢣⠀⠈⠻⣿⠁⠀⡇
⠀⠀⠀⠈⠀⠀⠼⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠂⠘⠿⠗⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠐⠁⠀⠂⠀⢠⠇⠀⠀⢸⡄
⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠀⠀⠐⠐⠀⠀⠀⠀⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣶⠲⠲⣂⡦⠽⠍⠚
⠀⠀⠀⠠⢀⠀⣀⡀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠇⡀
⠀⠀⠀⠘⠂⠚⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠂⠈⠉⠉⠁⠉⠉⠁⠢
⠀⠀⠀⠀⢀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⡀⠀⠤⠀⣀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡔⠈⠁⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢄
⠀⠀⠀⠀⡆⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⢀⠠⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠑⠐⠐
⠀⠀⠀⠀⡇⠠⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⣇⢂⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡖⢉⡁⠀⠃⠀⣲⡀⠀⠀⠀⠀⠀⠀⢄⡐⠠⠂⠀⠤
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠐⡀⢁⣰⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠂⠀⠀⠀⠀⡄⢸⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⠀⠐⠈⡄⠀⠈
⠀⠀⠀⠀⢄⣀⠀⠈⣀⢖⠁⠀⠀⢀⠎⢁⢀⠁⣐⡂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡭⠀⠀⢈⠐⠀⠀⢀⡀
⠀⠀⠀⠀⠘⠈⠙⠉⠀⠀⠀⠀⣠⠧⠆⠀⠀⠀⠀⠀⠀⠑⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⢀⠁⢀⠀⣀⢀⡀⣀⠠⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠈⠃⠁⠁⠀⠁⠈⠀⠀⡨⠋⠀⠀⠀⠀⠀⠀⠋⠀⠀⠁⠁⠀⠀⠀⠀⠔⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠚⠌⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⠀⢁⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡄⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠙⢿⣷⡄⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⣠⣿⡦⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠉⠁⠀⠀⣠⣿⣄⠀⠀⠈⠉⠁⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⣀⣠⣶⡿⠃⠹⣶⣄⡀⠀⠀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⣿⠃⠀⠀⠈⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠻⠷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣦⣤⣀⣀⣀⣀⠀⠀⣀⣀⣀⣠⣤⣴⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⡀⡀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⣴⠋⠉⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⡛⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡎⠀⠀⠀⣠⠂⠀⠀⢠⠂⠀⢀⠀⠀⡀⠀⠀⡆⠀⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⢠⠃⠀⠀⢠⠏⠀⠀⡎⠀⠀⡇⠀⠀⡇⠀⣷⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣇⠀⠀⢠⡏⠀⠀⢠⠏⠀⠀⡼⠀⠀⢸⠁⠀⢰⠁⠀⡇⢳⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡎⢿⣀⠔⠹⡇⢀⡴⢻⠀⢀⡴⠁⠀⣠⠏⠀⢀⡞⠤⠞⠀⢸⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡤⢤⡀⢸⠀⠀⠀⢀⠉⠉⠀⠈⠉⠉⠐⠶⠖⠉⠦⠤⠊⠀⡀⠀⠀⠘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢧⣐⡌⠚⠁⠀⠀⠀⠨⠕⣶⠆⠀⡀⣀⣀⣀⣀⠀⠲⣾⠭⠤⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠈⠙⣄⠀⠀⠀⠀⠐⠉⠀⠀⠈⠉⠁⠉⠉⠉⠁⠀⠈⠑⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠀⠀⡈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⢿⣄⣴⣧⣀⣤⣈⡑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣻⠶⠶⣏⠳⣄⠀⢒⡶⠲⣟⣫⣭⠦⠾⠦⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⢢⡴⠛⢧⡤⠖⠉⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣠⢼⡀⠀⠀⠀⠀⠀⣸⢄⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢆⣀⠇⠀⠀⠀⠀⠀⢇⣀⠟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠈⠉⠉⠁⠉⠙⡇⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⢀⡟⠀⠀⠀⠀⠀⠀⠀⣇⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣠⠎⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢀⣠⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⣤⣿⠃⠀⠜⠁⠀⠘⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⣿⠋
⠀⠀⠀⢀⣄⠀⠀⠀⠛⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⢳⡶⣤⡀
⠀⠀⢸⡏⠀⢰⣤⣤⣤⣼⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⢷⣴⣅⠀⠉⢀⣿⡇⢸⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⢹⡉⠀⠀⢸⡿⠃⣼⡇⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣠⠟⠀⠀⣠⣶⡿⠟⠋⠁
⠀⠀⢀⣤⣤⣴⡾⠃⣿⠃⢀⣿⣿⠀⠀⣿⡆⠀⠀⣷⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⣿⡇⠀⠀⣤⣄⠀⠀⢀⣼⡿⠋
⠀⠀⣾⠃⠀⠀⠀⠀⢻⡆⠘⣿⣿⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣿⠀⡀⠀⢀⣿⠃⠀⣼⣿⠃
⠀⠀⠘⣷⡄⠀⠀⠀⠀⢿⡄⠹⣿⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⣼⡟⢡⡀⠀⠀⢰⣿⠀⠙⢿⠛⠁⠀⣰⣿⡏
⠀⠀⠀⢿⣄⣴⠟⠻⡆⠈⠻⣦⡘⣧⠀⢿⡄⠀⢰⣿⠀⠀⠀⢰⣿⡁⣿⡇⠀⠀⣾⡟⢠⣤⡿⠁⠀⣴⣿⠿⣶⡀
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣼⡟⠛⢻⡇⠸⣧⠀⢸⣿⠀⠀⠀⢿⡏⠀⢹⡇⠀⢸⣿⣧⣼⠏⠀⣠⣾⠿⠋⠀⣿⡇
⠀⠀⠀⠀⣿⣷⣶⡟⠀⣼⡟⠀⠀⡈⢿⣄⣿⡄⠈⣿⡆⠀⠀⠸⣧⠀⠈⢿⣄⣈⡿⠀⠀⣠⣾⠟⠁⠀⠀⠀⢻⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⢀⣾⠃⠀⠉⠻⣧⡀⢿⣷⠀⠀⠀⣿⡆⠀⠀⠉⠉⣡⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⢆⣀⠀⠀⣿⣇⣾⢃⣼⠃⠀⢀⣼⡿⢾⣿⣧⡀⠀⢻⣧⠀⠀⢀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⣄⣠⡟
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⣿⠃⣾⠃⠀⢰⣿⡟⠀⠀⠀⠹⣷⡀⠘⣿⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⢰⡿⠋
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠈⠿⣾⡏⠀⣠⣿⠏⠀⠀⣴⠇⠀⢙⣷⣴⠟⠉⠀⠀⠀⠀⣤⠀⠀⠀⢀⣼⣷⠟⠁
⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠻⠿⠿⠟⠁⠀⠀⠸⣧⣤⣶⠿⢛⠁⠀⠀⠀⠲⣤⡴⠏⠀⠀⢀⣼⠟
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣾⡇⠀⠒⠶⣿⠋
⠀⠀⠀⠀⠀⠛⣷⠀⠀⣶⠀⠀⠀⠀⠙⢷⣿⣀⣤⠀⣴⣶⡶⠏⠙⢷⣴⡾⠿⠋⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠻⣶⠾⠋⠀⠀⠀⠀⠀⢀⣈⣽⣿⣏⡉⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠞⠛⠋⣉⣉⡛⠿⣷⣤⡀⠀⠀⠈⠙⠳⠶⠖⠋⠁
⠀⠀⠀⠀⢀⣤⢶⣄⢠⣿⣏⠀⠀⠀⠀⢦⣀⣿⠀⣉⣀⣀⠉⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠙⠷⠾⠏⢸⣿⠛⢷⣤⡀⠀⠀⠉⠀⢾⣋⣉⡽⠇⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠻⣷⣤⡀⠀⠀⠉⠹⠶⠾⣿⣻⡿⠀⢀⠀⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⣧⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠀⠀⠚⢡⡴⣶⣏⣿⠆⠀⠀⠉⠙⢿⣷⣦⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡶⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠉⠁⣀⣀⣠⣤⡶⠛⠉⢻⡆⠀⢀⣀⡀⠀⠀⠀⠀⢀⣴⠖⢶⡀
⠀⠀⠀⠀⢠⡾⠛⢶⣄⣠⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣤⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⢸⠃⡴⠉⠉⢻⣆⠀⠀⠀⠈⠃⠴⠾⠃
⠀⠀⣠⣤⣤⣿⣄⣀⣿⡷⠶⣦⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠴⢤⣾⡇⠀⢀⣀⣀⡀
⠀⠀⠘⢧⡽⠉⠉⠙⣿⠀⠀⢸⡿⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⠟⠉⠉⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠃⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠋⠁⠀⠀⠀⠀⠀⢿⣤⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⣾⠀⠀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⡶⠟⠛⠉

⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⣤⣤⠀⢾⣿⣿⡆⠀⠀⢠⣤⡄⣾⣿⣿⡇
⠀⠀⠀⠀⡀⠙⣻⡁⠀⠀⠀⠀⠀⠘⠛⣃⡀⠀⠀⠀⣀⣛⣛⡀⠺⢛⠛⠃⠀⠀⣘⣛⣃⠛⠛⠛⠃⠀⢰⣿⡦
⠀⠀⣟⠀⠙⠒⣿⣿⠀⠀⢀⡏⢀⣠⡴⣿⣷⠀⠀⢰⣿⣿⣿⡟⠓⠛⠁⠀⠀⠀⣿⣿⣟⠻⠿⠂⠀⠀⠀⠉⣷⣦
⠀⢹⣿⣿⣿⡏⣽⡿⠀⠀⣿⣿⣿⣿⡏⣿⡿⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠤⡀
⠀⢨⠉⠉⠉⠀⣿⡇⠀⠀⢬⠉⡍⠁⠀⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠈⣿⡟⠛⠋⠀⠀⡇
⠀⠀⠁⠁⠀⠀⣿⡇⠀⠀⠈⠉⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢿⡗⡀⠀⠈⢲⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⣿⠷⠞⠛⣦⡀⠀⠀⠀⢀⣤⣿⢟⣠⡀
⠀⠀⠐⢦⡀⢀⣤⣄⡀⠀⠀⠀⠈⠛⠛⣻⠛⠛⠃⠀⢀⣄⡀⠀⠀⠀⠀⢰⣿⡟⠛⠛⣿⣤⡈⣿⠀⠀⠀⣾⣿⠉⠉⢁⡼
⠀⠀⠀⠈⢳⣞⣿⣋⣻⠄⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⣹⣿⡃⠀⠀⠀⠀⠘⣿⡇⠀⠀⢿⣿⠇⠀⠀⠀⠀⠻⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠻⠒⠛⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣿⣿⣟⣿⠀⠀⠀⠀⣸⡟⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⣿⠃⠀⠙⠃
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣶⣶⣶⠄⠀⠀⣿⣿⡏⠁⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠉⠋⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠙⠋⠀⠀⠀⣠⣶⣄⣠⣴⣄⠀⠀⠀⠀⠀⣴⣦⣀⣴⣤⡀
⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣽⣷⣿⣭⣷⡄⠀⠀⣠⣽⣯⣹⣿⣯⣻⡄
⠀⠀⠀⠀⢀⣼⠛⠃⠀⠀⠀⠀⠀⠀⢀⣬⣛⠃⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠙⢛⠛⠉⠂⠀⢰⣿⣿⣿⡟⠻⡛⠋⠑
⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣭⠿⢦⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣶⣶⣶⡆⠀⠸⢿⣿⣿⣧⣶⣶⣶⣦
⠀⠀⠀⠀⠻⢿⠿⣿⡄⠀⠀⠀⠀⠀⠻⠿⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⢸⣿⣿⡏⠉⠉⠉⠉
⠀⠀⠀⣿⣿⣷⠀⠸⡷⠀⠀⠀⠀⠀⣿⣿⣷⠸⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠤⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡲⠒⠤⣀⢤⡀⠀⠀⠑⠺⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡰⠃⠀⠈⣷⣀⠀⠀⠀⡏⠉⢩⠟⡖⠚⠒⠓⡞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢅⠀⢀⠞⠀⠈⠑⠢⣤⣣⠔⠁⢀⣇⠀⠀⢀⣇⠀⠀⠀⠀⢀⣀⠿⠭⠭⠭⠭⠭⠽⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠈⡇⠀⡠⠊⠀⠉⠉⠁⠀⠳⡄⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⣀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⣤⣤⣀⣀⣠⣔⣹⣄⣸⣇⣀⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⢰⡋⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⡆
⠀⠀⠀⠀⠀⠹⣭⠭⠭⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣭⠏
⠀⠀⠀⠀⠀⠀⣷⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡞⢳⠀⢰⠋⡆⠀⡖⢳⠀⢠⠊⣦⠀⢰⠑⡄⠀⡎⢲⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢸⠀⡇⠀⠇⢸⡀⢸⠀⣿⠀⠀⠀⡇⠀⡇⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢸⠀⡇⠀⡇⢸⡇⢸⠀⣿⠀⠀⠀⡇⠀⡇⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⢸⠀⡇⠀⡇⢸⡇⢸⠀⣿⠀⠰⠀⡇⠀⡇⣸⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢹⠋⢱⠒⡖⠒⣾⡻⡆⢲⡶⢶⠒⢶⠶⡖⠋⡇⢸⠀⢸⠀⡇⠀⡇⢸⡇⢸⠀⠀⠀⠀⠀⡃⠀⡇⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⢸⠀⡇⠀⣾⠁⡇⢸⣷⣾⠀⢸⠀⡇⠀⡇⢸⠀⢸⠀⡇⠀⡇⢸⡇⢸⠦⣿⠀⠰⠚⡇⠀⡇⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣧⠀⣇⢸⠀⠸⡖⡇⠀⢿⢀⠇⠸⣇⣿⠀⢸⢀⡇⠀⣇⣸⠀⢸⡀⡇⠀⣇⢸⠃⠸⡀⡿⠀⢸⢀⠇⠀⣇⣻⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢩⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠉⠀⠀⠈⠁⠀⠀⠉⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠚⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⡄
⠀⠀⠀⠀⠀⢈⡷⠢⣔⠺⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡼⠀⢹⠇⠀⠀⣣
⠀⠀⠀⢀⡔⢡⡬⢋⣟⡏⠉⠀⠀⠀⠀⡤⠤⠖⡶⡏⣿⢻⢹⠒⠒⠚⣏⠀⢱⣂⣸⡀⠀⢸⠋⠑⠢⡀
⠀⠀⠈⠁⠀⢸⠀⠀⠓⣿⠀⠀⠀⠀⠀⣸⠀⠀⡇⣇⢹⢸⢸⠀⢀⣀⢸⡀⠀⠀⣠⠜⠋⠛⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠣⡀⠀⠀⠀⡏⠀⠀⠇⠸⠘⠘⠸⣤⢋⠞⢠⠇⢠⠞⠁⠀⠀⠀⣠⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⡀⠀⠀⠳⡀⠀⢸⠀⠀⠀⠀⢠⠏⠀⡾⠀⣞⠀⠀⠀⣀⡜⠀⠿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠘⠛⠻⠀⠀⠀⢀⠟⠋⠉⠙⠀⠸⣄⠀⠀⠛⠇⢴⡦⡆⠀⢀⠇
⠀⠀⠀⠀⠀⠘⠢⠤⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⡗⠀⡀⠤⠄
⠀⠀⠀⠀⠀⢰⠁⠈⢉⣛⠳⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣓⣧⡀
⠀⠀⠀⠀⡄⠺⡏⡩⠭⠭⢭⣓⠲⢬⣆⠀⠀⠀⠀⡔⢋⣩⠭⡽⡪⠓⢄⠀⠀⢀⢜⣛⣫⠉⣟⡢
⠀⠀⠀⠀⡏⠈⠉⠀⠀⠀⠀⠀⠉⠑⢲⡟⠀⠀⢸⠁⣼⣠⠾⣎⠀⡠⠎⠀⠀⢸⢸⡅⠀⠀⢳⠇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢠⠏⠀⠛⢁⡴⡡⠊⠀⠀⠀⠀⢸⠘⡇⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠏⠀⠀⡴⠯⠊⠀⠀⠀⠀⠀⠀⡸⠀⢇⣀⣀⣸
⠀⠀⠀⠀⠈⠒⠦⠤⣄⣀⡤⠤⠴⠒⠋⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢿⣶⢸⣿⠛⠛⠀⣿⠟⢿⣦⢰⣿⡛⠷⠀⣴⡿⠛⢷⣆⢸⣿⣆⠠⣿⠀⢠⣿⣿⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠋⢸⣿⠛⠛⠀⣿⠿⣿⡋⢈⡛⠛⣿⡜⣿⣄⠀⣸⡿⢸⣿⠹⣿⣿⢀⣾⣧⣼⣷⠀⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠛⠛⠛⠀⠛⠀⠙⠃⠈⠛⠛⠋⠀⠈⠛⠛⠋⠀⠘⠋⠀⠘⠛⠈⠋⠀⠀⠛⠃⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣄⢠⣄⠀⢀⣄⠀⣀⣤⣀⠀⢠⡀⢀⣀⣤⣄⢀⣄⡀⠀⣠⠀⣠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣼⣿⠈⢻⣶⡿⠁⣾⠋⢉⣙⡁⢸⡇⢸⣿⣭⣭⢸⣿⣿⣄⣿⠁⣿⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿⠀⠀⣿⡇⠀⠻⣧⣬⣿⠇⢸⡇⢸⣿⣤⣤⠸⣿⠈⢻⣿⠇⣿⣧⣤⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⢾⣏⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⡉⠈⠙⣿⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠁⠀⠀⠈⢻⣦⣴⣿⣦⣄⣤⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⣿⣀⣀⣀⣀⣀⣈⡉⠀⠀⢸⡟⠁⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣦⣄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⢀⣄⠀⠀⠻⣷⡀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢰⡿⠁⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⡄⠀⠸⣷⠀⠹⣿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣤⣀⣼⣿⣶⠾⠟⠛⠃⣼⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⡇⢰⣿⠀⠶⣿⣧⣤⣤⡄
⠀⠀⠀⢠⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⢠⣿⡷⠟⠁⠀⠀⠀⠈⠉⠛⠿⣶⣶
⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠛⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠋⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤
⠀⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣸⣷⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠛⠛⠛⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣿
⠀⠛⢿⡄⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣄⡀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡷⠀⠀⣸⣿
⠀⠀⢾⢿⣄⠀⠀⠀⠀⢸⣿⣀⣀⣽⡏⠙⢿⣆⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣼⡿⠛⠛⠛⠛⠛⢻⡟⢻⣿⠋⠀⠀⣴⡿⠛
⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠙⢷⣄⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣶⣶⣾⣷⣾⣿⣶⣶⡄⠉
⠀⠀⠀⠀⠀⠀⣹⡿⣶⠀⣾⠇⠘⣿⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣦⣀⣀⣀⣿⣀⣀⣀⣀⡀⢀⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢨⣿⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣀⣀⣀⣾⣟⡉⠉⢉⣉⣩⣿⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⣿⡇⠀⠀⠀⢀⣾⠿⣷⡀⠀⠀⠀⠀⣿⡇
⠀⠀⣰⡿⠛⠛⠛⠛⢛⣿⡀⠘⠛⠛⠛⠛⠛⠛⠙⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣧⣀⣼⡇⠀⠀⠀⠀⣿⡇
⠛⠛⠛⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣀⣉⣉⣁⣀⣀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠷⠿⠿⣷⡿⠶⠶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣶⣶⣶⣶⣶⣿⣧⣴⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣿⡇⠀⠀⠀⠀⠾⠿⠿⠆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠻⢷⣤⣄⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣿⠉⠉⠉⠁⠀⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠙⠀⣿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⣿⡇
⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠉⠉⣿⣶⣄⣀⣀⣀⣀⣀⣤⣾⠟⠛⠃⠀⠀⢿⣷⣤⣴⡄⠠⣤⠀⢴⣴⣤⣴⣤⣤⣿⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣉⣿⣛⣛⣿⣋⣉⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠉⠉⠉⠒⠒⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⡠⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⡖⠋⠀⠀⢀⣠⠖⠋⢀⡴⠊⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢀⡠⠶⡋⠁⢀⡠⠴⠚⠉⠐⢀⣠⠴⠒⡽⢀⡤⠖⡏⠀⠀⡴⠋
⠀⠀⠀⠀⢀⣠⠔⠋⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⠤⠒⠋⠁⠀⠘⠒⠋⠁⠀⠀⠀⠘⠃⠉⠀⠀⠈⠃⠉⠀⣸⠁⣠⠎
⠀⠀⠀⠚⠋⠲⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠚⠉⠀⠀⠐⠶⣤⣀⠀⠀⠀⢠⠀⠀⠀⢀⣠⠞⠳⢶⣤⡀⠀⢠⢇⠞⠁
⠀⠀⠙⣓⡦⠤⠤⠤⠤⠤⠔⠒⠂⠀⠀⠀⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⡐⠁⠀⣹⠿⣶⣤⣾⠀⢀⡴⢫⠴⣲⣦⣼⠀⠁⢀⡾⠁
⠀⠀⠈⠙⠢⠤⠤⣀⡤⠀⠀⢀⣠⠤⠶⣄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠐⢵⣄⡀⠙⣋⡟⣁⣈⣻⡁⠀⠀⣸⣿⣿⡟⠀⠀⢸⡃
⠀⠀⠀⢀⣤⣴⣚⣉⣀⣀⡔⠋⢀⡀⠀⠸⠀⣀⠵⠀⠀⢀⠠⡤⠤⢬⣀⣙⣛⣉⣡⠄⠀⠀⠈⣿⢦⣤⡭⠿⠛⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⣔⢹⡆⠀⠋⠁⠀⠀⣀⣠⠄⠀⣀⠀⠀⠈⠉⠁⠙⠧⣤⡤⠶⠋⠐⠬⣄⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠈⠁⠀⠀⢠⣶⣾⣿⣇⠀⢀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠀⠘⣿⣿⣿⣿⣷⣧⡀⠀⠀⠀⠈⠉⠙⠒⠒⠶⠦⠤⠤⢶⠖⠛⠉⠁⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢎⠈⠻⣏⠉⠉⠉⠻⣿⠿⠿⣿⣿⣷⣶⣶⣷⣶⡖⠛⠋⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠳⣄⠉⠳⣄⡀⠀⠈⢧⠀⠈⠻⣿⣿⣿⣿⣿⠀⢤⡀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠉⠓⠦⢤⣀⣀⣀⢈⣻⣿⣿⡯⠇⢀⡹⠆⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⠲⠦⢤⣤⣤⣠⣤⠤⠔⣚⡭⠔⠛⠛⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣤⡤⠴⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠒⢢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠄⠛⠀⠈⠁⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠌⠀⠀⠀⠀⠀⠀⢊⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠀⠀⠀⠀⠀⠀⠀⠘⣰⠀⢀⡤⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡧⠒⢠⡌⢤⡒⠮⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠀⠀⠀⠀⠀⠐⢢⠀⠀⢀⠀⢀⢀⠀⠀⣤⡴⠶⠆⠗⠒⠒⠒⠒⠒⠒⠒⠶⠁⠀⠀⠀⢩⠖⡿⢛⠇
⠀⠀⠀⠀⠀⠀⠰⡟⢂⠤⢤⡀⠛⢆⡀⣀⣀⣀⣀⡠⠞⠀⢐⠁⠀⠀⠀⡇⢸⠺⠶⢶⠄⣦⣤⣤⣠⣤⣠⣶⡂⠛⠚⠒⠒⢢⠜⠿⣿⡉⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢇⢀⠜⠁⠂⢼⡄⠈⣄⣀⣨⡄⠀⢀⡨⠶⠶⠶⠶⠧⣼⠀⠀⢼⣧⢻⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢨⠀⠎⠀⠀⠀⠈⢤⠋⠀⠀⠀⡀⠀⠀⠈⢂⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣀⠀⡆⠇⠀⠀⠀⠀⠀⢸⠀⠎⠁⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣰⠉⠉⢹
⠀⠀⠀⠀⠂⠀⠚⠃⠀⠀⠈⠉⠉⠉⠉⠉⠐⡆⠀⠀⠚⠀⠓⠀⠀⠀⠀⠐⠃⠘⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠠⡿⠀⠀⠈⡇
⠀⠀⠀⠀⢹⠛⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⣟⠛⢛⠛⠛⠛⠛⠛⢛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⡔⠒⠂⠀⠀⠓⡄
⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⢸⠀⠀⠁⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠀⠁⠈⠉⠈⠉⠁⢉⡆
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⢸⠀⠀⠀⠆⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡇⠈⢹⠙⠻⠉⡿⠉⣷⡆⢲⠂⠉⡇⠀⢻⠀⠸⠀⣀⣤⣦⣤⣼⣆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠠⠀⠶⠀⠤⠠⠤⠀⠤⠜
⠀⠀⠀⠀⠀⡇⠀⡸⠘⡶⠀⠇⠀⢿⠇⢸⠀⢠⡇⠀⡾⡰⠴⠤⠮⣿⠧⠄⠘⠫⡿⠶⠶⢤⠄⠀⠀⠀⠀⠠⠤⠤⠀⠊
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠉⠉⠉⠉⠉⠉⢹⣥⣶⣾⣿⣶⣿⣷⣶⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠜⠆⠾⡠⠆⠴⠤⢿⠀⠀⠉⠉⠉⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⡤⠴⠒⠒⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣛⣛⣁⣛⣻⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣯⣭⣽⣭⣿⣿⣿⣽⣍⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⣰⣿⡏⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡧⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣦⡀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠲⡿⠁⠀⠀⠀⢠⣿⣿⣷⣀⣀⣀⠀⢀⣀⣼⣿⠿⣿⠿⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠇⠀⠀⠀⢀⣴⣿⣿⣽⡿⠟⢋⣴⣿⣿⡇⢸⣿⡿⣿⣾⠙⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠟⠛⡹⢃⣙⣧⡀⢾⣿⣿⣿⡇⠾⠋⠠⠈⠺⡇⣸⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣣⡀⠀⠀⠀⣼⡁⠉⠁⠈⢿⣦⠈⠉⢩⠃⠠⠞⠉⠙⠗⠺⣮⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣇⠀⠀⣸⣿⡀⠀⠀⢠⣾⣿⣆⣠⣾⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣷⡀⢀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⢼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣏⣦⣐⡃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⣤⣤⣤⣤⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⢑⣝⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠈⠉⠙⠋⠉⠉⠉⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠉⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡃⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣤⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⡿⢁⣿⣿⣿⡇⢸⣿⣿⣧⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⠃⣼⣿⣿⣿⡇⢸⣿⣿⣿⣇⠸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠘⠛⠋⠀⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲⣴⣖⡂⣖⣶⢴⣶⢠⡖⢶⣰⣦⣰⢀⡶⡄⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠓⠂⠋⠓⠐⠞⠋⠓⠚⠙⠃⠛⠘⠛⠓⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣰⡖⢦⡖⣴⢒⡂⡆⣶⣒⢰⣆⣶⣶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠀⠙⠚⠃⠃⠛⠒⠙⠈⠋⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⣏⢙⣦⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣈⣋⠉⠟⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣡⡤⠤⠤⠤⠤⢀⡉⠻⣆⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⢸⠃⢸⠃⠀⠀⠀⠀⠀⠀⢰⡆⢸⠆⡷⢠⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠊⠁⠀⠀⠀⠘⣆⠘⢦⣀⣀⣀⣀⣀⣠⠼⠁⣼⠋⠁⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⣤⣤⣤⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⠛⠛⠛⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⢤⡀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠀⠹⣯⡽⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠸⠷⠟⠛⢛⣻⣻⣟⠁⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⢠⡆⣶⠀⠀⠙⢦⡀⠙⠂⠀⠀⠀⢠⠾⣆⣀⣿⣉⣉⣉⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣤⣈⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣟⠀⣹⠄⠀⢀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠿⣆⠰⠾⠷⠶⢶⡄⠀⠈⠁⠀⠀⠀⠈⠉⣿⠀⠀⣞⣹⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⢉⣭⣭⣭⣿⣭⣭⣽⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠤⠥⠤⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠒⠒⣶⡗⣶⠋⠀⠀⠀⠀⠀⠀⢀⡆⣿⠀⠀⠘⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢤⣤⣬⣭⣭⡽⠏⠉⠁⠶⣄⠀⠀⠀⠀⣠⡞⠃⣿⣒⠒⠒⢒⣒⣒⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠛⠃⠀⠀⠈⠉⠁⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠁⠈⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⡇⢳⠀⠀⠀⡖⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠛⠿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠁⠀⠀⠙⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠆⣤⠰⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⡀⠛⠛⠛⠿⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣀⠀⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣼⣿⣿⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢤⢎⠒⢠⠀⠀⠀⠀⠀⢠⡀⠄⠀⠀⠀⠀⢁⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠐⠀⠀⠀⠐⠖⠀⠀⠀⠈⠃⠘⠤⠈⠀⠀⠀⠀⢈⡁⣀⣠⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⡈
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠈

⠀⡀⠀⡠⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⢀
⠀⢀⠁⠈⠉⠑⠀⠀⠀⠀⠀⣦⠂⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠠⠄⡈⡀⠤⠀⠀⠀⠀⠂⠂
⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠽⠚⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠉⠑⠂⠀⠀⠀⠠⠀⠀⢀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠈⠀⠀⠄⠠⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠠⠉⠉⠁⠀⠀⠀⠐⡄⢠
⠀⠀⠀⠀⠀⠡⠀⠀⠀⠢⡈⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠠⠈⠃
⣤⣤⢦⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣷⣤⣤⣤⣤⣤⣤⣶⣤⣤⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠂⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⢱⠀⠀⠀⢀⠀⠀⠀⠀⠀⢄⠀⠙⣉⠑⣦⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⢦⡀⠰⡄⠈⠷⠄⣤⡴⢧⠙⠚
⠀⠀⠀⠀⠀⠀⠀⡆⠱⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⡈⠀⠀⠀⠀⠀⠘⣧⡀⣟⠀⢟⢡⠀⢀⡀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠑⠀⠐⠁⠀⠀⠐⠄⢀⣐⢀⡶⠃⠀⠀⠐⠙⠉⠀⠈⠉⠉⠁⠈⠀⠀⠀⠈⠀⠀⠑⠀⢀
⠀⠀⠀⠀⠂⠥⠀⠀⠀⠐⠀⠀⠁⠀⠁⠒⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠐⡀⠉⡄⠀⠀⠀⡀⢙
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢁⢀⣷⠀⡀⠀⡤⠞⠛⠛⠓⡦⣠⡞⠉⢂⡀⠂⠤⠌⡀⠔⠀⠀⡀
⠀⠀⠀⠄⠐⠒⠢⣀⠀⠲⠚⣧⠀⠀⠀⠀⠀⣾⢃⣾⠃⡜⡴⣫⡾⠀⡾⢱⡿⢰⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⠑⠀⠀⠀⠐⠈⠓⢉⠳⣊⢈⣉⠙⠄⢪⠗⣸⠁⠻⠴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠈⠈⢠
⠀⠀⢦⡀⠈⠀⠀⠀⠂⠀⠠⠴⠖⡲⠁⠀⠄⢠⣟⣴⠯⣞⠾⢴⣇⡾⢢⢟⡶⠀⡦⢄⡀⠀⠀⢁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢚⠖⠁⠐⠫⡊⣦⣡⠏⢀⡤⠤⠮⠥⣭⣁⡈⠋⢁⡴⢋⡽⠀⠀⡈⠁⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⣸⣏⣤⠀⣡⢤⡤⢠⣄⣤⡄⣬⢭⡟⣩⢤⠀⠠⠀⠉⠀⠄⠀⠀⠀⠀⠁⣈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢱⠃⠾⠵⣟⡱⠿⢫⣏⠼⠇⣾⢀⣣⠈⠀⡀⠃⠀⠀⠀⠁⠀⠀⢀⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠰⠂⠀⠄⠁⠀⠀⠙⠈⠁⠀⠀⠡⣄⢀⠀⠀⠀⠀⠀⢀⠪⡄
⠀⠀⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⢀⡄⠀⠀⣀⣀⡀⠀⠀⠀⠠⠀⠀⠀⡀⠸⡀⠀⣄⠀⠀⢠⠀⠐⠂⠈⠢⠁
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠋⠉⠠⠶⠛⠀⠀⡀⠉⠉⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠡⠚⣳⠤⠀⠀⠀⠚⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠌⠁⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢤⣤⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⣑⡏⠉⠔⠚⠢⠠⠄⢀⠀⠀⠀⠈⠠⠤⠭⠻⢷⣥⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠘⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡘⣩⣷⣶⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣥⠺⣿⣿⣿⡿⢟⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠣⠂⠀⢀⣽⡷⠆⠀⡠⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡄⣀⠰⠒⣾⣿⠇⠈⢢⡥⣜⠒⣤⠤⠔⠒⠻⡦⠀⠀⠀⠀⠈⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠴⣶⡾⠛⠂⠀⠀⡐⢽⡿⢿⠄⠀⢰⡏⠀⢠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣤⢄⣀⣀⣬⡧⣄⠀⠀⠸⠷⣄⢳⣈⣒⣶⢤⠠⣤
⠀⠀⢀⣀⠐⠋⠀⠀⠀⠀⢰⣲⣿⣿⣧⣼⣿⠏⣿⣷⣀⡀⠀⠀⠀⠈⠀⣋⠙⠾⣝⣛⣡⣿
⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠿⢿⡛⢿⣿⠇⣚⣻⣛⣿⡷⠀⠚⠳⠀⠀⠉⠀⠾⢻⣿⠅⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠻⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡐⠔⠀⣠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⠇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⢻⢿⣿⣿⣿⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⢀⣿⠀⠀⠀⠀⠀⠀⡠⠔⠒⢆⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠕⠋⠉⠝⢆⠀⠀⠀⠀⠀⡼⢋⠻⡄⠀⣽⠀⠀⠀⠀⢠⣯⣄⠀⠀⠀⣭⠆
⠀⠀⠀⢀⡴⠟⢦⣀⠀⠀⠀⠀⠘⢿⡀⠒⢒⡮⠗⠀⠀⠀⢸⠁⢻⠃⣷⠀⣿⠀⠀⠀⠀⠸⠿⣿⣿⣿⡿⠛
⠀⠀⠀⠙⠦⠤⠦⠋⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⢸⡒⠚⠒⣿⣠⣿⣄⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⠉⠉⠛
⠀⢠⠖⡩⠍⡑⢢⠤⠤⠄⠀⠀⠀⠀⢀⡤⠔⡢⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣖⣒⣺⢷⣶⣶
⠀⢸⠐⠀⠁⠀⢸⠀⢸⠀⠀⠀⢠⠊⠡⢢⡟⠟⠈⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⣤⠠⠄⠄⡏
⠀⢸⠀⠀⠀⠀⢈⠀⢸⠀⠀⠀⢸⡀⠢⡥⢐⣨⠖⠁⠀⠀⠀⠀⣀⣠⣧⡤⠤⣄⠀⠀⠀⠀⢸⣿⠀⠀⢡⡇
⠀⠈⠲⠤⠤⠔⠋⠉⠉⠀⠀⠀⠀⠘⠓⠛⠃⠀⠀⠀⠀⠀⠀⣿⢄⣈⣩⣥⡴⠟⠀⠀⠀⠀⠘⠿⠤⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⡶⣏⢿⣿⣷⡀⠀⠀⠀⠀⠀⢀⡠⠔⠓⠦⣄⠀⠀⠀⠀⠀⢀⡠⣴⡶⠀⠀⠀⠀⠀⠀⠀⠰⡛⢻⠂
⠀⠀⣸⡜⠂⠀⠹⣧⠀⠀⠀⢠⡒⠁⠀⠀⠀⠀⡈⢽⡂⠀⠀⢸⢳⠟⠛⠉⢉⣷⡀⠀⠀⠀⣀⠔⠋⠙⠢⡀
⠀⠀⠓⡤⡀⠀⠀⠣⡀⠀⠀⢸⡀⠀⠂⠠⠀⠈⣠⡾⠁⠀⣸⣍⡚⢀⣠⢞⡿⠛⠁⠀⠀⢸⠁⠀⠀⠀⠀⢱
⠀⠀⢀⡇⠈⡄⣀⣠⠗⠀⠀⠈⠙⠷⣤⣤⣤⠟⠁⠀⠀⠀⠓⠿⣿⡯⠟⠉⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠊⠉⠁
⠀⠀⠀⠀⡤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⢷⣴⡟⠅⠀⠀⠀⢾⠙⡦⠤⠤⢤⡤⣤⠚⡆⠀⠀⣴⣊⡉⠉⢉⣲⡄⠀⠀⠀⠀⡼⠉⠻⠯⠿⡆
⠀⠀⠀⣠⠞⠀⢆⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠘⡶⠃⠀⠀⢸⣌⡉⠉⣉⢼⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀⣴
⠀⠀⠀⣏⠉⠀⢸⡆⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠚⠁⠀⠀⠀⠀⢧⣍⣉⣠⠎⠀⠀⠀⠀⠀⡯⢀⣀⣀⡀⢽
⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠉⠉⠉⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⣀⡀⠄⠤⠤⡤⠄⠈⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⡠⠀⠀⡠⠔⠂⠉⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢠⡃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠄⠀⢀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⢀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠈⢄⠈⢆⠀⠀⠀⢀
⠀⠀⠀⠀⢸⠀⠀⠠⠁⠼⠒⠠⠄⠀⠀⠀⠈⢂⠉⠐⠂⠀⠐⢂⠀⠀⠀⢀⠀⠀⠀⠀⠠⠂⡀⠄⠂⠁⠀⠀⠀⠀⠀⠲⠑⢌⠀⠀⠀⠘
⠀⠀⠀⠀⠸⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠠⢆⠀⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⢀⢠⣀⠀⠀⠀⠈⡴⠀⠀⡆⠀⠀⠀⢠⣤⡀⠀⠀⠀⣀⠀⠀⠀⣄⣤⠀⠀⠀⢰
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠈⠒⠁⠀⠀⠈⠁⠀⠀⠀⠈⠈⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠌⠈⠁⠀⠈⡘⡄⠆⠀⠀⠀⠀⠀⡆⠀⠀⠆⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⢧⢠⣀⠀⠀⠀⠀⠈⠒⠈⠀⠀⠀⠀⢀⠠⠊⢸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢤⠄⠀⢠⠤⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠁⠒⠂⠤⡤⠀⠀⠤⠄⠐⠂⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠓⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢆⠀⡀⡠⠔⠀⠀⠀⠈⠒⠠⢀⡇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠐⠨⠨⣠⠀⠰⠳⠿⠟⠁⠰⠴⠐⠴⠆⠀⠷⠀⠘⣆
⠀⠀⠀⠀⢰⠱⠀⠀⢠⠀⠤⢦⠀⠀⠀⠀⠀⡀⠀⠀⡏⠀⣚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⢄⠀⠀⢤⢤⣤⣽⠀⠀⠰⡟⡇
⠀⠀⠀⠠⠈⠈⠢⠀⠈⠘⡁⠀⠡⢀⠀⠀⣀⠀⢀⠜⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢯⠀⠀⠤⣀⠤⣤⡤⢤⡠⠆⢀⠾⠀⠀⢀⠖⠛⠳⢆
⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠈⠒⠤⠄⣈⡁⣍⠈⣀⠤⢒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠀⡓⠢⠠⣀⣉⢨⡁⣁⡠⠄⡂⠀⠀⠀⢸⠀⠀⠀⠨
⠀⠀⠀⠅⠀⠀⠀⠇⠀⠀⠠⠀⠀⠤⠤⠤⠤⠤⠤⠀⠨⠄⠀⠀⠀⠀⠠⠍⠡⠄⠀⠀⠀⠀⠇⠀⠀⠤⠤⠤⠤⠤⠄⠀⠥⠀⠀⠀⠸⠀⠀⠀⠠
⠀⠀⠁⠐⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠒⠀⠀⠠⠤⠤⠤⠤⠀⠀⠐⠒⠂⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠓
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⠒⠂⢄⠀⠠⠀⣀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⠣⠀⠀⠀⠀⠀⢀⠀⠀⣀⠔⠒
⠀⠀⠀⠀⢀⠄⠀⠀⠀⢠⠤⢀⣉⢈⠑⠄⠤⠀⠀⠀⠀⡐⢡⣴⣶⣦⡀⠀⠀⢠⣶⣶⣶⠄⢡⠀⠠⠅⠀⠀⢀⠡⠁⠴⠞⠁⠄
⠀⠀⠀⠀⠀⣀⣶⣢⡴⠋⠀⠀⠙⣷⣵⡀⠀⠀⠀⠀⠀⠀⠈⠭⠤⠭⠀⠐⠢⡀⠰⠶⠒⠀⠀⠡⠀⠀⠀⠐⠓⢂⡰⢃⠔⠁
⠀⠀⠀⠀⢀⠡⠉⣡⡤⠀⠠⠶⠦⠈⣿⠁⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠤⠄⠠⠠⠕⠀⠀⠀⠀⢠⡀⠀⢀⡠⠒⠁⠶⠁⠀⢀
⠀⠀⠀⠀⢠⠑⡆⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⠅⠀⢀⢤⠤⢴⡖⠒⣶⠒⢲⡖⠦⣆⠄⠀⠲⠀⠈⡀⠁⠋⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⠐⠀⢀⣟⠁⠃⠀⠀⠀⠀⠀⡄⠐⠸⣖⣲⣿⠿⣻⢗⡾⢭⣶⡏⠀⠀⠡⠶⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠉⢷⠄⣀⣀⣴⣟⣥⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢏⣳⣠⠼⣭⣶⡿⠋⠀⢀⠂⣄⡀⠙⠋
⠀⠀⠀⠀⠀⡆⠩⡜⠀⠈⠁⠰⢻⠿⠦⣀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠈⠉⠉⠉⠁⢀⣀⡔⠁⠀⠈⢁
⠀⠀⠀⠔⠁⠀⠀⠈⠁⠀⠀⠈⢁⢄⠄⠀⠑⢄⠀⠀⠀⢀⠀⢲⠲⣈⠓⠶⠤⠄⠔⠩⢀⡵⢤⢤⣀⣀
⠀⠀⠂⠀⠠⠉⠠⠪⠀⠪⠢⠪⠀⠀⠠⠂⠆⠀⠂⡠⠀⠋⠠⠘⡇⠀⠈⠑⠢⢤⠐⠂⠁⠀⠈⠠⠙⠌⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⡠⠚⠄⢳⠔⠢⠤⡾⠈⢳⡤⠴⠚⠇⡀⠳⡇⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠈⠀⢆⠀⠁⢸⠄⠀⠀⣿⢛⠻⡅⠀⢀⠀⡆⣐⠁⠀⠄⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⡄⠠⠀⡇⠀⢠⠇⠔⡀⢇⠀⠸⠀⠀⠁⡀⢀⠀⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠁⠈⠈

⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣝⣄⡠⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⢸⣽⠀⠀⠀⠀⠀⣠⠔⠊⠉⠈⠳⢄
⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢰⡉⠀⠀⠓⠵⣄⠀⠀⠀⠀⢀⡞⡁⢈⢳⠀⢸⢸⠀⠀⠀⠀⠀⣿⣶⣄⣀⣀⣀⣴
⠀⠀⣠⠞⠛⠳⣄⠀⠀⠀⠀⠀⠘⠺⣄⠛⢁⡵⠚⠁⠀⠀⠀⢸⠀⡑⠀⢸⡄⢸⡎⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⠟⠉
⠀⠀⠙⠶⠤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢸⡛⠒⠒⢺⣥⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠉⡙⠛⠛⠛
⣠⠖⢒⡒⠒⢤⣀⡠⡄⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣤⠤⠴⠶⢦⠤⢤
⡧⠀⠀⠈⠁⢸⠀⠀⡇⠀⠀⠀⢀⠔⢊⣥⣢⢟⠎⢱⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⡉⢡⠈⡅⡏
⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢟⠠⡀⠘⢉⠄⢂⡽⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⢀⡇
⢧⡀⠀⠀⢀⡴⠤⠔⠃⠀⠀⠀⠸⢦⣄⣯⡴⠚⠁⠀⠀⠀⠀⠀⣤⠖⠪⠿⠿⠀⢙⡇⠀⠀⠀⠀⠘⡇⠀⠂⠈⢸⠇
⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⢤⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠰⡻⣎⢻⠿⢿⣦⠀⠀⠀⠀⠀⠀⡠⠔⠚⠁⠑⠲⣀⡀⠀⠀⠀⠀⣠⢴⣺⠽⣃⣀⠀⠀⠀⠀⠀⠀⠀⢫⣉⡼
⢀⣵⡈⠀⠀⠸⣿⠄⠀⠀⠀⡶⢉⠀⠀⠀⠀⠀⡀⠔⢿⠀⠀⠀⢸⠙⡟⠋⠉⠀⣨⡷⡀⠀⠀⠀⢀⠔⠋⠉⠉⠢⡀
⠈⠲⡄⠀⠀⠀⠹⡄⠀⠀⠀⣯⡀⠈⠐⠠⠄⠈⢀⣴⠟⠀⠀⣸⣍⡙⠁⣠⡴⣻⠿⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱
⠀⢸⠀⠙⡀⠀⣀⡼⠀⠀⠀⠉⠻⢶⣤⢠⡠⣲⠞⠁⠀⠀⠀⠓⢿⣟⣟⡵⠚⠁⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⢠
⠀⠈⠛⠓⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠋
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠐⣇⣀⣼⡏⠀⠀⠀⠀⡴⢢⣀⡀⠀⠀⠀⠀⢀⢤⠀⠀⠀⢀⡤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⢈⡟⢻⣧⡶⣦⡀
⠀⠀⠀⣹⠛⡇⠁⠀⠀⠀⠀⢳⣴⠏⠉⠉⠉⠋⠉⣧⢸⠁⠀⠀⢻⠒⠶⠶⠶⠶⣾⠃⠀⠀⠀⠀⡸⠀⠀⠀⠉⠉⢇
⠀⢀⡎⠁⠀⢱⡄⠀⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠈⡗⠤⠤⠤⠚⡏⠀⠀⠀⠀⠀⡗⠉⠉⠉⠉⠉⣿
⠀⢸⣇⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠞⠁⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠐⣺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣤⣤⢀⡛⢁⠰⣿⡂⠉⠁⣾⠀⠀⠀⣠⠀⢠⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠉⠉⠀⠉⠁⢶⣅⠛⠃⠉⠁⠶⠗⠀⢀⣤⡘⠟⠁⠈⠛⠀⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢋⠀⠀⢠⣤⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣀⢠⡦⠰⡶⠂⠀⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠘⠟⢛⣾⣧⣾⣿⣿⣿⣿⣿⣿⣟⡷⣀⠀⠀⠀⠀⠀⠈⣉⠨⣜⠺⠿⠿⠀⠀⠁⠰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⡀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⠀⠀⠀⠀⠀⠻⢣⣦⠀⣾⠆⠀⠀⠀⠀⠈⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⠣⠙⢳⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡄⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⠁⠀⠀⠈⡇⠀⢨⠹⡀⠀⡀⠸⡀⠀⠀⠀⠫⠗⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠻⣿⣿⣀⠀⠀⠀⡗⢆⠸⠀⠃⠀⢹⡄⡇⠈⠦⢼⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠢⣾⣿⣿⣿⣿⣿⣿⣿⣿⢛⠇⠀⠀⠀⠀⠿⠉⠳⡄⠀⣸⠁⠸⣼⠦⢀⣠⡶⡇⡻⢳⠀⠀⡇⠀⠸⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⣿⣷⠄⠀⢠⠀⠀⠰⠟⠓⠦⠕⠘⠲⠂⠙⣿⠿⠧⠴⠚⠁⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⣴⠆⣤⣶⡒⠢⣴⣒⢠⣄⣉⣠⡤⠖⡃⠀⠀⠀⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⠃⠀⢠⡼⣿⣴⡵⢮⣈⡿⢥⣄⡀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣬⠙⠛⠛⠿⣿⢿⣿⡿⢿⣿⣿⣿⣧⣄⣀⣀⣀⣤⣶⡿⣟⡛⠿⠿⢶⠷⢑⢦⣬⣿⣒⠂⠀⠀⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⠀⠀⠀⠀⠀⠈⡀⠀⠛⠘⣛⡛⠛⠛⢛⣛⡯⠬⣉⣳⣵⠶⠾⢳⣞⡯⣭⣍⣥⡄⠀⠀⠘⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢄⢸⡄⢠⡟⠉⠹⣇⣰⠿⢿⠹⣦⣌⠉⠡⢞⣛⡉⠥⠤⣟⣦⠤⠄⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡀⠰⠆⢹⠉⠏⢻⣧⣦⠀⣀⢻⡆⢸⠀⠛⠦⡀⠉⠳⠦⡘⢓⡘⠒⠂⠀⢠⣴⣄⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢠⣿⡄⢸⡐⢛⠚⢿⣖⣫⡼⠀⠀⠈⠀⠀⠀⢣⠀⠀⠀⠉⠀⠈⠀⣴⣦⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⡍⢁⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⣤⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠰⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⣶⣄⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠏⠀⠾⠿⠁⠀⠛⠉