Mcdonalds Emojis & Symbols

⠀⠀⠀⠀⠀⠘⠳⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣡⣴⣋⣷⣼⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⡛⠋⠉⠁⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠶⣿⡶⠶⠛⠛⠛⣛⡷⠀⠀⠀⠀⣴⠟⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠿⣷⣤⣤⣴⡶⠿⠷⠶⠖⠛⠋⠁⣠⠀⠀⢀⡾⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⡄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⠀⠈⠧⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢠⡶⣆⡾⡆⠀⠀⠀⢰⡇⠀⠀⢸⡏⠙⠲⠤⠤⠀⡄⠲⠞⠛⠉⢀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⠇⣿⠁⡿⠀⠀⠀⣼⠇⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⣷⡏⢻⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⣶⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠸⠇⠙⠀⠀⣰⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣤⣀⣼⠟⠀⢀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⠀⠀⢠⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠉⠁⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠓⠶⠟⠀⢀⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠸⡗⢦⣀⠀⠀⢹⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⠀⠰⠶⠞⠋⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣡⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣥⠼⠿⠒⠓⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣀⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⣠⠞⠙⡆⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⢰⣖⣛⣋⣉⣉⣹⣏⣁⣤⡤⠖⠊⡁⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢠⡇⠀⠀⡟⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⡤⠖⠚⠉⢹⡄
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣠⡄⣴⡄⠀⠀⠀⣸⠇⠀⠀⡟⠳⠤⣀⣀⠀⡀⣤⡴⠞⠋⠁⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⡇⣿⠃⣧⠀⠀⠀⣿⠀⠀⢰⡇⠀⠀⠀⠀⢰⡇⠀⢠⣶⣴⠛⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠈⠀⠀⣤⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⠀⢸⠀⠋⠀⢁⡄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢤⣀⣼⠏⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⣼⠀⠀⢀⡀⠀⢀⣼⠁⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠁⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠙⠳⠞⠃⢀⣤⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠿⠳⢤⡀⠀⢹⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠸⠀⠐⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠰⡄⢳⠀⣧⢀⢀⡔⣐⢤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣺⡇⠀⣷⠘⣤⣾⢺⣿⣠⣇⣇⡰⠁⡴⣹⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣄⣧⠄⢾⣧⢀⡇⣀⣿⣿⠎⢻⣿⣿⡿⣡⢞⣴⣓⣼⠁⡨⡹
⠀⠀⠀⠀⠀⠀⡀⢀⣄⢹⢠⣼⡇⠸⣿⡟⠺⡇⡿⣿⣿⠗⣀⢿⣿⣷⡿⢿⠿⣿⣧⡶⡱⣥⡦⡀
⠀⠀⠀⠀⠀⠀⢣⡀⢻⣪⣿⣿⡳⣤⢹⡗⣀⡇⣀⣿⠃⠀⣿⡌⣿⣿⡇⡜⡴⠛⣿⣷⠏⢀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠱⢴⡷⣿⡇⣽⢸⣯⣿⡿⠗⣿⣿⠀⢰⣿⣷⠗⠻⣿⣷⡇⣀⣿⣗⣵⢿⠱⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⢻⢇⣿⢸⡏⢿⡌⠉⣿⡇⣰⣾⡟⢁⣴⢮⣘⣿⣧⣿⣿⠟⣗⡡⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⡀⢑⠻⣿⣸⡇⣧⣿⡎⣿⣿⣷⣿⣇⣤⣿⣿⠿⠛⠁⠀⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⡇⠀⠭⠀⠉⠙⠛⠛⠳⠻⠽⠟⠋⠛⠋⠉⠀⠀⠀⠀⢸⠃⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢲⣷⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠠⠴⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⢀⡤⢶⣄⠀⠑⢄⠀⠀⠀⣼⡟⠀⢀⡴⠋⠻⣷⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⢠⠏⠀⠀⠙⢷⣄⠀⠣⡀⢠⣿⠁⠀⣼⠁⠀⠀⠘⣷⣀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠀⠀⣾⠀⠀⠀⠀⠈⠻⣆⠀⠑⣼⣟⠀⢀⡇⠀⠀⠀⠀⠘⣷⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⣿⢀⣀⣀⣤⣤⣤⣽⣧⠀⠘⣷⠀⢸⣧⣤⡶⠶⠶⢦⣿⣷⠀⠈⣧⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡇⠀⠀⢿⣛⣉⠉⠉⠀⠀⠀⠹⣯⠄⠘⠀⢸⡷⠶⠂⠀⠀⠀⠈⣿⡅⠀⢸⡶⠤⠍⠉⠉⠛⠳⠶⢤⣄⡀
⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⢿⣖⠀⠀⠸⡧⠖⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠘⣏⣉⠉⠁⠀⠀⠀⢹⣯⠀⠀⢿⠛⠒⠒⠂⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⢀⣼⡫⠀⠀⠀⠀⢸⣷⡄⠀⠀⢿⣊⣉⣁⣀⣀⣀⣀⣀⣿⣦⣀⣀⣷⣒⣀⣀⣀⣀⡀⢸⣿⠅⠀⠸⣏⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢾⣏⡴⠒⠀⢠⣤⠴⠿⠒⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠚⠿⠦⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠙⢷⡩⢴⡏⣿⡅⠀⠀⠀⠀⢀⠀⡀⠀⣤⠐⢀⠀⣠⢒⣄⢤⡆⣀⠀⣤⣠⡄⢠⡆⢀⠀⢠⠀⡀⠀⠀⠀⠀⢈⣹⣅⡄⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⣸⠗⣺⣧⢸⣧⠀⢰⡈⡙⢀⢻⡐⢝⠿⡄⣀⡡⠛⠦⠭⠞⠧⠽⠧⠿⢤⣅⡼⣇⢿⡀⠖⠘⠓⣔⢂⣀⠀⢐⡿⠶⠄⠀⢀⣴⠟
⠀⠀⠀⢀⡴⠟⡉⠀⢿⡈⣿⣆⠈⠥⠷⠞⠛⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠯⣋⠩⠀⣾⠗⢒⣠⠴⠋⠁
⠀⠀⢠⡿⢛⡡⠄⠀⠸⣇⢸⣷⡄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⡀⠀⢐⡿⠞⠋⠁
⠀⠀⢸⣟⣉⠤⠂⠀⠀⢿⣀⣿⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⡟⣿⣿⣿⣿⠝⡿⠻⠿⠿⠿⣿⣿⡿⠿⣿⣿⠟⠁
⠀⠀⠈⢻⣥⡴⠊⢁⡠⠘⠛⢛⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⠂⡷⠶⠖⠚⠋⠉
⠀⠀⠀⠀⠉⠻⠶⣯⣤⣶⣊⣁⣠⣤⣖⣊⣁⣠⣴⣶⣤⡤⠴⠶⠶⠚⣧⢸⣿⣿⣿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣯⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⡷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣿⣿⣟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⣿⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠰⠿⠿⠿⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢆⠀⠀⣀⣤⠶⠶⠶⢶⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠀⢠⡄⠄⢸⣧⡼⡇⠀⠀⠀⠀⡀⢠⡴⡂⠘⠁⠈⣦⠞⠁⣤⣤⣴⠶⠚⠓⠲⠀⠈⣷
⠀⠀⢠⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠃⠁⠀⣠⣤⠐⣯⠥⠘⣯⠥⠀⠀⠀⡏⠀⣴⠂⠀⠀⠀⠀⠀⣸⣀⡼⠏
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣚⠀⣇⢨⠇⠳⠚⠁⠀⠀⠀⢀⣸⠃⢀⡁⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢀⡤⣄⢺⡥⠆⢹⡥⠆⠉⠁⠀⠀⠀⣀⡤⠴⠚⠉⠸⣆⠈⣳⡄⡴⢲⡄⠖⠛⠛⠛⠛⠳⢶⡦⢤⡀
⠀⠀⠀⠀⠘⣆⠀⣀⢠⣞⣓⠸⡖⠃⠘⠓⠉⠀⠀⠀⢀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠙⠛⠛⡟⠁⡴⢅⠀⠀⠀⠀⠀⠀⣠⠉⢦⡙⢦
⠀⠀⠀⠀⠀⠘⣎⠉⠀⠤⠜⠁⠁⠀⠀⠀⣀⡠⠴⠒⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡀⠀⡆⠀⠀⠀⠰⠞⢋⣠⣦⢳⡈⣧
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠒⠁⠐⠀⠂⠀⠐⣻⠗⠀⠈⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠙⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠠⣀⣀⡴⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⢻⡆⢠⣤⣼⣿⣀⠀⠀⢀⣸⣷⣤⡤⠀⢠⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠉⠈⠻⢟⣋⣉⡵⠃⢀⡴⢃⠎⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣠⠖⣦⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⡀⢀⢠⡴⢛⣵⠯⠶⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⠟⣏⠘⣄⡀⠀⠀⢀⡔⠈⠱⣶⣌⣌⣥⣆⣤⠴⠖⠒⠚⠛⠛⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⡿⣰⠏⠛⠷⢶⡟⠀⠀⠘⢿⠟⠳⠿⠋⠀⠀⠀⠀⢀⣀⣴⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣏⣿⠹⣧⠤⢾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣤⣤⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣽⠇⢡⣀⣤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣄⠠⡶⠂⢲⣶⣶⠶⢤⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢀⡜⣿⣻⣟⣛⠋⠁⠀⣵⡶⡿⣿⠟⠀⠀⠈⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢸⢀⣿⢯⣿⡿⣻⢗⠾⢋⣠⢾⣿⣗⣲⡄⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⢿⣏⣼⣯⠊⢀⡡⢶⡛⠳⢝⣳⣝⣾⣇⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠻⠛⠉⠀⠀⠙⠶⠬⠙⠶⠯⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣼⢤⣄⣧⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣘⣀⠀⠀⡄⠀⠃⠀⠀⠀⠀⢀⢸⡄
⠀⠀⠀⠀⠀⠀⢀⠀⢰⣶⣼⣦⣷⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣷⣤⠃⠀⠀⠀⠀⢼⠀⢿⢟⣃⢠⣴⣶⣶⣶⣾⣶⠆
⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠘⠿⠿⠟⡇⡏⠏⠏⠹
⠀⠀⠀⠀⠀⡜⣌⣿⡟⢚⠟⠛⠿⠋⠹⠿⠹⠏⠈⠟⣛⡛⣛⠛⢛⣿⣿⣟⡓⠀⠀⠀⠀⠀⠀⠀⠀⡁⡁⡁⢈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠶⠄⠀⠠⠶⠄⠀⠀⢤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⢞⡣⠚⠿⢿⢲⣾⣿⠶⠦⠄⠠⠀⠀⠀⠀⠀⣠⣄⠀⣠⣦⠀⢠⣶
⠀⠀⠀⠀⢤⣤⣴⣾⣿⣷⣶⣶⣾⣿⣿⣶⠏⢸⣷⣶⢂⣭⡍⠀⢉⣀⣼⣿⠇⠀⠀⠀⠀⢠⣿⣿⡀⣿⣿⣇⢾⡿⠇
⠀⠀⠀⠀⠈⢹⣿⣛⡽⠏⠿⠿⠿⠭⠭⠭⠩⠒⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠉⢈⣠⣤⡥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⣠⣾⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣷⣄
⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀
⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣀⠀⢀⠀⠀⠀⠀⠀⢈⢉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣟⠃⠀⢠⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⢸⣿⣦⣿⣇⢠⡞⠳⠆⢸⡏⢻⣇⣴⡞⢶⡄⣶⠞⣷⡀⣖⣻⣶⢸⣿⢠⡾⢺⣿⠘⠁⣶⣟⡂⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠺⠃⠻⠙⠿⠘⠳⠾⠃⠸⠷⠟⠃⠙⠷⠟⠁⠿⠀⠿⠚⠿⠞⠿⢘⣟⣘⠷⠞⠟⠀⠀⠲⠾⠟⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁
⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠙⢿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⣼⠟⠀⢀⣀⣀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂⠀⠀⡴⠚⠻⣦⡀⠑⢄⠀⠀⣼⡟⠀⢠⠏⠀⠙⣧⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣗⠀⠀⣸⠁⠀⠀⠈⢿⣄⠈⢣⣠⣿⠂⠀⡟⠀⠀⠀⠘⣿⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠹⣆⠀⠹⣷⠀⢰⡇⣀⣀⣀⣀⣸⣷⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⣷⠶⠶⠾⠛⠛⠛⠻⣧⠀⠹⠆⢸⣏⣉⡉⠉⠉⠉⢿⣖⠀⠸⣟⣛⡛⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣤⠖⠛⢻⡯⠀⠀⢹⣖⡁⠀⠀⠀⠀⠀⢹⣷⠀⠀⠸⡧⠖⠂⠀⠀⠀⠸⣷⡂⠀⢿⠤⠤⠤⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⢀⣴⡋⠀⠀⠀⠸⣿⡄⠀⠈⣧⠔⠒⠀⠀⠀⠀⠀⣻⣦⠀⠀⣯⠭⠀⠀⠀⠀⠀⣿⣂⠀⠸⡖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⣾⣋⡤⠂⠀⣀⣤⡿⠷⠶⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠛⠳⠶⠶⠿⣭⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠈⠻⣖⣁⣾⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⡀⢀⡔⣂⢤⡄⢀⠀⣀⣀⠀⣤⠀⠀⢀⡀⠀⠀⠀⠀⠉⢉⣿⣉⡁⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢀⡿⢖⣿⠘⣿⠀⠀⡂⡓⢀⢮⡰⢺⢧⢀⣈⠜⠦⠭⠞⢧⠽⠦⠯⣼⣤⢿⣸⣇⠰⠀⠟⣔⢂⣀⠀⣸⡧⠤⠀⠀⣠⠞⠁
⠀⠀⠀⣠⠾⣋⠁⢸⣇⢻⣇⠀⠧⠗⠚⠋⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠫⢏⠉⠀⣾⠓⣂⡴⠞⠁
⠀⠀⢰⣟⣩⠤⠂⠀⢷⡘⣿⡄⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⢰⡟⠋⠁
⠀⠀⢸⣯⠴⠒⣀⠀⠸⣇⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⡏⢻⣿⣿⣿⢹⡟⠛⠛⣛⣻⡿⠿⠿⠿⠿⠋
⠀⠀⠈⠻⣶⣋⣁⡤⠂⢉⡉⠅⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⢸⣿⣿⣯⢸⠗⠛⠉⠉
⠀⠀⠀⠀⠈⠙⠛⠶⠿⠥⠤⠴⠾⠭⠤⠴⠶⠿⠗⠒⠛⠛⠉⠉⣿⢸⣿⣿⣟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡗⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⢥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠉⠢⡀⠀⠀⠀⢀⡔⠉⡉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠱⡄⠹⡄⠀⢀⠎⢀⠞⠉⢆⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠃⠀⠀⢱⠀⢱⠀⡜⠀⡜⠀⠀⠘⡆⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡜⠀⠀⠀⠈⡆⠀⢷⠁⢠⠃⠀⠀⠀⢱⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⡇⠀⠀⠀⠀⢣⠀⠈⠀⢸⠀⠀⠀⠀⠘⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠰⠒⠠⠔⠨⠂⣒⠒⡥⠖⠤⠤⠤⢄⠄⠲⡆⡣⠤⠒⡂⠄⢤
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡞⠠⢀⠄⣠⣘⡈⣀⣘⣁⢄⣘⡠⣀⢇⣨⣐⣀⣇⣄⣘⣀⢗⣀⡨
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠣⠤⠼

⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡂⣦⠤⠀⡂⠀⠀⠀⠀⡆⢤⠀⠀⠤⢤⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢶⠞⢻⠟⠋⠙⠛
⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⠀⠓⠠⠤⠇⠀⠀⠀⠀⣆⣸⡈⠀⠄⢼⠧⠀⠀⠁⠀⠀⠀⣀⣠⣤⣶⠶⣿⣿⣿⣿⡀⠀⣤⣬⠀⠀⢶⣶
⣿⣿⣿⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⠀⢸⠏⠉⠉⠁⠀⣼⣿⣶⣤⣤⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡁⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⢿⠟⠻⢿⢁⡄⠈⣿⠀⠈⠀⠀⣿⡆⠀⢸⣿⡁⠘⠛⠃
⣿⣿⣿⡏⣿⣿⣿⣿⣿⡗⣀⣤⣤⣶⣶⡿⢿⡇⢉⣿⣿⡇⢠⠈⡟⢉⠉⠛⠀⣦⠀⠘⠋⡑⠀⢻⠀⠀⣀⠈⠉⣀⠀⣸⣿⣷⣦⣤⣤
⣿⣿⣿⡇⣿⣿⣿⣿⣿⢾⣿⣿⣷⢹⣿⡇⠈⠃⠀⠋⣽⡇⢸⠄⣇⠘⠇⢀⠀⣿⣀⣴⣦⣤⣦⣾⣶⣾⣿⡿⠿⠿⠛⠛⠛⠛⠉⠉⠁
⣿⣿⣿⡇⣿⣿⣿⣿⣿⣽⣿⣷⣻⡆⣿⠀⣆⡀⣀⣤⣋⣧⣤⣴⣿⣿⠾⠿⠿⠛⠛⠛⠛⠉⠉⠉
⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠚⠛⠃⠉⠉⠉⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠶⠶⣶⣶⣿⣿⡇⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡉⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣵⣎⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠀⠀⠀⠛⢢⠀⢀⠀⠀⠀⠲⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⣿⣿⡇⠐⢦⡾⠅⡆⠀⠀⠀⠀⠀⢀⢀⠀⠀⠺⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡕⠁⠀⠀⠀⠀⠀⡎
⣤⣤⣤⣤⡄⠀⠀⠀⠀⣀⢸⣿⣿⣗⠚⠀⠀⠀⠀⠀⠀⣤⠒⠂⡱⠈⠀⠀⠁⠁⠀⠄⠀⠀⠠⠖⠀⠄⠀⠀⠹⣄⠁⠀⠀⠀⠆⠙⣖
⠉⠁⢀⠀⠴⠶⠒⠛⢇⡀⢠⡏⠛⢿⣿⡧⣤⣶⠸⠞⠀⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⣿⠉⢶⠪⣼⣄⣼⠀⢀⡄⠀⢀⠀⠠⠂⠌⠀⢆⠀⠀⢀⣀⡤⠂⠁⠐⠢⣴⣶⣧⠀⣀⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡏⠀⠐⠉⡍⠉⠉⠐⠨⠁⡙⠈⢈⠃⠀⠀⠀⠀⠁⢠⡄⠿⠁⠀⠀⠀⠀⠊⠛⠛⠠⢀⣀⡀⣀⠤⢀
⠀⠀⠀⠴⠾⠟⠛⢋⣽⣿⣿⣄⣀⢀⠀⠀⠀⠀⡠⠀⠈⠀⠘⠀⠈⠀⠐⠂⠀⠛⢃⠀⠀⠑⢀⠀⠰⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠛⠋⢀⣁⣠⡄⠀⡼⠈⡀⠐⠀⠠⠀⠘⠊⠒⡀⢁⡀⠀⠀⠀⠀⢀⣂⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⣀⠰
⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠶⠒⠛⠉⠉⠉⠀⣬⣄⣈⡆⠈⠀⠀⠀⠀⠀⠈⢰⡶⠁⣁⡀⠀⠠⣠⠀⠃⠠⠀⠐⠀⠐⠂⠘⣿⣿⣿⣿
⡶⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣔⠀⠠⠀⠀⠀⠠⠊⠂⠀⠀⠰⠋⠙⡛⠻⠁⢄⣀⠀⠐⠒⠒⠃⠈⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠀⠄⢠
⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠡⡀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣧⡘⣙⣆⠀⠀⠀⠀⠀⢠⠞⠹⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⢧⡶⠋⣻⣿⣿⡂⠀⠀⠀⢠⠟⣻⣤⠾⠻⡿⣯⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢃⣾⢿⣿⣿⣿⣷⠀⠀⠀⡜⢘⡶⠹⠛⢷⣼⡾⣯⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⣿⡟⠀⠀⠉⡛⢿⣿⣧⠀⣼⠃⣿⢡⠃⠀⠈⢿⡙⢿⡋⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣾⣿⠏⠀⠀⠀⠀⢃⠀⣿⣿⣄⡏⢨⡇⡞⠀⠀⠀⠈⣷⡙⣏⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠸⢱⠏⠀⠀⠀⠀⠀⠸⡀⡼⡏⣿⡄⡈⢠⠆⠀⠀⠀⠀⠸⡟⣟⡆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣠⣇⡿⠀⠀⠀⠀⠀⠀⠀⣿⣧⢻⠟⢣⠋⣿⠀⠀⠀⠀⠀⠀⢣⠀⠿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣹⣾⡿⣾⣄⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠶⠶⠤⠼⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣷⠇⢡⡖⢳⣴⢶⡆⣀⣤⡀⣤⡿⢿⣍⢉⣭⣁⡀⣀⡀⠀⠀⢀⠠⡀⣺⣻⠀⣤⣴⣰⡚⠟⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣸⡿⠛⠈⢸⢁⣆⣱⡎⣷⣯⣩⣿⣿⠆⣠⡿⢸⢁⣽⡿⣿⠟⣅⠈⣿⣶⣿⣿⣼⢸⣏⢨⣿⡇⢀⣟⣻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⢲⡆⠘⠛⠋⠋⠓⠛⠙⠛⠁⠙⠋⠉⠀⠈⠋⠛⠁⠉⠀⠀⠀⠛⠛⠓⠛⠚⠀⠛⠛⠛⠃⠈⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡟⢺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣩⠑⠛⣿⣻⡆⠀⠀⠀⠀⠀⠀⢰⠊⣟⣿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡂⣼⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠃⢛⣿⡇⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡚⠡⢂⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣴⠧⠭⡿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠏⢽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠁⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣗⣀⡸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⡀⢠⣰⡇⠀⠀⠀⠀⢀⡀⠤⠘⣄⡤⠒⠋⣉⣹⢿⡛⠓⣦
⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⢹⠀⠘⠙⠁⣀⡀⣶⠆⢻⡣⠀⠀⡸⠀⡌⠉⠁⠀⠀⣦⣠⠟
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣾⠄⣇⠝⠘⠋⠀⠀⢀⡠⡇⢠⡀⠀⡀⠀⣀⣹⣄⣀
⠀⠀⠀⢣⠀⠀⢀⠤⠰⡺⠊⣯⠅⠛⠁⠀⠀⣀⠤⠒⠉⠀⠀⠳⣤⢷⠞⢙⠈⠁⠀⠀⠉⠛⢗⠢⡀
⠀⠀⠀⠀⢣⠊⠈⠭⠇⠃⠀⠀⢀⡠⠔⢾⡍⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢁⠀⠀⠀⠴⢋⣠⢳⠹⡄
⠀⠀⠀⠀⠀⢃⠀⠀⣀⠤⠒⠉⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠀⠀⠀⠀⠐⠿⠃⠀⡇⣧
⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⣿⠀⡀⣠⡄⠒⠒⠁⣄⣀⡀⠀⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠸⣆⠙⠋⠹⢶⣒⣪⠏⢉⠔⡜⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢧⣖⣦⠀⠀⠀⠘⠦⠀⠀⠀⡄⠠⠖⢫⣞⣚⣁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢿⢨⠦⣄⣀⡞⠀⢼⣷⣶⣾⠖⠋⠉⠉⠉⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣥⠋⠀⠀⢹⡁⠀⠀⠁⠀⠁⠀⢀⣴⢲⡛⣯⡤⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣶⠴⠾⣧⡀⠀⠀⠀⠀⠀⠈⠹⠯⠗⠠⠤⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢻⣦⣤⠤⠴⠂⢛⣤⣿⣿⠛⠓⢤⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⡇⣿⣿⣿⣶⡶⢟⣩⣾⣷⣤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡧⢿⣌⡠⠖⣏⠳⢹⣮⣿⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⣦⣩⣇⠀⠀⠀⠀⣠⡊⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣉⣤⣿⣿⡄⠀⠀⢠⢫⠻⣮⣍⢫⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡾⠋⠙⡿⣿⣿⡀⢀⡏⣴⢁⠁⠘⢿⢿⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣯⣿⠏⠀⠀⠀⠃⠘⣿⣧⡸⢀⡏⡏⠀⠀⠈⣧⣻⡚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢏⡏⠀⠀⠀⠀⠈⣄⢿⣹⡧⣈⢰⠀⠀⠀⠀⠸⡻⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣼⠀⠀⠀⠀⠀⠀⣿⣇⣟⣣⡋⣿⠀⠀⠀⠀⠀⠇⠘⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣽⣷⣿⠀⠀⠀⠀⠀⠀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⠛⣠⢤⣠⣤⠀⠀⠀⢈⣿⣿⠛⠓⠋⠀⠀⠀⠀⠀⡀⠩⢥⠁⣀⣠⡤⣶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⢰⡿⠛⡆⡏⣬⢫⡘⣼⣉⣷⣿⠅⣸⢶⡏⣿⣿⡿⢦⠀⣾⣼⣾⣿⢴⡏⣹⡧⠀⣟⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠸⢸⢙⣲⡆⠉⠋⠉⠛⠋⠙⠉⠙⣉⠉⢀⣉⠋⠈⠁⠀⠀⠛⠛⠘⠛⠃⢛⠛⠋⠀⠛⠒⠃
⠀⠀⠀⠀⠀⠀⠀⡇⡞⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⣎⡉⢹⣿⠀⠀⠀⠀⠀⠀⡎⢹⣿⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠿⡃⡞⣸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣀⢠⣿⡆⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡿⣻⢀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣸⣄⠀⢘⣀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠙⡈⠉⠩⠉⠁⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠉⠙⣆⣎⣿⡹⣟⣿⣟⣧⣤⣻⣶⣿⣿⣿⣷⣶⣶⣄⠀⡇⠀⠀⠀⠀⢀⡄⠀⣧⣿⠀⠀⣀⣀⣀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠇⣤⣯⣴⣶⠞⡿⡿⣿⢿⡟⡛⠉
⠀⠀⠀⠀⠀⠘⡄⢾⣿⣟⣿⣿⣻⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠉⠉⠀⠂⡇⡇⢩⠨⡅⠁
⠀⠀⠀⠀⠀⠰⠰⠼⠿⠄⠬⠭⠭⠝⠁⠈⣻⣄⣉⣀⠈⠡⠬⠉⠍⠉⢱⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⠓⠀⠀⠚⠛⠂⠁⠀⠰⠶⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣿⣾⣿⡿⠀⡠⣦⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠛⠛⣟⠒⠓⠿⣟⣻⣿⣿⠾⠶⠄⠐⠀⠀⠀⠀⠀⢀⣴⡄⠀⣰⣦⡀⢀⣾⡆
⠀⠀⠀⠀⠤⣤⣴⣶⣿⣿⣶⣿⣷⣿⣿⣿⣿⡟⠀⣿⣶⡖⢉⣭⠀⠀⢉⣀⣼⣿⠟⠀⠀⠀⠀⠀⢸⣿⣿⡀⣿⣿⣧⣸⡿⠿⠂
⠀⠀⠀⠀⠀⠉⣿⣟⣋⣽⣟⠿⣿⠿⠭⠯⠭⠩⠵⠞⠛⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠉⠉⣁⣠⣬⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⠂⣶⡀⡀⠀⡇⠀⠀⠀⠀⢰⡂⣤⠤⠄⠀⣀⣀⣀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠾⢿⡿⠛⠛⠛⠛
⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠉⣿⣀⣀⣙⡇⠀⠀⠀⠀⢨⠀⠸⠆⠂⢀⣀⢸⣿⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡏⠀⠂⣀⡸⠀⠀⣀⣤⣄
⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠓⠛⠓⠲⠆⠀⠉⠁⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⠁⠈⣿⡿⠛⠿⠇⠀⠀⣿⣿⣀⠀⠈⠉⠻
⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠐⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⡄⠀⠏⠀⠀⣤⡄⠀⠘⣿⣿⠿⢿⣿⣶⡀
⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⣀⣠⢠⣤⣶⣶⣿⠿⠿⣿⣿⣿⣿⣿⡟⠻⠋⠉⠛⣁⣴⠆⠀⣹⡇⠀⠄⠀⢀⣿⡇⠀⠀⢿⣿⡄⠀⠈⠉
⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣟⣀⣤⣴⣶⣶⣿⣿⠻⣿⠈⢹⣿⣿⣷⠰⣆⢈⠋⠠⡀⠉⠃⠀⣶⠀⠀⠛⢁⠚⠀⠹⠇⠀⢠⡀⠀⠉⣠⠀⢀⣸⣿⣿⣶⣤⣤⣴
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢾⣿⣽⣷⡎⢿⣿⡇⠀⠻⠀⢨⠛⣙⣟⠀⣹⠘⡆⠘⠇⠀⠀⠀⣿⡀⣀⣦⣀⣰⣦⣴⣶⣤⣿⣿⣷⣿⠿⠷⠿⠛⠛⠛⠛⠉⠉
⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣻⣿⣿⣹⣷⢸⣿⠃⣄⠀⢀⠈⡘⠟⣻⡀⣁⣠⣿⣶⣶⣾⣿⣾⣿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠉
⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⣿⣤⣿⣶⠸⠶⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶
⠛⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠿⠛⠛⠋⢉⣉⣉⣁⣀⣠⢀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⢸⣿⣿⣿⣿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⠤⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠗⣁⢻⡛⠀⠠⠠⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⢀⠀⠀⣰⣀⠀⠄
⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⣄⠀⢸⣿⣿⣿⠇⢀⠀⢀⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⡀⠀⠐⠀⠀⠀⠄⠀⠙⡄⠤⠂⠈⠀⠀⠈⠉⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⠁⢈⠱⠿⠓⠀⡇⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⠄⢀⡀⠀⠀⠀⠀⢰⡀
⣤⣤⣤⣤⣴⠤⠀⠀⠀⢀⠀⣀⢨⣿⣿⣿⡟⠉⠀⠀⠀⠀⡇⠀⠀⣤⡂⠘⠀⡵⠀⠀⠠⠈⠀⠁⠀⡄⠀⠀⠀⠠⠞⠀⠤⠀⠀⠀⠈⣄⡨⠀⠀⠀⠀⠒⠈⠳⣂
⠉⡋⠀⠀⠀⣤⡴⠶⠾⢿⡊⠀⢀⣿⠙⠫⣽⣻⣷⢤⣤⡆⡷⡞⠀⠏⠁⢠⠀⠀⠀⠀⠈⠀⠀⠠⠄⠃⠄⠀⠀⡄⠘⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡛
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠓⣾⡛⢠⡤⢚⢸⡁⢸⡏⠁⠀⡄⠀⠀⠀⠀⢠⡇⢐⠀⢄⠈⠂⠀⠀⠀⢀⣠⠄⠃⠠⣄⣀⣠⣴⡄⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠈⡩⠼⡾⠻⠟⠓⡂⠒⠂⠬⡠⠄⢲⡀⠀⡀⠂⠈⢑⠆⠀⠀⢿⡟⠀⠀⠀⠀⠀⢉⢻⣿⣯⠀⠙⠀⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⠀⠀⠀⠘⠀⣀⠀⠀⠈⠁⠀⢰⠀⠀⡮⠀⢨⠀⠀⡀⠀⣀⣾⡆⠙⠃⠠⡄⠀⠀⠀⠀⠀⠀⢀⠈⠓⠲⠢⠤⠶⠉⠑⠒⡄
⠀⠀⠀⠐⠛⠛⠋⠉⠁⢰⣾⣿⣿⣷⣤⣄⠠⡀⠀⠀⠀⠀⠖⢀⠀⡄⢀⠁⠀⠀⢄⠀⡉⠀⠀⡍⠠⠀⠀⠀⠈⢢⡀⠐⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠛⠋⢁⣀⣠⣤⣤⠀⣠⠎⠀⡀⠑⠃⠀⠄⠀⠀⠋⠈⢁⡀⢀⡀⠀⠀⠀⠀⠀⢀⡡⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⣄⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠚⠛⠙⠋⠉⠠⢤⣅⡀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠄⠃⢤⣴⠁⠙⡀⡠⠈⢩⢁⠀⠑⠀⣄⠀⠐⠀⠀⠴⠂⠺⣿⣿⣿⣿⣿
⣤⣤⣤⡶⠶⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣇⣡⠄⠀⠀⠀⠐⠁⠀⣠⠚⡁⠀⢉⠉⡤⠒⠲⠾⠶⡝⢀⠀⠀⠀⠠⠤⠤⠴⠂⠙⠩⣉⠉⠉
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣥⣤⠆⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠂⠀⠀⣀⠛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⢠⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⢶⣶⣷⣄⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⡄⢀⠀⢀⠠⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢺⡀⠹⡄⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢹⠀⡇⠀⣇⣰⣻⡞⢠⡆⡗⠀⡠⠂⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⡇⠀⢸⠇⢹⣾⣿⢸⣿⣡⣾⣰⣧⡞⠀⡰⢣⠏⢀⡴⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⢆⢹⡶⠸⢿⣧⢀⣼⢠⣬⣿⣿⡋⠙⣿⢷⣿⡞⣠⢞⣴⣯⣑⡾⠀⣠⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢳⢠⣬⣷⠀⢻⣿⡟⠸⣟⢸⢿⣿⣿⣷⣀⢸⣿⣿⣾⣿⢿⣽⢿⣿⣡⡴⢣⢯⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⡗⣜⣾⣿⠻⣤⡈⢿⡧⠀⣿⠐⢺⣿⠃⠀⣸⣇⢻⡿⣿⡇⢸⢇⡞⠿⣹⣱⡷⠃⢨⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⣘⣌⣿⡏⢱⡞⣿⣸⣷⣾⣿⢸⢯⡟⠀⢀⣿⣯⣼⡧⣿⣧⣼⣼⠀⢀⣿⣯⢆⣴⡿⣡⡃
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠭⡙⠙⣿⡇⣼⡄⣿⡿⣷⣫⠭⣼⣿⡇⢀⣸⣿⣿⠟⢀⡨⠻⣿⣟⢰⣾⣻⣷⣟⡫⠂⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⠳⢿⢃⣿⡆⢻⡇⢠⢸⣿⢇⣾⣿⣟⢁⣴⡟⠋⣭⣿⣿⣿⣿⡿⠋⣼⠴⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡆⠀⣙⠻⢿⣸⣇⢼⣼⣿⡈⣿⣿⣿⣿⣿⣤⣤⣿⣿⠿⠛⠁⠀⠀⡏⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣇⠀⠠⢍⠀⠈⠉⠛⠛⠻⠷⠿⠴⠿⠛⠙⠛⠉⠁⠀⠀⠀⠀⠀⢰⡇⠈⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢹⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠒⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠒⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢷⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣤⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢒⢍⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⣻⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣾⣼⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢻⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠅⠀⠀⣀⣤⣤⣀⠈⢢⡀⠀⠀⠀⣰⣟⠂⠀⣴⠞⠻⣷⡄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀⣴⠃⠀⠈⠻⣦⡀⠙⢄⠀⢰⣿⡃⠀⣼⠃⠀⠀⠘⣿⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠄⠀⢠⡏⠀⠀⠀⠀⠙⣿⡄⠈⢧⣼⡿⠀⢀⡏⠀⠀⠀⠀⠘⣿⡄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⢸⡇⠀⠀⠀⣀⣀⣈⣿⣆⠀⢻⣯⠀⢸⣇⣀⣠⣤⣤⣄⣹⣯⡄⠈⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⠀⠀⢸⣷⠿⢿⣛⠛⠛⠛⠛⣿⣖⡀⠻⠀⢸⣯⣭⣭⣭⡍⠉⠙⣿⣗⠀⠸⣿⣿⣿⣿⠿⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⢻⣯⠄⠀⠈⣿⣻⣯⣭⠄⠀⠀⠀⠘⣿⣆⠀⠀⢸⣷⠶⢶⣖⠒⠀⠀⢿⣷⡂⠀⢻⣿⣿⣭⣥⣤⣄⣀⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⣠⣾⣋⡥⠀⠀⢸⣿⡥⠀⠀⢹⣯⠶⠶⠖⠀⠀⠀⠀⢹⣿⣆⠀⠀⣿⣿⣭⣭⡅⠀⠀⢸⣿⡗⠀⠘⣷⠶⠶⠶⠶⠦⠍⠁⠀⠀⠐⠈⠻⣆
⠀⠀⠀⢰⡿⣛⣥⠶⠃⢀⣈⣿⣯⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣤⣤⣿⣿⣛⡛⠻⠳⠶⠆⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠘⠻⣯⡷⢞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⡿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠟⠳⠶⠖⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢈⣿⣹⣿⣿⣿⣿⣿⡿⠿⡟⢻⡟⣩⣽⣧⢰⡶⢈⣯⠸⠗⣹⡇⢶⡆⣿⠛⡇⢸⡇⢸⠋⣹⠋⣿⣻⡿⢿⣤⣾⣿⣿⣛⣛⣛⡛⣠⡾⠃
⠀⠀⠀⠀⢀⣼⡿⠗⣿⣿⣿⣿⣿⣧⢰⣀⣦⣿⣬⣴⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣬⣤⣿⣿⢦⠲⣿⣿⣿⣯⣭⣍⣩⡾⠋
⠀⠀⠀⣰⣿⡿⠞⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣥⡶⠛⠁
⠀⠀⢰⣿⣵⠞⣛⣉⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠘⣿⡶⢛⣩⣤⠶⢸⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⢹⡏⣿⣿⣿⣿⣓⣿⢉⣋⣻⣽⡿⠿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠙⢿⣿⣉⣤⡶⢛⣫⣭⠿⠚⢀⣀⣤⡴⠤⢀⣀⣤⡄⠀⣀⣀⣸⣷⣿⣿⣿⣿⢥⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣯⣤⣶⣾⣿⣭⡶⠶⠿⠿⠿⠛⠛⠛⠋⠉⠉⣿⢹⣿⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣿⣿⣿⣓⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠸⠿⠿⠿⠹⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⡊⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠊⣥⡴⣿⢋⠀⠘⣆⢀⣠⡤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠘⣷⡹⠟⢻⡆⠘⣏⣁⡤⣲⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠸⣧⢺⣾⠗⠠⠋⠀⠈⢩⣩⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠉⣁⣤⠒⡷⠒⢶⠂⢜⠳⣼⡇⠹⣿⣦⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⢩⢿⡟⣶⣿⠈⠈⣧⣸⢀⣿⣇⠐⡿⢿⣧⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢰⠃⢸⡇⢽⣟⠂⡔⠤⠦⠎⢉⣤⡸⣇⠈⣿⣧⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⢀⣿⠀⢸⡇⠈⣿⣇⢳⡄⠀⠀⢛⣃⣀⣉⢢⣿⣿⣇⠈⣇
⠀⠀⣀⣀⣀⣀⡀⠀⢠⣿⠃⠀⡞⣿⠀⢸⡇⠀⣿⠁⣻⣿⣿⣿⣿⣷⣬⣿⠉⣿⢹⣿⡆⠸⡆
⠀⠘⡿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⡐⠚⠓⠒⠛⠒⠛⠿⠿⠽⠿⠿⠷⠿⣀⣿⣀⣿⣷⡀⣻⡀
⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣧⣾⣇⡴⠆⢰⠶⣦⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⡄⠈⠉⠉⠉⣱
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡽⣿⠛⠓⢠⣟⣠⡿⣞⣹⡞⢻⣀⣿⢦⣏⡤⣾⠁⢴⠆⠀⠀⢰⣿
⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⢈⠁⠀⡀⠀⠈⠀⠀⠉⠀⠁⠉⠈⠉⠉⠈⠙⠁⠘⠋⠀⠀⠀⢸⣿
⠀⠀⠀⢿⡄⠀⠀⠀⠀⣀⠀⡀⠃⣉⠘⢈⠁⠋⠃⢁⠀⠀⠀⠀⠘⠃⠃⠓⠀⠒⠉⠘⠐⠗⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣷⡀⠀⠀⠀⢿⣈⣿⢰⣿⡄⢻⣇⣸⡇⣿⣻⢾⡇⣿⢹⣿⡇⣿⠓⢸⡋⢺⣻⣾⡿⠂⠀⢸⣿
⠀⠀⠀⠈⣿⡇⠀⠀⠀⢸⡟⣿⢸⣿⣧⢸⣿⣿⣇⣿⣻⡆⣇⣿⢸⡟⣇⣿⣻⢸⡏⢸⣿⣆⣹⡆⠀⢸⣿
⠀⠀⠀⠀⢿⣷⠀⠀⠀⠘⠃⠛⠚⠃⠙⠘⠋⠛⠛⠙⠛⠁⠙⠋⠘⠁⠋⠙⠋⠈⠛⠈⠉⠉⠉⠁⠀⠸⣿
⠀⠀⠀⠀⢸⣿⡀⠀⢠⣦⣤⠀⣶⣠⣄⣤⠀⣤⡤⣤⠂⣤⠤⠤⠰⡿⢾⠀⠶⠾⠆⠤⠸⠿⠿⠆⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⢤⡿
⠀⠀⠀⠀⠀⢹⣿⡇⠙⢙⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣠⣾⣄⠀⠀⠀⣴⣿⡀⣿⣷⠀⢧
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⠀⡀⢀⣶⣿⣷⠀⢸⣿⣿⣦⣀⣤⣿⣿⣿⣿⣿⣀⣾⣿⣹⣷⣿⣿⠀⢸
⠀⠀⠀⠀⠀⣾⣿⠁⠀⢸⡇⠀⢀⣿⣿⡟⢿⣿⣿⣿⣧⣍⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⣠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⠷⠖⢶
⠀⠀⠀⣤⡴⠿⣿⣄⣤⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣇⣴⣶⡶⠦⠾⢤
⠀⠀⠀⣿⣿⣷⠚⠓⠃⠉⣉⠉⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣹⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⣀⣀⡀⠸
⠀⠀⠀⢿⣿⣿⠀⠀⢸⣿⣦⡬⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⠤⠄⠒⠒⠂⠈⠉⠉⠁
⠀⠀⠀⠀⠉⠛⠃⠒⠚⠻⢿⣇⣀⡀⠤⠤⠤⠐⠒⠒⠂⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⡊⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠊⣥⡴⣿⢋⠀⠘⣆⢀⣠⡤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠘⣷⡹⠟⢻⡆⠘⣏⣁⡤⣲⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠸⣧⢺⣾⠗⠠⠋⠀⠈⢩⣩⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠉⣁⣤⠒⡷⠒⢶⠂⢜⠳⣼⡇⠹⣿⣦⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⢩⢿⡟⣶⣿⠈⠈⣧⣸⢀⣿⣇⠐⡿⢿⣧⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢰⠃⢸⡇⢽⣟⠂⡔⠤⠦⠎⢉⣤⡸⣇⠈⣿⣧⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⢀⣿⠀⢸⡇⠈⣿⣇⢳⡄⠀⠀⢛⣃⣀⣉⢢⣿⣿⣇⠈⣇
⠀⠀⣀⣀⣀⣀⡀⠀⢠⣿⠃⠀⡞⣿⠀⢸⡇⠀⣿⠁⣻⣿⣿⣿⣿⣷⣬⣿⠉⣿⢹⣿⡆⠸⡆
⠀⠘⡿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⡐⠚⠓⠒⠛⠒⠛⠿⠿⠽⠿⠿⠷⠿⣀⣿⣀⣿⣷⡀⣻⡀
⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣧⣾⣇⡴⠆⢰⠶⣦⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⡄⠈⠉⠉⠉⣱
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡽⣿⠛⠓⢠⣟⣠⡿⣞⣹⡞⢻⣀⣿⢦⣏⡤⣾⠁⢴⠆⠀⠀⢰⣿
⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⢈⠁⠀⡀⠀⠈⠀⠀⠉⠀⠁⠉⠈⠉⠉⠈⠙⠁⠘⠋⠀⠀⠀⢸⣿
⠀⠀⠀⢿⡄⠀⠀⠀⠀⣀⠀⡀⠃⣉⠘⢈⠁⠋⠃⢁⠀⠀⠀⠀⠘⠃⠃⠓⠀⠒⠉⠘⠐⠗⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣷⡀⠀⠀⠀⢿⣈⣿⢰⣿⡄⢻⣇⣸⡇⣿⣻⢾⡇⣿⢹⣿⡇⣿⠓⢸⡋⢺⣻⣾⡿⠂⠀⢸⣿
⠀⠀⠀⠈⣿⡇⠀⠀⠀⢸⡟⣿⢸⣿⣧⢸⣿⣿⣇⣿⣻⡆⣇⣿⢸⡟⣇⣿⣻⢸⡏⢸⣿⣆⣹⡆⠀⢸⣿
⠀⠀⠀⠀⢿⣷⠀⠀⠀⠘⠃⠛⠚⠃⠙⠘⠋⠛⠛⠙⠛⠁⠙⠋⠘⠁⠋⠙⠋⠈⠛⠈⠉⠉⠉⠁⠀⠸⣿
⠀⠀⠀⠀⢸⣿⡀⠀⢠⣦⣤⠀⣶⣠⣄⣤⠀⣤⡤⣤⠂⣤⠤⠤⠰⡿⢾⠀⠶⠾⠆⠤⠸⠿⠿⠆⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⢤⡿
⠀⠀⠀⠀⠀⢹⣿⡇⠙⢙⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣠⣾⣄⠀⠀⠀⣴⣿⡀⣿⣷⠀⢧
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⠀⡀⢀⣶⣿⣷⠀⢸⣿⣿⣦⣀⣤⣿⣿⣿⣿⣿⣀⣾⣿⣹⣷⣿⣿⠀⢸
⠀⠀⠀⠀⠀⣾⣿⠁⠀⢸⡇⠀⢀⣿⣿⡟⢿⣿⣿⣿⣧⣍⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⣠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⠷⠖⢶
⠀⠀⠀⣤⡴⠿⣿⣄⣤⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣇⣴⣶⡶⠦⠾⢤
⠀⠀⠀⣿⣿⣷⠚⠓⠃⠉⣉⠉⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣹⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⣀⣀⡀⠸
⠀⠀⠀⢿⣿⣿⠀⠀⢸⣿⣦⡬⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⠤⠄⠒⠒⠂⠈⠉⠉⠁
⠀⠀⠀⠀⠉⠛⠃⠒⠚⠻⢿⣇⣀⡀⠤⠤⠤⠐⠒⠒⠂⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⢀⣴⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣦⡀
⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣶⣆⣴⣶⠀⣠⣤⣄⢰⡶⢶⡄⢀⣤⣄⠀⣤⣤⣄⢀⣤⣤⡄⢸⡇⣠⣤⣿⡆⡿⢀⣤⣤⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⢠⣿⢻⡟⣿⡜⣿⣠⡥⢸⣧⣼⠏⢿⣧⣿⠃⣿⠀⣿⢰⣞⣻⡇⢸⡇⢿⣥⣿⠇⠀⢨⣟⣷⠄⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠈⠻⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⢄⠀⠀⠀⠀⠀⠀⣠⠖⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣠⠒⣄⠀⢳⡀⠀⠀⠀⡼⠁⢠⠖⢦⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⠘⡆⠀⢳⠀⠀⡸⠁⢀⠇⠀⠈⢧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡇⠀⠀⠀⢸⡀⠈⣇⢰⠃⠀⡞⠀⠀⠀⠘⡆⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣸⠀⠀⠀⠀⠀⣇⠀⠸⡏⠀⢰⠃⠀⠀⠀⠀⢳⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⣸⠀⠀⠀⠀⠀⠸⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣸⠀⠄⡠⠄⠀⣀⡈⡇⠤⠤⣠⠃⣀⣀⢀⣀⣀⠀⢹⣀⣤⠼⠀⣀⠤⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣼⠁⠀⠁⠀⠋⢠⢈⡇⢰⣢⠀⠋⢠⡈⠋⢉⠈⠹⠁⠀⣻⠀⠃⣤⠀⣖⡁⠈⢥
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠃⠜⠢⠴⠤⠤⡣⠤⠤⠶⠱⠤⠴⠣⠜⠢⠴⠤⡤⠾⠴⡦⠤⠤⠓⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠈⠉⠒⢄⠀⠀⠀⠀⢀⣾⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣠⠖⢶⣄⠑⢄⠀⢀⣿⠁⣠⠋⠙⢷⡄⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⢠⠇⠀⠀⠙⣷⡈⢢⣸⡇⢀⡏⠀⠀⠈⣿⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣀⣀⣀⣀⣈⣷⡀⢻⡇⢸⣧⣤⣤⣤⣼⣿⠀⢳⣄⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣤⣾⣧⠀⢸⣿⣿⠯⠉⠉⠙⣿⡄⠁⢸⣷⣗⣒⡂⠀⣿⣇⠈⣿⣿⣟⣉⠛⠳⠶⣤⣀
⠀⠀⠀⣠⣞⡫⠀⢸⣿⡄⠀⢿⡭⠷⠆⠀⣀⣹⣿⡀⠈⣿⣿⣷⠂⠀⢹⣿⠀⢹⡿⠿⠭⠭⠙⠀⠀⠉⠳⣄
⠀⠀⢸⣿⡵⣚⣠⣬⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣛⣓⣀⣀⠀⠀⢹
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⣿⢟⣿⢩⣍⣿⢫⣽⡏⣭⢹⣿⡟⣿⢻⢟⠟⣿⣿⣟⣩⣿⣿⠿⠿⠄⣠⠟
⠀⠀⠀⣠⡿⠿⣿⣿⣿⣿⣠⣰⣽⣭⣿⣦⣶⣿⣷⣾⣷⣿⣿⣿⣷⣿⣾⣬⣥⣿⡧⠾⣿⣿⣿⣯⣩⠞⠁
⠀⠀⣼⣿⣯⠥⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠋⠁
⠀⠀⣿⡽⣞⣫⠼⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⣿⢻⣿⣿⣿⡟⣛⣻⣿⡿⠿⠿⠿⠟⠁
⠀⠀⠘⠿⣯⣴⣞⣭⠿⢛⣠⡤⠶⣂⣤⣤⣀⣠⣤⣿⣸⣿⣿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⣤⣶⠶⠤⡶⠶⠶⢶⣤⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⣘⡿⢿⡟⠓⣶⡲⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⢈⣿⣯⣼⣫⣿⣉⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠁⠀⠃⠀⡞⡅⠴⠊⢴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣦⣄⣰⣀⣄⣄⣀⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢛⣿⣿⣿⣯⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⠄⣀⠀⢀⠀⢻⣿⣿⢢⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⠀⠀⠀⠀⠀⠀⢘⡶⣄⠉⠺⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⣴⣄⣀⠠⠾⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣠⠀⡈⢠⣼⢿⣿⣿⣿⣿⣧⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠌⣡⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣠⣼⣷⣿⣽⣾⣿⣦⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⠘⣏⣱⡞⢭⣿⣿⠧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⢟⡘⣿⣿⣷⣤⡜⣿⠻⡯⣟⢒⡄⠤⠶⣾⣹⢿⠿⢋⡹⣿⡏⣸⡃⢹⣄⠁⠲⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⠀⠀⠈⠿⠛⠙⠛⠛⠓⠚⠙⠒⠖⠛⢛⠙⠛⠋⠛⠛⠛⠺⣾⣿⣷⢽⣙⣦⣀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣶⠿⠷⠾⠦⣬⣌⣀⣀⠼⣗⡋⣤⠀⠢⡤⡄⢀⠀⠀⣁⣰⣴⣿⣿⣏⠉⠻⠯⡙⢲⠟⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠻⣆⠀⠀⠀⠀⠂⠈⠉⠙⠛⢛⣛⢛⠛⠿⢷⣿⣿⣿⣿⣿⣿⣿⣍⠻⡿⣶⣦⣈⣿⡷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣉⠓⠶⣤⣤⣄⣠⣀⣀⡀⠀⠀⠀⠀⢰⢎⣿⣿⣿⣿⣿⣿⣿⣽⣦⡷⠿⠟⣫⣵⣿⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣍⡙⠲⠦⢬⣭⣍⣉⣛⣛⣛⣛⣻⣻⣟⣛⣛⣻⣛⣻⣿⣯⣭⣥⡴⠶⠞⣛⣿⣿⡿⢛⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢍⣛⠓⠶⠦⢤⣬⣭⣉⣉⣉⣋⣉⣉⣉⣉⣭⣭⣭⣭⣵⣷⡶⠶⠾⠛⣋⣩⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠠⠤⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡿⠶⠖⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡤⠤⠄⢀⣀⠀⡸⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠈⡉⠉⠉⠁⠀⠀⠒⠂⠐⠈⠉⠉⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⠤⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠘⠉⠭⠽⠟⠛⠛⠛⠋⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠻⠛⠛⠓⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⠤⣄
⠀⠀⠀⠀⠀⢀⡴⢚⠁⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢦⡀⠀⢀⣠⡤⠖⠛⣉⠥⠄⠠⠜⠻⣦⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠁⠀⠔⠊⠉⠴⠊⠩⡝⢳⣄⡀
⠠⢶⠤⣰⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⢣⡺⡤⣿⣌⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣠⢼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡲⠤⣄⣀
⡠⢀⠙⠺⠻⣷⣶⡤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣩⡾⡃⣀⣚⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣤⣽⣦⣀⠤⢶⢺
⠀⠐⠣⡅⣙⢄⣋⣭⣛⣓⣶⠶⢶⣤⡤⣤⡴⠶⠶⠶⠶⠚⡟⠛⠶⠿⢱⣚⡏⠩⠈⠓⢄⡀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢿⢿⠿⠿⠟⠛⠉⠉⢀⣀⣼⠿
⠀⠀⣾⣷⡔⠀⢨⠃⠂⠘⠑⠷⢶⣧⣲⡖⠃⢂⡵⠷⠒⠛⣓⣲⡒⠄⡽⣿⡀⠀⠀⠀⠀⠙⠢⣀⣴⡟⠛⢿⡟⠀⣠⣲⣷⣲⠶⢶⣒⠚⠿⢍⡳⢤⣤
⠀⠀⡟⠬⡙⠗⠦⣤⣀⠀⠀⣀⣀⠀⠀⣙⡉⠀⢀⠭⠒⣈⠡⠖⠴⠼⢂⣿⡁⢠⢠⡔⠀⠀⢠⣾⡇⠘⡳⡖⠀⡴⣱⡁⢸⡌⠉⢳⢦⣍⡒⠤⣉⣲⠖
⠀⢀⠛⣦⡘⠀⢀⡈⠉⠛⠖⠀⣀⣀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣠⠎⢱⠙⢦⡸⢃⠄⠀⣾⣿⡇⠀⣷⡉⢙⡴⣝⢧⡀⣷⠀⠈⣶⣄⣹⣲⣇⡰
⠀⠐⡀⠈⠀⠩⠴⠿⠧⠤⠤⢤⣁⣉⣥⣌⡱⣶⡴⠭⢄⣒⣂⠭⠔⠋⠀⡸⠀⠀⠙⢼⠃⢠⡟⣿⣿⠀⠸⣿⡋⠵⢾⣭⣏⣻⡖⠐⡧⣄⣈⣉⣏⣹
⠀⠀⠑⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠙⢮⡇⠈⢻⠇⠀⢳⡉⠲⣤⣄⠤⣞⠛⢟⠿⣓⠊
⠀⠀⠀⠀⠈⠉⠒⠛⠛⠉⠁⠲⠶⠶⠶⠦⠤⠤⠄⠀⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢿⠭⡛⡘⣤⡉⢉⠇⠈⠑⢤⣙⡚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣈⣆⠱⣸⣌⣄⠉⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣃⢸⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⡏⠀⠀⠀⠀⢀⡠⢄⢴⠊⠉⢱⡀⡏⠉⠀⣁⢀⠖⠤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠰⡁⠀⠈⢎⡆⠀⠀⢣⠡⠀⠀⢠⡌⠀⠀⡰⡰⠁⠉⢢
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣼⠀⣧⣤⣤⣤⣀⣱⡀⢺⠁⠘⡀⠀⠀⣾⠀⠀⢸⠁⠀⢠⠛⠳⡄⢀⠎
⠀⠀⠀⢰⡉⢖⠉⠉⠀⠀⠀⠘⠤⠃⠀⠀⠀⠉⢁⡣⢉⣇⠀⢇⠀⠀⢹⠀⠀⡍⠀⠀⠸⠀⡸⠀⡎
⠀⠀⠀⢸⠪⠭⢉⣛⣒⣛⠛⠚⠶⠚⠛⣛⣚⣛⡉⠭⠑⡟⡀⢸⠀⠀⢸⠀⠀⠇⠀⠀⡇⠀⠇⣼
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠧⣀⡇⠀⠸⠀⢸⠀⠀⠀⣃⡴⠊⠸
⠀⠀⠀⠀⡇⠀⠀⠀⣼⢷⡀⠀⠀⠀⢠⡾⣦⠀⠀⠀⢸⡀⠀⠈⠉⠒⠓⠒⠚⠒⠒⠉⠁⠀⠀⡇
⠀⠀⠀⠀⢡⠀⠀⠈⠁⠀⢁⣴⣶⣦⡉⠀⠈⠁⠀⠀⡏⡇⠀⠞⠋⠳⠀⠀⠀⠀⠞⠉⠳⠀⢰
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣿⡟⣻⠁⠀⠀⠀⠀⢠⠄⢻⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠁⢀⣀⠀⣀⠀⢼⢀⣸⡀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⡝⡤⠖⢀⣉⣛⠫⠽⠿⣓⠒⠶⣶⣶⣶⣶⣤⣬⡿⣍⡓⠛⣉⣐⡶⣚⠭⠭⠓⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⡴⠛⢒⡒⢛⡒⠢⠤⠤⠒⢬⠲⣦⣄⣢⣶⠖⠥⠦⠶⠶⠛⠛⠛⠚⠲⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠉⢲⠋⠀⠀⠰⠃⠈⠁⠺⡄⠘⣀⠘⢣⡄⠰⠂⣰⠂⡤⢸⡇⣨⡃⠘⠁⠀⠀⠀⠱⡖⠁
⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠆⠤⠤⠤⢀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⡀⠤⠤⠄⠒⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠉⠀⠀⠀⣠⠤⠀⠀⠐⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠒⠤⡄⠴⡴⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠞⠣⠒⠗⠒⠀⠀⠀⢄⢠⠤⠄⠤⣤⠲⠈⠀⡠⠶⠈⠑⠀⠤⣥⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣁⣂⣀⠁⠀⠈⠀⠀⠀⠀⠀⢂⠤⣎⣁⠠⠄
⠀⠣⠀⠐⠠⠄⠀⠀⠀⠤⠀⠀⠀⢠⠞⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠐⠁⠀⢠⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠄⠊⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠓⠦⢀⡀⠀⡠⠖⡩⠄⠀⠀⠀⢸⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⠈⠀⠈⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠭⠔⠉⠀⠀⠀⠀⠀⠘⡇⡞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠄⢠⡄⠀⠒⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠀⠄⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠈⠀⢠⠘⣠⠀⠅⠤⠀⠃
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⢀⡌⠀⠈⠀⠸⠁⠐⠀⠀⢀⠁⠉⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠠⠴⠄⠊⠀⢀⠘⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡜⠚⠀⠁⠂⠀⠀⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⣴⠄⢀⡀⠙⠂⡀⢀⡀⠀⠀⠐⠧⡄⠣⡀⠀⠀⠀⠀⠀⠛⡠⠄⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⢠⣄⣀⠀⠀⠀⢀⠀⠐⠠⠤⠀⠉⠈⠒⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠠⢌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠈⠀⢀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⢆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀
⠰⢦⡀⠴⠄⠦⠔⠃⠀⠀⣀⠤⢠⡄⡶⠠⢄⠀⡆⠀⠀⠀⡀⠀⡝⠤⢀⡀⢠⡄⢤⣤⠀⣀⡠⠄⠀⡢⠄⠠⠄⠀⠀⣀⠤⠀⢨⣅⡰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⡥⠀⣶⠀⠀⠀⠀⠀⠀⠀⠁⢀⢈⣛⡀⠀⢠⠀⠀⠘⠡⡤⠀⠁⠀⠕⠀⢀⡀⣤⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠐⠈⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢩⠁⠀⣠⡀⠑⠓⠐⠆⠀⠀⠀⠀⠈⠉⠀⠉⠀⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⣀⣀⣈⡀⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⠀⠈⠁⠉⠀⠦⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠷⠀⠀⠐⡶⠀⡀⠀⠀⣀⡀⠀⠁⠀⠄⠀⠺⢷⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠔⠀⠀⠠⠤⠀⡀⠠
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠌⠓⠀⠀⠁⠀⠒⠀⠀⠀⠑⠠⠌⠂⠉⠐⠂⠉⠀⠀⠀⠀⠔⠀⠑⠒⠂⢀⣁⡀⠀⠈⠁⡠⠀⠀⠀⠄
⠀⣤⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠆⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⡀⠀⠀⠀⢈⠄⠠⠐
⡇⠀⠀⠁⢄⠘⠦⣄⢠⡄⠔⠀⠘⣰⠀⠀⠀⣀⣦⠄⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠡⠀⠀⣤⠀⠀⠀⢠⠁⠀⢠⡏⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠄⡀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡀⠘⢇⣀⠀⣀⠀⠔⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢋⡤⠀⠀⠀⠀⠐⢀⠁⠀⠀⠠⠒⠈⠉⠉⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠇⠀⠀⠀⠀⢀⠄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠤⡀⠀⢀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⢰⠀⠀⠃⢄⣀⡀⢀⣀⡰⠞⠀⡈⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠊⠔⣈⠉⠋⣀⠲⠀⠀⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣊⠤⠖⠶⠤⡑⠀⠀⠡⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⣀⡀⣀⣀⠈⠁⠈⠣⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡧⠼⣀⠀⠀⠀⠀⠀⠆⠀⠴⠀⠀⢀⠤
⠀⠀⠀⠀⠓⠈⠜⢉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣰⠁⠀⠀⠀⠀⢠⠈⠁⠜⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢀⣌⠉⠉⠉⠉⠉⠉⠉⠁⠀⠁⠈⡀
⠀⠀⠀⡠⠴⡒⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⡰⠠
⠀⠀⡆⠀⠀⠸⠀⠀⡀⠀⠀⠀⠀⡔⠚⠀⠀⠂⠀⡀⠀⠀⠀⠀⠆⠂⡀⠀⠀⠀⠀⠀⢠⠂⡀⠀⠀⠂⠀⠀⠀⠀⠰
⠀⠀⢡⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⡄⠀⠀⠄⠀⠄⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⣀⡈⠀⠀⢀⠀⡠⠊
⠀⠀⠘⡄⠀⡁⣠⠑⠊⠁⢄⠀⠀⠀⠀⠀⠀⡀⡦⣰⣆⡤⠀⠀⠀⠘⠀⠀⠀⠊⠉⠉⠀⠣⠀⡇⣀⣱⠀⠀⡀
⠀⠀⠀⢇⠀⠉⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣀⣀⠀⠠⣄⠜⠀⠀⡇
⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠡⠤⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠒⠒⠒⠶⠦⠴⢃⠀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⠙⣿⣿⠏⣩⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣇⢸⡏⢰⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⠀⠁⣾⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⡄⠀⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣉⣈⣹⣇⣆⣉⣏⣩⣝⣋⣉⣉⣅⣏⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡀⠀⠠⠅⠀⠀⡠⠂⠈⠢⡈⠁⠠⠄⠄⠀⠂⠀⢀⠴⠀⠐⠛⠻⠀⠸⠇⠄⠄⢄⠀⠀⠊⠅⠀⠀⡠⠊⠉⠠⢀⠇⠘⡄⢀⠀⠀⠀⢀⠴⠀⠐⠛⠳⠁⠸⠔⠠
⠀⠀⠈⠀⠐⠀⠂⠁⠀⠀⢀⠜⠀⠀⠖⠀⠨⠀⠠⡀⠀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠑⠄⠀⢀⠘⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀
⠺⠂⠳⣀⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠠⠀⠠⠃⠀⠈⠠⠈⠀⡔⠓⡜⢂⠀⣾⠃⠺⢆⠽⣠⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠂⠔⢂⠀⣺
⠀⠘⠂⠁⠀⠀⡠⠐⠀⠁⠐⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠈⠲⢪⡖⡛⠀⢙⠒⠂⠛⠛⠏⠀⠀⠠⠐⠀⠀⠐⠢⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠈⠶⢢⠔⡛⠀⢛
⠀⠀⠀⠀⠀⠀⡶⠤⣂⢴⡤⢴⡆⠀⡏⠀⠄⢩⠂⠀⠀⠆⠐⠈⡧⢾⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠄⣂⢠⡆⢶⡆⠀⡍⠀⠈⢩⠂⢰⠀⠀⠀⠈⡳⢮⠃⠀⠈
⠀⠀⠉⠀⠀⠀⠉⠉⠷⠘⣣⠍⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠆⠀⠐⠂⣀⢀⡀⠁⠀⠀⠉⠀⠀⠀⠉⠉⠳⡜⣫⠝⠁⠀⢠⠀⠀⡀⠀⠀⠑⠀⠆⠀⠐⠂⢀⢀⡀
⠀⢀⠊⠀⠈⢢⠀⠀⠀⠈⠁⠀⠀⠀⠸⠄⠀⠄⠀⠀⢀⣲⠦⠀⠀⡁⠀⠀⡀⣥⠀⠠⠈⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⣶⠦⡀⠰⡉⠀⢀⡀
⠀⢨⠀⠀⡠⠂⢀⢀⣑⠄⢀⣴⠤⠂⠀⠀⠀⣦⣡⡾⠟⠁⠀⡀⠀⠀⠂⠀⠀⡀⠀⢀⡀⠀⡀⠂⠀⢂⡐⠄⢀⡕⠴⠠⠀⠀⠀⣤⣱⡾⠟⠋⠀⠀⠀⠁
⡄⢢⠘⠈⠀⠀⢈⠠⡔⠲⠵⠷⣄⠒⠀⠀⠈⢜⠁⠀⠀⠠⠊⠀⠀⠀⠒⠐⠀⠀⠄⠡⠚⠈⠀⠀⠄⠀⡴⠲⠾⠶⣄⠂⠀⠀⠀⢎⠀⠀⠀⠠⠊⠀⠀⠈⠂
⢀⡁⠀⣀⠀⠀⠈⢐⠂⠠⠄⢂⠄⢀⠀⢠⣂⠀⠀⠀⠀⠀⠘⠀⠇⡈⣄⠀⠀⠀⢀⡀⠀⣀⠀⠀⠐⢐⠂⠠⠄⢂⠄⠀⠀⣘⣀⢀⠀⠀⠀⠀⠸⠁⠇⡘⡀
⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡯⠇⠀⠀⢀⠀⡰⠂⠺⠀⠀⠠⠀⠌⠢⠰⠁⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⣠⡿⠇⠀⠀⢀⠀⡯⠒⠲⡀
⠀⠃⢀⠀⠀⠀⣠⠄⠒⠀⠲⠀⠐⠂⠁⠂⠈⠁⠐⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⢀⠀⠃⠀⢠⢄⡒⣀⢶⣄⠐⠂⠑⠐⠈⠁⠐
⠀⠂⠁⠐⠊⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⡀⡀⡀⠀⠄⢀⡀⠀⠀⢀⠀⠀⠀⠒⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⡆⣀⠠⠀⠒⣀⠁⠀⠦⢷⠀⠘⡉⠁⡙⠀⠀⠀⠉⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⣂⣀⠠⠀⠒⡀⠁⠀⢨⠷⠄⠘⠃⠉⠛⠀⠀⠀⠉⠀⠀⠉
⠉⠀⠉⢉⡄⠀⠀⠀⠀⢀⠨⠀⠁⢀⣀⡀⠄⠀⠠⠀⠀⡀⠴⣀⢦⠀⢀⡁⠉⠀⠉⠀⠋⢉⡆⠀⠀⠀⠀⠀⡤⠀⡃⠀⢌⡄⣄⠀⠃⠀⠂⠠⠴⣐⢦⠀⢀⡀⠉
⢉⣑⠈⢛⠄⠀⠀⡠⠊⠈⠐⡈⠃⠀⠖⠀⢀⠂⠀⣀⠖⠐⠒⠋⠺⠀⠰⡃⣀⣄⢢⣄⠨⢋⠖⠀⠀⡀⠊⠈⠀⢀⠃⠐⡔⠀⠀⠀⠀⠀⠔⠐⠒⠉⡳⠁⠘⡏⣑
⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⢀⠘⠀⠀⠔⠀⠰⠀⠨⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢋⠐⠀⠀⢀⠜⠀⠀⠆⠂⢀⠀⠈⡀⠀⠀⡠⠈
⠿⣆⡵⣠⠀⠀⠈⠃⠈⠃⠀⠀⠀⠀⠂⠀⠀⠃⠀⠈⠂⠊⠀⡐⡁⣜⢂⠀⣷⢃⡿⢂⠵⣠⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈⠂⠂⢀⡜⡁⣄⢂⠀⣾
⠒⠛⠈⠁⠀⠀⡀⠂⠁⠀⠁⠢⠀⠀⢀⣀⣃⣀⠀⠀⠤⠀⡀⠒⠢⢔⡚⠁⠙⠐⠓⠛⠋⠇⠀⠀⠀⠀⠉⠉⠁⠢⠀⠀⢀⣀⣂⣀⠀⠀⠤⠄⡈⠖⠢⢔⡺⠀⢋
⠀⠀⢀⠀⠀⠀⡷⢒⣒⢒⡒⢶⡇⠐⡅⠀⠀⢨⠂⢀⠀⠆⠀⠈⡗⠺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⢒⣂⢒⡒⢶⡆⠐⠍⠀⠀⢨⠂⢰⠀⠀⢐⠈⡷⢮⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠌⠶⡜⣣⠍⠀⠀⢀⠀⠀⠈⠀⠀⠁⠒⠒⠀⠐⢂⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠙⠌⠷⠜⣯⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⠒⠂⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠆⠀⠀⣐⣶⠶⡄⢠⣁⡀⣀⡀⡤⠀⠠⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣶⠶⡀⠰⣁⠀⣀⣀
⠀⢠⠀⠀⡀⠂⢀⢀⡠⠄⠠⡔⠴⠂⠀⠀⠀⣤⣦⡿⠟⠁⠀⠈⠀⠀⠂⠀⠀⡀⠀⢠⠀⠀⡠⠂⠀⢀⡈⠄⠨⡔⢤⠢⠀⠀⢠⣔⣤⡿⠟⠁⠀⠄⠀⠁
⡔⢢⠊⠀⠀⠀⠀⠀⠌⠒⣋⠶⡴⠒⠀⠀⠈⢊⠀⠀⢀⠄⠊⢀⡀⢈⠁⠂⠉⠀⣔⠠⠈⠁⠀⠀⠁⠀⡌⠒⣟⠧⢴⠒⠀⠀⠀⢎⠀⠀⠀⠠⠊⣀⡀⢈⠁⠂⠉
⢀⡁⠀⣀⠀⠀⠈⠜⠂⠰⠄⢀⠄⠀⠀⢠⡇⠀⠉⠁⠀⠀⠘⠒⠃⡌⣄⠀⠀⠀⢀⡁⠀⣀⠀⠀⠀⠈⠊⠡⠤⢈⠄⠀⠀⢘⡄⠀⠉⠉⠀⠀⠘⠒⠂⡬⣄
⠁⠈⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣨⠯⠇⠀⠀⢀⠀⡸⠂⠸⠀⠀⠠⠁⡀⠃⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⡀⠀⠀⣨⡿⠅⠀⠀⢠⠀⡯⠂⠒
⠀⠁⠀⠀⠀⠄⣠⢀⡔⠭⣳⠄⠘⠄⣉⣀⢈⡁⠜⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⠃⠄⣠⢆⡔⢭⣳⢄⠘⠆⣉⣀⣈⡁⠜⠀⠀⠀⠁
⠀⠂⠀⠐⠀⠀⠁⠂⠀⠀⠀⠐⠇⠀⠀⡀⠂⠀⣀⣀⡀⠀⠄⢠⡀⠀⠀⢰⠀⠀⠀⠂⠀⠑⠀⠀⠡⠀⠀⠀⠀⠈⡆⠀⠀⠠⠂⠀⣀⣀⣀⠀⢀⢠⡀
⠀⣀⠀⠀⠀⠀⣎⠀⠄⠀⠀⢈⠀⠀⠲⢿⠀⠘⠅⠀⠜⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⣀⠀⠀⠀⠀⣂⠀⠄⠐⠀⣀⠀⠀⢰⡷⠀⠸⠁⠀⠘⠀⠀⠀⠀⠀⠈⢀
⣁⣀⣉⣈⡀⠀⠀⠀⠀⠀⡈⣀⣁⢀⣀⣀⣄⠀⠠⠠⠀⣀⡒⣑⢢⡀⢀⣀⣁⣀⣉⣀⣃⣀⡂⠀⠀⠀⠀⢀⡤⣀⣃⢀⣌⣄⣀⠀⠃⠀⠂⣀⠐⣑⣦⡀⢀⣀⣁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⡆⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠠⢄⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠈⠙⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⣔⠃⠋⠓⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠠⠀⠂⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀⢈⠉⠈⠀⠀⠀⠀⡌⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⡀⠀⠀⠀⠀⠈⠂⡀⠀⠂⡀⠈⠁⠁⠄⠀⡁⠀⢀⠠⡄⢀⠈⠀⠀⠠⠄⡀⣀⢀⠀⣼⣇⢄⠀⠀⠀⠈⠀⠀⢀⡀⠠⠲⠀⢀⡀⢀⠀⠀⠐⠁⢁
⠀⢰⡀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠀⠀⠁⠐⢁⡄⠀⡀⠈⠑⡽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⣤⡠⡤⣤⡴⡀⠈⢤⡀⠔⢀⠠
⠀⠀⣦⣄⡠⠆⠀⠒⠁⠉⠀⠀⠀⠀⠡⠄⠠⡁⠀⠀⠁⠀⠀⠀⢀⠌⠀⠀⢨⡕⠀⠀⡀⢠⠀⠀⠀⠠⠀⠀⠠⠀⠦⠄⠘⣄⢋⠀⠤⠂⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠂⠀⠀⢀⡀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠐⠀⠄⠀⠀⢀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠠⠄⡀⠀⠀⢘⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌⠡⠒⢈⠀⠂⠀⠀⠀⠀⠐⠀⢀⣀⠈⠀⠀⠣⠊⠁⠆⠀⠀⠀⡀⠀⠀⠀⠔⠁⠀⠀⠀⠰⠀⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠂⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣄⣄⣀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⠊⢀⡐⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢠⣶⣿⣿⣿⠛⢛⡛⡻⡟⣿⣿⣿⣶⡄⠀⠁⠀⠉⠀⠠⠸⡈⣈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⡐⠂⠠⠁⠀⠀⠀⠀⠀⠑⠄
⠀⠘⡒⠐⠈⠀⠀⢀⠀⢀⣿⢛⡟⣿⢻⡛⢛⣿⢛⡛⠻⠟⠟⢻⣿⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⢀⠀⣂⢀⣀⣀⣀⠀⠀⡀⡂
⠀⠀⢡⠀⡄⠀⠀⠀⠀⠘⣿⢨⠁⢹⡜⣿⢸⣿⢈⡁⡇⠀⠀⡆⣿⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⡂⠀⠀⡁⠀⠁⠀⠀⠇⠀⠍⠛⠋⠀⠛⠀⠐⠈⠁
⠀⠀⠀⠆⠃⠀⠀⢀⠀⠀⠹⣼⣼⣮⣭⣿⣼⣿⣼⣧⣡⣬⣤⣴⠏⠀⠀⠀⠀⠰⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠠⠀⠐⠀⠀⠀⠉⠛⠛⠛⠻⠛⠛⠛⠛⠛⠉⠀⠀⠀⠂⠀⠀⡀⠀⠠⠄⠁⠀⠀⠀⠀⠈⠀⠀⠀⢐
⠀⠀⢅⠀⠀⠀⠂⠀⠒⠠⠀⠀⢠⠐⢀⠀⠀⠠⢀⠀⠠⡀⠀⠀⠀⠀⠄⠀⠀⠠⡈⠀⡀⠔⠀⠄⠀⠀⣀⣀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢉⠀⠸⠀⣕⠐⠘⠂⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⢀⠗⠁⠀⠀⠉⠄⠀⠀⠂⠈⠂⠀⣈⠀⠀⠀⠀⢙
⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⡀⠀⠐⢀⠀⠀⠘⠕⠀⡀⠀⠀⢘⡂⠀⠀⠆⠀⠀⣀⠀⠀⠀⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠑⠂⠀⠘⠀⠰⣀⣀⠬⠃⢈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠐⠬⠄⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡄⠀⠀⠀⠀⠀⠀⢀⠰⠸⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠁⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠖⠃⢀⠄⢀⠀⠒⠑⢀⠀⠀⠠⠀⠀⠀⠃⠁⠦⠀⠐⠀⠅⠀⢸⠀⠁⠈⠀⠂⠀⠐⠀⢴⣊⠖⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠠⠤⠆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⢀⠀⠀⠨⠂⠀⠀⠠⠊⠀⠀⢄⠀⠀⢀⡈⠀⠂⢰⣀⡠⡰⠱⢡⠄⠀⠀⠀⠀⡆⠀⠠⠀⠠⠀⠁⠒⠈⠀⠤⠀⠀⠀⠀⣠⠀⢀⠠
⠀⠈⠀⠀⠀⠄⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠠⢇⡀⠀⢸⢆⡀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠐
⠀⠢⠀⠠⠄⠂⠁⠀⠀⡀⠀⠀⡠⠔⠊⠁⠁⠀⠀⠈⠍⠀⡄⠀⠀⠈⠚⠚⠁⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⡄⠀⠀⡀⠀⠀⡄⠀⠄
⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠑⠂⢀⠉⠀⠐⠀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠁⠀⠠⠤⠄⠀⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠓⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⣎⣉⣳⡀⠀⠀⠀⠀⡤⡤⠒⡶⣠⠒⡦⡀
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⢠⠮⠭⠭⠭⠽⠄⠀⠀⠀⣸⠥⠄⠬⠦⠨⣆⠀⠀⠀⣜⠁⣼⡙⣧⢎⢫⣾
⠀⠀⠀⢠⡗⡒⡒⢖⠠⣒⡲⣶⠾⡀⠀⠀⠀⠘⡎⠉⠉⠉⢹⠁⠀⠀⠀⠙⣟⢻⡭⡛⢹⠁⠀⠀⠀⢹⠙⠓⠓⠚⠚⢉⡇
⠀⠀⠀⠀⢹⠒⠾⡉⣘⢿⠓⠞⡟⠀⠀⠀⠀⠀⢣⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⡟⢤⣺⠃⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠉⠁⠘⠳⣰⠞⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡁⡝⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡤⢒⣂⡉⣐⠲⡄⣠⢤⠀⠀⠀⠀⠀⣀⠤⢤⠒⠢⡄⠤⡀⠀⠀⢀⡠⠔⠒⠒⠠⢄⠀⠀⠀⠀⠀⢀⠤⠒⠢⢄
⠀⠀⠀⢠⢋⠖⠧⠎⢀⡠⡫⠞⠹⡆⠇⠀⠀⢠⠞⠁⠀⠀⠣⡀⢣⣀⣈⠆⠀⣎⣀⣀⣀⣀⣀⣠⡕⠀⠀⠀⢠⠋⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠈⠆⠏⠋⠻⠒⡿⢭⢅⠙⠂⠀⠀⡜⠣⡀⠀⠀⢀⡝⠁⠀⠀⠀⠀⠈⡄⢠⠈⡄⠰⢠⠁⠀⠀⠀⠸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⢆⠳⢖⢐⢢⣀⡰⢋⡞⠀⠀⠀⠀⡗⢄⣈⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⢡⣘⠀⢃⣃⠎⠀⠀⠀⠀⡼⢑⣤⠴⠊
⠀⠀⠀⠀⠀⠑⠢⠤⠭⠤⠒⠋⠀⠀⠀⠀⠀⢇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⢭⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⣔⣒⣢⢠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⢖⣂⠴⡒⣒⣄⠀⠀⠀⠀⠀⡤⠤⠤⠧⠧⠤⣄⣀⡀⠀⠀⠀⢸⠀⣇⠾⠼⠄⠀⠀⠀⢀⡔⡢⣄⡠⢚⠦⡀
⠀⠀⠀⠀⡎⡡⠒⠉⠒⠒⠒⢝⢦⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⣯⣗⠅⠀⠀⠀⡸⠀⡧⠋⠈⠣⡄⠀⢠⠊⠀⢱⠈⢳⠸⡄⠈⠆
⠀⠀⠀⢸⡴⠁⠀⠀⠀⠀⠀⠈⢿⠂⠀⠠⡆⠀⠷⠤⠄⠖⠋⠃⡲⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠸⡀⢀⠇⠀⢸⠀⡇⠀⡄
⠀⠀⠀⠸⠤⠤⠤⠀⠒⠀⠀⠤⠊⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠉⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠀⠑⢤⣃⠴⠛⢄⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠤⠤⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠀⣞⣵⣵⠗⠺⡄⠀⠀⠀⢠⠃⠘⡀⠀⠀⠀⠀⠀⠀⣠⠊⠱⢼⢌⢷⠀⠀⠀⣠⣀⡠⠤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⢰⣊⠭⣔⡺⣽⠝⠁⠀⠀⡇⠀⠀⠀⡞⣚⠓⠙⡆⠀⠀⠀⠀⣴⠥⠔⠚⠉⢉⡏⠀⠀⢸⠀⠘⠀⣀⠈⠀⠀⠋⠀⢹
⠀⠀⠀⢎⣪⠛⠊⠉⠀⠀⠀⣠⠎⠀⠀⠀⠀⠹⠀⡇⢰⠃⠀⠀⡠⠊⠀⠀⠀⠀⡠⠋⠀⠀⠀⣞⡋⢛⡓⠒⡞⠉⣖⡛⢳⣋⡢
⠀⠀⠀⠈⠡⡀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠸⠋⠁⠸⡄⠀⠀⠣⢄⡀⠀⠀⡔⠁⠀⠀⠀⠀⠘⠬⠅⠈⠫⠬⠍⠤⠬⠥⠜
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡄⠠⠃⠀⠀⠀⠀⠈⠢⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠁⠀⠀⢀⠠⠤⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠤⡀⢤⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠦⠤⠐⠀⠈⠀⠠⠀⡀⣤⠀⠤⢤⡌⠛⠂⠀⠤⠆⠉⠉⠁⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⣀⣡⡒⠦⠤
⠀⠂⠀⠀⠢⠄⠀⠀⠀⠄⠀⠀⠀⡀⠞⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠁⠒⠦⢀⡀⢀⡤⢊⠡⠀⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠔⠈⠀⠀⠀⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠥⠖⠁⠀⠀⠀⠀⠀⠸⡄⠃⠀⠄⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠄⠤⠀⢤⠄⠀⢂⠀⡰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡆⠀⠀⠄⠂⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⠄⠃⡤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⢀⠀⠘⠀⠐⠄⠀⠀⠁⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⠀⠀⠀⡐⠁⢠⡕⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠇
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀⠂⢀⠀⠙⠂⠀⡀⠀⠀⠀⠑⢧⠘⠀⠀⠀⠀⠀⠀⠐⢁⠤⠀⠀⠘⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⣀⠀⠈⠀⠀⠀⠀⠢⠤⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠈⠠⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠁⠀⡄⠀⠊⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠦⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠘⠲⡀⠶⠄⠦⠐⠃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠁⠤⠄⠀⠀⠀⠤⠄⠀⢀⡀⠀⢀⠠⠐⠠⠀⠀⠀⠠⠄⠀⠀⢀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣁⡀⠠⠄⠄⠀⠈⠠⠄⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠠⢤⠄⠙⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠠⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⠀⠀⠨⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠉⠉⠀⠦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠖⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠐⠈⠁⠀⠂⠀⠀⠀⠀⠐⠒⠈⣀⣁⠀⠀⠀⡁⠀⠀⠀⠀⠃
⢀⠤⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⢀⠀⠀⢀⠀⠀⠐⠢⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠈⢂⠘⠢⠄⠀⠠⠒⠀⠈⡠⠀⠀⢀⡄⠆⠆⠀⠙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠰⠀⠂⠀⠀⠀⠀⠁⠂
⠀⢀⠀⠀⠀⠱⡀⠀⠄⠒⠀⠀⢰⠁⠀⢰⠑⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠊
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⢆⣀⣀⡀⠀⠂⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⡀⠀⠀⠀⠄⠐⠈⠉⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⢀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⢠⠄⠀⠀⣤⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠢⠄⡈⠣⡙⠃⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⡐⠒⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⣤
⠀⠂⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡀⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠶⠾⡄⠀⠁⠀⢂⠐⠃⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠑⠀⠈⣉⠲⠀⠀⠀⠀⠀⠀⢀⡉⠀⠭⠭⣝⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣑⣤⣤⡤⠖

⠀⠀⠀⠀⣤⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠝⢱⠀⠼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠍⠱⠀⠼⢉⡀
⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡀⠀⠀⠀⠀⡴⠋⡏⡩⠦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡴⠫⡎
⠙⢣⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠆⠅⠜⢃⡶⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠐⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠰⠤⠒
⡄⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠖⡼⣿⡆⢊⠀⠀⠀⠌⠄⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣖⣾⣻⡆⠊⠀⠀⠀⠌⠆⢙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠀⠀⠀⠀⠶⢋⠘⠃⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠶⠛⠘⠇⢦⡴⠂
⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠨⣁⠀⡤⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣀⠂⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⡠⠦⡴⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡠⠢⡤⠀⠀⠀⠀⠆
⠀⠀⠈⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃
⠀⠀⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⢀⠉⡰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡰⠉⠆
⠀⠀⠀⠀⡶⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠃⠠⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠜⠹⠀⠼⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠱⠀⠍⠹⠀⠨⢡⡀
⠦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠐⠀⠀⠀⣴⠁⡏⠩⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡰⠉⡏
⠙⡃⡶⠀⠀⠔⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⠜⠃⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠒
⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆
⣗⠺⣻⡆⢂⠀⠀⠀⠌⠂⢉⠿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡷⣊⣖⢾⣹⡖⠊⠀⠀⠀⠈⠂⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠖⢋⠘⠃⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡴⠀⠀⠀⠀⠷⢛⠘⠃⢢⠴
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣁⠐⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣁⠂⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡰⠦⠶⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡤⠲⡴⠐⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠉⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃⠀⠀⢀
⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠈⠉⠰⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠃⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠂⠐⠀⠀⠀⠐⠈⠒⠒⠀⠁⠁⠘⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠄⠄⠀⡐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠰⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠉⠙⠓⠒⠒⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠛⠉⠙⠒⠲⢤⡀⠀⠀⠀⢀⣸⠤⠔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠖⠋⠁⠀⠠⠖⠡⠟⡷⣄⡀
⠀⠀⠀⠀⠀⠐⡒⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⡈⠹⠿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢟⣹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⣲⣄⣀⢤⠄
⠀⠀⠀⠀⠀⠀⢁⣮⠆⢽⡍⢿⣖⢶⠶⢶⠒⣒⣚⣹⠉⠞⣳⡽⠉⠈⠢⣀⠀⣀⣤⣴⡶⢛⣟⢛⡛⣉⣁⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠸⢛⠦⢄⣀⠀⠈⠉⠙⡓⠀⣉⠀⠘⠋⡥⢎⡟⢠⢀⠀⠀⣽⠉⢤⡏⠀⡎⢻⠛⢯⣄⡈⢙⣭⠗
⠀⠀⠀⠀⠀⠀⠘⠦⢀⣠⡌⠛⠁⠤⢄⢠⣈⣁⡀⠀⡀⣠⠎⠁⠣⣌⠄⢸⣿⡄⢸⣬⣖⡽⠄⣇⢀⠦⠽⢾⡜
⠀⠀⠀⠀⠀⠀⠐⢄⢀⠈⠉⠁⠈⠀⠈⠁⠉⠉⠉⠁⠈⢀⠄⠁⠀⠈⠢⣥⠙⣧⠈⣟⠬⣉⣁⡟⢴⣟⠓⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠐⠒⠒⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠙⡓⡁⢶⠨⠇⠈⠂⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠘⠏⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣼⣛⡲⢤⡀
⠀⠀⠀⠀⢠⠖⠋⡍⠉⡉⢉⠙⠳⣄⠀⠀⠀⠀⠀⠀⣴⠶⠾⠷⠶⣦⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⢚⣩⣭⡇⡿⢟⡙⢦⣹⡄
⠀⠀⠀⠠⣏⣀⣃⣀⣁⣀⣁⣘⣀⣸⡆⠀⠀⠀⠀⢾⣉⣉⣉⣉⣉⣉⡇⠀⠀⠀⠀⠀⢠⡟⠒⠻⡆⠀⠀⠀⠀⢠⡟⣴⣋⣐⢺⡇⣷⡯⢟⣫⣍
⠀⠀⠀⠀⣯⠤⠤⣤⡤⠤⣤⡤⠤⣽⠇⠀⠀⠀⠀⠈⣯⠈⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⣾⠛⢳⠀⣿⠀⠀⠀⠀⣾⢰⡇⢯⡽⢸⣧⠵⣚⠉⡇⢹
⠀⠀⠀⠀⢳⠶⣶⡒⠒⠒⠒⣶⠶⣾⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡶⠛⠀⡟⠀⠀⠀⠀⢹⡌⣇⢰⣷⡌⠄⠺⠿⣰⢇⡿
⠀⠀⠀⠀⠘⠳⠾⠷⣦⣠⠾⠷⠖⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣇⠀⠀⠀⠀⠀⠻⣌⠳⢭⣴⣏⡷⠞⣣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠟⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣠⢴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢀⣴⠻⡌⢿⢸⡟⣸⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡅⠻⣜⣳
⠀⠀⠀⠈⡏⠛⠛⠚⠛⠒⠛⠋⣿⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⣦⣀⡀⠀⠀⠀⢠⡞⠉⠠⠈⠠⠉⠄⠈⢳⡄⠀⠀⠀⠀⢀⡞⠰⠀⠄⠠⠈⡽
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⢁⡿⠀⠀⠀⠀⢹⡏⠹⡟⠉⢹⡏⢩⡟⠁⠀⠀⠀⠀⣸⣇⠐⠀⢂⣠⠞⠁
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⣤⣼⣧⣤⣤⣤⣤⣿⣭⣤⠀⠀⠀⠀⠀⢷⠀⣿⠀⣸⠁⣼⠁⠀⠀⢀⡤⡼⣃⡼⠓⠛⠉
⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠾⠀⠀⠀⠀⠀⠹⢦⣤⣤⣤⣤⣤⣤⣤⣤⠞⠀⠀⠀⠀⠀⠘⠧⠼⠤⠿⠴⠃⠀⠀⠀⠈⠳⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣉⣳⣆
⠀⠀⠀⠀⠀⠀⢀⣀⡴⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⣄⠀⠀⠀⠀⣾⣁⣈⣹⣄⣙⣦
⠀⠀⠀⠀⢀⣾⣩⣥⣀⣠⣩⣧⠀⠀⠀⠀⢀⡞⠉⠉⢹⠏⠉⠉⡟⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠲⢾⡀⠀⠀⠈⢷⠖⠲⠖⣶⣶⡞
⠀⠀⠀⠀⢻⣥⣄⣠⣤⣀⣤⣬⡇⠀⠀⠀⣼⢶⠶⠶⡶⠶⢶⠶⠶⡶⠶⢶⢾⡆⠀⠀⠀⠀⠀⢀⡴⠋⠳⢤⡀⢨⡇⠀⠀⠀⠘⣷⠖⢋⣡⣼⠁
⠀⠀⠀⠀⢸⡄⠈⡇⠀⣿⠀⣸⠃⠀⠀⠀⣿⣯⣛⣛⣟⣛⣋⣛⣫⣿⣚⣉⣿⡇⠀⠀⠀⢀⡴⠛⠳⣄⠀⠀⠙⣿⠀⠀⠀⠀⠀⢹⡞⢋⣠⡇
⠀⠀⠀⠀⠀⢷⠀⣷⠀⡟⢠⡏⠀⠀⠀⠀⠘⠲⠾⠭⠭⣬⣭⣭⣬⠭⠽⠷⠚⠀⠀⠀⢿⣉⠹⡄⠀⠘⣦⣠⡾⠃⠀⠀⠀⠀⠀⠈⣿⠉⡿
⠀⠀⠀⠀⠀⠘⠓⠛⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣻⠙⠖⡦⠀⠀⠀⠀⣠⠞⠳⣄⢀⡴⠛⣦⠀⠀⠀⠀⠀⣯⠭⣽⡇⣴⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⣏⡽⠷⣤
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⣷⠛⣯⣿⣹⠆⠀⠀⣰⠋⠐⣦⠈⣯⠀⢶⠈⢳⡀⠀⠀⠀⢸⠀⢸⠀⣹⠏⢹⣇⠀⠀⠀⠀⠀⠀⣠⢞⡵⣫⡞⠁⠀⠈⡇
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡟⠛⢻⡾⠃⠀⠀⠀⢿⠀⣰⠃⠀⣽⢠⡏⠀⢸⠇⠀⠀⢀⡾⠀⠸⣾⠁⠀⠀⢸⡇⠀⠀⢠⡖⣫⡵⣫⡴⠋⠀⠀⢀⡼⠁
⠀⠀⠀⢰⡋⠀⠀⢀⣴⠏⢀⡴⠋⠀⠀⠀⠀⠀⠈⢧⡈⢁⡴⠳⣌⠃⣰⠏⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠸⣏⡽⠛⠁⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠙⢦⣴⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠘⠛⠁⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠉⢳⣄⣀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠛⠓⠒⠒⠚⠃⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡩⢣⠀⣤⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠓⣀⢦⠠⠤⡏⠇⠰⠰⡅⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⢆⡰⢌⡄⠹⡤⠿⠲⠁⣎⡹⠆⠡⠀⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣄⢀⡸⠒⠎⠘⡀⡠⠞⢢⠀⠨⠁⠈⡀⢂⠈⠎⠖⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢹⠇⣤⠋⢄⠀⠑⢻⠲⠉⢇⠀⠁⠡⠐⠀⣃⣸⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣶⠀⠀⠀⠀⠀⣀⡇⠀⠈⢆⠈⡆⠀⠈⠓⠋⢇⢃⠘⡆⠀⠀⣣⡶⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣰⠃⠀⠀⠀⠀⢸⡗⠶⠦⢤⣬⣤⣽⣄⣦⣤⣥⣸⣬⣤⡴⣶⠞⠉⠀⠀⠀⠀⠀⡇
⠀⠀⣠⡤⠔⠒⠂⠀⣈⡧⡤⠓⠒⠤⢤⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⣤⣤⣤⣤⣧⣤⣀⣀
⠀⣼⣏⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⣀⢟⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠁⢀⠀⠀⠉⠉⠉⠛⠻⢷⣦⣤⡀
⠀⡷⠬⣍⣛⣒⠚⠛⠒⠒⠒⣒⣚⡉⠥⠚⡇⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⢉⡁⡄⠀⠀⠠⠀⠂⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⡏⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠈⠀⡇⠀⠸⡆⠀⠀⣀⣴⠾⠋⠁⡠⢰⠄⠉⠀⠂⢂⣠⠤⠖⠒⡈⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢿⣷
⢠⡇⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⡀⠀⠀⢀⡇⠀⠀⣇⣠⡾⠋⠁⠀⠀⢀⣈⣀⣤⠤⣤⠴⠿⠤⠤⣤⣉⣀⠀⢴⡴⠀⠉⠉⠠⡠⠆⠀⠀⠀⠈⣿
⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⢀⠀⠐⠊⠉⠁⣠⠔⠋⠀⠀⡄⠀⣀⠀⠈⠉⠛⠲⣄⠀⣆⠜⠀⠀⠀⠀⠀⠀⣸⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⢸⣷⠟⠁⠀⠀⠺⠈⢀⡠⠂⣤⠞⠁⠀⢀⡀⠉⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠄⡆⠀⣠⠞⠁⠐⠁⠐⠒⠁⢠⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣰⡟⠀⠀⠀⠀⠀⠀⠋⠀⡴⠃⠀⠀⠸⠥⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⢀⣤⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⣀⣤⠞⠋⣠⡇
⢸⡇⠀⠀⠁⠀⠀⠀⠀⡜⠀⠀⢨⣿⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠉⣀⣤⠶⠛⠉⢀⣤⠞⠉⡷⢤⡀
⣿⡇⠀⠀⠀⠀⠀⢠⠎⢀⡀⠔⠉⠳⣍⡛⠿⢿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠿⠟⠛⢉⣁⣤⠴⠞⠋⠉⠀⣀⣤⠾⠋⠁⣀⡼⠃⠀⣿
⣿⠇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣇⠙⠓⠦⢤⣈⣉⡉⠉⠉⠉⠉⠉⢉⣉⣁⣠⣤⠴⠖⠚⠋⠁⠀⢀⣠⣤⠶⠛⠉⠀⣀⣴⠞⠋⠀⠀⢠⣿
⣿⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⢦⣄⣀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⢀⣀⣤⠶⠛⠉⠀⠀⠀⢀⣴⡿⠁
⣿⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦⣌⠉⠙⠛⠓⠒⠲⠶⠶⠶⠖⠒⠛⠛⠋⠉⠁⢀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡿⠋
⣿⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠲⠶⠤⢤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁
⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⢛⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⢿⣝⡛⠻⠷⠶⠿⠿⠟⢛⣋⣩⡴⠖⠛⠁⠀⠉⠛⠷⠶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣴⠶⠶⠟⠛⠋⠁
⣤⣤⣬⣭⣿⣿⣷⣾⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣏⣼⣉⣯⣩⣿⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡏⠓⠒⠯⠝⢻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠆⠀⠀⠹⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢉⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣥⣤⡀⡥⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⠞⡃⠠⡠⢹⣦⣾⣟⣽⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣻⣿⣿⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⠙⢋⡿⠣⣮⣉⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣏⡉⠙⠁⠀⠀⠒⠦⠈⠉⠉⠉⠿⣿⣿⣿⣿⡟⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠻⠛⠲⠶⠶⣄⣲⣀⡀⡒⠒⠺⠽⠛⠛⢋⣼⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣛⣉⣤⣶⣶⣮⠙⠉⠉⠉⠉⠉⠉⢉⣭⣶⣶⣤⣀⣾⣿⣿⠏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡿⣭⣙⡻⣿⣿⣿⣷⡄⠀⠀⢀⣴⣿⢿⡟⣛⣹⣿⣿⣿⣿⢾⣾⡏⠎⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠆⣈⡴⣋⠿⡝⢁⣙⠳⢶⡟⡇⠈⠀⢽⠋⡛⠞⢻⠁⢀⣰⡗⣵⠐⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡔⢡⠗⡂⣨⣍⠳⢮⠀⣀⣚⠋⠘⠀⠀⠀⢡⣴⣿⣉⣸⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣏⡟⠳⠓⠜⠉⠉⠐⠚⠛⠿⢆⠍⣀⣎⣹⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⠤⠄⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠐⠒⠶⠖⠲⠆⠀⠀⠰⠒⠦⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⡍⣷⠀⠀⢀⡄⣶⣤⣠⣴⠀⣶⣄⡰⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣇⠀⠀⣽⠀⠀⠘⠃⠁⡉⡉⠀⢀⡀⠁⠀⠀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠋⢀⡇⠸⠀⡖⠀⠏⡖⡸⠂⣾⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠛⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛
⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠒⡰⠄⢢⣎⣁⠀⠐⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠶⠶⠒⣒⡒⠲⢤⡀⠀⡤⠀⠀⠀⠀⠀⠀⢀⣠⠖⠻⡄
⡟⠓⠺⣄⠀⢀⣇⣀⣹⡄⠀⢸⣄⠀⠀⠂⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⢀⠀⠈⢑⡦⢷⡀⣌⠐⢣⡄⢀⣀⡰⠟⢫⣾⠟⠁
⠇⠀⠀⠀⠉⠉⠀⠀⠀⣹⢿⣧⡎⠀⠀⠀⠀⠀⠀⠀⢸⡂⡈⠀⠀⡐⢀⡀⣈⢀⣀⣤⣾⠁⠉⠀⠛⠓⢀⣤⠶⠛⠉
⢰⠀⠀⠀⠄⠀⠀⠀⡐⠉⠀⢧⠀⠀⢐⠀⠀⠀⠀⢴⠉⠻⠽⠿⣭⠿⣯⠽⠛⣛⡻⢟⡟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⠸⠀⠀⠀⠀⠀⠀⠐⢀⣠⠴⠚⠀⠀⠀⠉⠉⠁⠀⠈⠲⢍⣀⣒⣐⣒⣀⡨⠭⠄⠒⠉⠀⠀⠰⠀⠀⠀⠀⠈⠀⠈⠁⡆⠀⠀⡀⠀⠀⠨⢆
⠀⠉⠙⠛⠛⠒⠚⠞⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢀⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠀⠀⠱⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡨⠓⠀⠀⠀⡈⠓⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⣼⠃⠀⠀⠀⣤⣶⠶⣤⣤
⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠰⢄⣨⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠢⡀⠙⢆⠀⠀⠁⣆⠀⠀⠀⡇⠀⠀⠀⠀⠁⢀⠠⠐⡄
⠀⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠤⠀⠀⠀⢀⠎⠀⠀⠐⠦⠀⠀⡀⢀⣨⡦⠠⠇⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠀⡁⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠀⢀⠀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⢂⣤⠾⠛⠁⠐⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠄⢙⣣⡄⠀⠀⠈⠀⠉⠀⠀⠀⠀⢸⣀⣴⠟⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠘
⠀⢀⠄⠒⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡤⠒⠛⠛⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⡤⢀⢄⡀
⠀⡀⢰⠀⠀⢧⠀⠀⠀⠀⣠⣄⣴⣄⠐⢃⣀⡀⠀⠀⠀⢠⠏⠀⠀⠈⠀⠀⠀⠀⢀⣠⢼⠀⠀⠤⣜⠷⠻⣇⢱⠈⡁⠀⠀⠀⠐⠀⠀⠈⠠
⠀⠄⣸⠀⠀⢸⠀⠀⢠⣾⠏⡠⠊⠀⠀⠀⠀⠉⢶⠀⠀⡟⠀⠤⠀⠀⠀⣠⣤⣶⠿⢳⣻⡀⠀⠀⣿⠄⠀⠟⣸⣄⡿⠃
⠀⡇⣇⠀⠀⣼⠀⠀⢼⡫⠜⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⣤⡤⠶⠊⣙⢋⠽⣷⢦⣎⡥⢴⠋⠀⡋⠘⠚⠷⠛⢛⡇⠀⠀⠀⠀⠀⡀⠠⠤
⠀⢶⢸⠀⠀⡇⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠀⠠⠃⠀⠀⠈⣼⣄⣸⣭⣴⡶⠿⠋⠃⣱⠎⠀⠀⢸⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠃⠀⠄
⠀⢸⡌⠀⢰⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢀⣀⣈⣉⣀⠤⠒⠊⠁⠀⠀⠀⠀⠃⠀⠀⠠⠓⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠳⣤⠟⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠂⠐⠚⠀⠀⠀⢀⠀⠐⡀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣠⡌⠢⡀
⠀⠀⠀⢸⠀⠀⠀⠐⠂⠀⠀⠐⠖⠒⠲⡤⠠⢤⡶⠀⠀⢀⠤⣠⠶⠶⠚⠋⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡆⢀⣬⡦
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠂⠀⠀⠁⢨⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘⠦⠂⣀⣒⠀⠉⠝⠃⠚⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⠤⣽⣋⣛⣛⣛⣛⣋⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⡤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⡖⠭⠒⢀⡍⡁⣈⡠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠃⠢⠀⠒
⠀⠀⣀⠁⠀⠀⠀⠈⠀⠀⠀⢀⡰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⡐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠖⠀⠀⠊
⠀⠀⠁⠀⠀⠀⠒⠒⠒⢒⣈⣩⠴⠚⡅⠀⠀⠀⠀⠀⠀⡠⠞⠍⠀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠐⠒⠒⢀⣀⡠⠤⠖
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡀⠠⠔⢻⠀⠀⠀⠀⠀⠀⣼⠁⠀⠐⠀⢠⠊⠁⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⢀⣠⠄
⠀⠀⢸⠄⠀⡀⠀⠀⠀⠀⢀⣀⡤⢾⠀⠀⠀⠀⠀⠀⠇⠀⠀⢂⠘⠀⠀⠠⠤⠐⢊⠁⠁⡔⠊⡥⠀⠀⠀⠀⠀⠀⢩⠝⣀⢋⠼⡟⢣⠉⡄
⠀⠀⠘⠀⠄⠀⠈⠉⠉⠭⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠔⠁⠀⠞⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⢼⣤⣦⣼⣤⢧⢿⠁
⠀⠀⠀⡇⠀⠀⡀⠄⠐⠀⠀⠙⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢜⣕⢕⡵⡡⡏
⠀⠀⠀⠘⠀⠀⠀⣀⣈⣀⡠⠴⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡯⡪⣾⢮⡇
⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢠⡆⠀⠀⠀⠀⠀⠀⣀⠄⠘⠀⠀⡚⢀⡀⠀⠃⢦⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠞⠁⠀⠀⢀⣠⠀⠀⠀⠀⣀⢄⠈⢱⠚⠇⢸⠁⠞⠂⡜⠓⢀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠐
⠀⠀⡠⠖⠂⠒⠉⠈⠁⣄⣀⣠⠞⠁⠘⠉⠀⠀⠀⠀⠁⠈⠃⣰⠸⠀⠟⠲⠀⣼⠇⠀⠈⠀⠀⠀⠀⡸⠤⠠⠄⠤⢀⡀
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠂⠅⠧⠼⠿⠏⠀⠀⠃⠀⠀⠀⠀⠀⣺⣁⣊⣐⣂⠐⠋⠻⠐⠠⢀⠤⠀⠈⠆
⡌⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠌⢀⡘⡈⠀⠀⠀⠀⢄⣁⣠⠎
⠇⠀⠀⠀⠀⠀⠀⡀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢨⠆⠀⢀⡈⠉⠀⠒⠃⠐⠂⠐⠀⠜
⠀⠀⠀⠀⠀⣀⣴⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⡀⠀⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠐⠀⠤⠌⠀⠉⢐⡋⣘⠁⢀⠀⢀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⣀
⠀⠀⢀⣠⠖⠊⠉⠄⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⢸⠁⠄⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢧⡀⠀⣀⡀
⠀⣠⠋⠀⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠂⠀⠀⡄⠀⡄⠀⠠⠀⠀⢀⡀⠀⠀⠀⢸⠁⠀⠈⠃⠪⡁⢟⣠⣄
⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⣡⠞⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡒⢠⠉⠂⡠⠀⠀⡄⠀⠘⠀⠀⠀⠀⠈⠓⠀⠤⠘⣤⣗⣲⣄
⠈⢙⡁⠶⠄⠤⣤⠤⠤⡬⢄⠒⠚⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⡁⠂⡠⠊⠀⢀⡰⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡢⡑
⠀⠈⡀⠀⠉⠀⠐⠈⠀⠐⣁⠤⠚⢀⡁⠴⢃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠕⠊⠀⢀⡴⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞
⠀⠘⠀⠘⠀⠤⠶⠒⠒⠒⠀⠚⠩⠉⠂⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢠⣪⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠂⣒⣨⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⢄⡀⠛⠛⠛⠓⠃⠀⠀⠃⠑⠒⠒⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠸⠤⣧⠀⠀⡆⠘⢵⠶⠟⠸⠿⠆⠗⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠟⢠⠀⡇⢀⠄⣤⡀⣰⢠⡄⡀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠀⠃⠃⠇⠸⠣⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠾⠁
⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣀
⠀⠔⢂⠶⠘⣆⣁⡀⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠶⠖⣒⡒⠒⠤⡀⠀⠤⠒⠀⠀⠀⠀⠀⣠⠖⢻⡀
⡏⠙⠳⣄⣀⣭⠤⣽⣄⣀⡼⡄⠀⠂⠀⠀⠀⠀⣯⠀⡀⠀⠀⠀⠀⠀⠈⢶⠼⡄⢌⢑⣦⠄⠀⠠⠟⣩⠾⠛⠁
⠇⠀⠀⠀⠀⠀⠀⠀⡜⢻⠾⠃⠀⠀⠀⢀⠀⢀⣧⣠⣀⣀⣌⣠⣄⣦⣤⣴⣾⠇⠀⠄⡉⣁⠴⠚⠉
⢰⢰⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⠀⠄⠀⠜⠀⢧⡈⢙⣛⣚⣛⡓⠋⠍⢝⡪⠟⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠋⠢⡀
⠘⠤⢤⣤⣤⣠⣦⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠚⠃⠉⠁⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠆⠀⠀⠁⠰⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠯⠄⠉⠙⠲⣄⠀⠀⠀⢹⡀⠀⠀⠀⢠⠏⠀⠀⠁⢀⣤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⣀⡒⠁⠀⠂⠀⠀⠀⠀⡠⠁⠂⠀⠀⠀⠢⡀⠑⢄⠀⠀⠃⡀⠀⠀⠘⠀⠀⠀⠈⠍⠉⡉⣝
⠀⠀⠀⠀⠲⠅⠀⠀⠀⠀⠀⠉⠁⠀⠀⢄⠀⠀⠀⣰⠁⠀⠀⠆⠀⠀⠀⣈⣦⠄⠆⠀⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠐⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⠀⢀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠃⠀⣠⡴⠚⠉⠀⠘⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⠀⡆⠀⠀⠀⠀⢰⣼
⠀⠀⠀⠀⠀⠠⠠⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠛⠁⢀⣠⣤⡦⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠔⢉⠉⢳⠀⠀⠀⠀⠀⢀⡀⢀⡀⡀⠀⠀⠀⠀⣠⠞⠙⠠⠁⠉⠉⠀⠉⢱⡀⠀⣀⣠⣁⣉⣡⡀⡀⠀⠀⠸⣽⣋⣦⣄
⠀⠀⢆⠀⢸⡄⠀⠀⣴⠟⢪⠟⠈⠐⠒⠣⣄⠀⢠⠏⠀⠀⠀⠀⠀⣀⣥⣾⣽⠀⠀⢉⣏⠉⠹⡟⡇⣧⠄⠀⠀⠈⠉⠀⠈
⠀⢰⡃⠀⢸⠃⠀⣺⣛⠔⠁⠀⠀⠀⠀⠀⠈⡀⠸⣄⣀⣤⠔⢲⠟⣿⣥⡴⣚⣡⡆⠀⡇⠢⢴⡽⠿⣏⠀⠀⠀⠀⠀⠀⢀
⠀⡇⡅⠀⢸⠀⠀⠈⠓⠢⠤⠤⠀⣀⠀⠀⠤⠁⠀⠈⣭⣄⣀⣋⣭⣾⡟⠋⢱⡜⠀⠀⢇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠁⡠
⠀⢹⠁⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅⣀⣉⣉⡠⠴⠒⠉⠀⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠉
⠀⠈⠣⡜⠁⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠂⡀
⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⣀⣤⣴⠟⠛⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⢶⠈⠢⡀
⠀⠀⠀⡁⠀⠀⠈⠁⠀⠀⡙⠉⠉⠛⠉⠑⡉⠀⠠⠐⠗⠛⠉⠉⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⡿⣼⢄⣶⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠆⣀⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠛⠗⠊⠀⠀⠀⡯⠥⠠⠄⠢⠴⠇⠀⢀⠂⠁⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⡌⠀⠀⠀⠐⠁⠀⠀⠀⠀⡀⠀⡤⢀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠁
⠀⠀⠀⠐⠄⠀⠚⠀⠀⠤⠀⠀⡰⠆⡅⠠⠃⢡⠀⢀⡞⠉⠀⢀⠀⠙⠄⠀⢠⡤⠀⠀⠄⠠⠤⡀⠀⠰⠭⠜⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈
⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠮⠀⢰⡂⠰⢀⡀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡕⠀⠐⠀⠀⠘⠀⠂⡀⠀⠺⠀⠐⠈⠣⠐⠂⠀⠀⠀⠀⠠
⠠⠒⠂⠀⠀⠀⠀⢤⢢⣤⡀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠱⠆⣀⣀⡀⠔⠃⠀⠀⠈⠠⠄⢃⠀⠁⠲⠀⠀⠓⠀⠀⠁⠀⠀⠁⠂⠀⠀⠄⠈⠁⢀⡄⠀⠰
⠀⠊⠁⠀⠀⡪⡿⠑⣯⢹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠠⠀⠰⠀⠀⠀⠀⠘⠒⢂⠉⠀⠀⠠⡄⠀⠀⠀⠀⠠⡮⠁⠀⠐
⠀⠀⠂⠀⠀⠀⠖⠴⠛⠁⠀⡄⠀⠀⠀⠰⡖⠀⣀⠀⠰⣃⠂⠠⠀⠐⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠊⠀⠀⣄⡐⠀⣚
⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠄⠁⡤⠁⠠⠀⣤⠇⠀⠤⠀⠀⠀⡔⠁⣀⢄⡀⠀⠄⠀⢠⠀⠴⠘⠀⠀⡄⢀⡁⠦⡀⠀⠈⠚⠁⠐⠊⡀
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⠠⠒⠀⠀⠠⠠⡀⣠⡀⠀⡠⠀⡄⠀⠀⠀⠐⡅⠌⠃⡐⠁⠠⠆⠀⠀⠀⠀⣀⠀⠀⠆⣠⠄⠖⢛⠀⠀⠀⠀⠀⠀⠁
⠀⣀⠀⠀⠀⠀⠀⠀⠠⠂⢉⠀⠢⠀⠀⠀⠙⢺⢃⢹⡏⡀⠇⡏⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⣻⡯⠎⠃⠀⠩⣄⡠⠌⠚⠀⠀⣀⠀⠀⠀⢀
⠁⠀⠉⠀⠡⠀⠀⢠⠂⠄⠒⠀⠀⡃⠀⠀⠀⠀⠐⠀⠀⠊⠀⠙⠈⠀⠀⢀⣀⣀⡀⠀⠀⠀⣴⡿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⠨⣜⡿⣃⠀⠁⢇
⠀⠒⠀⠈⠀⠀⢠⠀⢰⡀⣀⣀⣸⠀⠀⠀⠀⠀⠤⠄⠠⡀⠀⠀⠀⢀⠞⠁⢀⠀⠈⠑⠀⠀⠑⠛⠒⠂⠀⠀⠀⠀⠀⢀⡀⠀⠈⣇⢀⡹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠉⠉⡍⠀⠀⠀⣐⢢⢤⣌⢁⠀⠐⠀⠀⢰⡀⠰⣀⠠⠀⠀⡆⠀⠀⣀⠦⣀⠀⢀⡄⡠⢄⠀⣨⢆⠀⠀⠀⢀⠠⠐⠀⠀⢶
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠹⢮⣄⣞⣯⢋⡿⠀⠀⠀⠳⠆⣀⣀⢀⠔⠁⠀⠀⠰⠂⠂⠀⠨⣧⣤⣝⣤⢤⡜⠀⠀⠀⠀⡠⠤
⠀⠠⠄⠀⠀⡀⠈⢠⠀⠀⠀⠀⡆⢐⠀⠀⠘⣿⡎⢟⣽⠉⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⣰⡄⠀⡀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠐⡛⠂
⠀⠀⠉⠀⠀⠄⢀⠀⠀⠀⠀⠠⡁⢈⠀⠀⢰⡞⢞⡽⠀⠀⠰⠀⠀⠀⠒⠀⠀⢰⡚⠓⢀⠤⣀⣹⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄⠀⠧⠀⠰⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠰⣟⡌⠀⠀⠀⠄⠐⠂⠤⢀⡅⠀⠈⠥⠨⠀⠀⠀⠘⠀⠀⠀⠀⠆⣉⠡⠘⢑⠀⠈⢢⠄⠀⠤⢼⠁
⠀⠀⠀⢀⠄⠀⠀⠀⡾⠀⠀⠠⠤⠤⠄⠀⠈⠊⠀⠀⠀⠒⠂⠐⠐⠀⠂⠘⠀⠀⠀⠀⣀⠀⠀⠀⢠⡀⠀⢰⡆⠀⢀⡈⢹⠀⠀⢸⣒⡚⠛⡟
⠈⠀⠀⠈⠀⣠⠀⠘⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠐⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⣀⠁⠸⠀⠈⠃⠀⠀⠀⠊⠀⠀⠀⠂⠀⠀⠁
⠀⠸⢄⠀⠀⠉⡏⡉⠉⢹⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠄⣀⢑⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠂⠑⠀⠀⢠
⡀⠂⡘⡂⠀⠀⢠⠀⢀⡞⠀⠀⢀⠈⠀⠒⣈⠀⠘⠄⠀⠄⠀⠀⠠⠀⠃⠀⠃⠙⠀⠛⠀⠀⢴⣉⡤⣉⠂⡧⠀⠀⠀⠓⠠⠓⡀⠀⠀⠀⠒⠂⠀⠀⣎
⡶⡶⢺⠃⠀⠀⠈⠋⠉⠁⠀⠀⠈⠄⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⢏⠝⣬⠀⠀⠀⢘⠀⠀⠁⡁⠀⠀⠀⠀⠘⢀⠀⢙
⠊⢶⡍⠀⠀⢀⣠⠤⢦⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⢐⣀⠀⠀⢰⡁⠀⠰⠄⠀⠀⠀⠱⣍⣫⡖⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⢘
⠓⠊⠁⠠⣞⠿⠖⠓⠋⠈⠈⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠂⠀⢰⣀⣪⠐⠜⢓⠀⠀⠀⠀⠀⠀⢀⠤⣀⡀⠀⡀⠇⠁⠀⠀⠈⠀⠀⠁
⣀⠀⠀⠀⠈⠃⠠⠄⠀⠀⠀⠀⢀⠰⠁⠐⠄⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠈⠡⣀⡤⠐⠋⠠⠄⠀⠀⢐⣦⠃⢶⢱⡥⠀⠀⠀⠀⢪⠰⡄⠀⠀⠀⡤
⠛⠂⠀⠀⣀⠀⠀⠀⣠⠀⠀⢰⠢⣔⠈⣉⡃⠀⠙⠿⠟⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠪⠤⠴⠚⠁⠃⠀⠀⠀⢨⡀⠼⡀⠀⠀⠃⢀
⠉⠀⠀⠀⠙⠁⠀⠤⠀⠀⠀⠸⠤⣄⠈⣸⠃⠀⣀⠠⢀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠈⠃⠀⡃⠈⢤⠀⠈⠠⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠈⡀⠀⠑⠒
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠁⠀⠠⡅⠁⠈⠷⠀⠀⠀⠀⠀⠰⠗⠂⣀⡀⠀⠀⡉⢄⠰⠖⠂⠀⠀⠀⣰⠶⠂⠑⠀⠀⠑⠒⠀⠁
⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡘⣀⠁⠐⠲⠦⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡖⠒⠀⠈⠁⠙⠛⠿⠿⠿⠯⠝⠉⠉⠁⠀⣤⣶
⠀⠀⠀⠰⣄⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠖⠒⠒⠂⣀⠠⠤⠄⠀⢤⠤⢤⡤⠴⠶⢛⡛
⠀⠀⠀⠀⠻⡄⠀⠀⠀⢸⡀⠀⠀⠣⠀⢠⠀⠀⣦⡎⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⡀⠁
⡀⢀⠀⠀⠀⠂⠀⢠⠀⠀⠁⠀⠀⠀⡄⠀⡄⠀⠈⢠⠄⠀⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠌⡀⠀⠀⠀⠀⡀⠼⣇⠀⠀⡇⠀⠰⠃⡄⠃⠀⠰⣧⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠠⠟⠀⠀⢀⣀⣠⣀⣉⣀⣀⣇⠀⠀⠀⠁⠈⢀⠠⠄⠤⠤⠤⠔⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑
⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⢀⠀⠀⠒⠂⠀⠀⠀⠒⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡆
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⢹⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠋⠉⠉⠉⢉⠉⠛⠙⣻⠦⠐⡒⠀⠁⠀⠀⠀⢀⠀⠀⠐⣻
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠀⠀⡀⠀⠀⠀⣀⡄⢀⠖⢀⡀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠈⣾
⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⣄⠀⡀⠀⢀⣀⣠⣀⠀⠀⢀⠀⠄⢀⡈⡉⠀⠀⠐⠂⠂⠀⣀⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠖⠙⠆⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠤⠶⠦⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠛⠳⡶⠲⠶⠓⠔⠂⢀⠀⠀⠖⠒⠂⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⡐⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠠⢤⡈⣷⡀⠀⣀
⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠑⢄⠀⠀⢀⢀⣴⡞⢹⣧⣿⣱⡡⣥⢾⡼⡆⠀⠀⠀⠀⠀⣠⠀⢤⢀⣆
⠀⢰⠁⠀⠀⠠⠀⠀⠄⠀⠀⠈⡆⠀⠈⠢⣇⣧⡞⣼⡟⣸⣸⡕⡯⢁⡯⠃⠀⠀⢀⠈⠀⢱⣶⣿⣷⣀
⠀⢳⣂⡂⠀⠀⠀⠀⠀⣀⣀⣈⢗⡄⠀⠀⢹⠙⠃⠷⠴⠿⠧⠶⠜⢊⠁⠀⢠⠔⠉⠁⠈⢁⣉⣉⣀⠀⠩⠶⢤
⠀⣶⣦⣽⣭⣭⣿⣹⣷⡤⣼⢵⡞⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠖⠢⠖⣄⠖⣤⠒⠤⠲⡔⠶⣾
⠀⢫⣽⡯⠹⢖⣛⣻⣷⣾⣿⢿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡻⠶⠶⠶⠶⠖⣖⣒⣒⣲⣟⡇
⠀⠀⠑⠂⠀⠀⠀⠀⠐⠒⠚⠁⠀⠀⠀⠀⠀⠀⢆⣀⣀⣀⣀⣀⡜⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠤⢄⣀⢀⣀⠤⠔⠒⠉⠒⢄
⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⡠⠤⡴⠁⠘⠉⠀⠀⠔⠠⠕⠀⠐⠁⢁⡈⠀⡼⢒⡶
⠀⠀⣀⣔⣊⣁⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠬⠵⠦⠀⠀⠑⢢⣘⣌⣀⣉⣀⢀⣀⣐⣒⣒⣂⣈⣡⣴⡊⣤⠋
⠀⠀⢒⣒⣶⣶⣶⣶⣶⣀⣈⣏⣉⣻⡿⠯⣿⠏⡹⡄⠀⠀⠓⣖⠪⡭⢿⡶⢲⣲⣒⣶⣿⣿⣿⡿⢔⣵⡿⠂
⠀⠀⠁⠐⠚⠒⠚⠒⠒⠂⠀⠀⠉⠀⠈⠈⠁⠀⠉⠁⠀⠀⠀⠈⠁⠒⠀⠉⠉⠓⠂⠐⠒⠓⠒⠉⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⣀⠔⣹⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡔⢣⠃⠀⠀⠀⠀⠀⢰⣍⡠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡃⢸
⠀⢸⠁⠘⠎⣓⡦⠀⠀⠀⠀⢠⠒⢶⡀⠲⢥⠇⠀⠀⣠⠤⠀⠐⢆⡹⠲⠶⢦⣀⠀⢀⢔⢒⣄⢠⠚⡟⣿⠛⠛
⡀⠮⡝⣉⣉⣩⠖⠳⡀⢠⠋⡀⢁⠉⣈⢢⠜⡄⠀⠀⢿⡓⠒⠒⠒⠒⠒⢒⣚⠏⠀⠰⠧⠄⢉⠎⣣⠿⠉⠘⠂
⠑⠶⠤⣤⢤⠾⣶⡚⠀⠘⣍⠙⠈⢉⡠⢯⠴⢸⠀⠀⠈⣦⣒⣙⣭⣋⡑⠠⡼⠀⠀⢀⠀⣰⣯⣾⡋⣦
⠀⠘⣮⡱⢪⠼⣱⠃⠀⠀⠡⢍⡉⠉⠉⣀⠔⠁⠀⠀⠀⢰⠄⣰⢀⢀⠀⢰⠃⠀⠀⡗⠀⠨⠝⠉⠀⣺⡗⠉⡄
⠀⠀⠘⡾⠿⠾⡾⠀⠀⠀⠀⠀⢀⢙⣉⣀⠀⠀⠀⠀⠀⠀⠄⢽⠈⠤⠀⡏⠀⠀⠀⠹⡉⠛⠛⠓⢈⡽⠧⠕⠁
⠀⠀⠀⠐⡄⢠⠃⠀⠀⠀⠀⢈⡀⠀⠀⢀⡹⠀⠀⠀⠀⠀⢠⣞⡘⢚⣾⠃⠀⠀⢠⡖⠚⠒⠂⠒⠋⠙⢱⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⡛⢄⠀⠀⠀⢀⡀⠆⢈⡀⡀⠀⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠨⠜⠓
⠀⠀⠀⣠⡯⠠⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡴⠠⡞⠁⠀⠀⠘⠢⢐⠉⢉⡀⣐⠒⠴⠆⣐
⠂⠀⠀⠸⣄⡀⡴⠀⠀⢀⡄⠀⠀⠀⠀⡐⣙⠀⠀⠀⣐⣉⠉⠀⢠⠀⠘⢤⠀⠀⠀⠀⠀⠀⠉⠐⠀⢈⡄⠒⠀⠀⡀⣀
⠐⡄⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⡈⡇⡀⠔⠁⠀⢦⡉⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠊⠒⠀⠂
⠀⠈⠀⠠⣤⣤⣴⠴⠋⠁⠀⠀⠀⠀⠀⠀⠶⣉⡄⠐⠤⢂⢡⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂⠤⠒⠁
⠀⠀⠀⠀⢠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⢠⡀⢀⣤⣄⢠⣤⡄⣠⣤⠀⣠⣤⡀⣠⣤⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⣿⡇⠘⣧⡉⠀⣿⠀⣿⣀⠀⡏⢸⡇⣿⢸⡇⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠉⢰⡷⣿⢠⡌⣷⠀⣿⠀⣿⠁⠀⣯⢸⡇⣿⢸⡇⣿⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠐⠴⡀⠅⠠⠄⠀⠀⠀⢂⠀⢀⡤⠁⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠀⠉⠉⠀⠉⠀⠉⠀⠀⠉⠉⠀⠈⠉⠀⠉⠉
⠀⠀⣀⢲⡆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐
⠀⠔⠭⠭⣷
⠀⠉⠒⠛⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡮⠄⢀⣀⠴⠚⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⣀⡈⡔⡆⠚⠰⡤⢤⠀⡀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⢤⡉⠉⠉⠁⢠⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢃⠈⠀⠀⢀⠀⠄⡈⢿⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠾⠿⢃⣔⡉⠸⠤⡡⢤⡀
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠂⢀⠀⠘⢀⠄⢚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⣹⣼⣿⣿⡿⠋
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠑⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⠴⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠡⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠈⠁⠐⠀⠀⠴⠀⠀⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⢠⢖⠢⡔⠀⠀⠠⠄⢒⣤⣀⡐⣪⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠦⣀⢐⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆
⠀⠀⠸⣄⠈⠛⠓⠀⠈⠲⠄⠀⣀⠄⠚⢀⡆⠀⠀⠀⠀⠀⠀⠀⡀⢉⣸⠘⢢⡌⡐⠺⢏⠀⢀⠀⠈⡦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠔
⠀⠀⠘⢤⢀⡀⠀⠀⠔⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⡀⠼⠄⣀⡀⠀⠈⠁⢉⡈⠓⡢⠊⡡⢶⡄⢂⠶⠀⠀⠀⠉⢄⡀⢀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠐⠬⣑⠂⠒⠐⢃⡁⠶⠊⠀⠀⠀⠀⠀⠀⠓⠠⠤⠶⢆⣀⠈⠉⢠⠜⠉⠀⠣⠀⠀⠁⠆⠀⣲⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠶⠤⠤⠤⡆⢠⣀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣀⣀⣀⣠⡄⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⣀⣸⠀⠀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⣸⠀⢉⠉⠉⠙⡋⠉⠉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠆⢀⠠⠀⢠⠃⠀⠀⠀⣀⢰⡇⠀⠲⠌
⠀⠀⠀⠀⡀⠈⠀⡇⠀⠀⠃⠐⠀⡀⢀⠀⠀⢀⡡⠷⠓⠚⠉⠉⠉⠉
⠀⠀⠀⡞⢲⡺⣄⢡⠀⢀⠆⢠⡇⠁⠈⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⡀
⠀⠀⠀⣇⢸⡍⠳⣆⣰⠆⣠⠋⣰⡠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢫⡢
⠀⠀⠀⢻⠘⡇⠀⠈⠉⠛⠛⠛⠉⠀⣾⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⡹⢿⣿⣿⣷⣾⣶⣤⣀⣳⣄⣦⣄⣠⡴⡊⢁⣀⣤⣖⣁⣤⠾⠁
⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⢃⠠⠉⡛⡛⠛⠿⣿⠿⢿⡿⢿⣿⣿⡿⠿⢿⣿⠛⠙⠻⡤
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⡈⢀⣌⣉⡒⢒⢫⣀⡴⠶⡾⠵⠶⢥⠤⠤⠤⢤⡤⣮⣭⣵⡿⠃
⠀⠀⠀⠀⠀⢹⣇⠀⢀⣀⣀⣀⣀⣈⣍⠙⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⢈⠀⢀⣴⣿⣿⡟⢁⠇
⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉⠉⠉⠉⠓⢤⣀⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠋⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠦⠤⠤⠀⣀⣀⡤⠴⠒⠋⠁

⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠓⢦⡀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣠⠴⣤⠈⠢⡀⠀⢀⣾⠃⢠⠖⠛⣷⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣸⠁⠀⠈⢷⣄⠑⡄⣸⡇⠀⡟⠀⠀⠈⢿⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⡏⠀⠀⠀⠀⢹⣦⠈⢿⡇⢸⣇⣀⣀⣀⣘⣷⡀⢹⡀
⠀⠀⠀⠀⠀⠀⢀⣨⣿⠀⠀⣷⣾⣟⡛⠛⠛⢻⣷⠈⠇⢸⣯⡭⠭⠍⠉⣿⡇⠀⢿⣿⣿⡟⠶⠶⣤⣄⡀
⠀⠀⠀⠀⣠⠾⠋⠉⣿⡆⠀⢹⣿⣗⣂⡀⠀⠀⢿⣧⠀⠘⣿⣿⡭⠅⠀⢸⣿⡄⠸⣟⣛⣛⣲⡶⠄⠈⠙⠳⣤
⠀⠀⢀⡾⢟⣫⠄⢀⣿⣗⣀⣤⣿⣽⣶⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣧⣤⣬⣿⣦⣀⣿⣿⠿⠭⠭⠤⠀⠀⠀⠈⣷
⠀⠀⠈⠻⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⢿⡿⠿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣗⣒⣒⠀⢀⡿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠛⡹⣏⢾⣷⠘⣣⣿⣜⣽⣇⣿⣼⣯⣇⣿⣸⡁⠏⢸⣿⢛⣷⣿⣿⣯⠭⠭⣡⠞⠁
⠀⠀⢀⣾⣿⠭⢿⣿⣿⣿⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣟⣻⡷⠛⠁
⠀⠀⣿⡿⣞⣫⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⢻⣟⣭⠶⣓⣿⡿⢿⡿⠛⠛⠛⠋⠉⠉⠉⠉⠉⣿⢽⣿⣿⡯⣿⣭⠽⠿⠛⠋⠉⠉⠉
⠀⠀⠀⠙⠳⢾⣭⣶⣛⣩⣴⣶⣛⣭⣴⣶⡿⠶⠶⠖⢻⣸⣿⣿⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣄⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⢸⣀⣨⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠔⠊⠉⢣⠀⠞⠉⠉⠈⡆⠀⡤⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡔⠋⠁⠘⡌⠆⠀⠀⠈⡇⢸⠀⠀⠀⠃⡸⠀⠀⠀⡹⡰⠋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠋⠉⠄⠀⠀⠀⠐⠀⠠⠌⠉⠓⠲⡄⠀⣀⠼⠚⡄⠀⠀⠸⣀⡄⠀⠀⢸⠃⠀⠀⢠⣡⠃⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠁⠤⠀⠒⢀⠀⠁⡀⠀⢀⠀⠀⠈⠀⠴⡀⠘⡄⠀⢱⠀⠀⠀⢻⡇⠀⠀⡜⠀⠀⠀⡇⠀⢩⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠁⠀⠀⠀⡀⠒⠀⠀⠀⠀⣀⠁⠀⠐⠀⢱⡀⠰⠀⠀⡆⠀⠀⠸⡇⠀⢀⠃⠀⠀⢸⠃⠀⡎⠀⡎
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡆⠀⠀⠀⣾⣯⡷⠀⠀⠀⠀⣧⠀⠇⠀⢣⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⢰⠁⣴⠁
⠀⠀⠀⣀⣀⠠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣾⣿⣶⠈⠉⠁⠀⠀⠀⠀⢡⠑⢼⡀⢸⠀⠀⢠⠁⠀⣸⠀⠀⠀⡇⠀⡬⠊⠹
⠀⠀⠀⠑⢄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣹⡟⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠚⠦⠤⠼⣀⣀⣿⡀⠤⠴⠓⠉⠀⠀⡇
⠀⠀⠀⠀⠀⡽⢦⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⢀⠤⣄⠀⠀⢰
⠀⠀⠀⠀⢸⡀⠀⠙⠢⡉⠑⠒⠠⠤⠤⠄⠀⢀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠖⠒⠛⢳⠀⠀⠁⠀⠈⠀⠀⣀⠀⠀⠁⠀⠀⠁⠀⡜
⠀⠀⠀⢀⡤⢟⠑⠢⠤⠜⠦⡀⠀⠀⠀⣀⠠⠤⠒⣲⠪⣉⠁⠀⠀⠀⢀⣀⡀⠠⢼⠄⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⡞⠹⡋⠛⠋⠋⠉⠛⠋⠉⠙⠙⠉⠋⠁⠑⠚⠛⠒⠚⠋⠁⠒⠒⠒⠘⡇⠀⠀⠀⠀⠀⠘⢿⠏⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠙⢢⠍⣂⣀⣀⣀⣀⣀⣀⠠⠤⠶⠶⠄⣀⠐⠂⠐⠂⠀⠐⠀⠂⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⢀⣀⡠⠽⠦⠤⠔⠚⠋⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠤⠤⠤⠴⠒⠉




⡿⠿⠿⠿⡿⠻⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿