Pillow Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣤⣤⣤⡀⠀⢀⣠⢠⠄⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡻⢓⠞⢁⠊⠋⠀⠀⠈⢠⣷⠝⠁⡺⠾⠛⠉⢠⠇⠠⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⠀⠂⠀⡰⢀⠆⣠⣤⣾⠟⠁⣠⣾⢡⣴⣮⣴⣁⡀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⡔⢀⡀⠀⢁⠞⢠⠻⠋⠁⠊⠀⠁⠠⠍⣙⣿⢿⣿⠷⢛⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠐⠱⠋⡇⡤⣰⠏⠀⠀⠀⠀⣸⡏⠀⡠⠛⢋⠀⠀⠴⡎⠁⢠⣼⡵⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠉⠀⠀⠀⠀⠀⢣⠁⠀⠀⠀⣠⣄⡴⠛⠁⢀⣴⠟⢁⣠⠶⠋⠤⣤⣤⠀⠼⢷⠶⠒⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠀⠰⣔⣄⠀⠀⣼⠀⠀⠀⣴⡿⢋⢀⣤⠶⠉⢁⣀⣔⣠⣶⣥⣀⣉⣙⣳⢤⣄⣀⡀⠈⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡗⡀⠈⣿⣜⠀⠁⠀⠀⡴⠋⠃⢁⠐⣲⣶⣿⡿⣿⣿⢥⣈⠛⠻⠿⣄⡉⢙⢀⠙⢍⡑⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢀⣴⣿⣬⣤⣆⠅⠸⠁⣠⢋⡥⠘⠋⠉⠉⢀⠠⠄⡀⠬⣅⣀⠀⠈⢶⣶⣿⠟⢶⣍⢰⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣜⣿⣿⣿⣿⣿⣿⣧⣤⣿⣏⣴⣾⡿⠛⠤⣬⣠⣤⡌⠲⠄⠀⠀⢀⡀⢌⡿⣶⣼⣿⣗⠦⠤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢨⣿⠛⠉⠁⠀⠁⠀⠉⠉⠙⣿⠿⣿⣿⣿⣷⣿⠓⠲⠯⡁⣵⣿⡲⣶⠀⠺⢿⣦⠱⡄⠙⣿⣧⠝⠒⠀⢹⡇
⠀⠀⠀⠰⠄⠀⢠⣶⣒⠂⠀⠀⣈⣲⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠟⠻⣿⣿⣭⣽⣲⣮⣦⣙⠳⣼⣿⡇⠀⠙⢳⣿⡄⢻⣷⠀⠀⠀⣾⠃
⠀⠀⠀⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣶⣦⣤⣙⣐⣆⡲⣰⡀⠀⠐⠀⠀⠙⠛⠿⣿⣏⣳⡝⠻⣦⠘⠞⢇⡌⣶⡘⡟⣿⣶⣿⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⡀⠹⠛⠟⣿⣿⡿⣿⣿⣿⡄⣵⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡟⣷⡟⢦⢰⣆⠳⡼⢷⣾⢾⣿⣷⣷⣄⡀⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠉⣶⣿⣿⣿⣿⡿⠈⠿⠿⠿⢿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡿⡏⠿⠀⣿⣧⣽⣾⣿⣿⣿⣿⣷⣼⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⡄⠀⠀⠀⣠⣮⡟⡲⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣷⣍⣻⣥⡘⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⡀⠀⠈⠞⠛⡄⠀⠀⠀⣶⡄⠀⠀⠀⠀⠠⠞⠂⠙⠻⣿⣿⠿⠿⠏⣿⣿⣿⣯⠟⠛⠛⠿⠛⠿⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⠻⠀⠀⠀⠀⠀⠐⢠⣾⠋⠀⠀⢠⣠⡀⠀⠀⢀⣀⡄⢸⣿⠄⠀⢠⣿⣿⣯⡥⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⣼⣶⡀⠀⠀⠀⠀⠁⡟⠘⠷⣾⣿⣿⣧⣶⣴⣿⣿⣿⠿⣿⡇⠀⣻⣿⣿⣟⡁⠂⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡼⣿⣿⢿⣷⣴⠀⠀⠀⠰⠁⠀⠀⠀⠉⠻⣿⣿⣿⡟⠉⠈⠀⠈⠃⢰⣿⣟⠯⠉⠡⠿⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣒⣭⣴⡊⠸⠛⠶⠷⠀⢠⡄⠀⠀⠀⠀⠀⣿⣿⣯⠂⠀⠀⠀⢀⠒⣹⣿⣿⡶⢄⡘⠂⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⣦⠆⣼⠠⡴⠁⢄⣀⠀⠀⠀⠀⠠⢿⣿⣏⡀⠀⠀⠀⢸⡰⣿⡿⣿⡦⣴⠞⠁⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢛⣿⣾⣥⣄⣥⣽⣾⣿⠰⣄⣀⣄⣠⣼⣿⣿⣂⣀⣀⣤⠞⣿⣷⣿⡾⠗⠴⠂⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡿⣻⣷⣿⣹⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⡿⠟⠋⢰⣶⣿⣿⣿⠿⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⣇⣽⣿⣿⣿⣿⣿⣿⣦⡀⣹⣿⣿⣿⣿⣷⢟⣰⣿⣿⣿⣯⣭⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡶⢶⢶⣤⣦⣦⡴⣶⣶⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠋⠉⠀⠀⠘⠛⠐⠀⠐⠀⠂⠀⠀⠰⠂⠸⣿⣿⣿⠄

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⠀⠀⠀⠀⢐⣀⠤⣶⠤⢶⠦⢄⡤⣄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢳⢣⡆⣶⢸⢸⢸⡆⡇⠀⠀⠀⠀⠀⢨⡤⣭⠭⣙⡭⣝⣭⣝⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⢸⠇⡇⣿⢸⠀⣇⢣⠀⠀⠀⠀⠀⠠⠶⣤⠶⣬⠶⣬⠴⣬⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⡇⡇⣿⢸⠀⡏⣼⠀⠀⠀⠀⠀⢰⠾⣴⠷⣤⠶⣤⠶⣤⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡇⡷⣻⢸⢸⢸⣳⡿⡄⠀⠀⠀⠀⠰⠛⠶⠻⠶⠛⠦⠾⣦⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠉⠈⠈⠈⠀⠀⠁⠀⠀⠀⠀⠁⠉⠈⠛⠒⠛⠒⠋⠀⠉

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠛⠶⠤⠄⠶⠲⠆⠤⠲⠏⠃⠀⠀⠀⠀⠰⣶⣦⣤⣤⣤⣦⣤⣤⣤⡄
⠀⠀⠐⡄⢠⢰⡄⠇⠀⡄⢠⣯⠀⠀⠀⠀⠘⡾⢷⠻⡾⠳⡞⢷⠷⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⡇⡆⠈⣶⢸⠠⠀⡇⣹⡇⠀⠀⠀⣴⣠⣀⣤⣢⣦⣠⣄⣠⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠳⡇⡇⡏⠀⢦⡄⡇⣿⡇⠀⠀⠀⢀⠁⠉⠊⠋⠈⢋⠘⠉⢉⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣟⣿⣿⣿⠆
⠀⠀⠀⣤⡁⠀⠀⠀⠀⠃⠨⠘⠀⠀⠀⠀⠛⠚⣷⠛⠾⠳⠞⠳⠛⠛⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠁

⠀⠀⠶⠴⠤⡶⠴⡦⢔⡶⣀⠴⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠆⡆⢂⠠⢀⢰⠐⠘⠇
⠀⠀⢩⣫⣝⣭⣫⢍⡩⣝⣭⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡄⢸⠰⠈⠀⡀
⠀⠀⢐⢔⠦⣒⠴⡲⢖⠦⢒⢔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠂⠁⡇⣸⠀⡆⡆⡃⠄
⠀⠀⢨⣫⣟⣭⣻⣝⣫⣝⣭⣫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠆⡇⢹⠀⠁⢡⢁⠀⠇
⠀⠀⣜⣶⣶⣒⢷⣲⢖⡪⣒⠶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡆⠀⡀⢸⠀⢀⢸⠸⠸⡀
⠀⠀⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠁⠈⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠳⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣄⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢰⣟⠛⠷⠶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠛⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣤⣤⣤⡴⠞⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⡇
⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠁
⠀⠀⠸⣧⣤⣤⣤⡶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢹⡆
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠂⢀⣠⠟
⢀⡶⠋⠉⠉⠉⠉⡧⠤⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⢷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡾⠛⣁⣀⣤⠤⠤⠤⠤⠤⠤⠤⠄⠹⡄
⠀⠀⠀⠀⠀⣧⠀⠸⡗⢦⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠸⡆⠀⢳⠀⠳⡄⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢻⡀⠈⢷⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠻⣄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠶⠶⠒⠚⠛⠋⠉⠉⠉⠉⠁⠈⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠃⢸⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣤⡴⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠤⠤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠤⠒⢄⠀⠀⣀⣠⠤⠔⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠢⠤⣀⣰⠋⠈⣳
⠀⠀⠀⠈⡦⠀⠘⠓⠉⠁⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⡼⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⢸⠃⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⣾⢰⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠘⡇⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢸⡀⢃⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⣇⠘⡄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠘⣆⠱⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠘⢆⠱⡄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠈⢳⡘⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠙⢆⠁⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠁⣀⣀⠀⠐⢧
⠀⠀⠀⠀⠀⠀⠰⢏⣀⡰⠓⠒⠤⢄⣀⡀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⣀⡠⠤⠒⠚⠉⠁⠀⠑⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⠁

⣿⣿⠛⢛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⣿⣧⡀⠀⠈⠄⠀⠀⠀⠀⣹⣿⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⢸⣿
⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⠀⠀⠀⣠⣾⣧⢠⣶⣶⣶⣷⣄⠀⠐⡀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⢰⣄⡀⠂⢠⣾⡛⠙⠻⣿⣿⣶⡄⠈⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡔⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⠏⠠⠠⣿⠋⣡⡀⠀⠙⢿⣿⡄⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢼⣩⡅⣩⣭⣭⣭⣭⢈⣭⣭⣭⣭⣭⡈⠀⢀⠀⠀⠀⠄⠀⠀⢆⢠⠋⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠸⢀⣠⢠⠤⣬⣿⣇⡿⠿⠟⠛⠛⠚⢛⡟⠛⢿⡿⣁⣀⠄⠀⠐⠀⢀⠀⢀⠀⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠐⢀⠈⢰⡏⠁⠐⡄⠀⠀⢀⠔⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠄⠀⠀⠀⠙⠄⠀⠀⢉⡀⠈⡷⢖⣶⣞⣻⣄⣁⠔⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠉⠭⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠀⠀⠀⠀⠀⢀⠓⢒⡄⠀⠒⠦⡤⠤⠤⠴⠒⠋⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠒⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⢃⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⠀⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠴⠀⠀⠀⠀⠀⠀⣿⣿⢿⠇

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⣿⣿⡿⠿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠈⠙⠋⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠁⠀⠀⣤⣦⠰⣦⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢺⣷⡿⠛⠛⢦⣌⣛⣾⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠉⠁⠀⠀⠀⠀⣛⣛⠛⠛⠒⢺⡷⠶⠶⠦⠤⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠉⠉⠉⠉⠛⢻⡟⠓⠒⠲⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⠟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣾⣿⣿⣷⣶⣦⣾⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠆
⣿⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠉⠛⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣶⣦⡀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⢰⣖⣴⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⡼⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡴⢎⠾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠷⣿⡿⣯⣙⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠘⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡟⣻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡵⢂⡀⠀⠂⠑⢄⡀⣼
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣟⠁⠀⠀⠀⢠⡤⠖⣋⣥⠞⢩⣄⡀⠀⠀⢑⣻⣿
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⡽⠀⠀⠀⠀⠸⠷⢬⡥⣤⡀⠈⠿⢟⡒⠀⠉⢹⡟
⠀⠀⠀⢈⡉⠀⠀⠀⠀⣀⡴⠀⠼⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣀⣠⡤⢂⡴⢂⣀⠄⠀⠀⠀⠀⢀⡠⠂⠀⡀⠀⢠⣀⡄⣨⢙⣢⣾⡇
⠀⠀⠀⠘⠀⠄⣴⠶⠀⢈⠤⠀⢀⣠⢄⣆⢀⡀⠀⠀⣨⠅⠀⠀⠀⣀⡬⠁⠀⠋⠀⠈⠁⢀⣀⣀⣰⡞⠉⢀⣦⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢘⠛⠋⠀⠂⠀⠁⠐⠚⠉⠁⣸⣟⣿⣷⣾⣇⢁⣀⣤⣴⣿⣿⡄⠀⠀⠀⠀⠒⠘⠁⠀⠀⠀⠀⠀⠺⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢘⣢⣤⡄⠤⠀⠀⠀⢀⣀⢈⡙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣭⣭⣿
⠀⠀⠀⠸⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⣿
⠀⠀⠀⢰⣦⠤⢤⡄⠠⠄⠀⢀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⢸⣷⡶⠾⠀⣀⠀⠂⠀⣴⣿⡀⢀⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣾⣿
⠀⠀⠀⢸⣿⠿⠛⠂⠂⠁⠀⠘⠿⠿⠶⣿⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿
⠀⠀⠀⣼⣿⡄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣾⣷⡄⠀⣀⣹⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠿⠏⠁⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠙⠻⢦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣺⣿⣿⣟⣉⣀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠉⠙⠻⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠒⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣾⣿⣿⣿⠿⠿⣿⡿⠷⠶⠶⠾⠿⢾⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠈⠁⠈⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠀⠀⠉⠉⠉⠉⠙⠒⠲⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⣶⣿⣿⣷⣈⣿⣝⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣀⠀⠀⣠⣾⣿⣿⣟⠷⠞⠉⠉⠉⠀⠟⠿⢿⣿⣷⡄⠒⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⣿⣯⣹⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠐⢶⣷⣦⣿⣿⠀⠀⠉⠉⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⡜⠁⢀⢀⣿⣿⣿⣿⣿⣏⣻⠀⠀⠀⣀⠈⠑⡄⠀⠀⠀⠀⢙⣿⣻⣧⡤⠖⠚⠉⠁
⠀⠀⠀⣠⠴⠚⠛⢛⣷⣶⣾⣅⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⢿⠛⠉⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⣠⠟⠋⠁
⠀⠀⠀⢀⣐⠔⣀⠄⠉⠛⣿⣟⡿⣶⣄⠀⠀⠀⢸⠙⢿⡿⠻⠷⢋⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠉⠣⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠉⢻⣷⣶⣤⣠⠄⠘⠿⣾⣿⣷⣄⢀⡼⡆⠠⢐⠀⠀⠸⡄⠀⠀⢸⣶⣄⠀⠆⠀⠙⢢⠖⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣁⠄⠈⠿⣭⡻⣿⣼⠃⠄⠨⠀⠀⠀⠙⣆⠀⠀⠙⠛⣀⠤⣢⠖⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢶⣤⡤⢀⡀⠙⠿⣿⣦⡀⢀⠈⠹⣯⣿⣶⣂⠎⠀⠀⣀⣤⣾⡷⠒⠒⠉⠁⣘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣔⢀⡀⠀⠘⠿⣷⡴⠂⠀⠈⠉⠛⠦⣀⠹⠿⠛⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡤⠀⢀⠀⠀⠉⠑⠲⢶⣄⣀⠄⠈⠙⠲⢤⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣖⠁⠀⠀⠀⠀⠉⢻⣿⣦⣴⠄⣀⠈⢙⣦⣀⠈⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣭⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⣁⠤⠀⠀⠹⢿⣿⣯⡁⠀⣀⠘⢿⣷⣄⠀⠀⠉⠓⢦⡀⠀⠀⢴⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠙⠻⠿⣌⠄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠉⠁⠁⠀⢠⡞⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⠛⠻⠿⠿⣿⣷⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡬⣿⡀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⢤⡀⠅⠀⠀⠀⠀⠀⠀⠀⢣⡘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣷⣶⣶⣤⣤⣤⣀⣀⡀⠙⢾⣙⣷⣆⣀⡀⢀⠀⠀⠀⢀⠀⢂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣭⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⣼⢾⣿⣿⣿⣿⣷⣦⣀⣀⣀⠤⠤⠀⠠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⢻⠼⣿⠿⠿⠿⠿⠿⠛⠃⠁⠀⠀⠀⠀⠀⠐⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⠐⠁⠀⠀⠀⠀⠀⠀⠈⢧⡸⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣝⣻⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠳⢮⣻⢷⣶⣄⣀⣤⣷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣝⡳⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣡⣤⣤⡾⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣒⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⡀⣠⡀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⡶⠿⠿⠿⢿⣿⣯⣽⣶⣿⣭⠔⠻⡟⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠻⠯⣼⣗⣦⣶⢆⣠⡼⠓
⠀⢀⡤⠶⠚⠓⠒⢒⣾⣾⡿⢟⣍⣻⢯⡞⠁⠀⡘⢀⡠⠔⠒⠈⠛⠁⠒⠢⢤⡀⠀⠀⠀⢰⣆⠀⠀⠈⡻⠉⣧⠙⣒⡦⠄
⠰⠋⠀⠀⠀⣠⡾⠛⠋⠁⢠⣬⣳⠁⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠎⣿⢗⠄⠚⠒⠉⠈⠉⠁⠀⠘⠛⠃
⠀⠀⠈⠀⠈⠁⠀⠀⣠⠀⠛⠃⠁⠀⠀⠀⣰⠃⠀⠀⠰⠆⢀⠁⡄⠈⡄⠐⠂⠀⠀⠘⢆⠀⠀⠘⣷⣄
⠀⠀⠀⠀⢰⣷⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢩⡄⠡⣀⣣⣧⣼⣀⠌⣤⠋⠀⠀⠘⡄⠐⠰⢻⡙⠃
⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⢠⣤⠀⢸⠀⠀⣈⠀⠈⣐⣾⡷⣾⢎⣷⡊⡠⠄⡉⠀⠀⡇⢀⠆⠀⣿⣄⠁
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠈⡄⠀⠀⢀⠛⡐⠛⡿⢲⢫⠉⢂⠘⣃⠀⠀⢠⠃⢎⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⠄⠀⠱⡀⠀⠀⠀⠄⠐⡁⠐⢀⠁⠠⠄⠀⠀⠀⠌⠀⠈⠀⢠⢿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣌⠓⠀⠀⠘⠄⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠿⡠⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡿⠸⣿⡟⠷⢦⣄⡀⠀⠀⡶⠀⠀⢀⣀⠀⠠⡤⠐⠀⠀⠀⠀⢀⡀⡀⠃⠀⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃⠀⢻⠀⢨⡦⡈⠙⢆⠀⠃⠀⠀⠀⡋⠀⠀⡅⠀⠀⠀⠀⠰⡸⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣆⠈⠁⣨⡅⠘⠀⢰⠄⢲⡀⠀⢨⡇⠀⠀⠀⠃⠀⠀⠀⠀⡘⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠓⢀⠀⣰⠀⠈⠁⠀⠸⡻⣦⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡃⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠸⠀⠁⡑⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢃⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⣿⡆⠀⢸⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠁⠀⢸⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⣀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠑⣀⡁⠶⡉⣣⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣟⡄⡸⣾⠀⠀⠀⠐⠠⠀⡐⠂⡂⢢⡀⠀⠀⢀⠰⣄⠩⢤⠘⢣⣄⠹⣆⡙⣥⠚⡾⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⠛⠘⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡈⢤⡈⢤⡀⠻⡤⠑⢢⡈⢵⠆⠓⠀⠈⠈⠀⠸⢡
⠀⠀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠱⠦⠉⠠⠚⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢠⡤⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⣀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⡤⠧⠀⢀⡤⠀⠀⠀⠀⠀⠀⡤⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⡀⠛⠀⣠⡶⠀⠀⠀⠠⠇⠉⠉⠉⠉⠛⠉⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⢀⡤⠖⠀⠀⣀⣠⢠⣤⣤⠶⠶⠴⠁⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠰⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠛⠃⠀⠀⠀⠀⢲⣶⣾⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠘⠲⠆⠒⠊⠀⠀⠀⠀⠈⠉⠠⠈⠀⠁⠉⡗⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⠁⣀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⢤⠀⠀⠧⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⠁⠠⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⡦⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠀⠘⠀⠀⠃⠀⠅⠀⠐⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣐⢁⠺⠁
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠤⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠠⢤⠄⠈⠀⠀⠀⠈⡀
⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⢆⠴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⠁⠉⠀⠀⠀⠂⠀⠠⠤⠄⠤⠔⠈
⠀⠀⠀⢀⡀⡧⠀⠴⠆⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠓⡼⠆⠀⣀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠐⠒⢤⡄⠀⠈⠁⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈
⠀⠀⠀⢀⡀⠀⠀⠟⠀⠀⠴⠀⢁⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣚⠁
⠀⠀⠀⠀⠁⠀⠷⠀⢰⡀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠐⠆⠀⠀⠌⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⡶⢠⡀⢒⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠠⠈⠃⠀⠀⠀⣀⠀⠀⠀⠈⠇⡈⠕⠉⠀⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢁⠀⠃⠠⠄⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠖⠀⠤⢄⣀⣠⣤⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⡀⠒⠀⠀⠀⠀⠀⠀⠬⠽⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠁⠀⠐⠁⢀⠀⡀⣄⠀⠀⠀⠀⣀⣀⣀⡈⢻⠇⢀
⠀⠀⠀⠀⠀⠀⣸⣷⡀⡀⢀⣼⠿⢋⣡⡴⢚⣀⣠⡴⠞⠛⠋⢀⣠⣴⣾⠿⠋⠉⠉⠻⢿⣶⡾
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣾⣿⡴⢛⣭⠶⠛⠉⠀⣀⣤⣶⣿⠿⠿⠓⠒⠲⠶⢦⣤⣀⣀⠙⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣾⠟⠀⢠⣴⣿⣿⡿⠟⢉⣁⣠⣴⠞⠛⠒⠒⠲⠶⢶⣽⣦
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠋⣄⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡃⠀⠀⢀⢠⣤⡤⢾⣿⣦
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣍⠛⠋⢉⣻⣿⣿⣿⣿⣿⣵⣶⣤⣶⣿⢿⣾⣯⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⠟⡋⠁⠀⣴⣿⣿⣿⣿⣿⣁⣘⣤⢾⣿⣿⣷⣴⣦⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⡿⠿⡿⡿⠟⠋⢻⠿⠷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠁⣝⣛⣽⠏⠀⠀⠀⠘⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡮⠉⠀⣴⣀⣀⣠⣤⣬⡻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡻⢟⣿⣿⣿⣿⡿⠿⡃⣀⣠⣾⠙⠿⡿⢿⣿⣿⣷⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣦⣀⣠⣤⣭⡟⠁⢀⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠻⣿⣿⣯⣽⠏⢀⣴⠏⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢾⣧⡄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⣿⣿⠋⠀⣸⠏⢠⡾⠋⣸⠟⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣁⣀⠀⠀⠀⠀⠀⢸⡟⢠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠖⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣤⡈⠁⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠻⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠉⠙⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠒⠖⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⣴⠋
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠚⣋⣉⣭⣥⣤⣤⣤⣤⠤⠄⠀⠀⠀⠀⣠⠏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠤⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣰⡏
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢠⡟
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢀⡿
⠀⠀⠀⠙⠛⠋⠉⠛⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣤⡀⠀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡤⠦⢤⣄⣀⠀⣀⣠⡤⠤⠶⠒⠒⠛⠛⠋⠉⠉⠉⠙⠛⠛⠒⠲⠶⠤⣤⣀⡀⠀⢀⣀⣠⣄⡀
⠸⡇⠀⠀⠠⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠉⠁⠀⠈⣧
⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⢀⡇
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁
⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢦
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡤⠷⠒⠒⠛⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠘⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠲⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠹⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇
⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣷
⢠⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡟
⢸⡁⠀⢀⣘⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠐⠙
⠀⠉⠋⠉⠁⠀⠈⠉⠓⠲⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡤⠞⠋⠓⠒⠒⠒⠒⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠀⠀⣠⣤⣄⡀⢠⠔⠆⠀⣀⣀⠰⣇⠆⢰⠀⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⣛⣯⣍⢹⣿⠷⠤⠞⠿⠷⠥⠤⠇⠀⠘⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⣰⠛⠂⢀⣄⣜⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠎⠛⠛⠛⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⢀⡀⡀⠀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⣧⣉⣭⣿⣟⣿⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⠉⣉⡉⣙⣻⠀⠀⡁⠀⠀⠀⠀⣁⠀⠀⠀⢰⣶⣶⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠀⢰⠶⠓⠀⢰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡖⣴⠾⣾⠏⣽⠐⣮⡀⣞⠚⠛⣧⣟⣶⡄⠀⠎⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣇⣴⣖⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⣿⣇⣼⣄⠁⠈⠅⢈⡀⣁⠀⢄⡀⢀⣤⣤⣤⣤⣤⣤⣴⣧⣿⠷⣶⠀⠀⠀⣤⣀⣼⣯⣈⣉⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⡘⣿⣿⣿⣿⣿⣾⣿⣿⣤⣼⣿⣿⣿⣽⣽⣿⣿⣷⣤⣤⣄⣀⣠⣾⣥⣤⣿⣿⣭⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⡄⠀⢂⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠀⢈⠉⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠀⠑⠀⠂⠀⠰⠂⠀⡀⣉⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠉⠉⠁⠈⠀⠉⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⡀⠀⠤⡔⢷⣦⣠⣀⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢠⡍⠉⣁⣬⣆⣻⣿⣿⣷⣯⣏⡛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣠⣶⡿⣿⡏⢉⣉⣁⡸⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⡖⢠⣾⠟⠁⠈⠋⣠⣿⠋⠁⠀⠙⠻⠮⣝⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⡞⢠⡿⢁⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠈⠳⠙⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣾⢡⡟⢀⠀⠀⢀⣼⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⡟⠀⠄⢀⠀⣾⠃⠈⠀⠀⢀⣤⣤⣤⣄⠀⠀⢰⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡿⢰⣾⢡⠇⣸⣿⡇⠀⠀⠰⢃⡀⢈⣿⡞⢿⡀⠸⣯⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠗⠊⣿⠏⣰⣿⣿⠇⠀⠀⠐⠿⠏⠛⠐⠁⠈⢷⡄⠱⣦⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⢸⣦⣿⣟⠗⢶⡄⠿⢿⠿⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⢧⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣠⠿⢿⣿⣯⣽⣿⣿⣆⠸⣷⡀⠀⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⢄⣠⣾⣷⣦⠴⢶⣆⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣴⣟⣭⣅⣠⣤⣿⣿⣄⡈⠑⣶⡀⠀⠀⠈⢤⠘⢷⡄⠀⠀⠀⠀⠀⢀⣼⡇⣠⣶⡆⢻⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⢀⢺⣿⣋⣩⣽⣿⣿⣷⣿⢻⣿⣶⡟⠳⣄⠀⠀⠀⠀⢿⠁⠀⠀⠀⢴⣶⣋⣙⣧⣼⡏⢧⠸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⠿⠖⣉⣛⠉⠹⠏⢻⡛⠛⠛⠋⣿⠃⠀⠉⢓⠤⣀⠀⠘⠀⠀⠀⠀⠀⠀⢛⣡⠟⠋⠀⠀⣠⡿⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⣴⣿⡂⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⢄⣤⣤⣴⡶⠛⠁⠀⠀⢀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⢾⡭⠉⢉⣛⠿⡦⠀⠀⠀⠈⢦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣛⣾⠇⣤⣄⣴⡀⠀⡀
⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢄⠀⠈⠳⣤⣀⠂⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣸⠿⣿⡇⠘⣿⣿⡇⢻⠇
⠀⠀⠀⠀⢸⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣀⠂⠀⢹⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⡿⠀⣿⡇⠀⠘⣿⣧⠀⠆
⠀⠀⠀⠀⣸⣿⠀⠀⢰⡁⠀⠀⠀⠂⠀⠀⡀⠀⠘⣿⣷⡀⠉⢻⣷⣄⠀⠀⠀⢰⠋⢸⡿⠀⡇⢺⣿⡇⠀⠀⢹⣧⠀⢠
⠀⠀⠀⢠⡏⣿⡀⠀⠈⠀⠀⠀⠀⠀⣀⣢⠈⠀⠀⠸⣿⣧⠀⡌⣆⠉⠀⢤⡄⠀⠀⢸⡇⢰⠇⠀⣿⡇⠀⠀⢰⣿⡄⢸
⠀⠀⠀⣾⠀⠻⠇⠀⠀⠤⠤⠀⠀⠂⠉⠻⢿⡳⠆⠀⣿⣿⡄⢁⢹⡄⠀⠀⡤⠀⠀⣿⠀⣾⠀⠀⣿⡇⠀⠀⠈⣿⡇⠀⡆
⠀⠀⢰⡏⠀⣠⣴⣶⣶⡶⠶⠶⠶⠦⢤⣤⣀⣁⠀⡀⢹⣿⡇⢸⠈⣷⠀⢸⡇⠀⠀⠘⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣷
⠀⠀⢸⠁⠀⠈⠓⠾⢿⡇⠉⠁⠀⠀⠀⠀⠈⠉⠝⠛⢼⣿⡇⢸⡆⢻⡄⡺⠁⠀⠀⠀⠀⠀⠀⣼⠏⠃⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠉⠾⠾⢵⣄⠸⢯⠤⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠘⢕⣢⣤⠄⠘⠀⠐⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢼⣃⠀⠀⠸⡧⢠⠀⠀⢀⡄⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⡀⣀⣤⡋⠀⠐⢤⠋⠁⠠⣼⡛⡀⠸⣯⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⣀⡙⢱⡷⣼⡋⠀⠀⢻⢀⡀⣲⡗⠀⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠔⠒⡎⠉⣁⡽⠂⣄⡈⠁⠀⣠⢸⠗⠀⠈⠁⢠⣈⡿⠁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠉⢀⡖⠋⠙⠉⠀⠀⠀⢹⢙⠀⠀⠈⠛⣠⢨⠀⢀⡀⠉⡳⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠋⠉⠒⢤⠀⠀⠀⠀⣌⡆⠀⠤⠀⠀⠹⠀⡠⠒⢽⣂⢙⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⡀⢸⠣⡀⠀⠀⠀⠈⢣⠀⡀⢼⠋⢤⠰⢇⡙⢴⡄⠘⠋⠀⠘⠇⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⠕⠿⠎⠢⢈⡐⣒⣠⠶⠎⠁⠀⠀⠀⠲⣇⢸⡇⠀⣠⡊⡨⠭⣽⣆⢲⣌⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢎⡓⡶⠆⠀⠀⠀⠀⣀⠀⠀⡈⠡⠀⡠⡌⢀⣄⠀⠆⠈⠀⠀⠀⠈⡗⠾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠠⠖⠠⡼⠳⡔⢢⣀⠀⠞⣣⠆⢹⣄⠌⠘⠋⡰⠘⣤⣀⡀⠀⠰⠁⣠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠆⣶⠒⠢⠤⡇⠀⠹⡄⡿⠀⠛⠀⠀⠀⢣⠐⢢⡘⡷⠀⠀⠈⡻⠛⢋⡉⠐⠯
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⣽⡟⢶⡀⠀⠀⠈⠢⣀⣿⠃⢀⣶⡇⠨⢈⣾⡆⠈⣁⢲⠀⢸⣶⠃⢀⠈⠃⣰⡄
⠀⠀⠀⠀⠀⠀⢀⣽⣶⡄⢀⡀⢀⣈⠺⠦⣤⢴⣒⢭⡼⠀⢺⡿⠁⠀⣦⠀⢸⣞⢁⢿⠾⠀⣿⣐⢄⡐⠶⠿⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⢯⡙⠒⢛⣳⠀⠀⠠⠀⠀⢳⣠⣿⡋⢀⡀⢠⣟⠀⣟⡁⡗⢲⣤⢁⣴⠀⠻⣦⠓⢷⡇
⠀⠀⠀⠀⠀⢀⡀⢰⣄⠶⣶⠄⠀⠟⠋⣰⣦⠸⣖⣦⣄⣿⣿⡶⣋⡇⠀⣏⣳⣿⠻⣏⣚⣿⣺⣃⢠⡓⢍⠀⠚⣃
⠀⠀⠀⠀⠀⠘⢻⣾⣿⣷⢘⣻⣷⣦⣤⣾⣿⣦⣬⣿⣿⣿⣿⣿⡿⣵⣷⣿⣿⢿⡦⣿⡿⣿⣷⣾⣿⣧⣮⣧⢠⡉
⠀⠀⠀⠀⠀⠘⠀⠛⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠚⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⣠⠔⠒⠂⠄⠀⠀⠀⡀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠹⠿⠟⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠠⣶⣦⣄⡀⠀⠀⠀⠀⢫⢻⡀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⣿⠿⣦⠀⣄⣀⠈⠇⡷⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠹⠀⢟⡇⢻⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⣀⣤⡀⢰⡀
⠀⠀⠀⠀⣀⠄⢀⣨⣿⡐⢄⢠⣠⡖⠀⠀⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠈⢳
⠀⠀⠀⡰⠋⠀⣻⣿⣿⣷⡘⠿⢿⡇⠀⠀⠰⠋⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⢐⣿⣿⡇⢻⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠻⣿⣄⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠁⡜
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠈⠛⠿⢷⡤⡀⠀⠀⠀⠀⠀⠀⠶⠂⢸⠁
⠀⠀⠀⢠⡀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠈⠐⠢⠤⢄⣀⣀⣀⡰⠇
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠟⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⢠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣻⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣶⣦⣤⣤⣤⣶⡟⢻⣧⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡟⢻⣿⣯⣨⣿⣿⣿⣷⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠛⠿⠿⠛⠉⠻⠭⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣄⣠⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠙⠛⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠀⣀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⣿⡆⠀⠀⠀⠀⠐⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⡿⠋⠀⣠⣴⣆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠉⠛⠛⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣷⣄⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣾⣿⣯⡀⠀⠙⢿⣿⣿⡆⠀⠈⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦
⣾⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣦⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢀⣴⣿⣿⣿⣧
⠙⣿⣦⠀⠐⢶⣾⠂⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣦⣤⣴⡾⠟⠀⠀⠘⠛⠉⣀⣼⣿⡆
⠀⠈⠻⣷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣧⣤⣤⣀⡀
⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣶⣤⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠘⡷⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣿⣿⠿⣿⣦
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣶⣤⣤⣶⠟⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠋⠀⠀⠸⠟⠁⢀⣾⣿⣷⡀
⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠠⡿⠿⠛⣿⣷
⠀⠀⠀⠀⠀⠹⣿⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠋⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣏⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠁⠀⠀⠀⠀⠉⠉⠁⡀⠀⣿⣿⠃⠀⣠⡀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⣿⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣷⣤⣶⣿⣤⣾⣷⣴⣿⣿⣷⣾⣿⣿⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⢿⣿⣿⡟⠋⠀⢈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠙⠛⠛⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⣠⡶⢶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣉⢶⣷⣶⠂⡉⠑⠄⡀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡎⣠⣤⡤⣅⠀⢹⣿⣷⡁⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢰⣿⠫⣿⣷⠀⢾⡿⠻⢿⠊⠀⢀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣗⡀⠸⠃⠀⠀⠀⠄⣦⠀⠀⣾⢻⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢹⣿⣿⡷⠋⡰⠊⠙⢱⠀⠱⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢙⣋⢔⡠⠃⠀⠀⡨⠁⠀⢹⢏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⡉⠀⡚⠁⠀⡀⢴⣮⠀⠀⢀⣜⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡤⣤⡾⣅⠈⠉⠳⣄⡺⡗⢤⠌⣢⡤⠞⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠓⢒⡶⣶⢄⠀⢀⡈⠑⠻⠱⠿⠉⠙⠛⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣀⣀⣜⢿⢤⣦⡏⠘⠋⡛⢒⣂⢊⣤⣿⠀⣿⡁⢀⣶⠄
⠀⠀⠀⠀⠀⢀⠤⣒⣁⠤⢐⣋⢁⠼⠀⣙⣧⣛⡛⣿⣈⡟⠀⣉⡵⢖⠜⣰⣿⣃⡀
⠀⠀⣀⠄⠊⠀⢎⢀⠀⠀⢀⣀⠏⢐⠝⠂⠀⠈⣉⣀⣀⡤⢋⣀⠔⣡⡞⢁⣤⣾⠷
⢰⡉⠘⠠⠤⠄⠠⠀⠈⠉⢀⣀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣿⡾⢟⡽⠋
⠀⠀⠀⣩⠝⠃⠐⠐⠒⠀⠄⠤⠀⣀⣀⣀⠀⠉⠉⠁⣁⠴⣒⣿⢟⣭⡾⠋
⠀⠀⠸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⢡⢾⣿⡿⠋

⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠿⣿⠿⠻⠿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠤⠀⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣴⣾⣿⣿⣾⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⡀
⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢵⣻⡆
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠿⣿⣿⠿⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⣶⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⣴⣾⣿⣿
⠀⠀⠀⢻⣿⣿⣶⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠠⢸⠁
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣷⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠻⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣾⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧
⠀⠀⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠻⠿⠛⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⢀⠘⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢸⣧⣽⡄
⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠍⣺⣿⣇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣙⠿⠿⠟⠿⠿⠟⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⣰⡀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡴⠞⠛⠉⠀⠀⠀⠂⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣾⣿⣿⡿⠵⣶⡦⡼⣧⠮⣽⢿⠿⣿⣽⣿⣧
⠀⢠⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠉⠛⠃⠀⠀⠒⠀⠃⠀⠁⠶⠂⠿⢿⣿⣿⠄
⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣶⣶⣶⣶⣶⣖⣲⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣒⣶⣶⣶⣶⣶⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣟⡿⣿⣿⠿⠿⠛⠛⠻⠟⠛⠛⠛⠛⠻⠿⠻⢿⢟⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠊⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠏⠁⠈⡄⠉⢳⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⢐⡀⠀⠀⣤⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡏⠀⠀⢀⣠⣀⡈⢷⡄⠀⠐⠀⠀⣰⠃⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡃⢉⣿⠀⠙⠷⠶⠶⠚⣡⣏⡹⠈⠛⣦⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⣙⣓⣿⠀⠀⠀⠀⠀⠐⣯⠢⡅⣢⠜⣸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢺⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡤⡤⠴⠋⠀⠠⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣇⡀⢸⣒⣔⣶⣘⣆⡠⡤⠀⠀⠀⠀⣰⣶⣶⣼⡆⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣒⣻⣿⣿⣻⣶⣒⣦⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠉⠉⠉⠹⠿⣛⢛⡛⠛⢛⣛⡛⣛⣛⣛⣛⣛⠛⠛⢻⠋⠋⠋⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⡉⠉⠉⢁⣀⣀⣀⣈⣉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇
⠀⠀⠀⠀⠐⣶⡀⠀⣹⣦⠀⣴⠁⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡅
⠀⠀⠀⠀⠀⢻⣿⡷⣾⠗⣿⡿⡄⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠸⣿⣷⢸⢹⣿⠃⣇⣀⣀⣀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣮⣼⣿⠀⠠⠀⠀⡆⢰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡀⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣠⣤⣦⣤⣥⡼⠿⠻⠛⠻⢳⣶⣶⣶⣶⣶⣶⠶⠿⠾⠿⠿⢦⣷⣶⣦⣬⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢻⣯⣤⣤⣤⣤⣤⠜⠛⠛⠛⠛⠻⠛⢤⣤⣤⣤⣤⣤⡿⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄
⠀⢀⣾⣿⣿⣛⠽⠱⠂⠀⠀⠀⠀⡴⠲⣶⡶⠒⣗⣶⣦⣤⣼⡇⠀⠀⠀⣠⣤⣶⣶⣶⡷⠖⣢⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠛⢶⡀
⠀⢹⣿⣛⢋⠅⠈⠀⠀⠀⠀⠀⣸⣷⡿⠋⢐⡴⢚⣿⣶⠶⠤⣿⣆⣠⣾⠿⠋⠻⡍⠙⠻⡻⢿⣅⣱⡄⠀⠀⢰⡿⠛⠋⠙⢿⣶⣾
⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⡡⠔⠋⡴⢛⣾⠁⠀⠀⣸⣿⠟⠁⠀⠀⠀⠈⢧⣦⡜⡄⣝⢿⣱⡀⠀⠀⠇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠁⠊⠀⠀⠀⢸⡵⣨⠇⣠⣴⣾⠟⢻⡄⠀⠀⢀⣀⡀⠀⠈⠻⢾⣮⣸⢿⡇⠀⠀⠀⠀⠀⠀⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠰⣷⡾⠝⢉⣠⣴⣶⣿⣿⣿⣿⡿⣿⣿⣶⣄⠀⠪⡻⣾⠃⠀⠀⠀⠀⠀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠓⠣⣠⣾⣿⠿⢋⣩⣽⣷⣴⢌⣵⡾⠿⠛⣯⣷⡄⠳⠙⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⣰⣿⣿⣿⡿⣶⢮⣽⣿⠟⠇⠘⠀⠠⠄⢆⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢿⡟
⠀⠀⠀⣓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⣀⢀⠸⠁⠀⠀⠀⢤⠘⠂⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠃⢸⡇
⠀⠀⠀⣻⡟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠀⠋⠩⠈⠀⠀⠀⠀⠀⠀⡀⡀⣔⢿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠿⢿⡾⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣰⠀⠹⠁⠂⠀⠀⣤⢧⡄⢃⣰⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣿⡮⣆⠀⣿⡰⣤⠹⡀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣾⡦⢽⣠⣤⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠠⠂⢄⡎⠀⠀⠀⠀⣀⡤⠤⠤⣤⣀⡀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⢰⣤⠑⣄⢢⡑⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⡠⣮⠅⢰⠆⢀⣴⠀⣨⣭⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣧⣟⢐⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠄⡿⠀⠀⠀⣰⣳⣿⣠⣯⣥⠿⠿⠟⢏⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣟⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢠⣿⣿⣏⡉⠉⠃⠐⣀⡽⠏⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡶⠁⠀⠀⠈⠉⠛⠚⠛⠉⠀⢀⠔⢉⢠⣾⣿⣿⣿⣟⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣿⣿⣿⣿⣿⣿⣟⣷⣼⣇⣀⣀⣀⣀⣀⣀⡀⠀⣠⣇⢀⣀⣀⣀⣀⣽⡀
⠀⠀⠀⠀⣼⣦⣄⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠒⠊⠛⠛⠉⠉⠛⠛⠛⠻⠃⠻⠻⠿⠿⠿⠿⠋⠉⠻⠏⠙⠛⠛⠛⠙⠛⡋⢹⣿⣿⣷
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠂
⣀⡀⠀⠈⠀⣀⡰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀
⠀⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠤⠖⠀⢤⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪
⠄⠄⠂⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡐⠀⠀⠀⠀⠀⢄⢰⢠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢄⡋⠠
⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠰⠂⢀⣀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣷⠈⠻⠀⠀⠀⠤⠀⣁⠤⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠀⠀⠱⠀⠀⠹⠆⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠊
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢨⠀⠀⠉⡅⠀⠀⠁⢤⠤⠤⠤⠤⠤⣤⠠⠀⠀⠀⠀⠀⢀⡀⠅⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠰⠸
⠀⠀⠀⠸⠀⠀⢈⠀⠀⠤⡀⠆⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⡂
⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⣀⡀⠀⠀⠀⡀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠆⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠠⠖⢠⠜⠉⠣⠀⠀⠉⠓⢤⠤⠥⢆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡠⠊⢉⣰⠎⡀⠔⠉⠀⠀⠀⡀⠀⠈⠉⠐⢱⡆⡈⠉⠷⠒⠒⠛⠘⠤⠤⠄⠀⠄
⠀⠀⠀⠀⠀⣧⠔⠁⠀⡌⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠑⡼⠁⢉⠁⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡌⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠃⠀⠀⣰⠠⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢄⡀⢀⣀⣀⣀⠀⠀⠠⠊⠀⠀⠀⠀⠸⣇⠘⣖⣲⠆⠁⠈⢂
⠀⢀⠀⠀⠀⠀⣿⠄⠀⠤⠂⢁⡁⡀⢀⢀⡀⠀⢉⠐⠖⡀⠒⠐⣃⣤⡈⠉⠉⠀⠊⠉⠉⣨⣀⣀⣀⣀⣀⣀⡀
⠀⠈⠀⠀⠀⠀⡏⠤⡎⠀⣀⠿⢣⠄⠀⠀⠄⣉⠞⠵⡀⢘⠀⠀⠉⠘⠁⠉⠉⠉⠋⠉⢻⣿⣉⣉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠰⠄⠲⠚⠚⢁⠄⠊⠐⠄⠂⢀⠀⠁⠀⠉⣛⡛⢛⠂⠻⣃⠀⠂⠂⠀⣶⣼⢇⡀⡈⣧⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠃⠀⠄⠀⢀⠥⢠⠀⠈⠁⠉⠂⠁⢤⠤⢄⠁⠈⠡⠃⠀⠩⡉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⡞⠄⠡⠔⠂⠇⢀⠌⠈⠓⠒⠐⠒⠂⠈⢄⢀⠃⠐⠀⠀⠄⠈⠡⠀⠐⠠⢤⠔⠈⠀⠀⠀⢠
⠀⠀⢠⠘⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠃⠀⠀⠈⠉⠀⠉⠉⠉⠁⠀⠀⠓⠀⠃⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠤⠤⠬⠥⠍⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠐⠂⠠⢀
⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠄⠀⠠⠀⠄⡀⠀⠀⠀⢀⡀⠠⠤⠤⠀⢀
⠀⠀⠀⠀⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⣀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠌⠁⠐⢄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠁⠃⠀⢐⠀⠀⠀⠀⠉⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⡌⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠁⠀⠀⠀⠀⠠⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠁⣀⠠⢄⡀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠤⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢐⠀⢰⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧
⠀⠀⠀⠀⠾⣇⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⠠⡀⠀⠀⢀⠀⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠈⠢⡈⠃⠙⠄⣈⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠉⢁⠀⠈⢀⠓⠂⢀⠄⠒⠒⠀⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠃⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢁⣘⡳⠂⠀⢠⠁⠀⡀⠄⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠘⡄⠀⠀⢀⡴⠖⠤⠜⠓⠺⡄⠀⢀⡆⠀⠀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⡠⣈⠑⠒⠲⡌⠑⠀⠀⠀⠀⡎⡁⠀⣼⠅⠀⠤⠊⢱⡀⠀⢐⣆⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⡠⠐⠉⠐⠐⠂⢤⡊⠀⠂⣋⠠⠀⠰⡄⣀⠁⠠⠤⠀⢱⣀⠇⠀⠀⠀⠀⠀⢫⡀⠀⠀⠓⠈⣀⠀⠀⠀⠀⠑⣄⣴⣌⡐⢆
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⢉⣢⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠈⠆⠀⠀⠀⠔⠁⠙⢁⠇⠈⡂
⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡣⢀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢒⠒⠢⣼⠀⠀⢈⠀⠀⠀⡖⠪⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠉⠐⠂⠀⠉⠋⠀⠀⠑⠠⡋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢀⠃⠀⢀⣼⣀⡔⠀⢢⠀⠀⠐⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡀⠄⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠤⡤⠀⠀⠐⠀⢰⠆⠀⠀⠘⠿⠋⠀⠀⠀⠆⠀⠀⠓⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⡡⠐⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠠⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⣰⠠⠊⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠑⠂⠠⠂⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠂⢂⡀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⠈⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠂⠘
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⠆
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰
⠀⠀⠀⠰⠃⠒⠒⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠡⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠤⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠟⠛⠿⠿⣿⣷⣶⣤⣀⣹⣿⡶⣾⣿⣿⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣴⣾⣷⣶⣮⣽⣿⣿⣿⣿⣧⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣤⣦⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⡀⠀⣀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢻⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣾⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠙⠻⢿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧
⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡄
⠀⢹⣿⣷⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⣿⡿⠟⠿⢿⣿⣿⣋⣀
⠀⠀⢻⣿⡄⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣿⣿⣆⣿⣿⣿⣇⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠙⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣙⣿⡟⠉⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣋⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⠟⣁⣴⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣵⣾⠟⠉⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⡖⣶⠋⢉⠛
⣶⣶⣶⣄⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠜⠁⠀⠋⠑⣮⠛⠶⣄⢀⣀⠀⠸⠿⢷⠔⠻⠉⠀⣼⣵⣿⠤⡄
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣲⠊⠀⠀⣆⠀⠀⠹⡄⡈⣦⡉⠻⢦⣄⣀⠀⢢⣰⣦⡾⣷⣿⣿⣶⠂
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠰⠁⠀⣠⠔⠉⣷⣦⡀⢳⣁⡹⠗⠠⠠⣾⡯⠟⢿⣥⣾⡿⢫⣿⣏⡏
⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡐⠂⠀⠀⢠⠃⠲⠇⠀⠉⢸⣩⢀⢠⠴⠂⠁⠀⠀⣰⣟⡿⢳⣾⣿⣿⡇⢠⣴⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⡈⠀⢀⠤⠃⠄⢰⡆⠀⢀⡠⠋⠛⠀⣀⠀⠀⢀⣼⣿⣾⣭⣿⣿⡟⣧⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⠀⠀⠀⠀⡠⠘⠟⣧⣾⡁⠀⠀⠠⢤⣬⣾⣿⣷⣿⣡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠐⠒⠀⢀⡃⡸⠋⠀⠀⣀⣰⠿⠞⡫⠫⠻⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡎⢠⡆⢺⠆⠂⣠⢎⠁⢀⣠⡿⢡⠄⠚⠉⣣⣲⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡄⠀⢸⡷⢼⠇⡞⠀⠈⢁⣿⣅⣀⠀⢠⠖⣪⣾⡿⠿⢷⡿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⢸⣃⣾⣀⡇⠀⠀⣾⡈⢧⡈⠙⠳⣾⣿⠏⠁⣿⡏⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⢘⣠⢟⠩⢿⡿⠁⣠⣾⣿⣿⠿⣷⡄⣜⡿⠁⠀⠘⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⡦⣽⣖⢺⠾⢷⣴⠋⣠⡄⠹⣄⣋⣿⡞⠀⠄⡀⣱⣿⣯⡿⢟⣻⣿⣿⣿⣿⣿⡄
⣿⣿⣿⡿⠟⠋⠀⠐⢓⠋⠉⠉⠉⣽⠴⠛⢷⣶⣿⣿⣶⣿⣿⣿⣃⠀⠀⢀⣿⣡⡞⠻⣿⡻⢻⣟⣉⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⢂⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡀⠠⣀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡄
⠀⠀⠀⠀⣠⠆⡀⠀⢰⣣⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢐⠏⠦⠃⠀⣏⣿⣾⠙⠁⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠀⠀⢠⢿⡵⠀⠐⠈⠉⠩⠕⠒⠐⠒⠀⠂⠀⠀⠀⠀⠀⠠⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⢀⠄⠄⠒⡉⢍⠁⠈⠉⠛⠢⢄⠃⠀⠙⠁⠉⠁⠀⣀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠰⠀⠀⠀⠀⡇⠀⠄⠀⢀⡠⢀⠔⠁⠀⠀⠔⢀⣴⠶⢉⣭⣥⣭⣹⣿⣆⡴⢠⣄⠀⡩⠤⠶⠊⠙⠃⠀⠤⡔⣖⠲⠦⣉⡱⠦⣤⠛⠉⠁⠈⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡰⠋⠀⠀⠀⣠⠂⡟⠃⡀⠈⢢⡴⠀⠲⢷⣍⣝⣵⠋⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⣷⠀⠈⠸⠇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡜⠀⡀⢙⣦⠅⠀⠀⠄⠀⡀⠀⠉⠀⠁⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⢼⡆⠀⠀⢀⢠⡀
⢀⠀⢸⠀⠀⠀⢸⡄⠀⠀⠀⢸⡆⠀⠀⣴⠁⠀⣃⠈⢤⡀⠀⠘⡀⠠⠃⠀⠀⠀⠀⠀⣧⠀⠀⢠⡀⠀⠀⡀⠀⠀⠀⠀⢿⠀⡀⢸⢧⣿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡌⣇⠁⠂⠻⢰⣬⣿⣷⡟⠁⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⢸⠒⢨⠤⠙⣦⢚⡛⠁⠀⠀⠀⠀⢲⡟⣨⣎⣟⠀⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠙⣄⠀⢳⠌⣻⠿⡧⠁⠀⡄⠈⡀⠀⠚⠀⡿⠘⠀⠀⣾⠘⠀⠀⡸⠟⠉⠉⠂⠀⠀⠀⠀⢸⡇⡟⣿⣿⣿⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠃⣬⡟⠻⣶⠿⠦⣌⡀⠶⠀⠀⠀⠀⢀⡄⠠⠾⠿⠥⠞⠉⠀⠀⠀⠀⠀⠀⢲⡄⢀⣼⡿⠣⣿⢸⠃⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠀⠐⣀⠴⠀⠀⠀⠀⠉⠓⠒⠲⠴⢶⣥⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⢃⡌⠀⠋⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠀⠒⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣀⣠⣤⡤⠤⠤⣲⣾⢻⠏⠀⠁⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠈⠉⠛⣼⠟⢡⣾⠇⠎⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢨⠎⠉⠀⠙⠒⠦⢤⣤⡤⠴⠛⠁⠀⠀⠀⡼⠋⠀⠸⠏⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠄⡲⠀⠀⢄⣟⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⣼⡃⠀⢀⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠉⠁⠀⠀⠀⠃⠀⠀⡾⠊

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠧⡘⠓⠂⠀⢤⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡏⠉⠁⣀⠀⠀⠀⣦⠀⠀⠀⠈⠁⠈⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠅⠀⠀⠀⠀⠘⠀⠀⠀⠙⠀⠀⠀⠰⠆⢴⡦⠀⠟⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢮⠀⠀⠀⠖⢠⡄⣀⠀⠀⠂⣀⠘⠂⠀⠀⡀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠁⠀⠀⠀⠀⠀⠀⠉⠀⡃⢀⠉⢠⠐⡂⠀⠛⠀⠀⠰⠆⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⠀⢀⡀⠀⠓⠀⡤⠉⠤⣵⣸⣣⢀⣂⠉⠰⠆⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡁⠀⠀⠀⠀⢀⡤⠀⠀⠒⠢⢜⡙⠷⣿⡤⢠⠓⠀⢀⠘⠀⠀⠒⠂⠠⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠰⠠⠈⠼⠗⠕⠆⠉⠀⠀⠒⠂⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠒⠋⠀⠐⠂⠀⠂⠀⠆⠐⠂⠐⠐⢂⡐⠀⠚⡀⠀⠀⠈⠉⠀⠀⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣠⠄⠀⠐⠂⠁⣐⠃⠠⡄⢹⠀⠉⠁⠀⠀⠀⠀⣾⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⠄⠁⠀⢢⠀⠀⠳⠐⠖⠐⠖⠀⠀⣩⡞⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣄⡀⠀⠀⠀⣤⠘⠃⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⣾⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠃⠙⠿⣦⣄⣴⠀⠀⠀⠀⠠⠘⠀⠀⠀⠈⠁⠀⠀⡠⠞⢋⠁⠀⠀⠀⠈⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠋⠀⠀⢰⡆⠀⠀⠈⠛⠛⡮⣉⣥⣠⣤⡤⣤⣀⣴⣤⡴⠞⠛⠀⠀⢨⡀⠀⠀⠀⠀⢠⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⢘⠃⠀⡀⠀⠀⢠⠀⠀⠀⠉⡋⠙⡉⠉⠛⡀⠀⠀⣴⣖⡁⠄⠀⠀⠀⠀⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠲⠒⢣⢈⠀⠀⠀⠀⠠⠀⠀⠀⢘⡏⠀⠀⠀⠀⠄⠀⠀⠘⠉⠈⢤⡶⢄⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣤⣴⢾⠈⠙⠃⠀⠀⠀⠀⡠⠀⢼⠀⠀⠀⠀⠸⡄⠀⠀⡀⠀⠀⠀⠉⠲⡅
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣍⢁⠘⠀⠀⠀⠀⠀⠀⠈⣁⣤⢢⡀⠘⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⢸⣕⣦⠀⠀⢠⠂⠀⠀⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠂⠀⠀⠐⠀⠹⠃⠀⠀⠀⠈⠀⠀⢡⠀⠀⠘⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣦⠀⣀⠄⡄⠀⠀⠀⠀⢿⡆⠀⠐⠄⠀⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠙⠀⠀⠀⢹⠀⠸⠁⠰⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⣤⣤⣤⡀⠒⠂⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⢨⣾⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⢸⡏⠛⠫⠙⠻⠟⣻⣿⣿⣄⡠⠄⠀⠈⠢⡀
⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠂⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠑⡄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⣅⣒⣠⣤⣹⣿⡏⠀⠀⠀⠙⠢⡀⣀⣈⣂⣀⠀⡀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⢠⣄⣤⠀⠀⠂⢻⣿⣿⣿⠹⣿⠀⠀⠀⢀⠗⠈⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠸⣿⠋⠉⠑⡄⡀⠀⠙⠻⣯⠆⢨⢀⠠⠒⠁⠀⠀⠀⢀⡀⠀⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠐⠢⡊⠀⠀⠈⠁⠂⣼⠷⠊⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢈⡢⠄⠀⠈⠁⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⠊⠁⠀⠀⠀⠀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⡀⠔⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡤⢒⡊⠀⠀⢐⡊⠢⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠶⠀⠀⠰⠀⠀⠀⠟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠷⣀⠐⠂⡠⠮⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⠁⠀⠙⡌⢡⠋⠀⠈⣤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠐⠸⠇⠂⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣾⠃⡠⠀⠀⠰⠄⠀⠰⢄⠘⣷⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡀⠀⠀⢀⣞⣸⣌⠀⠀⠀⠀⠀⠀⠀⢀⣇⣇⣳⡀⠀⠀⢀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⢄⠈⣢⠔⠉⠁⠀⠀⠈⠑⠂⠐⠀⠐⠈⠁⠀⠀⠈⠉⠢⣄⠀⡀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠄⡀⡙⠐⠢⠤⠤⠤⠤⠤⠄⠄⡀⡀⠄⠤⠤⠤⠤⠤⠤⠴⠂⢋⢀⠠⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣜⠀⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⡄⠄⠀⢄⠀⠀⠀⠀⠈⠞⣀⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠉⠒⠤⡀⠀⢀⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣮⣽⣿⣿⣿⣇⣠⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣛⡃⠀⠐⣛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠏⠉⠋⠀⠈⠉⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⢛⢿⣆⠀⠀⠀⠠⠂⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣥⠘⠾⣿⣷⣤⣀⣴⣤⣬⣦⠶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣦⣄⡉⠛⢿⣏⡄⠀⢀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⣿⣿⣿⠀⠀⣿⡇⠀⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⣿⣷⠀⠀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⡆⠀⢹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⡇⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣇⠀⠀⠈⠋⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠈⠻⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣷⡄⠀⢨⡟⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣼⣷⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠙⠿⢿⡀⠠⠟⠉⠉⠉⠉⠉⠻⠧⠤⠞

⠀⠀⠀⠀⠀⠀⢰⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠈⢧⠀⡈⠉⠛⠛⠛⣛⣛⠛⠒⠒⠒⠶⠦⠤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⢠⠏⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡞⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⣰
⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣠⠞⠁
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡇⢸⠁
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢹⡇⢸
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢻⠃⣼
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣄⣼⠀⡿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣼⢽⡇⢰⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠛⢾⠃⣸⠁
⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⡟⢀⡟
⠈⠙⠒⠒⠷⢤⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢸⣟⡯⣿⠃⣸⠁
⠀⠀⠀⠀⠀⠀⠉⠲⢥⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⣾⣽⣷⠏⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣖⣠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⡇⠀⡜⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡾⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⡟⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⢦⡀⠀⠃⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠾

⠀⠠⣤⡰⣄⢄⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠠⡴⢂⡤
⠈⡳⢮⡛⢎⠘⡴⢟⣡⡤⠀⠀⢀⣘⠷⣜⠆⢏⡴⢂⡀⠀⠀⢀⠲⣦⡲⠰⣡⠞⣠⠀⠀⠀⢤⣌⠻⣎⠁⡵⢋⡴
⠀⠙⠲⣝⢮⠀⣡⢛⣥⠶⠂⡀⠲⢬⡳⣜⠆⢎⡴⣋⡥⠀⠠⢬⡛⢮⠃⠘⡱⢛⡵⠆⣀⠐⠶⣌⠳⡌⠀⠔⣩⠞
⠀⠀⣤⠈⢳⡀⢡⠏⢀⠰⣄⣿⣠⠄⠙⢮⠂⢈⡞⠉⣤⢸⣇⡄⠙⢦⡃⠘⡴⠉⢠⡄⡿⣴⢆⡈⠳⡄⢀⠞⠡⡄
⠀⠀⢠⠶⣂⠁⠈⠰⢬⡛⢎⠂⢣⠞⣃⡌⠃⠊⣀⡳⢮⠋⢟⡴⢃⡀⠃⠘⢠⣘⠷⡝⠘⡵⢋⡴⠄⠁⠈⡐⠶⠄
⠀⠀⠰⠛⠉⢠⣄⠙⠲⣝⠪⠀⢡⢞⡥⠖⢀⡐⠦⣝⢮⠃⢈⠜⣩⠖⢀⡐⠲⣍⡳⡕⢈⠜⡡⠞⠉⣤⡄⠉⠓
⠀⠀⠀⢤⣙⢮⢣⠞⣠⡌⠳⡀⢠⠋⣀⠲⡼⢧⠆⡈⠳⡁⢠⠎⣀⢶⡼⣣⢆⡀⠱⡄⢠⠎⢠⣌⢳⡙⡼⣣⡤
⠀⠀⢘⡲⣌⠣⠀⢞⡥⢖⣂⠀⢀⣐⢮⡑⠌⢩⢞⡥⢆⠁⢀⡰⣌⡳⡁⡱⣫⠴⣂⠀⢀⣘⠶⣌⠳⠀⢞⡥⢞
⠀⠀⠀⠙⢦⡱⠀⢊⡴⠋⠁⠀⠀⠈⠓⢌⠂⠰⣫⠞⠉⠀⠀⠙⠲⡝⠀⢜⡵⠋⠁⠀⠀⠈⠙⢮⡳⠀⢊⠖⠉
⠀⠀⠀⠀⠀⠙⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠋
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⡐⢦⠿⡴⢂⡀⠀⠀⠀⠀⢀⡐⣮⢧⢖⡀⠀⠀⠀⠀⣄⠲⡝⡴⢂⡀⠀⠀⠀⠀⢀⡰⣎⢟⡴⢂⡀
⠀⠀⠠⢬⡙⢮⠈⡵⣫⠴⣂⠀⠀⣐⠶⣝⠆⠰⣫⢴⣃⠀⠀⣐⠮⡳⠄⠜⣩⠖⣂⠀⢀⡐⠮⣝⢮⠈⡴⣋⡵⠆
⠀⠀⠀⠲⣍⢢⠀⢞⡵⠋⣁⢰⡆⣈⠙⢮⠃⠐⡵⠋⢤⢰⣆⡌⠑⢎⠀⢈⡴⠋⣁⢰⡆⣈⠓⢮⡣⠀⠜⣡⠞⠃
⠀⠀⢠⠄⠈⠧⠠⢏⡀⠶⣝⠏⢞⡵⢂⡀⠃⠘⢠⡙⢮⡃⢋⡴⣃⡌⠂⠊⣀⡲⢌⠋⠽⣡⠖⣀⠱⠀⠞⠁⠤⡄
⠀⠀⠰⢚⣥⠄⠀⠤⣍⡳⣌⠂⢊⢞⡩⠖⢀⡐⠲⢍⠳⡁⢨⢞⡥⠖⢀⡐⠲⣝⠢⡃⠘⡱⢚⣭⠤⠀⠠⣍⡳⠄
⠀⠀⠞⠉⣄⢸⣇⡤⠀⠙⣎⠀⣡⠋⣀⢶⡼⣣⢆⡀⠱⡀⢠⠋⣀⠲⡼⢣⠆⣈⠳⡄⠈⡴⠋⠀⣤⢺⡆⣤⠉⠂
⠀⢀⠐⢶⣌⠇⢞⡵⢋⣤⠘⠀⠁⢤⣝⢳⡑⣡⢋⡵⢆⠁⠀⠲⢬⡳⡅⢫⠞⣡⠤⠙⠘⠁⣄⡛⢮⠣⠼⣡⠶⠂
⠀⣌⡛⢶⡝⠄⢊⠜⣩⠖⠃⠀⠙⠳⣌⠳⡁⡱⣫⠞⠋⠀⠈⠙⠲⡝⡄⢠⢞⡵⠞⠃⠀⠘⠦⣝⢦⡑⠐⣡⠶⢛
⠀⠈⠙⢧⡙⠀⣣⠞⠁⢀⠀⡀⠀⠀⠈⢷⠁⡴⠃⠄⠀⠀⠄⠠⠤⠙⣦⢠⡞⠀⠀⢀⢀⠀⠀⠈⠳⡕⠀⢃⡞⠋
⠀⠀⠀⠀⠷⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠤⠹⠄⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣒⣒⣒⣒⣀⣀⣀⣒⣀⡀⠒⠒⠒⢒⣒⣒⣚⣓⣒⣒⣒⣒⣖⡒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡉⠉⠉⠛⠛⠋⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⢹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⣴⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⣿⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢂⡀⡀⣿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢸⠟⠳⠁⠞⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡐⠀⠸⠤⠤⠤⠤⠤⠿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⣦⣭⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡄⣴⠆⠀⠐⠹⠃⠉⠀⠀⢀⣠⣀⡀⠻⠁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⣀⡡⣽⡆⠀⠀⡆⠀⠀⢀⣴⠎⣹⣿⢰⠉⡆⠀⣆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠥⠨⠯⠴⠷⠿⣼⡤⠿⠶⠦⣾⣷⠶⠿⣿⡾⠦⠷⠾⠷⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠉⠉⠙⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⣀⡀⢀⣈⣉⣉⣉⣁⣉⠉⠉⠉⠀⢀⠀⢀⠀⢠⣤⣼⡄⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣤⡤⠖⠋⠻⠙⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⣷⡀⠀⠘⠆⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣠⠿⠛⠻⢦⣀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣶⠀⣿⣿⣿⢿⡿⣿⣿⣿⡿⣿⣻⣉⣀⣼⣦⣀⣤⡾⠃⠀⠀⠀⢀⣬⡉⠁⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣀⣀⡿⠀⣿⣿⣽⣉⣇⣶⣿⣌⣠⣷⠉⣿⣿⣿⡿⠿⢿⣱⡀⠀⠀⣀⣼⣿⣿⡄⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣟⣿⣟⣁⡀⠀⠀⠈⠙⠻⣿⣿⡇⣿⣿⣿⠊⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡤⠿⠷⡾⠓⠒⡶⠶⠶⠶⠒⢶⣿⣿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣿⣿⣿⣴⢿⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠎⠀⠠⠄⠀⠈⠭⠀⠠⠤⠂⠀⢿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⡏⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠫⠿⠭⠉⢉⣉⡙⠙⢋⡽⢻⣿⢟⣏⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⢀⠀⠀⠀⠀⠀⡄⠠⡄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡐⢤⡄⠈⠈
⠀⠀⠀⠀⠸⣄⡀⡀⣀⠀⡀⠤⠤⠄⠀⢸⣄⡀⢜⣄⢸⣄⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡭⠀⠀⡍⣒⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⡁⢀⠶⣤⡍⠄⠀⠀⠀⠸⠰⠀⠀⠀⡀⠄⠤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⠀⠀⡱⠁⠀⠈⢶⣄⠤⣖⠐⠢⢠⠐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠕⠼⡄⠀⢳⡇⡆⡳⣦⠀⢸⢛⡿⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠰⢠⡎⠄⢸⡇⠏⠀⢘⡏⠉⠐⢰⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢠⠖⣦⡀⣨⠿⠀⠰⡎⠸⣠⢶⡆⠀⠀⣤⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠥⠈⠛⡇⢬⡍⠀⠘⠐⠃⡆⠻⢀⠀⠻⣿⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣀⢧⣯⠀⠁⠈⠀⢀⠄⠀⠀⡴⠋⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⢄⡄⠈⠇⠀⣷⠁⠚⠀⣁⠸⠀⠠⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠿⠻⡴⡶⣿⣤⣤⣄⣀⣁⢣⣴⡾⠇⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⠳⠀⢣⠀⠀⣨⢈⠁⠓⠛⢭⡁⠀⠀⢒⠒⠂⡚⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠨⠀⠀⢘⣀⠀⣉⡊⠀⢾⠤⠀⠃⢠⡀⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠢⠀⠈⠁⠀⠄⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠆
⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⢀⠀⠄⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⡀⠔⠊⠁⠀⠈⠘⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⡠⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠛⠃⠀⠀⠙⢦
⠀⠀⠀⠀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠊⠀⠀⠉⠀⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⣠⡶⠟⠛⠛⠿⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠓⠢⠤⣬⣧⣀
⣼⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠉⠁⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉
⠙⠷⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤⣤⣤⣤⠶
⠀⠀⠙⢆⠻⣦⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣀⣼⠟⠁
⠀⠀⠀⠈⢧⠈⢳⣤⣀⠀⠀⠀⠁⠠⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠰⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠈⣇⠀⢳⡄⠉⠓⠢⢀⠀⠀⠑⢆⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⠐⠊⠀⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠸⡄⠀⢷⡄⠀⠀⠀⠁⠀⡀⠀⠱⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠄⠀⠀⠆⣀⣵⠾⠛⠁
⠀⠀⠀⠀⠀⠀⢹⡀⠈⢳⣄⠀⠀⠀⠀⠈⢀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⢶⣄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠉⠛⠶⣄⣄⠀⢳⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠙⠳⡜⠃⠀⠀⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⠀⢻⡀⠀⣠⣾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿