⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⡒⢟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣟⣯⢿⡿⢓⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣟⣻⣿⡿⢯⣶⣭⣛⠻⣳⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣖⡿⢿⣿⣯⣿⣫⣝⡻⠿⣶⣯⣖⡭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢶⣿⠿⣾⣯⣟⣋⡿⢛⠿⢵⣋⣉⣛⣿⣶⣿⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⢿⣿⣿⣛⣻⣶⡾⢽⣞⡉⠓⣶⣥⣶⣿⣿⡿⠛⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣸⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣺⣿⢷⣿⣭⣟⣛⡷⢶⢯⡝⣋⠹⠶⣦⣬⣿⣽⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⠜⢻⣿⣸⠀⠀⠀⠀⢀⣠⣼⣿⣿⠿⣿⣠⣟⢻⣿⣿⣟⡿⠻⢿⣤⣜⣻⢿⣟⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠔⠋⣏⣁⣠⣴⣶⣿⣿⣿⣟⣽⠖⣛⣿⢿⣺⣽⡛⠻⠬⣑⡛⢷⣾⣽⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣿⣶⣿⣿⣿⣿⣿⡿⠛⠋⣙⡡⣌⢩⣟⣿⣶⣿⣿⣿⣿⣿⣿⣶⣿⣫⢽⣟⣻⠝⢺⣋⠤⢎⡉⣦⣶⣽⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⠿⢿⣻⣁⡤⠒⢛⣃⣤⣔⣻⡿⢿⣿⣯⡽⣟⣛⡵⠶⣿⣭⣟⡚⡫⣵⣾⡅⡄⣒⣤⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠟⠋⠁⠈⠀⠈⣼⣿⡗⢪⣟⣶⠿⣭⣤⡛⢍⣓⡬⠟⣹⣷⢻⣿⣳⣾⠿⡯⣽⣖⣩⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣤⣴⣶⣭⣥⣿⣏⡻⠞⠾⣯⣥⣶⣛⡽⠖⣻⣥⣦⣆⠫⠍⣰⣍⣤⣾⣃⠠⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣖⣉⡭⠟⢋⣩⣿⠿⢿⣭⣤⣶⣈⣥⣐⣉⣙⠻⠶⢯⣍⣀⠺⡭⠿⣿⡤⠐⣨⣴⣿⢿⠛⠿⣿⣿⣿⣃⣀⣀⣀⣀⣤⠤⠤⢤⣤⡤⠤⣦⡒⠒⠒⢤⡀⠀⠀⠀⠀⠀
⣭⡽⠟⣚⢯⢤⣽⣟⡋⠤⠉⠙⠻⠿⢿⣯⣄⣀⠀⠀⣈⣉⠛⠻⠷⠿⠷⠞⠯⠋⠁⣀⣤⣄⣀⡈⠙⠛⠛⠛⠛⠛⠛⠻⡦⣄⠈⠙⠓⢦⣉⠳⢦⣄⣹⠀⠀⠀⠀⠀
⣥⣴⣞⢯⣹⣖⢺⡭⠉⡓⠲⢿⣯⣉⡉⠉⠓⠟⠛⠋⠁⠈⠉⠀⠀⡀⠐⠂⠀⣶⣿⣿⣏⣻⣿⣿⠟⠂⠀⠀⠀⠀⠀⣀⣈⣮⡑⢦⣀⣀⣬⣿⢾⡿⣏⡇⠀⠀⠀⠀⠀
⣶⡾⣯⣙⣷⢾⣯⣕⣦⡅⣴⣺⠟⠈⣻⣷⣾⡕⠄⠀⠀⠀⣠⣴⣾⣿⣷⣶⣤⣈⠉⠉⠉⠉⠉⠀⠀⣤⣀⣤⣴⣾⣷⠾⠟⠛⠿⡍⢹⠀⠀⠈⣿⡗⣿⠀⠀⠀⠀⠀⠀
⠵⣾⣫⢽⣟⣭⢽⣷⡵⠚⢉⡻⢖⣮⡵⠾⠋⠀⠀⢤⣶⣿⠟⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⣉⣁⡤⠤⠖⠒⠋⡇⢸⡇⠀⢀⣿⢃⡏⠀⠀⠀⠀⠀⠀
⣴⡞⣻⡿⠛⣿⣽⣻⠟⣉⣥⣿⣏⠳⠄⢀⣀⣀⣤⣤⣊⡀⠀⢻⢿⡇⠀⠀⠀⠀⠀⠀⠠⣶⣿⡟⢁⡤⡾⠋⠁⠀⠀⠀⣀⣠⣽⡇⠀⡇⠈⠁⣿⣠⠇⠀⠀⠀⠀⠀⠀⠀
⡀⠻⠟⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠉⠻⠟⣽⣿⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⣰⠋⠀⣀⣤⡴⠶⠛⠉⠁⢀⡘⡇⡴⢧⣄⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣉⣡⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⡞⢿⠿⠒⢲⠄⠀⠀⠀⣼⣿⣿⡼⢃⡖⢩⡣⢶⣆⣀⣠⡴⠽⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣼⣿⣷⣶⣺⣿⡇⠀⠀⠀⢸⣿⡇⡿⠏⣀⣼⡤⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⡿⠿⢿⠛⠉⠙⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠛⢿⣛⣾⣻⡿⠯⠀⠀⠀⣾⣿⡇⣇⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⠒⣾⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⠁⠋⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢠⣿⣿⡗⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡛⢳⣖⡉⠙⣿⣿⣟⣿⣾⣿⣿⠟⠁⠀⠀⠀⢠⠖⢻⢯⡝⢒⡆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣼⣷⣶⢶⡾⣿⣳⣀⠀⠀⠀⢀⣾⣿⣿⡿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⠟⢹⡋⠙⡄⠀⠀⠀⠘⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⣠⣿⣿⣿⡿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⠛⠀⠀⢸⡀⠀⡇⠀⠀⠀⠀⠈⠘⠛⠛⠙⠉⠉⠀⣠⣾⣿⣿⣿⠟⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢣⡤⠀⠀⢀⣼⡷⢶⣗⣤⠀⠀⠀⠀⠀⠀⣤⠀⢀⣠⣾⣿⣿⣿⠿⠋⢀⠜⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⠄⠀⠈⠁⠻⣽⣷⣾⡿⠟⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠟⢁⣠⡶⠋⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⡀⠀⢀⠘⠁⠀⠀⠀⣀⣀⣤⣶⣾⣿⣾⣿⣿⣿⠟⠋⢀⣴⠞⠁⣀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣥⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿⡿⠟⠋⠉⣀⣠⡴⢚⣁⣠⠞⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

╭╮╭╮╭┳╮╱╭┳━━━┳━━━━╮
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