Magic mushroom Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣠⣤⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣄⡀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠾⠿⠁⡉⠀⠀⠀⠈⣿⣷⣤⡄⠀⠐⠀⠀⠈⠙⠻⣶⣿⣷⣰⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣴⣟⣃⡀⣀⣠⣰⣿⠿⠃⣴⣂⡄⠀⠀⡷⢰⣄⡤⡌⠙⠛⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡏⠉⠁⠀⠀⠀⠈⠉⠁⢻⠉⠉⠈⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⠔⠛⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⢀⠁⡰⣿⣧⠀⠒⣫⠅⢀⢀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⠀⢀⠀⢈⣳⣦⡼⠄⠀⠀⠀⢠⡆⢰⣦⡃⠀⠿⠼⣹⣿⡿⠆⠈⠁⠚⠗⣾⡸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡎⠉⠁⣀⡰⢀⣀⠀⠈⠳⣬⣹⠗⠀⠀⠀⣸⣝⣷⡄⠀⠀⠀⡀⠁⠁⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠙⠻⠿⠛⢿⢿⣷⣷⣾⡇⠀⠐⢠⠛⠻⠿⠉⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠸⠀⠉⠛⠛⠛⡆⠀⡼⠀⢀⠇⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠶⠄⣶⡄⠠⠤⠆⣇⣼⠃⣠⠎⢀⡠⠊
⠀⠀⠀⠀⢀⠏⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣤⣤⠀⡀⠀⠉⠒⣁⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⢣⡀
⠀⠀⠀⠀⠈⠀⠀⠀⡘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣾⣿⣿⣴⣿⣿⣶⣝⢿⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⢸⣧
⠀⠀⠀⠀⡀⠀⠀⠀⢳⠀⠹⢿⣦⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⡀⢀⢸⣿⣇
⠀⠀⠀⣾⣅⡀⠀⠠⣤⣳⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣥⡖⣀⣮⣾⣿⣿
⠀⠀⠀⠈⠉⠙⠋⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡿⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⠋⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡦⠶⣤⠦⣤⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⣸⢦⠀⣹⡶⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⢵⠷⠈⣉⡤⣞⡛⠈⠳⣿⣓⣣⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣴⡵⡚⠅⢸⣴⣾⠛⣿⣿⣷⣤⣄⠰⣝⢨⣾⣿⡽⢯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⡿⠇⣠⡼⢋⡀⢀⢻⣬⣯⣉⣿⡧⢇⡜⣫⡻⣤⠼⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠃⢐⡰⢚⣩⣥⣭⣽⣛⡶⣭⣉⣯⢭⣶⠟⣋⣩⣥⡼⢷⣼⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⣠⣾⡧⠞⠟⣫⣾⢏⠻⢟⣄⣌⣽⣏⣙⣿⣟⣿⣛⠉⠉⣏⣿⣿⣶⣆⣉⣉⣙⠲⡄
⠀⠀⠀⠀⠀⣈⠔⡞⡽⠋⢛⣧⡿⣿⠖⠿⠿⣿⠍⠚⠋⠁⠛⠊⡏⢉⡉⢋⡻⠟⠻⢿⣍⣉⣻⣿⣿⡻⠿⣆
⠀⠀⠀⠀⠀⠇⢸⢾⣅⣲⠟⠒⠊⢁⣀⣤⣭⣦⡀⠀⠀⠀⠀⠀⡠⠀⣾⡯⠄⠀⠤⢀⣨⣽⡛⠛⡿⠛⣙⣳⠇
⠀⠀⠀⠀⠀⠘⣦⣨⣛⡳⠦⣤⣀⣚⢓⡿⠛⠛⢧⠀⠀⢰⠀⠀⣇⢸⠿⢶⣶⡀⡀⠀⠀⣀⠄⣉⣭⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⢕⡪⠉⠭⣭⣛⠶⣤⣿⠀⡀⢸⠀⠇⡉⢼⣀⣠⡱⠤⠒⡩⠉⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢆⠀⠀⠎⢀⠀⠐⣜⣷⠒⠂⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠸⡆⠀⠘⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡌⠀⠀⠀⡇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠆⠐⣅⠀⠀⠀⠀⠈⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⠸⡞⣄⠀⠄⢈⡼⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣽⣾⠶⠟⠋

⠀⢀⡴⠒⢦⡀⢠⣤⠀⠀⠀⣠⡄⢠⣤⡀⠀⢠⣶⣄⠀⠰⠀⠰⠆⣠⠀⡠⣦⢶⢤⠀⠀⠀⣠⣖⠁
⢐⡟⢳⣶⡾⠷⠀⣁⣐⡀⠈⠉⠉⣩⠟⠛⠀⣯⣷⣿⠇⠀⠀⢀⡰⠂⡀⠯⣻⣯⠿⡠⢠⠄⣄⠘⠻⠂⠁
⠙⠽⠿⣻⡀⢶⡿⠷⣤⣌⣦⡀⢠⣲⠈⢻⠟⠈⠉⡇⠺⢿⣦⣼⠿⢂⣈⠀⠋⠎⢚⡀⣈⠈⠍⠀⢸⠘⢺
⠀⠰⡇⢹⠀⠀⠈⠲⡾⠛⢛⣍⠀⢸⡀⠘⠀⠀⢀⡷⣀⣠⢰⠀⢠⡾⢟⣿⣦⠀⢎⡟⠻⠇⠀⠈⢨⣀⡀
⠀⠀⡆⢸⠀⠰⡀⢸⡇⠀⠬⠼⢆⠀⠀⣠⠔⠛⢦⣄⠈⠁⠀⡃⠙⣾⣾⣏⡏⠀⠀⠘⠁⠀⠉⠁⠈⠉
⠀⠀⢛⡛⠈⠛⠁⠸⠇⠤⠷⠀⠛⠁⠸⠷⣤⣤⣼⠛⠵⠈⠒⠃⠀⠀⠀⠧⠀⢗⠀⢀⠀⣠⡴⣆⢤⡀⡤
⠀⢦⣿⣿⡀⠀⢀⣴⣆⠀⠀⠀⣀⢀⣠⡄⠈⢱⠉⠀⠀⠐⠆⠉⣼⣠⣻⢄⣤⢄⣀⠀⢀⣻⣽⣮⠽⠦
⠀⠀⠈⢀⡀⠀⠀⢀⡅⠀⠀⠀⡉⠀⠙⠀⢐⠟⣀⣀⠀⠀⠀⠰⠈⠉⠁⠈⠍⠏⢁⡀⠓⢥⣾⢧⣄
⠀⠀⡇⡈⢷⠐⣠⡄⠀⠀⠐⠒⡡⡄⠠⠴⠋⣜⣈⣿⡿⠆⠄⠀⡠⠒⠒⠢⡀⠀⠈⠁⠀⠀⠸⠏⠈⡁
⠀⠀⠁⣇⣸⣧⠉⠋⢀⡴⢤⡜⢳⠛⠀⠀⢾⣷⡿⢾⠀⠀⣠⡀⠀⢀⣁⡴⢋⡠⢤⢔⣩⢓⣀⠠⠈⡤⠂
⢀⡼⣷⠉⣿⢁⡀⠀⠸⠶⡖⠃⠈⠤⡽⠂⠀⠉⠀⢺⡾⢂⣿⣧⠀⠈⠙⡀⠘⢳⢞⣈⣡⣽⣧
⠈⠛⠟⠀⡀⠾⠴⠳⠃⠀⢬⠀⠀⠀⠂⠶⠆⠠⣄⣄⠀⠘⣿⠿⢀⣀⠀⢀⠤⠈⠩⣭⡝⠾⠀⠀⠘⠇
⠀⠠⠄⠀⠑⠶⠀⡀⠀⠀⠎⠈⠁⠰⠆⢀⡇⠀⠀⠈⢈⠁⠀⠀⠻⠿⢃⠈⠁⠀⠀⠁⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡖⠦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⣿⣛⢻⣶⠟⠛⣷⣦⣤⡀⢀⡀⢀⡠⠔⠒⠒⡄⠀⠀⠀⠈⠄⠚⠀⠀⢀⠈⠒⢏
⠀⠀⠀⠀⡟⠾⠳⣦⣄⣀⠀⢀⣠⣎⠻⠷⣶⣟⠉⣱⣷⣤⣴⡿⠟⣩⣶⣿⠟⠉⡀⠀⢠⡠⠀⠀⠀⢠⠀⠆⢀⠀⠀⢀⡀⠀⠀⠀⠅
⠀⠀⠀⠀⢠⠀⠀⡀⠈⠉⢙⠋⠙⠛⢻⢶⣄⡙⠿⢛⣡⣤⣶⣶⣾⠿⠋⠀⠀⠀⣡⠖⠋⠀⠀⠀⠀⠀⠈⣡⡤⣷⡄⠀⢠⠖⡁⠌
⠀⠀⠀⠀⠀⠳⢷⣵⣄⠀⠈⠀⠀⠀⠂⠀⠈⠛⠛⠛⠿⠛⠛⠉⠀⠰⢠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠉⠻⡧⠰⠁⠀⠀⢀⣠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢄⡀⢀⠀⠀⠀⠆⠀⡀⠀⡠⠁⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣦⣄⣶⠇⠀⢀⣤⡞⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠒⣾⣶⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣀⣀⣀⣐⠀⠄⠀⠉⢁⣀⣤⠾⢿⣿⣿⣌⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⣨⣴⠞⣉⣀⣤⣭⣿⣷⣶⣌⠛⢿⣿⣿⣶⣮⣙⠻⣷⣝⠿
⠀⠀⠀⠀⠀⢀⣤⡘⡏⡛⠂⠀⠀⣀⡀⠀⠀⠀⠘⠒⢺⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿⠿⠿⠿⠿⠿⠿⠛⢛⣩⣽⣾⣷⣦⣝⢿⣿⣿⣿⣷⣦⡹⣿
⠀⠀⠀⠀⠀⢟⣟⡻⣣⣿⣀⢾⣿⣿⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠐⢧⡠⢄⣀⣠⣴⣾⣿⣿⣿⣿⣿⡟⠹⣿⣧⡙⢿⣿⣿⣿⣿⣮⡄
⠀⠀⠸⣿⡶⢠⢴⣿⣿⣿⡏⢲⠉⠟⠀⠀⠀⠀⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣙⡛⠻⠟⠿⠾⠿⠿⣟⣻⡟⠢⢤⣿⣿⡿⣦⡙⢿⣻⢿⣿⣿⡀
⠀⠀⠀⠉⢰⠀⢢⠀⡙⡊⠁⢸⠀⠀⠀⠀⠀⢀⠁⠀⡇⠀⠀⢀⣤⣴⡶⠶⡄⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⢹⠁⠀⡼⠣⠙⢷⣿⣿⣶⣤⣄⣐⠛⠳⡀
⠀⠀⠀⠀⢸⠀⠸⡰⠁⠅⢀⡸⠀⠀⠀⠀⢀⣌⣀⣸⡇⠀⠀⠘⠏⠀⠀⠀⠷⡰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠈⠪⡻⣿⣻⣿⣿⣿⣿⢶⢿⡄
⠀⠀⠀⠀⠐⣇⢺⡇⡔⣿⠁⠀⠀⠀⢀⠔⠋⠉⠉⡏⢀⠀⠀⠀⠀⠀⡖⢠⠤⡃⠸⢹⠄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⠈⠪⡻⣿⣿⣿⣿⣞⡦⠟
⠀⠀⠀⠀⠀⠈⠙⢷⣠⠇⠀⠀⠀⢠⠊⠀⠀⠀⢂⠁⠀⡀⠀⠀⠀⠀⠉⢲⠀⠫⡁⠉⠀⠀⠀⠀⣴⣦⠀⠀⠸⡇⠀⢹⠀⠀⠀⠀⠀⠈⠐⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣀⣀⡀⠙⠆⠀⡞⠘⡶⠄⣀⡃⠀⠀⠀⠀⠀⢸⣀⠴⠁⠀⠀⠀⠀⠀⣯⢿⣧⡀⠀⢿⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣴⣀⡤⣶⣿⣿⣿⠀⠀⠀⡁⢀⡟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣻⢇⡝⢦⡸⡆⠀⠸⡄⠀⠀⠀⠀⠀⠀⢠⡾⣷
⠀⠀⠀⠀⣴⣿⣿⣿⣽⢸⣿⣿⠿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⢠⣥⣯⠲⣡⠔⠁⢿⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸⡗⠛
⠀⠀⢠⣾⣿⣟⣳⣾⣿⠟⡟⠃⠄⠀⠀⢀⠀⣼⠀⠀⠀⠀⢀⣴⠾⠿⠛⣛⣛⡛⢛⣛⠻⢶⡀⠙⠛⠋⣿⠀⠀⠀⠸⡆⠀⢸⡄⠀⠀⠀⠀⠀⣏⠋⡇
⠀⠀⢀⣻⣽⣿⣫⣿⠗⡙⣰⡗⠀⠀⠀⠘⠀⡿⠀⠀⠀⣠⡌⢄⣒⡹⢥⡤⢀⣀⢜⣫⣀⣡⣻⡄⠀⠀⣿⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⢠⣿⣿⢾⣏
⠀⠀⠸⠙⠛⣛⣛⣩⡴⢿⠉⠄⠀⠀⠀⡀⢠⡇⠀⠀⢠⠷⢎⣡⣦⣼⣿⣷⣾⣷⣾⡷⢾⣧⣶⡆⠀⢸⡏⠀⠀⠀⠀⣿⡈⠀⡇⠀⠀⠤⠘⠛⣻⠎⢹⣆⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⢀⠀⠀⠀⣰⢻⢸⡇⠀⠀⠸⣶⢾⡫⠋⣉⡙⣭⣤⣤⣍⣉⣉⠓⣼⠃⢠⡿⠀⠀⠀⠀⠀⣿⠠⠀⡇⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠆⠀⢀⡾⠁⣿⢾⢷⡀⠀⠀⠻⡁⣴⣿⣻⡇⠀⣿⠀⠼⠸⠟⠕⠁⠀⣼⡇⠀⠀⠀⠀⠀⣿⢠⢤⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡼⢁⠊⠀⢰⠃⠀⣼⠃⠀⢈⢿⡄⠀⠀⠈⠐⠀⠸⣇⠀⢻⠒⢂⠈⠐⢶⣆⡀⣿⠇⠀⠀⠀⣠⠞⢉⣀⠴⡗⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡸⢀⠂⠀⠀⡇⠀⠀⡇⠀⠈⠀⡄⢷⡀⠀⠀⠀⠀⡄⠹⢳⠈⡗⢄⡀⠀⠀⢕⡇⠉⠀⠀⠀⡼⠁⡜⢁⠏⠀⠇⢡⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠀⡀⢣⠀⠀⠡⠇⣼⠃⠀⠀⠀⠈⠀⠈⣆⠀⠀⠀⠀⢢⠄⠋⠀⠀⠀⠀⣼⢀⡞⢀⠎⠀⠀⡇⣸⠄⢢⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠑⠚⠚⠓⠠⠴⠚⠁⠀⠀⠀⠀⠈⠂⠠⠈⠦⢤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠙⠿⠤⠁⠀⠠⢔⠋⠉⢒⡸⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⢶⣶⠶⢶⡶⣶⢶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣠⠤⠖⠒⡞⠉⠉⣿⠉⠛⠒⡶⣤⡀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⠀⢰⡝⡡⢠⢀⠂⢿⠀⠀⢸⢀⠑⡐⡌⢎⡿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠱⣌⢧⡈⠳⠥⣇⣎⣸⣸⠀⠀⢸⣬⠤⠷⢚⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠣⣌⠓⠒⠶⠤⠤⣿⠀⠀⢸⠖⠒⠋⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⣀⣤⣤⡤⠤⣤⣄⣀⡀⠈⠳⡄⠀⠀⢀⡇⠀⠀⣼⢀⡴⠋⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⡋⡁⡀⢸⡇⠀⣷⢀⢉⢉⢳⡄⢸⠀⠀⣸⠁⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣓⠶⠤⢼⡇⠀⢯⠦⠦⠶⢛⡡⠋⠀⢠⠇⠀⠀⣸⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⠈⠉⠙⢻⡇⠀⢸⡛⠛⠋⠉⠀⠀⢀⡟⠀⠀⢀⠟⢯⣉⣀⣸⠀⠀⡯⠉⠙⢓⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⠀⣧⠀⠈⣇⠀⠀⠀⠀⠀⡞⠀⠀⠀⡾⠓⠦⢬⣍⣹⠀⠀⣟⣋⣉⣩⡤⠞⠁
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡀⣀⣀⣀⠀⠙⢦⢸⡄⠀⢹⡄⠀⠀⠀⣸⠁⠀⠀⣸⠃⠀⠀⠀⢀⡏⠀⢀⡏
⠀⠀⠀⠀⠀⠘⣇⠠⣞⣉⣹⠃⢨⣋⣩⡽⢂⡼⠀⢷⠀⠀⢳⡀⠀⢠⡇⠀⠀⢠⡇⠀⠀⠀⠀⡼⠀⠀⣸⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠬⢽⡆⠘⡷⠖⠒⠋⠀⠀⠘⣇⠀⠀⢳⡀⡼⠀⠀⠀⣼⠀⠀⠀⠀⡼⢁⠔⠋⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢳⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢳⡇⠀⠀⠀⡏⠀⠀⢠⠞⠁⡇⢤⠴⢦⡤⠤⣀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠳⡀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢣⠀⠀⢠⡇⢀⡴⠋⠀⠀⢹⠮⢭⣻⠁⢰⠤⠿⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠙⢦⡀⠀⠀⠀⠀⢷⠀⠀⠈⢧⠀⠸⣧⠞⠀⠀⠀⡴⠋⠀⣰⠃⢀⡎⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠹⣄⠀⠀⠀⠘⡇⠀⠀⠘⡆⠀⡇⠀⠀⢠⠞⠁⢀⠞⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢳⡀⠀⠀⢻⠀⠀⠀⢹⠀⢷⠀⣰⠋⢀⡴⠋⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠹⣄⠀⢸⡄⠀⠀⢸⡆⠘⣶⠃⣠⠏⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠹⡆⢸⠇⠀⠀⢸⠇⠀⢹⢠⠏⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⡟⢸⡄⠀⢀⣼⣀⣠⠞⢹⡀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠉⠛⠋⠀⠉⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣠⣿⣿⣿⣿⣿⣿⡟⠉⣻⣿⣿⣿⣿⣿⣏⣈⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣿⣿⣿⣿⠿⠟⠛⣋⣉⣭⣭⢭⣤⠴⣶⡶⢴⡶⢤⣬⣭⣭⣭⣭⣙⣛⣛⠻⠿⣿⣿⣿⣿⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⣋⣥⠴⣶⣟⠻⢿⣦⡻⣿⣦⠻⣧⢻⡇⣿⣇⡿⢁⣼⠟⢋⣴⡿⠛⣩⣿⡷⢶⣬⣉⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢟⣵⣾⡙⠿⣷⣬⣛⠿⣦⣝⣻⣶⣽⣷⣿⣿⣇⣿⣿⡵⢟⣡⢶⣋⣥⠶⢟⣫⡥⠶⠛⢋⣩⣿⣦⡙⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⡾⣷⣍⡻⢷⣮⣍⣛⠻⠶⠾⠯⠿⠿⠿⢿⡿⠋⠙⣯⠀⠻⠬⠽⠖⣚⣋⣉⣤⣤⠶⠞⢛⣉⣥⠾⢿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠺⢽⣿⡷⢾⣭⣽⣟⣛⣛⣛⣛⣛⡫⣿⠃⠀⠀⠸⣇⠉⢛⣛⣉⣭⣭⡥⠴⠶⠞⣛⣋⣩⣴⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠻⠿⠶⣶⣤⣭⣭⠭⠥⠤⠶⣿⠀⠀⠀⠀⣿⣀⠒⠒⠒⠒⣒⣂⣉⣩⣭⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢸⡟⠀⠀⠀⠰⣹⡗⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⢸⡇⠀⢀⠀⡀⣿⣇⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣾⠃⡆⢸⠀⡇⢹⣿⠀⠀⠀⠠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠃⡼⠀⣧⢻⢹⡆⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⠀⡇⠀⢹⡼⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡌⡾⢰⡇⡄⣼⣯⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣾⣼⣧⣾⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⣠⠤⢶⡖⠒⠒⣖⠒⠒⠶⢤⣄⡀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣴⡛⡡⢀⢀⠀⣧⠀⠀⢿⢀⠠⠠⡐⣌⢿⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠛⢦⠻⡄⠻⢴⣁⣃⡆⠘⣻⠀⠀⢸⣘⣀⣥⠵⢞⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣌⠓⠦⠤⣭⣉⣉⡿⠀⠀⢸⡥⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡇⠀⠀⣼⠀⣠⠖⠋⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡶⠛⠉⠉⣿⠀⢸⡏⠉⠓⠶⣤⠈⣧⠀⠀⣸⠁⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣘⠾⣬⣌⣀⡿⠀⢸⣇⣀⣀⣡⠞⣠⠏⠀⢠⡇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠛⠒⠦⠭⣿⠀⠀⣯⠭⠥⠖⠚⠁⠀⢀⡞⠀⠀⠀⣯⡶⠒⠒⢻⠃⠁⣶⠒⠦⢤⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠙⠳⣄⠀⠀⢹⠀⠀⢻⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣼⢤⣙⠓⠷⢶⠀⠀⢿⠤⠶⠶⢋⣠⠞
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠑⢆⠘⡇⠀⠘⣇⠀⠀⠀⠀⣸⠁⠀⠀⢰⠇⠀⠈⠉⠙⡿⠀⠀⡟⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⡟⠀⣀⠤⢤⡖⠒⠶⠖⢦⣄⠈⡇⢹⡀⠀⠹⡄⠀⠀⢠⡇⠀⠀⢀⡟⠀⠀⠀⠀⢰⠃⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠳⣌⣛⠲⠶⡇⠀⣷⣚⣋⡡⠞⠁⠈⢧⠀⠀⢻⡄⠀⡾⠀⠀⠀⣸⠁⠀⠀⠀⢠⠏⢀⡤⠚⠋⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣇⠀⢻⠁⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⣰⠇⠀⠀⠀⡏⠀⠀⠀⣰⠋⡔⠁⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢧⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢻⡀⠀⠀⢸⡇⠀⢀⡼⠁⠀⢧⡺⢭⣩⡋⠉⡖⣦⣄⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠳⡄⠀⠀⠀⠀⠀⢹⡀⠀⠀⢳⠀⠀⢸⠁⣴⠋⠀⠀⢀⡼⠋⠓⡾⠀⢰⠭⠭⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⢦⡀⠀⠀⠀⠈⣧⠀⠀⠈⢧⠀⢸⡟⠁⠀⠀⣠⠞⠀⢀⡞⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⣆⠀⠀⠀⢸⡄⠀⠀⠘⡆⠘⡇⠀⠀⡴⠃⢀⡴⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⢳⡀⠀⠀⣧⠀⠀⠀⢳⠀⢣⢀⡞⠁⣠⠞⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠹⡄⠀⣿⠀⠀⠀⢸⠀⠘⣟⠀⡼⠃⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢹⡄⣾⠀⠀⠀⣸⠀⠀⣹⣼⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣼⠃⢻⣄⢀⣠⢧⣤⠴⠋⠻⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡋⢙⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣽⣿⣷⣄⠀⠀⠀⠘⠛⠛⠛⠛⢿⠟⠛⢻⡟⠉⠉⠉⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣀⣀⠀⣼⠀⠀⢸⡇⢀⣴⣿⡿⠟⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣷⣾⣿⣿⠀⢀⣴⣿⠟⣿⣿⣿⡀⠀⢸⣧⣾⣿⣿⣿⣦⣿⣟⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⡍⠙⡏⠉⠉⠀⣴⣿⣿⣷⣦⣾⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢦⣄⠀⠈⡇⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣷⣼⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣾⣿⣦⠀⢳⠀⢿⠀⣼⣿⣿⣿⣿⣯⡸⣿⣿⣿⣿⣿⡇⡟⠛⠛⣻⠛⠛⠛⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣙⣿⣟⣡⣿⣿⣷⠘⡇⠘⠀⠘⠛⠛⠛⠻⡿⠿⠿⣿⠿⠿⠟⢡⡇⠀⠀⡏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⣃⣄⣀⣾⠂⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⠠⢸⠇⠀⢸⠱⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠁⢫⠀⠙⡆⠀⠀⠀⢰⡇⠀⢰⡇⠀⢀⡀⣾⠀⢀⡏⠃⢀⣴⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢱⣴⣶⣦⡘⡆⠀⢸⡀⠀⠀⢸⠀⠀⠘⣡⡾⣿⣿⡄⠀⡼⠀⢠⣾⣟⣿⣅⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣷⠀⠈⡇⠀⠀⡞⠀⢠⣾⣿⣿⡿⣿⣿⡄⠁⠀⠘⣻⠛⠿⠿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⠿⡟⠋⡇⠀⢸⣶⣶⡇⠀⢸⡟⣻⠛⢻⠿⢿⠇⠀⠀⢠⠇⡌⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⣹⡄⢹⢀⣿⣧⣿⣿⠆⢸⢁⠇⠀⣾⡴⠃⠀⠀⢠⠏⡸⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣄⢧⠘⢷⡘⡆⠀⡏⢸⠀⠀⣿⡜⠀⣴⠋⠀⠀⡠⣠⢻⣌⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⠈⢇⠀⢳⣇⠀⡇⢸⠀⢠⡿⠁⢰⡏⠀⣠⢞⡴⠇⡁⠈⢳⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠈⢦⠘⣆⠀⠙⣄⡧⢸⠀⡼⠁⢀⡞⠀⡪⣐⢭⠔⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣄⠀⠀⠈⠣⡈⠧⠈⢧⠀⠈⠋⠘⠋⠀⠀⠞⠋⠉⠈⠀⠀⣠⠔⠋⠀⠀⢠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠆⠀⢸⣿⣷⡄⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠰⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⡀⠀⣼⣿⣿⣿⣿⣷⠀⢀⠀⠸⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⡴⡶⡛⣻⠉⠉⣿⢍⢟⢻⢶⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢿⡌⡜⡰⢸⡄⠀⣿⡌⣆⣣⠷⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠙⠲⠭⣝⣛⣻⠁⠀⣸⠭⠽⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡟⠀⠀⠀⠀⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢠⡇⠀⢠⠇⢀⡤⠖⠊⠁⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢶⣟⣹⡟⠉⣟⢒⣶⡄⢸⠄⠀⠀⠀⡞⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢭⡇⠀⣯⣭⠭⠴⠋⠀⠀⠀⡼⠁⠀⢰⠃⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⡏⠀⠀⠀⠀⠀⡝⠙⡶⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀⠀⠀⢀⡏⠀⠀⡾⠀⠀⠀⠀⢀⡞⠀⣸⠁⠀⣀⡠⠔⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠀⠀⠀⣸⠀⠀⢠⡇⠀⠀⠀⢠⠎⠀⣰⠃⢰⢋⣁⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠦⣄⠀⠳⡀⠈⢳⡀⠀⠀⡏⠀⠀⢸⠀⠀⠀⢠⠏⠀⣰⠃⠀⠈⠮⣓⣮⠋⣱⠦⣄⠸⡄
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠙⢦⠹⡄⠀⠹⣄⢸⡇⠀⠀⢸⠀⠀⠀⡟⠀⢠⠇⠀⠀⠀⠀⡸⠃⣰⠯⠭⠭⠞⠁
⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⢀⣀⡠⠞⠀⠹⡄⠀⠘⢾⡇⠀⠀⢸⡀⠀⣸⠁⠀⢸⠀⠀⢀⡤⠊⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠉⢇⠀⠀⠀⠀⢳⡀⠀⠘⡇⠀⠀⠈⣇⠀⡟⠀⠀⣿⣠⠖⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠳⢤⣀⣀⡀⢧⠀⠀⢳⠀⠀⠀⢹⡄⡇⠀⠀⢸⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣹⠺⡆⠀⠈⢧⡀⠀⣰⠃⢧⠀⠀⢸⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⢧⣀⣀⡞⠉⠉⠁⠀⠘⠦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠁⠈⣿⡇⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⡪⣷⠆⠿⠿⠀⢠⣴⡄⠀⠫⣉⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠠⠔⠅⠂⣠⣶⣦⢄⢂⡩⢁⣀⣀⠀⢀⢠⣽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠰⢿⠇⠀⠘⠀⠈⠙⠛⠀⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⣄⠈⢐⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⠿⠇⠀⠀⢸⠸⡟⢛⣿⣯⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⢈⣾⣧⠘⠛⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠰⢾⣶⢿⢿⣿⠿⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡤⢤⡀⠀⠀⠀⢸⠀⠀⢀⡞⠀⠀⢀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⡀⠠⡄⢹⢈⠁⢮⠃⠀⠀⠀⠀⢂⠀⣾⡅⡀⠀⢀⣿⠉
⠀⠀⠀⠀⠀⢀⡀⠀⠴⠶⠛⢡⠠⢻⡎⢌⣶⠏⠠⠀⢄⠀⠀⠈⣾⠙⣴⡷⠐⢶⣿⠆
⠀⠀⠀⠀⠀⠈⠻⣿⣦⡘⣆⢘⣣⣭⣱⣶⣿⢠⠁⢀⠠⣆⣴⣾⣿⣶⣾⣴⡂⣸⠁⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢚⣻⣿⣯⣞⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣷⣶⣟⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠋⠟⢻⠟⢿⡿⢿⣿⣿⣿⢿⣿⣿⠟⠻⠟⠿⠛⠌⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠆⠀⠀⠀⠀⠈⠀⠀⠋⠛⠁⠀⠁⠈⠀⠀⢀⣀⣠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⠈⠹⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠃⠀⣀⣀⣀⣀⣀⣀⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⠶⣻⣋⢽⡏⢙⣯⣍⣿⣿⣶⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⢽⣿⣯⣸⠃⠀⣿⣯⡿⢿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢢⡀⠀⠀⠈⠙⠒⠲⠶⢾⠀⠀⡿⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠏⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⢀⣠⠶⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⣁⣀⣀⣀⣀⣀⣀⠙⢷⡀⠀⠀⠀⣸⠃⠀⣸⠁⣰⠾⠉⠁⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣛⠿⢿⠃⣾⣽⡽⠗⣠⠇⠀⠀⢠⠏⠀⢀⡏⠀⢻⡀⠀⠀⠀⠀⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⢸⠛⠛⠉⠀⠀⠀⢀⡟⠀⠀⡾⠀⠀⠀⠉⠲⣤⣄⣀⣀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⡼⠀⠀⣸⠁⠀⠀⠀⠀⡼⠁⣼⠁⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢧⠀⠀⠀⠀⢰⠇⠀⢀⡏⠀⠀⠀⢀⡞⠁⣰⠃⡠⠶⠚⠋⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠹⡄⠈⢳⡀⠀⠀⣾⠀⠀⢸⠃⠀⠀⢠⡎⠀⣰⠃⠀⢧⡺⣟⣶⢠⣄⠀⠻⡄
⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠘⠳⢤⡹⡄⠀⠹⣄⠀⣿⠀⠀⣸⠀⠀⢀⡞⠀⢠⠇⠀⠀⠀⢉⡾⠁⣾⣻⣟⣠⠃
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣨⠇⠹⡄⠀⠘⣶⡇⠀⠀⣿⠀⠀⣸⠃⢀⡾⠀⠀⢀⡤⠊⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⢲⡖⢻⡉⠁⠀⠀⠹⡄⠀⢸⣧⣀⣺⣿⡇⠀⣿⢧⠚⡇⣠⠖⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠱⣤⣀⣀⡀⢻⣡⠈⢿⣦⢧⣟⢿⡀⣿⣿⢀⣿⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⣙⣟⣿⡞⣧⢒⠹⣷⡪⠊⣸⠇⣿⠁⡛⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⢻⣎⣀⡿⠉⠋⠁⠀⠙⢮⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⢿⣿⣿⣟⠛⠛⠻⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣾⣿⢫⡡⠀⠀⠸⣿⣿⣿⡐⡔⢔⢌⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣄⠘⢿⣦⣁⣃⣇⣇⣿⣿⣿⣸⣬⣼⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠉⠙⠛⢻⣿⣿⣿⠉⢉⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛⠛⢻⣿⣿⠛⠛⠿⢿⣷⡀⠀⠀⣼⣿⣿⣏⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⢹⣿⣿⠀⠄⡠⣠⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⡿⠿⠛⠋⠁⠀⢀⣿⣿⣿⣿⡉⠍⢁⣿⣿⡏⠉⠙⠻⣿⡷
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⡀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⣾⣿⣿⡿⠙⠻⠷⢾⣿⣿⣷⣶⣶⠾⠟⠁
⠀⠀⠀⠀⣠⣿⣿⠿⣿⣿⠿⠿⣿⣆⠀⢻⣿⣿⡄⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠻⣅⣀⣀⣿⣿⣀⣤⡼⠋⠀⠈⣿⣿⣷⡀⠀⢠⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⡿⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡅⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⣸⣿⣿⣿⠃⠀⠀⣠⣿⣿⣿⣣⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⠀⢀⣼⣿⣿⣿⠃⠻⣇⣀⣼⣿⠏⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⡿⠁⠀⠀⠈⣹⣿⡿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⡁⠀⠀⣼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠈⠻⠟⠋⠈⠉⠁⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢢⡠⠒⠒⠀⠀⢀
⠀⠀⠀⠀⠀⣠⠄⠐⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⣀⡀⠐⠘⠁⠀⠀⠶⢈⠉⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠊⠉⠑⠲⠒⠖⠀⠀⠀⠀⠀⠀⣀⡀⠀⠛⠧⣤⠤⠀⢠⣞⠁⣀⣀⠀⠀⠀⠀⠀⠘⣉⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠄⢀⣀⡀⠀⠐⠛⠇⠤⠒⠓⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠲⣢⠀⠛⠛⡃⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠘⣈⠀⠀⠀⠀⠀⠉⠙⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠰⠒⠀⢀⡀⠀⠁⠂⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢰⡄⠹⣬⢧⠀⣰⡇⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣺⣷⣄⡻⣾⣃⡿⠀⣿⡶⢀⠤⠀⠀⠀⠀⠀⠀⡠⢦⡀⠁⠀⣼⠉⠨⠇
⠀⠀⠀⠀⠀⠀⠚⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠲⠷⠗⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣀⣀⣀⣤⣤⣤⣄⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⡤⡤⠋⡅⠀⣀⠀⠙⠻⣿⣷⣿⣟⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢤⠀⠀⠀⠀⠀⢉⡀⢀⠂⠠⢻⡿⣿⣟⣯⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡦⠀⠀⠀⠈⠁⠄⡤⠁⢾⡧⢸⠀⢙⣽⣯⡿⣿⣽⡯⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣄⠀⡀⠀⠿⠂⠠⠆⠀⠀⠘⢂⡁⢈⠄⠈⣿⢏⣴⣦⢹⣿⣻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠁⠰⡄⠠⣠⣄⠀⠛⠀⣉⠅⠀⢀⠠⠹⣧⣙⣡⣾⢿⣻⣿⠧⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠥⠀⠐⠀⠀⠀⠴⠛⠥⠄⡠⠌⠊⣡⣬⣤⠐⡑⢨⡋⢹⠉⠢⢿⣏⢀⡦⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⣶⣿⣟⣿⠿⠛⠻⣿⣿⣶⣏⣸⠏⣻⣿⢛⣄⠀⠲⠒⢘⢂⡩⢿⣶⣤⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣟⣿⣿⣮⣿⣷⣿⣵⣦⣿⣗⢾⣡⣿⠿⠋⠤⢼⠙⡙⣈⠐⠀⠀⠀⠉⢡⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⠿⢿⣯⣬⣿⣿⣿⣿⣿⣷⣿⠴⠲⠦⡔⣁⢠⢱⡞⢏⣿⣾⠃⠀⠀⠈⠀⢀⡈⡛⣄
⠀⠀⠀⠀⠀⠀⢠⣿⢛⣻⣿⣧⣶⣦⡿⢿⣿⣟⣹⣿⣿⡿⠯⣤⡶⢻⣇⡴⣋⠴⠿⢾⠗⠁⢈⠃⡾⣼⣷⡆⠀⣤⢸⢳⠦⠤⡀
⠀⠀⠀⠀⠀⣤⣿⣿⡟⢉⡭⢹⣿⣷⣿⣿⠿⢛⣛⡛⣛⠛⠲⣟⢻⣾⡿⢤⣥⣖⡃⠁⠀⠐⠆⠄⠙⠻⠟⠙⠀⠘⡀⢾⡀⠀⢈
⠀⠀⠀⠀⡹⣩⣿⣿⢷⣼⣿⣿⢿⡝⣾⣿⡇⢎⡽⢉⠉⡿⠴⣁⡦⡳⣷⣿⠀⠀⣿⣿⡗⢶⣦⣤⣤⣤⣄⣁⣀⣀⣭⡴⣿⡿⠋
⠀⠀⠀⣰⡿⣿⣿⣿⠟⠋⣿⣩⢎⡑⣿⣿⣿⢠⢲⠙⢠⢬⣙⢏⣻⣿⣻⡇⠀⠀⣧⣄⠉⣼⡟⠃⠛⣻⡇⠉⡉⢿⡇⣪⠟
⠀⠀⢰⣿⡿⡟⣽⡋⠀⠀⣾⢰⣺⠋⣿⣿⣿⡇⡹⡻⡇⢲⣴⣿⣿⣿⣿⡇⢀⣸⣇⡈⢣⣼⡟⠘⠃⠿⡗⠀⠀⢪⠿⠃
⠀⠀⢿⣫⢰⣿⣿⠁⠀⠀⣿⠻⢛⡛⣿⣿⣿⣿⡝⢻⣾⣿⣿⣿⣧⣿⣿⠀⠀⢾⣧⡙⢣⣸⣿⠓⠇⠛⢻⡄⠞⠁
⠀⠀⠈⠛⠾⣿⣹⡇⠀⠀⢹⠆⣼⣏⢿⣿⣿⣿⡗⣾⣿⣿⣿⣿⣿⣶⣿⠃⠀⠸⣧⣜⢣⣜⢻⣜⡧⠟⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣼⣧⣖⠺⢾⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣯⣿⡀⡀⠀⣹⡮⠿⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⢻⡗⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⠟⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢁⣀⡘⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⡀⢠⣀⠰⠄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⣁⠀⠁⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⣀⠘⠠⡈⠁⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⢈⠀⠀⣀⣴⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡔⠀⢹⣾⣋⡐⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣠⠾⢛⣛⣉⣍⣻⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢞⣵⣾⣿⣿⠿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡾⣻⣽⣷⣿⣿⣿⣿⡿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣵⡿⠟⣯⡉⣭⡉⣽⢛⡳⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢫⡜⢧⢘⢡⡜⣥⢟⡼⠗⢾⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣵⠈⠳⣦⠻⣠⡥⠾⠼⣅⢶⢰⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢣⡈⠗⠶⣹⢟⡕⠒⣙⢒⠪⢷⡘⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⢼⣾⣏⣉⠴⢋⡥⣬⠼⣩⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠷⣾⣥⣼⣬⣥⡷⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣀⣀⠠⢤⣄⢀⢠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡢⣰⢽⣵⡿⣾⣻⢾⣿⣻⢿⣷⣝⡷⣿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡪⣹⢽⣽⢮⣿⡷⣿⡏⣉⢻⣛⣿⡿⣟⣿⣷⢿⣳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣿⣽⣺⣿⢾⣻⣗⣯⡿⠋⠙⠿⢿⣽⣽⡿⣿⣞⣳⢧⣟⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣯⣗⣿⣳⠷⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠿⣿⣫⣿⣿⢽⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣱⣯⠟⠉⣀⣀⣀⣄⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠉⠚⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡙⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣿⣿⣿⡿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⣉⣀⣀⣀⣤⣤⣤⣤⣴⡜⠻⠻⠻⣿⣿⣿⣶⣦⣤⣤⣄⣉⠻⣿⣛⠶⠄
⠀⠀⠀⠀⠀⠀⢠⡿⢟⣻⠿⠛⠿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣶⣶⣶⣶⠊⢻⣿⣶⣶⣾⣷⠀⠀⠀⢸⣿⣿⣿⠛⢿⣿⠿⢿⣷⣦⣤⣬⣍
⠀⠀⠀⠀⠀⠀⠰⣾⣤⣶⣾⡏⢻⣿⠁⠀⣿⠿⣟⣿⡟⠀⠀⠀⠸⣿⣿⠇⠀⣸⣿⣿⣷⣞⢻⠙⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠹⡿⢻⣁⣵⣾⣿⣆⣀⣷⣶⣾⣿⡇⠀⠀⠀⠀⣷⡟⠀⣰⣿⣿⣿⣿⣿⣿⣷⡾⠋
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣏⡁⢺⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠛⢯⣽⢻⢟⡙⣿⣿⣈⣿⡷⠚⣿⣿⣏⣤⣬⣿⣿⣿⣿⢿⣶⣾⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⣿⣼⢣⠸⣯⣬⡟⠏⣿⣋⣻⣷⡿⠋⢻⣟⣿⣷⣶⣿⣿⠗⢻⢻⣿⣿⣱
⠀⠀⠀⠀⠀⠀⠀⠑⣦⡳⣼⠘⣌⣶⢻⣟⢿⡟⡇⣽⣿⢿⢰⢻⣧⣼⣿⣿⠏⣼⠛⣰⢏⣾⣿⣯⢥⢆
⠀⠀⠀⠀⠀⠀⠀⠸⢮⠳⣼⢳⣌⠫⡸⣿⣶⣍⠣⢻⠸⡜⡟⠈⡾⠸⠻⠋⠊⡅⢙⡣⢨⢟⡵⢋⡞⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣩⣙⡖⢣⡙⢧⣉⣓⣬⡻⣄⠘⣇⢇⡇⣦⣰⡿⣵⣡⣞⠴⢋⡴⢔⣫⣴⣛⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠙⠦⢭⣠⣤⣤⣤⢽⣮⣿⣿⣾⣿⣽⣿⣾⣯⣭⣴⣾⣛⣫⠹⠯⠭⡩⠭⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠑⠑⡟⢻⢻⠻⠛⠙⠏⠻⠙⠃⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⣯⣿⢦⣄⡀⠀⠀⠀⣀⡀⢀⠀⠀⠀⡄⡄⠊⠉⠀⡦
⠀⠀⠀⡖⠶⣤⣄⣀⣀⣤⡻⠧⣾⣙⣿⡤⠾⠟⣫⣾⠟⠉⠀⣀⠄⠀⠀⠄⡄
⠀⠀⠀⢠⣠⣄⠀⠈⠉⠉⠙⠳⢬⣭⣵⣶⡾⠟⠛⢀⣠⠤⠚⠁⠀⠀⠀⠀⡵⠚⠧⣠⠘⡄⠂⠀⠀⣀⡀
⠀⠀⠀⠀⠉⠛⠓⠢⣀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣀⣼⠃⢀⣠⢴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠓⣿⣾⠋⠈⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣀⡀⠈⣉⣤⣔⡻⢿⣧⡻⣿⡏
⠀⠀⠀⠀⢀⢰⡿⡄⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⢠⣶⣿⣷⣶⣶⡿⢿⣿⣦⣙⢿⣿⣷⣮⡛⢾⡅
⠀⠀⡀⠰⣿⣷⣾⣄⢴⣾⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠸⣄⣀⣤⣤⣶⣾⣿⣿⡿⠻⣷⡝⢿⣿⣿⣦⣇
⠀⠀⠿⡇⠛⠿⣿⠏⠛⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠑⠈⠍⠛⠛⠛⠛⠛⣿⠁⢺⠻⣿⣦⣝⠿⠿⢿⡄
⠀⠀⠀⠀⠈⡠⠘⠀⡰⠀⠀⠀⣀⠀⣼⠀⠀⠞⠋⠉⢳⣠⣄⠀⠀⠀⠀⠀⠀⣿⠀⡏⠀⠘⢿⣿⣿⣷⣶⣬⣆
⠀⠀⠀⠰⣸⣇⢸⠉⠀⠀⢀⠒⠉⠿⡁⠀⠀⠀⠰⡂⠄⣃⣙⠆⠀⠀⠀⠀⠀⢻⠀⠇⠀⠀⠙⠿⣿⣿⣿⣿⠼
⠀⠀⠀⠀⠈⢻⠎⠀⠀⢠⡇⢤⠤⣀⠀⠀⠀⠀⠀⠈⡆⢱⠀⠀⠀⠀⣾⣦⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⣠⣀⣤⣿⣿⡆⠀⠈⠀⡏⠘⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣽⡿⡓⣄⣧⠀⢇⠀⠀⠀⠀⠀⣰⡆
⠀⠀⢠⣾⣿⣿⣶⣿⡟⠃⠀⠀⢸⠁⠀⠀⠀⢀⣤⣴⣶⣶⣤⣄⠀⢠⣾⣿⡷⠊⠸⡄⠘⡄⠀⠀⠀⠀⣿⡋
⠀⠀⢻⣿⢿⣿⡯⢣⡆⠀⠀⠀⣸⠀⠀⢀⢘⡩⢭⣁⠒⣂⢶⠊⡷⡄⠀⢸⡇⠀⠀⡇⠀⡇⠀⠀⢀⣼⣧⡇
⠀⠘⠙⢛⣿⣫⠾⡟⠀⠀⠀⡀⡿⠀⠀⡾⣈⣬⣵⣿⡾⢷⣿⣿⣧⡦⠀⡾⠁⠀⠀⣯⠀⢠⠀⠠⠘⠛⡟⠻⠄
⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⡜⣇⣧⠀⠀⢿⠟⣢⣤⠐⢶⠒⡦⣤⡱⠃⣸⠃⠀⠀⠀⣿⠀⣸⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⡰⠡⠀⡰⠋⣸⠋⠙⢧⠀⠈⠈⠽⢽⡀⢸⠉⠉⠡⣤⡀⣿⠀⠀⠀⡠⢛⡀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⡇⠀⠀⠈⡇⠀⠀⠀⡌⠝⠎⠓⠄⠀⢘⡇⠉⠀⢀⠎⡐⢡⠁⠀⢀⠀⠀⠸⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠱⠤⠴⠄⣈⡴⠃⠀⠀⠀⠀⡘⣄⡀⣀⠐⠉⠀⠀⠀⢸⣔⡠⠁⢀⠤⠎⠘⡆⢠⠇
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣀⣀⣤⡤⠤⠶⣶⠦⠤⢤⣤⣀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⠾⢋⢉⠀⠀⣷⠀⠀⢸⣂⢠⠀⡈⢍⢻⡆⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠒⢦⡀⢧⠀⢿⣡⠃⠎⡼⢰⢻⠀⠀⢸⡄⡆⢣⣘⣬⠗⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠙⣎⠳⢦⣉⣛⠒⠓⠚⣾⠀⠀⢸⣟⣛⣩⡥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠉⠉⠉⠉⡿⠀⠀⢸⡏⠀⣠⡴⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⣴⠶⢶⡖⠒⢺⡶⠶⣤⣤⣀⠙⣆⠀⠀⢰⡇⠀⠀⣸⣠⠞⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⡍⣄⡤⣼⡇⠀⢸⡇⢀⣤⢬⣿⠆⣿⠀⠀⣾⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⣻⣶⣶⡇⠀⢸⡷⠞⣿⣫⣵⠞⠁⠂⣸⠃⠀⠀⣸⢁⣀⣤⣤⡤⠤⢀⣀⣀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⢤⡀⠀⠉⠙⡇⠀⠘⡏⠉⠉⠁⠀⠀⠀⢰⠏⠀⠀⢠⡟⠿⣤⣟⣀⡇⠀⢸⡇⢈⣉⣳⠆⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠦⣄⠀⢿⠀⠀⢻⡀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡾⠙⠲⠤⢤⣩⠇⠀⢸⣏⣉⣩⡥⠴⠊
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣀⣀⣀⠀⠈⢧⠸⡇⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀⣸⠃⠀⠀⠀⠀⣼⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢿⠀⣶⣚⣻⣿⠀⢸⣟⣿⣿⠆⣸⠂⢻⡀⠀⠙⣦⠀⠀⣸⠃⠠⠀⢰⡏⠀⠀⠀⠀⣰⠃⠀⢐⣿⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠶⡭⣭⣿⠀⢸⡭⠴⠶⠛⠁⠀⠈⢧⠀⠀⢹⣆⢠⡏⠀⠀⠀⣼⠀⠀⠀⠀⣰⢏⡠⠞⠋⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⢷⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣾⠃⠀⠀⠀⡟⠀⠀⠀⡴⠃⡾⢁⣠⢤⣤⣄⣀⡀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢧⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠹⡄⠀⠈⢸⡇⠀⣠⠞⠁⠀⠙⣮⣓⠲⡿⠀⣸⣩⣷⠆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠳⣄⠀⠀⠀⠀⠀⢻⡀⠀⠀⢹⡀⠀⢸⣇⡼⠃⠀⠀⢀⡼⠁⠈⣽⠃⢠⠟⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠘⢧⡀⠀⠀⠀⠈⣧⠀⠀⠀⢳⠀⢸⡏⠀⠀⠀⣰⠏⠀⢀⡜⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⣦⠀⠀⠀⢸⡆⠀⠀⠈⡇⠀⡇⠀⢀⡼⠁⢀⡴⠋⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⢳⡀⠀⠀⣇⠀⠀⠀⢻⠀⢹⣀⡞⠀⣠⠟⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡄⠀⣿⠀⠀⠀⢸⠀⠀⢿⠀⣼⠃⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡀⡟⠀⠀⠀⣸⠀⠀⣸⣼⠇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⡾⠁⠳⣄⣀⣴⠷⠤⠴⠋⠸⣦⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉

⠀⣤⠐⠐⠀⠀⠀⢠⠀⠀⣤⠀⣴⠛⣾⠏⠉⢉⠁⢠⡿⣋⣉⣿⣏⠀⠀⠞⠀⠀⠖⠀⠀⠀⠿⡇⠈⢰⡄⠀⢀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠹⣶⣿⣿⣧
⠀⠀⠄⠀⢹⠆⠀⠙⠀⠀⢸⠹⡇⢸⠇⠀⠀⠀⠀⠈⢻⣿⣷⢙⡇⣀⠀⡀⠀⢤⣵⡆⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠚⠃⠀⠭⠴⠀⠘⣿⢠⠄
⠰⣞⡗⠒⡀⠲⣄⠀⡤⢴⡟⠀⠉⠘⣄⠀⠀⠀⠠⡄⠘⣿⠃⡝⠿⠿⠛⠁⣴⠀⡛⢀⢐⣠⣤⡤⢤⣶⣤⡤⢤⡤⣤⣤⣠⢄⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠸⣃⣴
⠈⠉⣄⡀⣙⢠⣿⢶⡄⠀⣿⡶⠀⣷⣿⣦⡄⠀⡀⢠⠾⣿⡀⢦⡆⠀⣠⠀⠁⠀⡀⠀⢦⠈⣶⣶⣤⠀⠂⣀⢀⡀⠙⠆⠁⠀⣿⠀⠀⠙⠂⠀⠄⠀⠀⠀⠀⠀⣼
⠈⠃⢈⡑⠿⠀⢻⣿⡱⣿⡿⠛⠋⠉⠋⢹⡇⢸⡏⠰⠀⢄⠀⡬⠁⠐⠋⣠⣄⣼⡧⠀⢎⠀⠠⢼⠃⠰⠆⠩⠶⠁⠀⠁⠠⡈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡈⠧⠀⡆⠘⣿⢧⡻⠀⢀⠀⢠⣀⠙⣿⠘⠃⠀⢠⡌⠘⠃⠀⢠⣾⡿⣿⠉⠁⠹⡄⠀⠀⠈⠳⠀⠀⠠⣦⡄⠀⠀⠀⠁⠐⢀⠈⠃⠀⠀⠀⢀⠀⠀⠄⠀⢡
⠀⠈⠁⠁⠀⡇⠀⣿⣿⡅⢻⠀⠒⠘⣿⢂⣥⢠⣞⣂⡸⠧⢸⣄⠂⠸⠏⠀⠀⢠⠀⠛⠎⡀⠀⢠⣶⣶⡗⠀⡹⠇⢐⠶⣶⠀⠠⡦⠀⠀⡆⠈⠀⠘⠀⠀⡀⠀⠿
⠀⡻⠢⣄⣴⠀⢰⠙⣿⠀⣀⢠⣖⣩⣏⢘⡉⣠⣽⣼⡷⠐⠛⠿⠀⠀⠀⠐⠃⠈⠀⠀⠀⠈⣷⡀⠛⠛⠉⠀⠀⠀⠈⡀⣈⢁⣂⠤⠀⣤⠀⠀⡄⠀⠀⠀⢹⡄
⠀⡠⠀⠹⠋⠀⠘⠁⠴⣟⢱⣄⠸⡿⠻⣿⠙⣏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⢀⠀⠠⠀⠈⠁⠀⠀⠐⡀⠀⠑⡆⠀⣁⠟⠋⠁⠀⠁⠀⠀⠚⠃
⣔⢀⣆⡄⠀⠀⠈⠳⣤⣝⣿⠀⢰⠀⠤⣲⠀⣹⡆⣠⡀⠀⠀⠀⠀⠀⠐⣄⣰⡁⠀⣀⠀⠀⠀⠀⣂⣀⠐⠋⠁⠂⢠⣿⠀⠀⢐⡐⠂⠀⠀⠂⠀⠀⠤⠀⠀⢀
⣿⣶⡁⠑⠄⢠⠄⠀⠻⣿⡏⡄⠀⣤⡄⠁⢤⠀⠈⠁⠀⢠⣴⣶⣦⠀⣠⣬⣿⣿⠛⠝⢧⡀⠀⢀⣍⠉⠀⠀⠀⠀⣼⠏⡼⠛⠻⡟⠂⠀⠈⠀⠃⡀⠀⠀⠀⠿⠃
⣷⣿⡆⠀⠀⠀⠀⠇⠘⣻⠇⠘⢻⡿⠄⠠⡊⠀⠚⣃⠀⠈⠻⡷⢾⡟⠈⢻⠄⠈⠀⠀⢸⣁⠀⣾⣿⣄⡀⠀⠀⣸⣿⣾⣅⠀⠁⠑⠂⠸⠋⢠⠂
⠀⠻⡇⢸⡆⣦⣀⠀⣀⣻⣶⣨⡟⣇⢄⡾⠻⠗⣠⠠⠈⠁⠷⣶⣮⡄⢠⣼⠆⠀⠀⠐⢺⠿⠿⢩⢿⡈⣷⡄⢰⣿⣟⣠⠟⠀⠀⠀⣀⡀⠀⠴⠇⠐⠛⢲⣄⣰
⢀⡀⠀⠛⣠⣿⠏⠰⣿⣿⣿⢋⠀⡘⣦⠓⠀⠙⣿⣗⠀⠀⠣⢘⡧⣉⠈⠱⠂⣴⡖⠀⣳⣶⣶⡿⣿⣷⣿⠁⣿⣿⣿⣿⣾⠃⠀⢐⡿⠿⠢⡆⢀⣴⣾⡀⠈⢿⣀
⣠⣾⣇⠀⢿⣡⡆⠀⣿⠋⠉⣿⣄⠃⠈⡀⠀⠀⡌⠛⢻⡾⣆⣈⣷⡋⢈⣲⣀⠙⣿⡿⢛⡿⣧⢠⣿⣯⣽⣯⣿⠷⠞⠙⣿⣿⣿⠛⠛⠰⠀⢁⢨⡿⣿⠁⠈⠃⠘
⠟⠁⠋⠀⠁⢠⢀⣆⣸⡇⠀⢿⡏⡠⠀⣀⣠⡆⠀⣶⣤⡥⠋⠉⠀⠃⢸⣻⡟⠛⠋⢰⣿⣷⠏⣼⣇⣸⣿⢿⣿⠀⠀⢀⣿⠋⠉⠀⠀⠀⠱⣾⣿⣧⡿⣿⠎
⠀⠀⠀⠀⠀⢠⣥⡍⢡⡖⢀⣸⣧⣠⡤⣿⣿⠇⠀⠯⠀⠀⢀⣤⣤⣤⣾⠉⠉⠹⣷⡀⢻⡿⢿⣿⠟⠻⣿⣿⡿⠀⠀⠈⠀⠀⠀⣠⣤⣤⣄⣠⡀⠀⠘⠧⠀⠠⠶
⢸⡇⢶⠀⠀⠈⠉⢷⠟⣷⠈⣛⣿⡟⢳⣮⣽⡇⠀⠀⠀⢰⣏⠁⢸⣿⡏⠀⠀⠀⢸⡇⢙⡷⢺⡽⣀⢀⣿⠃⣀⠀⠀⠀⠀⢰⣿⡟⠉⢩⠽⢿⡏⢀⣈⣛⣀
⢸⡆⠆⣾⡻⣄⠰⠄⠈⠻⣿⡟⠉⠀⠀⠀⣼⢷⡎⠑⣶⡏⣿⠻⣿⣿⠀⠀⠀⣀⣼⠃⢿⠃⠀⠀⡄⢀⣿⣄⣿⣼⣇⡀⠀⠀⣴⡆⠀⠛⠷⢸⡿⠛⠉⠉⠙⠉⡀
⠸⡇⠰⠛⡇⠈⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣿⢸⡇⣼⠉⠷⣿⠛⣿⡇⠀⠀⠘⠋⠈⣴⠋⠀⠀⠀⢸⣿⣿⠇⠉⠙⠛⠛⠃⡄⡀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠠⠄
⢠⡇⣀⣷⠶⠀⣀⢠⡴⢀⠟⣿⠛⢳⠆⢶⣿⠿⢡⠿⠀⠀⣿⣆⡸⣇⠀⠃⠀⢠⠘⣿⠈⠀⠀⠠⡧⢽⣿⠀⠀⠐⠀⠀⠀⠷⠸⡆⠀⠀⠀⢿⡄
⠀⠀⢿⠁⣶⣄⡙⠃⡄⢙⣏⣽⣇⣼⡀⠰⠻⣦⣼⢀⣤⡾⣃⠙⢣⠿⣠⣶⣦⢸⠀⣿⣦⢤⣶⡷⠶⢦⠉⠀⢀⣤⣶⣿⣦⡀⠰⠖⠀⠀⠀⠸⠁
⢠⣶⣼⠈⣿⡆⠋⠀⠹⠛⠋⠈⣤⢈⡀⠈⣳⣿⡝⡿⢻⣿⠙⠿⢇⣴⢿⣾⣿⣮⡐⣋⣴⡾⠋⢀⣤⠆⠀⠀⢀⡻⠏⡅⠈⢳⡀⠀⠂⠀⢀⡇
⠀⠀⠉⠘⠿⡟⠀⢀⠀⠀⠸⣿⡇⠀⡻⢤⢻⣿⡟⠀⢨⡟⣧⠀⢸⢿⡾⠋⣷⢸⢹⣿⠁⣀⣤⢿⣷⣦⡴⢶⣿⣷⣶⣦⡀⢈⠁⠀⢰⣶⢋⡀⠀⠀⡸⣁⠀⠈
⠀⠘⠃⠂⠠⠀⠠⠀⠐⡃⠀⣻⠏⢢⢁⠈⣹⣿⣿⡀⣼⠃⣀⠀⡀⠈⡃⠀⢤⣾⣯⣿⡟⢻⡇⢸⣿⠁⢱⣞⡛⢣⣬⡿⠙⢛⣇⢀⡌⠛⣿⠇⠀⠀⠱⠟⣤⣠⡶
⠀⠀⢠⣼⣧⡄⠀⠀⠀⠀⢨⡏⠙⠛⠉⠀⡽⢻⡭⢻⣿⠆⠷⣈⠛⠛⠛⢰⡄⢉⣥⠤⣥⢀⡟⡀⠈⣻⣿⢻⣿⡟⠰⠛⠀⢿⣟⣴⡟⠛⣯⣄⣀⠴⠡⠞⢻⣿⣷
⠀⠃⠼⠋⠀⠄⠀⣿⢆⡁⣰⠀⢠⣶⡆⢀⠁⢬⣶⣼⣾⡿⠦⣬⠲⣶⣶⣧⡄⠀⠠⣶⣧⣽⡏⠁⠉⠉⢹⣟⣻⠀⠀⠀⡀⢀⣿⡌⣧⠸⡏⠉⢙⡂⣸⣿⣿⠇⣿
⠨⣷⠈⠀⠠⣀⢴⠋⠀⠀⠷⠀⠈⢀⣝⡻⠰⡟⠟⠁⠈⢡⣴⠃⠸⠛⠀⣘⣁⠀⣠⣈⣿⣝⣋⠀⠘⢷⣄⣻⣛⣴⣷⣀⠤⠈⣩⣤⣴⣿⠁⢸⡿⢁⡿⣿⢉⠸⠿
⢘⣽⡇⣴⠈⠃⠈⠁⠞⠁⠰⡆⠀⢠⣹⣿⠀⠠⠀⠰⣢⡟⠙⠀⠞⠰⠈⢿⣟⣧⣙⣷⣾⡿⠁⠸⣇⠐⠍⣿⣯⢹⣇⠀⠀⢀⡜⠁⡼⢻⡇⢠⣶⢋⣴⣇⠈⡀⠠
⢸⡿⡷⣸⡟⠀⢰⡶⢳⡄⢀⡀⢹⣯⡉⢡⠟⠀⠈⠀⢹⡗⠂⠀⠀⠀⠃⠀⣻⡉⢋⣬⢹⡛⠀⠀⢨⠀⠀⣤⣿⡾⣿⡷⠈⡻⢻⣷⣴⠏⠀⠰⠏⢸⣿⢻⡆⢹
⢸⡃⢿⡟⠷⠀⡼⠣⠚⠁⢨⣁⠰⣇⠠⠽⠲⠄⠀⢀⡜⠁⠠⠀⣀⣤⡀⠈⣿⡿⠟⢋⠈⠇⠀⠀⣼⡀⠀⢱⠿⣧⣿⣷⣾⣿⣘⡿⢡⡶⠂⠉⠀⢀⡇⠈⠣⠀⠈
⢘⣿⢸⣿⠀⠂⣽⣦⣶⡆⢻⡏⢀⣙⠀⠀⠟⣰⠷⣾⡇⣠⣾⡆⠀⢈⣷⠀⠈⠻⠾⠛⠁⢀⡟⠀⠈⠀⠀⠀⠀⡿⠉⣛⠛⠁⣀⡄⣠⣶⣦⣁⠀⠸⣷⣿⠇⢀⠠
⠸⡟⢠⡿⢀⡂⣿⠟⢈⠛⠀⠁⠈⠀⠉⠀⠀⢹⣆⢻⡷⣿⣿⣷⡄⠀⢿⠀⠀⠀⢚⠀⠐⠀⢀⠀⠀⠀⠀⣀⡤⣅⣀⣽⠺⠂⠁⠀⠀⣈⠉⠃⠠⣿⠀⠹⣆⡈
⠀⠛⣀⣷⠿⣇⠉⠀⣼⠿⠟⢁⠈⠀⠀⠀⢠⣴⣿⡌⠁⠘⠃⢸⣿⡄⠸⠀⠀⡰⠃⠈⢤⡀⠘⣃⠛⣿⣿⣯⠇⢉⠁⡙⠃⠀⢠⡀⡀⠁⠀⡀⢀⠀⠀⠘⠿⢻⣿
⢸⠛⡛⢉⡆⠈⠀⠀⠉⢠⡄⠘⠳⠆⠀⠀⠈⣉⣿⣆⠀⠀⠀⠸⠿⠷⢀⠀⠀⠁⠀⠀⠀⠀⠚⠃⠀⡬⠟⢣⡔⠉⠼⠃⢀⣄⡀⠈⠀⢈⡀⢠⠄⠀⠀⢿⡇⠀⡏
⠘⠛⣇⡘⠁⠀⠀⠀⠄⠀⠀⠀⢀⣁⠀⠀⢰⢈⡿⣹⣇⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢀⠀⠴⡠⠘⠃⣴⡆⠀⠀⡀⢻⢀⣬⡍⢱⠀⢰⡋⠙⠛⡀⢠⣷⣆⡀
⠀⠀⢡⣄⡀⠀⠀⠀⠀⠀⠀⠐⠾⠋⠀⠘⠛⠛⢿⢻⣯⣄⠆⠀⠀⠀⠻⡏⠀⠀⠀⠀⢀⠀⣄⠀⠺⠋⠀⢀⠀⠋⣡⠘⠋⠹⣀⣴⡟⠀⠀⣄⣿⠛⠋⠋⠀⢀⠰
⠀⢀⣖⠛⠋⠉⠉⠁⠒⠀⠀⢀⠘⣅⣠⣤⡆⠀⠐⠿⠙⠙⣷⣤⠀⣰⠆⢷⣶⠀⠀⣈⠿⠿⢏⡀⡀⠀⠀⠚⢧⣤⠎⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠀⢀⣴⡟
⠀⠈⣿⠀⠀⠀⠀⠀⢀⠀⠀⡘⠃⠙⢿⣿⡷⠤⠤⠀⠠⠀⠛⢁⣤⡉⠀⠈⣿⣿⣾⡿⠳⣤⠀⠉⠀⠀⠀⠀⠀⡾⠓⢳⠚⡇⠛⠀⠳⠶⣤⣄⢀⡄⢹⣿⣿⡁⣜
⢘⣇⣸⣄⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠹⠀⠀⠀⠀⢠⣄⢀⡿⠿⠇⠀⢀⠟⣿⣿⡇⢀⠀⠀⠀⢰⣾⣷⣶⣄⠐⠀⢸⣷⠀⣀⠖⢿⠀⠁⠙⠻⡇⠈⠙⣉⣃⡈
⢰⣿⡟⠉⢠⠾⠀⠀⢰⠆⢰⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⠧⢰⠧⠀⢀⠀⣾⡿⠆⠀⠄⠁⠀⠈⣙⠟⣻⣿⣠⠀⢸⣟⠀⢉⡤⠦⠀⠀⠀⠸⠃⠐⣿⠃⠇
⠀⠿⠐⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⠘⠋⠰⢆⠨⡶⠀⠀⢰⣿⣤⣄⣀⡀⢢⢘⡁⣤⣀⣀⣀⡀⠀⠉⠀⠀⣠⡗⠀⠀⠙⠒⠀⡄⠀⠀⠽⢢⣰⣷⠀⣹⣧⡀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⣶⣶⣶⣶⣲⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠻⢿⣿⣟⣿⣿⡟⠀⠀⣤⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢦⣶⣿⢾⣧⡘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣨⣿⣿⣆⢿⣯⣛⢜⣀⣦⠀⡀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣌⣙⢻⣿⣿⣿⣿⣿⣌⠿⢿⡾⠿⠁⠀⠁⠀⠀⠀⠀⣠⡾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⣈⣁⣀⣀⣤⣤⣤⡶⠾⠟⠉⠉⠉⠳⣽⣿⣿⣿⣧⣿⣿⣦⣦⣀⠀⠀⠀⢀⣈⣤⣾⣿⣧⣿⡆
⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡛⠃⢏⣹⣅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣦⡄⢀⢰⣴⣶⡀⠀⠀⣠⣾⣿⣿⣾⣿⣿⣿⣿⣻⣿⣌⣿⠋⣿⣷⡿⣗⡓⣏⣛⢻
⠀⠀⠀⠀⠀⠀⠉⠠⢀⣤⣿⣿⣧⣤⣿⣿⣿⣤⣤⣴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣨⠃⠀⢻⣿⣻⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢿⣹⣿⣿⠟⠿⢿⣿⣿⣰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⠂⠀⠈⢱⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⡀⠙⡿⠋⣀⣀⡈⣻⣿⣟⢿⣇⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣷⠈⠀⠀⠸⡿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⢫⡛⢿⡟⠙⢛⢿⡟⢿⣾⣿⣿⣻⣧⢿⡟⠀⠀⠈⣭⢽⣿⡄⠀⣀⡖⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠙⢾⣧⣿⣻⣿⡏⢀⣸⣋⠀⢙⣶⣿⣷⣶⡀⠀⠹⡯⣥⣶⠙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢄⠉⠉⠉⠻⣼⢡⣙⣿⣿⣿⠿⠟⠀⠀⠀⣀⣀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢻⡏⠻⠍⠽⢁⠀⠀⣈⡤⠤⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⣀⣤⡤⠤⢤⠤⠤⣤⣀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⢴⢋⢁⠀⠈⡇⠀⢸⡂⠀⠠⠨⡹⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⢦⠳⡈⠣⣇⣆⡄⣀⡇⠀⠸⣇⣄⡦⠷⣛⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠳⣌⠓⠲⠤⠬⢭⡇⠀⢨⡗⠒⢚⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣠⡤⢤⡤⠤⣤⣤⣀⡀⠑⣄⠀⠀⢸⠁⠀⢸⢁⡴⠋⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠰⣯⠀⡀⢸⡇⠀⡇⠀⠀⢙⡆⢸⠀⠀⡏⠀⠀⡜⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⢭⣓⣻⡅⠀⣗⣚⣚⡭⠔⠁⠀⡼⠀⠀⢰⣃⡤⠤⢤⠤⢠⡤⣀⣀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠓⠦⣀⠀⠘⡇⠀⢹⠀⠀⠀⠀⠀⣰⠃⠀⠀⣮⡙⠲⠦⢼⠀⢀⣧⣤⠬⠗⣠⠇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⡄⢳⠀⠘⡇⠀⠀⠀⢠⠇⠀⠀⡼⠁⠈⠉⠛⡏⠀⢸⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⣞⢀⡤⠖⢲⠂⠲⠒⣲⡄⣸⠘⡆⠀⠹⡄⠀⠀⡞⠀⠀⢰⠃⠀⠀⠀⣰⠃⠀⣼⣀⣀
⠀⠀⠀⠀⠀⠘⠲⠭⠭⣿⠀⢻⠭⠥⠒⠁⠀⠹⡄⠀⠹⡄⢸⠁⠀⠀⡞⠀⠀⠀⣰⢃⡤⠚⠉⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡆⠀⠀⠀⠀⠀⢳⡀⠀⠹⡏⠀⠀⢠⡇⠀⠀⡴⠃⡏⣠⠤⢤⠤⣄⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⣆⠀⠀⠀⠀⠀⢧⠀⠀⢱⡀⠀⢸⠀⣠⠞⠀⠀⢸⠮⢭⡟⠀⣶⣾⣓⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠳⣄⠀⠀⠀⠘⡆⠀⠀⢣⠀⢸⡞⠁⠀⢀⡴⠁⢀⡜⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⢦⡀⠀⠀⢹⠀⠀⠈⣇⠸⡄⠀⢠⠞⠀⡰⠋⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠹⣄⠀⠘⡇⠀⠀⢸⠀⢧⣰⠋⣠⠞⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⣆⠀⡇⠀⠀⢸⠀⠘⡇⣰⠃⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢸⠄⡇⠀⠀⡼⠀⢀⠟⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠋⠀⠙⠲⠚⠉⠉⠉⠀⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⣤⠀⠃⠀⠻⢅⡶⠀⠀⠀⠀⠀⢀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠙⢧⠀⣠⠤⡀⣐⣄⡄⠀⠀⢴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠁
⠀⠀⠀⠐⢿⣯⢉⠒⢠⠄⢤⡧⠀⠀⢘⠄⠀⢠⢄⢬⠀⠀⠀⠀⠀⠀⠀⠛⢀⠀⠀⠀⠀⠀⠀⣀⢢⠀⣾⠁
⠀⠀⠀⠀⠀⠙⢎⠀⠃⠂⣯⠕⣋⠄⠨⣆⠀⠀⡺⣄⢢⠄⣀⠋⠁⠠⠀⣤⡒⠀⠀⢰⡇⠈⠁⠉⢰⣄⣉
⠀⠀⠀⠁⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⡈⡅⣿⠘⡐⣻⣂⠀⠀⠀⠘⢿⣂⣀⢼⡆⠀⠀⣀⣼⠋
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠈⠁
⠀⠀⠀⣀⢤⣇⣾⡶⠄⢀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣉⠁⠃⠁⠔⠀⣴⣶⡀⠀⠀⠀⠠⠀⠀⢦⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀
⠀⢠⣬⡇⠀⣰⣧⡔⣲⣨⣶⡄⠀⠀⠀⠀⠀⢨⡿⢿⣷⡠⣄⠀⠀⠀⠀⡌⡠⢀⢄⠀⢦⠀⠀⠀⡄⠀⢱
⠀⠈⢹⡅⠀⠉⢸⡸⢿⣻⣏⣡⡖⠀⠀⠠⢤⡗⠚⣲⣤⠱⠿⠷⠀⠀⠀⡇⣠⠐⠀⠁⠈⣷⢁⡀⠑⡀⢸⠃
⠀⠐⠞⢃⠀⠀⠙⢧⣸⢁⢛⣃⣠⠀⠀⠀⠈⠛⠄⠈⢋⣾⡟⢰⡿⠀⠀⠑⡘⠄⢀⡀⢢⣼⣄⠷⡖⢘⠑⠄
⠀⠀⠀⠀⠁⠀⠀⠠⠀⠉⠉⠅⠀⠀⠀⠀⠀⠠⠀⠈⠉⠒⠒⠂⠃⠀⠀⠀⠲⠧⠠⣁⢈⢈⢀⡤⠖⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⣬⣷⠶⠛⢾⠿⢶⣤⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣡⣾⣿⣾⣿⡷⡀⣸⣧⡀⠎⣽⢷⡝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢫⣼⢇⠋⠙⢉⣠⠷⠿⠬⢳⣮⡻⠧⢿⠸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡲⣛⡵⡞⠉⢭⢀⣴⣟⣽⣶⣶⣆⠐⠂⠌⣙⠿⡉⣧⣿⡿⢿⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⣾⣾⡍⡆⢱⠀⣿⡿⠛⠁⣾⠿⢿⣿⠿⣷⣦⠘⡷⢘⢿⢿⡿⠏⢹⡎⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣾⠛⠿⠟⠁⣸⣼⣋⣡⣀⠡⡘⢇⣼⣷⣤⣿⡿⡟⢃⣜⣙⣯⠻⢖⠀⢳⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡇⠈⢐⡶⢛⣉⣤⣬⣭⣙⣛⡻⣦⣍⣙⣫⣭⣥⣶⠿⢋⣉⣁⣤⠬⢿⣦⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣁⣼⡾⠻⢫⣶⠟⢿⣿⠏⡉⡍⢙⠿⠚⢿⣿⣶⢶⡿⠿⠛⠋⢏⠻⣻⣷⣾⣼⠙⠛⠓⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠄⣠⣤⢟⣽⢿⣷⠇⣸⣴⣯⣵⣬⣶⣶⣾⠞⣫⢿⠭⢭⣻⡟⣿⢺⠟⠶⠶⣷⣶⣷⣾⣿⠿⢿⢻⣿⣿⣿⡦⣬⣧
⠀⠀⠀⠀⠀⠀⢠⠎⢩⢣⡟⢁⣀⡴⠿⣟⡽⠟⠋⠩⣉⡛⢌⠩⠡⠀⠀⠀⠀⠀⠆⡠⡀⢂⡤⢒⠉⠁⠉⡛⠲⢦⣦⣽⣿⣿⣴⣩⣝⡷⡀
⠀⠀⠀⠀⠀⠀⠸⡀⠸⢻⣊⡩⠗⣂⠉⠅⢀⣠⡤⢶⣦⠽⢦⠀⠀⡆⠀⠀⠀⣀⢠⡑⣴⣿⠖⠦⠀⡒⠂⢀⡹⠶⠬⠉⠉⣙⢛⡡⣍⢷⠆
⠀⠀⠀⠀⠀⠀⠀⢳⣄⡪⠙⠿⠷⣦⣄⡀⢘⡫⠊⡿⠛⠛⠛⡆⠆⠀⠀⡀⠀⠸⡾⠁⣿⢿⢿⣷⣒⡀⠀⠀⠀⠀⣠⡌⢉⢅⡶⠼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠭⡑⠢⢕⣛⣛⢛⠛⠷⣧⣆⣐⡇⠀⠀⠀⡇⢠⢀⡇⢰⣿⠀⢀⠱⠌⠀⠤⠚⠋⢉⣠⡴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠚⠛⠳⠤⣘⣋⡃⠀⠆⣰⠇⢸⠸⠀⢂⣿⣉⠉⠁⠠⠀⡲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠄⠀⡐⠜⠀⢸⠀⠀⢊⠎⢧⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡈⠀⢠⠆⠀⠀⢸⡄⠀⠀⠡⠨⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡼⠀⠀⠀⢠⠳⠀⠀⠄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠘⠀⠃⠐⠈⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢶⠀⣹⡇⠀⠀⠀⠀⠀⠀⠇⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢆⠀⢻⡄⠀⠀⠀⡀⠀⡄⢸⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣂⠹⣷⠱⡀⠀⡃⢀⣣⢇⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣵⣽⣾⣷⠾⠛⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣠⡤⠖⠚⠋⡏⠁⠈⣯⠉⠉⠙⡳⢦⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠸⡄⢸⡝⡔⡰⠠⢀⣷⠀⠀⣷⢠⢡⠐⣘⡬⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢳⡙⢦⣉⠓⠷⠧⠼⣿⠀⠀⣿⠞⣚⣋⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⠉⠙⠛⠛⡇⠀⠀⣾⠉⢁⡤⠴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣠⡴⠖⠒⡖⠒⢲⠲⠦⢤⣀⠈⢧⠀⠀⢰⠃⠀⠀⣇⡴⠋⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡸⣷⡀⡐⠀⡇⠀⢸⠀⡀⡔⣸⠇⡸⠀⠀⡞⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠭⢭⣝⡇⠀⢸⣟⣙⣭⠵⠚⠁⠀⡼⠁⠀⠀⣏⡤⠴⠶⠶⠒⢠⠤⢤⣀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠙⠢⣄⠀⠀⢷⠀⠈⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⣍⡓⠷⠶⡕⠀⢸⣥⣤⠦⠟⢀⡜
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⢸⡄⠀⢹⡀⠀⠀⠀⢠⠇⠀⠀⢰⠇⠀⠉⠙⢒⡇⠀⢸⠖⠒⠒⠋⠁
⠀⠀⠀⠀⠀⢰⠃⢀⡤⠤⣴⠒⠶⠲⠶⡄⢘⡆⢧⠀⠀⢧⠀⠀⠀⡞⠀⠀⠀⡟⠀⠀⠀⠀⡼⠀⠀⡞
⠀⠀⠀⠀⠀⠈⠣⣌⣚⣒⣿⠀⣿⣛⣩⠥⠚⠀⠘⣆⠀⠈⢧⠀⢸⠁⠀⠀⣸⠁⠀⠀⠀⡼⢁⡠⠔⠋⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠸⡄⠀⠀⠀⠀⠀⠸⡄⠀⠈⢧⡏⠀⠀⠀⡏⠀⠀⢀⡼⢡⠏⣀⣀⣀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠱⡄⠀⠀⠀⠀⠀⢹⡀⠀⠈⢇⠀⠀⢰⡇⠀⣠⠎⠀⠈⢦⣓⠦⡾⠀⣝⣳⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢆⠀⠀⠀⠀⠀⢧⠀⠀⠘⣆⠀⢸⣇⡞⠁⠀⠀⣰⠋⠈⣹⠃⢠⠗⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠳⣄⠀⠀⠀⠘⡆⠀⠀⠸⡄⠸⡏⠀⠀⢀⡞⠁⢀⡜⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢳⡀⠀⠀⢻⠀⠀⠀⢷⠀⣇⠀⣠⠏⢀⡴⠋⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠹⣄⠀⢸⡆⠀⠀⢸⡀⠸⣴⠃⣠⠞⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⣆⢸⡇⠀⠀⢸⠇⠀⢳⢰⠏⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⢸⡄⠀⠀⣼⡀⣀⠞⢿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠙⠒⠋⠉⠉⠁⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣴⡞⡍⣧⢭⡾⢿⡷⣟⣳⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⣳⣻⢦⡞⣛⢷⠾⣧⠼⣟⠭⢹⡞⣛⢿⣳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⠶⣟⣳⠷⣤⠛⢶⠿⣶⢿⣿⣟⣿⡷⢾⣐⡯⢹⡽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣱⢞⡳⣷⣬⣼⢓⡻⣶⢾⣽⠶⣟⣏⡷⡻⣅⣹⣯⡷⡳⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣐⡼⢬⡵⠷⣞⣻⢬⣥⠟⢿⡽⣛⢯⣂⡿⡺⡿⠷⣏⣹⣞⡶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⢾⣜⣃⡿⠿⣤⡿⣜⣣⣿⠶⣏⠭⣻⡞⣳⣶⣧⡽⢽⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢛⢾⣕⣹⠦⣥⣯⣀⣰⣧⠾⣿⢉⣿⢉⣽⢫⢻⣤⡿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠺⢭⡽⣦⠾⣇⣬⣇⡵⣯⠾⣏⣼⣋⣽⣷⣻⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣶⣯⡪⠿⠃⠉⠋⢡⠀⠉⠻⡴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡟⠀⠀⠈⠀⠀⠀⠸⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⠌⠃⠀⠀⠀⡠⣔⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡀⡀⠀⠀⠀⠣⠎⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢣⣲⠅⠀⠠⡄⠐⢃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠴⠀⠀⣎⡱⠀⣤⡄⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣄⠠⠌⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⣁⣀⣤⠤⠞⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠁⠀⠀⠀⠀⠀⠈⡻⢿⠛⠀⠀⢿⣿⣿⣿⡷⠀⠐⢏⣉⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠄⡅⠀⠀⠀⠀⠀⢫⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠣⡤⠃⢹⠡⡔⠊⢂⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⡔⠀⠀⠀⢀⢎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⣸⣀⢼⠏⠈⠀⠀⡠⠊⢒⡦⠀⠀⠀⠉⠀⠀⠀⠐⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠓⠀⠀⠀⠀⠀⠓⠚⡋⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣢⠀⠀⠀⠀⠀⠀⠰⠓⣠⡐⠒⢠⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡌⠆⢐⠝⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡘⠂⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠓⢒⠚⣄⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⢃⣴⣶⡄⠀⠀⠀⠀⡦⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠈⠙⠋⠀⠀⠀⠀⢰⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡂⠀⠀⠀⠀⠉⠀⢌⡆⠀⠀⠂⠀⠀⠀⠀⠀⢸⡀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣦⣀⣤⡖⠊⠉⢉⣐⡒⢤⣀⣌⡱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠺⢽⠴⠬⣝⡛⡿⠀⠀⠀⠀⠸⣿⠘⣛⣫⠵⠼⡿⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠌⠲⠿⢾⡩⣝⠓⠀⠒⠀⢰⠛⠉⠀⣨⣝⡶⠳⠞⠁⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣃⠵⡺⣷⣯⣷⢒⣬⣷⣿⡎⠓⠘⢲⣷⣾⣵⠒⣿⣵⡿⠷⠮⡘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⢪⣝⣘⠃⡙⢿⣽⣷⣆⣲⢿⣏⠛⢉⠘⣃⣫⠕⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣙⡿⢿⠟⠙⣸⡿⢿⡆⠛⠿⡿⠿⠁⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣪⣤⣤⡀⢲⣿⡃⢻⣿⠂⢾⣥⣦⣝⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⡟⢀⣀⣀⠈⢡⣀⣀⡈⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠇⡿⣿⣭⣭⣬⣼⣤⣤⣭⣽⣿⢷⠸⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣞⢾⢍⠙⠓⠒⣒⣚⠒⠚⠚⣹⣷⣧⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢣⠌⣷⣄⡟⡋⠋⢿⣠⣾⢆⡸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⡇⡎⠙⣁⠀⠀⢈⠏⣇⢺⡥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠸⣇⣣⣜⣼⡇⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣜⠏⠛⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⢀⡀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⢾⣿⣿⢰⣿⣿⡦⣿⣿⡇⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠉⠉⠀⠈⠉⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⢀⣴⠾⡻⠛⢍⢻⢹⣟⣶⣶⢶⡄
⠀⠀⠀⠀⣾⠔⣉⣲⣶⣾⣿⢾⣿⣿⠷⠚⠋⠈⠁⠐⠒⠶⣿⡶⡄
⠀⠀⠀⠀⢻⣿⣽⣿⣿⣿⣷⢀⣿⡿⣛⣒⣠⣤⡤⣤⣶⣶⣾⣿⣿⠎⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⣀⠙⠋⠉⠉⠙⢿⣿⡿⠞⣋⣠⣴⣾⢾⣷⣥⡶⠭⠞⣽⣧⣤⣶⣶⣷⣯⠉⠻⣦
⠀⠀⣰⣟⠛⣯⣏⣋⣳⣶⣼⣿⣿⡀⢔⣾⣿⡇⢠⣿⣿⣿⣖⢋⣻⣿⡏⠀⣿⣿⣿⣶⢀⠽
⠀⠀⠘⠿⢿⣮⣿⡟⠛⣿⣿⡿⣿⣷⣿⣯⣼⣄⣼⣿⣽⣷⣽⣿⣟⣻⡷⢠⣿⡭⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⣡⠾⢿⣿⣿⡟⢻⣿⣿⡟⢈⣿⣿⡏⢹⣿⣿⣿⣿⡈⣻⣶⡶⠶⠒⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⠺⣿⡀⣾⣿⣿⣇⢸⣿⣿⠇⣾⣿⣿⠵⠿⣿⣿⣿⡿⡗⠉⠈⠻⡖⠒⠂⠀⠀⠀⠀⠈⠳⢄⣀⡤
⠀⠀⠀⠀⠠⠁⠠⡿⠿⠿⣿⣿⣿⣽⣿⢏⣼⣿⣿⢖⣲⡖⣿⠿⠒⡞⠉⠳⠀⠀⠀⠀⠀⠀⠀⣠⣴⣖⠒⠾⣿⣿⡿⢻⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠾⠿⣿⡿⢿⠏⠆⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠈⣿⣷⠿⠟⠛⠋
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠄⡀⠀⠁⠀⠀⠀⠘⣿⡏⠀⠀⠀⠠⢄⠈⡆⠀⠀⢳⡄⠀⠤⢚⣉⣛⠟⣿⣟⡹⣧⣿⣾⢸⣳⢆⠀⣀
⠀⠀⠀⠀⢹⣶⣄⡀⠀⠀⠀⠑⣾⡀⠀⢀⠀⠀⠹⣧⠀⠀⣠⠤⠦⠿⠿⠤⣀⣾⢃⣤⣾⣿⡟⢋⣴⡭⠛⣿⣿⣿⣵⡾⡷⠾⠷⠃
⠀⠀⠀⠀⠸⠛⠉⣉⡀⠀⠀⢀⡿⢁⡴⣡⣶⣶⣶⣭⠀⠠⠁⠀⢀⠠⠴⢶⡟⢁⢻⣿⣿⣿⣿⣮⣴⠇⠀⣨⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣄⠞⠹⢡⣠⣿⣿⣿⣿⣿⣄⠃⠀⠀⠁⠀⠀⠀⡷⠘⠌⢿⣿⣿⣿⢟⣉⠄⣸⣿⣿⣿⠟⣋⣥⣄
⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣀⠀⠀⢿⡛⢸⣿⣿⣿⣿⡀⠀⠀⣴⣶⠤⠚⠁⠀⠀⠀⢀⣀⣤⣿⠀⠀⣿⣿⣦⣴⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠘⡇⢸⣿⡿⣻⣿⣷⣆⢬⠑⠻⠿⣿⣿⣿⡇⠀⠀⢠⢶⠀⢤⣤⣤⣤⣤⣄⡀⠐⢿⠀⠀⠈⠓⠉⢉⠀⢀⠉
⠀⠀⠀⠀⠀⡄⠐⠛⠙⠊⠻⣿⣿⣿⣄⢳⠀⢠⣦⡈⢸⡇⣄⠀⠀⠸⢢⣦⣿⠏⣦⢻⣿⣏⠀⠀⠁⢠⣤⣄⡘⣦⣅⣸⡆
⠀⠀⠀⠀⠀⠸⣄⠀⠙⢷⡄⡿⠻⣿⣿⡆⠀⠀⠹⠇⠘⢰⡿⠢⣦⣶⣾⠋⠁⠀⡿⠨⠉⢹⠛⣛⢻⣻⡋⠙⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠒⠋⠉⠁⠀⠀⠀⠀⠀⠛⠇⠀⠀⠈⠁⠀⠀⠰⡇⣷⠑⢤⠭⠿⠯⠶⢦⡀⣼⠿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⢀⠀⠀⢀⠀⠀⡀⢀⣀⡦⠂⠀⠀⠀⠀⠀⢂⠀⠛⠉⠃⠀⠀⠀⠀⠀⠀⢋⠁⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡚⠦⠶⣿⠋⡿⠩⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠋⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⠋⣉⣉⠉⠉⠙⣿⠿⣭⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠈⠈⠉⠉⠹⠿⠿⠿⠿⠛⠻⠛⠛⠛⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣆
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⣠⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣴⣶⣄⣤⡄⢀⡀
⠀⠀⢠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣾⠁⠀⠀⣽⣿⣿⣿⣿⣿⣇
⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢼⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⡀
⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣷⠀⠘⠁⠘⣿⣿⣟⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣵⣿⣿⣿⣿⣿⡆⠀⠀⠀⠿⠿⠃⢀⣦⣴⣿⡁⠀⠀⠀⠀⠀⠀⢀⣠⣄⣛⣿⣿⣿⡿⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠉⠋⠙⠿⠃⠀⣀⡀⢤⣤⣤⣴⣿⣿⠿⠀⠀⠀⠀⠀⣠⣀⡏⠉⢛⣿⣵⣿⡿⠃⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠄⢀⣤⠻⠿⠚⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⣠⡘⠿⣿⠶⢤⠈⠉⠉⠻⢿⢿⣙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⢤⠻⢿⣿⣧⠀⠀⠀⠀⠀⡘⠻⢿⠿⣯⡀⠀⠀⠀⠀⠀⠀⡠⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⣿⣿⡄⠀⠀⠀⠀⠰⣾⡶⠀⠈⠁⠀⠀⢿⣄⡀⢀⣴⣦⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠞⣿⣿⣷⠀⠀⠀⠀⠀⠈⠀⠞⠛⠃⠀⡀⠀⠘⠗⠘⢿⠏⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣏⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣴⣤⣄⣀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠟⡱⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⠢⢴⣦⡀⠀⠀⠀⢱⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠈⠛⠻⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⣿⢿⣿⣿⠀⠀⠀⠐⠂⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡿⢚⣿⣿⣇⠀⠐⠀⠀⠀⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡟⢿⣿⣿⡀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣇⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠟⣿⣿⣿⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠴⠛⠻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⣃⡼⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠁⠘⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡟⡀⢿⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡌⣳⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠛⢯⣁⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠸⣋⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡐⢫⣼⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋

⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠠⢇⢀⠈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠂⠀⠀⡀⡆
⠀⠀⠀⠀⠀⠌⢀⡀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⢁⠜
⠀⠀⠐⠐⠀⡄⠀⠁⠀⠀⠀⠰⠀⠀⠀⢰⠀⠀⠀⠀⠮⠀⠙⠁⠀⠀⠀⠀⢰⡀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠐⢤⠤⠄⠔⢈⠀⢸⠔⠋
⠀⠀⠀⠒⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⢀⡤⠂⠀⠐⠋⠐⣀⡀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠿⢰⠶
⠀⠀⠀⠀⠀⢻⣄⢀⡠⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠄⠀⠀⠀⠀⠄⠂⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠹⠸⣤⠔⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠠⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠴⢂⡐⠲⠆⢀⠂⠠⡴⠂⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠈⢀⠀⠀⠠⠇⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣏⡍⣼⣿⣧⠜⢃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠋⠀⠁⠀⡀⠀⠉⡄⡌⠁⠀⠳⡀⠐
⠀⠀⠀⠀⠠⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣾⡧⠀⠀⠀⠀⠀⠀⠀⠠⡔⡂⠄⢀⠤⠀⠀⢠⠈⢒⠒⠀⠍⠳⡀⡜⡤⢈⢤⣰⠆⠃
⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⠀⠀⠀⢻⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⡠⠉⠤⠄⢀⡆⠠⠀⢀⠀⠀⠐⠫⡀⢀⡔⢰⣏⣜⣈⡬⡶⣇
⠀⠀⣄⢀⣀⣀⠀⣤⣤⠆⠁⠀⠀⠀⠀⠀⠀⠀⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠗⠀⠐⡠⠋⣠⠆⠀⠸⠀⠀⠀⠀⠀⠋⠁⢊⡭⠀⠀⠁⠑⠁
⠀⠀⠈⠈⠈⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⡠⠓⠀⠀⠢⠊⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⡀⡋⣈⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢉⠁⠉⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠⡀⠐⠒⡐⢄⢀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠠⠤⣼⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠴⣖⡍⣈⡱⠇⠐⠊⣠⠞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠌⢉⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣮⣽⣿⣾⠋⢀⠄⠴⣜⠙⡠⣶⠏⠁⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠁⠀⢀⣴⢠⣖⠆⠘⢂⠀⣀⠐⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠚⣀⢠⣼⣊⡮⠚⠁⢀⠴⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⡐⠂⠀⠀⠨⢗⠒⢎⠚⠤⠉⠠⠄⠀⣫⡄⠀⠀⠲⠐⠀⠀⡠⠀⠀⠀⢠⢁⡀⢀⢎⡥⠞⠛⠁⠀⢀⡴⢃⠀⢡⣹⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⢁⠐⠀⠀⢻⡌⠀⠻⠀⠀⠀⠀⠀⢀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣠⠛⠋⠀⢠⣤⣤⣴⣥⡀⠈⠱⠲⣿⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠨⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⠥⠤⣌⣙⣿⣿⣷⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠡⠂⠘⠀⠔⠓⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠂
⣿⢿⡿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣟⣛⣻⣿⣟⣻⣿⣟⣟⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⣿⣿⣿⡿⠷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣇⡀⣠⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠋⠉⠹⣿⣿⣿⣿⠟⠉⠙⢿⣦
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⠀⢀⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣄⠀⢀⣼⣿⣧
⠀⠀⠀⠀⠘⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣧⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⢠⣿⣄⣼⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡉⣹⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠹⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⠀⠀⠀⢀⣶⠀⣤⠀⢀⣼⡟⠀⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣧⡀⠀⣾⠁⠀⣠⡾⠃⣠⣿⣧⣾⣿⣇⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣾⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠒⢛⢻⠒⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⢻⣹⣥⣀⣠⢄⠀⠈⢩⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠏⠁⠢⠋⠙⠶⢀
⠀⠀⠀⠀⠀⢠⣶⡴⠿⠛⠛⠻⢿⣿⣾⣾⣤⣀⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠑⠓⠂⠒⢗⡆⡄⡀⠠⢠⡀
⠀⠀⠀⣰⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠋⠺⣶⣠⣿⣦⡀
⠀⠀⠀⡻⢏⠛⠀⠀⠀⠐⣿⣿⣷⣶⣿⣿⠓⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣺⣄⠀⠀⠀⢀⣠⡀⣀⣀⣀⣀⣀⢀⡀⠉⠁
⠀⠀⠀⠀⠉⠀⣴⢲⠀⢲⠮⣿⣿⣿⣿⣿⡇⠀⢀⣀⠾⣽⡇⠀⠀⠀⠀⠀⢛⠶⠀⡀⠀⠀⡘⢿⡇⣾⠋⣩⣭⠁⠀⠀⠀⠄
⠀⠀⢰⠿⢰⡇⢴⡟⣠⠈⢻⡙⡛⢿⢿⣿⣛⠀⢯⠘⣣⣼⡗⠀⡀⠀⠀⠀⡠⢀⠄⢁⠅⠀⠆⠙⣱⣥⡀⠁⣿⠀⢀⠒⠄⠁⢂
⠀⣈⢻⡃⣾⡴⠺⢦⣻⣿⣬⣽⢧⣠⣦⣤⣿⣶⣻⣷⣧⣿⣇⡞⠁⠀⠠⠌⡀⠐⢀⡥⠐⡪⠄⠂⠀⠈⠋⠛⠃⠀⢀⣤⣴⠳⠈⠠⠂
⠀⠾⠋⠉⠻⠋⠄⠈⢻⡿⣞⢷⡏⢙⣷⣯⣻⣿⣟⠁⠙⠛⠿⠛⠃⠀⣒⠤⠄⣰⠄⠈⠈⡻⡦⢘⣫⠖⠙⠳⢀⢒⢁⠀⠈⣵⣀
⠀⠀⠀⠀⠈⠁⠀⠀⠼⠿⠟⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠋⠈⠀⠈⠁⠀⠉⠓⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠢⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡁⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⡇
⠀⠀⠀⠀⢸⣆⠀⢀⣾⡄⠀⠈⠀⠘⡎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠿⠏
⠀⠀⠁⠀⠘⠿⠀⠘⠿⠇⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠨⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡴⠀⠀⠀⠀⡀
⡄⠀⠀⠀⠀⠀⠀⠈⣦⣤⠀⠀⠀⠀⠀⠀⢀⡌⡄⠀⠀⢠⠀⣗⡤⠀⢠⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⡄⣾⠻⢁⠀⡄⠀⢸⣧⡚⠋⠸⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠰⢠⣼⠖⠁⠀⠈⠉⠀⠀⠀⠀⠌
⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⠃⠀⠀⠀⡀⠀⠰⡀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠸⠔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠁⠀⠀⠁⠀⠀⠀⠀⠘⡆⠞⠠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠍
⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲⠒
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⢿⡄⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣴⠸⠿⣝⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣄⣄⠉⠀⡀⠀⣀⣀⠀⠀⠀⠐⣋⢉⠀⠀⠘⠿⣀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⣀⠀⡀⠀⢀
⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣠⡤⠖⠚⠛⡏⠁⠈⣯⠉⠉⡙⡳⢦⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠸⡄⢸⡍⡔⡰⠠⢀⣿⠀⠀⣷⢡⢡⠐⣘⣬⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢳⡙⢦⣙⠓⠷⠧⠴⣿⠀⠀⣿⠞⣚⣋⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠉⠙⠛⠛⡏⠀⠀⣿⠉⢁⡤⠴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣠⡴⠖⠒⡖⠒⢲⠶⠦⢤⣀⠈⢦⠀⠀⢰⠃⠀⠀⣇⡴⠋⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡸⣷⡀⡐⠀⡇⠀⢸⠄⡀⡔⣸⠇⣸⠀⠀⡞⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠭⢭⣝⡇⠀⢸⣟⣉⣭⠵⠚⠁⠀⡼⠁⠀⠀⣏⡤⠴⠶⡶⠒⢠⡤⢤⣀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠙⠢⣄⠀⠀⢷⠀⠈⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⣍⡓⠷⠶⡝⠀⢸⣥⣤⠤⠟⢀⡜
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⢸⡄⠀⢹⡀⠀⠀⠀⢠⠇⠀⠀⢰⠇⠀⠉⠙⢒⡇⠀⢸⠖⠒⠒⠋⠁
⠀⠀⠀⠀⠀⢰⠃⢀⡤⠤⣴⠒⡶⠲⡶⡄⢘⡆⢧⠀⠀⢧⠀⠀⠀⡞⠀⠀⠀⡏⠀⠀⠀⠀⡼⠀⠀⡞
⠀⠀⠀⠀⠀⠈⠣⣌⣚⣒⣿⠀⣿⣛⣩⠥⠚⠀⠘⣆⠀⠈⢧⠀⢸⠁⠀⠀⣸⠁⠀⠀⠀⡼⢁⡠⠖⠋⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠸⡄⠀⠀⠀⠀⠀⠸⡄⠀⠈⢧⡏⠀⠀⠀⡏⠀⠀⢀⡼⢡⠏⣀⣀⣀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠱⡄⠀⠀⠀⠀⠀⢹⡀⠀⠈⢇⠀⠀⢰⡇⠀⣠⠎⠀⠈⢦⣓⠦⡿⠀⣝⣳⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢆⠀⠀⠀⠀⠀⢧⠀⠀⠘⣆⠀⢸⣇⡞⠁⠀⠀⣰⠋⠈⣹⠃⢠⠗⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠳⣄⠀⠀⠀⠘⡆⠀⠀⠸⡄⠸⡏⠀⠀⢀⡞⠁⢀⡜⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢳⡀⠀⠀⢻⠀⠀⠀⢳⠀⣇⠀⣠⠏⢀⡴⠋⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠹⣄⠀⢸⡆⠀⠀⢸⡀⠸⣴⠃⣠⠞⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⣆⢸⡇⠀⠀⢸⠇⠀⢳⢰⠏⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⢸⡄⠀⠀⣼⡀⣀⠟⢿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠙⠒⠋⠉⠉⠁⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠥⡠⠀⠀⠀⠀⠀⠀⠀⠠⢃⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡄⠀⢠⠀⠀⡈⠈⠂⠠⡄⢀⠀⠀⠀⠀⠀⢀⡾⠛⠉⠩⠈⠈⠛
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠀⠀⠃⠀⠃⠘⠀⠐⠃⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠐⠂⠂⠂⠂⠂⠀⠀⠀⠁⠀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡗⠜⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⠀⠀⢀
⠀⠀⠀⣀⣤⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠨⡄⠴
⠀⠀⠀⠙⠛⠓⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠸⣿⣿⡓⣄⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢅⠀⠞
⠀⠀⠀⠀⠀⠌⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣾⣹⣿⣿⣿⣷⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠆
⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⢼⡿⠟⡟⢰⡋⣿⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠨⠹
⠀⠀⢠⡀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣄⡇⠘⠗⠤⣋⣵⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰
⠀⠐⠛⢠⣿⢰⣶⡼⣧⡝⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢻⣿⠿⣿⣿⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡴⠄⠀⠈⢷⠀⠀⠀⠙⠻⠿⢿⣶⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠙⠲⠤⣀⡀⣀
⠀⠀⠀⠀⢠⡠⠀⠈⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⠀⠀⠈⠉⠀⠐⠀⠈⠀⡁⠝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠰⠈⣁⠖⠁⠀⠀⢀⠄⠐⠀⠀⠀⠀⠐⢄
⠠⢈⠀⢀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⠀⠀⠀⠀⠀⠀⠐⠀⠀⠤⠠⠄⢀⠄⡤⠒⠒⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡠⣄⡀⢁
⠡⢈⣀⠀⠠⠔⠒⠉⠡⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠴⠖⠛⠃⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇⠀⠄⠒⠀⠀⠀⠈⠀⠀⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⡀⠠⠀⠀⢱⣒⡒⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡆⠀⠀⠀⠀⠀⡆⢠⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠸⠔⠓⠠⠀⠀⠀⠀⠀⠀⠸⠀⠠⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢡⠈⢀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⡠⠂⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠠⠀⠂⠀⠄⠀⠂⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠠⠀⠀⠀⠀⠐⠈⡀⠂⠂⡈⢠⠀⠄⢧
⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠢⢌⠐⢀⠨⠀⡀⡈⡀⠐⢂⠀⣀⠟
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⡀⣀⡤⠠⠤⠤⠤⣀⠀⠁⡀⠀⠀⠀⠁⠀⡀⠀⠀⣀⠀⠀⣀⣀⡀⠄⠁⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠐⠲⠂⠂⠈⠁
⠀⢀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⣀⣠⠤⠄⠄⠈⡃⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠐⡀
⢀⠂⡤⠚⠁⢀⣀⡠⠒⠀⠓⠀⠈⠳⠖⠂⣀⠠⢂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢱
⠈⢘⡀⠀⠈⠐⠛⠛⡀⠀⠀⣀⣀⠊⠉⠡⠐⠂⠀⡠⠔⡀⢄⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢠
⠀⠐⠌⠈⡁⠈⠥⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠉⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠥⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠐⠄⠀⠁⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢀⢈⠀⠀⠒⠁⠀⠠⡀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠒⠈⠉⠉⠉⠐⠂⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⡄⠀⠑⠊⢀⠜⠀⠠⢀⡤⠔⠀⠀⠀⠐⠒⠂⡢⣀⠉⢀⡥⠖⠁⠀⠀⠀⠀⠀⠀⣀⣠⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠄⠀⠒⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠐⠒⡇⠀⠈⠐⠋⠉⠉⠉⠁⠀⠀⠀⠉⠁
⡈⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠀⠒⠀⠀⠂
⠀⠈⠙⢤⠀⠀⠀⠂⠄⠀⢹⠌⠀⠀⠀⠀⠀⠀⠘⠄⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠰
⠀⠀⠀⠀⠑⡌⢀⠀⠀⠀⡄⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⣀⣀⣀⣀⣈⠒⢄⡀
⠀⠀⠀⠀⠀⠘⡄⠡⠀⠁⢡⠀⡤⠄⠀⠀⠀⠀⠈⠀⠀⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠠⠂⡁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠀⡀⣀⠀⠀⠠⠓⠀⠘
⠀⠀⠀⠀⠀⠀⡔⠘⡀⢁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠠⠠⠥⣀⠀⠀⠀⠠⢀⠄⠀⠀⠈⡀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠈⡄⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠰⢟⠀⠡⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡀⢴⡮⠰⠂⢔⡢⢰⠄⡄⡀⠡⡀⠀⠀⠀⠐⠀⠐⠂⠅⠀⠀⠱⡴⠟⠐⠀⠁
⠀⠀⠀⠀⠀⡀⣾⠀⠐⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠈⠁⠒⠷⠀⠻⠿⠋⡷⠂⡵⠈⠳⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠱⢈⠀⣀⠐⠁⠀⠀⠀⠀⠐⠂⠄⣀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⠀⠀⠀⠸⠛⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠒⠀⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⢀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠀⠛⠁⠀⠀⠀⢠⡬⠢
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠛⠉⠁⠀⢀⡀⠀⠀⠀⢠⣆⠀⠀⠀⣀⠀⠉⠒⠐⠀⠠⠄⠀⡀
⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⣀⠀⠀⢀⡀⠀⠘⠁⠀⠀⠀⠈⠁⠀⢀⠀⠉⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠑⣆
⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠃⠀⢀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢓⡲⠋
⠀⠀⠀⠀⠀⠉⠛⢿⣟⣶⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⢤⠤⠔⠒⠐⠚⡉⠵⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠿⢶⣤⣍⣷⣌⣁⣀⣨⡏⢀⣤⡶⠶⠗⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⠉⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣽⣥⣀⣀⣠⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⣷⣤⣆⡤⠼⠲⡅⠀⠀⢠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢆⢰⠀⣿⡟⠀⠀⠀⠀⢣⠀⢀⡇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢑⢌⣿⣀⣿⠁⠀⠀⠀⠀⠈⠇⢸⢁⡎⡹⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⢸⣧⢹⣿⠀⠀⠀⠀⠀⠀⠀⣼⡸⢀⡧⢀⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡟⣼⣿⡟⡇⢀⠀⠘⠀⠀⠀⢻⡗⣹⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢁⡇⣿⣋⡗⠸⠀⠄⠀⠀⠀⣼⣡⠇⣼⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⣧⡇⢸⠀⡇⠀⡆⣿⣿⣾⣋⠥⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⣿⣷⣼⣆⣧⣷⡿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣙⠛⢗⣤⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡶⠿⣷⣿⠉⠷⢿⡞⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⡻⠃⣤⣈⣉⣠⣶⣄⣴⣮⣰⣯⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣶⡤⠿⢞⣛⣋⣭⣭⣭⣭⣉⣉⠛⠿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⣉⣴⣶⠟⠛⣋⣩⣍⣀⣠⠀⠉⣻⣷⠄⠈⣿⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢰⡟⠁⣈⣻⣿⣿⣿⣿⡿⠿⣛⣩⠞⣋⣠⣾⢟⡻⠿⣟⠿⣶⡖⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣼⣿⣾⣄⠀⠀⠉⠃⠉⠋⠉⠙⢻⣿⣿⠉⠉⠈⠀⣿⢡⢾⢳⣿⡟⣤⡑⢮⣹⢯⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣽⣿⣧⣾⣷⡤⠀⠀⠁⠀⠀⠀⠈⣿⣿⠄⠀⠀⠀⠀⡾⡷⣏⢣⣴⣞⡷⡄⢿⣻⡷⣾⡃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢚⠓⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠰⠿⠓⠚⠋⣻⣥⣀⣠⡄⣻⣳⠿
⠀⠀⠀⠀⠀⢎⡵⢶⣾⡿⣷⣼⠾⢷⣷⣶⣶⣦⣄⠀⡇⠀⢠⣿⣿⣿⠀⠀⠔⠀⠤⠀⣴⠾⣹⣿⣿⣿⠷⠧⢿⡛⡆
⠀⠀⠀⠀⠀⢾⣳⢼⣿⡳⣾⣧⠀⢰⣿⣿⣿⣿⢿⣼⢇⣴⣿⣿⡿⠁⠠⠂⠀⠀⣠⡞⢙⣶⢿⣿⠫⠻⠙⣾⡎⣟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠥⠼⠟⠉⠀⠀⡟⢾⣟⣷⣿⠟⠛⠿⠟⣿⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠨⠙⢄⣠⡸⠿⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡘⡄⠀⠉⠀⠈⣧⡀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠙⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⠿⠿⠳⠀⠀⢠⣮⣹⣷⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣴⣤⠀⠀⠿⢻⡟⡉⡹⢏⣀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⣀⡆⣀⡿⣷⣼⣿⡄⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠿⢋⠟⠁⠀⠘⣿⣿⡟⣿⣷⢿⣹⡄⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⢆⠀⠀⠀⢻⣼⣾⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡂⠈⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢈⠙⢡⣄⣀⣀⡤⣤⣤⣴⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣁⣀⡴⠃⡀⠀⠀⠀⠈⠙⠿⣻⣿⣧⣾⣶⢣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⣀⠀⠀⠀⠀⠋⠀⠘⠛⠀⠀⠀⠁⠙⣻⣯⣿⣯⣿⡟⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠛⠀⠀⣀⠀⠀⠀⢀⠘⣃⡘⠦⣀⠘⣼⢻⣽⢿⢷⣿⠇⣿⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃⡘⠻⠟⣀⡏⠀⠈⣾⣽⣾⠿⠿⣶⣿⢛⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡄⠀⣀⠀⠸⠿⠁⠀⢴⡆⠀⠀⠀⠙⣓⡒⠉⣠⠄⠦⣹⡟⢠⣶⣶⡌⢿⡿⢻⣿⣟⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠋⠀⢀⡀⠀⠀⠀⠀⠀⣴⡆⠀⠹⡃⠒⠁⠂⠀⠹⣷⡘⠻⠛⣡⣿⣿⣿⣯⣿⡏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠿⠛⠁⢀⠀⠀⠈⠁⣈⣴⣿⠁⠀⠀⠀⡴⠠⠅⠂⡀⠂⠀⣀⡙⢿⡿⠿⠿⢯⡹⣾⢿⠋⠠⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠚⠀⠀⣀⣀⣀⣀⣀⣉⣠⡚⠓⡀⠀⠀⣄⢀⣴⣶⣷⢾⣉⡂⠁⢠⡀⢰⠆⠀⠘⢸⣿⡀⠰⠎⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⣶⣿⣿⣟⣿⣿⠟⡉⠙⢿⣿⣿⣷⣮⣄⣾⠟⣨⣵⡿⢛⣣⡀⠄⠲⠉⠀⡑⢀⣨⠟⣿⣶⣴⣶⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡷⣿⣿⠿⣯⣼⢿⣿⣧⣾⣿⣿⣼⣿⣣⣦⣸⣿⡟⣾⡏⣴⣿⣿⡏⢁⣀⣰⠘⠟⠓⡈⠀⠀⡁⠀⠀⠀⠋⣙⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣇⣽⣧⣼⣿⢛⡛⣿⣿⣻⣟⣻⣿⣿⣿⣿⢈⣉⣛⠛⣤⠴⠄⡁⢌⡐⢾⢊⡷⣠⠆⠀⠀⠐⡄⢀⡡⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⣛⠛⣿⣾⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⡌⠩⣋⡙⡧⠰⢀⡖⠘⣿⡈⣴⠟⡷⠀⢠⡀⣀⠄⡄⠀⢰⠂⠀⠘⢧⣄
⠀⠀⠀⠀⠀⢠⣿⠏⣉⣹⣿⣿⣜⣿⣷⡿⡛⢿⣿⣿⣥⣿⣿⣿⡿⠛⠵⢹⣿⠉⢻⣷⡐⢀⣠⠚⠛⢋⠿⠛⠀⢀⠄⠠⡿⢳⣼⣿⣇⠀⢀⠀⡈⢹⡟⠛⠶
⠀⠀⠀⠀⢠⣾⣿⣿⠟⢉⣀⠙⢿⣿⣿⣾⣿⣿⡿⠿⣿⠛⠛⢛⡛⠛⠶⢿⠿⣷⣾⣿⣤⣬⣠⣒⠃⠀⠀⣀⠰⠾⠀⢀⠛⢫⣿⠇⢻⠀⠘⠛⠁⣿
⠀⠀⠀⠾⢻⣶⣿⣿⣄⣸⣿⣶⣿⣿⡛⢯⣽⣿⣶⠀⢽⡛⠞⢩⣙⡏⣴⠞⣦⠚⣅⣷⣾⡏⡍⠩⢿⣶⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠶⠀⠁⠀⢘⣈⣷⣦⣴
⠀⠀⣲⣴⣿⣿⣿⣭⣿⣿⠿⡿⢃⡻⣿⣨⣯⣿⣏⣠⡄⢳⠕⣦⣭⢄⣠⡖⣯⢖⣭⣿⣿⠁⠀⠀⣿⠛⢱⣄⢸⣟⣭⢉⣿⢿⡿⠷⠿⠶⢶⣶⠟⡉⣫⡾⠁
⠀⣰⣿⢛⣿⣿⣿⠟⠁⠀⢹⢷⡞⣧⣌⣿⣿⣿⣿⡇⢒⣷⠈⠷⠶⣎⡽⢃⣴⣿⣯⣽⡏⠀⠁⠘⣿⢶⡅⠈⢾⣏⣁⢀⡉⣸⡇⠁⠘⠀⠉⣿⣎⣴⠟
⢠⣿⣿⣿⠛⣿⡏⠀⠀⠀⣼⠰⠷⣩⡏⣿⣿⣿⢿⣷⠉⡿⢷⡟⠒⣥⣶⣿⣿⣿⣿⣿⡇⠈⡀⢸⣇⣀⠈⢠⣼⡟⢋⠸⠃⠻⣿⠁⠀⠀⠃⣸⠟⠁
⣿⢿⠁⣼⣿⣽⡇⠀⠀⠀⣾⠾⡿⠰⠶⣿⣯⣿⣿⣿⡇⠲⣿⣾⣿⣿⣷⣿⣿⣱⣿⣿⡇⠀⢀⣿⡟⠉⠶⡅⢸⣿⡿⢰⡄⠶⠛⣤⠀⣴⠞⠁
⠹⢾⣄⣿⣟⢿⡇⠀⠀⠀⢸⣏⡳⢴⣶⢿⣿⣿⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣙⣿⣇⠉⢀⢹⡿⠛⣦⡝⠣⣿⡇⢤⡀⣠⣤⠿⠋
⠀⠀⠙⠛⠿⣾⣷⠀⠀⠀⠀⣿⠑⠶⢴⠎⣿⣿⣿⣿⣿⣸⣿⣿⣿⢻⣿⡿⢻⠿⣿⣿⠋⣀⠉⢘⣷⡶⣄⠰⠷⣈⣷⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⣦⣿⣞⣛⡺⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡑⣿⠿⣤⣿⡆⢀⠀⠀⣸⣷⠼⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣟⣻⣿⣿⣇⣿⣿⢛⡶⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣣⣿⣿⣏⣿⣿⡿⠧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡿⠋⠠⣄⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⡀⠀⢠⡙⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⡀⠀⣀⠀⢡⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠐⠁⠀⠋⠆⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡄⠀⠱⢆⠀⠀⠼⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡘⠢⡄⠈⠑⢆⠀⠀⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠁⠀⠀⠀⣀⣾⡟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠐⠚⠙⢲⣰⣿⠋⠰⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠃⢄⣴⣿⣿⠶⠶⢶⣦⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢡⡶⠟⣋⣥⣴⣶⣶⣶⣽⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢛⣴⢟⣻⣿⣿⣟⠻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣟⣵⡿⢯⣕⣶⣽⣿⣿⣿⣿⣫⡾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢋⣬⣷⣿⡿⠿⠛⡛⠻⠿⣯⣾⣏⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠟⣏⡀⢺⡆⠘⣿⡄⢺⡇⣤⡉⡻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⢱⣦⠙⠷⣈⠁⣶⡈⣶⡎⣥⠜⠃⢻⠆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣶⠆⠙⢷⣄⠻⠇⣨⣤⣿⣤⣍⡀⣷⢴⡟⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢁⠙⣶⢤⡌⢻⣴⠟⣧⠤⠰⠆⣬⢙⣧⠈⣷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡻⡆⢃⡈⢻⡿⣧⠾⢠⡆⠶⠀⠤⢈⡽⣇⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣄⠸⢷⡏⣤⢠⡖⣀⢴⡟⢸⡒⢋⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣷⣾⣤⣤⣿⣤⣤⣾⡶⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠐⠂⡀⠂⣴⣤⡴⣠⢶⣶⠶⠦⠴⠖⡲⢶⣴⣆⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣶⣶⣰⣤⣖⣢⣶⣴⣴
⠀⠘⠂⢀⡴⢄⣤⠀⠀⠀⠉⢉⡜⣵⣿⡿⠀⠀⠑⠈⠛⠀⣿⣿⣿⠁⢀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⣰⢹⣿⣿⣿⣿⣿⢢⣼⣗⣻⣿
⠈⠀⢀⣟⠦⣹⣿⣳⡜⣚⢸⣏⠞⣽⠟⠑⠀⠀⢰⣀⣀⣀⣿⣿⣟⠃⣸⣿⡠⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⢰⣷⢋⡔⠛⣿⡦⣽⣗⣨⡓⣻⣿⣿⣿
⠀⡧⢹⣿⣶⠏⡿⢧⢿⣹⣿⣿⣾⣿⣠⠀⠀⢀⣾⣿⢿⣿⣿⣿⠋⠀⣾⣿⢼⠆⠀⠀⠀⠀⠀⠻⣿⡿⠟⠛⠁⠀⢀⣤⣛⡷⡾⣀⢐⣯⡤⣽⣗⣾⣷⣽⣿⣿⣿
⠀⠂⠀⢿⡷⠞⢻⠯⣄⣩⣧⡀⣈⢁⡁⠀⠀⠀⣹⣿⣾⣿⣿⣿⣿⣾⡍⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢿⣟⣿⡎⣿⣧⣽⣟⡳⣿⡿⠿⠟⠉
⠘⠃⠰⣆⠰⣶⡿⢆⣸⣧⣨⡅⠀⠈⠀⠀⢠⡾⠿⢿⣿⣿⣿⢿⡿⢿⡇⢀⣀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⢀⡸⣅⣿⣿⣟⣻⡿⣭⣖⣿⠷⠞⠋⠁
⠀⠛⠀⡋⢫⣝⢃⣨⣿⣿⣿⣷⣾⣄⠀⡇⣹⣷⣤⡼⣿⣿⣿⣫⣷⣦⣷⠘⠈⠀⠀⠀⠀⠀⣧⠰⢾⠐⠊⠁⢠⣷⣿⣿⣛⣮⠼⣹⠟⠁⠀⠀⠀⡀
⠀⠀⠚⠶⠆⠐⢛⣿⣿⣿⣿⣿⣯⠝⠀⡇⣿⠀⢻⠁⠻⢿⣿⣿⣿⣿⢿⣾⣟⣄⠀⣀⡄⠀⠛⠓⠀⢠⠄⢰⣾⣿⣿⣷⣾⣝⠓⠟⠁⣀⢀⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⣿⣧⡾⣀⠀⠀⣿⡿⠟⠛⠙⠿⢿⣟⠛⠛⠁⠀⠀⢰⣆⣠⣴⣿⣿⣿⣿⣿⣿⣯⣒⣾⣋⣣⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠁⠉⠉⠀⠀⠀⢻⠟⠁⠙⠰⢿⣿⠀⢰⠀⣠⣤⣢⣾⡁⠀⣽⡶⢑⣥⣿⣿⣿⡿⣿⣿⢿⣏⡶⢖⢽⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⢴⠍⢿⣿⡶⣟⣿⣿⣿⡙⠳⠟⣡⣾⣿⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠈⠀⠀⠀⠉⠀⠐⠋⣿⡉⡍⠰⣤⡾⢟⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⣧⡀⠀⢀⠀⠀⣀⡎⠉⠁⠸⣧⣬⠦⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣾⣿⠞⠩⣓⣿⣿⣿⠷⠿⡿⠿⡿⠛⢛⣝⠿⠂⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣃⠈⠀⠄⠀⣼⡿⠁⠀⢴⡶⠻⠋⡀⠀⢀⡀⠄⡀⣠⣿⡿⣿⢷⣿⡷⠺⠟⠋⠹⢙⣻⣆⡐⠋⠀⠀⣴⠞⢋⣤⡼⠃⠀⠀⢄⡚⠀⡀⣃⠀⠄
⠀⠀⠀⠀⠀⠀⠧⢠⡤⣄⣠⣤⣬⣀⣐⣿⣿⡏⡀⣍⣰⣮⡟⢻⠛⡍⣉⣵⠶⠂⢈⠄⠀⠀⢀⣀⣾⢿⣏⡀⠊⠀⠀⠴⠚⠛⠁⠀⠀⠀⢀⣿⣿⣷⢄⣴⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⢂⣟⣫⠀⠀⢡⠘⢟⣁⣺⣇⣙⣘⠀⠀⠀⣉⣤⣺⣿⡇⢠⠈⠀⢀⡀⠀⠈⠀⣠⣤⣿⣿⣿⣿⣿⣿⠓
⠀⠇⠀⠀⠠⣶⣿⣿⣟⣿⣟⠛⢛⣉⣝⣟⠉⣿⡱⢿⠽⢯⡞⣀⠀⢬⣿⠒⠻⢿⣛⠋⣿⢄⣾⣿⣿⡯⠉⠁⣦⣤⣄⣸⣿⣷⣶⣾⣿⣯⣿⣿⣟⣿⣿⣟
⠀⠀⠀⠀⢰⠶⠁⠀⢈⠛⢿⣿⣿⣿⣿⡟⢠⢈⣥⣴⣴⢟⡔⡄⠀⠀⠑⠠⠀⠀⠸⠗⠈⠀⠛⢿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠄⠎⠉⠻⣟⣇⠠⢶⣾⣿⣧⣾⠗⠀⠀⢀⣄⠀⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣀⠃⠠⣀⡀⠲⡤⠿⠏⠀⢈⣑⠾⠋⠁⠄⠀⢸⡌⠘⢣⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⢠⣄⣤⣤⡤⠄⣿⣿⣿⡆⢨⣽⣤⣤⣆⣠⡜⣿⣻⡿⠒⠂⠀⠄⠛⠛⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⢂
⠘⠋⠉⠁⠀⠀⢿⣿⡿⠁⣼⡟⠷⡶⠿⣿⣿⣷⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠛⡛⡉
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠤⠧⠀⢨⢹⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⠆⡠⢾⣿⣿⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠆
⠀⠀⠀⠆⠡⠦⠟⠴⠧⠘⠺⠇⠞⠢⠹⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣴⣶⣿⡿⠛⣿⠟⣶⣦⣄⡀⠀⠀⠀⠀⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣾⣯⣿⣭⣿⡟⣿⣿⣟⣻⣯⡼⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣋⣿⣿⠿⠿⠿⠿⣿⠿⠿⣿⣶⣿⣏⣽⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⣯⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⢀⠀⢄⣀⣤⣦⣾⡴⡂⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣝⣳⣿⠋⠁⠀⠘⢿⣦⣄⣀⠀⠀⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡏⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣀⠀⢀⡀⠠⠧⡀⠀⣠⣾⢿⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠄⠛⢿⣿⣯⣽⡿⣾⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡽⠆⠀⠀⠂⠀⠀⠀⠀⠊⠓⢺⠉⠊⠀⢤⣉⡉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠈⠛⠛⠛⢛⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣀⢀⣇⠠⣅⡀⠀⢀⣠⢀⣰⡇⣠⡀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⣿⡏⠉⠉⠀⠀⠀⢸⣏⠉⠉⠙⠛⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⢀⣴⣿⡟⠉⠀⠀⠈⣿⡄⠀⠀⠀⠀⠈⠻⢷⣦⣶⠾⠋⠀⣨⣿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠙⣷⣄⣀⣀⣴⡿⠀⠀⢠⣴⠿⠛⢷⣦⡀⠀⠀⠀⢰⡿⠁⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⡀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⣿⠁⠀⠀⠀⢹⣷⠀⠀⠀⠘⣿⣄⡀⠀⣠⣿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠉⢻⡆⠀⠀⣀⣀⣀⣤⣤⣤⣤⣿⣦⣤⣤⣤⣾⣯⣤⣀⣀⣀⠈⠙⠛⠛⠋⠁⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣀⣤⣾⣿⠿⢿⡛⠛⣿⡋⠉⢹⡇⠀⠀⢿⠁⠀⠀⢹⡏⠉⠉⣿⠛⠻⢷⣶⣤⣄⡀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠙⢧⡀⠈⠳⠀⠘⠃⠀⠀⠃⠀⠀⠘⠀⠀⠀⠛⠀⠀⠠⠋⠀⢀⡾⠁⠈⣹⡿⢷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⡴⠀⠀⠀⣠⠀⠀⢸⣿⠀⠀⠀⠀⠀⢾⣧⠀⠀⢀⠀⠀⢤⡀⢀⣹⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣴⣯⣤⣄⣼⣿⠀⠀⠀⠀⠀⢸⣿⣀⣤⣼⣦⣶⣾⣿⡿⠿⠛⠉
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⣿⡏⠀⠀⠀⠀⢰⠘⣿⡟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢸⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⢸⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢠⢣⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢠⠏⣸⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⡞⠀⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣸⠃⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠘⠁⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⣀⣀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⢷⡶⢤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠁⠀⠀⠈⠀⠉⠒⠌⠀⠀⠉⡓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠘⠀⠀⠀⠀⠀⢀⣠⣶⠿⢛⡷⢾⣆⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠃⠀⠀⠀⢀⣀⠤⠒⠻⠁⠈⠀⠀⠀⠜⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣠⣴⠦⠘⠫⠁⠀⠀⡖⠀⠀⠀⠀⠀⣀⣤⡶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢄⣿⠀⠀⠀⣴⣾⣿⡿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⣀⡀⢀⣀⣤⣤⣤⣴⣾⡎⠙⢳⣤⣾⣿⣟⡃⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣉⠈⣀⣶⣿⣿⣿⡇⠀⢸⣿⣟⣩⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠒⠟⠺⡇⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠈⠘⢿⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⡇⠀⠀⠀⠁⠀⠓⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣾⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⣠⡿⠉⠁⠻⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣤⣄⣦⣌⡗⠤⡀⠈⠄⠀⠀⠸⠀⣼⠏⠀⠀⠀⠀⠈⢅⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⣿⠁⠹⣶⣿⠷⢾⠞⠀⠀⣿⣿⡔⠊⠈⡁⠐⠐⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠈⠀⠀⠀⠀⠹⠜⡶⣶⡿⠉⢹⣶⣞⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⢠⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⡀⠀⠰⠀⠀⠀⠀⠀⠀⢰⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⢦⡀⠆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡇⠀⠀⠀⠀⣦⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢹⡀⠀⠀⢸⣧⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠦⠴⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣴⡿⣉⡏⢉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤
⠀⠀⠀⠀⣠⣶⣶⣍⢹⠉⠉⣩⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⡿⠛⣯⣠⢾⠀⠀⢫⣭⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠀⠀⣠⠤⠄⠠
⠀⠀⢠⣤⣤⡛⠉⡇⢸⡴⠾⡷⣾⡛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⣛⣩⣟⣛⢠⣷⡿⣏⠉⡏⢹⠛⢿⠦⠤⠗⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠈⠈⠁⠀⠉⠓⠒⠂
⠀⠀⠈⠉⢋⠉⣸⠂⢧⠙⣄⡇⣼⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠐
⠀⠀⠀⠀⠈⢣⣿⣄⡀⢳⣿⣿⣿⠄
⠀⠀⠀⠀⠈⠨⠟⠿⣿⣟⢿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢰⣾⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠂⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠈⠀⠀⠀⠀⠀⣺⣿⠄⠀⠀⠀⠀⠀⠀⠹⠿
⠀⠀⠀⢰⣶⠀⠀⠀⠐⠆⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⣤⠀⠀⠀⠉⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⢀⠀⠀⠀⠤⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀⣶⣆
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⠒⠒⠲⠢⠤⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠙⠁
⠀⠀⠛⠀⠀⠀⠃⢀⠀⠄⠁⠀⠀⠀⠈⠀⠀⠀⠀⠠⡀⢈⠁⠂⠤⢤⣤⠤⠥⠤⠒⠒⠂⡒⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⡀⠑⠤⣀⡀⣂⣤⠤⣼⣄⣌⣤⢂⡠⠄⠀⠀⠄⢊⠕⠀⡀⠀⠈
⠀⠀⠀⠠⣤⣆⠀⠀⠀⠀⠑⢄⣀⠈⣡⣶⠶⢶⣾⠃⠀⠀⢀⢹⣿⣄⡀⠠⠤⠐⠊⢁⡠⠎⣠⡴⠁
⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠠⠬⣙⠋⢭⣭⣽⠃⠀⠀⠀⠘⡽⡍⠳⣤⣉⢈⡩⠁⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⢀⠀⠀⠀⠀⡟⠛⠓⠊⠒⠂⠀⠉⠀⠀⠒⠀⠄⢀⠀⠀⠀⠀⠀⢀⡀⠤⠂⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠁⠠⠆⠀⢀⠀⠀⠀⡀⠠⠆⠀⠘⠃⠀⠀⠈⠋⠀⠇⠀⠀⠀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠒⡵⠖⠀⠐⠥⠆⠀⠀⠀⠀⠀⠀⢀⠧⡀⠀⠁⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢶⡆⠀⢈⠄⠀⠑⠀⠀⠀⠀⠀⠀⣱⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠰⠀⠀⠀⠀⠈⠈⠁⠀⠠⠄⢡⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣠⣦⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠒⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆
⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠁
⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⢠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠓⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣴⣄⣽⢿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⠿⢀⡙⠋⢠⡌⢁⣝⢹⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣤⡬⠦⣛⣛⣛⣯⣍⣙⣙⠻⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣩⡶⢾⣛⢩⣩⣅⣠⣄⣈⣹⣷⠀⣹⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⢯⡀⢬⠿⣿⣿⣿⣛⣫⠵⠋⣥⢖⡋⣽⣛⠿⡻⢿⡴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣛⣦⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠋⣬⣳⢻⢃⣳⡌⢳⣯⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⣽⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⡿⠽⠞⢿⡋⠉⡈⢳⣧⣿
⠀⠀⠀⠀⣔⡵⣶⣶⣷⡐⠤⢰⣴⣦⣄⡀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠔⢂⣼⣯⡿⠷⢸⠻⡆
⠀⠀⠀⠀⠺⣗⣼⢿⣞⣧⠀⢸⣿⣿⡻⣷⣝⣠⣾⣿⠟⠀⠀⠀⠀⡴⠀⡀⢣⣿⠉⠏⢱⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠘⡙⠟⠻⠟⠉⠙⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣤⡙⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⣴⣴⡀⠀⢀⡸⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣀⣁⡀⠀⣾⢿⠟⠻⡗⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣠⡈⣸⣷⣼⣧⡀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠟⠙⠁⠀⠸⣿⡿⣻⣷⣻⣵⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⡄⠀⠀⢷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣟⣿⣿⣿⠏⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠴⡈⡧⢩⠦⡅⠀⠀⠀⠀⠀⣼⠁⠀⠀⠰⠆⠀⡀⠀⠉⠀⠀⠀⠀⠀⢁⣸⣦⠤⠛⠉⠀⣾⡿⣿⣿⣿⣟⠛⠛
⠁⠀⠀⠀⠄⠴⠀⠈⠀⢀⡼⠁⠴⢦⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠘⣾⡷⡀⠸⠀⠀⢀⡟⠀⠠⡏⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠁⡀⠀⠀⠀⠀⡁⠀⡠
⠀⣰⣿⠀⠁⠀⠀⢀⣾⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢐⡄⠀⠀⢰⡇⠀⠷⣄
⢠⣿⡏⠀⢀⡄⠀⠈⢿⣦⣀⣰⡏⠀⠁⠀⠀⠀⠀⠀⢀⣰⣦⣀⠀⠀⠀⠀⠀⡀⠀⠰⠟⠀⠀⣾⡅
⢸⣿⣷⠀⠈⠷⠄⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⠈⣷⡀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠛⠁
⠘⣿⣿⡇⠀⢀⣠⣴⣿⣿⣾⣿⣿⣶⣦⣄⠀⠀⠉⠀⠀⠇⢠⡜⠃⠀⠀⠀⠉⠀⢀⣴⣶⣶⣿⣿⣿⣷⣦⣄
⠀⠈⠉⡀⠀⠻⠷⠛⠛⠛⠛⠋⠛⢛⡛⣿⠿⠆⠀⠀⢰⡇⢼⠆⠚⡇⠀⠀⠀⠰⠿⠟⠋⢉⣩⣀⠭⠀⠐⢡
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠓⠊⠉⠀⠁⢀⡆⠀⢰⠇⣶⠄⠘⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⡀⢡⡭⠃⠀⠀⢀⡀⠀⠀⠀⠀⢀⣰⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣷⠰⠂⠀⠀⢠⠄⣠⠀⢀⡈⡉⠀⢀⡀⠀⠀⠈⠙⠂⠀⠀⠀⠀⢻⡇⠀⠀⠀⠰
⣠⣦⣾⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡶⣶⣾⣾⣷⣾⣻⣿⠧⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇
⠉⠀⠈⠁⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠡⣼⣿⣿⣿⣿⣿⣧⣀⠀⠀⠉⠁⠀⡐⡀⣄⠀⠀⠷⠋⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡿⠀⠀⠀⠀⠀⠀⢫⣽⠟⠃⠙⠿⠏⠀⣠⠀⠀⠀⠀⣄⡈⠀⠀⠀⠆⠀⠐⠀⠈
⠀⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣧⠀⠀⠀⠚⡄⠀⡄⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣀⠀⠀⠀⢠⢷⢢⠂⡀⠀⠀⣞⠂⠸⡄⠀⠀⠉⠉⠘⠉⠉
⠈⠻⠋⠀⠀⠀⢀⡴⠾⡄⠀⠀⠀⠀⠛⠒⠀⢠⣿⡄⠀⠀⡒⠀⣀⡀⠀⠀⠀⣠⠇⠀⢹⠀⠀⠀⠠⠤⠄
⠀⢀⠀⠀⠀⡴⢩⠄⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢯⠀⠀⢸⡇⠀⠀⢠
⠀⠀⠀⠀⢠⠐⢈⣘⠀⠀⠀⢀⢀⡀⢀⣄⠀⣾⣿⠁⠀⢠⠀⠀⣽⣇⠀⠀⠀⠘⠶⠶⠟⢁⠀⠀⢿⡤
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⢴⠃⡊⡥⠀⠀⠀⠛⠋⠀⠀⠀⠀⢠⣿⡏⠀⡀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠒
⠀⠀⡀⢰⢄⡀⠸⣄⠁⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠉⠀⡀⠀⠀⠀⡓⠂⠀⠀⣤⣶⣷⣴⢆⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⣑⣤⡄⠀⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⢀⣀⠤⢤⢤⣤⣤⣉⣁⠖⠲⠤⢄⡈⠑⠢⢄
⠀⠀⠀⣠⠴⠋⠀⢀⡠⠔⠈⠉⠀⠀⠀⠀⠀⢉⠄⠋⠀⠀⢀⠞⠁⠉⠙⠒⠽⢦⣀⡀
⠀⠀⠸⠥⠶⠿⠭⢭⠤⢤⠤⠄⠀⠄⠒⠂⠉⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣓⣦⡀
⠀⠀⠀⠀⠀⠀⡰⠁⡠⠃⠀⡆⢰⠀⠀⢀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣀⣀⢀⣀⡀⣉⣉⡉⢹
⠀⠀⠀⠀⠀⠰⠁⡐⠀⠀⢠⠀⢸⠀⡰⠁⠀⠀⢀⣾⠀⠀⣀⡤⠖⠋⠁⢠⠀⠀⠀⠁⣀⠴⠋
⠀⠀⠀⠀⢀⠃⡰⠀⠀⠀⠘⠀⢸⡴⠁⠀⠰⠀⠘⠀⠊⠙⠀⣀⠀⠘⣦⠘⡇⠀⣀⠀⢵⡀⢃
⠀⠀⠀⢠⠜⠚⠧⠀⡐⠀⠁⢀⡞⠀⠀⠀⠀⡄⠀⠈⠀⠐⠒⠒⠀⠈⢉⡠⠒⠉⠀⠀⠀⠹⡞⢄
⠀⠀⠀⠼⢶⠒⠺⡀⢣⠀⢰⠈⣀⠀⠄⠀⠄⡇⠸⢦⠾⠀⣠⣤⣤⠠⠙⢤⡀⠀⠀⢀⠀⠀⣘⣮⠤⡀
⠀⡄⠀⠀⢸⠀⠀⣷⠟⢀⡨⡆⠈⠁⠀⢰⣾⣿⣄⠀⣀⣼⣿⣿⡾⠃⢀⡦⣤⠋⠀⣴⣉⠀⢀⠜⠀⠀⡀
⡆⡇⠀⠀⢸⠀⠀⡇⢀⣮⢠⣾⡀⠘⡆⠸⣿⣿⡟⠀⠸⡿⠛⠉⣀⠤⠞⠋⢀⢴⡇⠈⡇⠀⢸⠀⠀⠀⡇
⡇⠂⠀⠀⠘⠀⠀⠇⠀⣿⣿⣿⣧⠀⢰⠀⡸⠋⠀⠀⠀⠘⠳⡎⠁⢀⠀⣴⣿⣿⡇⠀⠃⠀⠈⠀⠀⠀⠁
⢃⠠⠀⠀⠀⡆⠀⠘⠀⠘⠿⣿⣿⠆⠚⢋⡁⠀⣰⣿⣷⡀⠀⣉⠛⠛⣾⣿⡿⠛⠀⠘⠀⢀⠇⠀⠀⠀⢀
⠈⢷⡼⣦⣤⣿⣀⢀⣇⡀⠀⠈⠉⠀⠀⠙⠁⢄⣿⡿⣿⣇⠄⠙⠁⠀⠈⠉⠀⠀⣠⣇⢀⣼⣦⣤⣞⣾⠟
⠀⠀⠙⠿⣛⣿⠿⢿⠿⣯⣀⣐⣶⣷⣶⣄⠀⢼⡿⠃⢿⣿⠄⢀⣴⣾⣷⣖⢀⣤⠿⢿⠷⣿⣟⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⠀⠈⠃⠀⠈⠀⠀⠀⣠⡀⠀⠀⠈⠀⠀⠏⢸⠐⠉⢸⠹
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⢀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠠⡄⠀⢸⣸⠠⠈⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠹⣻⢱⠀⣀⣎⠡⠀⠀⠀⡀⡗⠜⠁⠀⠀⡄⢠⣀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⢸⢹⠘⢧⠐⠔⣠⡆⡦⠀⠀⡰⢠⡇⢸⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠈⢈⢸⢸⢈⢸⢃⡇⡇⡆⢄⡐⠀⠀⢧⡼⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠈⠁⠀⠉⠘⢸⠀⠀⡇⢰⠀⠀⠃⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠄⠀⠀⠀⢇⠼⠀⠀⡄⢸⠀⠀⠀⠐⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⡇⢰
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣧⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠐⠒⡒⠒⠒⠂⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠠⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⡄⠀⠀⠀⠠⣀⡠⠂⠀⠀⢠⠂⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠘⠀⠀⠀⠀⠀⠔⠒⢢⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠒⠲⠌⠉⣁⡈⠁⠀⠀⠀⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠐⠁⠉⣄⣀⠤⡄⠂⠂⠉⠀⠀⠀⠀⠀⠀⠀⠗⢄⠀⠀⠀⠉⢉⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠑⣀⠠⠐⠋⠁⢀⠔⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢈⡐⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢁⠀⣀⠄⠊⠁⢀⠜⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠰⠀⠀⠀⠄⠀⠰⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠙⠒⠀⠀⠀⠐⡆⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠂⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⡴⡶⢶⠛⢿⣻⣳⣶⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢷⣛⣴⣺⠁⢸⣿⣿⠿⣻⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⢲⡄⠀⠀⠈⠓⠒⠒⢾⠀⢸⠗⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠹⣆⠀⠀⠀⠀⢀⡏⠀⣸⠀⢀⣠⡴⠋⠉⢳⡄
⠀⠀⠀⠀⠀⠀⢸⠠⣶⣖⣶⢲⣶⣤⡌⢳⠀⠀⠀⡼⠀⢀⡇⢰⠏⠁⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠭⡇⢸⠭⠭⠵⠊⠀⠀⣰⠁⠀⡼⠀⠈⠳⢄⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⢠⠃⠀⢰⠃⠀⠀⠀⣠⠏⣿⠋⠋⠉⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⠀⠀⠀⠀⡞⠀⠀⡏⠀⠀⠀⡰⠃⢰⠃⡠⠴⠞⠉⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀⠈⢇⠀⢳⡀⠀⢰⠇⠀⢸⠁⠀⠀⡼⠁⣠⠃⠘⢦⣿⣶⢦⣤⡈⢳⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⠳⣌⢦⠀⠹⣄⢸⠀⠀⣸⠀⠀⣸⠁⢠⠇⠀⠀⠀⡹⠃⡼⠿⠯⠜⠁
⠀⠀⠀⠀⠈⠧⣀⣀⣀⣠⠴⠋⠈⢧⠀⠘⣿⡄⣤⣿⡀⢀⣿⡄⣾⠀⢀⡴⠊⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠳⣄⠀⠀⠈⣧⡄⢿⣟⡡⡿⣇⢸⣿⣷⢿⡞⠁⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠿⣷⣶⣼⡼⣊⣿⣚⠜⣹⢸⣇⣽⢼⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⣷⣃⣸⠟⠛⠋⠀⠳⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠛⠛⠛⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢛⢉⢀⢀⠀⢿⣿⣿⣿⡄⢌⢢⡰⡑⠎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠸⣿⣇⠣⠇⡎⡞⢸⢸⣿⣿⣿⠈⡌⠆⣱⣨⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠈⠛⠿⢶⣶⣷⣾⣾⣿⣿⣿⣷⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⣠⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠋⠉⢹⣿⣿⡏⠙⠛⠻⠿⣿⣷⠀⠀⠀⢀⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡂⢀⢂⢀⢸⣿⣿⡿⠠⡐⡐⠕⣸⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢾⣾⣼⣿⣿⣷⣤⣵⣶⠾⠛⠁⠀⠀⣰⣿⣿⣿⣿⢟⢛⠛⠉⣿⣿⣿⠛⠛⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⡀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣦⣥⣂⣂⣿⣿⣿⠰⢀⣂⣡⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠉⠙⠛⢻⣿⣿⡿⠻⠟⠛⠛⠉
⠀⠀⠀⠀⠀⣴⣿⣿⠿⢿⣿⣿⠟⠻⠿⣿⡆⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣇⣐⡐⢸⣿⣿⣀⣀⣩⡾⠃⠀⠀⢻⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⣿⣿⣿⢃⣴⣾⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣰⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⠏⣾⡟⠛⠛⣿⣿⡿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⠋⠀⠈⠻⠶⣤⣿⣿⣁⣀⣨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⣿⣿⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠸⣿⣿⣿⡿⢿⣿⣿⠟⠀⠀⠸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠋⠉⠃⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠴⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠾⢭⡀⠀⠈⠢⠱⡀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⠤⠀⠀⠈⠒⢄⠀⠑⡌⢈⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠃⠀⠒⠂⠂⠐⠢⠦⢤⣤⣈⣼⡇⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠤⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⣠⡴⠂⠈⢉⢛⡶⢠⣄⣀⠀⢀⠀⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢶⠶⠊⠉⠁⠀⠀⠀⠁⠞⢠⠋⠀⢀⡀⣉⢁⡀⠀⢀⠤⠀⠀⠀⣀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⡠⠞⠁⠈⠀⠀⠄⠁⠀⢀⣀⠤⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⠀⠘⢀⡎⢠⠀⠀⠀⠐⠀⠤⠄⣤⢞⡉⢉⡄⠀⠐⠒⠀⠙⠲⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣸⠁⢸⠀⠂⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠘⣧⠀⠀⠀⢠⣿⠀⠈⠧⣤⡀⠀⠀⠀⢀⣀⡀⡄⠀⠀⣀⠀⠀⢀⣀⡤⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢻⣇⠀⠸⣸⡿⠀⢰⠀⠀⠉⣡⠉⠉⠱⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠘⣿⣇⠀⢿⣷⠀⢸⠀⠀⢠⡇⠀⠀⢠⠂⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⡞⣄⢸⣿⡄⣸⠀⣠⡟⠀⢀⢄⡌⡘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠈⢿⣦⡹⣆⡻⠱⣯⠼⠟⠀⢀⣡⡾⢊⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢛⠛⡛⠁⠘⢵⠎⠠⢴⠿⠿⠟⠋⠑⠊⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠖⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠒⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢉⠤⠀⠒⠒⠠⣄⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠰⠀⠟⡀⠛⠸⠆⣬⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠤⣠⠤⣄⡢⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠃⣀⠙⢠⠉⢐⠓⠐⢆⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣀⢉⠿⢭⣅⣀⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠭⠀⠥⣬⢤⡤⠼⠖⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠰⡶⠚⠉⢠⡔⠒⠚⡆⢐⣩⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢞⠉⠉⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠳⠀⠀⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⠀⠀⠈⡎⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡐⠀⠀⠀⠀⠠⡀⡧⡀⠀⠀⠀⠀⠀⢀⡄⠲⠊⡙⢲⡄⠀⠀⠀⠀⠀⠀⠸⣺⡠⡀⠀⠀⠇⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⣿⢦⡀⢀⡰⣧⠿⠠⠏⠀⠀⠀⠀⣰⡧⠍⠼⠮⠥⣴⣠⡧⠀⠀⠀⠀⠀⠀⠑⠽⠭⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⢤⡶⠒⢦⡠⠈⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⣦⣴⣿⠋⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⣿⣏⠉⣻⣷⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⡬⣄⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⠬⢭⡙⡻⠳⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠤⠅⠃⠀⠀⠀⠀⠀⠀⠌⠀⣀⡨⠽⠭⢅⣀⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠁⠀⢴⠋⠉⣦⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⠒⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡸⣄⠀⠀⢠⣜⣆⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠒⠃⠁⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠒⠿⠟⠋⠉⠉⣛⣃⡀⠀⠀⠀⠀⠀⡤⠈⠱⠄⣡⣤⣵⣆⠀⠀⠀⠀⢀⣴⣿⣟⣛⣛⣛⣻⢦
⠀⠀⠀⠀⣒⡺⠷⣃⣥⢴⣦⣬⡿⠛⠀⠀⠀⠀⠤⣾⣿⡿⠻⣿⣿⠿⠟⠀⠀⢰⡄⠤⠀⠀⠀⣹⣿⠉⠁⠀⠀⣧
⠀⠀⠀⢙⣻⢁⣿⣷⣾⣆⣾⣿⣿⡴⠶⠆⠀⠀⠀⠀⠀⠠⣤⡷⠹⠁⠀⠀⠀⠈⣿⣄⣠⠀⣤⠋⣿⠀⣦⢀⣼⡟
⠀⠀⠀⠀⠌⢸⣿⣿⣋⣩⣝⡿⣿⡇⠀⠀⠀⠀⡤⢠⣓⡇⠀⢀⣄⢀⡏⠀⠀⠀⠘⢿⣿⣤⣾⣴⣽⣷⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠉⣩⣿⣿⡿⠿⣿⠿⠷⠀⠀⠀⠙⢂⣶⣿⣦⣶⣾⣿⣦⣴⡇⠀⠀⠀⠐⠉⠙⠉⠋⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢠⣴⣿⣷⣤⡉⠻⣿⣶⣄⠀⠀⠀⠀⢀⣤⡶⠶⠶⣶⣄⠀⠀⠀⠀⠀⣤⠖⣳⡦⠀⠈⢻⣿⣿⣶⡦
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠟⠀⣿⣿⣻⣆⠀⠀⢰⠏⠁⠀⢢⣀⡀⡈⢳⠀⠀⠀⢸⣿⢛⣉⣠⣤⣤⣤⣍⣙⠋
⠀⠀⠀⠀⠿⣿⣾⣯⣤⣶⢶⣦⣬⣻⡿⠙⠀⠀⢻⣀⣰⣾⣟⣿⣍⣁⡸⠁⠀⠀⠘⢿⣯⣽⣿⣇⣄⣿⢿⣿⣥⣄
⠀⠀⠀⠀⠀⠁⠛⠻⠿⠇⠸⠋⢉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⣩⣍⣹⡟⠄⠹⣡⣝⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠁⠐⡀⢠⣄⣤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⠃⢀⣀⣹⣉⡁
⠀⠀⠀⠀⠀⠀⠸⠛⠻⠿⠿⠟⠳⠂⠀⠀⠀⠀⠀⠀⠀⠤⠼⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠿⠿⠻⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⣀⢀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⣿⡟⣿⢹⣻⡿⣶⢏⣿⣯⢿⢹⡇⣿⡹⢸⡿⡎⢻⣟⠿⢳⡧⣿⡇⡾⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣷⡿⠈⢷⠀⣿⠘⣿⠀⢸⣿⡇⣿⡃⢸⡇⡛⠸⢁⠆⡿⢀⣼⢱⡇⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠶⠈⠀⠋⠀⠏⡼⠸⠇⠷⠹⠂⠀⢘⣤⠤⠈⡈⢀⠏⠇⠾⠁⡰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⠐⠀⢀⡘⠢⠀⠊⣐⣡⣤⣑⡺⠊⠀⠀⢑⣅⠀⣀⠀⡄⡾⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡠⠞⠁⠐⣙⡧⠋⢹⠏⣂⣀⡤⠠⠄⠀⠘⣬⡒⢈⠀⡁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢁⠎⡠⠒⠲⢬⡆⠀⠈⠘⢍⠉⣠⠂⢠⠙⣦⡐⠙⢮⡳⡘⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣎⠁⠠⣀⣤⣧⠶⢣⣶⣾⡿⠋⢀⣯⡀⢐⣿⡇⠀⠱⡅⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣦⣄⠀⠛⣿⣿⣶⢤⣳⡆⢂⣄⣾⣿⡀⢸⣇⡀⠀⠀⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢿⣷⣤⠿⣿⣿⣷⡀⢹⠋⠑⠻⠟⠁⢿⣿⣿⠀⡴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢍⠀⠀⠘⠻⣼⠟⠗⠈⢂⢁⣀⢀⠄⠈⠈⠻⠾⠃⢠⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⠚⠺⣙⠂⠃⡉⠈⡀⠂⠠⡿⢟⠁⠀⠠⡄⠘⡄⢀⡜⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣖⢣⠈⣹⡉⠨⠠⠈⣉⠀⢰⡄⠚⠛⢁⣴⣈⡢⢣⠎⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣾⡁⠠⡀⠀⠂⠀⠀⢀⣛⠶⠈⠁⠀⣏⣉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⠃⠀⢀⠖⠀⠀⠀⡸⠁⢀⠴⢖⠜⢹⠁⠈⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡁⠘⢾⡼⡯⢜⡹⢓⠆⠀⣉⣴⠀⠊⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢰⠘⠿⡅⡘⠓⠊⠁⠘⠹⠀⢀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠐⠂⠀⠈⠰

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠟⠻⡹⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣤⡀⠀⢐⢏⣥⣶⣷⠶⣶⣶⣶⣌⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⠙⡿⣿⣿⣿⣦⣸⡋⠿⣿⡿⢸⣿⣿⣿⡿⠏⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠇⢻⠘⡀⠁⠸⠋⠈⠻⡷⡌⠓⢌⡇⢸⠥⢽⣉⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⣤⣤⣤⣤⢤⣴⣶⣶⣶⡶⢾⠀⢰⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠟⠿⠿⠻⢷⠘⡿⠟⣋⡀⠄⠊⠀⣼⠁⡇⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡦⢿⡁⠀⠀⠀⠀⢀⡟⢲⠁⣠⠴⠿⠻⠿⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢣⠀⠀⠀⠀⢸⠧⣼⠻⣷⣿⣿⣿⡟⢲⣶⣤⣭⣙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠒⠆⠀⠀⠀⣏⢀⡎⠑⠈⡙⠻⢿⠇⡾⠻⠿⠟⢉⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠙⡄⠀⢰⠁⢸⠀⠀⠀⠀⠁⡾⣴⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢱⠀⡌⢱⡇⠀⠀⠀⢀⡾⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢉⣷⠀⡼⠀⠀⠀⢠⠟⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡁⢘⠓⠁⠀⠀⢰⠓⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠘⠞⠁

⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⢿⠟⠻⣿⣿⢿⣿⡟⠿⢻⡿⣻⣿⣿⡿⣟⡛⣿⠛⡿⡻⣟⠛⢻⡟⢻⣛⡛⠛⣿⣟⡛⢻⣿⠛⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠟⠻⣿⢟⠀⠀⠀⠀⢠⡟⠻⣷⠾⣿⣿⣿⣿⣿⣮⡟⠩⣷⠁⠠⣹⡇⣠⡹⣾⠟⣿⣶⣴⣭⢳⡎⢻⡟⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠂⠤⠨⣛⠄⠔⣤⣴⣮⣶⡰⠱⡘⢽⣿⣿⣿⣿⣾⣿⣿⣷⣶⡶⢟⠀⡙⢿⡼⢿⣻⠛⢈⢻⣯⣣⣿⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢠⡤⠷⠒⠈⣟⣷⣦⡸⣼⡇⢸⠙⡶⢻⣿⣿⣯⡓⢶⡈⣯⣍⢿⣦⣐⢺⣿⣿⢿⡿⣶⣿⡇⣿⢸⡏⡀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣧⡜⠨⣿⣏⡌⣷⢿⣏⡈⣲⡇⣿⡟⠮⠽⣌⣇⢩⡜⣨⡥⠽⢿⣾⣿⣿⣽⣿⡟⠿⢀⣿⣜⣿⣷⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣛⠿⣿⡉⠄⡙⢿⣧⣿⣺⣿⣿⣯⣶⣯⠹⣒⣛⣦⣬⣭⣥⣭⡽⢖⠼⣿⣿⣟⣻⣿⣧⣄⡾⣣⣿⠏⣽⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣷⢿⡷⣀⢡⡌⢻⣽⣿⡿⣵⣶⣿⢠⣷⣿⣿⣿⣿⣿⣷⣹⣟⢾⡶⢿⣿⢮⡽⣾⣿⣿⣴⣿⣿⣶⠟⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣦⣿⣾⡷⢫⣼⣷⠨⣟⡹⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⣽⣿⣿⣜⢿⡁⢹⠟⣹⠿⣷⣴⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣧⣹⣿⣶⢯⡘⣿⢗⣛⣸⣿⡇⢼⣿⣳⣿⣻⣿⣿⣿⠋⢿⣿⣿⣿⣿⢛⢳⣏⠺⢻⣿⣾⡟⣟⡋⢸⣥⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠏⣠⠤⡌⢧⣹⣿⣿⣼⡏⣾⣗⣾⢋⣿⢿⣿⣴⣛⣿⠘⠺⢿⡾⠋⢁⣤⡈⢰⣄⢺⡋⠹⣿⡟⢣⣼⡏⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠚⠀⡀⠘⡀⢇⣼⣿⠿⢷⣱⣿⣘⣿⢷⣠⡻⢿⡟⢿⣦⠖⠿⣧⠆⢏⢤⢻⡉⣿⡘⡟⢀⣿⣇⣿⣏⡛⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⣼⠿⡆⠁⢰⠟⢹⡇⢪⣄⣶⡈⢣⡏⠙⣿⣧⠀⢸⣇⣠⣤⣾⣧⣎⡰⣸⠷⣫⣽⢞⠻⣟⡱⢿⣿⡻⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠠⣶⣷⡇⠆⢸⠗⢿⡅⢹⣎⣿⣷⡿⣿⣦⢹⡿⣄⣸⢿⡍⠀⢀⣻⢿⣵⠟⢀⡷⠶⣯⢶⣦⣤⠞⣿⠷⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣴⣿⡿⣿⣤⣷⣶⢢⡄⢰⢎⣿⢿⣧⠘⣇⠸⡇⡨⠆⢸⡧⡶⠋⠙⣦⠀⢂⡾⣧⣾⠃⠀⡘⣷⠂⢹⣶⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡀⠉⠙⢿⡿⠟⠛⢿⣟⡀⠘⢠⣯⣿⡾⢿⣳⡉⠀⠤⣿⠐⣆⣠⠶⠷⡶⣆⣽⣻⣿⠄⣨⡴⠇⠹⠿⠙⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣟⡻⢶⡌⠇⣈⠃⠈⠸⠇⠀⡜⢳⣾⣷⠀⢽⠁⠙⠖⠃⠈⣿⠀⠀⢀⣶⣮⣥⣿⠓⡾⣯⡤⢀⠀⣤⣼⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣾⣫⡶⣻⣷⣭⠔⠀⢹⣿⠸⢋⣿⣷⠿⠑⡼⢇⣶⣄⣀⣟⢿⡷⠛⠙⢿⣿⣿⡟⣼⢲⡿⣿⡎⢴⡟⠙⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣭⡿⣵⢷⣧⠈⠀⠀⣭⠀⣿⣭⠾⡛⡶⠃⠙⣯⣿⣿⣿⣹⣿⣷⣀⣤⣼⣜⡻⢣⣚⣿⣾⡿⣘⣿⡃⣠⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣻⣣⣿⣾⡏⠂⠀⣸⣶⣦⡋⣿⣷⢡⣦⡄⠛⣤⣤⠛⣼⣿⣿⣿⠉⠀⠈⣮⣿⠊⣭⣽⣿⣿⣿⣿⡗⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢝⢻⣶⡶⡋⠡⠟⠛⠥⣀⢹⢹⣯⠉⠘⠶⢿⠀⢹⣎⡿⠾⣯⣿⡤⠶⠲⡾⣭⣫⣼⣛⡉⢿⡝⢿⣿⠂⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣦⡻⢚⣿⣿⣤⡀⠂⣤⠀⡈⣿⣏⣟⣻⣆⢸⡟⠪⢹⠷⡄⢿⣿⢆⠀⠀⣿⣤⣽⠟⡏⠹⠿⣧⠈⠓⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣾⣏⡾⡹⣧⠨⣿⣿⣷⡿⠾⢭⠁⢻⡟⢻⣤⠼⣃⡠⠚⢻⣿⣆⣠⣿⡉⠙⠃⣷⠟⢦⠻⣶⠀⣼⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢹⠟⣭⣙⢷⣿⣤⡆⢻⣿⣿⡞⢠⡄⠃⠰⡟⣸⣧⣤⣧⡃⡀⢩⣿⣿⣽⡟⢻⡷⢶⡇⢴⡈⣶⡏⢼⣯⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠄⠞⣓⢻⡎⣷⢀⠀⣾⣿⠾⣧⠘⠁⡄⢂⡿⣇⢩⠙⣿⠀⠁⣸⣿⣿⣹⣷⣿⣀⡿⠿⡤⢃⣧⡷⠈⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣾⣷⣿⣿⣷⣾⣷⣾⣿⣷⣾⣷⣿⣷⣿⣾⣿⣿⣷⣶⣿⣾⣿⣿⣷⣿⣿⣿⣶⣶⣿⣾⣷⣶⣾⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⠀⠉⠁⠀⠀⠙⠤⠭⠓⠀⠄⡀
⠀⠀⠀⠀⠀⣠⠂⠁⠀⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠑⢄
⠀⠀⠀⠀⠊⠀⠑⠀⠀⠀⠀⠠⡀⠀⢈⠆⠀⠀⠘⠀⠘⠀⠀⠀⡱⡀
⠀⠀⠠⢣⠀⠀⠀⣀⣀⠤⠤⠠⠄⠄⠤⠀⠄⢠⠄⡤⠀⣀⠀⠀⠢⠨⡄
⠀⢀⠃⢁⠄⠈⠛⠠⠄⡑⠀⠠⡁⣀⢀⣠⡠⡡⢊⠠⢂⠁⠬⠒⠢⡀⢠
⠀⠈⠄⢈⡀⣀⣀⢀⣐⣀⣥⠞⠉⠉⠀⠀⠉⠉⢲⣬⡆⠀⠀⠈⢀⡑⡘
⠀⠀⠀⠐⠅⡒⢤⣰⣡⣡⣻⡄⠀⠀⠀⠀⠀⠀⣸⣏⣍⣕⡤⢒⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠀⠀⠀⠀⠀⠰⠛⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢶⣛⣭⣿⣳⣶⣪⣳⢶⢞⣻⣲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣠⣎⠀⠀⢸⢗⡿⣽⠴⠿⣭⣗⣏⢯⡷⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠒⠒⠂⠂⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣾⣯⣾⣼⣧⣀⣀⣼⡻⠿⣾⣷⣶⣿⣿⣿⡿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⣿⣿⣿⡿⠿⢞⠻⡛⢛⠻⡙⡏⡛⢛⠟⡻⠻⢿⠿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠉⠁⠒⠤⢑⣮⣲⣧⣧⢧⢧⣯⣊⣴⡊⠥⠐⢊⣉⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠠⠭⠭⣭⣿⣷⡟⠉⠀⠀⠀⠀⠀⠉⣿⣿⣧⡬⠤⠤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣿⣿⣯⣵⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡃⠀⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⢙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣷⣦⡀⠀⠀⠻⠿⠷⢿⡿⠿⣿⠛⠛⢋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⣿⢿⣿⡄⠀⢀⣀⣄⣸⠁⠀⣿⢠⣾⣿⠛⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⠿⠟⢃⣴⣿⡋⣻⣿⣦⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⡇⢸⠀⢠⣾⣿⣿⣿⣿⣿⣿⣏⣿⣯⣿⣿⣿⣽⣿⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣄⢃⠸⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣸⠉⢹⠋⠉⡙⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⠺⠛⠛⢎⠀⢡⠀⠁⠀⢹⠉⢩⡏⠉⠁⡏⠀⣼⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡍⠙⡄⠀⠀⢸⠀⢸⠀⣀⡠⠇⢠⠇⢀⣼⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣶⣼⠀⢱⠀⠀⡏⠀⣨⣾⣿⣿⡄⠎⠠⣿⣿⣷⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⢿⠟⡇⠀⣤⣤⠃⢸⡿⡿⢷⠿⡷⠀⠀⡞⡀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡘⡀⣧⢸⠰⢿⢿⠷⢸⠱⠀⣰⠞⠀⠀⡜⠰⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢱⠈⢦⡆⢈⢸⠀⣼⠃⣸⠁⢀⢄⡌⠓⢦⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⡙⢆⢣⡈⠣⣸⢸⠠⠋⢠⠇⢀⠑⠩⠈⡠⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣦⡀⠀⠑⠌⠂⠑⠀⠈⠈⠀⠀⠉⠁⠀⠀⠤⠊⠀⠀⣴⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠁⠀⢐⣶⣄⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⣴⡆⠀⠀⠻⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠀⠀⢰⣿⣿⣿⣧⠀⠀⢻⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠘⢿⣿⡿⠏⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⢿⣾⠿⡇⠀⢠⣄⡀⢠⢀⣴⣤⡶⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠛⠉⠁⠘⡅⠀⠁⠁⠈⠙⠻⠀⡎⠉⢘⠋⣤⠀⢸⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⠀⡄⠁⠀⠀⡘⠈⠀⠘⣿⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⡄⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⡀⢿⣇⢠⣷⣇⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠸⠳⠿⣿⡷⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣹⡄⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠂⠶⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠐⠀⠀⠸⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠏⠁⡀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠰⢧⢰⡄
⠀⠀⠀⠀⠀⠀⢰⣆⡆⠸⠃⢠⠀⠀⠿⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠘⣾⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣅⠠⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠧⠄⠀⠀⠀⠀⠀⡆⡆⠀⣿⣶⡄
⠀⠀⠀⠀⠀⢰⣾⣿⠈⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⠆⠀⠀⣀⣤⣾⣿⣿⡿⠟⠛⢃⡀⣲⠀⢳⠰⢀⣿⣿⣷
⠀⠀⠀⠀⠀⣼⡟⡟⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⣶⣦⠶⠆⠀⠀⡀⣀⣀⣀⣤⣤⡶⣶⣾⣿⣟⡻⡯⣖⡯⠛⠀⠀⠀⠀⡠⠁⠀⠸⠆⠈⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣷⡆⠀⡃⠀⠀⠀⠀⠀⠀⢀⣴⠃⠛⢀⣠⠶⣿⣿⣭⡙⣄⣸⣼⣷⣿⣿⣿⡥⠚⣋⠅⠀⠀⢀⠀⠀⠄⠀⠀⠐⠀⣄⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣤⣖⠛⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⠿⠛⠰⣶⣿⣿⣿⡿⣶⣾⠶⠁⠀⠀⠀⠀⠀⠸⢸⣼⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⡀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠛⠋⠉⠭⠖⣫⡿⢛⣁⣤⣀⣀⣰⣾⣿⣿⣿⠿⠟⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⡆⠛⠀⠀⠀⠸⢿⣿⣿⣿⣾⣦⠄⠀⢂⢀⣴⣾⣷⣿⣿⣿⠛⠹⢏⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠒⠒⡟⠋⠉⠉⠉⠉⢻⣡⠀⠀⠀⠀⠀⢀⠆⠀⡄⠀⠀⠀⠀⠀⡠⠀⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣀⣀⠀⠞⠄⠀⠀⠀⠀⠀⠀⠆⠀⠈⠄⠀⠀⡀⠀⠘⡟⠀⠀⠀⠀⠀⣈⠣⠠⠇⠀⠀⠈⠀⡀⠀⠀⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡉⠳⣄⠈⠀⢠⡀⠠⡀⠀⠀⠀⠐⠒⠂⠀⡀⡜⠀⡷⠀⠀⠄⣰⣿⠁⠀⠀⠀⠀⠀⠀⢄⣡⠞⣷⡏⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⠆⠐⢲⡀⠉⠀⠹⣰⣃⠀⠀⠀⠀⠀⠘⡇⡄⣿⡆⠘⢸⣿⣿⣧⠄⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢠⣛⡁⢰⣤⠀⣿⣿⣖⣀⣤⣤⠀⠚⡁⠀⠘⣿⠇⠀⠹⣿⠿⣷⣶⣦⣀⣀⣀⡀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⣹⣴⣦⣿⡞⢿⣿⣿⠟⢻⣿⣝⣴⠁⠀⢀⡿⠂⠠⡅⠠⣰⡟⠻⣧⠋⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢾⣿⣽⣷⣯⠛⠿⣾⡁⡀⢤⣿⣦⣄⢈⣤⠖⡁⠀⢠⣿⠀⢲⣿⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢇⢃⡀⢠⣿⣿⣿⣿⣿⡏⣿⡄⢱⣾⣿⡿⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⠔⠚⠋⣏⠉⢹⡍⠉⠙⠲⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⢦⡱⡘⢧⣂⢂⠀⣿⠀⠘⣐⣐⡰⢼⡣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠑⢍⡒⠪⠭⠭⡿⠀⢠⠗⠒⢚⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⣤⠤⢴⠔⢤⠤⢤⣀⠙⣆⠀⢀⡇⠀⢸⣠⠞⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡻⣄⣀⣸⠀⢸⣀⣀⣨⢇⡜⠀⡼⠀⠀⡞⠁⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣉⠒⠒⢻⠀⢸⡿⠓⠒⠉⠀⢰⠃⠀⢰⢷⣒⡋⡏⠀⡖⠒⠦⡄⢸⠄
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠓⢄⠈⡇⠀⢇⠀⠀⠀⢠⠇⠀⢀⠟⠒⠬⢭⡇⠀⣿⣯⠭⠴⠊
⠀⠀⠀⠀⢰⠃⣀⡤⡤⠠⠤⢤⡄⢣⢱⠀⠘⡄⠀⠀⡎⠀⠀⡜⠀⠀⠀⡸⠀⢰⠃
⠀⠀⠀⠀⠘⠦⢽⣓⡇⠰⣟⠭⠕⠃⠀⢇⠀⠸⡄⢸⠁⠀⢰⠃⠀⠀⣰⢃⠤⠚⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠘⡆⠀⠹⡏⠀⠀⣼⠀⠀⡴⠁⡃⣤⢤⡤⢀⣀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠣⡀⠀⠀⠀⠸⡄⠀⠱⡀⠀⡇⣠⠎⠀⢀⡝⠚⡽⠀⡾⠞⠥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠙⢦⠀⠀⠀⢳⠀⠀⢳⠀⡟⠁⠀⣠⠎⢀⡴⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠱⣄⠀⠘⡆⠀⠈⡇⢸⠀⡴⠁⡰⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⢆⠀⡇⠀⠀⢣⠈⣾⢁⡞⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⡆⡇⠀⠀⡎⠀⣸⡞⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠞⠁⠙⠦⠞⠓⠚⠁⠙⠒⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣦⣶⡇⠀⣀⠀⢀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠛⠁⠺⠁⠃⠀⠛⠻⠈⡌⠉⠛⣄⠀⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⠛⠁⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠄⠀⠀⢀⠈⠀⢹⡅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⡆⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢸⣿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠲⠀⢘⡇⠡⠀⠘⠀⠀⠀⠀⠀⢀⡠⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠨⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠸⠁⣀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠰⡆⣤
⠀⠀⠀⠀⠀⢶⡤⠈⢀⡄⠀⠛⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⠁⢸⣏
⠀⠀⠀⠀⢀⣾⡷⠀⠀⠣⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠈⣠⣤⣬⣯⠤⠄⢀⡀⢠⠀⠸⣿⣧
⠀⠀⠀⠀⣾⣿⠂⡀⠀⠘⠀⠀⠀⠀⣠⣄⠤⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⠯⡟⠋⠁⠀⠀⡰⠁⢈⡄⢘⣿⣿
⠀⠀⠀⠀⣿⣾⠀⠁⠀⠀⠀⠀⠀⣠⡏⠛⣀⡴⣾⣿⣏⣫⣹⣼⣿⣿⣿⠕⢊⡉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⣿⣿⠃
⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⣠⣾⣿⣶⣯⣩⡴⠾⢿⡿⣿⡿⠿⠛⠋⣐⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⠀⠘⢱⣿⣿
⠀⠀⠀⠀⢸⣿⡇⢤⠀⠀⠰⣿⣿⣿⣯⣄⠀⠀⠈⣡⣾⣵⣶⣷⠶⡾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠉⠙⠛⠛⠛⠲⠀⠾⠛⠛⠛⠛⢿⡀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠸⣿⣷⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡇⠀⠀⠀⣀⡕⠀⠂⠀⠀⠀⠂⠀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣷⡈⡓⢀⠈⠢⠀⢄⣀⠀⠀⠉⠀⠀⡌⠀⣇⠀⢠⣾⣇⠀⠀⠀⠀⠀⠠⠖⢹⡟⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠿⠄⣀⢀⣿⣆⠀⢀⡀⠀⠇⠈⢿⣆⠈⢿⣿⣧⣄⡀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⣫⣤⣿⡾⣿⣿⡿⢻⣿⣢⠇⠀⢸⠇⠀⡀⢁⡾⠻⣯⠋⢉⣵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠿⣿⣿⣏⠙⠿⢅⣐⣼⣧⣤⣡⠖⠁⢀⣼⡇⢸⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠀⠸⣿⣿⣿⣿⣿⠿⠼⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠷⠶⢤⣠⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠙⢳⣄⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⡤⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣤⠶⠓⠀⠑⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⢶⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣥⡀⠀⢠⣶⣵⠞⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠤⠤⠶⠶⠶⣶⣿⠇⠀⢻⣶⣿⣟⠩⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣠⠜⠛⠻⠟⠇⠀⢸⡿⠵⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠂⠉⢇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀⡶⠿⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠀⢠⡞⠁⠀⠀⠀⠡⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢿⢲⡏⠳⣈⣰⣤⣠⡄⠀⠀⣰⣟⣀⠤⠀⠀⠠⠠⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠟⠉⠀⠈⠁⠀⠀⢟⡫⣀⣠⡴⠖⣤⣀⠼⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠃⠀⠸⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢱⠀⠀⠀⢸⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠧⠄⠤⠼⠁

⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣦⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠭⠙⠉⠉⠙⠓⢄
⠀⠀⠀⠀⣀⣤⣤⡤⣤⣴⣷⣿⣽⣿⣿⣿⣿⣻⡿⣿⣇⠀⠀⠀⠀⣀⠤⠒⣒⢀⣴⡂⠁⡡⠋⠁⠀⠀⠐⠲⠢⢄⠀⠂
⠀⠀⣰⣿⣿⣷⣾⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⡼⠁⠀⠀⠀⠈⠁⠠⢊⠀⠘⠀⠀⠀⠀⠀⠄⠈⡀
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡀⠶⠄⠀⠀⠐⠁
⠀⠀⠘⢿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⠀⠀⠀⠈⠙⡄⠀⠉⠀⠂
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⢐⣠⡀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣿⣶⣢⣴⣦⣄⣀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡁⣀⢀⠈⠉⠳⠛⠀⠂⢤⢴⣶⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⡆⠀⠀⠀⠀⠀⠈⠃⠀⠀⠨⠉⠖⢄⡀⠀⠀⠀⠛⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣟⣿⣿⢿⣿⣿⠿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠆⠤⢤⠤⢤⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠑⠀⠀⠀⠂⠠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠄⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⣿⣿⣿⣷⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡇⢠⡄⢸⠀⠀⠂⡛⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠛⠸⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠨⣛⣦⣷⣾⣴⡀⢰⠟⠋⠁⡈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣲⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣠⣾⣿⣾⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣿⣿⡀⢀⣿⣿⠀⠀⣴⣿⣿⣿⣿⣛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣾⣿⣿⣿⣿⣿⢛⢻⣿⣿⡏⢹⠀⠀⠀⠀⠀⠀⠀⡹⠉⠉⠉⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢿⡛⢯⡉⢇⠀⡇⠀⡽⠉⣩⠛⢻⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⢲⣭⠞⠉⠉⠚⣥⠞⠥⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠁⠀⠀⢠⠒⣢⡒⢢⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡠⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⡀⠀⠀⡜⢻⣿⣿⠛⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⢫⣠⣤⣿⡉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢳⡀⠀⠙⠚⠯⡽⠉⠀⣠⣴⣾⣿⣿⡷⡄⠀⡴⠉⢿⣿⣿⣿⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢠⣞⣽⣿⠿⣿⣿⣷⡇⠀⠙⠢⢺⠛⢛⡧⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⣀⡤⠃⠀⠀⢀⣠⣶⣿⣿⣿⣿⣶⣿⣯⣿⡇⠀⠀⠀⠀⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡉⢀⡀⠀⠀⢠⠿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣩⣽⣏⣹⡀⠀⠘⠦⢽⣿⣿⠿⣿⣿⣧⣠⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣿⣿⣿⣧⡼⠀⠀⠀⠀⠀⢉⠇⠙⠛⠛⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠼⢧⡼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠴⠞⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⠶⢶⠶⠶⣶⣶⣶⡶⠶⢶⡶⠶⣶⣶⣶⠶⠶⡶⣶⣶⣶⣶⡶⢶⢶⢶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣷⣿⣧⣿⣼⣿⣾⣷⣿⣧⣿⣽⣾⣾⣿⣾⣿⣼⣷⣶⣾⣽⣿⣾⣿⣾⣧⣿⣿⣿⣷⣿⣿⣿⣷⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠻⣿⣿⡟⠉⠉⣹⣿⣿⠛⠛⠛⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠙⣿⣿⣧⠀⠀⢻⣿⣿⡀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠋⠉⠙⣻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣷⣄⠀⠈⠻⣿⣷⣄⠀⠙⢿⣷⣄⠀⢻⣿⣆⠀⢸⣿⣿⠀⠀⣼⣿⣿⠿⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣍⠀⠈⠙⠿⣿⣷⣦⣄⣈⡙⠛⠿⢶⣤⣉⣻⢷⣄⡙⢿⣦⠀⢻⣿⠀⠀⣿⣿⠃⠀⠀⣠⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠻⢿⣿⣷⣶⣤⣤⣤⣤⣉⡭⠟⣩⣴⡾⠛⠉⣠⣴⣶⠶⠖⠒⠚⠷⠄⠻⣧⠀⣿⣿⠀⢀⣾⣿⣿⠟⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⣀⠀⠀⢉⣉⣉⡍⢩⣾⠋⠀⣼⣿⡏⠀⠀⢼⣿⣿⠁⠀⢠⣶⣿⣿⠿⠶⢾⣧⡘⣿⠀⢸⣿⡟⠀⠀⢀⣀⣹⣿⣄
⠀⠀⠀⠀⠀⠀⣰⡿⠻⠿⠿⠿⠿⠟⠛⣹⠋⢰⣿⡇⠀⠀⠻⣿⣿⣦⣀⠈⠻⢿⣧⡀⠘⣿⣿⠁⠀⢀⣤⣤⣉⡻⢇⢸⣿⠀⢀⣼⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣅⣀⣀⣠⣤⣴⠞⣼⡇⠀⢻⣿⣿⣦⣤⣤⣤⣭⣭⢉⣛⣷⠶⠬⠙⠶⣌⠻⣇⠀⣿⣿⡿⠛⠿⢦⡘⣿⠀⣾⣿⠟⠁⠀⠀⠉⢻⣆
⠀⠀⠀⠀⢰⣿⠿⠿⠿⠟⠛⣉⡞⢰⣿⣇⠀⠀⠉⠉⢉⣩⣩⠖⢡⣶⣿⠁⠀⠰⣾⣿⠟⠛⠓⠬⣧⠸⣿⠀⠀⣀⣀⠙⢿⢰⣿⠃⠀⣠⣴⣶⣶⣬⣿⡆
⠀⠀⠀⠀⣿⡇⠀⣀⣠⣴⡾⣹⡃⠘⣿⣿⣷⣶⡶⢟⡉⣴⠃⠀⠘⠛⣛⣛⡳⠶⠬⡙⢧⡀⢰⣶⣮⣅⢻⠀⣼⣿⣿⣷⣄⢺⡇⢀⣾⣿⡿⠿⠿⢿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⡿⠟⢁⡄⣿⡇⠀⠈⠉⠉⢁⡴⡟⢸⣿⣷⡶⡚⣩⠟⢁⡐⠻⢿⣏⠙⠛⢆⢿⠏⠙⢿⡇⣿⠏⠀⠈⠻⣧⠃⣾⠟⠁⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⣸⡟⠉⠀⣀⣴⢿⡇⢻⣿⣦⣤⣤⣾⠟⢸⡇⠈⠉⣡⠞⢹⡿⢛⠝⢁⠒⣶⣾⢷⢸⣦⡘⡇⣠⣄⢣⡟⢀⣴⣶⣄⠸⣾⠏⢀⣴⣾⣿⣿⣷⣦⣸⣇
⠀⠀⠀⣿⣷⣶⣿⡿⠋⣸⡇⠈⠻⠿⠿⠛⢁⣾⢸⣧⣤⣾⢃⡇⠀⡴⣿⡞⢁⠈⠉⡿⢄⢰⡟⢻⢡⡿⢿⡼⢇⣾⠿⠿⣿⡆⠟⣰⣿⠟⠛⠉⠛⠻⣿⣿⣿
⠀⠀⠀⣿⡿⠛⠁⢀⣾⠇⣿⣄⠀⠀⠀⣠⡿⢹⡈⢿⡿⠃⡜⢿⣾⠣⠙⢸⣿⣦⣖⣁⣼⠇⣁⢈⠟⠀⠈⣇⡾⠁⠀⠀⠘⣿⣸⠟⠁⣀⣀⣀⣀⠀⠈⣿⣿
⠀⠀⠀⢸⣇⣠⣶⣿⠃⣤⠘⣿⣿⣿⣿⡿⠃⣾⢷⡀⠀⢰⡇⣌⠛⠀⣷⢬⣧⣄⡠⠼⠷⣿⢏⣪⣶⣷⢰⢏⣤⣾⣿⣷⠀⡿⢁⣴⣿⣿⣿⣿⣿⣷⡀⢸⡏
⠀⠀⠀⢸⣿⡿⠟⠁⣰⡿⣆⠈⠛⠛⠋⠀⣰⡏⢈⢿⣶⣿⡇⢹⡲⣄⣸⣦⡙⠭⣅⣒⣛⡓⠋⠉⣿⢃⡴⠟⠋⠉⢻⣿⢀⣷⠟⠋⠁⠀⠀⠈⠙⣿⣷⣾⡇
⠀⠀⠀⠀⣿⡅⢀⣼⡿⢀⡹⣷⣄⣀⣀⣴⣿⡇⢸⣦⡙⠛⠁⠈⣷⡸⣝⡛⣋⣀⣀⣽⡿⠟⣠⣚⣩⣥⣶⣶⣦⠀⢸⡟⢈⣡⣴⣶⣶⣶⣦⡄⠀⢸⣿⣿
⠀⠀⠀⠀⠸⣿⣿⡿⠁⣸⣷⡈⠿⣿⣿⣿⠟⠀⢸⡇⢙⢦⣤⣤⣿⣷⠈⠻⣮⣍⠛⠶⣬⣭⣭⣉⠁⠈⠙⣿⡿⢠⡿⠾⠛⠋⠉⠉⠙⠻⣿⣿⡄⢸⣿⠃
⠀⠀⠀⠀⠀⠹⣿⡀⣠⣿⠃⣻⣄⡀⠉⠀⠀⢀⣾⣿⠈⣷⡨⣝⠛⠋⠀⠀⣸⣿⣷⡄⠀⠙⣿⣿⠇⢀⣴⢟⣡⣭⣴⣶⣶⣶⣶⣄⠀⠀⢹⣿⡇⣾⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⣿⡌⠻⣶⣶⣶⣿⣿⡟⠀⢸⣷⡈⢿⣝⠛⣛⡛⢛⣉⣀⣤⠾⢟⣡⣴⣋⣥⣭⣀⣀⡀⠀⠉⠛⣿⣿⣧⠀⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⢠⣿⡇⢳⣄⡉⠛⠛⠉⠀⠀⣸⣿⡇⠀⢻⣷⣌⠙⢷⣬⡉⠛⠶⣶⣤⣄⡉⠉⠙⠻⣿⣿⣦⠀⠀⢸⣿⡟⢀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⢸⣷⠙⠷⣶⣤⣴⣾⣿⣿⠇⠀⠀⣿⣿⡆⠀⠹⣿⣷⡄⠀⠙⣿⣿⣦⠀⠀⠘⣿⣿⡇⠀⣼⡿⣡⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣼⣿⠀⢻⣦⢉⣉⠙⠉⠁⠀⢀⣴⣿⣿⠇⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠇⠀⢠⣿⠟⢀⣼⣿⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣆⣸⣿⡆⠹⣿⡛⠻⠿⠿⠟⠛⠉⠀⣀⣴⣿⡿⠋⠀⣠⣾⡿⠋⢀⣴⠿⢣⣴⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⣹⣷⡈⠻⣷⡛⠛⣿⣛⠛⢋⣁⣤⠴⠞⣛⣩⡐⠚⢻⣷⣶⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣦⣼⣿⣦⣈⣻⣷⣤⣉⣻⣷⣦⣬⣽⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉