Fond Emojis & Symbols

⠀⠀⠀⠀⣠⣀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡈⢁⠀⢀⡄⠀⠀⠀⠀⠀⠀⣖⣊⡟⢢⠀⠀⢀⣾⠌⣼⣄⠀⠀⠀⣴⣷⠻⣿⠋⠀⠀⠠⣤⣀⣀⣤⠀⠀⢀⣿⣾⣷⡇
⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢇⠀⢈⠏⠀⠀⠘⢿⣿⠉⠉⠀⠀⠀⠀⠀⠒⠀⠟⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡍⣥⡂⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠰⠢⣄⠀⠀⣿⣿⣿⣿⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠉⠀⡇⠀⠀⢘⣇⣒⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠀⢤⣈⠉⠉⠷⡀⠀⣀⣭⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠈⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠰⢇⡄⢀⣜⠇⠀⠀⠀⢀⠬⣅⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠰⣿⡶⠾⣷⠄⠀⢨⣿⣿⠈⢡
⠀⠀⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠘⠂⠀⠀⠀⠉⠀⠊⠉⠀⠀⠀⠙⠙⠃⠁
⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠺⢿⣿⠟⠀⠀⢿⣿⣿⣿⣷⠀⢃⣄⢀⣄⠃⠀⢐⢠⡐⠶⠀⣠⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠉⠁⠀⠈⠁⠀⠉⠀⠀⠒⠈⠵⠞⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠤⠴⠶⠒⠒⠂⠀⠀⠀⠀⠀⠐⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠭⣓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢁⡢⢭⣑⠊⠙⠛⠶⣤⡀⠀⠀⣀⡤⠤⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢔⡨⢕⡪⠅⡂⠉⠐⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣉⣓⣮⣍⡂⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⣀⣠⣤⣴⣶⣛⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⣤⣤⣴⣿⡤⠴⠖⠛⠋⠉⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠸⠻⡝⢷⠤⠤⠤⠤⠴⠶⠶⠶⠒⠛⠛⠉⠉⠁⠀⠀⢀⠠⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠹⣾⣀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣀⣤⠴⠖⠚⢻⣧⡶⠞⠛⠛⠛⠛⢛⡿⠿⠶⠶⠶⠤⠤⠤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣻⡄
⢀⡴⠛⠉⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠭⠭⠤⠴⠒⢲⣶⣶⠖⢀⡀⠀⠈⠉⡽⢯⣀
⡾⠁⠀⠀⠉⠒⠀⠀⢸⡄⠀⠀⠀⠀⠀⢀⣀⣀⣐⣒⣒⡂⠤⠤⠤⠬⠭⠭⠍⠉⠁⠀⠀⠀⠀⡇⠀⠈⠙⠲⣤⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣒⣒⡲⠶⠶⢤⣤⣤⣤⣄⣀⣈⣉⣉⡀⠐⠠⠤⠤⠤⠤⠄⠀⢧⣤⣤⡴⢶⡾⠛
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⢍⡉⠙⠛⠛⠛⠛⠛⠛⣛⣻⣷⠶⠶⠶⠶⠿⠿⠿⠶⠶⠷⠀⠀⣸⠁
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠚⠉⠉⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⣀⣀⣀⡤⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣄⡘⢷⡢⠄⠀⠀⠀⠤⠴⠖⢒⣒⣛⣫⣭⠭⠶⠶⠒⠛⠋⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⡃⡿⠿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⡛⣿⠃⠈⡁⠄⠁⠀⠀⠀⠿⠟⠻⠏⢹⣿⣿⣿⠆⣼⣿⣿⣿⣿⠿⠿⠿⣿⣿
⣿⣿⣿⡿⠟⣰⡿⠋⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⣝⣡⠬⣿⣯⣥⠋⠀⣀⣴⠾⢿
⡻⢻⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠈⠁⠠⠖⠒⠋⠁
⣿⢆⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿
⠛

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⢤⣄
⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⡴⢞⣫⡭⠤⢬⣭⣉⡛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣋⣩⣭⣭⣙⡓⠦⣄⡀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⣸⠁⠀⠀⣰⢏⡴⠋⣠⠖⣲⣒⠦⢌⠙⢦⡈⢳⡀⠀⠀⠀⠀⠀⡼⢋⡶⠋⣡⠤⠤⠤⢬⡉⠛⢮⡙⢦⠀⠀⠀⠘⣇
⠀⠀⠀⢀⡟⠀⠀⠀⡏⢸⠀⡜⠰⣟⠉⠉⣹⠆⢳⠀⢻⠀⣷⠀⠀⠀⠀⢸⡇⡟⠀⣜⠁⢰⡞⢛⡆⠈⢢⠀⢹⠈⣇⠀⠀⠀⢹⡄
⠀⠀⠀⢸⠇⠀⠀⠀⢿⠘⢧⡘⠦⣉⣙⣉⣉⡠⠋⢀⡼⢀⡟⠀⠀⠀⠀⠘⣇⠻⣄⠈⠢⣈⣙⣋⡠⠔⠃⣠⠟⣰⠇⠀⠀⠀⠈⣧
⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣄⣙⠲⠶⠼⢤⠤⠶⠖⣋⣵⠞⠁⠀⠀⠀⠀⠀⠘⠳⣬⣛⡲⠶⠶⠦⠶⠖⣛⣥⠞⠁⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠁⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿
⠀⠀⢸⡯⠭⠭⠶⠒⠒⠒⠒⠒⠒⣶⣾⡷⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⢩⡟⣿⡟⢿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢧⣧⣧⡾⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠘⢧⣭⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠙⠶⠖⠒⠒⠒⠒⠒⠒⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⣤⠀⠀⡄⢠⠀⣠⠀⠠⠀⡄⢠⡀⢠⠀⠤⠀⡴⢠⠀⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠
⠀⠀⠀⡐⠘⣆⠀⣇⣹⠄⢣⡀⡀⢸⣇⢰⠇⢸⠛⣠⠀⡟⠃⠘⠆⢀⡔⠀⠀⣇⡄⢸⠀⠆⢠⣈⠰⠀⡇⠰⣘⠀⡇⢘⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁
⠀⠀⠀⢰⡂⢰⠀⢰⠂⠀⡔⠀⣄⡠⠂⠀⡄⠀⠀⠴⡄⠰⡖⠀⠦⡀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⢀⣀⢀⠀⠀⢀
⠀⠀⠀⠸⡁⢸⡀⢸⡀⠄⡇⠀⣏⠑⣄⠀⠅⢠⠀⡄⠙⠀⣇⠀⠀⠹⡇⠀⠀⠀⠁⠀⠀⣳⠈⡛⣄⠨⠄⢈⠸⡀⡇⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⡔⠀⢢⡀⠰⢀⠀⡀⠀⢠⠀⢰⢀⡆⠠⣀⠆⠀⢰⠐⠀⡆⠀⠆⠀⠀⠀⡀⢀⣀⡀⢀⢀⠀⢀⣀⠀⡀⠠⡀
⠀⠀⠀⠱⠀⠘⠁⠸⠀⠀⠡⢀⠸⠀⠠⠈⠄⠠⡀⠇⠀⠸⠀⠀⠣⠠⠀⠀⠀⠀⠆⢸⠠⠇⠠⠰⠀⠨⠀⢌⠆⠸⠄⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⡀⠐⠀⠰⡀⣾⣀⠃⠀⢦⠀⠀⠲⣀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⣠⠀⢀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠏⠀⠤⠀⠧⠄⠀⠧⠀⠠⠥⠤⠀⠀⠀⠀⠀⠀⠀⠟⠀⠘⠁⠏⠀⠌⠄⠈⡇⠀⠮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⢰⠀⠀⠀⡄⠀⠀⢀⠀⠀⢀⠰⠀⠀⡀⠀⠀⠀⢠⠀⠀⠄⡀⠀⢀⠠⡀⠀⠀⠄
⠀⠀⠀⠀⠀⢸⠸⠀⠀⢨⡀⠀⢠⣎⡀⠀⡀⠓⠀⠀⢼⠆⠀⡀⠹⠀⠘⣅⡇⠀⠀⡆⠀⠀⡈⡳⠀⢈⡴⠃⠀⠇⠸

⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠝⠀⠸⠀⠀⣦⣀⠀⠀⠀⠀⢶⢃⠄⢀⠊⡠⡄⢂⠀⠻⣝⠀⠰⠇⡐⢁⠀⠀⠾⠂⠈⡆
⠀⠀⠀⠀⢹⡀⠰⠀⢰⠀⠐⠂⠀⠐⠀⠀⠃⠀⠈⠉⠀⠳⠞⠿⠂⠘⢌⠓⠗⡢⠀⠶⠟⠀⠀⠎⠀⠳⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⡾⣿⠄⠀⠀⠀⠀⠀⠀⣰⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⡡⠟⠀⡀⠀⠰⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡓⠀⠀⠀⡠⠁⠐⡼⢸⡔⠊⣭⣀⡉⠙⣿⣿⣅⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠹⢐⣚⠀⢀⠀⠔⠁⠐⡀⠛⠻⢿⡶⣼⠛⠿⠃⢀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⢏⠠⠤⢄⠀⠄⠤⡖⠈⠀⡁⢹⠑⡀⠀⢨⠀⠀⣰⠿⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠩⣡⡤⢾⡆⣡⡀⠀⣧⠓⠈⠁⠃⠈⠳⠆⡘⠀⠠⠷⢾⣯⡻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⡇⠉⢓⢾⣿⠿⠆⠤⠅⡀⠠⡄⠀⠂⠄⠀⠑⠄⠀⢀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠦⠳⢇⠀⢉⠊⠀⠸⣶⢠⡔⠈⡢⠀⢶⣿⣃⠒⠐⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⡼⠢⢠⠤⠠⠊⢉⠇⠀⡠⠗⠒⠅⣰⣠⠉⡲⠀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠆⣐⣦⢀⡀⠀⣤⠈⠱⠎⠠⡄⣤⣤⠌⠖⢉⠣⢠⡏⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠼⠇⠀⢁⣤⣤⠀⠀⠃⠀⠀⢀⣄⠀⢰⠃⢀⠸⡇⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣏⣀⣈⣂⣁⣀⣀⣠⣐⣂⣘⣋⣀⣈⣀⣈⣀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⣠⣤⣄⠀⠀⠈⠿⣿⡿⠃⠀⠀⡸⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣀⠀⠐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠠⠤⠀⠀⠀⠶⠿⠷⠄⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⢲⢿⣿⡇⠀⠃⠉⠃⠀⠀⠂⠀⠀⠐⠃
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣿⠇⢀⡀
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠏⠀⠀⢇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠚⠂⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢠⣿
⠴⠁⠀⠀⠀⠘⠂⠀⠀⠀⠘⠓⣀⣀⣀⠀⣀⠤⠄⠤⣀⠀⠀⠑⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣿⠟
⠂⠒⠒⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢀⡀⣀⡀⢐⡤⢤⠀⠀⠀⠀⠀⠀⠀⠂⠠⢷⣶⣾⣿⣶⣾⣿⣿⡷⠊
⡀⠀⠀⠐⠀⡀⠀⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⢿⣿⣿
⠛⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡄⠠⠖⠁⠀⠈⢩⣿⠛⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢘⠋
⠀⠀⠀⣀⠐⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⡷⠤⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠉⠻⠦⠀⠀⠀⠀⠠⠤⢄⣿⣿⣇⠀⣿⣀⣠⣌⠀⠈⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠤⠿⢿⣿⣼⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⣅⠀⠀⡰⠁⠀⡀
⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡉⠁⠁⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠐⠀⠋
⠀⠁⣀⣧⠀⠀⠀⢀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠰⢂⣨⡽⠋⠉⠛⢧⠈⠀⠀⠀⠒⠤⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠄
⠀⠀⠀⠈⠋⠀⡄⠀⠀⠀⠀⠀⠀⠁⠒⠒⠂⢩⠊⠀⠐⠁⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠤⠴⣦⣤⣤⠀⠀⠀⠀⠀⠀⢀
⠐⠂⠀⠀⠀⠀⠀⠀⠐⢄⣀⡄⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠉⠉⠈⠓⠲⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⢈⡀⠀⡀⠀⠀⠀⠈⠙⠈⠈⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢳⡀⠸⣇⣀⣠⣴⠿
⣀⠀⠀⠬⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢷⣶⡀⠀⠀⣸⠂⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠸⣷⣾⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⢿⣷⣄⠰⠁⠀⠀⣠⣿⡷⠂⠀⠀⠀⠀⠀⠀⢰⠟⡻⢧⡀⠀⠀⠁
⣀⠀⠐⠀⠐⠀⠀⢀⠀⠀⠀⢀⠐⠀⠈⠀⠀⠈⠓⠦⠀⠀⠘⢿⣿⣶⢾⠀⣾⣿⢟⠀⠒⠀⠀⠀⠀⠈⢀⠈⠀⠀⠀⠙⠒⠤⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠰⠀⠀⡂⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣤⣌⢋⡰⢤⢻⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠁⠀⠀⠠⠒⠂⠈⠉⠝⠛⠛⢻⡿⢿⠁⣡⡐⣽⣿⣅⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠌⠗⠀⠀⠂⠀⠀⢀⠀⠈⠁⠤⠵⠀⢀⠀⡈⠁⠈⠁⡈⡁⠸⠬⠇⠀⠀⠀⠀⢨⠶
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⣤⠐⢠⡔⡆⠀⠀⠀⢠⡀⠀⠀⠠⠀⠀⠠⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⠀⢐⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣑⢄⠀⠀⠀⠣⠄⠀⠨⣀
⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠁⠀⠀⠀⠇⠘⠄⠀⠀⠀⠀⡿⠹⠯⠀⠀⠂⠀⠀⠈⠢⡠⠤⡠⠂⠀⠀⡆⠅⠠⢐⠉⠤
⠀⠀⠨⠠⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⡄⢤⢀⡀⡄⢤⢀⡀⡄⢀⠀⠀⠀⠰⠇⠀⠐⠛⠃⠀⠐⡁⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⣗⡂⠀⠠⠛⠂
⠀⠀⠨⠨⠁⢀⠀⠀⠀⢀⡁⣈⣁⣀⣀⣀⠀⢀⠛⡀⢸⢀⠛⡀⢸⢀⡛⡄⠀⠀⠂⢰⠀⠐⠀⡉⠀⠿⠀⠠⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⢰⣆
⠀⠐⠂⠒⠂⠐⠀⠀⠀⢠⠧⠤⠤⠤⠤⠼⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⢸⠀⣿⠅⣔⠄⠀⠀⠀⠛⠃⠈⠀⠀⠀⠀⠀⠀⠃⠁⠸⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢘⡟⠛⢻⣿⣿⣿⠀⣯⡇⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⢸⠀⠰⠀⠙⠀⠀⠀⠄⠀⠀⠀⣤⣤⢤⢠⢠⣤⣤⣄⣤⣤
⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⢀⠀⠀⡀⠄⠀⠀⡁⢡⢠⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⡁⢸⠀⠠⡤⠀⠀⠰⠉⣉⠱⠀⠀⠀⢀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⡅⢈⡈⠀⢀⠀⣀⠀⠀⢀⢀⠀⠀⡁⡀⠀⠈⠀⠀⠀⠘⢤⣡⠴⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⣀⡀
⠀⠠⠠⠄⠤⠠⠤⠀⠀⠀⠀⠀⠀⠐⡁⡀⠀⡀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠒⠂⠐⠂⠐⠓⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢄⠀⠀⠄⠀⠁⠀⠀⢐⣿⠄
⠀⠰⠒⠆⠆⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⡀⠀⠀⠀⠀⢀⠀⠀⢐⣠⡐
⠀⠀⠶⠶⣶⡦⠀⠀⠀⠀⠀⠞⠀⠰⠀⠚⠀⠤⠠⠀⠀⠠⠀⠤⠀⠀⠀⠀⠰⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠉⠀⠀⠐⠿⠂⠘⠀⠀⠨⠫⠠

⠀⠀⠀⢀⢀⢠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦
⠀⠀⠘⢩⣿⡿⡾⠋⠃⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡏⡯⠁⠰⢶⡠⢶
⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⠂⠚⠐⠀⠀⠞⠐⠉⠉⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡠⢂⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄

⢀⣀⡀⣀⡀⣀⣀⢀⢀⡀⣀⢀⢀⣀⢀⣀⣀⠀⣀⠀⢀⡀⣀⢀⣀⣀⠀⣀⣀⢀⡀⣀⣀⢀⣀⠀⢀⣀⢀⡀⣀
⣧⡻⣿⡎⣾⠟⢱⣿⢸⡇⢿⣬⣼⠟⣬⡟⢃⣼⣿⣤⡟⠸⠿⢈⡄⢡⡾⠿⣦⠸⠇⣿⡅⠢⠐⣿⠸⡟⣌⠡⣿
⣿⠟⢴⡆⣿⠸⠶⣬⣸⡷⠶⡶⢶⡶⠮⠶⣶⠮⠽⠆⣶⢇⣽⠘⣿⢸⢡⡇⣿⢰⡟⢶⠸⢟⡂⣤⡜⡟⢸⣿⣶
⣵⠶⠿⣶⡔⣧⣠⡇⣴⣶⡜⣟⠳⡔⣧⣼⠄⣷⢸⣆⣉⣉⣿⢠⣦⣿⢠⡥⢥⢌⣙⣩⡜⣏⣡⢘⣧⢻⣦⡐⠶
⠇⠾⠷⠈⠿⠸⠿⠠⠭⠭⠄⠿⠀⠻⠤⠶⠾⠋⠤⠄⠻⠇⠶⠶⠆⠆⠶⠇⠿⠸⠏⠭⠹⠄⠯⠰⠶⠮⠭⠥⠶

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡆⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⢀⣤⡾⢛⣴⣶⣶⡔⣀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠘⢤⣯⡀⠈⡻⠿⢋⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡟⠀⠀⠀⡂⢸⣯⡁⠀⠙⠛⡏⠤⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⣦⡇⠀⠀⠑⢄⠻⢿⣶⣦⡴⠂⠀⠸⣷⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣄⡙⡅⠀⠀⠀⣼⠗⢀⣉⠝⠀⠀⢀⠀⣷⡞⠀⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣽⣠⠀⠀⠘⢿⡇⣀⣔⣺⡿⠥⢿⣇⢄⠀⠀⢸⡼⠋⠀⠀⠈⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⠚⢉⠥⠖⢲⣖⣚⠿⣋⣾⣽⣟⢐⣿⣿⣿⢓⣄⢈⡧⢠⣄⠀⠀⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠒⠙⠛⢦⣤⣼⣯⠳⣦⣤⣈⡉⠩⠗⠛⠉⣉⣭⡔⢯⣿⡏⠣⡹⣦⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣷⡄⠀⠀⢸⣾⣯⠻⣷⣦⣙⠻⠔⢲⣄⢀⡴⠿⣽⣷⣜⣿⡀⢀⣸⢈⣷⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⠀⠀⣿⣿⡸⣿⣦⣬⡼⢷⣍⣶⣆⣀⣶⣛⡽⣋⣿⣷⣾⣿⣿⣏⣩⣩⣽⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⠆⠀⢻⣼⣓⢬⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣷⡽⣿⠏⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⣼⣿⣯⣿⣿⣿⣿⣿⢋⡿⣥⢿⣿⣿⣯⣾⣟⣸⣟⣿⢹⣟⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡤⠚⢱⢣⣿⣿⣿⣿⡜⣏⢾⢿⣵⣻⣿⡏⣰⣷⣿⣼⣏⣿⣿⣿⣿⣿⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢈⢨⣿⣿⣿⣿⣿⠿⣯⣷⣭⣿⣿⣿⢰⣿⣿⣧⣿⣿⡟⠻⣿⣿⣿⣵⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢘⣤⣿⣿⣿⡿⢃⣴⣨⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠀⢸⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⠋⣠⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠊⠁⣠⠿⡛⠛⠛⠻⠿⣿⣿⣿⢁⣾⣿⣿⣿⠟⠛⢫⣤⠉⣿⡄⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⠴⠁⠔⠁⠀⠀⠀⠀⠀⠙⠷⢈⣛⣛⡙⠀⠀⠀⠀⠀⠀⠻⣀⡀⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⠀⠀⠈⢻⠋⢸⣧⣼⡇⢸⣍⡁⠀⠀⢻⣏⣻⠜⣯⣉⠀⡼⣷⠀⣿⠙⣷⢸⣯⣉⢸⣯⣹⡇⠀⠀⠀⣀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠛⠁⠀⠀⠀⣸⠀⢸⡇⢸⡇⣸⡀⡀⠀⠀⣿⡈⣧⢘⣇⢀⢠⡿⢺⡆⣻⣀⡿⢸⣇⢀⢸⡇⢹⡄⠀⠀⠈⠛⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠁⠈⠉⠉⠀⠀⠉⠀⠈⠀⠉⠉⠉⠀⠀⠁⠉⠉⠀⠈⠉⠉⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠿⡶⠂⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀
⠀⠀⣤⡀⠀⠀⠀⠀⠀⢰⣆⣀⣀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠐⠈⠁⡀⠀⢸⠟⢀⣀⡀
⠀⠸⢿⠇⠉⠉⠈⠀⢠⠀⠉⠉⠁⠈⣟⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷⢬⠃⠘⠿⠿⠆
⠀⠀⠈⡀⢀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣤⣀⣀⣚⣿⣫⣿⠤⣂⣠⣤⣤⣿⣴
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠙⠦⠀⠀⠈⠑⠆⠀⠀⠠⠴⠿⠟⠛⠋⠉⠉⠱⠿⠿⠟⠉⠠⠾⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠄
⠀⠀⠀⢸⠇⠀⠀⠄⠂⣿⠆⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⡤⠿⢿⡿⠆
⠀⢠⣿⡄⠈⠉⠙⠛⠂⢏⠙⠿⡿⠗⡑⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡒⠒⡠⠄⣾⣴⣿⣦⣀⣠⣤⣤⠤⢤⢤⠶⠶⡶⠶⣤
⠀⢠⣼⣴⣤⣤⣤⣤⣶⣶⣶⣤⣧⣘⣛⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣭⣭⣭⣭⣿⣿⣿⣿⢿⢿⣷⡤⡤⣶⣾⣛⣟⣛⠿⠛
⠀⢸⣿⡿⠿⠿⠻⠫⠻⠻⠝⠝⠝⠝⠭⠯⠫⠻⠻⠳⠶⣤⡀⠀⠀⠸⠿⠿⠟⠟⠝⠝⠵⠱⠣⠫⠎⠎⠜⠔⠵⠱⠫⠫⠟⠗⠟

⠀⣠⡄⠀⠀⠀⠀⢀⡀⠒⠂⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠊⠀⠁⠤⡀
⢠⣿⣿⠌⠁⠁⠀⠄⠀⠀⢰⣿⣿⠀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢢⣶⣿⣷⣄⠀⠀⠘⣧⣤⣄
⠀⣹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣏⢉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠉⠻⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⠻⠻⠻⠻⣿⣿⠉⠉⠉⠉⠸⠿⠷⠀⠤⠤⣤⡶⠶⢖⢶⠆⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠓⠁⠁⠀⠀⠀⠈⠉⠈⠈⠈⠈⠀⠀⠀⠁⠁⠁⠁⠈⠈⠈⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⣠⣾⣶⣄⣀⣀⣤⣾⠛⣧⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣠⣄⣀⠀⠀⠇⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⡇⠀⠀⡀⠀⢀⣿⣿⣆⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠿⠇⣻⣿⣿⣿⣿⡤⢤⡿
⠀⠈⠉⢻⡏⢳⣾⣾⣿⣶⣿⣶⡇⣴⣾⣿⣆⠘⠻⡟⠟⠀⠀⠀⠀⡉⠉⠁⠩⠌⠉⠉⣉⣉⠉⣙⣿⣶⠾⣿⢿⣿⣿⣿⣶⣶⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⣿⣿⣿⣿⣦⣶⣷⣤⣦⡀⠀⠀⣟⣢⢤⢾⡻⡻⡝⢝⢯⢫⡻⡹⡝⢝⢿⢻⡳⡿⣿⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠈⠀⠁⠁⠉⠈⠈⠀⠁⠁⠉⠈⠈⠀⠁⠁⠉⠈⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⠈⠈⣀⠤⠤⠀⠠⠤⣀⠀⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠤⠤⠀⠐⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠉⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠠⠤⠤⠔⠒⠉⠀⠀⠀⣀⣀⠠⠄⠴⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⢀⠀⣀⠄⠤⠄⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠓⢤⡀⠄⡀⠀⠀⠀⠀⠀⠉⢶⠂⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⠤⣀
⠀⠀⠀⠀⠀⠜⠀⠀⡠⠒⠒⠂⢌⠂⢄⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠒⠈⠀⠀⢀⡤⢹⠂
⠀⠀⠀⠀⢸⠀⠀⠰⠁⠀⠀⠀⠀⢣⠀⠙⠢⣄⠀⠀⠀⠸⠀⠀⠀⠂⠀⠀⠀⢀⣀⡀⠠⠤⠄⠰⠂⠒⠂⠈⠉⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠀⠀⢸
⠀⠀⠀⠀⠘⡄⠀⠸⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠑⠢⠤⠇⠒⠶⠖⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠘⢄⡀⠘⠢⠤⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠄⢀⣀⢀⢀⡀⠤⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠙⠓⠤⠌⣑⡢⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡽⠋⢠
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠀⢀⠔⠁⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⢀⡀⠀⠀⠈⡄⠀⠀⠀⠀⢀⡀⠤⠒⠉⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡒⠸⠦⠤⠒⢎⠉⠁⠒⠂⠰⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠂⠠⠤⠄⣀⣀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⢀⠅⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠐⠒⠂⠉⠉⢀⣁⠀⠀⠀⠀⢃⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠼⠦⠊





⣾⣶⣶⣶⣶⡾⣷⣾⣿⡿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⠾⡷⠶⠶⠶⠶⣶⡾⠿⠾⠾⠷⠿⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⡌⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠚⠑⠀⠒⠋⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⠌⠛⠓⠀⠘⠓⠒⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠘⠳⣄⡀⠛⠀⢻⣧⠀⡤⠐⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢀⣤⠀⠀⠀⠛⠀⢀⡼⠿⠖⠀⠸⠿⢷⠀⠀⠀⠀⣷⠀⠂⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡁⠀⠀⠉⠠⣀⣐⣶⣶⣾⣷⠶⢶⣶⠶⢶⣾⣶⣶⣶⣀⠠⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⡁⠠⣈⣵⠶⠟⠛⠉⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⡌⠙⠻⢷⣮⣁⠀⠉⠁⠈⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠀⡠⠂⣤⡾⠋⠁⠀⢀⠀⠀⢈⣀⣤⣦⣤⣤⣌⣉⣁⡀⠁⣀⠀⢀⠉⠻⣷⣤⠀⠀⠀⠿⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⣴⡾⠋⠀⢀⡠⢀⣹⣶⠾⠛⠛⠉⠉⠉⠉⠉⠛⠛⠿⣿⣦⣼⣃⡀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠊⠉⠁⠄⢠⡾⠋⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠙⠻⢿⣷⡆⢀⠀⠀⠙⣷⡀⠂⠘⠛⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⠊⣰⠟⠁⠠⠀⢻⣶⡟⠁⠀⠀⣀⣴⣾⠿⠿⠛⠛⠛⠿⢿⣿⣶⣦⡀⠀⠈⠻⣿⣦⠀⡄⠀⠈⢿⡄⠀⠀⢀⣜⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠒⠈⢁⠈⣠⡟⠀⠀⠀⣳⣿⠏⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠈⢿⣷⡀⠀⠂⠈⣿⡆⠀⠚⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣀⠀⠈⣠⣿⠀⠀⢠⣼⣿⠃⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠸⣿⡇⠀⠀⠀⢸⣇⠐⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠂⠀⣿⡏⠀⠀⢀⣿⡟⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⡀⠀⢰⣿⠃⠀⠲⢏⡀
⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⡇⣿⡇⠀⠀⢈⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠤⠤⠤⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⡄⠀⠀⠈⣳⠄
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⡇⣿⡇⠀⠘⠛⣿⣇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠰⢾⠃
⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠁⣿⣧⠀⠀⠉⢻⣿⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⣼⣿⡀⠀⠀⢸⣿⠃⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠘⠷⣄⡀⠀⠘⣿⡀⠀⠀⠘⣿⡆⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⢰⣿⠟⠓⠀⠀⣼⡏⢀⠀⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⢠⢿⣧⡀⠈⢀⣸⣿⣦⡀⠀⠀⠛⢿⣷⣤⣤⣀⣀⣀⣀⣀⣤⣴⣾⠟⠋⠀⠀⢀⣴⡿⢧⠀⠋⠀⣸⡿⢀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⡈⠸⢻⣷⡄⠀⠁⣠⢿⣷⣦⡀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⣠⣿⣏⠑⠀⠀⠀⣰⡿⠁⠈⢠⣤⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠁⠀⠃⡘⢿⣦⡀⠀⠈⠉⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠿⣥⠈⠓⠄⢀⣼⠟⢀⠆⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⣤⠘⢀⠙⠿⣦⣀⠀⠀⠀⠈⠙⠿⠛⣿⢷⣶⠶⣶⣿⠟⠛⢛⡿⠉⠤⠀⠀⢀⣠⣴⠟⢁⠔⠉⢰⡦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠐⠲⣌⠛⠿⣦⣤⣄⣠⡀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⣀⣠⣶⡾⠟⢋⡥⠲⣀⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⠀⠀⠉⠢⠀⢉⡙⠛⠿⠿⢶⣶⣶⣶⣶⡶⠶⠶⠾⠟⣛⣋⡡⠤⢈⠁⠀⠀⠹⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠓⢾⡆⠀⠈⢁⡄⠒⠒⠂⠀⠀⠀⠀⠀⠒⠒⠀⠀⢉⡁⠀⠀⢸⠓⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⠄⠻⣇⠀⢀⡀⣶⡄⠀⠀⣸⣆⠀⠀⢀⡘⠛⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠁⢸⠟⠶⠂⢹⡏⠑⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⢀⣀⣀⠀⠠⣾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡌⢉⣉⠁⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠓⠶⠶⠶⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⣤⡀⠀⠀⠀⠀⠠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠉⠉⠉⠉⠁⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡉⠀⠙⠂⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡶⠦⠤⠤⠴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⠀⢠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠀⠸⣷⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢠⣿⡆⢰⡿⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣧⡞⠙⣧⡼⠃⠙⢿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣦⣌⣉⣀⠀⠘⠃⠀⣀⣠⠷⠙⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣤⣄⡈⠉⠉⠉⠀⠉⠉⠉⢁⣠⡴⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠉⠉⠛⠛⠓⠒⠚⠛⠛⠉⠁⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣬⡛⠛⠛⠒⠀⠀⠀⠀⠀⠐⠛⠛⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠶⠶⠶⠶⠶⠶⠊⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⢀⣤⣄⠀⠀⠉⠛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠉⠀⢠⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⣩⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠾⠟⠋⠀⠀⠀⠘⣧⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⠏⠹⡇⢸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡉⢄⠀⢷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠻⣿
⠀⣶⠀⠀⠀⠀⠀⠻⣼⢦⠘⡇⠀⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠀⢸⣿⣇⠈⠉⢛⣫⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠀⠘⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠀⠉⢻⣿⣿⣿⣿⡆⠀⢿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠱⢦⣀⣠⣤⠀⠀⠈⠛⠿⣿⣿⣇⡜⡘⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠩⠿⢿⣶⣶⡇⠀⠀⠀⠙⢿⡼⣷⢿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣹⣤⣿⠿⡥⠃⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣈⠻⣷⣦⣤⣴⣿⣿⠟⠁⡆⠀⠀⠀⠀⣰⣿⣿⣿⡇⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⡇⠀⢰⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣦⡀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡴⠛⠿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣌⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢻⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡀⠀⠀⠠⢁⣤⠀⠄
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⢸⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠌⠁⠉⠀⠈⠁⠉⢄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠁⠘⠃⢄⠀⠀⠀⠀⢀⠘⠁⠱⣿⡂⠀⠁⠢⠀⠀⠀⠀⠀⢀⠔⠋⠁⠁⠁⠐⠂⠶⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⡆⠀⠀⠈⠀⠀⠀⠈⠑⠂⠂⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⡀⠀⠀⠄⠉⠀⠀⡀⠀⠀⠀⠀⠣⢀⠀⠀⠐⡁⠀⣀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠣⠓⠙⠿⣿⣿⡿⠋⠺⠆⠀⠀⠀⠀⠀⠉⠃⠂⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣤⠀⠀⠈⠀⠈⠁⠀⠀⣠⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠡⡆
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠐⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠷⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣻⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣀⡼⣿⣹⣿⣿⡆⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡝⣯⡇⠈⢻⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠤⠤⠐⠒⠂⠉⠉⠉⠉⠐⠒⠒⠤⢄⣀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠃
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠒⡖⠉⢢⠄⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢇⠀⡸⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⠐⠒⠒⠒⠀⠒⠒⠒⢿⣿⣿⣿⣿⡿⠂⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡠⡜⢄⠉⣇⣀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡠⠚⠢⢠⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠳⢘⡌⠢⡨⠊⠀⠀⠰⠝⠊⢀⠀⠀⠀⠊⠈⢃⡀⠤⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡭⡢⡀⠙⠢⠅⢀⡴⢊⠁⠀⠰⠇⠀⠈⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠰⡹⠁⠹⠂
⠀⠀⠀⡖⠢⡀⠘⢄⡚⡀⠀⢀⠔⠉⠀⠣⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⢀⡠⠐⠁⠀⠀⠀⠛⠃⢀
⠀⠀⠀⠘⢄⠑⠄⡄⠀⠀⠘⠀⠀⠀⠀⠀⣠⡾⢑⢄⠀⠈⠐⠁⠀⠐⠂⠁⠀⠎⠐⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⢯⣲⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠞⢛⣼⠃⡐⠀⢀⠀⡰⡡⢀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠠⡒⠁⠀⠀⠀⠉⢤⡾⠋⢉⠔⠀⠀⠈⢄⣔⢲⠇⠀⠂⠂⠢⡀⢀⠾⠆⠀⠞⢂⠄
⠀⠀⠀⠀⡀⢄⡀⠀⠈⠈⠁⠀⠀⢀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⢀
⠀⠀⡄⠊⡤⠊⠑⡀⠀⠀⠀⠀⠒⠀⠆⠀⠀⠀⠰⡟⠋⡰⠀⠀⠈⢇⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⢎⠀⠀⠅⠅⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⣵⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡁
⠀⠀⠀⣊⡇⠀⠀⠀⠀⢀⠊⠀⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠠⠒⢀⠀⠀⠒⠀⠀⠠⡀⠀⠀⠀⡞⠂⠂
⠀⠀⠀⠀⠀⢶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠀⠀⠐⢄⣀⣶⣠⡔⠁⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠄⠄⠌⠍⡒⠀⠀⠀⠀⢀⠴⣗⢄⠀⠀⠀⠀⠀⠀⠀⠌⠍⢿⡇⠀⡃⠀⠀⠀⣀⣀⡀
⠀⠀⢠⢆⠀⢊⠈⠌⠀⠀⠀⠀⣰⡁⠀⠈⡪⠇⠀⠀⠄⠀⠀⠀⡂⠀⢺⣇⣀⡁⠀⠸⠛⠃⠉⢁
⠠⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⢠⢊⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⠀⠂
⠀⠀⠄⠆⠶⠲⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡄⢀⡤⠖⠋⠉⠀⢀⡠⠴⠒⠚⠛⠛⠛⠒⠀⠉⠛⢦⣄
⠀⠀⣀⢶⡒⠈⡷⠉⠀⢀⠀⠀⠈⠁⠀⠀⣀⣠⠤⠴⠒⠒⠀⢀⣀⣠⠽⢚⡥⣰⠃
⠀⠀⠉⢢⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡤⠶⠊⠉⠠⠒⣩⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣤⡤⢤⣤⣀
⠀⠀⣰⠃⠄⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⣠⡴⠞⠁⡌⣇⠀⠀⠀⠀⢀⣀⡠⠔⣉⠤⠒⠉⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⡴⠋⡙⠛⢶⡄
⠀⢰⠃⡜⠀⢠⠂⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢱⣹⠀⠀⣠⠞⠩⠎⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣀⡠⠀⠹⡄
⠀⡟⢠⡆⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⢷⡠⠔⠀⡇
⠀⡇⢸⡇⠀⢀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠆⠀⡇⢰⢻⠸⡀⠀⠀⠀⠀⠀⢈⣉⣉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⣠⠟⡾⠇⠀⣸⠃
⠀⣧⠀⠇⣠⠋⣠⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⢀⠓⢦⣄⣦⠤⣄⣀⠀⠈⠙⠲⢤⡀⠀⠉⠓⠶⠶⠾⣫⠀⡷⠴⠚⠁
⠀⢻⡀⠀⡏⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⣸⠁⠘⣇⣸⠰⠀⠀⣤⠀⠀⠉⠙⢦⡀⠀⢀⠙⣆⠐⠀⠀⠀⠊⠁⡔⡇
⠀⠘⣷⠀⠀⠙⢮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣰⠃⠀⠀⠈⢿⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⢸⡍⢱⡈⠀⠀⠀⢀⠄⡼⢡⡇
⠀⠀⠸⣧⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢞⡵⠃⠀⠀⠀⠀⢸⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠼⠁⠀⠀⠂⣡⠞⢁⣾⠁
⠀⠀⠀⠈⠳⣄⡙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡤⠎⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠒⠉⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠈⠙⠓⠺⠷⠦⢄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠋⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠤⠤⠖⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠙⠒⠤⣄⡀⠀⠀⣀⣠⣷⣤⠤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠤⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⣀⠀⠀⠀⠀⠀⢀⡨⢆⣀⢎⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠰⡄⠀⠀⠀⠀⢡⠈⠧⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⡆⠣⢄⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠙⠒⠶⡶⠜⣦⠤⠴⠚⠉⢈⠀⠀⠀⠀⠀⠀⠸⣄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠲⡄⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⠤⠿⠗⢒⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢑⣠⠀⡀⠀⣀⣠⣼⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠞⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠾⢦⢰⣴⡉⡿⠾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⣤⣄⣀⣤⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡤⡀⠀⣏⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠜⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠰⠩⠽

⣿⣿⡭⡄⠀⢸⣿⣿⠇⠀⠁⠈⠁⡰⣤⣀⢈⢿⣿⣿⡄⠀⠀⠀⠀⠒⠦⣀⠀⣤⠃⠼⠄⠠⡀⠀⡋⠀⠀⠀⢠⠏⣸⠏⠀⡿⢁⠀⣹
⣿⣿⢰⠅⠠⣿⡈⣿⠀⠀⠀⠀⠀⢀⠨⡿⣧⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠑⢿⡞⠀⠀⠈⣿⢀⡧⠠⠀⠀⣾⡐⣼⠄⢣⡦⡴⠚⢯
⣿⣿⠷⠂⠀⣿⢡⡏⠀⠀⠀⠀⠀⡀⠁⠐⢬⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣼⠟⠒⢶⡾⣿⡾⣠⠠⠤⠄⣿⣿⣿⡄⢢⡵⡖⢀⡄
⣿⣿⣿⣿⣦⣿⣿⣷⠄⠒⠀⠀⠀⠙⢦⡀⣤⣾⠛⣷⣟⠻⣇⠀⠀⠀⠀⣰⡾⣏⠁⠀⠈⢁⣟⣟⣿⡟⠋⠉⢻⣿⣟⠙⡆⢱⡧⠙⠑
⣿⣯⡀⠀⠀⢸⠶⠀⠀⠀⠀⠀⠀⠀⠀⡙⠚⠃⠀⠘⣿⣄⣿⣿⣦⡀⠀⣠⣋⠀⠀⣀⠙⢧⣓⣮⣿⣷⣄⠤⣬⣯⣿⣶⡇⢀⠗⢠⣿
⣿⣿⣿⡥⠭⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣴⣄⣤⠙⠛⢿⣿⣿⣷⣄⠀⠹⣞⠀⠈⠀⠼⣵⢹⣯⣿⣍⣙⣿⠁⣰⣿⠡⢸⡆⢸⣿
⣿⣿⣾⡧⠀⢸⣶⣶⣶⣶⣶⡶⠶⠶⣶⣾⣿⣿⣿⣷⡄⢸⣿⣿⣿⣿⠿⠿⣶⣾⣿⠅⠰⣿⡟⢀⠛⠉⠉⠉⡁⠙⢾⣿⣏⢸⡄⠀⢸
⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⡷⠔⠚⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠐⠶⢶⣿⣿⣇⣦⡿⢧⡟⢀⣔⠒⢦⣴⡷⠀⢻⣿⣴⣥⠀⠸
⣿⣿⣿⡇⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣟⣛⢿⣿⣿⣿⣿⣭⣴⣶⠞⠛⡿⣿⣍⢿⡟⠀⣾⡛⣷⣆⠙⠀⠀⠘⣿⣻⣄
⣿⣿⣿⡏⠀⢸⣿⣿⣿⡄⡇⠀⠀⠀⠀⠆⠀⢸⡿⣿⣿⣯⣿⡿⢿⡟⠛⠛⠀⣤⠀⣮⣿⡌⠃⢹⡟⢹⣿⠉⠛⠆⠀⠀⠘⣿⣿⣄⣤
⣿⣿⣿⡇⠀⢘⣿⢿⠏⠣⠃⠀⠈⠁⢰⣾⣎⢸⡆⢸⣟⣿⠻⠇⡤⠖⡇⠀⠠⡧⠈⠳⠡⡇⢹⣸⢀⠘⠋⠀⠀⣀⠤⠙⣿⡿⣿⣷⣾
⣿⣿⣿⡷⠀⣈⣿⡷⠀⡇⡤⠀⢀⣄⣼⠍⠙⠛⢳⣶⣿⣿⡶⢰⢳⢼⣳⣴⡀⠐⡖⡀⠀⠳⣼⠟⠢⠶⠶⠞⢏⠙⣶⣤⢹⣿⣿⣼⡇
⣿⣿⣿⡏⠁⢸⠏⠄⠀⡷⡃⠀⠀⠈⣁⣠⢰⣾⡛⠉⠛⣿⣧⣄⣡⣼⣿⡿⣽⣶⣿⠛⠁⢠⣄⡀⠀⠐⠄⢧⠈⠰⠃⠀⣸⣿⣯⡰⠄
⣸⣿⣿⢃⠀⠀⣀⠀⣆⢸⠈⠑⠄⠌⠁⢹⡏⣿⣶⡦⣛⣛⣻⣿⢿⡿⠿⠿⠿⠿⢣⣠⣴⣾⠻⡇⠀⠀⠘⢿⣧⠀⠀⢼⣿⣿⣿⣿⡄
⣿⣿⣳⣻⠴⠊⠀⡀⠠⣾⣦⠀⡐⠀⠊⠿⡇⠸⣿⣿⣯⣍⣟⡁⠀⣈⠗⠀⣀⡴⢾⣿⠙⢿⠀⡇⢠⠀⠀⠀⠀⠂⣀⡌⣿⣿⣿⡿⣇
⣿⡏⠀⠀⠀⠀⣦⠁⠀⠈⠛⠀⡟⠻⡿⣿⣿⠀⢹⡟⢶⣟⣿⠟⣻⣷⣴⣟⣻⣷⢸⡟⠀⣿⠀⠹⡄⠀⠐⠀⣦⡞⡏⣸⣿⢸⣿⡿⠟
⠋⠀⢀⣠⣴⠶⠛⠀⢀⣸⣿⠀⣧⢀⡎⣿⣿⣇⠀⣿⣻⡟⠉⠀⠀⠀⠈⠹⣿⡇⢸⡇⠀⢛⠐⣯⣷⠀⢠⣴⠃⠀⠀⣿⣿⠨⣿⣄⣰
⣶⢋⠭⣿⢁⡄⠀⡀⠀⠈⢿⣄⢹⣿⣿⡇⣻⣿⡄⢹⣿⢅⡀⠀⠀⡀⢀⡀⣹⣾⣾⠀⠀⣸⡆⢸⣻⣧⠈⠁⠀⠀⢠⣿⣿⢠⣿⣿⣿
⠀⠀⠀⠰⠄⠃⡀⠀⠀⢳⣌⣉⣩⣁⠈⠹⠉⣿⡿⠘⡃⠈⠁⠀⢘⢹⣆⠛⣮⡯⡿⢀⣼⣿⣧⠀⠿⢿⣆⠀⠁⠀⣸⣯⣻⢲⣿⣿⣿
⣤⡇⣦⢀⣀⠀⠀⠀⣀⣾⠉⠛⢻⣿⣟⡃⢸⣾⢃⡄⡿⢠⡀⠀⡾⠀⠿⣿⣻⣿⣷⣿⣿⡟⣿⡄⠐⣿⣿⡄⠀⢠⣿⣿⣿⠘⣽⣿
⣿⠷⢤⣴⢡⠈⡛⠀⣀⣠⡀⠀⠀⢻⣏⠷⡮⠏⢻⣿⡃⢀⡿⠛⠳⠶⠶⠿⠿⢋⣋⣻⣿⡇⠿⡁⠀⣿⡿⣷⡀⠸⣿⣿⣿⣼⣿⣯
⠶⠚⠋⠉⢭⣉⠙⠓⠶⠀⡙⠂⠀⣈⢩⣿⣿⠀⠀⢹⡤⠛⠀⠀⠀⠀⠰⠀⠀⠀⠁⠉⣰⣷⠀⠀⣰⠏⠀⢻⡇⠀⣬⣾⣿⣵⣿⣧
⠷⠄⣀⣶⢶⠈⢧⡀⠀⠐⢸⣷⡶⠀⠀⢈⡿⣣⣤⣸⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠙⢻⣇⠰⡟⠀⠀⠀⣿⡈⢹⣿⣿⡏⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⢧⡤⠴⠶⠤⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠦⢤⡼⠇
⠀⠀⠀⣧⣤⣤⡤⣤⣤⣤⣈⣉⡙⠲⠦⣄⡀⠀⠀⣿⠀⠀⢀⣠⠴⠖⢋⣉⣁⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠘⠷⠶⠒⠒⠒⠲⠿⠿⠿⠷⢾⣿⣶⣄⣿⣠⣶⣿⡷⠾⠿⠿⠷⠖⠒⠒⠒⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⢠⣾⡏⣹⡟⣻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣿⣶⣾⣷⣿⣷⣿⣿⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⠿⠿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠚⠉⠉⠉⠛⠓⠲⢦⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⢷⣀⣠⣶⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣛⣻⡿⠀⠀⠀⠀⣾⣿⠿⢿⣿⣿⣆⠀⠀⢸⡆⠀⠙⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣼⠈⠛⠿⠛⠁⢤⣤⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⢸⠇⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣠⣤⣤⣾⠀⠀⠀⠀⠀⣿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣄⣼⡿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⡏⢟⡇⠻⢿⠿⣇⠊⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠋⡿⡿⠿⢶⢷⡌⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠿⡏⠂⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠂⠁⠀⠀⢠⡀⣀⢂⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⡙⢋⠇
⠀⠀⠀⠀⠀⣠⣶⡿⠿⢫⠙⠿⠶⠒⢂⠐⠛⣄⠻⠿⠻⠁⠀⠀⠠⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢦⢢⣦⣼⡇
⠀⠀⠀⢀⣾⣷⣮⡀⣠⣀⡄⣀⠀⣰⣺⣠⣀⢿⠋⠀⠀⠡⠀⠀⠀⠈⠝⠀⠀⣿⡛⠶⣤⠀⠀⠀⣼⣿⣶⣿⣿⡿
⠀⠀⢀⣾⣿⣿⡟⠁⠈⣛⣾⡿⠒⠺⣿⣿⣉⠀⠀⠀⢀⡴⡆⠇⢠⠀⠀⠀⠀⠈⠛⠂⠈⠁⠀⢸⡿⢿⠿⢿⡿⠁
⠀⠀⢸⣿⣿⣟⠂⠀⣼⢿⡿⠁⠀⢠⣿⣿⡇⠀⠀⢀⠊⢠⠇⠀⠠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢹
⠀⠀⢸⣾⣿⡏⠀⠀⢻⣸⣄⣼⠯⠛⢱⣶⣬⠀⠀⠈⠀⠁⠀⠀⠄⠈⠒⠦⠄⠀⡀⠀⠀⠀⠀⠀⠒⠃⡠⠂
⠀⠀⠘⣿⡜⡿⠁⠀⠸⣷⡜⣿⡷⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁
⠀⠀⠀⢿⡷⣘⣴⣦⢀⠀⣤⣿⠃⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠬⢀⡀⣀⢀⡀⠤⠄⠐⠊
⠀⠀⠀⠘⣿⡹⣿⣷⢀⢸⣿⣇⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⢀⠈⢀⠘⣿⣷⡍⢻⣶⣿⡉⠑⠚⠁⠀⠀⢀⣠⠤⠖⠊⠁
⠀⠀⠈⣾⣶⣿⡇⣾⣿⣽⣿⣿⡿⠇
⠀⠀⠀⠙⠝⠟⠿⣿⣦⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠄⠒⠀⠀⠈⠀⠀⠀⣀⣔⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠖⠉⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⠜⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⡴⠃⣰⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣉⣀⢀⠀⠀⡀⡀⠐⠨⡢⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣴⠇⢰⠃
⠀⠀⠀⠀⠀⠀⢰⣰⢿⣿⣿⢿⣟⠓⢆⣒⡒⠽⡲⣦⣀⢱⡀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⣿⠇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠿⢿⣶⡾⠟⡟⠛⠛⠂⠁⠪⣷⣿⣆⢠⢊⣠⣴⠶⠛⠉⠀⠀⠀⠀⠠⠤⢀⣀⠞⠁⢀⣼⣽⠏⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠒⢁⡴⠊⠙⠒⠦⢄⣒⠤⣄⣈⣿⣿⣿⣿⣭⣤⣤⣤⣤⣀⠀⠀⠀⠄⠠⣤⣀⡀⢀⣾⣿⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢀⡙⢿⣿⣿⡿⣿⣿⣯⣭⣭⠭⠭⠍⠉⠒⠂⠒⠈⠉⠹⣿⣿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠋⠉⠙⠛⠛⠯⢶⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠄⠀⠀⢽⠇
⠀⠂

⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣷⣶⣄⡀⠀⠈⢻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⠛⠉⠀⢀⣤⣶⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣏⠻⠟⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⣛⠛⠛⠉⠁⠀⣴⣶⣦⣤⣤⣄⣀⣠⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢛⣥⣶⣦⡙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢿⣿⣿⣿⣶⣝⠻⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣝⠿⣿⣿⣿⣷⣄⡀⠀⢀⣴⣾⣿⣿⣿⠿⣋⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣾⣿⣿⣿⡿⢛⣥⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣿⠟⠋⣴⣿⣿⠿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠶⠿⠷⠶⢶⣶⣤⣄⣀⣀⣠⣤⣴⣶⠶⠶⠶⠶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠉⣀⣀⣠⣤⠤⠤⣤⣄⣀⠈⠉⢻⡟⠉⠁⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣉⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠉⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠁⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠒⠲⢤⠀⠀⣿⠀⠀⣀⡠⠤⠴⠒⠒⠒⠚⠛⠓⠒⠒⠆⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣼⠃⠀⣀⣠⠤⠖⠒⠛⠉⠉⠉⠉⠙⠒⠦⡀⠀⣸⠃⠀⢀⣀⡤⠴⠒⠒⠚⠛⠉⠙⠛⠒⠲⠄⠀⠀⣷⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣧⡟⠀⠈⠁⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿
⠀⠀⠀⠀⠀⠀⣿⡿⣼⠁⢀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠲⠀⢰⡇⠀⠀⣠⠤⠖⠒⠋⠉⠉⠉⠉⠉⠉⠓⠒⠦⠄⠀⢹⣼⣿⡀
⠀⠀⠀⠀⠀⣸⣿⢣⡏⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⢤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⢀⣿⡟⣼⠁⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠠⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠀⠀⣿⣿⣧
⠀⠀⠀⠀⣸⣿⢣⡏⠀⠀⠀⠀⣀⣠⡤⠤⠖⠒⠒⠒⠒⠤⢤⣨⠄⠀⡿⠀⠀⠀⢀⣀⣀⣠⡤⠤⠤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⣿⣿⣼⠁⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⢸⣿⢿⡇
⠀⠀⠀⢰⣿⣯⡟⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣒⣒⣶⠶⠦⣤⣀⠀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⡓⠂⢸⣿⢸⣷
⠀⠀⠀⣸⣿⣿⠃⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣠⣶⣿⣿⣿⣿⣾⡯⠽⠿⠿⠿⠭⠭⣽⣿⣿⣿⣿⣿⣷⣦⣿⡏⣿
⠀⠀⠀⣿⣿⣿⣾⣿⠿⢛⣋⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋
⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠀⠐⠒⠀⠉⠉⠁⠐⠒⠒⠢⠤⢤⣄⣀⣀⡀
⠀⠀⠀⢠⠴⠶⠀⣉⡉⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠶⢤⣤⡄
⠀⠀⠀⡆⠄⠀⠀⠀⠀⠉⠉⠑⠒⠲⠤⠤⣄⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠊⠉⡟
⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠦⠤⣄⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⣇⣀
⠀⠀⠠⢤⣾⡛⠛⠒⠒⠦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⣀⡀⠀⠀⠀⣠⣤⣶⣛⣋⡉⠭⠵⠒⢆
⠀⠀⠀⢸⡅⠉⠙⠒⠦⣄⡀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣤⣀⡀⠀⠀⠀⣷⠀⢀⣙⣿⡶⠞⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⣠⣤⠤⠴⠖⠚⠛⠉⠛⠓⠾⠾⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢰⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⣧⣄
⣰⡿⠿⠶⣦⣍⣛⢷⣦⣄⡀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠒⣒⣛⣭⣭⠽⠶⠚⠛⣿⠁
⣿⠁⠀⠀⠀⠈⠉⠛⠛⠿⢿⣷⣦⣄⡀⡼⢡⢀⣀⣀⣠⣤⠴⠶⢒⣚⣋⣩⣭⠥⠶⠖⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠇
⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣯⣭⣴⠶⠶⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡤
⠀⠉⠙⠛⠷⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⡀⠀⠀⢄⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠾⣿⣤⡶⠶⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⡿⠿⠟⠛⢉⣡⣴⣿⡿⢷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠛⠛⠉⢁⣠⣴⣶⡿⠿⠛⠉⣁⣤⣾⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡿⠿⠛⠋⠉⢀⣀⣤⣴⣶⡿⠟⠋⠉⣀⣠⣴⣶⣿⣿⠿⠛⠛⠉⣉⣡⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠟⠛⠋⠉⠀⢀⣀⣤⣶⣾⠿⠟⠋⠉⣀⣠⣴⣶⡿⠿⠛⠋⠉⢀⣀⣠⣴⣶⣿⣿⣿⣿⠿⠿⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠛⠉⠁⠀⠀⣀⣠⣴⣶⣿⠿⠟⠋⠁⣀⣠⣴⣾⠿⠟⠛⠉⠀⣀⣠⣴⣶⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣠⣴⣶⡿⠟⠛⠉⠁⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠋⢁⣀⣤⣴⡾⠿⠛⠉⠁⣀⣠⣤⣶⣾⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢰⣿⣿⠉⠁⠀⠀⣀⣠⣤⣶⣿⡿⠿⠛⠋⣁⣀⣤⣶⠾⠟⠛⢉⣁⣠⣤⣶⣾⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⣶⣶⣾⣿⣿⠿⠛⣋⣡⣤⣶⣾⣿⣟⣋⣩⣤⣶⣶⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣾⣿⠋⠉⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠏
⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠿⠛⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⡿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⠿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡿⠛⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣴⣶⣿⣿⣿⠿⠟⠋⠉
⠙⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠙⢿⣿⣷⣶⣦⣴⣶⣶⣶⣿⣿⣿⠿⠛⠉

⠀⠠⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠚⣡⣞⡭⠠⠀⠀⠀⠀⠄⠀⠠⠁⠀⠀⠀⢰⠁⠀⠀⠀⠃⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠚⠀⡄⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠌⣤⠀⣥⠒
⠀⠘⡛⡍⠰⡫⠃⠀⠀⠀⠘⡄⡆⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢂⡄⢀⠔⠈⠚⠖⢄⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣴⣶⣶⣶⣲⣶⢴⡆
⠀⠀⠁⠒⡯⢳⠃⠀⠀⠀⢀⡛⣡⣀⡀⠑⠒⠒⠂⠀⠀⠉⠉⠉⠁⠀⠀⢀⣀⣀⣠⠴⠟⠁⡒⡀⠀⠀⠀⠀⠀⠤⠓⢂⠀⠀⠀⣄⣀⠀⢀⡀⢀⡀⢀⡀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠎⡙⢨⢁⠉⡌⠘⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⣀⠀⡄⠰⢂⢰⠃⠀⠀⠀⠀⠀⣇⠀⢭⠀⠀⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠿⠀⠀⡌⠰⠁⠄⡈⠰⢀⢣⢳⡿⢠⠀⠀⠰⠬⣭⣬⣥⠴⡄⠀⠘⠯⣒⡓⢒⣂⣨⡔⠉⠳⣖⠆⠀⠀⠨⠇⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡘⢀⢃⣬⣠⡄⠆⢆⣦⡤⠔⢚⠀⠀⡆⠸⣇⣨⡜⠀⠠⠀⠀⢀⣿⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣀⢘⡃⠀⢸⠀⠀⠀⠌⡠⢠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡿⠡⠃⠰⠀⢰⣦⠆⣷⠛⠦⢰⠀⠀⠈⠀⠈⠀⠀⠐⠁⠀⠀⠋⠙⠀⠀⠀⠘⠈⠀⠀⠀⠀⠰⠭⡆⠄⠀⠸⠀⠀⠀⠲⠂⠢⠀⠀⠀⡏⠈⠐⠁⠀⠇
⠀⠀⠀⠀⣯⡈⢀⠀⣀⠀⠀⠀⣛⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠁⠀⣺⠀⡀⠀⠈⡋⣤⠀⠀⠀⡇⢀⠀⡀⡈
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⣀⡀⠠⠏⠱⡀⠀⠀⠀⠀⠀⢀⡀⢰⡆⠀⠀⠀⠀⠀⠈⢉⡄⠀⢚⡤⠹⠀⠀⠈⠓⠀⠀⠀⠤⠁⠀⠀⠇
⠀⠀⠀⠀⠀⢠⠋⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠘⡀⠀⠀⠸⡆⠸⢃⠘⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⡤⠖⠁
⠀⠀⠀⠀⠀⡆⠐⠒⠀⠀⢀⠀⡀⠀⠀⠀⣠⣤⡀⠀⠂⠀⠀⠀⠀⢁⠀⠀⠀⠈⠃⠈⢀⣅⠀⠀⠀⠀⠔⡖⢲⢳⢂⡏⣖⣴⢰⠀⠀⠀⢀⣤⡆
⠀⠀⠀⠀⠀⣷⠆⠡⠠⣂⠔⠛⢻⣆⣠⡾⠃⠈⠛⠀⠰⠰⠀⠀⠓⠛⠀⠀⠀⠓⠐⠒⠀⠁⠀⠀⠀⠀⠈⠍⠉⡀⡀⠀⠀⠠⠋⠀⠀⢀⣼⠿⠇
⠀⠀⠀⠀⠀⠈⠓⠚⠋⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⡀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡿⠃⠀⠀⠀⢰⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡄⠀⠀⣀⢠⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⡇⠤⠧⠀⠀⠀⠀⠀⠀⣴⣿⣾⠏⠀⠀⠀⢠⢄⠏⢫⣠⠖
⠀⠀⠀⠀⢀⡠⢐⠚⠏⢛⠛⢅⡂⢄⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⡈⠀⡰⢉⠉⠁⠤⠠⠁⣤⡀⠈⠒⠂⠀⠀⣠⣾⣠⡾⠋⠙⠁⠀⠀⠀⠀⠦⠆⠀⠀⣸⠞
⠀⠀⠀⡔⠁⡰⠁⠀⠀⠀⢂⡀⢙⡄⢑⡄⠀⠀⠀⠀⢀⡁⡠⠂⠉⠀⢠⣆⠁⡀⠄⠒⠂⡠⠋⠀⠀⠀⠀⢠⣾⠋⠿⠋⠀⠀⠀⠀⠀⠀⠀⣀⠶⣝⢶⣢⡄
⠀⠀⣾⠀⠴⡇⠉⢲⢛⣏⢙⣁⣢⡩⠶⠉⠀⠀⠀⠀⠧⠔⠁⠀⠀⠀⠀⠈⠑⠒⠂⠉⠁⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢊⢱⡖⠁⣮
⠀⠀⠀⠈⠑⠉⠉⠉⠁⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡾⠖⠛⣥⡬⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⢀⠠⠐⡂⠐⢒⢩⡹⠟⠛⠉⠀⠀⠀⠀⢸⡉⠀⠤⠀⠀⢛⡀⠀⠀⠀⠀⡷⠺⢏⢈⡱⢶⡏
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡠⠊⣁⠔⢈⠤⢂⠡⢐⠨⠂⠁⠀⠀⠀⡟⣵⡇⠀⠀⠸⠄⣉⡒⢈⡁⢬⠇⠀⠀⠀⠐⢦⢳⣊⣙⢶⡚⠃
⠀⠀⠀⠱⠎⠂⠀⠐⡧⢠⡏⠀⠀⠀⠀⢀⡀⠊⡠⠞⢤⢂⡡⠂⡡⠒⠁⠀⠀⠀⠀⠀⠀⠓⠚⠁⠀⠀⢞⠂⢠⣍⠠⠐⢘⡅⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠂⠈⠁⠙⠀⠀⠈⠉⠁⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡤⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⡀⠺⠜⠁⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠉⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠦⡀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠸⣀⣠⡀⣤⣤⠆⠀⠀⠀⠀⠀⣠⠖⠛⠓⢦⠀⠀⠀⠀⠂⠀⠢⠐⢀⡜
⠀⠀⠀⢀⢄⣆⣒⠩⠕⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⣤⠀⠀⠀⠀⠀⢸⢃⢱⣶⢄⣆⠂⠀⠀⠀⠂⡟⠀⠈⠻⠈⠂
⠀⠀⠘⡇⠈⠁⢀⣤⡀⢀⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠓⠋⠉⠀⠀⠀⠀⠀⠸⣌⠪⠶⢋⠎⠀⠀⠀⠀⣶⠄⠀⠀⠀⠷⠃
⠀⠀⠀⣧⠀⠀⢘⣷⡆⠘⠀⠀⠀⠀⠀⠐⠀⠈⢒⠤⠖⡈⠀⠀⠀⠀⠀⠁⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠃⠉⠁⠀⠀⠀⠀⠀⢈⡒⢐⢒⠒⡆
⠀⠀⠀⠘⢄⣀⣀⡉⠥⠒⠀⠀⠀⠀⠀⠀⠣⠐⠁⠀⠀⠀⠈⠀⠒⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠛⢀
⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⢛⣁⣀⣀⣙⣊⣁⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡍⠉⠉⢦⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⡆⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠈⢦⠀⠀⠳⡄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠱⡄⠀⠙⣆⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡍⠁⠙⣆⠀⠘⢆⠀⠘⢦⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢸⣽⣭⣽⡇⠀⣿⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠀⠈⢦⠀⠈⢧⡀⠀⠳⡀⠈⢳⡀⠀⠑⣄⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⡗⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⣿⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠱⡄⠀⠹⣄⠀⠘⢆⠀⠱⣄⡎⠀⢀⣐⣒⣒⣛⣿⣿⣿⣯⣤⣄⣤⣤⡁⠀⠀⠀⠀⠀⢠⡿⡿⣷⡄⠀⣿⡇⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⢦⠀⠘⢦⠀⠈⠣⡀⠘⠛⠛⠛⠛⠛⠋⠉⢉⠉⣉⣉⡩⢽⠉⠉⠁⠀⠀⠀⠀⠀⠸⢿⣿⡿⠃⠀⣿⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠱⡄⠀⠳⡀⠀⢙⡤⠤⠤⢒⡒⣊⣭⠭⢉⠁⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢦⡀⠙⣄⠜⠀⠀⣀⣀⣒⠭⣥⣲⣲⣶⠲⠦⠞⣙⡢⣼⠀⠀⠀⠀⠀⠀⢸⣛⣛⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠱⣄⠈⠻⠓⠛⠂⠙⠉⠉⠉⣀⣀⠤⠒⠚⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⢦⡀⠀⢀⣀⠤⠔⢒⠩⡅⠀⠀⠀⠀⣀⡤⠴⣺⠄⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⢀⠟⠊⠁⠀⠀⠀⠂⣐⡨⠤⣒⠪⠝⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⣽⣽⣿⠇⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠸⠀⣀⡠⢤⣒⡬⠍⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠵⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠶⠶⠶⠤⢤⣤⡤⠴⠒⠊⠉⠉⠉⠉⠙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⣸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⡇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣧⠀⠀⠀⠀⢻
⠀⠀⠀⠀⡇⠀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⡀⠀⠀⢀⣴⣾⣿⣂⣠⡤⠤⠤⠴⠤⠤⠤⢄⣀⣀⣈⠙⠛⠷⠄⠀⣰⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠑⠒⠊⠋⣁⣠⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠭⣍⡒⠒⠤⢈⡀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠙⢷⡀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠈⢸⣇⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⡎⠉⠺⡄⠀⠀⢰⡏⠀⠀⠀⢀⣤⣤⣄⡀⣷⠀⢠⡏⠀⠀⠀⣠⣶⣶⣶⣦⣀⣷⠀⠀⠀⠀⣼⠁⠀⡷⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠻⣄⡀⢣⠀⠀⢸⡇⠀⠀⢰⣿⣿⠿⠉⣱⣾⠀⢸⡇⠀⠀⢸⣿⣿⡿⣏⠀⣹⣿⠀⠀⠀⢰⡿⠴⠚⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⡏⠉⣧⠀⠀⠻⣄⠀⠸⣿⣿⣿⣿⣿⠃⠀⠈⣷⡀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⣧⡀⠀⠈⠛⠶⠾⠿⠟⠋⣠⠄⠀⠀⠈⠳⣦⣄⣙⣻⣿⣿⠟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢄⡀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠈⠻⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣉⣉⣁⣀⣠⣤⡤⠶⠚⠉⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣲
⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠈⠉⡏⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⠀⣠⠃⠈⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠒⠐⠋⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡴⠀⠀⠀⠀⠀⠀⢸⠦⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠉⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠠⢀⠀⠀⠀⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⠄⠊⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢃⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠒⠀⡜⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡎⠀⠀⠀⠀⠀⠈⠂⠀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⡀⠠⠊⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠘⢋⠹⠉⠉⠉⠻⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⡇⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠩⣍⠉⠀⠀⣀⣵⣄⠀⠀⢀⠜⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⢀⠀⠭⠕⠒⠉⠀⠈⠛⠮⣁⣀⣀⡠⠞⠁
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣠⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠄⠠⠄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⠀⠀⠂⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡐⠁⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⢠⢜⡂⠈⠁⠆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⡖⠠⡆⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠐⠢⣠⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣰⠋⠁⠀⠀⢴⡤⠖⠓⡦⠄⠠⠀⠘⠀⠚⢃⡤⣀⣀⠀⠀⠀⣟⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣀⠒⡐⢆⠀⠀⠀⠈⡆⠀⠀⠀⠘⡶⠁⠀⠀⢀⠀⣄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠂⠀⠸⣇⠀⠀⠀⢸⡇⠀⡄⠀⠐⠀⢁⠈⠀⠀⠀⠀⠀⠉⣇⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠠⠀⠀⠐⠂⣨⡀⠀⠀⡄⣿⠀⠀⠉⠘⣷⡐⠁⠆⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡏⠰⠀⢀⠀⢸⡁⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡂⠐⢼⡇⠀⠀⠐⠚⣧⠀⠀⠀⢀⠀⠀⠀⠠⠀⠂⠘⡾⠀⠀⠀⠀⢬⢸⡗⠁⠰⠉⢐⠁
⠀⠀⠀⠀⠀⠂⡀⠈⠹⣤⠀⠀⠉⢀⢸⡏⠀⠀⠀⠀⠘⠳⣅⠀⣸⠀⠀⠀⠀⠆⣠⠞⠁⠀⠀⠀⠀⠀⣻⣠⠀⠀⡷⠈
⠀⠀⠀⠀⠐⠀⠀⠂⠠⠷⢄⣀⡀⠈⢹⡷⠀⠀⠀⢈⠀⠄⣌⠿⢧⣄⡀⢤⣰⠟⠁⠀⠀⠀⠂⠠⠂⠈⣿⠀⣠⡾⢁⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠉⢳⣼⡇⠀⠀⠀⠀⠁⠀⠁⢀⢀⣩⡿⠿⣧⣞⣀⠀⠀⠼⠀⠁⠀⣸⣧⡾⠋⠀⠈⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢹⡇⠀⡀⠃⠀⠀⢦⣠⡾⠛⠁⠄⠀⠀⠉⠙⠿⢿⣦⣀⡄⠀⣿⣿⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢙⢀⣴⠟⠛⠲⠀⠂⠰⠁⠀⠀⠀⢤⡀⡬⠻⢿⣦⣿⣿⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠘⠀⠀⢻⣆⠐⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠈⠀⠀⠹⣿⣿⡇⠀⢀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠁⢀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠰⠀⢠⣿⣿⡇⠀⠀⠀⡵⠚
⠀⠀⠀⠀⠀⠀⠉⠑⣮⡀⠀⠀⣜⠁⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⠋⠠⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠹⣆⡀⣾⠁⡄⠀⠀⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠾⣯⠈⠀⠈⡄⠂
⠀⠀⠀⠀⠀⠀⢀⡰⠆⠈⠉⠛⠛⠻⢷⣤⣿⣿⡇⠀⠀⠀⠀⠀⣠⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⣼⣿⣧⠈⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢻⣿⡟⠁⢹⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⣿⣿⡇⠀⠈⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡇⠀⠀⢀⣿⢸⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⡆
⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠶⠾⠿⠿⠷⠶⠶⠶⠾⠿⠿⠟⠛⠛⠿⠿⠛⠛⠳⠶⠶⠤⣤⣄⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠟⠛⠛⣍⠉⢹⡏⠉⣩⠟⠛⠻⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠉⠀⠀⠀⠀⠀⢈⣻⣾⣷⣞⣁⣀⣀⡀⠀⠀⠉⠻⢿⣷⣄
⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⣀⣴⣶⣮⣉⠉⣹⢿⣿⣿⡛⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣆
⠀⠀⠀⢀⣾⡿⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⣸⡇⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⢠⣿⡟⠁⠀⢀⣴⣿⣿⠋⠁⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⢠⣿⡟⠀⠀⣰⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣆⠀⠀⠈⠳⠄⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⣼⣿⠁⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠋⢹⣦⣿⣶⣄⠀⠀⠈⣿⣧
⢠⣿⣏⣴⡾⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⢙⣿⣿⣷⡀⠀⢹⣿
⢸⣿⣿⠏⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣶⣦⡀⢸⣿⣾⣿⣿⣿⣷⠀⢸⣿
⢸⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠉⣿⣿⣿⣧⢻⣿⣿⣿⣿⠀⢸⣿
⠈⣿⣷⠀⠀⢸⣿⡇⠀⣠⡾⠛⠛⠛⠒⠒⠒⠶⣦⠀⠀⢸⣿⡇⠀⢀⣼⣿⣿⣿⡄⢀⣿⣿⣿⣿⠀⣼⣿
⠀⢻⣿⡄⠀⢸⣿⡇⠀⠹⣿⣿⣷⣶⣶⣶⣶⣿⡿⠀⠀⢸⣿⡇⠐⢿⡿⢻⣿⣿⡇⣾⣿⣿⣿⡏⢠⣿⡟
⠀⠈⢿⣷⡀⢸⣿⡇⠀⠀⠘⣿⠛⠛⠛⠛⢻⡟⠀⠀⠀⢸⣿⡇⠀⠈⣡⣿⣿⣿⣷⣿⣿⣿⣿⣧⣾⡿⠁
⠀⠀⠘⢿⣿⣾⣿⣿⣆⣀⣼⣛⣧⣀⣀⣀⣟⣻⣄⣀⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠉⢉⠱⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣆⢴⣏⣀⣀⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⢿⠻⠿⠃⠁⠝⠉⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠻⠟⠁⠀⠀⠀⠀⠑⢐⠀⠀⠀⢀⡈⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣆⠦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡗⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢿⣿⡁⠬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠲⣶⡀⠀⠀⠀⠀⠀⠀⢺⣤⠋⠀⠀⢀⢻⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣦⡝⠁⠀⠀⠀⠸⠘⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢀⣾⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠉⠀⠀⢀⠀⠀⠀⠀⣠⠟⠛⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠖⠛⣳⠀⡤⠀⠀⠀⡀⡤⠔⣻⠟⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣤⠶⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠛⠛⠛⠋⢻⣿⣏⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⡄⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠉⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠁⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⣼⣧⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡀⢸⣿⠘⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠂⠀⠀⠀⠀⠘⢻⡇⣿⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠿⠀⠀⠀⠀⠃⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⢻⠿⡿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠟⠁⠀⠀⣠⣿⢃⣾⠃⠀⣾⠇⠀⣠⡿⣧⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⡜⠁⠀⠀⢠⣿⣧⣃⣤⢾⡟⠀⢀⡆
⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⣠⡾⠛⠻⠟⠁⠀⠀⢿⣤⡾⠋⠀⠀⢻⣀⣀⣴⠖⠀⠀⠀⠀⢀⡿⢁⡴⠋⠀⠀⢀⡴⣿⣏⡟⠉⠀⣾⠁⢠⠚⠷⣴
⣀⣀⡴⠞⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡷⠋⠀⠀⢀⡴⠋⠀⠻⠛⠀⠀⠀⠿⠖⠁⠀⠀⠸
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⡾⠛⣦⠀⢀⣠⣾⠆⠀⠀⠀⠀⠀⣴⡶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢀⣿⣿⣰⣿⡶⠿⣿⡏⠀⢀⡄⠀⢠⣾⠋⢠⣾⠇⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⡼⠁⢀⠄⠀⠀⠀⢴⡆⠀⠀⢀⡀⠀⢀⣴⢿⡆⢠⡀⠀⠀⠀⣠⣿⣿⠁
⠀⣴⣿⣿⢋⣿⠋⠀⣸⣿⠀⢀⣾⡇⢠⣿⣃⣴⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⣰⠟⠀⣠⢷⣠⡤⠊⣠⠏⠀⠀⠀⣼⠃⣠⣞⡡⠋⠀⢸⠃⠀⠀⣰⣿⡿⠁
⡾⠋⢿⣇⡼⠃⠀⠀⣿⡇⢠⣾⠉⠓⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣡⡞⠁⢠⢾⣏⡠⠀⠀⢠⠏⠀⠀⣠⠎⠻⣴⣿⠋⠀⠀⣠⡟⠀⠀⢠⣿⡿⠁
⠁⠀⠀⠉⠀⠀⠀⠀⠻⢷⠿⠁⠀⠀⠸⣇⣀⣀⣤⡴⠂⠀⠀⢀⣿⣿⠟⠃⢀⡴⠋⠈⠉⠀⠀⠀⣏⠀⢀⡼⠁⠀⠀⢾⣿⣀⣠⣾⠏⠀⠀⢠⣿⡿⠁⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣟⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣠⠟⠀⠀⡠⣄⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⡆⠀⢸⡆⠀⠀⠀⠀⠀⢀⣾⣿⢃⡾⠋⠀⣠⣶⡇⠏⣠⣾⠏⠀⣴⠂⢠⣾⣿⣿⠋⠀⠀⡀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢠⣿⢻⡆⠀⣠⣿⠃⢀⡀⠀⣠⡿⠋
⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣴⣿⣏⡟⠋⣹⡟⠀⡴⣿⣤⣿⡿⠋⠁⠀⣠⠎⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣧⣾⣿⠃⠀⣸⡇⢰⣿⣡⣾
⠀⣴⠏⠀⠀⠀⠀⠶⣾⣿⡏⠀⢀⣴⠏⠸⠿⠟⠀⠀⢿⣧⠞⠁⠀⠹⣿⣄⣀⣤⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⢹⡏⠀⣰⡟⠙⣿⠟⠋⠁
⡾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣠⣿⠛⢿⠟⠀⠀⣿⡇⣴⡿⠁⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠻⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣠⡖⢶⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⣠⣾⠟⣶⡀⢠⡏⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⡇⣼⣧⣶⢿⣿⠃⠀⣀⠀⠀⣴⡟⠁⣴⡿⠀⢸⡇⠀⠀⣠⣾⠟⠀⠀⠀⣠⠖⠀⣸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠁⣶⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣰⣿⡿⢻⣿⠉⠀⣾⡏⠀⢠⣿⠀⢰⣿⣠⡾⠛⠀⠀⠀⠳⠶⠿⠋⠁⠀⠀⢠⣾⠏⢀⡼⠁⣠⠈⠀⡠⢀⡟⠁⠀⢀⡖⠀⣰⢏
⢠⠇⠀⢠⣿⡿⠃⠀⠀⠀⢠⣾⠟⣿⢃⣾⠃⠀⢰⣿⠃⢠⡿⠉⠳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣴⠋⢀⣴⠋⡙⠋⢀⡞⠀⠀⣠⢾⣇⣼⡿⠋
⠏⠀⢀⣾⣿⠃⠀⠀⢀⣴⡟⠁⠀⠉⠛⠁⠀⠀⠈⢿⣴⠟⠁⠀⠀⠹⣇⣀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⣴⠋⠘⠛⠀⠀⡼⠀⢀⡴⠁⠀⢸⣿⠀⣀
⠀⠀⣸⣿⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣠⠟⠁⠀⠀⠀⠀⠀⠿⡶⠋⠀⠀⠀⠈⠛⠛⠋
⠀⠀⣿⡏⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁
⠀⠀⠻⢧⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⣾⠟⠁⢠⣤⣄⠀⠀⣠⣶⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢷⠀⠀⠀⢀⡀
⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⣾⡟⠁⠀⢠⣿⣧⣿⠶⢻⣿⠃⠀⢠⡄⢀⣔⢋⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠏⠀⠀⢠⡏⡃⠀⠀⣠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⠂⢬⠁⡇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⢁⡠⠤⠆⠀⠀⠀⠩⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠌⠀⠀⢰⠊⢠⣲⢅⠀⠂⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⡏⠀⣯⣿⣧⡅⢀⣀⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢣⡀⣛⢭⢏⢀⡮⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡅⠀⡇⠀⢀⡔⡊⡙⢢⣠⠢⠀⡀⠀⠔⠡⠉⠑⣶⠛⠉⠳⡀⠀⣀⠂⣄⠀⡴⢐⡒⢦⡀⠀⠰⠀⣄⠐⠄
⠀⠀⠀⠀⠀⠀⡀⣨⢔⣻⠞⢸⠁⠀⣸⣿⣾⠁⠚⡃⠂⡂⠐⢀⢀⠀⠀⢾⣫⡶⢠⢱⠈⠆⠄⢨⡵⠀⠘⠂⢹⣾⣇⠀⠀⠆⢻⣃⡦⠑⣄
⠀⠀⠀⠀⠀⡈⣠⡾⣻⣿⡆⢀⡶⠛⠓⢏⡯⢠⡤⠃⢘⠀⠀⠀⠈⠡⢀⢀⣿⠠⠀⠐⠂⠀⠀⠀⡁⡃⣠⢄⠘⢿⠾⠞⢷⢃⢉⣌⡷⡈⠈⢢
⠀⠀⠀⠀⡴⢹⠷⣋⡼⣮⣿⡏⢀⡀⠀⢢⣀⠋⣇⠐⠍⣷⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⢡⡼⢁⡠⠤⡜⠀⢠⡄⢻⡼⣎⣛⡈⠰⠄⢆
⠀⠀⠀⢰⢠⡟⣟⣹⠟⡫⠟⠀⢸⡇⠀⠈⢋⣴⢾⡇⠀⣿⠀⠀⠀⠀⢀⡜⠘⣇⠀⠀⠀⠀⠀⣰⠶⠔⠋⣀⣜⠀⡄⢸⣷⢸⣿⠉⠳⣟⡓⠴⡈⡄
⠀⠀⢀⢣⠟⢚⠟⠁⠊⢠⣤⣦⡀⢿⢀⠀⡨⠝⠋⣠⡎⢿⠀⠀⠀⠀⣏⢸⠃⢸⡇⠀⠀⠀⠀⢁⣀⣠⣾⠿⠌⠓⣶⣿⠏⣘⣻⣝⢦⡈⠑⣦⠉⠹⡄
⠀⢀⢢⣮⠟⡡⣪⠜⣰⡿⠀⠘⢻⠷⡇⠀⠀⣠⢶⣻⣥⠞⠀⠀⠀⠀⠘⣄⣠⡟⠁⠀⠀⢀⣄⠛⢋⣉⣀⣤⣤⡇⡿⠛⠚⠋⢹⢹⡧⡛⣁⠈⠳⣧⠠
⠠⠗⠋⣁⢰⣄⢷⡼⡟⠀⠀⠰⡝⣴⢻⣸⣯⠟⠛⠉⣿⠀⠀⠀⠀⠀⠀⢾⣼⡇⠀⠀⠀⣠⣂⡤⠈⣻⡿⢸⡿⡎⡰⠁⠐⠁⠘⡄⣷⡹⣄⡟⠀⠈⠓⠦
⢠⢞⠃⠀⠂⠹⢸⣯⣧⠀⠀⠀⠨⣟⡸⣿⣏⠀⣀⠀⣿⡀⢀⡤⠀⡠⠄⠿⡾⠗⠀⠤⠄⠠⠤⢄⠠⡽⣷⡞⢨⡟⢄⠈⠀⠀⠀⡅⣿⣿⣽⠆⡏⠨⢀⢦
⢈⠉⠀⠀⡠⠀⠀⢸⡉⡚⠇⠀⠀⠈⢻⣜⢿⢰⢋⣜⣏⣀⡄⢀⣀⢲⡏⡂⠂⡀⢷⡊⠀⠀⠙⠐⡀⢦⡛⣰⠟⣠⠆⠀⠀⠀⠠⢣⣿⠟⣉⡼⠃⠃⠀⠘⡆
⣠⠛⠰⠊⣠⣶⣾⣷⣷⠛⡆⢀⡀⠀⠈⣿⡖⣢⢟⣽⣿⠴⣿⢚⣫⠥⠎⠀⠸⠃⠐⠭⣝⢶⣷⠐⠸⠘⠃⣩⡄⡿⠀⠀⠀⢀⢫⣿⠭⣾⣣⢃⡀⠀⡘⠣
⠻⠂⢠⣶⣿⣿⡟⡁⡞⠀⣝⣈⣏⢀⣀⢟⣼⠷⣻⠵⣿⣿⣧⣘⣃⡷⠟⠻⠿⠛⠻⢗⣙⣠⡿⠦⡙⠼⠧⠥⣤⡳⣤⣘⣁⡣⠂⠛⡀⡘⢿⣽⣿⣿⣇⠀⢂
⠀⠿⢾⣿⣿⠁⡔⡃⣇⣤⣬⣾⠟⢟⣡⣾⡒⠛⠛⠉⠈⠉⠀⠀⠈⠀⢠⣤⡀⣀⡀⠀⠉⠀⣀⡀⠀⠀⣀⣀⣄⡱⣿⡍⠻⣽⣿⣛⠘⢁⡌⡋⣮⣿⡟⢀
⠀⠀⠠⣜⣇⣴⣧⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡷⣄⣠⣄⣿⣿⣟⣿⣿⣷⣠⣿⣽⣿⡷⢶⣟⣽⣿⣿⣿⢿⡾⣗⣶⣿⣷⣼⣠⡇⢸⡿⡢⠁
⠀⠀⠀⠈⠛⠶⠿⠼⠿⢿⢿⣻⣿⠿⠛⠙⢟⠻⢿⠿⣿⣿⡿⢿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣷⣿⠫⠛⡹⠆⢉⣿⣯⠭⠙⠻⡟⠋⠁⠉⠈⠙⠗⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠁⠀⠂⠙⠋⠑⠂⠩⡏⠯⠋⠉⠀⠈⠛⠉⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣓⠒⠒⠲⠦⠤⠤⠤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡴⠊⡉⠉⣭⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⠉⠁⢐⠂⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⠶⠤⢬⣭⣥⣴⣿⣿⣿⣿⣿⣿⣷⡿⣻⠀⠀⠀⠀⠀⠀⠀⢀⡜⠓⠒⠂⠠⠤⠤⠤⠤⠃⠀⠀⠀⠀⠀⢠⡟⢹
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⡿⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⡿
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡿⣱⡿⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢠⡿⠁
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⡿⣱⡿⠁⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢠⡿⠁
⠀⣾⣿⣿⣿⣿⣿⣟⣛⣿⡿⠿⠿⢿⣿⣿⣿⡟⣽⡟⣰⡿⠁⠀⠀⠀⠀⡾⢧⢤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢠⡿⠁
⠀⣿⡇⠈⠉⠉⠉⠙⠛⠛⠻⠻⠿⠿⣶⣶⣾⣾⡟⣰⡟⠀⠀⠀⠀⠀⠀⣷⡇⠀⠁⠀⠉⠉⠛⠋⠛⠛⠷⠒⠒⠶⢤⢼⠏⣰⡟⠁
⠀⣿⣧⣤⣤⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⡟⠀⠀⠀⠀⠀⠀⠀⣯⣡⣤⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠻⠿⠶⠶⣶⣶⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠚⠻⠶⠶⢤⣴⣂⣀⣔⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⢿⢿⡿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠶⠦⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠤⣄⣀⣀⡀⠀⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠦⠤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠊⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡷⠆
⠀⠀⠀⠈⢳⠮⠄⣀⡀⠈⠉⠙⠒⠲⠦⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡁⠠⠶⣶⣄⠀⣀⣠⣴⣾⣿⠭⠥⠶⠀⠀⠀⠁⠑
⠀⠀⠀⠀⢸⠄⠀⠀⠉⠛⠲⢤⣄⣀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠤⢤⣄⣀⡀⠀⠸⡆⢀⣠⣼⣿⡟⠋⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⡤⠴⠖⠒⠒⠋⠉⠉⠉⠛⠛⠛⠛⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢰⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣦⣤⣀
⠀⣼⡿⠭⣴⣤⣉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠒⠒⣂⣉⣁⠤⠴⠶⠞⢿⠏
⢸⡿⠀⠀⠀⠈⠉⠛⠓⠲⠭⣿⣷⣦⣄⡀⠀⢠⠇⠀⠀⠀⢀⣀⣠⣤⣤⡴⠶⠖⣒⣋⣉⣩⡤⠤⠶⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣶⣷⣟⣛⣋⣭⣭⣶⠶⠶⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⡀
⠀⠘⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠶⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⡴⠶⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣄⣀⡀⢠⡄⠀⠀⠀⢀⣀⣠⣴⠶⠶⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠾⠛⠛⠉⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠐⠂⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡴⣻⠿⠿⠿⢿⣶⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⡰⠫⠍⠭⠍⠉⡓⠒⠒⠒⠲⠤
⠀⠀⠀⠀⠀⢠⣮⣜⣁⣀⣖⣉⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠾⠅⠀⠀⢀⡀⡠⠁⠀⠀⠀⢀⡼
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⠇⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⠏⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⠏
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡟⣼⠏⠀⠀⠀⣰⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠏
⠀⣿⠋⠛⠛⠛⠿⠿⠿⢿⣿⣯⣽⣵⡟⣼⠏⠀⠀⠀⠀⣇⠋⠙⠛⠛⠳⠶⠶⠶⣤⢤⣤⣠⡟⢠⠏
⠀⢿⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠉⣼⠏⠀⠀⠀⠀⠀⢯⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢠⠏
⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠻⠷⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠓⠲⠦⠶⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠻⠿⠛⠛⠛⠛⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠇

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢒⡒⠦⣄⡀⠀⢀⣠⣴⠤⣶⣶⣃⣀⠀⠀⢀⡤⠖⢒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⣦⠀⠙⠖⠉⠀⠀⠀⠐⠚⠉⠙⠛⠶⠋⠀⣜⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣆⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠋⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠘⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠠⠀⡀⠙⠛⠋⠀⠀⢀⣀⣀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠠⠄⠠⠁⠀⠀⠀⠫⢄⠼⠃⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⡀⠀⠀⠀⡀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⢄⣿
⠀⠀⠀⠀⠀⠀⢿⣿⡖⠈⠀⠀⠀⠀⠁⠀⠀⠀⠱⠴⠛⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⠂
⠀⠀⠀⠀⠀⢀⡟⠈⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢹⡄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⠙⠳⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠴⠖⠛⠉⠀⠀⠀⢷
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳⣀⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⡴⠃⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠙⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⢤⣤⣤⣬⡗⡀⠀⠀⢲⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⢀⠀⠀⡘⣯⣤⣤⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢀⣴⣶⣄⠀⣀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠙⠛⠋⠁⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐
⠀⠀⠀⠀⢀⣀⣀⠌⠀⠀⣀⣀⡀⠉⠙⠛⠿⣿⣿⣿⣟⡁⢄⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⣷⠀⡠⢊⣻⣿⣿⣿⠿⠟⠋⠉⢀⣀⣀⠀⠀⠡⣀⣀⡀
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠂⢸⣿⡷⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⡇⠔⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠙⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⠴⣄⠀⠀⠀⠀⢀⣤⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣠⠏⠀⠀⠀⣰⠋⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢀⡾⠀⠀⢠⠶⠒⢦⠖⠲⢦⡀⠈⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⠖⠋⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠛⠶⣄⠀⠈⠳⣄⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣤⠀⢹⡆⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣳⣼⡟⠓⠒⠶⠶⢦⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢦⣤⡟⠁⠈⠳⢦⣄⣀⣀⡼⠃⠀⠀⠀⠀⡇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠳⢤⣀⠀⠀⠈⠉⠙⣦⠀⠀⠀⠀⠀⡿⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡟⠓⠶⠦⠶⠃⠀⠀⠀⠀⠀⡇⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⣄⣠⣤⣤⣠⣤⣀⣠⡇⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡗⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢠⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⢸⡇⠀⣀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠙⣟⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠛⢾⡷⠛⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠿⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠾




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠄⠀⢠⠀⢀⠀⡠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⡀⠂⠒⠀⡆⠒⠀⠂⠀⠸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠧⠤⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⢀⣀⣀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⢀⣀⡀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠐⠁⠈⠃⢸⠀⢸⠀⢰⢻⡀⢸⠤⡇⢸⠀⠀⡇⠀⠀⠀⠧⡀⠀⢸⠀⢸⣀⠇⡜⠀⠈⡆⣧⡜⠀⡧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣥⣤⣈⣤⣤⣃⣸⣀⣸⣀⣏⣈⣁⣸⣤⣏⣸⣤⣄⣧⣤⣀⣀⣤⣜⣀⣸⣀⣸⣀⣇⣘⣤⣔⣁⣇⣈⣆⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⡇⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⢸⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⣿⢸⡇⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⢸⡇⣿⢰⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡿⢹⡇⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⢸⡏⢿⣄
⠀⠀⠀⠀⢀⣀⣼⡏⡇⢸⠇⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠸⡇⢸⢹⣦⣀⡀
⠀⠀⠀⠀⣿⣿⡿⣇⡇⢸⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⡇⢸⣸⢿⣿⣿
⠀⠀⠀⠀⣿⡿⣧⢸⠇⢸⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⡇⠸⡏⣼⢻⣿
⠀⠀⠀⢰⣿⡇⢻⢸⠇⣸⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⣇⠘⡇⡟⢸⣿⡄
⠀⠀⠀⢸⣿⠁⠸⢸⠀⡟⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⢻⠀⡇⠇⠘⣿⡇
⠀⠀⠀⢸⣿⢸⠀⠸⠀⡇⣸⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣇⢸⠀⠃⠀⡇⣿⡇
⠀⠀⠀⣿⡟⠈⠀⠀⠀⡇⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⢀⠀⠀⢹⣿
⠀⠀⠀⣿⡇⠀⠀⠆⢀⠇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⡀⠸⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⢸⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⡇⠀⠀⠀⢸⣿
⠀⠀⢸⣿⠃⠀⠀⠀⢸⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠠⠀⡇⠀⠀⠀⠘⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠸⠀⠂⠤⣀⡒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢒⣀⠤⠐⠀⠃⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢄⣀⣀⠈⠙⠲⢭⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⡭⠖⠋⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⣿⡟⠀⠀⡠⠀⠠⠀⠤⠤⠈⣉⣙⡒⠦⢬⣙⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⣋⡥⠴⢒⣋⣉⠁⠤⠤⠤⠄⠀⢄⠀⠀⢻⣿
⠀⠀⣿⡇⠀⠐⠀⠀⠀⠀⠠⠄⣀⣀⠒⠩⠭⣓⡚⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⢓⣚⠭⠍⠒⣀⣀⠠⠤⠀⠀⠀⠀⠢⠀⢸⣿
⠀⢠⣿⡇⢄⣀⠀⠤⢬⣍⣐⠒⠦⢬⣍⡓⠲⠤⣍⡙⠲⢬⣙⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⣋⡥⠖⣋⣩⠤⠖⣊⣩⡥⠴⠒⣂⣩⡥⠤⠀⣀⡠⢸⣿⡆
⠀⠰⣿⣷⣦⣬⣉⣙⠒⠦⢬⣍⣓⠒⠤⣍⣙⠒⠤⣍⡑⠲⢌⡙⠢⣍⠻⣷⡄⠀⠀⢠⣾⠟⣩⠔⢋⡡⠔⢊⣩⠤⠒⢋⣩⠤⠒⣊⣩⡥⠴⠒⣋⣉⣥⣴⣾⣿⠆
⠀⠀⠈⠉⠛⠛⠿⠿⣿⣷⣶⣤⣌⣉⡑⠒⠬⠉⡀⠂⠈⠀⠀⠀⠀⠀⠁⠀⠙⣦⣴⠋⠀⠈⠀⠀⠁⠀⠈⠁⠐⢂⠉⠅⠒⢚⣉⣡⣤⣶⣾⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣷⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠐⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢈⠑⠦⣍⣛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣉⡓⠦⣬⣉⠒⠌⠉⠛⠷⣦⣄⠀⠀⠀⣀⣠⡤⠴⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣂⠬⣍⡒⠬⣕⡢⠌⠙⠒⠄⠀⠀⠀⠙⢷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⠲⢭⣑⠲⠬⣁⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠒⠒⠟⠻⠶⣤⣍⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣀⣤⣤⠶⠞⠛⠛⠛⠓⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠾⠿⠷⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣀⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢉⡿⣍⠿⣯⣉⣉⣉⣉⣉⣀⣤⣤⣤⣤⣴⠶⠶⠿⠛⠛⠋⠉⠁⠀⠀⠀⢀⣀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠸⠀⠹⣆⢸⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠁⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇⠀⠀⣀⣀⣘⣿⣧⣶⣶⣶⡶⠶⠶⠶⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⣀⣠⣴⠶⠞⠛⠉⢉⣿⣴⠟⠛⠉⠉⠉⠉⢙⣛⣛⣛⡛⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣦
⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠭⠭⠭⠍⣉⢛⣓⣒⣒⣒⣒⣒⣒⡒⠀⠀⠀⠀⠈⢉⡿⣭⡀
⣸⠏⠀⠀⠀⠒⠤⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠥⠤⠤⠤⣀⣀⣀⣀⣐⠒⠒⠒⠒⠶⠶⠦⠀⠀⠀⠀⠀⢸⠁⠀⠉⠓⠦⣄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⢀⣀⣀⣈⠉⠉⠙⠛⠛⠒⠒⠒⠲⢶⣶⣶⠶⠬⠭⢭⣍⣉⡙⠛⠛⠒⣒⣀⠀⠀⢸⠀⠀⠀⠀⢀⣈⣙⣷⡦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣭⣭⣭⣍⣛⣛⣛⣟⠠⠒⠠⠢⠑⠩⠀⢩⣤⣤⣄⣀⡀⠙⠛⣛⣒⣒⣒⡀⠘⢷⡶⠾⠟⠛⢻⡟⠉⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣉⡉⠉⠉⠛⠛⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠿⠿⣶⣶⠶⠿⠀⠀⠀⣾⠁
⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⢀⣴⡶⠚⠃⢀⣀⣠⡤⠤⠤⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠀⠀⠀⣿
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠤⠤⠐⠂⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠶⠶⠶⢚⣛⣋⣩⣭⣤⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣙⣮⣍⣁⣀⡀⠀⢈⣉⣉⣭⣤⡤⠶⠶⠖⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠲⠈⠉⠉⠉⡉⠓⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⣧⡠⠞⠉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠠⠀⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⡀⠀⠉⠐⢠⡁⢸⢀⠀⠌⠀⠊⣠⠖⣨⠅⠀⠉⠁⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠄⢿⠘⠀⣤⢠⠞⡡⠊⠀⠀⢀⠀⣰⡀⠀⠀⠀⠈⡀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⠀⢠⣣⠊⠀⠀⠀⢀⡄⠐⠉⠙⠄⠈⠒⠀⠙⠖⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡤⠖⢚⣋⣡⣬⣉⣛⠿⠟⠛⠉⠉⠙⠓⠲⠶⣧⠘⠃⠀⠀⣄⠀⠀⠀⠒⠄⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠛⢁⡤⠞⠋⠁⠀⠀⡀⠀⣠⠀⠱⣄⠀⠠⣄⠀⠀⢈⠙⢦⠀⡀⡈⠁⠤
⠀⠀⠀⠀⡀⢀⠎⢀⠔⠉⠀⠀⠀⢀⠤⢊⠠⣼⠇⠀⠐⡀⠑⢄⠀⠙⢦⠀⠀⠀⠹⠆
⠀⠀⠀⠈⠰⠁⠀⠁⠀⠀⢀⡤⢖⡡⣠⠴⠟⠉⡀⠀⠀⠈⠢⠀⠀⠀⠀⠑⠀⠀⠀⠩⠄
⠀⠀⠀⢀⢃⠈⠀⢀⡤⢚⡩⠒⠉⠀⠑⠊⠠⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⢉⠲
⡀⠀⠀⣘⡎⠀⠀⠠⠈⠁⠀⠀⠠⠄⠀⠀⠨⠀⠀⠀⠂⢴⣀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠐⣇⡉⡀⠁
⠆⠀⡠⣿⠀⠠⠊⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⢀⣤⣄⡎⠁⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⣤⡁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠀⢱⡀⠀⠀⢀⠃
⠀⠀⠀⠀⢹⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⠆
⠀⠀⠀⠀⠐⢣⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⣸⠆⠄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠠⠙⢆⣈⠒⠤⣀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⣀⡴⠾⢻⣏⡀
⠀⠀⠀⠀⠈⠒⠀⠞⠃⣄⠀⠐⠛⠲⠦⣤⠠⠀⠀⠀⢀⢠⠤⠄⠉⠁⠀⠀⠈⠳⠀⠂⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢠⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠒⠨⠥⠤⠶⠶⠒⠀⠉⠉⠁⠀⢰⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⢑⢆⠀⠠⠄⢀⠀⠀⠄⠀⠠⠐⠁⠎⠈⡆⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠃⠀⠀⠀⠈⠀⠚⠀⠀⡀⢀⠌⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠢⠄⡀⠀⢀⠠⣘⠕⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢢⡀⠀⠀⢀⡳⠉⣀⠄⢁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠤⠔⠂⠒⠈⠀⠀⠀⠀⡤⢑⣟⣉⡚⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠐⠲⠖⠘⠋⠀⠁⠐⠀⠀⠒⠈⠁⠀⡇⠀⠀⠀⠀⠀⢰⡄⠀⠦⣠⠉⡁⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡇⠀⠀⠀⠀⣠⣋⣤⡄⠀⠉⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠀⠠⠀⠜⠁⠉
⠀⠀⠀⠀⠀⠉⠡⣀⡄⠀⠀⠀⠀⠀⠀⣆⠥⢀⠀⠀⠀⠀⢀⠐⠇⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠈⠀⢠⠂⠃⢀⡴⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣦⣤⣶⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣨⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠋⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠀⠈⠃⠀⠀⠀⢼⣿⣷⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⠉⠉⠙⠛⠿⠿⣿⣿⠟⠛⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢚⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⡟⠛⢻⡆⠀⠉⠹⠛⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢸⡏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⢡⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢐⣠⣼⣿⣿⣿⣶⣿⣅⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡎⠙⣿⡿⣿⣿⣿⣿⣿⣟⠒⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⣀⠀⠀⢠⡅⠐⠀⠉⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠈⠑⢤⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⣛⡆⢀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⡢⡀⠱⡀⠁⠀⠀⠀⠀⠀⠀⢀⢔⣫⣵⠊⢁⢁⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⡀⢔⡬⠒⠉⢁⠸⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡥⠚⠁⠀⠀⠀⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈⢆⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢆⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢁⠊
⠀⠀⢀⠄⣒⠃⣿⣶⣤⠄⡪⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠶⠁⠀⠀⠀⠐
⢔⣪⣿⣛⣽⡿⢞⣩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⢈⠕⠉
⠀⠈⠉⠻⣵⠚⠅⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⠠⠂⠁
⠀⠀⠀⠀⢱⠆⣆⠠⠊⠁
⠀⠀⠀⠠⠌⠊
⠀⠀⠀⠀⠀⢠⠀⠀⡠⠠⡀⡠⡢⠀⠀⡰⠂⠀⢀⢄⠀⠀⡀⠀⢀⠐⢀⠀⠀⡀⡀⡀⢀⢀⢀⢀⠀⢀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣶⣶⡀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣷⣿⣯⣥⠄
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠽⢿⣿⣿⣥⠄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⣀⣹⣶⣦⣿⣿⣿⣟⡥
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⣾⡞⠁⢹⣿⣿⣿⣯⢾⠏
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⠴⢿⣾⠞⣯⢻⣸⣧⣯⣤⠄
⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢤⣰⣿⢻⣀⣰⣿⣋⠙⣿⣿⢿⣿⡿⠆
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢁⣏⣓⣿⣿⣿⣿⠛⢾⡿⠴⣿⠋⣩⠽⣇
⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠳⢾⣍⡿⠛⢿⣽⣿⣌⣿⡛⠙⣧⣾⣷⣤⠈
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣴⡷⢋⣹⣯⡤⠿⢶⠤⣿⡙⠛⣿⢧⢞⣙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡏⣸⣿⡁⡞⢽⠳⡍⢳⣸⡄⢸⡝⢦⢸⣟⣉⠉⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠻⣿⣴⠻⣄⡙⣷⣮⠷⢛⡫⠋⡇⢸⠀⢨⢿⡁⣠⣾⡅⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡏⠙⠒⡾⠻⣄⠈⠫⣭⣭⣟⣋⡤⣾⣴⠋⡰⠋⢀⣿⢁⣀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⡞⢆⢀⡄⣈⠉⢳⣙⣤⣹⣇⠀⢻⡓⠲⠾⠶⠤⠴⠚⢁⡼⠋⢀⣤⠿⣿⠈⣉⣠⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠶⣷⣿⣸⣇⣿⢶⣋⣉⠤⢬⡟⠓⣤⣉⣓⣲⣶⡦⠴⠒⠛⢒⣫⢿⣯⣅⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠒⠶⢿⣿⣿⡛⠛⢉⢩⣿⡿⠂⢲⠞⢳⠤⠽⠓⢤⣤⣤⣔⣋⣁⣀⣁⣈⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣉⠛⣹⠿⣿⠗⣺⣿⢻⡇⠀⠉⠀⣀⣠⠴⣾⡉⠉⠗⣨⠏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣰⠃⢈⡵⢿⣨⡷⠛⢛⣯⠤⠶⠛⠁⠉⠳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠋⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢻⡆
⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠐⠐⠄⠀⠈⣿
⣰⠟⠉⠈⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣰⡟⠀⠔⠁⠀⠀⠘⠀⠀⢻⡄
⣿⠀⠀⡰⠀⠢⡀⠙⢷⡀⠀⠀⣀⣤⡴⠶⠛⠛⠋⠉⠉⠏⠉⠉⠙⠛⠲⢤⣀⠀⠀⠆⠀⣼⠇
⣿⠀⠀⡇⠀⠀⠈⠂⠈⢻⡶⠿⡋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⣿
⢻⡆⠀⢁⠀⠀⠀⣠⠾⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠰⠶⣶⡄⠀⠈⢦⣸⡏
⠘⣧⠀⠈⠄⢀⡞⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⡄
⠀⢹⡆⠀⣰⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠔⠀⠀⠀⣠⣔⡎⠑⠳⣌⠀⠀⠀⠈⢿⡀
⠀⠀⢿⡄⡏⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⣤⡆⠘⡆⠀⠀⠀⠘⣧
⠀⠀⠈⢿⡇⠀⠀⠀⠐⢤⣴⣖⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢎⠻⠿⠟⠁⣰⠃⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠑⢿⣿⣿⣶⣶⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢧⡙⠿⠟⠃⣠⠇⠀⠀⣠⣖⣲⣶⠆⠀⠀⠀⠠⠄⢄⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠉⠒⠒⠊⠁⢀⠤⠂⠉⠛⢻⠉⠀⠀⢀⠃⠀⠀⠀⠉⠢⠀⢀⡾⠋
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⡄⠀⠀⡰⠓⠲⠖⠋⠀⠀⠀⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠈⠁⠉⢀⠀⢀⠔⠀⠀⢀⣠⠴⣿⡉
⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠖⠛⠉⡀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⡟⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⡄⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠉⠂⠠⠄⠠⠄⠒⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⡿⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡾⠃⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⣀⡴⠟⠁⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⣧⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⢛⣿⡤⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣼⣡⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣰⠋⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⠷⠶⠶⠶⠶⢾⣤⣀⣀⣀⣀⣀⣼⣤⡴⠶⠾⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠒⠶⠒⠒⠒⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡴⠖⠒⠒⠶⠦⠤⠼⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠉⠉⠉⠉⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠾⡟⠛⠛⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⢶⣾⣿⣿⣿⠛⠋⣹⠏⠉⠀⠀⠀⢰⡶⠒⠖⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣤⣣⣤⣀⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⠿⢻⡟⠚⠘⠟⠻⡏⠁⠘⢿⠐⣿⠀⠀⠀⠀⠀⠀⠀⠙⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⣾⣷⣶⣿⣽⣽⣷⣆⣶⣟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠛⠻⠿⠿⢿⣾⣿⣿⡿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀⠁⢀⣀⡀⠀⠀⣀⣠⣀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣶⣾⡿⠓⠛⠛⠛⠉⠉⣩⡤⠴⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠤⠠⠤⣤⣄⣀⣀⣀⡀⠀⠀⣤⠶⠚⢉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠁⢸⠋⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠒⠒⠠⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠸⢀⢄⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠊⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡘
⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠑⠄⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⡀⠀⠈⢆⠀⡔⠁⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠻⡀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢤⡀⠀⠀⠀⠑⢄⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢳⣄⠀⠀⠀⠈⣇⠐⠄⣠⠤⣄⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠐⡂⢄⠀⠀⠀⠈⢆⠀⠀⠀⢫⠢⡄⠀⠁⠘⡄⠀⠁⠀⡄⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠘⡄⠣⡀⠀⠀⠈⢆⠀⠀⠀⢣⠻⣄⠀⠀⠰⠀⡇⢠⠁⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⡀⠐⡄⠀⠀⣸⡄⠀⠐⠉⡄⠈⢂⢀⣀⡇⠈⠪⢄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⡇⠀⠀⠸⠱⠀⠀⠀⣱⢖⢜⠀⢀⡦⣀⠀⠀⠑⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠘⠁⠰⠁⠀⢀⠃⠀⠃⠀⠀⢸⡌⠛⣼⣡⠃⢸⠑⠤⣀⡀⣈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡌⠀⠀⡆⠀⠀⢀⠘⢄⠀⠀⠑⢄⢆⡰⠁⠉⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠘⠀⠀⠀⠇⠤⠤⡎⢢⣈⠑⢤⡤⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠀⠀⢣⣣⡸⠑⠮⠖

⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠶⣄⠀⣀⣤⠶⠖⠛⠛⠛⠛⠛⠓⠶⢦⣄⡀⢀⣴⠞⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⣼⠃⣠⠶⠲⢦⡀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣴⠖⠶⣤⠀⢻⡄
⠀⠀⠀⠀⠀⡏⢰⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⣇⠀⣷
⠀⠀⠀⠀⠀⣷⠘⣧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⠇⢠⡏
⠀⠀⠀⠀⠀⠘⢷⡈⠁⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠁⣠⠟
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⠉⠀⠀⠈⠙⢦⡀⠀⣠⠞⠉⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⡏⠀⠀⠀⢀⣀⡀⠈⣷⢰⡇⠀⣀⣀⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢀⡴⣿⠀⠀⠀⠀⠘⣇⠀⠀⠀⢿⣿⡗⢀⡿⠸⣇⠀⢿⣿⠇⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⡟⢦⡀
⠀⠀⢀⡾⢁⡟⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⣀⣠⠞⠁⠀⠙⢦⣀⡀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⣷⡈⢳⡀
⠀⢠⡟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⢻⡀
⠀⡾⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢷
⢸⠇⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠈⣷⠸
⣿⠐⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡟
⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⢿⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀
⠸⡇⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠛⠉⣇⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⣸
⠀⢻⡀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣠⡿⣀⣠⣴⠾⠛⠁⠀⠀⠀⠀⢠⡟
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣽⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠈⢳⣄⡤⠶⠚⠓⠲⠶⣤⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠒⠶⣦⣠⡟⠁
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⠀⠀⣀⣀⣀⠀⠀⣀⠀⠀⣠⣤⣄⠀⢸⣗⠀⠀⠀⠀⣿⡁⠀⢀⣀⣀⠀⠀⣀⠀⠀⣀⣤⣀⡀⢸⡇
⠀⠀⠘⣧⡾⠉⠀⢉⡿⠋⠉⠻⣟⠁⠀⠉⣷⣼⠛⠛⠛⠛⠛⠛⣧⣰⠋⠀⠈⣿⠋⠉⠙⢾⠉⠀⠈⣿⣼⠃
⠀⠀⠀⠈⠛⠶⢤⣼⣧⣤⣤⣤⣿⣤⡴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣿⣤⣤⣤⣾⣦⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠐⢀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠀⠀⠁⠀⠀⠀⠂⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠠⡠⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠤⠀⠦⢴⠶⠄⣀⣀⠀⢀⠀⠀⠀⡀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠐⠞⣢⠶⠁⣰⠀⣒⣠⠠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠠⠀⠀⠀⠐⠒⢛⡐⢸⠏⠀⠀⠀⡰⠃⣿⠀⣸⡇⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢣⠇⣸⠀⠀⠀⠈⠐⢣⡟⣨⢻⡆⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢨⡇⠋⠀⡟⠀⠀⠀⠀⡒⢼⡇⣸⢺⡇⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⡇⠀⠅⢀⣀⠀⡀⢀⣿⢠⡜⢸⡇⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣋⠀⠠⠀⢫⣽⠉⢛⡇⡤⠚⢾⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡇⠀⠀⣀⣈⣀⣉⣁⣉⣻⠀⣋⡸⠃⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠈⡀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠒⠂⠐⡄⠀⠀⠀⠤⠲⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⠘⢠⠀⠀⠉⠀⢄⠁⠀⠀⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢁⠠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠠⡰⠀⠄⠘⠀⠀⠁⡉⠬⢠⠀⠀⠈⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠑⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡀⠀⠀⠀⠀⠆⡀⡜⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⣇⠠⡀⠀⠀⠀⠀⠀⡄⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⡴⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⠘⠘⡸⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠅⠏⠅⡀⠀⠀⠀⠀⠀⡴⠄⠘⠈⠉⠉⠉⠀⠀⠁⠙⠀⢚⠧⠋⠁⠀⠠⣀⠵⢼⠄⠀⡀⠈⠒⠰⢇⡵⣠
⠀⠀⠀⠀⠀⠀⣀⣂⠛⠖⠃⠀⠀⠀⠠⣄⣵⣤⠅⠀⠀⠀⠀⠀⠀⠀⠐⠦⢛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠶⠒⠚⠓⠦⣄⡀
⠀⠀⠀⠀⢀⣤⡤⠴⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⡾⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⣨⣽⠦⣄⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣽⣶
⠀⠀⢀⣼⡇⠀⠈⠙⠻⢦⣄⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⠾⠿⢛⠋⠩⡟
⠀⠀⣾⠁⠙⠲⣦⣄⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠉⢂⣤⣴⣶⡾⠿⠿⠛⠏⣛⡙⠈⠅⠀⣀⣠⣤⣿⣶⣤
⠀⠀⢻⣄⠀⠀⠈⠙⢿⣷⢦⣄⡀⠈⠙⠦⣄⠀⠀⢀⣿⠏⠁⠀⠀⢒⣀⣩⣥⣴⣶⣾⣿⣿⣿⣿⠿⠟⢋⠇
⠀⠀⢸⠛⠷⣄⡀⠀⠀⠈⠳⢮⡙⠳⢦⣄⡈⠙⢦⣌⣿⣷⣾⣿⣿⠿⢿⣛⣿⣿⡿⠿⠛⢉⣁⣤⣴⣶⠿⠓
⠀⠀⠘⣧⠀⠈⠛⢦⣄⠀⠀⠀⠉⠳⣄⠈⠙⠳⢦⣌⡛⠋⠉⢁⣶⠿⠛⠟⣋⣡⣤⣶⣿⡿⣿⠟⠁
⠀⠀⢀⣈⣷⣄⠀⠀⠉⠳⣦⡀⠀⠀⠀⠙⠂⢀⣀⣈⣽⣷⣦⣼⣿⣶⣶⣿⠿⠛⠉⠉⠀⢐⣧⡀
⠀⢀⡿⠁⠀⠼⣧⡀⠀⠀⠈⠻⣶⣄⠀⠀⠀⣾⡿⠛⠛⠉⠉⠉⠋⠩⠁⣀⣠⣤⣴⣶⣿⡿⠿⠛⠃
⠀⠀⣷⣀⠀⠀⠀⠙⣦⠀⠀⠀⠙⢮⠻⢦⡀⣿⣇⢀⣀⣤⣤⣶⣶⣿⡿⠿⠿⠿⠛⢻⢿⣤⣀
⠀⠀⠈⠙⠷⣤⡀⠀⠈⠳⣄⠀⠀⣰⣶⡿⠿⢻⣿⡿⠿⠿⠛⠉⠁⠀⢀⣀⣠⣤⣴⣿⣷⣾⣿⠃
⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠘⢧⡀⣿⡀⠀⠤⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿⠟⠛⠉⢸⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡙⢿⣷⣶⡿⠿⠿⠟⢛⣩⣭⣶⠾⠟⠛⠉⠀⠀⣀⣤⣴⣾⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⢰⣿⠿⠋⠉⠀⠀⢀⣠⣴⣶⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣻⣿⣀⣠⣤⣶⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠈⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⠀⠀⠀⣀⣠⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠑⠠⠁⠰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣑⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣏⠀⠀⣼⣿⠟⠉⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣦⣴⣿⣿⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⢻⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠇⡀⠀⠀⠀⠻⣿⣿⣿⣿⠁⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⠈⠿⠿⠛⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠸⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠐⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⠒⠂⠉⠉⠉⠁⠀⠉⠉⠉⠉⠀⠒⠒⠂⢠⠤⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⣴⣾⡭⣥⡂⡶⢂⣀⡀⠀⠠⠤⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⢠⢤⣀⣔⣒⣶⡮⠽⠂
⠀⠀⠀⠀⠀⠀⣳⡏⠀⠀⠀⠀⠀⠀⠀⣉⡉⠙⠛⠛⠓⠒⠚⠶⡾⠿⠛⢛⢛⠟⠫⠋⠫⠈⣻
⠀⠀⠀⠀⠀⠀⣩⣧⣄⣀⣀⡀⠀⠁⠀⠐⠚⠛⠓⠒⠀⠀⠀⢸⡑⠔⢈⢔⢄⡀⣠⣸⣾⣾⣾⡶
⠀⠀⠀⠀⠀⠀⠙⢦⡈⠁⠉⠉⠙⠙⠛⠗⠶⠦⠤⢤⢶⣀⣠⣌⣷⣴⡷⡿⠿⠿⣟⡛⠻⢅
⠀⠀⠀⠀⠀⠀⣀⡜⠙⣢⡐⠀⠀⠀⣀⢀⣀⣀⣤⣄⣄⣤⣤⢴⢿⣯⢿⢿⢟⢟⢟⢟⢟⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠐⡕⡀⢹⡻⢿⠿⠛⡛⡻⡫⡋⡩⡫⡣⡢⡣⠪⡒⡑⡁⡡⡡⡡⠡⠠⡠⡑⢝⣿
⠀⠀⠀⠀⠀⠀⢀⡨⣎⠄⠃⢨⢇⢌⢀⢄⢀⢄⠄⢄⢄⢔⢈⢎⢌⢄⢔⢄⣔⣔⣕⣕⣤⣼⣻⠯⣤⣶
⠀⠀⠀⣀⠔⡌⠁⠀⠈⠻⣤⣾⣵⣷⣷⣷⣷⡿⢾⡿⠿⠿⠿⠟⠛⠿⠟⠛⠺⠟⠛⢛⠛⣛⣿⡿⡟⠁
⠀⢀⣾⠷⠖⠺⠿⠿⠧⣖⣐⣰⣈⡭⢍⣀⣀⣀⡐⠒⠈⠉⠓⠂⠀⠀⠁⠀⠀⠈⢁⣠⡾⢟⠡⡀⢧⡀
⠀⢨⣿⠀⠀⢐⣂⡆⠀⠀⠀⠀⠍⠉⣉⠙⠓⠲⠶⠭⢭⣔⣐⣂⣤⠤⣀⣀⣠⣴⢟⠫⡉⢀⣚⣴⡿⡟⠲⠠⠄⡀
⠀⠀⠙⠳⠤⠬⢿⣤⣀⣁⣀⠐⠂⠠⠁⠔⢂⡠⠄⠤⠀⠀⠈⠉⠉⠉⡻⢻⠫⠏⠈⢴⣰⣺⠟⠳⠄⠀⢀⣠⣶⠟
⠀⠀⠀⠀⡠⣶⣿⣿⢟⡙⠛⠛⠿⠶⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⠀⠠⢠⣼⠿⠋⠀⠀⣠⣴⠾⢏⠡⡏
⠀⠀⠀⢰⣼⠓⠉⠉⠙⠳⠯⣅⣂⠠⠄⡀⠀⠉⠉⠉⠙⠛⠷⢶⣶⣤⣼⣶⣾⡏⣡⣤⣶⡿⠟⢿⠉⠂⠀⣘⡇⢀⡀
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠐⠠⢍⠙⠓⠦⣭⣐⡀⠄⣀⠀⠀⠀⠀⠀⢀⣡⣜⡯⠷⡛⠁⠜⢤⢂⠢⣃⣵⣾⡟⠒⣀⡀⠁
⠀⠀⠀⡀⠙⠫⣦⡀⠀⠐⠀⡄⡀⠉⠓⠀⢀⠈⠙⠓⠢⢬⣄⣢⣷⢾⠻⡻⡡⡃⡜⠐⢌⣨⡤⣷⡻⠽⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠛⠷⣦⣄⠀⠉⠓⠤⢄⣀⠀⠀⠀⠀⠀⡎⡀⡀⡑⡑⡐⠄⣌⣬⢾⡮⠷⠏⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠊⠴⣀⡠⠉⡂⠀⠀⠀⡟⠔⠐⢌⣴⣼⣾⡿⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠨⣔⡂⠽⣾⣾⡽⠛⠃⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠑⠀⠠⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⢰⠄⠐⠰⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠉⠛⢢⡀⠀⠀⢀⠀⠀⠀⠠⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢢⣤⠊⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡴⠛⠥⠀⠀⢩⣿⡄⠀⠀⠆⡀⠘⠃⢀⢚⠃⠀⠀⠀⣤⡆⠀⠘⣰⠋⢹⠛⣶⣦⠠⠂
⠀⠀⠀⠀⠀⠠⠂⠀⢁⣐⠦⣍⡂⣙⠪⠗⠆⠀⠚⠛⠀⠀⠀⠈⠱⠴⠃⠘⠀⠀⠀⠀⠀⠍⠀⠀⠀⠉⠀⢈⠁⡋⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣛⠦⣝⠊⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡂⠰⠀⣀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠶⠀⠀⠛⠃⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⡆⠀⠠⠆⠸⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠔⠃⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠈⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢤⡄⠒⠀⠀⠀⠙⠄⠀⠂⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢐⡒⢊⠙⢡⠀⡀⠃⠀⠀⠀⠀⢰⡀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠘⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⡤⠀⠐⠊⡀⠐⠀⠀⠁⠀⠀⠀⠀⠘⢡⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠀⡴⠂⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⣠⣊⣰⠄⢈⠁⠋⠀⠶⠉⠰⢘⠀⠀⠀⠀⢸⡈⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠃⢀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠰⠖⠀⠀⠚⠂⠀⠛⠀⠀⠀⠀⢸⡇⠀⠙⠿⣣⡄⢠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡄⢀⡉⠡⡦⠀⠀⠀⠀⢠⢠⣤⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠈⡋⠀⠙⠁⢀⣱⠀⠀⠀⠀⠐⠋⠁⠐⠆⠛
⠀⠀⠀⠀⠀⠀⡠⠂⡒⠤⡴⠋⠈⠑⠶⠚⠁⠀⠀⠁⠀⠀⠀⠀⠀⠤⠱⠆⠀⠐⠃⠉⠁⠀⠀⢘⠐⠀⠀⠀⠁⠹⣤⣀⡀⠐⠢
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠠⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠟⠛⠛⠛⠉⠑⠋⠈⠃⠙⠀⠀⠰⠶⢶⠶⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⠀⠀⠡⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠉⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⠎⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠌⠀⠀⣴⣾⣷⣄⠀⠀⠀⠀⠀⣰⣾⡷⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣼⣿⡟⠀⢹⠀⠀⠀⠀⢠⣿⣿⡀⢸⡆⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⢿⣿⣶⡿⠀⠀⠀⠀⠘⡿⣿⣷⣾⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢮⡿⠟⠁⠀⠀⠀⠀⠀⠘⠦⠿⠟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⣀⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠷⣤⣀
⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠉⠻⢶⣄
⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⣀⣀⣈
⢠⣯⣤⣤⣀⠀⠉⠑⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠟
⠈⢿⣝⠛⠻⣷⡀⠀⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢂⠀⠀⠀⣼⡟⠀⠀⢀⠖
⠀⠀⠙⢧⠀⢹⣧⠀⠀⢀⡞⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢦⠀⠀⢻⣇⠀⠀⡏
⠀⠀⠀⡼⢀⣼⠇⠀⢀⡞⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢣⡀⠀⠛⢦⡀⠇
⠀⢀⡞⠰⠋⠁⠀⡠⠋⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠉⢸
⠀⠘⣧⡀⠀⠀⠈⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣀⣠⠞
⠀⠀⠈⠙⠳⣶⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣏⠛⠟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠞⠋⣼⠋
⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠉⢛⣿⠟⠛⠶⣤⡀⠀⠀⠀⠀⣠⣶⠶⢶⣤⣀⣀⣀⣀⡼⠛⣷⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⣇⡀⠀⠀⠀⣙⣦⣄⣀⣴⠋⠛⠚⠻⣿⣌⣉⠉⠉⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣾⣿⣆⠀⠀⠀⠤⡘⠃⠃⡁⠄⠀⠀⠀⠄⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠉⣛⡛⠻⠁⠀⠀⠀⠉⠀⠄⡁⠄⢄⢠⢀⡂⠐⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⠀⠰⠦⠀⠠⠃⠀⠀⢹⠢⠋⠛⠃⠀⢀⣀⡄⠗⠀⠀⠠⠥⠂⠀⡽⠯⡃⠀⠐⢃⠠⣤
⠀⠀⡤⠛⢂⠔⢄⠐⢏⠴⡟⢠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡄⠀⣨⡟⠀⠀⠀⠀⠀⡠⢮⡰⡀⢳⡶⠈⠉⡴⠄
⠀⠀⢀⡣⠠⣀⡘⠀⠞⠀⡀⠀⠃⠡⠀⠀⠀⠀⠀⠀⠼⡆⠊⠶⠴⠁⠀⠀⠀⠀⢾⢷⢛⠛⠁⠁⢨⢃⡀⢈⠁
⠀⠀⠠⠀⠈⠃⡇⠀⠄⠀⠵⢁⣁⣠⣶⢂⠀⠀⠀⠀⠀⠀⠂⢠⡀⠀⠀⠀⡴⠻⠀⢓⠀⠀⠀⠀⢈⠠⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠀⢃⢀⡠⠼⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡴⠀⠈⠀⠁
⠀⠠⢠⣄⢀⣀⢄⣈⠀⠀⠀⠀⠠⠤⠒⠶⠈⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⢈⣦⡥⠀⠀⠀⠠⠄⠀⠄⠠⠀⠀⠀⠘
⠀⠀⣉⣐⠅⠄⡽⠢⠋⠌⠐⠊⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⡄⠀⠀⢀⠠⡞⠈⢀
⠀⠈⠀⡰⠂⠃⢨⣀⠀⠄⠀⠀⡀⠠⢠⠤⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⢿⠆⠀⡀⣀⠐⡤⠲⠘⠀⠘⡃⠈⠙
⠀⠀⠸⣴⡗⡧⡛⠀⠛⠉⠀⡘⠎⣾⡁⠂⣤⢶⠈⠐⣖⣡⡄⢿⣾⠏⣿⣹⣿⠞⠰⣇⣇⡰⠁⠀⠤⠃⢤⠁
⠀⢀⠀⠀⠀⠀⢁⡷⢠⠀⡖⠀⠀⢨⢠⠀⠯⠄⡱⠳⠚⠿⣋⢁⢱⠂⡝⡋⢁⢀⡀⠘⠀⠀⠰⠀⠀⠠⠨⢀⣀⣀
⠀⠠⠀⠀⠀⠁⢊⡀⠈⠈⠁⠀⣰⠋⢳⠖⠁⠀⢰⡞⢀⣠⣸⠈⢞⡟⠀⠀⡍⢄⠒⢤⠀⠀⠀⠀⠀⠀⠀⠏⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⢺⢁⣿⣄⡟⣁⣘⣶⠃⠀⠀⢀⠇⡨⠀⠂⠀⠀⠀⠀⠀⡀
⠀⣈⣄⣠⣆⣀⣁⣀⣠⣒⣀⣼⣿⣬⣿⣼⣡⣞⣼⣍⠋⠈⠉⠁⠠⠀⠀⢸⠅⠃⠀⠀⡆⠀⠀⠀⠀⠀⠂⠈
⡀⠋⠉⠿⣉⠙⠟⠉⠉⠉⠉⠋⡋⠙⢻⠛⣿⣿⡏⡙⠀⠠⠒⢃⡐⠦⠀⠀⠐⠒⢃⠀⠀⠀⠀⠁⠀⠈⠀⠀⠐
⠔⠓⠐⠂⠐⠊⠘⣞⣻⣟⣻⠛⢛⠚⡛⣛⣿⣿⣿⣇⠀⠀⠀⠈⣁⠀⠀⠀⠁
⠂⠓⠺⠟⠛⠛⠛⠙⠛⠛⠑⠑⠚⠛⠛⠛⠋⢿⡟⠙⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⢀⠔⠉⠉⠲⢄⠀⠀⢀⣠⠤⠤⠤⠤⠤⢤⣀⣀⢀⠤⠚⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⢠⠃⠀⠀⠀⠀⠀⠑⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢱⠀⣀⣀⣠⡤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⢻
⡎⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⡎⡠⠠⡘⡄⢸
⡇⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠣⡑⢤⠇⡰⢊
⣇⠀⣠⠊⣼⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⢢⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠤⠌⢋⡴⠋⠁
⠈⠒⠁⠀⣿⠀⢿⣿⡿⠀⣀⠤⠀⠠⢄⠀⠸⣿⣿⠇⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠈⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⡜⢠⣤⠀⣤⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠣⡀⠁⠀⠈⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠑⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⢤⣀⢰⠆⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⢹⠀⠀⠀⠀⢀⣧⣀⣀⣀⣀⣀⣀⣠⡤⠤⠴⡇⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢸⡆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢠⡇⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠞⠳⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠹⣄⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡠⠤⠴⠶⠖⠒⠒⠒⡒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠉⠉⠉⠓⢬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⢒⠲⠦⣢⡄⠀⢠⡪⠕⢒⣛⠶⠲⠤⣀⣀⠒⠒⠒⠂⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣾⣿⡟⠒⠓⠰⠬⠉⠐⢚⣉⣡⣤⣤⣭⣽⣾⣿⣶⣿⣧⣾⣿⣿⣿⣿⣦⣮⣯⣝⠍⠉⢉⡉⠉⢻⣿⡇
⠀⠀⠀⠀⢰⣿⣟⣁⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣛⣿⢷
⠀⠀⠀⠀⢯⡬⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠉⠙⠛⠛⠋⠉⣼⡇⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠿⠷⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠋⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣀⡀⠀⠀⢀⡤⣄⠀⠀⠀⣀⣀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⣿⡿⠀⠀⢸⠀⢸⡆⠀⠘⢿⡿⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠓⢤⠀⠀⠀⠀⠀⠈⠲⠚⠀⠀⠀⠀⠀⢠⠔⠛⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣠⣤⡀⢀⣤⣤⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡁⣿⣻⣿⢸⣟⣿⡇⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡖⠚⠉⠁⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠁⠀⠈⠉⠙⠒⠶⠦⢤⣤⣄⣀⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠈⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠁⠀⠘⢦⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠙⢦
⠀⣀⣤⠖⠛⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠳⣄
⣿⡉⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠈⢧⠀⠀⠀⠙⣦
⡇⠙⣆⠀⠀⠀⠈⢧⡀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣀⡤⠞⠉⠀⠀⠀⠀⠈⢳⡄
⠙⣄⠈⢧⡀⠀⠀⠀⠳⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠘⢦⠀⠳⡄⠀⠀⠀⠙⢆⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠈⢧⡀⠹⣆⠀⠀⠀⠈⢳⡀⠀⠀⠀⠳⣄⠀⠔⠊⠁⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠳⡄⠙⣦⠀⠀⠀⠀⠹⣄⠀⠀⠀⠘⢦⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠹⣆⠈⢷⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠘⣦⠀⠻⣄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠙⣦⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢷⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠻⣄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⣦⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠘⢧⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠻⣄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣀⣠⣴⡾⡫⣏⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠘⣦⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣋⡽⠗⢋⡡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⢷⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⢫⣵⣾⠽⠛⣋⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠳⡄⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣷⡯⠶⢛⣩⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠙⣆⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣯⡽⠟⢋⣡⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⢦⠀⠀⠀⠀⠈⢳⣀⣤⣶⣿⣿⣿⠿⠛⢉⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⢳⣀⣀⣤⣶⡿⣿⣿⠿⠛⣉⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣿⢟⣫⠿⠛⣉⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣟⣉⡤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠐
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⢉⣙⡆⠀⣀⡀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠀⠀⠀⠀⢀⣠⢄⡠⠚⠐⠤⣀
⠀⣀⡤⠔⠒⠉⢁⣠⠤⢖⣚⡭⠅⠒⠉⠉⠀⠁⠀⠀⠀⢀⠄⠈⠀⠀⠀⣀⣠⠤⠖⠊⠙⢬⡏⠀⠀⠀⠀⠀⠉⠒⢄⡀
⡜⡽⠓⡤⣒⡭⠗⠚⠋⢁⣀⡤⠴⢒⣟⠁⠀⠀⠀⢀⠔⠁⡤⡖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀
⡇⡄⢈⡷⠉⢹⣦⠒⠊⠉⠀⠀⣀⡤⡒⢱⠀⢀⠔⠁⠀⠸⡁⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⡇⡁⢸⡇⠀⠀⡏⠀⠀⠀⠠⠊⡡⠲⢬⣶⢾⡋⠉⢁⠂⢄⠙⣄⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⡴⡞⠁
⡇⡁⣸⡇⠀⠀⡇⠀⠀⣀⣷⠟⣁⠤⠤⣳⣯⣈⠑⠢⠀⠀⣙⠜⢢⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡤⠖⠋⣁⠔⣳⡆
⣇⣇⡟⡇⠁⢠⡇⠀⢾⣁⠈⠉⠀⠀⠀⠀⠀⠉⠙⠦⣌⠂⢷⡨⣀⡵⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⠍⢀⠴⣊⠕⠋⠀⠙⠲⣤
⠀⠀⠷⢯⣈⢸⡥⠶⣿⢮⡙⠲⢤⡀⠀⠀⠀⠀⠀⠀⣈⡷⣼⠿⡉⠀⠈⢢⡀⠈⢦⡀⣀⣀⣤⠤⠶⠒⠛⢉⣉⢿⣤⣊⠵⠊⠁⠀⠀⠀⣀⡤⡞
⠀⠀⠀⠈⠉⢻⣽⠲⢬⣑⢬⡢⢄⠉⠓⠦⣄⢀⡤⠚⠁⣠⢾⡀⠈⠳⣄⠀⠳⣄⣰⠯⠁⠀⣀⡤⠤⣒⣩⠭⠒⠋⠉⢙⡦⠀⢀⣠⠴⠛⠉⣠⢷
⠀⠀⠀⠀⠀⠈⠻⢝⠢⡈⠑⠮⣷⣍⡂⠄⢊⣧⣀⠴⢪⠿⣉⠈⠓⢄⡀⠙⠦⣌⠻⠬⠥⠤⠖⠊⠉⠁⠀⠀⣀⡴⠞⣹⣤⠞⠋⠁⣠⠔⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣕⠤⡀⠉⡻⡗⠒⢋⡥⠚⢹⡀⠈⠳⣄⡀⠙⠢⣄⠈⠓⢦⣀⠀⠀⠀⢀⡤⠖⠋⢁⡤⣚⠵⢻⣥⠴⣊⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⣒⡿⠖⠉⠀⠀⠀⠉⠢⣄⠀⠙⠦⣄⠈⠓⢤⡀⠈⠓⡴⣚⠉⢀⡠⢒⡥⣚⡥⠞⣿⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠈⠛⢦⣀⠉⠳⢼⣏⠄⣀⣥⣺⠕⠛⠁⣠⠔⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠈⠓⢦⡀⣈⡭⠟⠋⠀⣀⠔⣪⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⣼⢕⠊⢁⠴⣋⠴⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡓⢻⣏⣨⡴⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿