Seafaring Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢾⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⡇⠀⠀⣹⣀⡠⠤⠐⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠂⠀⠀⠀⠀⠈⠄⠀⢀⣤⣤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⣀⣤⣤⡶⠶⠚⣟⠛⢻⣁⣈⡩⠝⠻⢟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⡏⣀⣧⣤⣽⣿⡾⢿⣿⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠖⠚⣋⠽⠛⠛⠁⠰⠃⣾⠘⠁⣀⣠⣴⣶⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠙⠀⠀⠹⣙⣉⣩⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣤⣶⣶⣿⣟⠛⠉⣀⡘⠀⠀⠀⠀⠀⠩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠹⠉⠉⠉⠉⡏⠉⠛⠻⣷⠀⠀⡀⠀⠀⠀⠀⠀⠈⠕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⣻⠀⠀⠡⣀⡇⢀⣀⣀⡀⠀⠢⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡇⣴⡏⠀⡀⠀⠛⠂⣭⣭⠭⢛⣿⣿⣷⡄⠑⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢠⣦⠀⠀⠀⠀⣻⣿⡇⢰⣇⢀⠀⠀⢿⣿⣦⡀⠀⠀⠉⠉⢐⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⠠⢹⣿⣿⠀⠀⢹⣿⣿⡉⠛⠛⠿⢦⣄⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣄⠐⢈⡌⠸⣿⡀⡄⠀⢸⣿⣿⣰⠀⠈⢻⣿⣷⡄⢀⠄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠌⠉⠐⠛⣄⣻⣷⣠⠀⢸⣿⣿⣿⣿⠋⣩⣿⣿⣟⣵⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣎⣉⣉⣛⣻⣟⣉⣻⠶⠒⠈⢀⠿⠟⢛⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⣿⣷⣶⣿⣿⣿⣉⣀⠄⠒⠈⠀⠀⡆⢀⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⢿⣿⣿⣷⣄⠀⡀⠰⠄⠁⠈⠍⠋⢠⠵⠾⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠦⠼⠿⠶⠢⣶⣦⣉⠙⣛⣩⣥⣭⡄⠤⣤⣾⣶⣶⣶⡴⠶⠟⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠿⠋⠊⠰⠿⠿⠕⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠋⠉⠉⠉⠉⠛⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⣤⣀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣠⡶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⠀⠀⠀⠈⠉⠙⢛⣉⠀⠀⠀⠀⠀⢉⡛⠛⠉⠁⠀⠀⠀⣀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁⠉⠛⠉⠛⠶⠛⢛⣿⠟⣀⣀⣤⣄⣀⡙⢿⡛⠛⠲⠛⠋⠙⠉⠉⠉⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⠛⠉⠁⠀⠈⠉⠙⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠶⣤⡴⠞⠉⠛⠶⣤⣄⣀⣀⣀⣀⣀⣠⣤⠶⠛⠉⠻⠦⣤⠶⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢒⠒⣒⡒⠒⠒⠒⠒⠒⠒⠂⠀⠒⠒⠒⠒⠂⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⣄⣀⠈
⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⢉⡜⢨⣿⣿⣾⣷⣄⡰⢦⡀⠀⠀⠀⠠⢤⠒⠒⠂⠀⠀⠂⣀⡀⠀⢀⡀⠠⠀⣀⡀
⠒⢐⣉⣉⡀⠈⠤⠈⠒⠋⠀⠈⠒⠒⡿⡟⠠⠚⣫⢛⣽⣿⡿⣿⣟⠀⢩⣀⠀⠀⠀⠀⠈⠛⠾⣿⣷⣾⣿⣿⣿⣾⣷⣦⣤⠷⣲⢦⣬
⠚⠿⠟⠻⠟⠋⠐⠞⡿⢿⣿⣿⠶⠚⢚⡡⠔⣉⢶⣿⠿⣫⣾⣿⣿⣄⠀⠈⠛⢶⡀⠀⠠⡀⡀⠀⠉⠛⠻⠿⢿⣿⣿⣷⣯⣴⣵⣶⣤
⠀⠀⣀⣴⠾⠟⣲⡦⠤⠒⢀⡠⠔⣚⠥⢒⣩⠶⣻⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⢓⣻⠶⣷⢛⠛⠳⠒⠓⠤⠤⠂⠤⣤⠀⢀⡄⡀⠀⣠
⠩⠭⠔⣒⣨⡭⠖⣚⣛⣯⠵⢒⣉⡤⢞⡩⢶⡿⢿⣿⠟⣫⡿⣿⣿⣿⣜⢴⡤⡀⠀⠁⠬⢉⡳⠬⠷⠟⡭⢶⢤⡀⢤⡾⠘⠛⢯⡯⠶
⣒⣂⣭⡥⠶⡞⠛⣋⣭⠴⣚⣭⢶⣊⣥⣾⡷⠞⢩⡶⢟⢵⣾⢟⣿⣾⢿⣶⣵⡎⠠⠀⢤⡀⠁⠀⢀⠀⢀⡭⢀⢀⠀⠀⢀⠀⠐⢋⣉
⢥⣶⣶⠿⢷⣚⣭⠵⣒⣿⠿⣛⡭⠗⢫⡵⢞⡪⢵⣪⠟⢫⣾⠿⣛⣵⠿⣫⣿⠿⣿⣶⡴⣶⣦⣶⣶⣾⣶⣾⣧⣠⣥⣭⣭⣾⠟⣻⢁
⠹⠶⠞⢛⡩⠅⣒⣫⠭⣒⡯⣀⣈⠥⢈⣠⡴⠞⣋⣴⠶⢋⡵⠞⣋⣵⡿⢋⣡⣾⠟⣋⠔⣫⡿⢛⠕⢛⣿⣿⣋⣿⣿⣿⠟⣫⠟⢃⣞
⣶⣶⡶⢶⠶⣿⣷⣶⣿⣶⣾⣿⣶⣿⣿⣷⣶⣿⣿⣶⣶⣾⣶⣾⣿⣷⣶⣿⣿⣶⣾⣷⣿⣷⣶⣷⣶⣿⣿⣿⣷⣿⣿⣶⣾⣷⣶⣾⣿
⣿⣿⣦⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢠⠄⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠐⠀⠀⠀⡠⠖⠋⠉⣉⠉⠉⠙⠦⣄⠀⠀⠀⠀⠐⠀⠀⠁⡄⠴⠀⠀⠀⠉
⠀⠐⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠁⠀⠈⠀⠀⠈⣧⠠⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠐⠁
⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⡇⠀⠐⠀⠀⠑⠀⠄⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢻⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡏⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣥⡁⢂⡀⣠⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⢈⠀⢻⠂⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡇⢐⣞⡠⠎⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠙⠚⠚⠃⠉⠀⡀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⡅⢠⠔⠂⠀⠀⠀⠀⠀⠁⠁⠀⠠⡄
⠀⠀⠀⢀⠀⠴⠞⣀⠄⠀⠉⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠈⠀⠐⠂⠙⡌⠁⠀⠐⠂⠘⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢠⢀
⠀⠀⠀⠀⠀⢠⣀⣠⣥⡤⠆⢠⡄⠤⠀⠀⠀⠙⠂⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢱⢀⢘⡉⢃⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⡀
⠀⠀⠀⠀⡷⢤⠓⠞⠀⡀⡸⣠⡤⢤⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠠⠈⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠉⠀⠀⠘⠰⣿⠟⠁⡿⠁⣩⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠂⣀⠈⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢀⢄⠀⠀⠀⠀⠀⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢁⡄⢈⠈⠀⠰⣀⠶⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣰⡦⢤⣟⢃⡉⣶⣦⠐⣣⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣘⠀⢿⠌⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠚⠃⠀⢠⡄⠀⠘⠀⠀⠔⠀⠀⠀⠴⠤⠟⠏⠉⠁⠂⠀⠀⠀⠀⡀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⠁⠀⢐⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣈⠀⡀⠂⡞⠀⠓⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠈⠁⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠺⣤⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠑⠀⠘⠀⠀⠀⠀⠀⠉⢿⠱⣆⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠃⠀⠀⠀⠐⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈
⠀⠀⠀⠀⠀⠐⠀⣤⣠⠄⠀⠀⠀⠀⠀⠹⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢶⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠁⠀⠀⠉⢣⡏⠀⠀⡀⠀⠀⠀⢤⢿⡃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠀⢙⠀⠀⠀⠁⠀⣀⡥⠤⠀⠀⡀⠀⠀⠀⠂⠌⡤⠠⠄⢀⡀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠃⠀⠂⠈⠈⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣏⣹⣉⣿⣭⣭⣽⣯⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣽⣯⣭⣽⣿⣯⣽⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⠀⡀⠀⠄⠀⠀⠘⠀⢇⠀⠀⠏⢛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⣆⢨⣇⠀⠀⡇⠸⡄⠀⠀⠸⡆⠙⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢠⣇⠉⠉⠈⠉⠀⠐⢢⣀⡇⠀⠀⠀⠹⡄⠘⣆⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠸⣿⠅⠐⠶⠂⠀⠷⠀⠈⢧⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣆⠀⠘⢧⣀⣀⣘⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡿⠀⠀⠀⠀⠔⢰⣞⣿⠀⢄⠀⠀⠀⠀⢻⡤⢠⠴⠼⢿⣷⣄⣈⡹⠒
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠒⢹⡧⠖⢲⡏⣿⠈⠉⠙⠏⠘⣊⣥⢤⡴⠂⢸⡣⠂⣀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡟⠶⠶⡾⡷⡶⠮⣀⣷⣀⣤⣼⣤⣥⠿⠾⠿⣷⣶⣿⣿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⣧⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⡉⣠⣴⣶⣶⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡶⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠆⠄⠤⠄⠘⠛⢃⣨⠐⢧⣤⠢⣠⣤⢰⡤⣠⣶⠀⣤⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡄⠀⠀⣄⣠⡄⣦⡀⠀⢈⣉⠁⠰⢦⣵⣌⣉⡈⠑⠛⠙⠛⠿⠶⣴⣦⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⢚⡯⣽⠻⣇⠀⠒⠛⠛⣀⣘⣛⠯⣍⣘⢿⣿⣒⠒⢠⡄⠀⠻⡛⢃⡶⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢁⡀⣶⢆⠙⣯⡤⣤⣀⢹⣄⢴⡞⠻⠍⠛⠉⢙⣲⣍⡓⠦⣍⡉⣉⡙⠻⢷⣿⣸⠀⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢖⣸⠂⠙⣋⣾⠈⢹⣠⣌⣬⣿⡏⠀⠉⠉⠓⠒⠦⣤⡙⠻⢿⣿⣶⣤⡈⠙⠳⢦⣬⡛⠷⣦⠈⠢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⢐⣴⠿⠓⣦⣍⢿⣷⣋⣥⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡿⠎⠛⠻⣜⠻⢶⣮⣝⠲⣬⣧⡀⢱⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡾⣟⠠⠄⢀⠟⢳⣌⠽⣟⣀⡀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⠶⣄⠀⢬⣓⣄⡈⠛⠳⣜⡙⢧⢰⡃⠈
⠀⠀⠀⠀⠀⠀⠐⠀⢾⢠⠀⠄⣰⠛⡿⢿⡉⠙⣿⠆⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠈⠛⢦⣈⠻⣿⡲⢤⡀⢳⣴⠶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⣛⠰⡟⠀⠀⣿⣿⣶⣶⠀⠀⠲⣀⣶⣶⣶⣦⡀⠀⢀⣾⠋⠀⠀⠀⠀⡉⠓⢤⡁⠈⠳⣆⢉⡓⡔⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠹⣷⠂⠠⠞⠛⣿⠚⢠⢰⡿⢻⣿⣿⣏⢳⡄⠘⣿⠀⠀⠀⠀⡞⠁⠀⢀⠙⢦⡀⠙⣦⠀⠙⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠙⢉⠑⠂⠀⠛⣀⠀⠀⠛⠶⣿⣿⣿⣿⠃⢀⡿⠀⠀⠀⠀⠁⠀⠀⣤⠀⠈⢻⡄⠈⢧⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠐⠦⠀⣀⣀⣡⠎⠈⣱⢞⡥⠀⠙⠃⠀⠄⠀⠀⠙⠛⠋⠁⠠⣾⡇⠀⠀⠈⢉⡀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⠰⠎
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣙⣡⣦⣤⣀⡌⠁⠘⠁⢰⠞⠀⠀⠀⠀⠡⢰⠀⡀⠙⠛⠶⠀⠀⠻⠶⠂⠀⣀⡀⠀⠀⠀⠹⣦⠈⠷⠂
⠀⠀⠀⠀⠀⠘⠓⠀⠘⠃⣿⣿⡿⠿⣿⣿⡿⢁⣴⣋⠀⣶⠃⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠖⠉⢀⠀⠀⠀⠀⠠⣿⣶⡜
⠀⠀⠀⠀⠀⠀⣆⣠⠄⠈⠡⣤⣶⡶⠳⠦⠟⠛⣭⢿⣶⡃⢠⢠⡄⡀⠀⢀⣼⠀⡀⠲⣿⣿⡿⢻⡿⣧⣀⡀⠠⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠹⠅⠀⠀⠐⠈⠷⠂⠠⠈⠟⠂⠘⡛⠉⢛⣦⡀⠀⠙⠰⣽⣿⡄⡇⠀⣌⠁⢠⣿⣷⣿⡿⠃⠀⡤⠀⣴⠃
⠀⠀⠀⠀⠀⠀⡀⠀⣤⠄⠂⣶⠀⠰⢶⣺⠖⢛⣽⠀⢀⣰⣿⣟⣿⣦⣴⣿⣿⣧⠀⠀⠀⢀⣿⣿⠏⢡⡀⢠⣾⣡⣴⡁⠂
⠀⠀⠀⠀⠀⠀⠇⢾⠀⠀⠀⢠⢿⡟⠩⣅⠀⣤⣥⠀⠙⠉⢠⡝⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣄⣤⣤⠞⢩⡿⣧⡀⣤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⢰⣧⣤⡤⠄⠓⠀⢠⣄⡰⣎⣁⣈⠋⢉⣻⣿⡿⠀⠀⠀⠼⠿⠿⢛⣋⣁⣠⠾⡷⠋⢿⠀⣟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠋⠀⣧⣰⠿⠛⠆⠑⡬⣽⡧⢈⢉⡿⠋⢁⠠⠊⠁⠀⠀⡄⠀⣾⣙⣽⡃⠄⠙⣾⣅⢂⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀⠀⠁⠧⠀⠒⠀⣺⡽⠂⢁⣫⠞⣡⣾⠅⠀⡞⠀⠀⠘⠀⢀⣿⣿⣭⣴⣚⡁⢹⡶⠛⠁⢹⣆⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠆⠰⠞⠓⢴⡶⠛⠋⢠⢻⠏⠀⠀⢂⣡⣤⣤⠶⣶⡿⣿⠿⣤⣍⡁⠀⢼⡟⣂⣄⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠓⢠⣤⡄⢀⡀⠀⢘⡠⠃⣾⣄⠴⠒⠋⠛⠉⠀⠀⡟⠰⡟⣧⠉⠀⠉⢱⣿⢭⡁⢠⡟⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠰⠀⠀⠈⠱⠁⠚⠁⢦⠈⢡⠀⡇⠀⢲⠶⢶⢀⣰⣦⣔⠀⠀⠇⠈⣇⣀⡼⡟⠛⠷⣤⡿⠁⠀⢊⠃
⠀⠀⠀⠀⠀⠀⠀⢶⡆⢿⣄⠀⢠⡄⠀⡀⣀⡀⠀⠘⣶⠋⠀⢣⠔⠂⠀⡀⢼⠋⠉⢹⠉⡾⢷⢀⡟⠉⠓⢷⣀⣴⠛⠁⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠾⢁⠀⠹⠲⢾⡇⠀⠰⣿⡄⣄⢠⣿⠾⣶⡄⠀⠠⢄⣄⡀⠈⠁⣼⡎⠀⠀⢻⣇⣠⡤⠾⠋⠀⠠⠄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠴⠀⠶⣄⡄⠉⠀⡽⠇⠀⠀⢿⠀⢴⠖⠀⠉⠛⠀⠀⢻⠉⠩⠉⠉⠉⠁⠉⠐⠆⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠠⠄⢰⣦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⢶⡖⠠⢀⠀⠀⠀⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠄⣠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠐⡇⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡰⠀⠀⡈⠀⣀⣀⡈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⠶⠦⠰⠂⠀⠀⠠⠤⣄⠠⠶⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠶⠀⠉⡀⠀⠀⠀⠀⠃⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⡴⠒⠁⠸⠠⠁⠀⠠⣤⠀⠀⠀⠀⣶⡌⠁⠀⠀⠀⠀⠀⠀⠀⠶⠆⡸⠀⠠⠀⠠⠀⠁⡀⠀⠀⠁⠀⠂⠢
⠀⠀⠀⠀⠚⠂⠃⠀⠀⠀⠀⠀⠒⣀⣄⣴⣀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠄⢀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⣻⠀⠂
⠀⠀⠆⠀⠀⡐⢠⠖⣦⠀⠀⠁⠉⢉⡈⠋⠀⠀⠀⠀⣠⠤⠀⠴⠖⠒⣤⠰⠖⠀⠦⣀⡈⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⡀⠀⠀⠦⠠⠈⠁⢠⠒⠉⠛⠂⠁⢀⡠⠈⠈⠉⠁⠀⡄⠀⠀⠀⠁⠀⠀⠀⠰⠏⠀⠈⠀⠀⠀⣠⠤⡄⠞
⠀⠀⠈⠀⠀⣦⠀⠀⠰⠀⠄⠀⠀⡠⠖⠉⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠁
⠀⠀⡆⠀⠚⠘⠖⠢⠞⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠁⠂⡀⠀⠀⢀⠼⡇⢠⠞
⠀⠀⠀⣀⠐⡆⠀⠀⠀⢀⠙⠉⠀⠀⠀⠀⠀⠀⣠⡦⠀⡠⠤⠿⠶⠂⠀⠒⠛⠛⠁⠀⠀⠐⠒⠀⠀⠀⠀⠀⠂⠀⠹⢀⠀⢺⠀⠒⠛⢀⡄
⠀⠀⡴⠎⠋⠀⠀⠀⣠⠁⠂⠀⢀⠀⠀⠀⠀⠈⠀⠀⡼⠄⠂⣶⠂⠐⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠄
⠀⠀⣅⠀⠀⠀⠀⡰⠃⠀⠀⠀⠉⠁⠀⢀⡤⠀⣰⠀⠁⢀⣀⡷⠤⢾⣈⠩⠧⠴⠗⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠈⠃⠀⠀⠀⠀⠠⡄
⠀⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⡠⠂⠀⠈⠁⠀⡈⠀⠄⠀⢀⣀⣀⡠⠀⢀⣀⡀⠀⠖⠀⠑⠛⠁⠀⢠⠔⠂⢤⡄⠀⢀⠃⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠⡆⠀⠀⣤⠦⢼⠖⠻⠋⠈⣯⠉⣷⠆⠉⣟⠙⣧⡀⠀⠀⠀⠀⡴⠾⠶⠆⠀⠀⠁⠀⢀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠀⣠⠞⢹⠀⢸⠇⢀⠖⠂⠉⠛⠩⠒⠒⠉⠈⠛⠋⣿⣷⠛⣦⠀⢀⣾⠀⠀⠀⠀⠀⠈⠀⠀⣀⠸⠟⠛
⠀⠀⠁⠀⠀⢸⠀⡄⠀⠀⠀⠀⢀⠔⠁⠀⠘⠶⢸⡆⠘⠀⠀⣤⣀⠀⠀⢀⣀⠀⢰⠄⠛⠙⠙⠻⡥⠼⡴⠆⢻⠄⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡰⠋⢀⠔⠃⠀⠐⢸⡇⠘⣁⣸⣯⡨⠶⠂⠘⣻⠁⣯⣀⣀⣄⣀⣀⣀⡀⣠⠀⢩⠰⠀⠀⠄⠀⢠⡿
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡰⠁⡴⠁⠀⠀⢀⡤⢴⡧⠼⠂⠀⠀⢀⠐⠀⠀⠀⠀⣩⡹⠬⠿⣿⣏⣠⣹⣲⡄⡞⢀⡄⠀⠀⡀⠸⣇
⠀⠀⠀⠀⠀⠀⠳⠖⠀⠶⠤⣤⣀⠀⠠⠞⠁⠀⢈⣇⣀⢠⣄⣀⣼⣀⠀⣀⣀⠀⣿⠀⠀⠀⠰⠋⠉⠈⠁⢀⣧⠸⠆⠀⠰⠋⣸⠋
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢤⣄⠉⠙⠳⣤⣤⣠⡶⢿⣷⣤⣧⣿⢘⣏⣀⡏⣏⣶⡺⣷⢠⣄⣴⡖⡞⣲⢿⣿⣿⣿⢿⡿⠂⢀⡟⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠡⡈⠁⠀⢡⣄⠓⠘⢘⣷⣯⡴⢤⣯⠭⢭⣽⡿⠯⠭⠿⣾⠛⠱⠒⠊⣠⠴⠷⠁⠗⠀⢠⡋
⠀⠀⠀⠀⠀⣠⠊⠙⣦⠀⠀⠀⠀⠘⠆⠠⠚⢻⡶⠛⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⣀⠠⠄⠀⠀⠲⣿⣀⠁⠀⠀⠀⠀⣠⠋⢈⡂⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠁⠈⠀⠳⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠀⠀⠀⢀⡴⠁⠈⠀⠀⡶⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⡈⠀⠈⠲⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⢠⣆⠀⠊⠀⠔⠙⠀⠀⢰
⠀⠀⠀⠀⠄⠁⠂⠀⠀⠀⠀⢀⡀⠈⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠴⠀⠉⠀⠀⠀⡨⠾⠇⠀⠀⠀⡀⠀⠐⠛⠋
⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠊⠁⠒⠀⠀⠀⠸⠀⠓⠃
⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡈⠰⡌⢈⡁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠘⢋⠀⠀⠀⠀⠀⢴⠶⠆⣀⣤⠴⣄
⠀⠀⡀⠁⣀⠀⠀⠀⠈⠀⢠⠖⠀⠸⠤⠅⠀⠀⠀⠀⠀⢈⣀⡀⠁⠠⠀⠰⠇⠀⣠⡆⠀⠀⠂⠀⡄⢀⠄⠚⠃⠈⠉
⠀⠀⠀⠈⠁⠀⠀⠀⠞⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠙⣆⠀⠈⠀⠀⠚⠉⠘⠿⠙⠶⠀⢠⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⠈⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢐⠁⣠⠏⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠙⢋⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂
⠀⠀⠀⠁⠀⠠⠀⠐⠇⠞⠃⠀⠀⠀⠀⢀⠁⠈⡀⠀⠈⡀⠉⠀⡀⢀⠀⠀⠠⠀⠉⠀⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⣤⠒⠢⡀⠀⠈⠑⠀⠂
⠀⠀⠀⠘⠃⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠤⠠⠄⠀⢀⡍⢡⡆⢠⠈⠀⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠁⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠂⣤⠤⠀⠀⠀⠀⠐⢠⠀⢀⠁⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⢀⠀⠀⢒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠄⠠⠄⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠈⢠⠯

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣈⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢙⡎⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣄⣸⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡄⠀⠀⠀⠀⠀⠀⢀⣈⠉⠉⡏⠉⣁⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠶⢾⣟⣿⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡃⠀⠀⠀⠀⠈⠣⣀⣠⣇⣀⡜⠃⠀⠀⠀⠀⠀⠀⠸⣭⣽⡿⠿⠃⠀⠀⠀⠀⠀⠀⠉⢸⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⣀⣠⡤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠐⠆⠂⡗⠂⢔
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡠⠊⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⣽⣿⡿⠃⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠴⠤⢞⢉⡦⠤⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠢⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⠦⣀⣏⡀⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⣦⣠⣀⠀⣠⣤⡰⠂⠀⠀⠀⠀⠀⠀⢰⣶⠀⠂⠀⠀⠀⠀⠀⢠⣼⡉⠽⠍⣹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿
⠀⠀⠀⠀⠀⠀⢸⠁⠙⡊⣛⣛⠁⢸⡆⠀⠀⠀⠀⣴⣿⢋⣭⢻⣷⣴⡆⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⣎⠻⣿⠁
⠀⠀⠀⠀⠀⠀⢈⡵⠻⠞⠉⠻⠷⢎⡀⠀⠀⠀⠀⠹⠿⢮⣯⡾⠿⠙⠃⠀⠀⠀⠹⢿⠂⢤⠄⢺⡿⠁⠀⠀⠀⠒⠲⢮⣟⣓⣨⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣮⠗⠀⠀⠀⠀⢀⠀⠀⣼⣿⡀⢀⡀⠀⠀⠀⠀⢠⠚⠈⢀⠁⠒⡄
⠀⠀⠀⠀⠀⠀⠐⣄⣿⣿⣿⣿⣣⠔⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣄⣀⣈⠁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠛⠟⠋⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣆⠀⠀⠀⠀⠀⢫⡛⠿⠿⠿⣛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡤⢴⠲⠒⡦⢤⣀⠀⠀⠀⠈⠁⠉⢄⠀⠀⠄⢀⠀⠈⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠈⠀⠀⠞⠄⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡠
⠀⠀⠁⠈⠀⠀⠀⢀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠀⠀⠁⠀⠖⠈⠀⠀⠀⠀⣖
⠀⠀⠀⠀⠀⠐⠀⢸⡒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⡟⠀⠘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠃⠦⠀⠀⣠⡰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠠⢰⡄⠀⠂⠀⢠⡼⠃⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠛⠳⡄⠃⣈⡟⠂⠼⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡘⠛⠣⠆⣠⣠⣀⣄⠰⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢀⠠⣤⠘⠀⠚⠒⠋⠀⠰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠀⠘⠀⠀⠀⠉⠁⠀⠐⠀⠀⠀⣀⣄⡀⠀⠴⡀⠀⠀⠈⠀⠁⠐⡂⢠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣠⡄⠀⠇⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠐⠴⠟⢠⠆⠀⠀⠁⠀⡀⠦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢴⠀⠀⣤⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠁⠀⠰⠒⠉⢦⠃⢀⠀⠤⠂⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠃⠀⠀⠄⠀⠋⠁⠐⠀⠀⠲⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⣀⣘⣀⣠⠀⢀⡀⢀⠀⠀⠀⠀⠳⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠠⡄⠀⢶⠺⣽⠛⠉⢉⡀⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢱⡆⠸⠆⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠠⠀⠀⡀⠀⠀⠀⠠⠀⠁⠀⡀⠀⠀⢤⠁⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣀⠈⡘⠲⢋⠉⣀⣤⣀⠲⣶⡖⣙⢶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⠁⠈⢃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡈⠐⠿⠟⠁⡈⠏⠠⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⡀⠀⠀⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠆⠠⡀⡀⠀⠠⠄⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⢠⠰⠓⣀⠀⠁⠉⠀⠰⠀⣰⡀⠀⠀⢤⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⢤⠠⠶⠆⠸⠰⣤⡇⠰⡆⠀⠀⠀⠀⠈⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⢲⠙⣧⡙⠹⠃⠶⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣁⣀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠶⢻⠄⠉⠋⠐⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠀⠶⠈⠁⠀⠁⠀⠀⠀⠰⠆⠀⠀⢀⠀⠘⠂⠀⠀⠀⠛⠉⠘⠉⠂⠀⠀⠁⠀⠀⠀⠁⠀⢄⠀⢠⡄⠀⡤⢤
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠀⠰⠄⠀⣀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠊⢰⠃⠈⠉⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⡀⣠
⠀⠀⠀⠀⠀⡄⠈⠁⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠡⣇⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠠
⠀⢸⡄⠠⡄⠀⣴⠀⠀⠈⠁⠀⠸⠶⣶⢦⡀⠀⢠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡤⠄⠂
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠸⠄⠀⠀⠀⠀⢁⣰⢢⡆⠀⠀⠀⠈⠁⠀⠀⢻⣀⣀⡈⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⠇⠀⠠⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠓
⠀⢰⡄⠀⠀⠀⠀⠈⠻⡼⠀⠀⠀⡀⠀⠀⠀⠰⢠⢿⠃⠀⠀⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⢸⠃⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⣁⡀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣣⡀⣉⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠁
⠀⢐⠀⠀⠀⡀⠁⠀⠀⠀⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠘⠦⠀⠀⠈⠐⠒⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠉⡄⠀⠀⠀⠀⠠⠂
⠀⢸⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠈

⠑⢄⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣢
⠀⠀⠑⣄⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⢣
⢀⠤⠒⠉⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠁⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠒⠄⡀⠀⠀⠀⠃
⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠉⠒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡤⠤
⠒⠄⠀⠀⠀⠀⠀⠀⠀⢐⣀⠤⠤⠒⠊⠉⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⡀⠤⠐⠒⠉⠁⠀⠀⠀⠑⡄
⣀⣀⢠⡠⠤⠴⠒⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⢃⠀⠒⠂⠈
⠢⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⠉
⠰⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⢀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠖
⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠈⠁⠀⠐
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢤⠀⠀⢀⠙⡴⠢⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠐⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣶⠒⢂⠀⠀⠈⣠⡴⠂⡀⠂⠀⠀⢤⠄⠠⠀⠀⠀⠐⠀⠥⠤⠎⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⣦⢠⡀⢸⠀⢸⠀⠀⡀⠓⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⣀⠄⠰⠫⠄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣬⣭⣛⠺⡁⠀⡙⠎⠀⠄⠀⢀⡸⠠⣀⠈⠀⠀⠀⠀⡄⠀⠀⠦⠀⠊⢡⣈⠀⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠉⠀⠀⢸⠏⠙⠖⡄⠀⠀⠁⠐⠀⠀⠁⠀⠀⠀⢀⠀⠄⠰⢅⠀⠀⠀⣠⠦⠀⠀⠍⠛⡐
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠄⠘⠵⢦⠋⠀⠀⡀⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠎⠀⠀⠀⠁⠒⣦⠀⣾⢁⠃
⠀⠀⠀⠀⠀⠀⢸⡸⠀⢀⡠⠚⠁⢀⡠⢊⢴⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠋⢊⠃⠄
⠀⠀⠀⠀⠀⠀⡈⠠⣄⡠⠭⠭⠀⢐⣈⢔⣣⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢲⠂⠀⠀⠀⠀⠀⣇⠌⡐
⠀⠀⠀⠀⢀⠎⠘⢆⢤⣉⠭⢿⡯⠭⢀⣻⣹⠄⠐⠂⠀⠁⠀⠀⠀⠀⠀⡐⣱⠒⠒⠚⡆⠀⠀⠰⣿⣆⡼⣰⠃
⠀⠀⢀⠀⠧⠤⢀⣀⣁⠀⠀⠀⠉⠒⡊⢁⠟⡀⠀⠀⠀⠀⠄⠀⠀⡀⣘⠢⣸⣐⣛⣙⣃⠛⠀⡀⣛⣛⢃⠏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⢓⠂⠄⢤⡆⢀⡀⠠⠠⠐⠐⠀⠉⠁⠀⠈⠢⡈⠢⡀⠀⡏⠀⠀⣀⢧⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠢⡂⠀⠫⢄⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣤⣾⠟⢻⡟⠙⠋⠀⠀⢀⣠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⡄⠀⠀⠀⠈⡄⠘⠛⠛⠋⢇⣀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠀⠀⠀⠀⠀⢁⠐⣀⡴⠖⠛⢇⣤⣾⣿⣿⣿⢿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⡴⣿⠍⠀⠋⣼⣿⣿⣧⣹⣿⣵⣿⠿⠿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠙⠿⣆⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⢠⣔⣤⣤⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠀⠀⢰⡋⣴⣿⣯⣥⡌⠻⣄⡀
⠀⠀⠀⠀⡀⠀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⢁⣤⠀⣴⣷⣿⣿⣿⣿⣿⣿⠿⣀⡈⠙⠒⠒
⠀⠀⠀⠀⢉⡽⠟⠉⠋⠙⣛⡉⢉⡉⢉⡉⣁⠀⠀⠀⠴⠞⠋⠵⠟⢻⣿⣿⣿⣿⣿⣿⢿⢿⢟⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣵⣷⣌⡉⠥⠾⠿⣶⣤⣄⣄⣀⡀⠀⣈⣙⣛⡯⠅⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠈⠉⠉⠉⠓⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⠟⠻⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⣛⣩⣭⣥⣤⣾⣷⣦⣤⣭⣍⣛⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣩⣴⣾⣿⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣦⣍⡻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣫⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣍⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⣡⣾⣿⠟⠁⠀⣠⣠⡟⠀⠀⢀⣀⣤⣿⣧⣄⡀⠀⠀⢀⡀⠀⠀⠀⠈⠛⢿⣷⣌⢻⣦⡀
⠀⠀⠀⠀⠀⢠⣾⠏⣴⣿⠟⠁⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⢹⠉⠉⠁⠀⠀⠀⠽⣤⡦⠀⠀⠀⠀⠻⣿⣦⡙⣿⡄
⠀⠀⠀⠀⢠⣿⢃⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣶⣾⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡘⣿⡄
⠀⠀⠀⢀⣿⠇⣾⣿⠁⠀⠀⠀⠀⢀⣤⣾⠃⠀⠀⠶⣾⣿⣿⣿⣿⣿⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠘⣿⡀
⠀⠀⠀⣼⡏⣸⣿⠇⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢸⣛⣛⣛⣛⣛⣇⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠘⣿⣇⢹⣧
⠀⢀⣠⣿⠃⣿⡿⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⡄⠀⠀⣼⠉⠉⠉⠉⢩⢹⠀⠀⢀⣼⠿⢩⣭⣻⣿⠄⠀⠀⠀⠀⢻⣿⠘⣿⣄⡀
⢀⣾⣿⡿⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠀⠀⣿⡀⠀⠀⠀⢈⠘⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⡆⢿⣿⣷
⢿⣿⣯⡐⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠂⠀⠀⠀⠐⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢂⣽⣿
⠀⠹⣿⣿⡀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⣿⣿⠟
⠀⠀⠀⢻⣇⢻⣿⡄⠀⢀⣀⣠⣄⡀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⢠⣿⡟⣸⡿
⠀⠀⠀⠘⣿⡌⣿⣷⣤⣽⣿⣿⢿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣶⣶⣿⣿⡿⠿⠫⢥⣾⣿⢡⣿⠃
⠀⠀⠀⠀⠹⣷⡘⣿⣿⣿⡿⢿⡳⠾⣯⣽⣛⡿⠷⢿⣻⣷⣿⣭⢛⣯⣥⣝⡛⢛⣛⣛⣻⣿⣿⡿⢿⣛⣻⣿⣿⢃⣾⠏
⠀⠀⠀⠀⠀⠹⣷⡌⢿⣿⣿⠿⣟⣛⣓⣲⠿⠿⣿⡿⠿⣟⣯⣾⣯⢽⣷⣯⣭⣧⡭⠿⢷⣮⣔⡾⠿⣿⣿⡿⢡⣾⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣦⠹⣿⣿⣿⣭⣿⣯⣭⣟⣻⣿⣿⣛⣫⣵⣾⣿⡶⣖⣒⣲⢾⣿⣷⣶⣭⣻⣿⣿⢋⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡛⢿⣿⣿⣿⣿⣷⣿⣾⣿⡭⢍⣛⣋⣑⡻⠿⣿⣿⣷⣯⣭⣽⣿⡿⢋⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣍⠻⢿⣿⣶⣶⣶⣶⣚⣛⣯⣭⣽⣟⣿⣶⣮⣿⣿⡿⢟⣩⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣬⣍⣛⠛⠿⠿⠿⣿⣿⠿⠿⠿⠛⣛⣩⣵⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣷⣶⣌⢡⣶⣾⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠁⢈⠟
⠀⠀⠀⠀⠀⠀⢀⢀⠄⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡠⠒⠠⠖⡠⠒⠈⠉⢀⣴⠕⠉
⠀⣘⠣⡀⠀⠀⠀⡎⠀⠈⢀⣈⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠔⠈⠀⠀⠀⢀⠁⠀⠀⠀⠈⠀⠐
⠀⠁⡀⠈⠢⣤⣀⢀⡴⣲⠿⠛⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡦⠀⠀⡄⠀⠀⠀⢀⠄⠂⠀⠀⠈⠀⠀⠀⢠⠎
⠀⠐⢌⠂⠀⢀⣀⢻⡿⠁⠀⠈⣠⠁⠉⠒⡉⠂⠀⠀⠀⠀⠙⠆⠀⠛⠀⢂⠙⠀⠀⠀⡠⠠⠀⢀⠤⠂⢐⠀⣰⠋
⠀⠀⠀⠈⠐⠂⠉⢻⡗⠀⢀⡄⠧⠀⠀⠀⠈⢧⡄⠀⠀⠀⠀⠀⣀⠀⠄⠁⠀⠀⢀⠜⢡⠀⠀⣨⡾⠋⠁⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡄⢰⠀⠀⠀⠀⠀⠀⢬⠒⠖⠒⣉⠝⠚⠁⠠⠔⠁⠀⠀⢰⠃⠀⠀⡟⢀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⠥⠔⠂⠀⠀⠀⠀⠀⠀⡌⠀⡆⢸⠖⠩⠄⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠐⢸⡔⠀⢄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠆⠀⡰
⠀⠀⠀⢠⡾⠤⣌⢀⠀⠀⠸⣤⠸⠦⣐⣤⣀⠀⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢊⣥⡆⠀⠀⠀⣰⠁
⠀⠀⠐⠜⠀⠀⠹⠢⣉⡀⠀⠀⠁⠒⠠⢌⡩⠬⠅⠀⣤⣀⣀⣀⣤⣤⠤⡴⠖⠹⢀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢥⣀⠀⢈⠁⠠⣐⢚⡥⠾⠃⠀⡆⠠⠤⠖⠪⠀⠀⡆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠠⣉⠈⠉⠐⠁⠀⠀⠀⠀⠀⢠⠀⢀⣤⣤⠤⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠁

⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀
⠠⡀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠠⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠑⡆⠂⠉⠀⠒⠒⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠉⠁⠀⠈⠐⠤⡀
⠐⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠤⣀
⠀⠐⡄⠀⠀⠀⠈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁
⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠑⢄⡀⠀⠀⢈⣆⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠑⢄⠘⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣠⠦⠆⠐⠐⠒⠒⠒⠒⠒⢄⡀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠁⢀⡔⠉⠉⠂⠆⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⣀⠠⠀⠘⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⣀⠔⠁⠀⠀⠀⡀⣀⠠⠤⠄⠐⠓⢤⡀⠀⢠⢞⠘⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠢⡀
⠀⠉⠉⠁⠀⠀⠀⠒⠂⠤⠔⠠⡀⢀⣣⣤⠮⠤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⢈⠟⠀⠈⠛⠁⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠎⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢰⠀⢀⡀⠠⠠⠀⠒⠂⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡠⠔⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠊⠐
⢀⠄⠀⡒⠨⠆⠒⠉⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠃
⠐⠈⠁⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠆
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡲⠿⢻⡟⠀⠙⠻⢷⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⢀⡴⢋⡴⠶⣄⠀⠀⢱⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣋⣰⠋⠀⠀⠀⣷⣀⣼⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠈⠙⢧⡀⠀⣶⡾⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⣀⣀⣽⣶⣷⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢀⣠⣴⠶⠚⠋⠉⠉⠉⠈⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⡤⣞⣽⣊⡥⢴⣲⣭⣵⣶⡶⠶⡶⠶⣶⣦⣤⣔⣢⢤⣀⠹⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⢔⣯⣾⠿⣫⣵⠾⠛⡋⠉⣀⣀⣤⣤⣤⣤⣄⣀⠈⠉⠛⠿⣾⣝⡻⣿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣼⣡⣿⢟⣵⡿⠋⠁⣠⣤⠿⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⡾⢦⣔⠀⡙⠻⣮⡟⢿⣮⡳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⢯⣾⡟⣵⡿⠋⢤⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠉⠻⣦⣠⠈⠻⣯⡻⣿⣝⣆
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣰⢣⣿⢏⣾⠏⠀⣤⠟⠁⠀⠀⠀⠀⠀⣀⣤⠤⠰⡇⠠⢄⣼⠇⠀⠀⠀⠀⠈⠹⣦⡂⠙⣿⡝⣿⡎⢧
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⡯⢣⣏⣾⠇⠀⣾⠃⠀⠀⠀⠐⣦⡔⠉⠀⠀⠂⠀⣿⠀⣾⡯⠉⢲⣤⠆⠀⠀⠀⠘⢷⡂⠘⣿⡼⣿⠘⣆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡾⢀⡿⣼⡏⠀⣽⠃⠀⠄⠀⠀⣴⠉⢻⡓⢤⡀⠀⠀⣿⣾⣿⡡⣺⡿⠉⢢⡀⠀⠀⠀⠈⣷⡁⠸⣷⢹⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢰⡇⢸⣇⣿⠀⢰⡟⠀⠀⠀⠀⢸⠀⠈⠀⠑⢄⣨⣶⠀⣽⣿⣧⣾⠏⠀⠉⡀⢡⠀⠀⠀⠀⢸⡇⠀⣿⡏⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠃⣸⢹⣿⢀⢸⡇⠀⠀⢀⣀⡇⠨⠀⠀⠀⠈⠛⠉⣼⣿⡟⠙⠃⠀⠀⠀⠅⢈⣄⣀⠀⠀⠈⣿⠀⣸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⢸⣸⣿⠀⢸⡇⠀⠀⠀⠈⡏⢙⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⡋⢙⠉⠀⠀⠀⢠⣿⠀⢸⡇⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡗⠺⣭⣿⠀⠸⣧⠀⠀⠀⠀⠸⡀⢀⠀⡠⣣⣾⣿⡟⣿⠿⢿⣌⢂⠀⡀⠀⡜⠀⠀⠀⠀⢸⡇⠀⣾⡇⠀⣤⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⢸⣷⠤⢿⣄⠀⠂⠀⠀⠻⣀⣼⡶⠋⣿⡟⠀⣿⠀⠀⠙⠳⣿⣀⡜⠁⠀⠀⠀⢀⡿⡀⢰⡿⠀⣰⣿⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⣏⢿⣆⠀⢿⣏⠓⠶⢤⣤⣟⡣⡄⣸⡿⠀⠄⣿⠀⠂⠈⣠⠜⠛⠆⠀⠀⠀⢠⡾⠅⢠⣿⠃⢠⣇⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣮⢿⣆⠀⠹⣦⡀⠀⠀⠈⠉⢙⡟⠒⠲⠶⡷⣶⣋⣉⣀⣀⣀⣀⣀⣀⣰⡟⢤⣤⡿⣳⣾⢯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⢾⣧⡻⣷⣄⠊⠛⣦⣄⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣴⡟⠛⢀⣴⢟⣽⡿⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⠳⣝⡏⠈⠻⣷⣄⡀⠙⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⢶⠛⠙⠀⣠⣶⢟⣵⣿⢟⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠙⠻⢷⣦⣄⣀⠀⠉⠉⠉⠍⠉⠉⠁⣀⣠⣤⣶⢿⣫⣷⡿⣿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠙⠦⣄⡠⣀⡈⠉⠛⢛⣻⡿⢿⠿⢿⠿⠛⠛⠉⣁⣠⠿⣛⡽⠚⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠽⣶⣾⣿⡿⠿⠿⠷⢶⣖⣛⠯⠽⠒⣋⣥⠴⠖⠛⠉⠉⠉⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠶⠖⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠉⢩⡍⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣀⣈⣁⣀⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢹⣄⣀⣀⣰⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠂⢀⣾⣿⣿⠿⠿⠛⠛⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠞⠽⡆⠀⡟⢝⢢⣠⡤⠄⠓⠀⡂⠀⠀⠀⠹⡄⠀⠀⠀⠁⡤⣤⠈⠿⠟
⠀⠀⣤⢤⠀⠀⠈⠀⠀⠙⠛⡿⡮⢤⣹⢼⡥⠞⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⢄⡀⠈⠀⠀⠄⠙⠂
⠀⠀⠛⠁⠀⠀⠀⠀⢀⠀⠀⣧⣥⠴⢺⡾⡍⢓⢶⡿⣤⡀⠀⠐⠛⢋⠁⢸⡇⠀⢣⠀⠀⠀⠉⠁⠠⠊⠀⠀⠀⢀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠚⠛⠷⣕⣾⣠⣹⣯⠞⠁⣀⠀⠀⠀⠶⠶⢯⡼⡷⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⠁⠙⠆⢀⡘⣧⢀⡤⠀⠞⡿⢽⡛⠓⠀⠀⣤⡀⣴⡄⠀⠒⠆⠀⠀⠃⠀⠀⠚⠦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠛⣿⢻⣍⡀⠀⢠⠇⠀⠀⠀⡀⠀⠀⡽⢫⡄⠀⢠⡶⠶⢤⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠉⠀⠀⠀⠀⠀⠸⡏⢠⠎⠀⠀⠀⠀⠸⣄⠀⠀⠙⡆
⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠐⡈⠁⠀⠀⠀⠄⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⠷⠶⠛⠀⢀⣤⡀⣸⡇⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠐⡂⠔⣀⠀⠀⠀⠀⠀⣄⢠⠀⣄⢠⠀⡤⢤⡤⢤⢠⠶⡀⣤⢠⡄⠀⣠⣶⡟⡌⠉⠉⠀⠀⠀⢃⡀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⡿⠆⣀⠀⠀⠀⢿⣾⢠⢿⢸⠀⡇⠀⡇⢸⢸⠀⢰⣿⢸⡇⠀⠉⠈⠉⢀⣀⠀⠀⠀⠐⢠⠊
⠀⠀⠀⠰⠉⠉⢲⠀⠀⣸⡧⠸⢣⠆⠀⠀⢸⢻⣸⠉⡷⣄⡇⠀⡇⢸⡞⣄⢾⠹⡖⣇⡀⣠⣶⣿⣿⡇⢀⣷⣦⠀⠈
⠀⠀⢠⠃⠀⠀⠘⠀⠀⢿⣧⣴⢏⡼⠁⠀⠀⠀⠀⠀⠀⡀⠄⢠⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠛⠉⠁⠙⢿⣿⣧
⠀⠀⠺⠀⠀⢠⣇⠀⠀⠀⠙⠿⠚⠁⠀⠀⠀⠀⠀⠀⠁⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣈⠉⠉⠀⠐
⠀⠀⠀⣰⡄⠀⠀⠀⠁⠠⢤⡤⠤⠴⠊⠀⠀⠀⣀⠀⠀⠰⠵⠀⠀⠀⡠⠤⠎⠀⠀⠀⠈⢿⣿⠏⢰⣶⣾⣿⣷⠆⠀⠀⢀
⠀⠀⣤⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠁⠀⠀⠁⠀⠘⠛⠛⠉
⠀⢄⣀⡉⡄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⡀⠀⠀⠀⣰⡀⠠⠀⠰⠂⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⠀⠀⠀⠀⢂⡀
⠀⠀⡀⠈⠁⠀⠀⠀⠐⠢⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡉⠁⠀⢰⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠘⠀⠀⠀⠰⠿⡅
⠀⠀⠀⠀⠐⠾⣷⠆⠀⢠⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠏⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠄⠀⠀⡤⢶
⠀⢸⠁⡀⠀⣴⣿⠀⡐⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐⡂⠀⢠⣴⣶⣦⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒
⠀⠛⠛⠃⠄⠝⡇⡈⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⡆⠁⠀⠀⠙⣿⣿⣿⣿⣷⣄⠀⠀⠈⠑⠶⠈⠀⢰⡄⠀⠀⠀⠀⠠⠞⠂
⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⣤⠷⠀⢻⣿⣿⣿⣿⡿⠇⠀⠀⠀⢾⡟⢹⣿⠻⠿⠿⠀⠀⡀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋

⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⡆⣤⠄⢀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠃⠬⠡⠌⠂⠘
⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠠⠤⢄⣀⠀⣼⡄⣁⣠⠤⠐⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⡤⡤⡤⠤⠴⢀
⠀⠀⠀⢸⣿⣿⣿⣿⢟⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢐⠷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⢿⣿⣿⣿⣯⣴⣿⡿⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⢀⣤⠀⣀⡀
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢡⣄⣉⡤⠍⠤⡄⢛⡊⠅⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⣴⣷⠂⡏⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣷⣶⣶⡶
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣸⣿⣿⠇⡷⠦⠀⠀⠀⢀⣤⡾⣻⣿⣿⣿⣿⢿⡳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣾⣶⠄⠀⠀⠀⠀⠀⢀⠄⠀⣰⣿⡿⢫⠞⠑⠀⠀⠀⠀⠻⣫⡾⣻⡟⣿⢹⡟⣎⢿⣮⡟⠁
⠀⠀⠀⠈⠛⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⠊⠙⠄⠀⠀⠀⠀⠀⠺⣿⣱⡟⣸⣿⢸⣇⢻⣮⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⢿⠿⢾⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⠛⢶⣄
⠀⠀⠀⠀⠀⡠⢠⢠⠀⣷⠒⡔⢮⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢉⣤⣼⣿⣗⡀⠈⢣
⠀⠀⠀⠀⠈⡴⣣⠯⡦⢸⠰⡘⢦⡉⠁⠀⠀⠀⠀⠀⠀⠀⢤⡲⣿⣮⢿⡹⣷⣶⣤⣀⠀⠀⠀⠀⢻⣿⠿⠶⣦⠈⢻⡄⠀⠁
⠀⠀⠀⠀⢀⠼⢣⢧⡇⡇⣇⠹⣄⠉⠀⠀⠀⠐⠛⠻⢿⣿⣿⣿⣿⣿⣧⢷⡻⣿⣿⡿⠛⠁⠀⠀⠘⢿⣛⣋⣛⢷⣰⡷⢀
⠀⠀⠀⠀⠈⠢⠁⡾⠁⠇⠘⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣭⣷⠟⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢄⠀⠀⠑⠀⢀⣀⣀⣇⠀⠂⠁⠀⠀⣠⠀⠀⢠⠃⠀⠀⡴⠁⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⡠⠷⡊⠉⠉⠀⠀⣀⣈⣦⣀⣀⡀⡔⠁⠀⢀⠎⠀⢀⠞⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣏⡠⠔⠊⠁⠀⠀⠘⡤⠒⠒⠉⠁⠀⠀⠂⠀⠈⢻⠒⡤⣋⠀⣠⠋⠂
⠀⠀⠀⠀⠔⠚⣇⡇⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⡀⠀⠈⠀⠀⢜⣔⠁⢀⡽⠧⣀⡀⢀⢂⠀⢀⣀⡠
⠀⠀⠀⠀⠉⠐⠪⠄⠀⠄⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢄⢀⡴⠋⠈⣱⠮⣄⡀⠀⠈⢸⠁⠉⠄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣠⠜⠫⡀⢀⡜⠉⢣⠀⠉⠓⢦⣞⣀⣀
⠀⠀⠀⠀⣀⣤⢤⠧⠴⠦⡄⢀⣀⣰⠚⡟⠛⠋⠉⠉⠀⠀⠀⡼⠋⠀⠀⢨⡀⠀⢀⡜⠀⠀⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡏⠉⢇⠀⠀⡇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣸⠈⠑⠼⡀⠀⠀⠀⠀⢀⠢
⠀⠀⠀⠀⡀⠤⡔⢳⢊⣹⣇⣠⡼⡤⠤⢵⠴⠶⠶⠖⠚⠁⠀⠈⠠⠀⢠⠃⠀⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣱⠋⠉⠀⠳⡀⠀⢱⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠠⠌⠀⠈⠣⡀
⠀⠀⠀⠀⠀⢠⠟⠦⣀⠀⠀⢘⣤⠔⠇⠀⠀⠀⡜⠀⠉⠒⠤⣀⣠⠃⠀⠀⠀⠐⠀⠁⠀⠀⠀⡀⠘⠢
⠀⠀⠀⠀⢠⠏⠀⠀⠈⢢⡔⠁⠈⠣⡘⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠑⠢⠄⣀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠳⣤⣄⣀⡙⡇⠀⠈⡄⢀⣀⣀⣠⣃⣀⣠⣤⣤⡤⡭⠶⠤⣤⡶⠖⠒⠛⠉
⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠉⢹⠋⠉⠉⢁⠏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠉⠢⢄⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠢⠂⠃⠂⠘⠞⠚⠘⠂⢀⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠈⠁⠈⠀⠈⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠼⠔⠀⠉⠁⠈⠀⠀⠐
⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠂⢄
⠀⢀⠄⠪⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⢸⠀⠀⠀⢀⠄⢀⡀
⠀⠈⢄⠀⠀⠀⠈⠐⠢⠤⡀⡀⠤⠐⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠘⡀⠀⠀⠀⢸⠠⠐⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⣰⡤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⡀⠀⠀⠀⠀⢀⠤⠐⠈⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⢢⡤⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠁⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠄⠀⢀⠠⠐⠈⠀⠀⠠⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠁⢙⠁⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢁⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⡏⢹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⣴⣿⣿⣿⣿⣿⠟⢋⣥⣶⣶⣿⠃⠘⣿⣶⣶⣬⡙⠻⣿⣿⣿⣿⣿⣧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣷⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⣿⣿⣿⣿⠏⣴⣿⣿⣎⠛⢿⣿⡇⣀⢀⢸⣿⡿⠛⣱⣿⣿⣦⠹⣿⣿⣿⣿⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣧⡀⣸⠃⠈⠓⠘⣇⢀⣼⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⠥⠿⠟⠛⠛⠉⣍⡁⠀⡖⣡⣌⠢⠀⡬⠉⠉⠛⠛⠻⠿⠬⣿⣿⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣿⣷⡒⣶⣤⣤⣄⣀⣉⠉⠀⢦⣛⣛⡴⠀⠓⣀⣀⣠⣤⣤⣶⢲⣾⣿⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡿⠁⢹⡄⢠⡀⢠⡏⠈⢿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⣿⣿⣿⣿⣆⢻⣿⣿⢟⣠⣶⣿⡇⠐⠁⢸⣿⣶⣄⡻⣿⣿⡟⣰⣿⣿⣿⣿⡿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⢿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⠁⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢻⣿⣿⣿⣿⣿⣦⣌⡛⠿⢿⣿⡄⢠⣿⡿⠿⢛⣡⣴⣿⣿⣿⣿⣿⡟⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣇⣸⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⢁⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋⠉



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠟⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠿⠿⠟⠛⠛⠛⠻⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⡀⠀⣸⠿⠿⠿⠄⠀⠀⣠⣶⣄⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣿⣿⣿⣿⣧⣴⣧⠙⠜⢡⣷⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠿⠛⠋⠁⠹⣿⡏⢱⣿⣺⣷⣉⣻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠉⠉⠉⣉⣩⣽⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣶⣦⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣠⣤⣤⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢻⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⠀⣀⣀⣤⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠉⠉⠉⢀⣠⠄⢀⣴⣶⣶⣶⣶⡶⠋⠘⠛⠛⠛⠛⠉
⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣿⣿⠋⠀⢀⣴⣶⣿⣿⣿⣿⣿⡿⠃⠀⠈⠉⠉⡉⠉⠉⢀⣠⣤⣤⣤⣴⠃
⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠁⣠⣴⣶⣶⣶⠿⠁⠀⠐⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣛⣻⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠄⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠄⡄⠁
⠀⠀⠀⠀⠀⠀⣀⡀⡠⠤⠤⠁⠀⠀⢤⣀⠶⠂⠀⠀⠀⠀⠀⡜⠩⠧⠀⡁⠀⠀⡠⠫⠍⠤⠃
⠀⠀⠀⣀⡔⠉⠀⠒⠉⡀⠲⡂⠀⡀⠷⠀⠀⠀⠀⠀⠀⠒⠂⠃⠀⠀⠂⠁⠄⠀⠈⢀⠀⠄
⠀⢰⠀⢀⠄⡠⡀⠠⠀⠐⠚⠟⠒⠀⠀⢀⡀⠀⠤⣄⠤⠂⣀⠀⠂⠀⠀⠀⠀⢅⠈⠈⠁
⠀⢈⠀⠀⠄⠀⠁⠔⠊⠚⠁⣀⠔⠊⠉⠀⠤⠀⠀⠁⠀⠀⠰⠉⠀⠀⠀⢠⠤⠜⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⡰⣆⡀⡓⠂⢀⠔⠈⠀⠀⠀⠰⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢀⠀⠈⡤⡀⠀⠀⠀⣀⠀⣘⠁
⠀⠈⡀⢀⠀⠈⠁⡐⠋⠀⠀⠀⠀⢠⡇⢀⠠⠧⡄⠠⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢸⠩⠼⢁
⠀⢰⠋⠉⠀⢀⡜⠀⠀⡀⠀⠀⠀⠀⢠⠆⠂⡖⢀⡀⣤⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈
⠀⢸⠀⠀⢀⠎⠀⠀⠀⣰⠀⠰⠂⢸⠀⠠⠒⠉⠙⠒⠈⠈⠁⠀⠅⡤⠀⠀⣀⠀⡁⠀⠀⠀⠀⠀⠐
⠀⠘⠀⠀⠰⠀⠀⠀⠀⣷⠀⢀⡤⢼⠄⠖⠐⣇⣳⠄⢸⠚⣆⠀⠀⠀⠠⠴⠤⠀⠈⠀⢀⡀⠀⣠⣀⢸
⠀⢈⠀⠀⡇⠀⠀⠀⠐⠁⡠⠋⡅⢸⠂⡔⠀⠉⠉⠃⠈⠉⠉⢩⣿⣙⡄⢠⠇⢀⡀⠀⠀⠀⢠⠘⠛⠁
⠀⠀⠀⠀⡁⠀⡀⠀⠀⠀⠀⠀⠈⢙⡏⠕⢐⣖⣂⠀⢴⣆⠾⠀⠀⠀⠈⠉⡉⠈⠃⠀⠀⠀⣸⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠐⠠⠀⠄⠀⠀⠀⢤⡇⠏⠈⠉⠁⠂⠈⠉⣁⠄⠿⠿⣀⣿⠡⢰⠀⠀⠀⡀⢿⡀⠠
⠀⠀⠀⠀⠉⠏⠀⠒⠲⠤⣄⠁⠀⢸⣧⡂⡶⡔⣷⢀⠤⢄⣣⡀⠀⢈⣀⣀⣤⣼⣚⣦⡐⠁⡟⠀⢀⣀
⠀⠀⠀⠀⠀⠑⠀⠈⠑⠄⠀⠙⢙⠹⠽⢿⣟⡫⣼⣾⣾⣾⣿⢷⣿⠿⠦⠞⣉⣿⡯⡏⠀⠌
⠀⠀⠀⢀⡄⠁⡆⠀⠀⠈⠂⠐⠛⠷⠂⠉⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠺⣅⠁⠄⠀⢀⠎⠉⠀⠀⢀⢺
⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢄⠀⠂⠀⠱⡀⠀⠀⠀⠀⠀⠀⠤⢀⠀⡰⠃⠠⠀⠘⠁
⠀⠀⠐⡐⠀⠁⠀⠀⠐⠀⠂⠀⠀⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠈⠀⠀⠀⠿⠁⠀⢤⠀⠠⠒⠁
⠀⠠⠂⢀⠀⠀⠀⠀⠁⠀⡀⠀⠈⠐⠀⠄⡀⠀⢀⠀⠀⢀⡀⠀⠀⠒⠉⢊⠀⠀⠈⠈⠋
⠀⢀⠄⠀⠀⠀⠄⠒⡨⠠⣆⠐⠀⠀⠀⠀⠂⠠⠀⠀⢠⠀⢀⡀⠀⠀⠘⠉⡁⡾⠙⠃
⠀⠈⠐⠃⠀⠠⠆⢠⠃⠀⠀⠀⠀⠀⠀⠐⣍⢣⠀⠀⠀⠒⠋⠳⠖⢦⢀⡔⠄⠀⠀⠀⠀⠀⢀⠄
⠀⢀⡠⠀⠀⠀⢠⡀⠢⠀⠀⢀⠖⠀⠀⡀⠀⠞⠀⠀⠀⠀⠴⠀⠐⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠠⠀⠄⠈⠈⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠐⢐⡦⡀⠂⠄⠀⠁⠀⠀⠀⠀⠀⠐⠋⠈⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⢢⠤⠀⠀⡀⠐⠀⠨⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⣒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡤⠖⠚⢹⡇⠉⠒⠦⣄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢷⣄⣀⠤⣾⡇⠠⢄⣀⣴⠟⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢈⠿⣿⣦⣿⡇⢠⣾⡿⢏⠀⠈⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣘⣁⣀⣈⣀⣈⣉⣻⣇⣼⣿⣷⣾⣦⣤⣼⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠹⡉⠛⢻⠛⣻⣿⠋⣿⣦⣠⡀⢠⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢈⣿⡿⠛⠀⣿⡟⠻⣿⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢟⠉⠈⠙⠀⣿⠇⠉⠈⢙⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠒⠤⠄⣿⠤⠴⠚⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠎⡉⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠉⠒⠠⣍⡒⠤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣠⣤⣄⡀⠀⠈⠑⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⠀⣤⢄⣀⡜⠁⢀⡴⠋⠁⠀⠈⠙⢦⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢥⡇⠀⠀⠀⠀⡔⠉⢆⠀⠀⠀⠀⠀⡠⡫⠊⠁⠀⢀⡠⢘⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⣠⠔⣉⠉⠭⣉⣿⡲⡀⠀⠀⠹⠛⡟⠀⠀⠀⠀⠀⣿⠁⠀⢀⠔⠁⢀⠎⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡾⠁⠀⡌
⠀⠀⠀⠀⢰⠁⡜⠁⠀⠀⠈⡇⢸⠄⠀⡠⠃⡰⠁⠀⠀⠀⠀⠀⣾⠀⢠⠋⠀⠀⡌⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠋⠀⠀⡰
⠀⠀⠀⠀⣾⠟⢆⠀⠀⠀⡠⠃⡜⢆⠉⣀⠔⠁⠀⠀⠀⠀⠀⠸⡆⢠⠃⠀⠀⡸⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⢠⢻
⠀⠀⠀⠀⠑⠵⢤⣉⣉⣉⣤⠮⠒⡌⢷⠻⠼⢖⢄⠀⠀⠀⣠⡳⢁⠏⠀⠀⢀⣇⡀⠀⠀⠀⡰⠁⠰⠁⠀⠀⠀⠀⢀⠇⠈⡄
⠀⠀⠀⠀⠀⢀⠊⢣⠰⡊⣴⣺⢷⢘⡌⢆⠀⠀⠑⠵⣖⠮⠛⠁⡘⠀⠀⣠⠋⠑⡦⠕⡒⡴⠁⣰⠁⠀⠀⠀⠀⢠⠋⠀⢠⠁
⠀⠀⠀⠀⠀⢸⠀⡇⠱⡑⣌⠥⠒⢉⣠⡼⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⠁⠀⠀⠉⠒⠼⠁⢠⠏⣒⠤⣀⠀⡰⠁⠀⠀⡜
⠀⠀⠀⠀⠀⠘⡄⠸⡄⢱⣠⣴⠾⠛⠉⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⠁⢠⠋⠒⠢⠟⠒⠿⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠘⣶⠛⢹⠻⡀⠀⠀⠷⣄⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠃⠀⠀⠀⠀⢠⠃⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠱⡀⠀⠸⡈⠢⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢃⠀⠘⣦⠜⠓⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠜⢆⠀⠈⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡡⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠉⠀⠈⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠀⠀⣠⣤⣤⣤⣤⣤⡀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠋⠁⠰⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⣈⣉⡉⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢴⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢠⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠐⣠⣧⣤⢦⣤⣧⣤⣶⣶⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⣿⣿⣴⠾⢛⣿⣷⣿⣯⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠛⣿⣿⣿⡻⢁⣠⠾⢛⣿⣿⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⣿⡟⣠⡴⢛⣥⣨⠖⣉⣠⣴⣿⣿⣷⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⣿⣟⣿⣷⣦⣿⣛⣀⣾⠿⢛⣛⣡⣾⣿⣿⣇⡀⠠
⠀⠀⠘⠷⣴⣦⣤⣤⣶⣶⣌⣻⣿⣷⣿⡉⠹⠿⠛⠋⠁⠀⠀⠉⠉⠉⠛⠙⢿⣯⣤⡀
⠀⠀⠀⠀⠀⠈⣻⡭⠋⠛⠛⠋⠉⠛⠛⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢀⡀


⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⠀⣴⣄⡀⠀⠀⡀⠀⠀⠉⠚⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠼⡇⠀⠀⠀⣰⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣤⠀⣀⡄⠠⠀⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠀⠀⠀⠢⠄⠀⠠⢿⡄⠀⠀⠐⠀⣘⡶⠿⠂⠀⠐⣯⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉⠁⠁⠀⠀⠀⠀⣶⣟⢀⣀⣷⡄
⠀⠀⠀⠠⢤⣤⠀⡀⠀⠀⠤⠤⠴⡞⠦⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠢⠤⠾⠶⠾⠶⠶⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⡀⠘⡀⠤⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠆⠀⠀⠶⡆⠀⠉⠐⠀⠀⡈⢄⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠂⢀⡀⡄⠃⢀⠀⠀⠀⠠⠕⢈⠣⣤⡀⠀⠀⠀⢀⣀⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠡⠀⠀⠈⠑⠀⠤⢀⠴⡄⠉⠀⠠⣭⢡⠉⠰⡇⢠⠈⢳⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢄⠀⠀⠀⠀⠀⠙⠍⠀⢄⣀⠈⣠⢶⣧⣀⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠘⡇⠈⠀⠀⠀⠀⠀⠀⠂⠀⣠⠑⠆⠈⠀⣣⠍⠉⢸⠀⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⣦⣄⣀⢀⠀⠀⠈⠀⠀⠀⠀⢸⣟⢐⡄⣈⡅⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣶⢶⣋⣿⣿⣿⣿⣞⣟⣻⢦⣤⣄⠀⠠⠀⢸⡋⠉⠁⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠼⢋⠟⢩⣾⣽⣯⢩⣿⣿⡛⡟⣿⣿⠛⣿⡟⣶⣺⣷⣶⣶⣾⢳⡶⢶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢼⣳⠀⠉⣌⠀⢿⡐⣷⡾⣁⠘⢠⠬⠒⠳⣃⠻⠌⠩⠛⣤⠀⣹⠛⣻⢻⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠫⢘⠟⢀⡷⠙⡆⡉⠀⠘⠀⠀⢀⠟⠁⠀⣶⠆⠀⣤⣌⠀⠴⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠅⠀⠄⠐⠄⠀⠁⡇⢸⠁⠘⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⠐⡈⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⣀⠀⢄⠀⢺⢣⠷⠴⣤⢀⠀⠀⠀⠀⠀⠁⠀⣀⢀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠹⡄⠀⠀⠀⠀⢿⢿⡤⢘⠛⠃⠀⠀⠁⠀⠀⠀⠤⠽⠦⠘⣛⢀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡀⠀⠉⠀⠀⠀⠛⠂⡉⠁⠀⢠⡈⠈⠓⡀⠀⢀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡀⠀⠠⠒⠃⠉⣑⣣⡄⠀⠁⠆⡐⢤⣂⡠⠇⢲⠄⠀⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠑⠊⠁⠊⠒⠈⠁⠈⠉⠠⠀⠒⠦⢤⠀⠀⢁⡉⠀⠞⠀⠀⠈⠛⠁⠀⡁⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠓⠢⠤⡠⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠆⠄⠀⡀⠀⠠⢀⠀⣈⠉⠈⠀⠀⠀⠀⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⢀⡀⠤⢠⢐⡀⡆⣂⢂⣐⣐⢒⡐⠂⡀⣄⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⡀⠄⢂⣡⡴⠼⠋⠉⢀⣀⠀⠠⠤⠌⠉⣍⠹⢓⠶⠬⣓⢤⡀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡠⠢⣀⠶⠚⠓⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠉⠙⠺⣆⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡰⠎⠡⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠐⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡔⢀⡶⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠎⣿⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠂⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⡬⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⢠⠃⣀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠭⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠁⠨⢁⡫⠤⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠨⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣓⠂⠀⠀⠀⠀⠀⠄⠈⠀⠁⠀⠀⢠⠀⡨⠋⠘⢲⡌⢽⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠥⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢌⣡⡞⠫⢽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠱
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣨⡄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢀⠞⠀⠀⠀⠀⡠⠀⠐⠁⠀⠀⠀⠀⠠⢤⠄⠀⠀⢠⠃⡙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡯⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⠒⠈⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠐⡶⢯⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⢥⠀⠁⠀⠀⠀⠀⠀⠀⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠊⠾⠹⠜⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠢⡀⠀⠀⠑⠀⡀⠀⠀⠀⠀⢠⡧⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠔⢢⠶⠚⠆⡶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠲⢄⡀⠀⠀⠁⠂⠤⢀⣈⡁⠀⠀⠀⢀⣀⠠⠄⠒⠛⠉⠁⠀⠀⠀⢀⡄⢂⠁⠈⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠙⠂⢀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠡⠐⠀⡢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠈⠉⠒⠢⠠⠄⡄⡀⢀⠄⡤⡤⠤⠒⡈⠡⠀⠀⠣⠀⣠⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣄⣀⡀⠂⠀⠀⠀⠂⠠⠈⠀⢂⠈⣀⣥⠰⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡉⠈⠐⠒⠓⠒⠒⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠄⠊⠠⠂⠀⠐⢀⠄⠂⠡⠀⡠⠀⠀⠔⠀⠠⠂⠈⠄⠂⠀⠐⠀⡠⠒⢁⠔⠈⠄⠀⠔⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠤⠤⠤⠤⣤⣤⣄⣀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣀⣀⣀⣉⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⡴⢻⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠜⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⣀⣤⠞⠾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠛⣹⡟⠁⠀⠀⣼⠛⠋⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⠀⣤⣼⣿⣷⠦⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⠀⢠⡟⠀⠀⠀⠀⢻⡿⠿⠟⢻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡄⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠞⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⢶⣶⠋
⠀⠀⠀⠀⠀⢀⡞⠁⢠⡟⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⡾⠞⠛⠉⠙⠀⠀⣿⠀⢀⡀
⠀⠀⠀⠀⢀⡾⠁⢀⡾⠀⣠⠀⢠⡇⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⡇
⠀⠀⠀⠀⣼⠃⠀⢸⠃⣼⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⣾⣿⣶⣇⠤⠄
⠀⠀⠀⢠⡟⠀⠀⣿⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠿⠷⠾⠖⢲⡟⠋⠉⠉⠉⠀⡇
⠀⠀⠀⢸⡇⠀⠀⠿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⣠⣤⣤⢴⣶⡗⠊⠉⠉⠁
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⡿⠛⣻⠛⠹⠋⠉⠉⠰⠁⡞⠁
⣄⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣰⠋⠀⠐⠁⠀⠀⠀⠀⠀⠀⢸⣧⢠⡤⠤
⠈⢳⣄⠸⣿⣷⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠙⢷⣌⠻⣿⣷⣄⡀⠀⠀⠘⣷⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣆
⠀⠀⠀⠀⠻⣷⣌⠙⢿⣿⣶⣿⣿⣿⡆⠀⠀⠀⠙⠿⣶⣶⣿⠶⣿⡟⢿⡟⠛⠛⠛⠟⠛⠛⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠈⠛⠿⣿⣿⣿⡉⢳⠐⠲⡤⢬⣀⣈⡂⢿⡅⠈⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠠⠂⠠⡉⠛⠷⣼⣀⣸⡧⢸⣇⣹⠇⢾⣇⡀⠰⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⣀⠀⠀⠈⠉⠛⠻⠧⣼⣄⣻⠀⠉⠒⣯⣥⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⡂⢻⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⣎⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⢲⣦⣤
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠀⠒⢿⣿⣧⠻⣄⣠⣄⡀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠂⠀⠉⣛⠛⠻⣻⡿
⠀⠀⠒⠀⠒⠈⣨⡅⣠⡦⣶⠊⠀⠈⠙⢷⡿⠁⠠⠙⠒⠛⠶⠦⠄⡀⠀⠐⢂⠀⢒⣈⢉⠓⢂⣿⠇⠀⠂
⠀⠀⠀⠀⠐⠶⠋⠀⠙⢥⠀⣴⣦⣤⣄⣀⣁⣤⣠⡀⠀⢠⡄⢀⣤⡤⡀⠀⠈⣉⣉⣾⣷⣾⠟⢋⣀⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡩⠟⠋⢩⣭⣀⣻⣿⡯⣿⠈⠳⠌⠛⠿⣯⠭⠭⠀⡁⠙⠛⠓⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⢄⠠⠊⢔⡠⠄⠺⣏⠑⠀⠀⠉⠛⠂⠀⠀⠒⠀⢠⠦⠐⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡠⡔⣒⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡄
⠀⠀⠀⠀⢀⡀⠤⢠⠀⣀⠀⠀⠀⠀⠰⠒⣟⣏⢭⠅⠃⠀⠀⣀⣀⣤⡤⠚⡁⠀⠊⠁⢲⠶⢤⠤⣄⡀⠀⠀⢍⠀⠈⠁
⠀⠀⠀⢸⢼⢶⢺⠻⠉⠉⣀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⡖⠋⠹⣉⡀⠀⠀⠁⢀⢀⣀⣉⠤⠖⠁⣢⣿⠂
⠀⠀⠀⠘⠚⠉⠈⠀⠀⠀⠘⢻⡿⢛⠁⠀⠀⠀⠀⠀⠈⠻⠶⣤⣄⣈⣉⣉⣉⣉⣡⣤⣤⣤⡶⠾⠋⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣤⠆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠉⠉⡤⠑⠀⠀⢀⡀⡔⢢⠀⠻⠇⠀⠀⠀⠀⠀⠠⠀⠀⡤⡤⣦⢤⢤⡀⠺⠿⣀⡖⡗⢟⢻⢹
⠀⠀⢀⡠⡤⠴⠀⠀⠀⡈⠀⠀⠀⠁⠀⠀⠀⠀⠛⠀⠈⠐⠃⣠⠀⣇⢀⢹⣸⡼⠋⠀⠀⠏⠳⠶⠼⠼⠼⠄
⠀⠀⠀⠀⠀⠀⣀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠼⠀⠠⡻⠀⠈⠉⠉⠀⠀⠀⢐⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠄⠖⠈⠀⠀⠀⢀⢀⢀⠀⠀⣈⠋⠀⠀⠀⠸⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠈⠑⢦⣀⣷⣦⡀⠀⠀⢠⣶⣶⣄⣴⠀⢰⣷⠿⣿⡟⠃⣿⣯⣩⢹⣿⣹⠗⠀⠀⠀⠈⡗⠒⠂⢰⠂⠐
⠀⠀⠀⠠⢤⣀⣀⠀⠀⠀⠉⠃⠀⠀⣿⣁⣿⡏⢿⣧⣼⠏⠀⣿⡇⠸⣯⣤⣤⠸⡿⠙⠷⠀⠀⠠⠀⢹⠋⠓⣾
⠀⠀⠀⠀⠀⠈⠃⠀⠀⡤⠶⣄⠀⠀⠘⠛⢉⣤⣄⢩⡤⢤⡀⣴⢶⡀⢀⣴⢶⢠⡶⠖⡂⠈⠀⠀⠀⠾⠲⠶⠻⣤⠐⠐⠂
⠀⠀⠰⠖⠶⢶⡀⠀⠀⢧⣀⠞⠀⠀⠀⠀⠘⠳⢦⣼⣷⠾⠛⣿⠾⣧⢼⣇⣠⠜⣟⢋⣁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠻⠷⠖⠀⠀⠀⠀⠀⢈⠠⠂⠈⠛⠛⠁⠛⠀⠀⠉⠀⠀⠀⠉⠁⠀⠛⠉⠉⠀⠀⠀⠀⠉⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡰⠀⣔⢈⠀⢀⡀
⠀⠀⠀⠀⠉⠰⠶⠀⠀⠀⠀⢀⠖⠉⢠⠄⡀⠀⢁⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢦⣀⡀⠉⠀⠄⠈⢁⣸⠔⠋⠀⠀⠇⠀⠀⠄⠀⠈⡷⠀⠀⢀⠀⠄
⠀⠀⠀⠃⣄⡀⢀⡀⠤⢾⡁⠀⠀⠀⠉⠋⠍⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁⠀⠀⣌⠀⠄⠀⢀⡀⠀⢠⠐⢀
⠀⠀⠀⣴⠇⠀⠈⠇⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠋⠀⠐⢦⣤⠄⠒⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⣇⠀⠀⠀⡀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠐⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢱⣶⡟⢛⡟⠻⣶⡎⠀⠀⠀⠰⠴⠿⠿⠆⠀⠀⢀⠀⠀⠀⣸⠅⠀⢀
⠀⠀⢠⠖⢂⣤⠄⣠⣿⡥⣤⡤⠖⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣿⡃⣑⣶⣷⣎⢈⣿⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠑⠊⠉⠉⢹⠉⠉⠁⠒⠁
⠀⠀⠈⠉⠁⠀⠀⠁⢹⠀⠀⠀⠘⠋⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡠⢻⡟⢅⣠⣿⠁⠀⠀⠲⠒⣻⣿⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠷⣾⣷⠾⠟⢅⠀⠀⠀⠀⠘⢻⣿⠀⠀⠰⡁⠀⠀⢠⣘⠀⠀⠀⢀⡆
⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠑⠄⣠⠀⢸⡁⠀⣠⠈⠁
⠀⠀⠿⡂⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠉⠛⠯⠛⠉
⠀⠀⠀⠘⠦⣄⠀⠀⣸⡄⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢻⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠉⠻⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠛⠁⠀⠀⠈⠁⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡶
⠀⠀⠀⠀⠠⠄⠤⠼⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣰⣀⣁⡈⠀⠀⠀⠀⠀⠴⢂⣀⣀⡸⣃⣀⣀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⡅⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢠⣤⠤⠠⠜⣏⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡦⠀⠀⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀
⠀⠀⠀⠀⣰⣶⣠⢴⣀⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⢠⣄⣷⣶⡶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠡⠁⠙⠁⠀⠘⣇⠀⠀⢰⡀⠀⠀⠀⢘⠃⠀⠀⠀⣀
⠀⠀⠀⣀⣘⠻⣿⣿⣿⣧⡀⠞⡁⠀⠀⠀⠀⠀⠀⠀⡀⠙⡅⠀⢰⣾⣿⣯⣿⣯⣿⠇⠀⠀⠠⣜⣻⣃⣴⣖⣢⣄⠀⠁⢹⠈⠀⠈⠣⡀⡤⠀⢸⡇⠀⢀⡠⠋
⠀⠀⠀⠟⠛⢪⠛⠿⢿⠃⠐⠺⠯⠉⠁⠀⠀⣁⣈⠛⠱⡶⠞⠓⠒⠛⠛⠿⠛⠛⣃⠀⠐⠶⠀⠈⠻⣿⣿⣿⣿⣿⣄⣀⡞⠀⠀⠀⠀⠀⠛⠶⣎⡷⠚⠉

⠈⢆⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠱⠀⠀⠀⠀⠀⣸⡀⠀⠀⠌⠀⠀⠀⢸⡀⠀⠀⠀⡞⠀⠀⠀⢠⠞⠁⠀⢀⠜⢶
⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢳⣀⠤⠔⠒⠒⠊⠉⠉⠈⢣⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡰⠃⠀⠀⣰⠋⠀⠀⠀⠁
⠀⠀⢀⡷⠀⠀⢀⣠⠴⢒⠁⠙⢆⠀⠀⢀⣀⣤⠤⠖⠒⠻⠉⠒⠲⠦⣏⣀⠀⠀⡴⠁⠀⢀⣼⢁⠀⠠⠎⠐
⠀⠀⢸⣠⡴⠚⠉⠀⠀⠀⠀⠀⠈⢷⡊⠉⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢸⡀⢩⠾⢄⡀⢠⡞⠀⠁⢄
⠴⠚⠹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠠⠄⣀⠀⠀⡊⠀⠂⠄⣜⣡⠋⠀⠀⡽⠻⢄⡀⠀⠀⠑⠀⠀⠀⠀⢀
⠒⠒⠦⣞⢁⠀⢀⡀⠄⠀⠀⠉⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⣠⠞⠉⠙⢦⣞⡁⠀⠀⠉⠉⠉⡏⠉⠙⢉⠉⠁
⠀⠀⠀⠈⢩⠂⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠂⢙⣦⠞⠁⠀⢀⡴⠣⡈⠙⠳⢦⣄⡀⢠⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣀⣠⡤⠖⠋⠀⠱⣄⣠⠟⠀⠀⢱⠀⠀⠀⠈⢙⡿⠶⠦⡧⣤⣄⣀
⣠⣤⠤⠴⠷⠒⠒⠲⣆⠀⣀⣀⣹⠉⢿⢉⢉⠉⠁⠀⠐⠒⢂⠀⢠⡞⠃⠠⠀⠀⢼⣅⠀⠀⢀⡞⠀⠀⢀⠁
⠀⠀⠀⠀⡆⠀⠀⠀⡏⠉⢹⡀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⡵⢏⠀⠀⠀⠀⠀⢸⠀⠑⠢⣞⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⣀⣧⠤⠴⢻⠃⠀⠀⢧⠀⡀⢘⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠑⡀⠀⠀⢀⡇⠀⠀⠈⠈⠑⢦⣠⠀⠀⠀⢠⠃
⠒⠉⠩⣅⣸⡤⠶⠻⡖⠚⠛⠛⡏⠉⠉⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠞⠀⢑⠾⢤⣀⠀⢶⣞⠳⢦⣴⠇⠂
⠀⠀⠀⡼⠀⡆⠀⠀⠘⢦⠀⠀⢱⣀⣀⣇⣀⣤⠤⣤⣀⡀⠀⠀⠀⠀⠠⢠⡍⠠⢤⣉⠀⠠⠈⢹⠾⢄⠙⠦⠙⢦⠨
⠉⠉⣹⠛⠶⣄⠀⠀⠀⠀⣳⡤⠔⢇⠀⠀⠀⠀⢰⠃⠀⠉⠑⠢⢄⣀⢀⠎⠀⠀⡀⠀⢀⠂⠀⠁⠀⠀⠐⠄⡀⠀⠑
⠀⣰⠃⠀⠀⠈⠳⣄⡠⠚⠁⠙⢄⠸⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢈⠟⠒⠤⣄⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⣰⠇⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⠣⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠉⠛⠢⢤⡀⠀⠀⠀⢀⣀⣀⣤⣤
⣏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠦⢤⣽⣀⣀⣀⣧⣤⣤⡤⠤⢤⡾⠴⠶⠶⠶⠒⠺⡖⠛⠛⠛⠛⠻⢭⡉⠉
⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠰⠇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠑⠦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢲⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠰⠀⠇⠀⠤⠄⠀⠀⠀⠀⠀⠤⠄⠇⠰⠇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠆⠤⠀⣼⠁⠀⠀⢹⣄⠀⠤⠶⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠉⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⡠⢴⣶⢶⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠴⠀⠘⡄⣠⠟⠋⠛⢆⡁⡜⠀⠰⠤⠤⠤⠤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⣠⠀⠀⠀⠘⠈⠂⠀⢀⡀⡤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠈⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠐⠒⠂⠲⠀⣶⡇⠀⠀⠀⠀⠀⠀⣷⡆⠰⠂⠂⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣾⣿⡷⠒⠒⠒⠒⠒⠲⣿⣿⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢨⠿⠁⡇⠀⠀⠀⠀⠀⠀⡏⠹⢯⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠲⡞⢣⣤⣧⠤⠤⠤⠤⠤⢤⡧⣤⢛⡶⠒⠒⠒⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠾⠉⡈⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡘⡹⢦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⢞⡥⠊⠀⠇⢠⣇⣀⣀⣀⣀⣀⣀⣇⠀⢇⠈⠢⣙⢦⡀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠴⠋⢀⠔⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠈⠑⢄⡈⠓⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⠔⠉⣠⠜⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⢤⡀⠓⢌⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠔⠁⠀⢸⠀⠀⠀⠀⠀⠀⢈⡯⠉⠉⣩⡉⠉⠨⣏⠀⠀⠀⠀⠀⠀⢨⠀⠀⠑⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⡎⠀⠀⠀⣿⡇⠀⠀⠈⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⡇⠀⠀⠀⣿⡇⠀⠀⠀⡟⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠲⡞⠀⠤⠄⠀⣀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⡇⢀⣀⠀⠤⠄⠐⠶⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠤⠤⠤⠬⡇⢹⡶⠶⢾⣿⡗⡶⠶⢺⠃⡻⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢁⠀⣿⣿⣿⡿⢿⣿⣿⣿⠀⠃⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣰⣄⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣴⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠉⠉⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠉⠉⠉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠀⠀⠀⠀⠀⠄⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠄⠤⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⣀⣼⣷⠶⣄⡀
⠀⠀⠀⠀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⣡⠞⠁⠈⠢⡀
⠀⠀⠘⠤⡐⢂⣉⡵⠦⡀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⣀⣠⣴⣾⡿⠛⠉⡠⠞⠁⠀⠀⠀⣠⣾⣆
⠀⠀⠀⠀⠈⠢⢔⢛⣮⣍⠶⣄⠀⠀⣜⣀⣠⣤⣶⣾⣿⠿⠛⠋⠁⠀⠔⠉⠀⠀⠀⠀⣠⣾⡿⢋⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠑⢶⣊⣻⣭⠵⠴⡿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⢋⣴⠟⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠄⠒⠒⠻⣦⣀⡛⣮⠡⠤⣐⢖⠐⡤⢄⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⣁⠴⠋⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⠟⡆⠘⢸⡟⣿⠃⡇⢸⠚⣀⣤⣴⣾⣿⠿⠛⣁⠤⠊⠁⠀⠀⠀⣠⡾⢋⡅
⠀⠀⠀⠀⢀⡇⠤⣐⣒⠆⠀⢰⣿⢀⣧⣥⣬⠷⢷⡛⣿⡿⠛⠋⣁⠤⠐⠈⠀⠀⠀⠀⢀⡠⠞⢁⣴⣿⠃
⠀⠐⠽⠋⠉⠹⡀⠀⠀⠀⠀⡼⠉⠀⢛⣉⣁⣲⣉⠽⠦⣚⣺⡉⠀⠀⠀⠀⠀⢀⡠⠒⠉⢀⣴⠟⠋⠎
⠀⠀⠀⠀⠀⠀⠈⠢⠄⠤⠚⠁⠀⠀⠀⠻⡉⠁⠈⠒⢍⡩⠷⣜⣓⣄⡠⠔⠊⠁⣀⣤⠾⠋⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⣤⠴⠷⠮⡩⠕⠐⠛⢢⠶⠛⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣤⣶⠾⠒⠋⠉⠀⠀⢀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣦⣠⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⢀⣀⣤⣾⣿⣷⡚⠓⠂⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⡤⠊⠁⢈⠂⠀⠀⠙⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⡧
⠀⠀⠀⢀⠀⠉⠘⠒⠤⠀⡤⠀⡀⠴⠦⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠈⠳⡄⠀⣀⡴⠋⠀⠀⠀⢀⠀⠀⠘⢛⣟⠃⠟⠙⠛⠛⢻⣿⣦⣄⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠷⠶⠶⠶⠓⠚⠉⠀⠀⠀⠀⠚⠰⣦⠀⠀⢹⡶⣤⣀⣀⢢⣄⣮⣵⣿⣷⠶⠶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣀⣀⣠⣀⣾⣿⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣯⡉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣇⢁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⢻⢠⣏⠂⡴⢐⢸⡇⣴⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠋⠀⠙⠊⠋⠉⠉⣇⠘⢺⡗⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡾⠋⠡⠊⡀⠀⢸⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠘⢷⣶⣆⡘⠁⠀⠸⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣤⣴⣿⣾⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣰⡄⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠶⠚⠙
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⢻⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣀
⠑⠃⠀⡰⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⡞⠋⠁⡢
⠀⠀⣸⡇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⢰⡞⠂
⠀⠀⢿⡇⠀⡞⠀⢀⡔⠀⠀⢠⡄⠀⢡⠀⣧⠀⢠⠰⡟⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠁⠀⣻⡇⢠⡇⢀⡿⠁⠀⠀⠀⠀⠘⡉⣇⣻⠀⡆⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠄⠀⣿⣇⡼⠁⣼⠇⠀⠀⠀⠀⠀⠀⢹⣿⡟⣸⣏⣴⣿⢃⡀⠀⠀⣀⣀⡤⠘⢿⣼⣸⠟⠶⣶⣶⣦⣤⣀⠐
⠀⢠⣿⡟⢁⣼⠇⠀⠄⠀⠀⠒⠀⠀⠀⠙⠷⠟⠿⠿⠛⠚⣠⣴⣾⣷⣶⣶⣆⣀⣿⡗⠇⢤⣼⡾⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣤⣀
⠀⣸⠟⡴⠟⢁⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡏⢀⣹⣧⡷⣀⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣰⠟⣭⣷⣦⣽⣧
⢰⣿⣫⠔⠚⠋⠉⠀⠈⠉⠙⢶⡀⠀⡀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠒⣶⣿⣶⣿⡿⠙⢿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⡖⠔⡄⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⣾⣿⣿⠟⠫⠁⠈⠲⡟⢿⣿⣷⡄⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠋⠈⠉⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠀⠀⢀⣀⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣛⣋⣭⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠙⠻⣭⠭⠿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⢠⠐⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⡂⣄⠀⠀⣸⠀⡈⠁⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠀⠀⣀⠀⠀⠀⢀⡶⠀⠀⡄
⣀⡄⠈⣿⠀⠀⠀⠀⠀⠀⠤⠀⡰⣄⠀⠸⠇⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠈⠐⢶⠗⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠰
⠶⠦⠛⠉⠹⣋⢛⣴⣦⣤⡆⠄⣐⠀⢣⠰⠛⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⠔⠊⢁⠀⠀⡀⠀⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠙⠂⠘⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠮⠡⡀⠀⠀⠈⠉⠉⠻⠂⠀⢠⣄
⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⠄⣀⣀⡄⠔⠂⠈⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣀⢀⣀⡀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠉⠑⠖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠰⠿⡓⠡⠆⠂⠤⣥⣖⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⠦⡖⠀⠀⠀⠀⠀⠀⠀⠃⠐⢠⡼⠉⢝⠲⠀⢀⣶⠠⠔⠀⠁⠀⠀⠆⠈⠁
⠀⠀⢠⢤⡤⣶⢏⡌⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠙⢤⠤⣶⢺⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⢄⠚⣶⡄⠀⠀⠀⣆⡁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠙⢤⡆⡀
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⠌⠠⠋⠀⠉⠀⠀⣰⢃⡃⠀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠠⠀⠀⠀⠘
⣤⣤⣦⣜⣀⡛⠀⠈⠈⠀⠐⢀⠊⠀⠀⠀⢰⡾⠞⠁⠎⠀⠀⠐⠀⠀⠀⡆⠐⠀⠈⠐⠁⠒⠀⠉⠀⢀⣠⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤
⠈⠁⡉⠀⠐⠃⡤⠀⠤⠠⠞⠁⠀⠀⠀⠀⠛⠁⠈⠂⠀⠀⠀⠀⠀⠀⠍⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣀
⠠⠐⢀⠄⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⣠⡀⢄⠀⠠⠁⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢰⡆⡀⠀⠘⠿⠃⠂⠀⢈
⠟⠀⢁⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠈⠀⠀⠀⠀⠈⡴⠀⢀⡀⠀⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⢀⡀⠢⠠⠈⠓⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡄⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⢄⠀⠀⠀⠀⠀⠀⡂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠆⠀⠀⠀⠀⠀⠘⡂⠀⠀⠠⢾⡿⠈
⠀⠀⠀⠀⡨⠣⠄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢣⠹⠌⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠁⠈⠀⠀⣠
⠀⠀⠀⠘⠀⠀⠂⠀⠄⠀⠀⠀⢀⣰⠆⠀⠀⠀⣀⠀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠄⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⣀⡔⠁
⠈⠀⠀⠀⠀⠄⠤⠊⠈⠀⢣⡀⠠⠁⡆⣀⠖⠉⠀⠁⠀⠈⢋⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠔⠈⠀⢀
⠀⠈⠐⣄⠀⠀⠀⠀⠀⢈⠄⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢰⡵⠂⠉
⠺⠃⠀⠁⠐⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠠⠀⠉⠊⠉⢳⠂⠀⢄⡰⢾⠀⠀⠚
⢂⠒⠀⠀⠀⠀⠀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈⠺⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠿⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡷⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠘⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣰⠲⠶⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⢦⠠⠋⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢶⣤⣄⣀⠀⢰⣟⣻⣟⣿⣶⣶⣶⣤⣼⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⣼⣩⡙⠲⢾⣽⡏⢉⣛⣿⣿⣏⡙⢻⠿⡇⣤⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠿⣿⣿⣎⠁⠀⠀⠾⠯⠉⢻⠿⠿⢿⣯⣿⣿⣿⣷⣷⠀⠀⠈⢇⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣶⣿⣖⠤⢤⣀⠀⠀⠀⠁⠒⠦⠤⢭⣭⣽⣿⡿⠶⠶⠛⣾⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢻⣿⣿⣿⣿⣯⡀⠀⠀⠈⠀⠐⢢⠤⢤⣒⣤⡿⠶⣿⣿⣶⣾⣏⣩⣝⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠁⣀⡘⣿⣿⣿⣿⣷⠦⠤⢀⡒⢠⠄⢤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠀⠀⡠⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⡟⣶⣶⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣤⡀⠻⣿⣿⣿⠃⢀⠴⠳⠾⠛⠿⢿⣿⡿⣽⣿⣿⣿⣿⡿⢟⣿⢲⣿⣿⣿⠃⣠⣶⣶⣾⣷⣤⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢙⣆⠘⣯⠁⣀⠀⣠⣶⡷⢎⣀⡀⢰⣶⣷⣤⣈⠻⠿⠿⢿⣯⣤⣶⡇⠈⣠⣽⣿⣿⣿⣷⣭⣭⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⣴⣶⣿⣷⢶⣶⣤⣄⠀⠀⠀⣀⣠⣴⣾⣿⣤⡏⠰⣿⣿⣿⣿⠀⢦⣭⣥⣾⣯⡙⠿⣿⣯⣝⣿⣿⣿⣿⠿⠠⣽⣿⣿⣟⣯⣥⣶⣶⣭⣭⣥
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⡿⠶⣶⣿⣿⣿⣿⣿⣿⠇⣴⣿⣿⣿⣿⡷⠘⠿⠟⠛⠿⣟⣶⣮⣭⣭⣽⣿⣭⣤⣶⢤⣬⣽⣿⣿⣿⡿⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡿⠏⣠⣔⣶⣿⣟⣿⣿⣿⠋⠀⢿⣿⣿⣿⣿⣐⣒⡓⠀⠀⠀⠀⠈⠉⠙⠛⠛⠟⠛⠋⠁⠀⠀⠁⠀⠉
⠀⠀⢀⣤⣤⣤⣼⣯⣭⣭⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⠀⢻⣿⣿⣿⣿⣿⣛⡂
⠀⠀⠀⠉⠉⠉⠉⠛⠛⢿⣿⣿⡿⠟⣋⣝⠻⠋⠉⠀⠀⠀⠀⠀⠙⠻⢿⡿⢿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⢿⣍⣹⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠟⠛⠉⣉⡠⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠏⠛⠁⠀⣄⣠⢦⣿⣿⣿⣿⣿⣿⡿⠿⢛⡛⢿⣿⣿⣿⣿⠋⠄⠠⠀⠀⢽⣦
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠊⢴⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⡛⢿⢣⣻⣿⡏⠃⠀⠀⣤⠀⠁⢸⣿⡇
⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠿⢿⣿⣷⡤⡺⣿⣿⣿⣿⠟⠋⠉⠈⠀⢀⠀⠀⠃⢧⠈⡆⢿⣿⣇⣄⠀⠃⢬⢀⣸⣾⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣥⣠⣼⣿⣿⣿⡿⠿⠛⠉⡏⢰⠻⣦⠀⠀⢸⡀⠀⠰⡘⣤⣇⢸⣾⣿⣮⣻⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣏⣽⣿⡟⢻⠟⠋⣹⣀⢀⣀⣬⣧⣺⡟⢿⣴⣴⣾⣷⣤⣤⣵⣌⣛⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⢻⣿⣿⣷⣾⣷⣿⣿⣿⣤⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢭⡏⠈⠢⠤⠌⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⢿⡿⠫⢉⡉⠉⠉⠛⣿⣿⢿⣿⣿⣿⣿⡏⣾⣛⡄⢉⣿⣿⣦⢹⣟⢇⣠⣿⣯⠂⠀⠀⠀⠀⠀⠄⢻⠿⣿⣿
⠀⠀⠀⠘⠟⣽⢛⠀⠉⠉⠀⠂⠀⠀⠀⠻⣷⡽⣿⣯⣿⣿⣿⣿⣇⡸⣿⣿⣿⣷⣬⡠⣉⡛⠿⢦⣥⣀⣀⠀⠀⠀⠘⠓⠈⠙
⠀⠀⠀⠀⣼⣛⣊⠈⠁⠀⠀⠀⠀⢠⡾⠟⣉⢹⣽⣿⡟⢯⠍⠛⠾⠦⠉⣽⠛⣿⣿⣿⣿⣿⡗⠲⣤⣍⣙⠛⠻⠿⠁⠀⠘⠀⣱⡄
⠀⠀⠀⠀⣿⣅⣈⣀⣤⣤⣤⢶⣦⠟⠁⠀⠁⣼⣿⣿⣿⢋⣶⣶⣶⣶⣶⣶⠐⣿⣿⣤⣿⣿⣿⣤⣀⣠⣍⣝⣿⣿⣶⣤⣶⠛⠓⠚
⠀⠀⠀⠀⣿⡆⠛⠮⠙⠷⠟⠋⠁⠀⠀⠈⣠⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⡅⢿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣉⣿⣿⠏
⠀⠀⠀⠀⠘⢧⣤⡀⣀⠀⠀⠀⠐⢀⣤⢾⣵⣿⣿⣿⢃⣷⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⡿⡃⠀⠁⣉⣾⣿⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠳⠶⢆⣀⣂⣈⡿⢞⣿⣿⣿⣿⡏⡸⣻⣿⣻⣿⣿⣿⣿⣿⡆⣿⣿⣟⣫⣅⣤⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣿⡿⣾⣿⣿⡿⢃⣷⣿⣿⣿⡟⣿⣿⣿⣿⣧⡸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡷⣻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣷⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢹⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠉⠉⠉⠉⢧⡙⠉⠉⠉⠉⠈⢿

⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣷⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣍⢻⠄
⠀⠀⠀⠀⢀⡔⢻⣿⣿⣿⠼⠛⢨⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⡃⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣟⢛⡛⠛
⠀⠀⠀⡼⣿⢰⡶⣶⣶⣦⡀⠀⢸⣿⣶⣤⠀⠀⠀⢐⢆⣼⣿⡋⣟⢃⠀⠿⠞⡆⠀⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠉⠒⠙⢿⣟⣿⡿⠟⠑⠚⠉
⠀⠀⠀⢿⣿⣿⣙⢿⣻⣿⡇⠀⢼⣿⣿⡇⠀⠀⢀⣬⣼⣿⣿⣋⣿⠁⠀⢸⡎⠀⢶⢎⣀⡀⠀⢀⣿⣿⣿⠿⣿⣿⣿⣗⠀⠀⠀⠀⠈⢻⣿⢷⡄
⠀⠀⠀⣈⣿⣝⣿⣶⣹⡿⢪⣤⡈⢛⡏⠀⠀⠀⠀⠀⣬⣿⣯⣤⣬⣦⣤⣴⣴⣤⣨⡿⠋⠁⠀⠀⠙⠯⣿⣾⡿⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⣬⡁
⠀⠀⠀⣼⣿⣿⣯⣅⣠⣠⡼⠿⣿⣿⣶⡦⠀⠀⠀⠀⠻⣿⣿⣿⣯⣍⣩⣽⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⣿⡇⣿⠧⣘⡑⢠⣥⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣦⡀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⢀⣶
⠀⠀⠀⢛⣷⠂⣤⣉⣭⠛⣽⣟⡽⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⣤⣤⣀⠀⠀⢀⡀⠀⠀⠀⣠⣿⡟⢻⠇⠀⠀⠀⠀⢘⣿⣶⠀⠀⠈⣿⣿⣿⣄⡀⠀⣶⣿⡇
⠀⠀⠀⠀⠛⢕⣤⣴⣄⣐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⣤⠃⠈⠙⠿⢶⣿⣿⣤⣴⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠘⠛⢿⠷⣶⣾⣿⣿⠸⢿⣿⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣆⣠⣴⣶⣿⣿⣋⣼⡿⠃⠀⣠⡞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠁⠺⢷⣿⣿⣾⣾⣿⠋
⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⠈⣹⣿⣛⡉⠉⢠⣾⠋⢯⣿⠶⠋⠁⢉⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁
⠀⠀⢠⣿⣣⢿⣝⢿⣆⠀⠀⠀⠀⢠⣠⣦⠈⠶⠻⡀⠀⠀⢸⣿⠋⠀⠁⢠⡿⠁⠀⣨⣽⡿⢶⣤⣼⣤⡴⠋
⠀⠀⣿⡛⣿⣿⣧⢶⣷⠀⠀⠀⠀⣾⠛⡇⠀⠀⠀⠉⠒⠀⠘⣯⡓⠚⠛⣾⣇⣠⡾⢁⡿⢅⠀⠀⠉⠀⢠⣶⣾⣷⣶⡀
⠀⠀⠘⢿⣧⣿⣼⡿⠋⠀⠀⢀⠴⣿⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠞⠃⠀⠁⠀⠈⢇⣸⠂⠀⠀⢰⣻⣯⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣼⣻⡧⠎⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣡⣤⣤⣄⡿⠃⠀⠀⢴⣆⣉⠛⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡽⠃⠀⠀⠀⠀⠀⠀⠀⣼⣷⡽⠿⢿⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⠙⠃⠀⠀⠀⠈⠹⣿⣿⣿⣿⢤⣰⣷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠞⡏⠈⢣⣀⠞⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠻⠯⠿⠺⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠏⠀⠀⠀⠀⠀⠀⠀⠙⠚⣮⡗⠒⢻⣭⡒⠓⢻⣿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⢻⡶
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⡏⢀⣹⣴⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⢹⡇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⠟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠚⠛⠋⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠈⠉⠉⠉⠉⠁⠂⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣀⡀⠠⠤⢀⣀⣀⡀⠤⠄⢀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠉⠙⢿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡟⣿⣿⣧⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣄⠙⢿⣿⣯⣝⣛⠛⠻⠿⠿⠟⠛⣛⣫⣽⣿⡿⠋⢠⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣉⠀⣿⣷⣄⠉⠛⠿⠿⣿⢿⣿⣿⡿⢿⠿⠻⠛⢉⣠⣶⣷⠀⣈⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⣿⣿⣿⣿⣿⣸⠑⠒⠂⠤⠄⠄⠀⠤⠤⠐⠒⠋⣿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⢷⠸⠘⡀⠈⠙⠻⢧⣖⣀⣀⣀⣀⣀⣀⣀⣀⣲⡬⠟⠋⠁⢀⠃⠆⡾⠉⠒⠢⢄⡀
⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢸⠀⡆⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⢠⠀⡇⠀⠀⠀⠀⠙⢢⡀
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⡄⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢠⡇⠀⠀⠀⠀⠀⠀⠹⡄
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡔⠉⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠉⢢⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠰⢦⣄⣀⣛⣙⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣭⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣟⡽⠚⠋⠉⠀⠈⠁⠀⠀⠀⠠⣄⠀⠰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⣿⣿⠿⠿⠿⠿⠀⠺⠿⠿⠿⢿⣿⡆⠀⢀⣿⣿⡆⠀⠀⢸⣿⡿⠿⠿⠿⠇⠀⠿⠿⠿⠿⠿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣧⠀⠀⢸⣿⡇
⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡟⢸⣿⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⢸⣿⡿⠿⠿⠿⠃⢰⣿⡇⠘⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⣼⣿⢠⡆⣿⣿⠀⢸⣿⡇
⠀⠀⠀⣶⣶⣶⣶⣿⡿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡿⢸⡇⢸⣿⡄⢸⣿⣷⣶⣶⣶⡆⠀⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛
⠀⠀⠀⠀⠀⢀⣤⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⠀⢰⣶⣾⣿⣿⣷⣤⣄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⣤⣀⣠⣄⠀⢀⣤⣀⣸⣷⠀⢀⣀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⣶⠶⠆⢲⣄⡶⢰⡶⢶⡆⣶⠀⠀⡶⠶⣦⢰⡶⢶⡄⢰⣶⠀⠶⣶⠖⢰⠀⣶⠶⣶⢰⣆⢰⡆
⠀⠀⠀⣿⣦⠄⠈⣿⡃⢸⣇⣸⡇⣿⠀⠀⡇⠀⣿⢸⣧⡼⠇⣼⢻⡄⠀⣿⠀⣼⠀⣿⠀⣿⢸⣿⣼⡇
⠀⠀⠀⣿⣀⡀⣸⠟⣧⢸⡏⠀⠀⣿⣀⡘⣧⣀⣿⢸⡏⢷⢀⡿⠺⣇⠀⣿⠀⣿⠀⣿⣀⣿⢸⡇⢿⡇
⠀⠀⠀⠈⠉⠁⠉⠀⠈⠈⠁⠀⠀⠉⠉⠀⠉⠉⠁⠈⠀⠈⠀⠁⠀⠁⠀⠁⠀⠈⠀⠉⠉⠁⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠈⠁⠀⠈⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⣶⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠃⣿⠘⡀
⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢻⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⢬⣿⡇⠰⣿⡇⢨⣤
⠀⠀⣠⠾⠁⠀⠀⠒⣘⣐⣢⣖⣚⣶⣾⢷⣶⣤⠀⠀⠀⠀⠀⠀⠿⡏⣿⣿⣿⣿⡿⠿⢾⢣⣴⢆⠀⠀⠀⠈⡟⢷⠀⠹⠃⢾⡏
⠀⠀⠀⢶⣧⣿⡿⣿⡶⠖⠿⠶⠿⣿⣿⣿⣛⡋⠀⠀⠀⠀⢀⠀⠗⠒⠛⠉⠀⠀⠀⠀⠀⢃⡽⠛⠀⠀⠀⠀⠀⠈⠂⠀⠀⠘
⠀⠀⢰⡏⠉⠛⠛⠛⠃⠀⠂⠀⠠⣠⡽⣿⣉⡷⠀⠀⠀⠀⠈⠙⠢⣤⣴⣦⠀⠀⠀⠀⢠⡎⣀⣶⡶⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠂⠐⠂⠒⠀⠒⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠂⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⡀
⠀⠀⣴⠛⠉⠉⠉⠓⠲⢷⣶⣦⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⣷⣤⣤⣤⣤⣀⣀⡀
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢻⣷⣶⣶⣶⡿⠛⠛⠛⠛⠛⠛⠛⠉⠙⠛⢻⢿⠛⡛⠷
⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠉⠒⠂⠂⠐⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠴⠟⠋⠁⠀⠙⠻⠖⠀⠀⠀⠀⣠⠄⠈⠉⠛⠛⠛⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣾⣿⣆
⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⣴⣿⡂⠀⠀⠠⣾⣿⣿⠨⠀⠀⠀⡂⢰⠀⠀⠀⠀⠀⠀⠀⣀⡔⢋⠅⠾⣷⣶⣤⡀⠀⠀⣾⣿⣿⠏
⠀⠀⠸⣄⠀⠀⠈⡐⠀⠀⢀⡙⠛⠃⠀⠀⠀⣿⣿⣿⡀⠂⠀⢰⠃⢺⡀⠀⠀⠀⢠⣾⠧⠾⣀⢁⡔⠃⠼⣏⠙⢻⡦⠀⠙⠋⠁
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⣬⡀⠀⠀⠀⣤⣼⠇⠀⣴⣯⠼⣷⠒⢶⢇⡏⠠⠀⠀⡉⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣯⢟⡼⢀⠀⠆⠂⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⡉⠉⠉⠉⠉⠁⠀⠐⠒⠒⠢⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢆⠕⠐⢀⣀⡠⡄⢴⢲⠰⡤⡤⢤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⠁⢀⡠⡒⣉⣦⡷⠾⠾⠟⣓⣓⣛⠺⠞⢲⡿⢇⣲⣠⡄⣀⠀⠀⠀⠀⠈⡒⢤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⢆⣩⡶⠛⠋⣁⢥⡞⢁⣨⠿⠽⠯⠯⠭⠭⣽⣟⣗⡾⢟⣿⢭⣗⡦⣀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡴⠁⠀⣠⢎⡱⠞⢃⡤⢾⣯⠟⠚⠉⡁⠐⣶⣹⠀⠀⠀⠀⠞⣯⣝⠙⠲⠤⣽⡷⣿⣻⢷⣤⡀⠀⠕⡈⢦⡀
⠀⠀⠀⠞⠀⢀⡴⣩⡾⠁⡰⢋⡴⠊⠀⠀⠈⠀⠀⠀⠛⠛⠀⠀⢀⣾⢄⡗⠈⠀⠂⡠⠀⠉⠛⢾⡹⠫⡟⢦⣈⢔⡤⠙⣦⡀
⠀⠀⠌⠀⢀⠾⣵⠃⢀⡾⡷⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢯⠴⢸⣓⠀⠀⠀⠀⠀⠀⠠⠄⠉⠢⡈⢢⡛⡬⢊⠕⡈⢷⢄
⠀⡜⠀⠀⡼⣹⡛⢠⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠃⣂⡣⣼⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⣜⡄⡪⢒⠈⣟⣆
⢠⠁⠀⢰⠳⡏⢠⢃⡞⠀⠁⠀⠀⢀⠀⢀⠤⠂⠀⠀⠀⣾⢃⠾⠩⠁⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠹⣮⢻⡔⠥⡢⠸⠬⣇
⠨⠀⠀⡧⣹⠂⣾⡿⠀⠀⠀⠀⠐⠩⠒⠁⠀⠀⠀⠀⣰⢡⡶⣚⢭⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡘⡆⢣⠪⢐⡀⡗⢼⡀
⡆⠀⢠⣳⡇⢰⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣲⣹⢡⡤⢙⣯⢸⣿⠀⠀⠤⢤⣤⣤⣤⡄⠀⠀⠀⠈⡟⠋⠇⢸⣿⢐⡥⢂⢸⠳⡇
⡇⠀⠸⣽⠅⢈⣸⠀⡁⠀⠀⠀⠀⠀⠀⢀⣀⠤⢛⡇⠘⠷⠶⠿⠛⣾⢶⣶⡲⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡧⣊⠅⢸⣝⡇
⡇⠀⠀⣿⠅⣻⣿⠀⢆⣀⠀⠀⠠⠶⠾⠿⠾⠿⢿⠀⠀⢀⡴⢀⡾⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⡆⢕⠭⠸⢬⡇
⢡⠀⠀⢿⡀⡸⢿⠀⣻⡿⠄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⣾⡏⡟⠛⠿⣦⣄⠀⠀⠀⠀⣀⢀⠔⠂⠀⠀⠀⠄⢀⣦⢁⠅⡊⡟⢾
⢸⠀⠀⠘⣆⢸⠈⡆⠩⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⣠⡟⢻⣧⢁⠀⠀⠀⠈⠀⢀⠤⠊⠖⠁⠀⠀⠀⠀⠠⠁⣸⡟⢴⡪⣰⡙⡎
⠀⣧⠀⠀⠘⣌⣧⣴⡈⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⡓⠀⠀⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⢋⠗⡩⢰⢇⢹⠁
⠀⠘⣧⠀⠀⠘⢾⣯⣷⣄⠠⠀⡀⠀⠀⠀⠀⡟⠀⣴⡓⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠒⣰⣧⢞⣯⢶⠷⣌⡇
⠀⠀⠡⡱⣄⠀⠀⠙⢷⣎⡳⣄⠐⠠⠀⠀⢀⠇⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⢀⣘⣛⠛⣋⢠⡟⢦⡟
⠀⠀⠀⠹⣜⠣⡀⠀⠀⠙⠻⣿⣗⢦⡈⠀⢼⡞⡌⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⢀⡴⢋⢜⡥⡋⣠⠣⣘⠎
⠀⠀⠀⠀⠈⠣⣍⢳⢄⠀⠀⠀⠉⠳⢌⣓⣬⣐⡈⠀⠐⠀⠠⠀⠤⠀⠀⢻⣥⠀⠂⠘⠀⢀⣠⢴⣻⣶⢗⡵⠊⣴⠙⣦⠏
⠀⠀⠀⠀⠀⠀⠈⠺⣌⡝⠦⣄⠀⠄⢀⡈⡉⠓⠻⠿⢶⣒⡒⠂⢤⣤⣤⣤⣤⠰⢒⣒⡩⠿⢚⠟⡫⣶⠕⣫⠚⣌⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣸⡹⠲⡮⣌⣐⡡⠢⠔⡤⣂⠄⡩⢍⡩⢉⠍⣉⠍⣠⢔⡠⣺⠕⢉⡪⡔⢫⠈⡧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⢥⣸⡉⡏⠖⢲⠠⠬⡤⣭⢤⢥⡈⣵⢯⠤⡥⢾⠓⡉⢏⢣⡸⠖⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠚⠂⠦⠵⢼⣌⣆⣣⣘⣄⣧⡴⠼⠖⠛⠉⠁
⠀⠀⠐⠭⢪⢕⡩⢒⡩⢐⡡⢔⡢⢒⠤⢂⠤⣢⠔⡠⢒⠔⣠⠔⡠⢀⠤⢀⠤⢀⠄⣀⠔⣂⠔⣠⠔⡠⢂⠔⡢⢒⠔⡪⣪⢔⡡⣪⢞⠔⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣟⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡵⠀⠀⠀⠉⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠠⠊⠀⠀⠀⠀⠀⢸⠄⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⡜⠀⠀⠀⠀⠀⠀⣀⡾⠶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⠞⠀⠀⠀⢀⡴⠞⠛⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⠋⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⠷⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣤⣀⣠⠤⠔⠶⢾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠿⠶⠊⠛⠉⡋
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠁
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠂
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⢿⠷⠒⠛
⠀⠀⠀⠀⢀⠏⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⠶⠄⠀⢺⡟⠋⠀⠀⠀⠀⠀⠸⠆⠀⢀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⣀⣠⣤⣤⠴⣶⡶⠖⠛⠛⠉⠉
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⠒⠶⠂⠉⠙⠉⠉⠉⠀⠀⢀⡜⠁
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⢶⡀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠾⠛⠚⠛⠁
⠀⠻⣶⣄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠈⢿⡷⣌⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠙⣜⢳⡈⠳⢤⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣹⣦⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠈⠳⡙⢦⡀⠉⠲⣄⣀⣀⣀⣀⣀⣷⣀⣀⡀⠀⠀⠛⠓⠶⠶⠾⠻⡛⢻⡟⠉⣿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⣄⠠⠈⠙⠫⢌⡉⡉⠙⣏⠉⢻⠛⠓⡶⢶⣶⣠⣀⣀⠉⢸⡇⠀⠸⣷⠄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⢧⡀⠀⠀⠈⠙⠛⠷⢉⣄⣸⠀⢀⣿⣀⣸⠋⠙⡿⠳⢾⣇⠀⠀⠰⠾⠄⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡳⣄⠀⠀⠀⠀⠀⠀⠉⠛⠱⠶⢿⣠⣽⣟⠁⡇⠀⢸⡏⢻⢦⣄⠲⠖⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣜⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠹⠷⢤⣼⡇⢨⢸⠁⠛⣷⣟⣩⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⢳⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢾⣅⡀⠺⢻⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡹⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⣿⣿⣿⣿⣿⢶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⢘⣷⡙⣆⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠈⠠⠄⠉⠿⠿⠿⢿⣾⣿⣿⡇
⠀⠀⢀⡀⠀⢀⡠⢄⠲⠏⠁⣀⠀⣀⠀⠤⠙⠿⣿⣆⢹⣷⠟⠛⠳⣄⣀⣀⡀⠀⠀⠀⢀⠈⠀⠂⣠⠀⠀⠀⣀⠀⢀⡀⡀⣠⣿⠁⢀
⠀⠀⠀⠉⠀⠀⠁⢀⣼⡆⢠⣾⠿⠿⠇⠀⠀⠀⠀⠙⣿⠛⠀⠀⠀⠀⠉⠀⠙⠛⠋⠰⢄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠆⠈⣃⣿⡟⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠺⠿⠉⠒⠊⠙⣄⣠⡴⣶⣤⣤⣄⣀⣀⢀⣦⣀⣀⡀⠀⢀⡀⠀⢀⣤⡴⣇⠀⠀⠀⠀⣀⣀⣠⣵⣶⣾⠿⢏⣩⡉⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢿⡟⢀⢝⣻⡿⠛⠚⣉⡉⠁⢶⣿⣟⢻⣏⠉⢷⣌⠛⢿⣿⣟⣛⡙⠉⠑⠀⠍⠲⣾⡿⠬⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠤⠤⠤⠾⠿⠛⠁⢡⠀⢀⡐⠩⣛⣷⠻⢟⠣⠩⠙⡮⢦⣄⢉⠀⠂⢉⡉⠍⠁⡤⣀⢈⡀⠤⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣄⡀⠢⠈⠂⠈⠳⠔⠃⠈⠙⢷⣄⣀⣀⠀⠀⠁⠀⠉⠓⠂⠀⠀⢦⠘⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠠⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⣀⡀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠠⡴⢦⡚⠟⠛⠛⠋⠁⠉⠙⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⢉⢄⠠⠄⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠦⣼⢇⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠁⢘⡆⢀⠀⠀⡬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠈⠉⠉⠋⠙⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠆⠦⠼⢀⠀⢠⠃⠐⠃⠀⠀⠰⠃⠀⡠⠈⢠⠰⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡜⠂⡌⡿⠃⠀⠀⠀⠀⡀⠀⠐⠈⠃⠀⠘⢸⡄⢣⢹⡀⠀⡤⠂⡄
⠀⠀⠀⠙⠀⠀⠀⠀⢠⡄⠉⠙⠛⠋⠁⢀⣀⡠⠄⡎⡠⣶⡄⠀⠀⡇⠀⠀⡎⢧⣸⠀⡇⠀⠉⠈⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⠉⠀⠀⣰⣆⢷⠶⣧⣣⣪⣼⣄⢀⣘⣌⠻⡦⠇⠀⢀⠀⠀⡀⠆⡀⣀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡶⠿⠷⣿⠿⠿⠿⠾⣇⢽⠟⠛⣿⠋⠛⠟⠟⠛⠈⠀⢠⢿⠉⠁⠀⠈⠁⠘⡁⠈⠀⣸⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⣄⠀⠀⠈⠓⠓⡟⠃⠀⠀⠀⠀⢀⣠⣴⣿⣭⡀⠀⢀⣠⡴⢟⣣⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢹⢿⠁⠀⢀⣄⣰⡗⠆⠀⠀⠀⣴⣿⣿⡁⠹⠿⢗⣛⡩⡵⠞⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠈⠛⢹⡇⣁⠀⠀⠀⠈⠀⠉⠉⠁⠈⠛⠳⠦⠒⠊
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠠⠆⠀⠀⠀⠁⠛⣷⡄⠀⠀⢀⣀⠶⢿⣛⡈⠓⣄⡀⠀⠀⢀⣤⠐⠀⠄
⠀⠀⠀⠀⠀⠀⢰⣏⠤⠀⠀⠀⠀⠀⣾⠋⠤⢻⠀⠀⠘⢭⣕⢠⣬⡍⢘⡏⠀⠀⢀⣿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⣿⡏⠒⢀⣀⣤⣶⡶⠃⠀⠀⣺⡇⠀⠀⣸⡏⢸⣿⠇⠈⣿⠀⠀⠀⢿⣧⣠⡁⢀
⠀⠀⠀⠀⠀⠀⢸⣏⡾⠯⠛⠟⠋⠀⡀⢐⣴⡿⠀⠀⠄⡿⠁⢸⣿⠀⠀⢹⡄⠀⠀⢠⡙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⡀⢴⣮⠟⠀⠀⠀⣸⠇⠀⢸⣿⣀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠘⠚⠉⠀⠀⠀⠀⢀⢃⣠⠞⠁⣿⠈⠳⣄⢸⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣮⠿⠁⠀⠀⠀⠀⠀⠈⠹⣷⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠀⠀⠀⠀⣼⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢄⡀
⠀⠀⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡿⣙⢒⡹⠁⠈
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⠦⣤⣤⣀⣈⣀⣀⣀⣀
⠀⣿⣿⣿⣿⣿⢯⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠁⢸⣿⡇⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠍⠉⠁⠈
⠀⢻⣿⣿⣿⢷⣫⣾⣿⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠙⠿⠿⠿⠿⠟⠃⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠐⣀⠒⢀⡙⣊⣉⠷⠟⡛⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣶⣶⡷⠬⠅⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡅⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⢀⣴⡆⢰⠋⠀⠀⠀⠀⠀⠀⣴⣦⣤⣶⣤⣶⣦
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⣿⢘⠦⠀⠀⠀⠀⣠⣴⢿⣿⣿⣿⣿⣿⡷⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⣶⠄⠀⠀⠀⠀⠀⢀⠀⠀⣼⣿⠿⣡⠚⠂⠀⠀⠀⠘⢟⣵⢿⡿⣿⢿⡟⣏⢿⣬⡟
⠀⠛⠷⠾⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠊⠳⠀⠀⠀⠀⠀⠰⣿⣫⣿⢡⣿⢸⣧⢻⣎⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⡿⢾⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢠⠖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠄⠊⠀⢀⢀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡙⢷⣄
⠀⠀⣠⢀⢤⡇⢸⠊⢎⠢⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣴⡶⠿⣯⡀⠀⠳⡀
⠀⠀⠠⢫⢾⢷⢸⡎⣎⠳⣌⠀⠀⠀⠀⠀⠀⣀⣀⣮⣻⣿⣎⢷⢻⣷⣶⣤⣄⡀⠀⠀⠸⣿⢿⣿⣷⡄⠻⣆⠀⠁
⠀⠀⡔⢫⢏⡏⣿⢣⠘⢧⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣮⣯⣿⣿⠿⠛⠉⠀⠀⠀⠻⣯⣩⣭⡻⣼⡿⢀
⠀⠀⠀⠀⠸⠃⠻⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡿⠛⠉⠁

⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢄⢀⣀⣦⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⢰⣴⠀⠀⠀⠀⠲⠶⠶⠷⠂⠀⠀⠀⠀⣞⡵⠀⠀⠀⠀⢰⠟⣥⣧⡈⢻⡆⠀⠀⠀⠀⠀⠀⣉⣉⡂⠆
⠀⠀⠀⠀⢠⣛⠄⠀⠀⠀⢠⣇⣼⡈⠀⠀⠀⠀⠢⠤⠧⠄⠀⠀⠉⢻⡍⡿⣿⠟⢹⡟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠙⢀⡠⠄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⡟⡁⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠼⠛⠶⣦⠶⠛⠄⠀⠀⠀⠀⣢⠄⣶⣲⣦⣶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠼⠿⠟⠛⠛⠹⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣄
⠀⠀⠀⠀⠀⡠⣤⣤⣄⡀⡀⠀⠀⠐⠰⠹⠢⢏⡑⠕⠂⠀⠀⠀⠀⠉⠉⢹⣿⠟⠀⠀⠀⣰⠖⠶⠾⡿⢷⣶⣤⣤⣤⣤⣀
⠀⠀⠀⠀⢰⡟⠈⠀⠀⠱⠹⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣈⣦⡀⠀⠀⠀⠙⠀⠂⠙⢦⡉
⠀⠀⠀⠀⠸⡷⠀⠀⠀⠀⣴⠀⠀⠀⡀⠀⠻⣷⣤⣀⠀⠀⠀⠀⣹⣿⣿⣾⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠻⠖⠾⠓⠁⠀⠀⠀⠙⠳⠶⠶⠷⠎⠖⠂⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⠸⣇
⠀⠀⠀⠀⠀⠀⣀⣚⣡⠀⠀⠀⠀⠀⢀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⡚⣻⣷⣦⡌⠆⠀⠀⠀⠀⣜⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠋⠛⣤⠈
⠀⠀⠀⠀⠀⡀⠀⢸⠀⢀⠀⠀⠀⠀⠀⢼⠄⣿⡿⡧⡀⠀⠀⠀⣶⡿⠆⠀⠀⠀⠀⠴⢀⣀⠀⠀⠀⢠⣶⣥⣴⣾⣅⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠢⢼⠂⠁⠀⠀⠀⠀⢀⣴⠐⡹⣧⣧⡹⠀⠀⢀⣿⣏⣠⠀⠀⠀⡄⠀⠈⢉⣀⡃⠀⠙⠛⠛⠻⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⠎⠁⠁⠀⠀⠛⠛⠿⠙⠓⠀⠀⢳⡴⠒⠐⠃⣤
⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣴⣞⣁⠍⠀⠀⠀⠀⣤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢿⡷⠄⠉⠀⠀⠀⠀⢀⠀⢐⣠⣴⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠷⠄⠀⠀⢰⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣼⡿⠁⣀⠀⠀⢀⣠⣴⣾⡟⠛⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣾⡿⠀⣠⠟⠁⠀⠈⠉⠉⢠⣶⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣔⠛⠒⡒⠒⠒⠲⠒⠶⠶⠶⠶⣶⣤⣴⣶⣦
⠀⠀⠀⠀⠞⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⢹⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣤⣶⣿⣿⡿⠿⡇⢸⣿⣿⣿⣿⣷⣶⣬⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣵⣾⣿⣿⣿⣿⣇⣠⣤⡇⢸⣿⣿⣿⣇⡽⠛⢿⣿⣷⣄⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣴⣿⣿⡋⢈⣿⠟⢻⡇⠀⢰⡇⢸⣿⠀⢀⣿⠛⠶⣤⣿⢝⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⣿⣯⣈⡿⣮⡠⣀⠘⣷⡱⣼⡇⢸⡟⣤⣿⡫⠀⣀⢈⣵⣿⡿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠁⠈⢿⣮⡳⣾⣷⣿⡇⢸⡇⢿⣧⡷⢊⣵⡟⠁⠈⢷⣀⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠻⡟⠳⣼⣖⡦⢽⣿⣮⣹⣿⣇⣸⡧⠸⢋⣴⣿⡿⢔⣺⡵⠟⢿⣤⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⣸⣅⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⠿⢿⣾⣿⣷⣿⣿⣿⣭⣤⣄⣸⣿⣿⣿⣿
⠀⠀⠀⠈⡜⡖⠀⠀⠲⠶⠶⠶⢬⣭⣭⣥⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠱⠒⢘⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣬⡥⠶⠶⠶⠂⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠉⠛⣻⠶⣶⣤⡬⣽⣿⣿⣶⣿⢿⡭⣥⣤⣶⠾⣟⠛⠋⢹⠏⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠛⣧⣰⣼⠶⠟⡿⢋⣴⣿⣿⡇⢹⡏⢸⡳⣦⡹⣟⠻⠶⣥⣦⣾⣦⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⡟⠉⢧⠀⠀⢚⣴⠿⢻⡿⣿⡇⢸⡇⣾⡟⡟⢿⣮⡳⡀⢀⣾⣿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣔⣾⣟⣴⠟⠁⢠⡿⡱⢻⡇⢸⣷⠛⢿⣽⠀⠉⢻⣦⡋⢉⣻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⠛⠦⣾⣏⠀⠸⡇⢸⣿⠀⠈⣿⣤⣶⣯⣈⣻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⢿⣿⣶⣴⣏⣽⣿⣿⡇⢸⣿⠛⠉⢻⣿⣿⣷⣿⡿⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠿⢿⣿⣿⣿⣇⢸⣿⣶⣿⣿⡿⠿⠛⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⢸⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣟⣉⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⠱⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⡶⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠋⠃⠀⠠
⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧
⠀⠀⠀⠀⠀⢣⣥⡆⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠀⠈⠀⠲⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠘⡃⡔⠀⠀⢸⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠄⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠢⢞⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠘⠁⢐⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢁⡀⢀⠀⠀⠀⡀⠀⠐⠋⠘⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠈⠃⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠖⢰⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⠀⢀⡂⠀⠀⠀⣀⣀⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣅⠉⠀⢀⠛⡔⠀⠁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣶⣌⣠⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠘⠃⢋⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠂⠀⠀⢠⢷⡾⠋⠁⠄⠸⡷⠆⠀⠐⠃⠀⠰⠆⠈⠁⠀⣄⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠲⠖⠓⠲⠲⠤⣀⠀⠀⠈⠁⠀⠄⠀⠐⠀⠄⢀⣀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⠀⠀⠀⠀⠀⣰⠏⠁⢀⠀⠘⠂⠐⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣂⢄⢀⡖
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠠⠀⠈⠄⠈⠱⡆⠀⠀⢀⠀⢠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⢀⣿⠀⢀⠀⡀⠀⠀⠀⠋⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⣯⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣢⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣤⣄⠛⡀⢀⣶⠞⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⣠⠀⠀⠁⠇⠀⠀⢠⣰⠞⠁⠀⠀⠰⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⣀⠀⠀⠈⠂⠀⠉⢓⠁⢶⢃⡤⠋⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠉⠐⠶⠶⠚⠚⠃⠀⠀⠀⢠⡀⠀⠠⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠠⠊⠷⢀⡀⠈⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠙⠀⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠒⠒⠀⢈⢥⠀⠀⠀⠀⠀⠀⠆⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢐⣀⡴⢀⣀⠀⠠⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⡀⠐⠚⡀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠄⠈⣉⡀⢏⢠⠄⠄⠀⢐⢨⡁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢵⠀⠘⠃⠀⠸⠇⠀⠀⠀⣀⠀⠀⠄⠀⠈⠁⠂⡠⠊
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⣆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠢⠒⠂
⠀⠀⠀⢀⡀⠀⣬⣔⡶⠶⠒⠇⠐⠾⠉⠇⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠈⢣⠀⣹⠈⠁⠀⠀⠙⠀⠀⠀⠈⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡐⢤⠄⠤⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠘⠦⡰⠐⠆⠀⣀⢰⣄⣤⠴⢦⡼⠁⠀⠀⠀⠁⠀⠀⠀⠠⠠⠀⠒⠀⠢⠀⠁
⠀⠀⠀⠉⠀⠁⠀⠚⢸⣿⠟⠃⣿⠃⣈⣭⠁⠀⠀⠀⠀⠄⠀⠀⡀⠀⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠴⠆⠀⠈⠀⠲⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⠀⠀⣀⠀⠀⠀⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⡰⠂⣀⠚⠈⠃⠠⡄⢀⡄⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣈⣀⣤⡦⠐⡣⣄⣆⠠⡦⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠘⠳⡌⢷⡐⠻⠟⠤⠉⠀⠀⠀⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣉⣀⡅⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠀⡀⢀⢀⣤⣤⣶⣧⣌⣿⢠⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠰⠆⠉⠀⠉⠀⠀⠀⠰⠆⠀⠀⢀⠀⠘⠠⡄⠀⠀⠉⠛⠉⠉⢯⡽⠛⠉⠊⠰⣸⠠⣦⣠⣷⣤⢀⣶⣦⠀⡀⠀⠐⠀⣊
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠃⠀⡘⠆⠀⢀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⡍⠀⠋⠈⠈⠠⠉⠀⠁⠀⠀⠁⠀⠋⠓⠴⠭⢸⣥⣾⣷⣾⡄⠡⠀⠀⠀⢿
⠀⠀⠀⠀⢀⡀⢀⡐⠁⡞⠀⠉⠁⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠠⢀⡄⠉⠀⠁⠀⠀⠀⠂⠀⠀⠉⠐⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠋⢹⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠉⠀⢴⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠄⢸⣄⠀⡀⡀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠲⠀⠀⡎⠀⠀⠈⠀⠐⠟⢻⡓⣤⡀⠰⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡤⠀⠀⠀⢀⣀⠐⠐⠀⡀⠧⠀⠡⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠖⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧⠀⠀⠦⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡟⡜⠅⠀⠀⠀⠀⠀⠀⠘⣦⡤⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⡆⠀⢠⠀⠀⠈⠹⠃⠀⠀⡤⠀⠀⢀⠘⠙⠻⠁⠀⠀⠢⡄⠠⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⢀
⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⢀⡀⠴⠒⠒⠀⠀⠀⠀⠀⠀⡉⠐⢶⡀⠒⠀⠀⣀⠀⠀⠈⠠⠄⠀⠁⠦⠀⠀⠀⠐⠠⠁
⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠂⠠⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⣀⣚⣶⣂⡀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡬⠵⠚⢛⣿⣉⣤⣯⣤⣉⣿⡛⠒⠮⣅⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡵⢾⣧⠴⠖⠋⠉⠘⣀⣠⢿⣄⣀⠋⠉⠙⠲⢤⣹⣷⢭⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⡵⢋⡴⠊⠉⣀⢤⣲⡬⠷⠓⠛⢸⡗⠒⠮⢥⣖⠤⡀⠋⠳⢄⠙⢮⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣣⣿⣴⠋⠐⣦⣮⠞⠉⠀⢠⠀⠀⠃⢸⣧⠀⢀⠄⠈⠙⠪⣵⣴⠊⠳⣄⣷⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣱⠃⡼⠉⢠⢮⠞⠙⠷⣄⡀⠀⢧⠀⠀⢸⣿⢀⡞⠀⠀⠄⣠⠞⢣⡳⡐⠙⢏⠙⡎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⠃⡸⠁⢠⣧⠏⠀⠀⠑⠌⠻⣶⣜⡷⠀⢸⣿⣿⠁⠂⣠⡾⠃⠀⠀⢹⡵⡀⠈⣆⠸⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⢶⡧⠀⣆⡏⠀⠐⠲⢤⣈⣂⠈⠻⣿⡀⢺⣿⠃⣰⣿⣟⣠⡤⠖⠂⠀⢳⡱⢀⣸⣶⣧⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣺⣇⠇⠀⡇⢸⣀⣰⣼⣥⣤⣤⣶⣶⣿⣿⣷⣦⣬⣷⣼⣷⠾⠛⠉⠉⠑⠂⠀⠀⠀⠼⢯⣀⣸⡇⢹⠀⠀⣿⡓
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠋⡏⢻⠉⢹⢯⠍⠩⠭⠉⣉⡉⠉⠉⣉⣭⢿⡿⣟⠿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠛⢻⡏⢹⠩⠀⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⡇⣷⣾⡖⠀⡞⡇⠀⢀⡠⠴⠚⣻⣿⠟⢡⣾⡇⠹⣷⣄⠙⢛⠳⠦⣄⡀⠀⣸⢳⠀⢼⣷⡾⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⡀⢧⠀⠰⡿⡄⠀⠀⢀⣼⠟⠁⢔⣿⣿⡇⠀⣿⠻⣷⣄⠢⠀⠀⠈⢰⢧⠃⠀⡞⢨⢇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢳⡈⢧⢀⠱⡿⣄⣠⠟⠁⠊⠀⡼⠹⣿⡇⢠⠙⣇⠈⠙⠷⣄⢀⡰⢫⢂⢀⡼⢀⡏⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠳⡿⠣⡀⢈⡾⡷⣄⡀⠀⠰⠁⠀⣿⡇⠘⠀⠘⠄⠀⢀⡨⢿⢷⡁⣠⠿⣷⢏⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣝⢦⡙⢦⡀⢈⠚⠽⣲⠦⣤⣀⣹⡇⣃⣀⣤⠴⣞⠭⢃⠁⣠⠜⢁⡴⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢝⢦⣾⠗⠦⣀⡀⠉⠘⠃⢻⣧⠋⠘⠂⠁⢀⣠⠴⢿⣧⠴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢑⡢⢤⣉⣹⣿⠒⠶⡿⠖⢺⣷⣋⣉⡤⢖⡫⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠭⠩⠟⠛⠿⠛⠫⠭⠭⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣝⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢔⡣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠑⠤⣉⡁⠒⠚⠟⠭⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠒⢉⣁⡴⠋⠒⢤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠲⠤⠐⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠸⢍⡤⠤⠒⠒⢉⣢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⠃
⠀⠀⠀⠀⠀⠀⠑⢶⡊⢉⣳⣤⡬⠗⢭⡭⢑⣒⠂⠴⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠴⣒⣒⡊⠭⠭⠒⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⠤⠛⢶⣈⣙⣦⡀⠀⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉⠉⠁⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⡉⣉⣷⣤⠜⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠲⢽⣦⡠⠬⠷⣶⣎⣉⣫⡲⢶⡒⠒⣤⣤⡤⠤⠤⠤⠤⠄⠖⠒⠚⠉⠉⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⢟⢾⡉⠙⡍⣤⣖⣶⣽⠝⡄⠘⡀⣱⣀⣀⣀⣠⣀⠠⠤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⡎⣷⠀⢸⢹⡏⠻⣆⠀⡇⢀⠋
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⢒⣊⣩⠇⠀⠀⢰⣿⠀⣸⠤⠄⢒⣚⠿⢿⡓⢒⣄
⠀⠀⠀⢸⣹⠞⠓⠊⢫⠉⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⠀⠀⠈⠲⣖⠊⣙⣧⣤⠝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡤⠼⠳⣎⡉⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡂⢉⣙⢦⡤⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠤⠛⠒⠉⠉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠸⢼⠇⠀⠀⠀⠀⢠⣶⣦⡀⠀⢰⠀⠀⠁⠀⠀⠀⢘⣈⠁⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠧⠀⠀⠀⢸⡇⠈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹
⠀⠀⢠⠀⠀⠀⠀⠀⠚⡀⠁⠀⢠⡥⢿⣄⠀⢻⣶⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⢸⡀⠀⠀⠀⠀⠠⠁⡄⠀⠈⠀⠈⠙⣧⢸⡆⠀⠤⣀⢒⣾⣿⣀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⢀⣀⣀
⡿⠋⠉⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⢀⣿⡥⣾⡿
⠃⠀⠀⣸⠏⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣧⠀⢀⡀⠀⠀⠰⣶⣦⣼⡄⠀⠀⠀⠀⠈⢧⠀⠈⢿⡇⠀⠃
⠀⠀⠀⢫⠾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡏⠁⠐⠂⠀⠀⠀⠀⠈⠐⠀⠀⠀⡀⠈⢇⠀⠀⠈⢀
⠀⡠⠀⠀⠀⠀⠉⠀⣀⣀⣤⣶⠛⠛⡐⠂⠀⠀⢤⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡼⠶⣶⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⠏⠉⢛⡷⣾⣛⠉⠉⠀⠀⠀⠈⠈
⠀⠀⢤⡀⢀⠠⠖⠉⠀⢀⠈⠉⠀⠀⡠⠀⢤⡀⠀⠀⠀⠁⠀⠀⠱⡍⠢⢭⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠐⠓⠀⠀⠐⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⡶⣧⡇⠀⠀⠀⠉⠉⠛⠛⢷⡴⠞⠁⠀⠀⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⡀⠀⠀⠸⠇⠀⠀⠀⣀⡘
⢙⣀⢀⠀⠀⠀⢀⡦⠀⠀⠀⢀⣀⣀⡦⠀⠀⢀⠀⠀⠀⠀⢀⠎⠲⣀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠐⣾⠐⠉⠳⠒
⠋⡏⣸⠧⠤⠖⠋⢀⣶⢟⡺⢯⣍⣭⡄⠀⠀⠠⠀⠀⠀⢠⡟⣗⠀⠈⠑⠂⠀⠀⠀⢻⠀⡔⠻⠆⡠⠚⠐⠟
⢀⡁⠀⠀⠀⠀⠀⢸⡟⢸⣋⣐⡤⠄⠀⠀⠀⠀⠳⡀⠀⠈⡤⠚⣀⠀⠀⠀⠀⠀⠀⢈⣾⣱⡁⢀⡷⠤⣴⠋⢰
⠘⠀⠀⠀⠀⠀⠀⣠⡿⢛⠿⡿⣿⢯⣧⣠⡀⣰⠀⡗⠀⠀⣹⡉⠱⠆⠀⠀⠀⠀⠀⢸⣬⡉⠙⣿⡀⠠⣟⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠏⠐⣾⠚⠇⠈⣷⡦⣤⣴⡇⠘⠀⠀⠀⢹⡖⠆⢛⠀⠀⠀⢀⡜⡀⠠⠿⣤⣯⣤⣟⣁⣠⣀
⢶⡄⠀⠀⠀⢀⡀⠀⠀⢩⠀⠀⠀⣿⣼⠛⢿⡸⡆⠀⠀⠀⠘⣷⠬⠋⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠉⠈⠉⠉⠉
⠉⠀⢀⡴⡞⢯⠉⠳⠄⠈⠀⠀⢀⣿⡇⠀⠰⣇⠁⠀⠀⠀⠀⠿⡂⠴⣢
⠀⠀⢸⠀⠀⠀⠀⣄⡗⠀⠀⠠⠞⡿⠁⠠⠴⠋⠀⠀⠀⠀⠀⠈⠣⠿⠟⠀⠀⠀⠀⠀⢀⡔⠛⠛⠐⠒⢠⡀
⣀⣀⣰⣛⣆⣀⣂⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣐⣒⣄⣀⣀⣀⣀⣄⣀⣀⣀⣀⣸⣀⣘⣛⣀⣀⣀⣘⣄
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢠⠄⠐⠶⠀⠈⢈⡠⠊⠁⠀⠐⠃⠸⠃⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢟⠏⠉⠀⠈
⠀⠀⢰⢁⡾⠀⠀⠀⣀⡼⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠂⡔
⠀⠀⠈⠠⢤⣀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢠⠄⠁⠀⠶⠘⢲⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⡤⠀⠀⠀⠶⠁⢀⡴⡁⠈⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢶⣶⢶⢲⠒⡆
⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠐⡷⣮⡏⠿⠘⢰⠃⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢤⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣤⣴⡖⡖⡆⠀⠀⠀⠚⠳⠧⠆⠎
⠀⠀⠀⠾⠀⢠⠆⠀⠀⠰⣄⠀⢸⣴⡇⠀⠀⠀⠀⠤⠔⠀⠀⠀⢲⣾⡏⡇⠀⡇
⠀⠀⡀⠀⠰⠈⠀⠀⠀⠐⢂⢼⣿⣷⠯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⣰⡾⣠⠀⠀⠀⠀⡤⣡⠻⡟⠻⡕⠀⠀⠀⠀⢠⢿⣷⠀⣠⡤⣶⣶⡶⠀⠀⠀⣄⠒⣄⠀⢠⠀⠀⡆⠂
⢠⠀⠀⢐⣿⠁⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠩⠬⠱⡰⠉⠁⠀⠀⠀⠀⠈⠁⠘⢀
⢸⡄⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡽⣆⠁⠀⠀⠀⠑⣃⠀⠀⠀⠀⠀⠀⣀⡝⠀⠄⠀⣤
⠀⢳⡄⢰⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢸⣿⠁⠝⠀⠠⠄⠀⠄⡑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠃
⠇⣺⡄⣾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⡄⠚⠃⠀⠈⠠⠢⠁⡀⠒⠬⣆⠀⠄⠀⠀⠀⠶⠄⠀⠁⠈
⣇⣟⣼⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠸⠾⠛⠋⠈⠙⠀⣆⠀⠀⠀⠀⠀⡀
⠘⠋⠁⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⡇⠀⠀⠈⠢
⣤⠶⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠈⣆⠘⡇⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⡀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠨⡇⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡯⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢆⣰⡂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⢀⠀⢀⠄⠀⠀⢸⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢀⡃

⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢰⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀⠀⠀⠀⣀⣤⣤⣤⡀⠀⣀⣤⣤⣤
⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⡟⣽⣿⡏⣧⠀⠀⢠⣤⣤⣿⡟⣿⣿⣿⡿⠃⠀⠀⠻⠿⠾⣿⣿⣤⣟⡿⠶⠿
⠠⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⡿⢸⣧⠀⠀⠀⠘⠛⠋⠹⠇⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃
⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⣲⣶⣶⣄⠀⠀⠀⠀⠰⣿⣷⢀⣀⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣷⣦⡴⣶⡦
⠀⠀⠈⣿⣏⣹⣿⠁⠀⠀⠀⠀⠈⢱⣿⡿⢃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡶⢿⣿⣷⡩⢿⠃
⢀⠄⠀⠿⢿⠿⠿⠂⠠⡀⠀⠀⠀⠪⠉⠰⣿⣷⠆⠀⠀⠘⢿⣿⣿⣿⡿⠏⠀⠀⠀⠸⡟⣧⣜⣻⣿
⠈⠁⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠄
⠀⠀⠀⡀
⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⢠⣾⡂⢀⡀⠉⠉⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣿⡆⠀⠠⣄⡀⢀⣠⣤⣀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⢠⣇⢻⣿⢾⣃⡤⣶⠀⠀⠀⠀⣸⣿⣿⡿⠿⠻⠛⠁⠀⠀⠀⠑⣾⣿⣿⣿⡆
⢀⡾⢿⡿⢷⡆⠀⠀⠀⣿⣿⡿⠉⠀⠉⣾⣿⡷⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠻⠷
⠘⠁⠘⠇⠈⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⡀
⢀⣴⣿⡾⣶⣄⠀⠀⠀⠀⢠⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣷⣦⣀
⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⣼⣿⣟⣟⣧⣄⡀⠀⠀⠀⠀⠀⠈⠿⠈⠉⠑
⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⡟⠿⠿⠗⠀⠀⠀⠙⢻⠿⠿⡿⠿⠿⣟⠋⠀⠀⠀⠀⢀⠂⠂⢂

⠀⢀⠀⣀⠀⠀⠀⣠⣤⠀⠀⣠⡄⢀⣠⡀⠀⠀⡤⠠⠄⠀⠠⠀⢀⣠⣄⣀⡀⠀⠀⣀⣀⣀⡀
⠀⠸⠀⠉⡜⠀⠀⠙⠿⠃⠐⠿⠀⠐⠛⢋⣤⣤⣤⣶⣶⣤⣤⣄⣈⠙⠉⠉⠁⠀⠻⢿⣿⣿⡿⠂
⠀⢠⠠⠊⠀⠴⢶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠁⣀⣀⠀⠀⠀⠀⡀⠄⠀⢸⢰⢺⡇
⠀⡄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠘⠿⣿⣿⣿⣿⣿⡿⡛⠛⠛⠛⠛⢻⣿⠛⠁⠀⢤⢠⣿⠇⠀⠀⠈⠈⠈⠁
⠀⠈⠑⠀⠀⣾⣖⠀⠀⢠⣤⠀⠀⠉⠉⠀⠀⠀⢡⠄⠀⣀⠀⠀⢠⣶⣆⠀⠈⠻⠀⠀⠀⠈⠛⠀⠀⠀⠀⣶⢠⡄⡆
⠀⢰⣿⣷⡄⠙⠇⠀⠀⠘⠋⢠⠀⠀⢠⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠉⠁⢠⣴⡶⠿⡇⠀⠀⠀⠀⣍⡀⠀⠛⠘⠃⠃
⠀⠘⣿⠀⠀⠀⠀⠘⠃⠀⡀⢸⡇⠀⠈⠉⠡⢠⢀⣤⢠⠉⠉⠀⡤⠀⢀⠘⠻⢷⣦⡇⠀⠀⠀⢸⣿⠄⠀⢠⢀⣀⡄
⠀⠀⣿⠀⠀⠀⠀⢸⣦⠀⣿⢸⣷⠀⠑⠀⠀⠀⠄⠀⠀⠀⢀⠠⠈⠀⠈⣀⣀⠀⠀⠀⠀⠀⢠⠀⠋⠀⠀⢸⠸⠯⡇
⠀⠂⠻⠤⢝⣤⡄⠀⣿⣆⣿⣿⡿⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⢿⡇⠀⠐⠄⠀⠀⢰⡀
⠀⠘⢷⣲⣼⡽⠀⠀⠈⠿⣿⠟⢁⣀⡈⠉⠀⠀⡆⢰⢶⡶⠂⠀⠀⡄⠈⠀⠀⠀⣰⣿⣿⣿⣦⠀⣳⠀⠀⢸⣶⣴⡇
⠀⠀⠀⠉⣿⣇⠀⠐⠀⢀⣴⣾⣿⡟⠓⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠰⣿⡄⠀⠈⠈⠉⠁
⠀⠠⡀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⠃⠀⠀⢰⣿⣷⡄⠐⠐⠄⠀⠄⠀⠀⠀⠀⣀⣸⣿⣿⣿⣥⣄⢼⠃⠀⢀⢤⣤⡆
⠀⠀⠀⠀⠘⣿⠿⡿⢛⡉⠿⠛⠁⠀⠄⠀⠀⠉⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⢿⠿⣿⢻⡆⢀⠀⠰⠛⠹⠇
⠀⠀⠀⣶⣤⠈⠓⠁⠋⡀⠀⠀⣴⠀⠘⡶⠀⠸⠏⢹⡏⠀⠀⣿⠘⣿⡄⠙⢛⣱⢇⡇⣿⢸⣇⡀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠋⢻⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣤⣀⣤⣴⣿⣿⣿⣿⣿⣿⣦⣤⣀⣠⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⣿⣿⠿⠛⠛⠋⠉⠁



⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣻⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢏⣵⠶⠶⣦⡹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣷⣾⣷⣾⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⣿⣿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠿⠛⠛⠛⠛⠿⠷⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⢀⣀⠤⠤⠄⠄⠀⠄⠤⠤⣀⡀⠈⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡤⠊⠁⠀⢠⡀⠀⠀⠀⣀⣀⣰⣆⣀⣀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⡴⠋⠀⠀⠀⠀⢸⣷⡶⠉⠁⠀⠀⢸⡇⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠙⢦⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⠎⠀⠀⠀⠀⡠⠚⠁⠁⢣⡀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠱⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⠋⠀⠀⠀⢀⠞⠀⠀⢠⡀⠀⠱⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠳⡀⠀⠀⠀⠙⡄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡎⠀⠀⠀⢀⠊⠀⠀⠀⠀⠙⢦⣄⡱⡖⠚⠉⠉⠓⠲⢄⣀⡴⠋⠀⠀⠀⠀⠑⡄⠀⠀⠀⢱⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢰⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡨⠋⣠⣾⣿⣿⣿⣿⣶⣄⠙⢅⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠐⢺⠗⠻⠿⠿⠿⠿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠿⠿⠿⠿⠿⠺⡗⠂⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢡⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡌⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠘⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢸⣦⡈⠛⠻⠿⠿⠟⢟⢁⣴⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢣⠀⠀⠀⠈⢣⠀⠀⠀⢀⡴⠋⠀⠈⠑⠒⣤⣤⠒⠊⢣⠀⠙⢦⡀⠀⠀⠀⡜⠁⠀⠀⠀⡜⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⢧⠀⠀⠀⠀⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢣⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⡴⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠳⡀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⣤⣠⠖⠁⠀⠀⠀⢀⠞⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⢦⡀⠀⠀⠀⠀⠉⠒⠦⠄⣀⣀⣸⣇⣀⣀⠠⠄⢾⣿⣿⣆⠀⠀⢀⡴⠁⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡦⡀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠿⠀⠀⣠⠔⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣢⢄⡀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⢀⡠⣖⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⣗⡢⠤⣀⡀⠉⠉⠉⠈⠁⠈⠉⠉⠀⣀⠤⢔⣺⣽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢮⣭⣭⣤⣄⣠⣤⣭⣭⡵⠶⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⣠⠖⠉⣠⣤⣀⣀⡴⠶⣄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁⠐⠠⢀⠀⠀⠀⠈⠓⠄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠊⠀⠀⠊⠀⠀⠙⠋⠀⠀⠈⠃⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠈⠢⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣠⠎⠀⠀⠀⣠⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⡠⠀⡜⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡜⠁⠀⠀⠀⣰⠟⠉⠀⠀⠉⠓⠀⠀⠀⠀⠀⢧⠀⣇⡀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⠎⢠⡶⠟⠓⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣀⠹⠖⠃⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣰⠃⢀⡏⠀⠀⠀⠀⠀⠀⠔⠒⠶⠚⠛⠳⠀⠀⠀⠈⢁⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⡘⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡘
⠀⠀⠀⠀⠀⠰⠁⢰⠃⠀⠀⠀⠈⢦⡀⠀⠀⠐⡆⠀⠀⠀⡀⠀⢠⠀⠀⠀⢰⠁⡀⣠⠔⠃⢢⠉⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⢠⠁⢀⡏⠀⠀⠳⡄⠀⠈⠳⡀⠀⠀⠸⡄⠀⠀⣧⠀⢸⠀⠀⢗⢊⣀⢠⠃⠀⠀⠀⠆⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠆⠀⡾⠀⠐⣄⠀⠘⢆⠀⠀⠙⢄⠀⠀⢱⡄⠀⢹⠀⢸⠀⠀⠀⣠⠇⠘⠀⠀⠀⠀⠸⠀⠀⠀⠈⠉⢢⢀⠄⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠘⠀⢰⠃⠢⡀⠈⠳⡄⠈⠣⡀⠀⠈⢳⡀⠀⠻⡀⠀⡇⠸⠀⠀⠈⣹⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠉⠁⡇
⠀⠀⠀⠆⠀⡟⠀⢄⠘⢦⠀⠈⢦⡀⠙⢆⠀⠀⠱⡄⠀⠱⠀⠀⠀⣀⣠⢤⡇⠀⠀⠀⠀⢸⣷⡀⢰⠀⠀⠀⠀⣠⡤⠀⢤⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⢸⠃⠀⠈⠢⡀⠑⢄⠀⠙⢦⠀⠑⠀⠀⠀⢀⡠⠴⠚⠉⠁⠀⠀⡇⡀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠉⡇⠀⠀⠛⠆⠀⢠⠀⣼
⠀⠀⡆⠀⣸⠀⠀⠠⡀⠘⢦⡀⠱⣄⠈⠓⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢛⠀⣿
⠀⠀⡇⠀⡏⠀⢀⠀⠘⢦⡀⠙⢆⠈⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⢿⢀⠀⣿
⠀⠀⠁⠀⡇⠀⠀⠓⢤⡀⠙⠦⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡾⢸⠀⣿
⠀⢀⠀⢠⡇⠀⠠⢄⡀⠙⠂⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡆⡀⠈⠃⡇
⠀⢸⠀⢸⡇⠈⠲⠤⣙⠂⡔⠁⠀⠀⠀⠀⠀⠀⣀⢠⢤⣶⣾⠯⣟⣭⢧⠃⠀⠀⣾⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣽⡁⡆⠘⠀⣧
⠀⢸⠀⠸⡇⠈⡙⠒⠂⣘⠀⢀⡠⢀⡠⠔⣘⢤⣫⢭⣻⢳⡹⡽⢜⢺⡟⠀⠀⡼⢝⣾⠳⢮⣝⡲⢤⣀⡀⠀⠀⠀⣠⣯⠛⢶⣧⣇⡆⠤⠺
⠀⠀⠀⠈⡷⠊⠉⠉⠉⠁⠉⠉⠴⠞⠲⠚⠽⠻⠍⠞⠍⠥⠳⠘⠯⠳⠁⠀⠀⠟⠯⠿⠂⠃⠠⠟⠳⠮⢝⠓⠢⠴⠷⠉⠃⠛⠻⡏
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠕⠖⠺⠶⠷⠸⠗⣦⡇
⠀⠀⠀⠀⣶⡠⠄⠔⠤⠀⣰⣀⣄⣄⣄⡐⠢⢦⢤⡖⣰⣶⡄⠤⠶⠀⠀⢰⣐⣤⡤⣰⠄⣖⠀⡤⠀⠆⢀⡤⠰⣀⡦⠖⢰⣦⠶⠀⠀⠀⢆
⠀⠀⢠⠀⢹⡆⠀⠤⢞⢈⡁⡄⡬⠴⠴⢦⢏⣯⠷⢾⠕⠂⠀⣀⣀⣠⠶⣷⣾⣶⡶⠸⡉⣩⠄⠖⠀⣫⠀⢟⣨⠋⠀⠀⡿⠋⠀⠀⡔⠈
⠀⠀⠈⠀⠘⣧⠐⢂⡎⢩⢈⠧⠜⣻⣏⡏⡸⢁⡤⠞⠋⠀⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⣧⣰⠆⠘⡅⠨⢆⡝⠁⠈⠀⢸⡇⠀⠀⢸⠂⠀⢀
⠀⠀⠀⠇⠀⢻⡗⢩⢬⣁⠤⠖⢋⣱⠼⣩⣗⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣓⣒⣶⡏⠀⠀⠀⠀⠀⡏⠉⠉⠉⠓⠒⢲

⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆
⠀⠀⠠⣄⢀⣿⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⡿⣷⣀⣀⣀
⢀⣀⠀⠘⠛⣿⣰⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢧⣿⣥⣴⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣯⣿⣿⣿⣽⣿⡿
⠈⠉⠙⢻⣿⢹⣷⢤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣿⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣯⣿⣭⢿⡇
⠀⠀⠐⠋⠁⢸⡏⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠈⠙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠛⢿⣷
⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣾⠋⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⡴⠿⢦⠀⢀⣀
⠀⠀⢠⣄⣙⣿⣟⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⣿⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⣷⣶⣾⡆⠉⠙
⠀⠀⠈⠉⠉⣿⡏⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⣿⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⣶⠀⠀⣿⡇⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⣿⣸⣛⣛⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠻⣦⣄⣿⣇⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣋⣿⣇
⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⣦⣀⣤⣾⣦⣄⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠘⣿⣿⣿⠋⠂⠄
⠀⠀⣼⡿⢯⣸⣉⠟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⢩⠝⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣄⡠⠊⠉⠙⢄⣠⣼
⠘⠛⣿⡗⢒⢯⢟⡒⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⣰⡏⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⢸⣿⣿
⠀⠀⣸⣿⣧⣼⣤⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⡿⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⣱⣶⣶⠁⠀⡹
⠀⠀⠉⠀⠈⢹⠍⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠿⠿⠿⠗⠊

⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⣀⣁⢨⡭⣄⣁⣂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⢈⣤⣊⠽⠓⠛⠉⠉⠙⠛⢚⠿⣷⣪⡐⠄
⠀⠀⠀⠀⠊⣴⡵⠋⣡⡤⣴⣒⢲⠢⢤⢄⡀⠀⠈⠙⢿⡌⠄
⠀⠀⠀⠀⣼⣟⣴⣯⠶⡋⣁⡼⣿⡿⡿⢳⠿⣶⣄⠀⠀⠙⢀
⠀⠀⠀⢰⣿⡍⠇⠀⠀⠣⡙⠾⠿⠛⣡⠎⠀⠀⢙⡧⠀⠀⡘
⠀⠀⠀⢸⣷⠉⠓⠶⣶⣦⡬⣝⣲⣯⣥⡔⠾⠛⠉⠀⠀⠀⡄⢀
⠀⠀⠀⢌⠻⣆⠀⠤⢄⣀⡀⠈⠀⠀⠀⠀⢀⡀⠔⠃⠀⡜⠀⢸
⠀⠀⠀⠈⠳⡈⠑⠦⢄⡀⠉⠉⠉⠉⠉⠉⠀⠀⢀⠄⠃⠰⠃⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠭⢍⣛⢒⠩⠍⠖⠋⣠⠂⠠⠋⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⡐⠐⠁⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⠀⠈⢀⠜⠁⠀⡔⠡⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠀⣀⣴⠓⢃⠀⠀⠀⠀⠠⠐⠀⠂⠒⢂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠠⢄⡀⠀⠀⠀⠒⠀⠁⠢⠰⠤⠦⠾⠖⠛⠉⠀⠀⣼⠀⠀⠀⠈⠀⠀⠉⠈⠉⠀⠀⠀⠀⢀⢠⠤⠐⡀
⠀⠀⠀⠰⠀⠐⠀⠈⠀⡀⠂⡁⠐⠢⡀⠐⢄⠀⠀⠀⠀⠁⠀⠈⣼⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠓⠒⠚⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣀⣀⣐⣤⣾⢻⡄⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠋⠀⠁⢰⠇⠶⠌⣁⠠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠁⠀⠀⠀⠀⠀⣤⢠⡤⡈⠢⡶⠶⠛⣦⣴⣀⣶⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡥⢼⠔⣵⣄⣴⡿⠋⠁⠱⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⠛⠾⠁⠀⠘⠀⠠⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠤⠤⠤⠤⠴⠶⠟⠁⠊

⠀⠀⠀⠀⠀⠀⠸⠿⠛⠿⠂⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⣻⣶⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠀⠀⠀⠀⠀⠀⠑⠓⠀⠀⠀⠀⢸
⠛⡻⠀⠀⠀⠀⣀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣵⣠⣶⣶⡶⢶⣖⠒⠀⠀⠀⠀⠀⠐⠛⠀⠺⠿⠿⠀⠀⠀⠀⠀⡏⡀⠀⠠⣧⣷⣾⣷⣾⢿⠇
⠀⠀⠰⠶⡀⠳⣿⣜⢿⣛⠛⢛⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⣼⣿⠿⣟⡆
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣳⠫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣤⣄⡀⠀⠀⠀⠀⠘⣯⣾⡿⠁
⡀⠀⠀⠀⠀⠀⠣⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣠⡴⠾⠟⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⣀⣸⣾⠆⠀⠀⠀⢰⣶⣶
⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⣠⠀⣄⠄⠄⠀⠀⠀⡟⠉⠀⠀⠘⠃⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠠⢤⣀⣄⣠⠎⣽⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠑⢤⣀⢹⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⣀⣀⣀⣺⠩⠁⣀⣬⣤⣤⣒⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠛⢷⣿⡟⠢⠀⠀⠀⡀⢀⣿⣿⣶⡎⣀⠀⢈⣀⣠⣤⣴⡿⣽⣿⢾⡷⣷⡷⠟⢿⣿⣿⣿⣿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⡀⠀⠀⢀⣤⣾⣿⣿⣷⣿⣶⣿⣿⣛⣿⢿⣟⠿⣯⡭⠾⠃⠀⠀⠈⠙⢻⡿⠟⠉
⣤⣄⣤⣴⣆⠀⠀⠀⠀⠀⠰⠝⠿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠐⠀⣠⠬⠟⠚⡻⠟⠀⠀⠀⢀⡠⠔⠋⠁⠀⢀⣀
⠉⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⣽⣿⣀⡀⡠⠄⠒⠀⠠⠽⠖⣚⣋⣉⠠⠄⠀⠶⠿⡿⠿⠂⠀⠀⠀⠛⠛⠃
⠀⠹⣿⠏⠀⠀⠰⠶⠶⠀⠀⠀⠀⣠⠒⠛⣿⣿⠋⠐⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠬⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠟⠛⡉⠉⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⡿⠂⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣶⣶⣭⣵⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠄
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠟⠯⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⢀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠃⢈⣿⡷⠂
⠿⠟⠛⠒⠤⠀⠀⢸⡁⡠⠄⠀⠀⢠⣶⣴⣤⣷⠄⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢺⠟⠛⠁⠀⢺⠟⠁⠀⠀⢰⠤⠤⠴
⠀⠐⠂⠀⠀⠀⠀⠀⠑⠚⠃⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⡀⢠⣶⣾⣿⣯⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⢀⣠⢄⣀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠁⠀⠿⣷⣷⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣢⠤⢀⣀⠀⢀⡤⠀⠈⠀⠀⠀⠀⠺⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⡍⠁⠀⠈⠑⠾⢃⣄⠁⠀⣀⢀⡀⠀⠀⠀⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣍⡁⠐⣄⢀⠕⠀⠀⠀⠀⠀⠀⠉⠓⣌⣡⣻⣿⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠾⠟⣀⣴⣶⢶⣦⣄⠀⠀⠀⢹⠁⠿⠿⢆⣄⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠙⠛⠸⢼⡿⢹⣄⠀⠃⠀⠀⠀⠀⠙⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⠔⢈⣀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠮⢷⠖⠈⠙⣦⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠓⢦⡄⣀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢲⣄⠋⠿⠀⢀⠂⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠙⢧⡈⠒⠻⣉⣾⠷⣲⡶⠂⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⠀⠈⠉⡅⠣⣨⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠙⠶⠊⠉⠙⠾⠟⠀⢦⣞⣽⡟⢹⡟⣦⣄⠀⠀⠨⡄⠁⠀⠈⠀⠈⠻⠓⠬⣱⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⣸⠿⣿⡷⣾⠙⣾⡏⢑⣄⠀⠇⠀⠀⠀⢠⠀⠀⠀⠐⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⢰⠄⢤⣄⠀⢀⠞⠋⠀⠀⠉⠻⢤⣹⣧⣼⠀⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠨⠗⠊⠁⠠⠊⣰⣤⣀⠀⠀⠀⠀⠀⠉⠛⠎⠁⠁⢸⠛⠲⡀⡀⢰⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣤⡀⠀⠀⠀⣀⠤⠈⠛⠉⣠⠄⠀⢀⡄⠀⠀⠋⣧⡈⢉⡂⠠⣀⠀⠀⠀⠀⠈⠟⠾⣄⡀⢻⠃⢸⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢞⣀⠀⠤⢄⠀⠀⠀⢠⠎⠀⠀⠌⠀⠀⠁⠠⠬⠁⠪⡑⠦⡀⠀⠀⡀⠤⠀⠉⠐⣎⣛⠈⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠓⠚⠉⠲⢦⣀⡵⣄⡀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢦⡙⣆⠘⠑⠦⣀⠀⠀⣇⠈⠙⠒⠤⣄⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠔⠁⠀⠉⠀⠀⠀⢠⠃⠀⠈⠋⠐⠒⣤⣀⠀⠀⠀⠀⢻⣤⡀⠀⠈⢢⡀⡧⢀⣠⡤⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⡄⣠⣾⡅⠀⠀⣠⡄⡀⠀⢀⡏⠀⠀⠠⣀⠀⠀⡇⠁⠑⢄⠀⠀⠀⠀⠈⠒⢠⠀⡶⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⣟⢻⡄⠀⠀⠀⡴⠁⡆⠀⠀⠊⠀⠀⠀⠀⠈⠉⠒⠣⠄⡀⠈⠁⣠⢅⡀⠀⠀⠀⠀⠘⠒⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⡛⢧⠆⢀⡞⠀⠀⣇⡀⢀⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⠹⣀⠀⠁⠢⡀⠀⠘⠂⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⠰⠁⠘⣶⠿⠶⡄⣤⣯⣀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠂⠠⠌⢢⡁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣄⣰⡔⢻⡴⣴⢾⣿⣯⠎⣽⣿⣄⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠠⢽⣟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣛⣶⣤⣿⣵⣾⣃⣯⣼⣿⣿⣿⣿⣿⠹⢹⣦⡀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⡴⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣄⣠⡔⣹⣶⣄⠀⠐⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡄⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠢⠤⠐⠧⠸⠧⠤⠤⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⡻⣃⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡵⢂⣠⣤⣾⣀⡀⠀⠀⢀⣤⣄⣈⠙⠛⠛⡻⠿⠛⠙⣛⣋⣀⣈⣫⣆⣄⡰⢶⣶⡶⠈⠛⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠿⠛⠀⠈⠾⠿⠿⠛⠓⠂⠡⠄⠈⠁⠚⠛⠛⠛⠛⠋⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠁