Poseidon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡴⠋⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢦⠴⠚⢉⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣴⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⠁⠀⠀⠀⠀⢿⣿⡆⠀⣀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣗⠀⠀⢀⣠⣶⣶⣤⣿⡿⣿⡿⢟⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⣿⣷⣾⣿⣿⣿⢿⣿⣿⣿⣶⡾⢿⣿⣿⡄⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠹⠿⠿⠛⢉⣿⣏⣛⣻⣏⣭⣛⣳⢶⣝⡻⠿⠿⠷⢶⣶⡤⠄
⠀⠀⠀⢀⣀⣀⡒⠶⣦⣀⡀⠀⠀⠰⠶⣿⣿⣿⣿⠟⣤⣭⣭⣽⣿⣿⣿⣦⡀⠀⠀⠈⠁
⠀⠀⠀⠈⠉⢉⣛⡻⢶⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⡶⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶
⠀⠀⠠⠴⣚⣻⣿⡿⠷⠞⣛⣛⣋⣉⣉⣉⣉⣛⠛⠛⠿⣿⣸⣿⠫⠟⠟⠽⠿⠿⠿⠦⠼⠿⠿⠿⠿⣿⣿⣿⡿
⠀⣠⣴⡿⠛⠉⠁⠀⠉⢉⣀⣐⡲⠶⠦⠤⣬⣉⣉⡿⠂⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠔⠈⠁
⣾⣿⣷⣶⡶⣿⣿⣿⣿⡿⣛⣻⣿⣿⣿⠅⠂⠈⠉⠀⠀⠀⠀⣾⡿⠛⠉⠙⠉⠋⠈⠛⠈⠛⠙⠛⠁
⠟⢋⣥⣶⣾⣿⣿⣿⠟⢰⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣤⣀
⢸⣿⠟⣩⣾⣿⣿⠃⠀⠘⣛⣥⣶⣖⠒⠶⠶⠶⠤⣤⣀⣀⣀⣀⣈⣹⣿⣿⣻⠶⠂
⠀⠉⣼⣿⡟⣼⡇⣾⠀⠀⠉⣏⠈⢸⠇⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣛⣛⣛⠛⠋
⠀⠀⠘⠿⢁⣿⣧⣿⣆⠀⠀⠹⡄⠸⣆⠀⠀⠀⠀⣀⣠⠤⢤⡄⠙⠻⣿⣿⣧
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⡀⠀⠘⠂⠈⠓⠲⠒⠛⠩⢤⣴⠏⠀⠀⠀⠙⠋⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣛⠷⠶⢶⣦⣤⣄⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠉⠛⢷⣄⠒⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⡇⢇⢱⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠘⣗⣹⢸⡘⢦⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣿⣶⣞⡀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠻⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣽⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡟⠈⠙⠓⠒⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⣿⡟⠁⠁⣬⣶⣶⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⡇⠀⠀⠀⠀⠀⢉⣿⣦⣀⣰⠻⣿⣶⣶⣾⣿⣿⡛⠿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠁⢶⣄⠀⠺⣿⣿⠟⢿⣿⡇⠐⠒⣬⣽⣿⣿⣿⡇⢀⣿⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠻⠟⠁⠀⠀⠈⣿⣿⣻⣹⣿⢿⣿⡿⠋⠀⠙⢿⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣉⣠⢵⣿⣿⣀⠀⠀⠀⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢀⣼⣿⣷⣾⣿⣿⡎⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢰⢶⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢠⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣸⢦⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢣⣤⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣈⡙⣷⠂⡙⣿⣿⣿⣿⣿⡿⢻⢿⣾⣿⡅⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣻⣿⣿⣿⣿⣾⡻⣿⣾⣿⣿⣿⣿⣡⣶⣿⣿⣿⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⢋⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠿⣾⣿⣿⣿⣝⠻⠏⠙⣯⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣌⡿⢧⡉⠛⢧⡀⠆⠹⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⣿⣯⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣿⣿⡿⠀⢀⣀⣤⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣐⣄⠉⠛⠁⠀⠲⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣇⢠⡀⢀⠁⠀⠁⠀⠀⢀⣀⣀⣀⣀
⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠦⢴⣶⢾⣿⣿⣿⠿⠭⠥⠤⠽⠿⠿⣿⠿⠿⠿⠾⠷⡦⠤⢴⡦⣼⡦⠤⣶⡶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⠀⠹⠏⢁⣀⢠⣤⣤⣀
⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⠐⠈⠀⠀⠀⣀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣀
⠀⣀⣀⣈⣩⣥⣬⣧⣤⣤⣤⣤⣤⣯⣾⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠰⣆
⠀⠈⠳⡴⣢⣖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠶⣉⢷⡶⣀
⠀⠀⠀⢰⡙⢯⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⡀⠠⣀⡘⢦⣱
⠀⠀⠀⠀⠱⢬⡹⢝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⡰⠒⠛⠈⠁⢂⠈⡟
⠀⠀⠀⠀⠀⠀⠙⡀⠀⢕⠀⠀⠀⠀⡀⢲⡌⠆⠐⣠⡄⠀⠘⠁⡆⠀⠀⢉⣋⡏
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠙⠦⡀⠈⠀⠀⠀⠀⠚⠁⠀⠁⠀⠀⢿⢄⣐⣠⠟⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⡀⠀⠠⠰⠀⠀⡴⠀⠀⠀⠀⠀⠀⠉⠚⢻⠟⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣄⢀⠦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠋⣁⢠⡴⡆⠣⡀⠀⠀⠠⠀⠀⠀⠁⢀⣴⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣰⣿⣏⠡⠂⠀⠄⠀⠈⠻⣦⡀⠀⠀⠀⠒⠉⠈⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⡀⠜⠡⠞⠋⣿⢇⠈⢦⡁⠀⠀⠀⠀⠀⠓⡄⣀⡀⢀⠀⠀⠀⡠⠜⠃
⠀⠀⠀⠀⠀⠀⡌⠲⠀⡠⠐⢸⠏⠃⡀⠀⠀⠀⠀⠀⠐⠒⠈⡟⠇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠠⣇⠤⠎⠀⠀⠘⠈⠠⠄⠀⠀⠀⠀⠀⠀⠐⠀⡧⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠆⠢⡐⡄⠠⠠⢄⠠⠀⠀⢈⠁⠢⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⠁⠀⠐⣷⠁⠀⠀⠀⠀⠀⠂⠀⡠⠠⠀⡀⠈⠂⠀⠀⠀⠀⠺⣍⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠂⢀⣄⠢⠠⣰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠗⠆⢂⣀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢨⡄⢀⢘⣇⠁⠀⠸⡠⠩⡀⠀⠀⠀⠀⠀⡀⠐⠀⠃⠸⡧⠀⠄⢀⣒⢄⠤⠀⡀
⠀⠀⠀⠀⠀⠪⠞⡁⠈⠺⡗⣧⠚⠬⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠂⠀⠀⢀⠑⠒⢶⣦⠈⡿⠑⡖⢀⠠⣄
⠀⠀⠀⠀⠀⢅⡈⣒⣦⡍⠛⠀⠑⠈⢹⠆⠀⠐⠀⠀⠀⢘⠀⠀⠋⠂⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠁⠉⠡⣀⠑⠤
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡠⠀⠀⡼⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⢦⡈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠒⢚⠰⢁⠄⠀⡇⠁⠀⠀⠀⠘⠆⣀⣄⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣽⠒⠁⠀⠀⠹⠀⠀⠀⠀⢠⠆⠈⠑⠳⠦⠠⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠌⠈⠉⡁⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⠇⠀⠐⠀⠀⠀⠀⠀⡀⠈⠀⡿⠀⠀⠁⢄⠀⠀⠀⣄⡀⠤⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡜⣧⢄⠀⠀⠀⠀⢀⡠⠚⠀⠀⠰⣏⠃⠀⢀⠀⠁⡀⡐⣟⠀⣀⠀⠉⠉
⠀⠀⠀⠔⢄⠠⣶⡀⠀⢎⡾⠋⠀⠠⢄⠠⠀⠈⠉⠀⢀⡀⠀⣠⣤⣤⣤⣀⣉⣁⣀⡀⠀⠛⢁⠚⢦⡀
⠀⠀⠀⢣⣠⢁⡞⠈⠙⢫⡀⠠⣂⣀⣆⡠⣶⡟⠋⠑⡌⠉⠉⠃⠂⠀⡞⠉⠸⠏⢀⣸⠟⠉⣽⠷⠶⣼⠂
⠀⠀⠀⠀⠁⠂⠀⣀⡶⠟⣏⢀⠉⣧⠈⠁⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠁⠀⠉⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⡙⠅⠀⠈⠹⠄⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠿⣅⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⡿⠰⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣠⣴⡖⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠄⠀⠀⠀⠀⣀⣤⣴⡾⠿⠇⠈⣧⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠠⠀⠀⠀⢀⣾⣿⠟⠁⠀⠈⠀⠀⠈⠄⠀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡰⠛⢿⣿⣀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⣼⢿⡿⠉⠀⠀⠀⠀⠀⠉⠀⢴⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣀⠠⠊⣱⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢘⡿⠗⡌⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠿⣅⡀⠶⠀⠀⠀⢀⣀⠀⠀⠉⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣜⠆⠉⠁⠀⠀⠀⠀⠉⠛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣿⣿⣷⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⢀⠀⠀⠀⠀⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢻⣿⣿⣿⡄⡼⡀⠀⢰⣄⠀⠀⢻⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣿⣿⣷⣿⣇⣆⢸⣿⣦⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⠘⣿⣿⡆⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⠷⣿⣿⣅⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢙⣿⣿⣿⣿⡿⢠⣿⣿⣿⠀⠀⣿⠆
⠀⠀⠀⠀⠀⣀⣤⣤⣼⢷⣤⣿⠃⠀⠀⢸⣿⣿⣿⣿⣇⠘⣿⣿⣿⡆⠀⣿⡄⠗
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⣿⠐⠀⠈⡤⢹⣿⣿⣿⡏⠀⣿⣿⣿⣇⠀⢿⠁⢂⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠰⠎⣿⣿⣿⣇⠀⢿⣟⠻⣿⣄⠀⠠⣐⠂⠀⠀⠦⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡟⣶⠄⢿⣿⠏⠻⣷⢸⡏⢸⣿⣿⣦⡴⠼⢇⠻⣷⢾⡿⣷⣀⣀⢰
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣮⣿⣶⣬⣿⡃⠰⢿⣼⣇⣼⣿⣿⣿⣿⠶⠾⢷⠛⣾⣷⡾⠻⡿⢾
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠛⠿⠿⠿⠿⠿⠿⠇⠀⠰⠂⠀⠉⠿⠿⠿⠿⠿⠿⠀⠀⠀⠘⠿⢿⣿⣿⡇⠈
⠀⠀⠀⣿⣿⣿⣿⣿⠇⠠⠤⠤⠤⠲⠖⠲⠆⠀⠀⠶⠆⠐⢒⠒⢢⠤⠒⠐⠶⠶⠶⠂⠒⠾⠻⠘⣧⠶
⠀⠀⠀⣿⣏⣿⣿⣿⠃⠀⠀⠀⠀⡁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠏⠁⠀⡀
⠀⠀⠀⠙⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁


⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⡀
⠀⠀⠀⣧⠀⠀⠀⠀⣿⡄⠀⠀⢠⣧
⠀⠀⠀⣿⡆⠀⠀⠀⢻⡇⠀⠀⠈⢻⡀
⠀⠀⠀⢻⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣤⣤⡄
⠀⠀⠀⢸⣇⠀⠀⠀⢸⣿⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠾⣿⣿⣦
⠀⠀⠀⠘⣿⠀⠀⠀⠸⣿⠀⠀⠀⢸⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠉⠁⠀⠀⠀⢻⡎
⠀⠀⠀⠀⣿⣇⣠⢤⣀⡋⠀⠤⠤⠄⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣏⣀⣀⠀⣀⣤⠘⣧
⠀⠀⠀⠀⠉⠉⠉⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⠏⢹⠀⠙⠉⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣦⠚⠀⡃⠰⡿⠢⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡟⠃⢰⡶⠙⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣀⠀⣠⣤⣴⢿⠛⠻⢆⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠭⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠋⠠⣮⣠⣤⡀⠈⠐⢒⠟⠉⢂
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠐⢒⣋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠛⠉⠉⠉⠙⠻⠿⠿⣿⡿⠗⠁⠀⠀⠀⠛⠉⠁⠀⠀⡐⣿⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⡀⠀⠙⠀⠀⠀⣠⢞⣼⠃⣤⡄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣶⣄⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠃⣼⠇⢀⣿⠇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣿⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢠⣬⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣠⠏⠀⢠⡟⠀⢸⣿⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⣿⠀⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡴⠃⠀⠀⠘⠀⠀⣸⡏⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠤⣿⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⢠⡟⠁⢠⠀⡄⠀⠀⠀⣿⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣆⡀⠀⢹⣷⣄⣤⢿⣯⡿⠋⢻⣿⣿⣿⣿⣾⣷⣦⣤⣶⣿⡟⠀⢠⠃⡼⠁⠀⠀⢸⣿⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠘⣿⣶⣤⣤⣿⣿⣯⠾⠋⠀⠀⠀⠻⣾⢻⣿⣿⣿⣿⠟⣸⡟⠀⢠⠏⡼⠃⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⠷⣶⡟⠀⢀⡞⣼⠃⠀⠀⠀⢠⣿⡇⢸⡧⣀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⡿⠀⠀⣼⣿⠏⠀⢰⡆⠀⢸⠏⡇⢸⡇⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣹⡿⠀⠀⣼⣧⡟⢸⠀⣾⡇⠀⣼⠀⠋⠸⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢰⣿⣿⠀⡆⠀⣿⡇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⡁⢻⣷⣀⣿⣿⠇⢸⠃⠀⣿⡇⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣱⢿⣿⣿⣿⡿⠀⣿⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣷⡜⣯⢿⣟⠷⣤⣧⣀⡸⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢿⢻⡆⠙⣧⡻⣆⠀⠀⣀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣾⡟⣷⡀⠈⢻⣄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢻⡍⢷⡄⠀⠙⠟⠒⠊⠉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣄⠀⠀⠀⣴⠀⠀⠀⡄
⠀⠀⢸⡆⠀⠀⢻⡆⠀⠀⢳
⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⣤⡀
⠀⠀⠘⣇⠀⠀⢸⡧⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠟⠛⢾⡷
⠀⠀⠀⣿⠀⠀⠀⠻⠀⣀⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⢀⡀⣧
⠀⠀⠀⠘⠉⠉⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⠹⠂⠛⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠚⠀⠁⠹⠁⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠋⠀⠀⣰⠿⣿
⠀⠀⠀⠀⠀⠀⡞⠘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣿⣿⣿⣿⣶⠿⠋⣤⣀⣀⠁⠰⠶⠒⢂
⠀⠀⠀⠀⠀⢰⣷⠀⣨⡁⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠉⠙⠛⠛⠻⢋⠀⠀⠀⠛⠉⠀⠀⡄⡟⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠸⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡾⢀⡔⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠹⡄⢻⡄⠀⠀⠀⠀⢀⡴⠛⠋⢩⣞⠋⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡜⠁⢸⠁⢸⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢳⣸⡇⠀⠀⠀⢠⠋⠀⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⢿⣦⠊⠀⠀⠁⠀⣼⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⢿⡄⠀⢀⣴⣿⢿⣿⣿⣶⣦⠀⠀⠀⣀⡴⠃⠀⢠⠀⠀⢀⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠸⣔⠀⢈⣿⣿⣫⠜⠁⠈⢿⡙⣿⣿⣿⣿⠟⡿⠁⢠⢣⠏⠀⠀⣸⣿⡆⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⣷⣥⣿⣿⠋⠁⠀⠀⠀⠀⠙⢾⣿⣟⠄⡾⠁⢠⢇⡏⠀⠀⠀⣿⡇⣷⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⠁⢀⣾⡞⠀⢰⡇⢠⡏⡇⣿⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⠇⠀⣼⣿⢡⠀⣿⡇⢸⠁⠀⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠋⢿⣆⣸⣿⠇⡼⠀⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⢫⣿⣿⡿⢠⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⠈⢯⢷⡝⠾⠧⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⠿⣇⠈⢳⡑⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠐⡝⢦⠀⠙⠃⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⡀⠀⠀⢠⣷⡀⢠⣿⣄
⠀⡿⡆⠀⠈⠁
⠀⠀⠘⠀⠀⠈⡀
⠀⠀⠀⠘⠂⠀⢛⠈
⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢷⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⣇⣀⣀⡀⡅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣘⣃⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣹⠿⠛⢉⣴⣯⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣥⠀⠀⠀⢦⣄⠀⠈⠉⠀⠀⠸⣿⣿⣿⢇⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠒⠖⠒⠛⠻⠿⠛⠻⣦⠀⠀⠀⣄⠀⠉⠉⠉⣠⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⠄⠀⠙⠓⠀⠀⠀⠈⢻⡦⡀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠙⢦⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⢼⠀⠀⠀⠀⠀⠈⠁⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡐⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣠⠏⠀⠰⠀⠀⠀⢀⣀⠀⠀⠒⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⢀⠇⠀⠑⠶⣶⣄⣩⣥⠴⠦⠀⠀⣿⣿⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠘⢤⠀⠂⢴⢾⣟⣷⡾⠋⠀⠀⠀⢹⣿⡇⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⢺⣮⣭⡿⢡⠇⠀⠀⠀⠀⢻⡇⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣷⡄⠀⢻⡿⢡⣾⣧⠀⠀⠀⠀⢾⡇⣦⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢻⣭⣶⡿⢱⣿⣿⡿⣀⠀⠀⣀⣾⡅⠿⠆⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⡯⠿⢱⡾⣿⣿⡽⣣⡀⠀⣉⣿⣷⣾⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢟⣋⣮⣾⢋⡿⣡⣿⣇⢣⢀⠿⣿⢿⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡾⠿⢿⣏⡿⣡⣿⣿⣿⡀⠀⠀⢻⡆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⢿⠶⢾⡝⡵⢫⡟⣿⣿⣧⡀⠀⢸⣧⡜⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⣦⣃⠾⠗⣩⣾⡿⠟⠉⢿⣦⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⣯⢶⡟⠋⠁⠀⠀⠀⠈⣿⡟⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠀⢷⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡸⠂⢠⡀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠈⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠈⢇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣼⣿⡏⠁⣠⣄⣀⣤⣤⣀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⣠⡾⣰⣿⠿⠟⢛⣛⣯⣭⣶⣶⣿⡟⠄⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡱⠊⣡⣶⡭⣵⠟⢋⠔⠢⣭⣭⣭⣿⡿⠿⣿⣿⣿⠀⢀⣴⡾⢃⡴⠋⠀⠀⢠⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠆⢡⢣⣤⡶⠶⠒⠚⣁⣤⣶⣶⠦⠤⢬⣝⣶⣌⡙⠛⠷⠟⣋⣠⠞⠁⢀⣠⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣧⡹⠿⠛⠛⠛⠻⣤⣾⡿⠛⠁⣠⠴⠚⢛⣛⡛⣛⣛⣶⣶⣶⣿⣿⣿⣿⣿⡿⣿⠀⢀⡔⢀⣤⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⡀⠀⣺⣿⢅⣒⣒⠍⠀⣚⣛⣛⣻⠿⠿⠿⠟⢛⣩⣵⣾⣿⠿⠛⠋⠁⣰⠟⢰⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⣿⣿⡔⠛⠁⠄⣀⣭⠽⠿⣿⣯⣟⣛⣿⣿⣿⣿⣿⣣⠐⣦⡀⢸⡏⠀⠈⢷⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⣿⣭⣿⣿⣿⣿⣿⣶⣾⡿⣃⣴⢞⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣧⣽⠁⠀⠀⣸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣿⣿⠒⣫⠏⠉⣸⣿⣿⣆⡙⢿⡏⢾⣏⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣴⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⢀⢴⣿⣿⣿⡇⣙⢿⣇⣼⢷⡇⣿⣷⡙⢿⣿⣿⣿⣿⣿⠋⣴⣿⡿⠟⠋⠁⣦⢀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣬⣆⠀⣄⣿⣾⣿⢿⡈⢷⣍⣦⣿⡁⢊⣼⣿⡌⠻⣿⣿⣿⣿⣿⣫⣾⢽⣛⣶⣶⣶⣾⣋⡞⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠁⢈⠀⠛⠻⠿⣧⡐⣌⢷⠙⢿⣟⣿⣿⡿⠻⣿⣤⣌⣛⣛⣿⡿⠟⠛⠛⠛⣿⡿⣿⣿⣥⣶⡿⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠻⢷⣥⣰⡹⣶⣄⡙⣾⣿⠀⢠⡝⣮⣿⡇⠀⠹⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣍⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⢰⡍⢻⣿⡎⡟⣷⣿⢣⢸⡇⢧⢸⣿⣿⠀⠀⠹⣿⣿⣿⡿⣿⣿⣿⠟⠀⠙⠿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡰⡎⠿⡇⡆⡿⣿⠃⣿⡈⣾⣜⠁⣾⣿⣿⣿⡆⠀⠀⠙⣿⣿⣿⣿⣯⠁⢀⣀⣤⣤⣼⣷⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠇⣿⢰⢡⢇⡇⡿⢘⣷⠱⡼⣿⡄⣿⣿⣿⣿⡓⠀⠀⠀⠈⠛⠿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡸⢃⡞⢡⣷⣿⡾⡱⢃⡾⣿⠇⣿⣿⣷⣿⣿⣿⣿⡇⠈⠳⣤⣀⠀⠀⠈⢙⣷⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠗⣋⣴⢿⣿⠏⠐⢡⡿⣡⡿⣰⣿⢯⣿⣿⢿⡉⠹⡧⠀⠀⠀⠀⠀⣠⡴⣻⣿⣿⣿⢟⣯⣿⣿⣿⡿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢰⣿⢏⡾⢳⢀⡇⣿⣵⢏⣾⣿⣷⣿⣾⠃⠈⠁⠀⣠⠶⠋⢀⣤⣾⣯⣾⣿⣿⢿⣵⣿⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡟⢸⡇⣿⣧⣷⠘⡏⣾⣿⠹⠛⠉⠁⠀⠴⣾⡞⣡⣴⡾⣿⣽⣿⣿⣿⣟⣵⣿⣿⢿⣯⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣮⢳⡈⣷⢹⠇⣿⡇⣷⣙⢷⣠⣀⣴⠇⢀⣨⣿⣿⣻⣽⣾⣿⣿⡿⣫⣿⢟⣿⢟⣵⣿⣿⡧⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠃⠉⢻⡜⢈⡾⢃⣼⡿⣿⡿⠉⠉⣀⣰⣿⣽⣿⣿⣿⣿⣿⣿⣷⣿⡿⣫⣿⢋⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⣠⡿⠀⠈⣸⣵⣾⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⠃⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣰⡟⢠⠇⠀⣩⣟⠿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⣠⣿⣶⣿⣿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣴⣯⣶⡿⠿⠛⠋⠉⠉⠉⠉⠉⠙⠛⠿⠿⢿⣿⠿⠿⣯⣽⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠰⠞⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠿⠿⠛⠛⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⡄⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠟⠛⠛⠻⠿⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⢻⡄⠀⠸⣧⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢀⣿⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠘⣿⣴⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠁⡰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢀⣿⡟⢁⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣇⣡⣆⣀⡳⢖⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠏⣀⢀⣈⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠹⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣆⣠⣬⠁⡴⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣠⠴⠛⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣿⡷⢦⣥⣶⣾⣿⣿⣽⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢱⠐⢊⡩⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢿⢃⡎⣰⢣⡾⣿⢻⣿⢸⣿⠿⠿⢯⡳⣄⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡂⠡⠔⣋⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠘⢾⢧⡟⣼⢡⡟⣾⣿⡾⠉⠀⠀⠀⠙⠊⢷⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠐⠲⣾⣏⠳⣄⠀⠀⠀⣠⡏⠀⢶⡀⠀⠀⠈⠳⣿⣸⡷⠟⠉⠀⠀⣀⠀⣄⠀⠀⠀⢬⡳⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣿⡴⠘⢦⣠⠞⠉⢠⠄⣾⣷⡄⠀⠀⠀⢀⡉⠀⠀⠀⢀⣴⢟⣾⣟⣷⣆⠀⠈⠹⣾⣆⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢸⣿⣿⡄⠀⠁⠀⢀⡼⢸⣏⣿⢲⣶⣦⠶⠞⢧⠀⠰⠦⠬⢿⡿⣿⠏⠛⠿⣤⣄⡀⠉⢻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠈⣿⣿⣿⠂⠠⠞⣋⡴⠟⠋⠘⣾⠉⡏⠀⣀⡼⠀⠀⠱⠀⣼⢠⠏⠀⠀⠀⢀⡟⠀⢀⣦⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢿⣇⠙⠷⠒⠉⠁⠀⠀⠀⢰⡿⣄⣇⠀⢀⠲⡀⠀⠀⢠⠏⡇⠀⠀⠀⢀⡞⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡴⢿⣧⠀⠉⣛⠶⣦⣤⣤⣤⣿⢼⡇⠀⠀⠀⠉⣲⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⡆⠀⠀⠀⢀⡠⢾⡇⠹⣿⠧⡘⣮⣳⣦⣽⣷⣤⣤⣼⣿⣄⠀⠀⣀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⣤⠞⠉⡀⠺⣿⣦⡙⢧⡙⢮⣳⣬⣛⠿⣿⣿⣿⣿⣿⣧⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣮⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⢿⡿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠆⠘⠳⣄⡤⠀⢹⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠉⢳⣯⠀⢿⣧⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣶⣞⣿⣄⡾⠋⠀⠁⠀⠀⣿⡇⠀⠀⢸⣦⣽⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣧⢻⣿⣿⠁⠀⠄⠀⠀⠊⢹⠋⠀⠀⠘⠿⣿⣿⣏⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣤⣤⣾⣿⣷⠿⡝⠆⠀⠀⠀⠀⠼⠏⠁⠀⢀⣴⢶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣶⣾⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⣷⡟⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⣿⣿⣟⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠑⣾⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣄⣼⣾⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣼⠆⠀⣀⡀⢀⣀⠀⢠⣿⣤⠀⠀⠈⣹⠗
⠀⠀⠀⠀⠀⠠⣟⣿⡙⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠶⣿⡟⠱⣬⣃⣄
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠁⢈⣩⠿⡟⢁⠀⠀⠻⣿⠻⣿⣿⡧⢙⠷⣄⠈⠛⣵⢦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⡀⢀⣀⠀⠀⠀⣔⡀⠀⠸⠄⠈⠓⠀⠀⠀⢸⡅⠉⠒⠞⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢫⣷⠎⠉⢀⡠⠜⢻⣿⣤⣶⣶⠀⠀⠀⡄⢀⣾⣿⣾⣶⣿⣌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠁⠘⢋⣶⠾⣏⣼⣶⡿⢿⣿⣿⣾⣷⣀⠀⠈⡟⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⡟⣴⣾⣿⣿⡶⠶⣦⣵⣿⣿⣿⣾⠷⠹⣿⣿⣿⠻⣿⠏⠋
⠀⠀⠀⠀⠀⠀⢠⣤⠂⣼⣿⣿⣿⣥⣾⣿⣿⠃⠻⡆⢻⣿⣿⣟⣼⣟⢾⡁⠿⣸⣇⢂⠘⠄
⠀⠀⠀⠀⠀⠀⣼⣿⠁⢨⣿⡿⠽⢫⣭⣭⣄⣠⣾⣿⣾⣿⣿⣿⣿⢿⣦⠹⡆⠈⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣹⣿⣶⣾⣿⣿⣿⣿⢟⣹⣿⣿⣿⣿⣿⣦⣑⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠏⠁⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢿⣄⡙⢎⢻⣾⣿⢿⠟⢿⣿⣿⢻⣯⣿⢹⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠁⠹⣿⣿⣿⣿⣗⣤⣾⣧⣿⣛⠿⠙⠁⢈⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣥⡀⠀⠄⠉⠹⣄⠀⢤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⢀⡀⠂⠩⣻⣿⣶⡤⣹⣷⠶⣿⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣤⣄⣠⣝⣶⣴⠛⠛⠉⠀⠀⡴⠞⠛⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠸⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣘⢇⡶⣠⢂⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣟⣮⡟⠙⠋⢻⣯⣄⠀⠀⠀⠀⠀⠀⠀⠑⠒⢦⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢿⢿⠷⡦⠰⢜⣿⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⡯⣾⣿⣮⣿⠆⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⢙⣁⣸⣿⣾⡄⣼⠇⠘⡛⣦⣄⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣍⠀⠸⠋⠉⠉⠿⠁⠈⠈⠙⠧⠀⠁⡷⠀⠀⠀⠀⣉⣶⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⠠⠄⡼⠏⢠⣼⡇⠀⠀⠀⠀⡌⠀⠀⠀⢀⣶⡄⠘⠃⠀⠀⠀⠉⠛⠇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢳⠀⢀⠉⢀⣼⣇⢀⣿⣿⣷⣦⣤⡠⢌⠁⢤⣤⣾⣿⣿⣷⣀⠒⣆⠀⠀⢀⠃⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣛⠀⠀⠐⠞⠀⠈⠹⠉⣿⣿⡇⢀⡴⠈⠁⠀⠀⠀⢻⣿⢿⣿⡟⠉⠀⢀⣼⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⡽⠓⠛⠻⢷⣤⣶⠂⠀⣽⣿⡷⢾⠳⠂⠐⠀⠚⠆⢸⡏⠂⠙⣷⣆⣼⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠁⠈⢤⠹⣿⣁⢈⡟⠂⠠⠖⢀⠀⠘⣿⠀⠇⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡁⣿⡌⢳⠈⠀⠀⠀⢀⡆⢀⣷⢋⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣛⡐⠦⠆⣈⢀⠀⠀⠀⠀⠐⢠⣶⢌⣧⡾⢛⡂⠀⠁⢤⣦⠼⡋⣶⡥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣾⠛⣟⣣⣴⣶⣦⣄⠀⠀⠀⣠⣾⣿⣿⣷⣭⣿⣶⠤⠶⠶⠤⢾⣿⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢿⣶⣿⣫⣥⣾⣟⠻⣦⢀⣼⣿⢿⣷⣿⣿⡇⣸⢻⣦⣶⡼⣿⣻⣿⣿⢽⡟⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢿⣧⣼⣿⣺⣻⡳⣻⣿⢿⣭⣿⡙⢇⡱⣉⡴⣿⣿⣿⣿⡰⣸⣷⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⣿⡿⣷⣶⣿⣿⡭⣼⢳⣽⣿⣿⣛⣦⡙⠞⠢⠉⡾⣿⣿⣿⣟⣧⢻⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣶⣋⡽⢽⣦⣽⣿⣿⣾⣿⣿⣿⣧⣽⣠⢇⡘⠼⢿⣿⡿⢻⣿⣿⡿⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣿⣿⣶⣿⣿⡿⠟⠙⢿⣿⣾⣟⢾⣰⢁⣄⠺⠾⡷⣯⣽⡟⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⣯⣽⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠤⠖⠒⠢⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢎⠄⠠⠆⠀⠦⠌⠢⠑⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⠆⠀⠀⠀⠀⡜
⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠐⢩⠀⣀⡀⠀⠀⡀⠁⠀⣄⠁⢀⠀⠀⠀⠀⠀⠀⢠⠎⠜⠁⠀⢀⢀⠀⠒⠁
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡼⠀⠀⡆⡀⠀⡀⢈⡷⣈⠃⡁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠐⠔⠁⠀⣠⢆⠔⠃
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢋⠀⠀⠆⢄⠱⡌⠂⠑⢮⣀⣠⠱⠈⠢⡀⠀⠀⠀⠀⠘⠇⠀⠀⣇⠀⢀⠔⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⡛⢁⠀⠀⠀⣠⠐⠖⢠⡉⠀⠀⠰⡀⠀⢀⠀⠀⠀⠈⡠⠀⠲⠦⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡀⠁⠀⠘⢚⡵⠀⡀⠈⠁⠀⠘⠀⠀⠀⠜⡠⢊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠀⠀⡇⠀⠐⠈⠁⠀⠂⠈⠓⠒⠂⢰⠀⠃⠀⢈⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠐⠁⠂⠀⠀⠀⠀⠉⠀⠠⡠⢊⠄⠖⠀⠀⠀⡀⠀⠀⠐⠉⠩⣅⡐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⠓⢂⡀⠀⠀⠑⠤⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡴⠃⡠⠤⢤⣦⠱⢀⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢅⣀⢀⣀⠀⠁⠉⠉⠈⠁⣠⠤⠤⣄⣀⠀⣀⡀⠉⠉⠁⠀⠈⠢⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⠝⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠔⠚⠓⠦⠤⠤⠆⠀⠀⠉⠉⠉⠀⡠⠂⠀⠀⠀⠀⠠⠖⠛⠲⢤⣄⣤⡤⠀⠐⣄⢀⠠⣀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠀⠀⠐⠋⠙⠲⠦⠴⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠙⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣦⠲⠿⣵⡢⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠂⠉⣉⣉⠻⣿⡄⠄⠳⣾⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢤⣊⣡⠄⠀⠀⠀⠀⠀⢸⡗⣹⠀⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠒⠒⠈⠉⠀⠀⣀⠀⢀⢀⣀⣤⣾⣯⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢴⣷⣦⣀⣴⣿⣷⡀⣠⠖⣶⣦⣠⠶⣶⣶⣟⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠯⣟⣵⣿⣿⣿⣄⣛⣿⢁⣟⢻⠉⢰⣟⣁⡟⠉⣯⣀⣈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣠⡿⢛⠉⠀⠈⡇⠈⠉⠈⠙⢏⠉⠹⠋⠙⡏⠀⠉⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠌⣾⣯⢠⡟⠀⣯⠄⠀⠈⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⡰⠀⠂⠀⠀⠀⣠⣾⣿⣿⣼⠃⡼⠻⠀⠀⣼⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢂
⠱⠀⠀⠀⠀⣼⣼⣿⣿⡿⠏⣰⠇⠀⠀⡰⠇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢀⠀⠀⠈⠂
⠀⠉⠛⠛⠛⠩⢟⡟⠋⠀⠀⠀⠀⠈⣰⠋⠀⠀⠀⠀⠀⠀⠀⣈⡓⡀⠀⣿⢍⡑⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠃⡸⠃⠠⡄⠀⠀⠀⢰⡿⣻⣴⣄⠠⣀⠀⠈⠀⠉⠻⡇⢀⡿⠀⡀⠴⠀⠀⢸⡿
⠀⠀⠀⠀⢠⣣⡧⠀⠀⢹⠀⠀⡄⣿⣿⡏⠠⠌⣴⢻⣦⠀⠀⠀⢀⣿⠶⡷⠂⢠⣬⡆⠀⢸⠛⠗
⠀⠀⠀⠀⠀⠃⠀⠀⢀⣾⠀⠀⠁⣿⣧⡟⠶⠞⠋⣁⣠⣠⡿⡋⠏⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⠈⣃⢸⣿⣧⣴⣶⣿⣸⣿⡇⠀⠀⠀⠀⢀⡄⢀⡀⢀⠀⠀⠈⠃⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠐⠄⠹⢆⠀⠈⠉⢀⠹⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⣶⣾⣿⣿⡿⣋⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢌⡓⠤⠬⠴⠿⠟⠛⠋⣁⠀⠀⠀⠀⢠⠔⠲⡤⠐⠾⠁⠀⠐⣶⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢶⣤⠀⢤⣤⣰⠟⠉⠀⠀⠀⠀⡀⢀⡀⢀⣤⣀⣴⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠛⠛⠆⠀⢁⣀⣠⠼⠫⠟⠛⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠶⠖⡒⠀⣷⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⢀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⠤⠿⠛⠁
⣿⣟⣻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡤⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠑⠘⠀⠀⠀⠀⢀⣏⣱⣀⡤⠶⠂⠑⠂⠄⠀⢈⠠⠻⣶⠟⣛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠑⣀⢀⠒⡯⡭⣼⠏⠀⠀⠀⠀⠀⠀⠰⣤⠴⢾⡇⣞⢉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡇⠀⠀⠉⠂⠡⣸⣀⡏⠀⠀⠀⠀⠀⡀⠀⢀⡇⠀⢸⣇⠙⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⣉⣂⣄⠄⠀⠀⣀⠔⡲⠢⠄⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣠⢷⡀⡀⡏⠳⠚⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢉⠟⠀⠄⠀⠀⠁⠀⣇⠀⠀⡒⠛⠀⠀⠀⠀⠀⢀⣠⣾⡟⢀⠟⠁⠀⡀⠀⡿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⠏⠀⣾⡧⠀⢸⡆⠀⠈⣑⣭⡁⠀⠀⠀⢀⡄⡀⢹⣿⡿⠁⠀⠀⢠⠜⠀⠀⢳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣠⡤⣠⡀⠰⠙⣿⣿⣿⠟⠀⠀⠀⠀⢈⣴⣷⠿⠛⠀⠀⠀⠀⠀⢱⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢧⠃⠠⠂⢼⣷⣿⠏⠀⠀⡀⠀⠀⠸⠟⣻⣤⠛⢀⣔⣀⡢⠄⠀⢸⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠂⠐⠀⠒⠋⠉⠁⠀⣜⡰⠁⠀⠀⠀⠹⣿⠄⣠⡀⠀⠀⠀⠄⠀⠜⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠋⠑⠤⢤⣤⣤⣤⡶⠶⣦⡾⠋⠀⢀⠀⠀⠀⠀⠀⠢⠀⠙⢿⡿⣀⠁⠀⠄⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠄⠱⡬⣷⢀⣿⠶⠊⠁⠀⠀⠀⠼⠀⡀⠀⠀⠀⠀⣀⠀⠀⠑⢆⠀⢀⣄⡴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢡⠊⢀⠼⠉⠀⠀⠀⣀⣠⣴⠶⢤⡀⠄⠀⠀⠀⠀⠱⣤⠐⠄⠀⠙⡌⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠘⡄⠃⠀⣠⡴⠞⠩⡙⠂⠀⠓⢀⡵⣄⠀⠀⠀⠀⠀⠛⢳⡄⡀⠀⠀⠁⠈⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⠀⠐⠾⣃⡀⡀⠀⠀⠈⢹⣀⠈⠀⢸⠓⠀⠀⠀⠀⠁⣀⣇⢘⣦⣀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠂⠀⡀⠀⡈⠉⠉⠉⠉⠘⠳⣄⠀⠀⢀⠄⢀⠔⠒⡌⠀⠈⡿⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠄⣌⠀⣙⠈⣣⠀⢆⠀⡀⠀⠀⠀⠉⠒⠀⠀⡀⠐⢀⡧⢀⣠⠃⣿⡠⠔⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠑⠤⠞⠉⠁⣀⡠⠀⡀⢠⠀⠄⠈⣿⠁⠄⢸⡇⠀⠇⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢿⡀⠀⢀⠁⠀⢘⠒⢎⠀⠀⡲⠤⠾⣦⠄⠚⠻⣦⣤⠞⠁⠀⠘⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠙⠒⠎⠀⢀⠂⠀⠀⠑⠛⣆⠐⢀⣽⣀⣉⡰⠃⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠺⠆⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣄⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣤⡀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠹⢿⣿⣿⡄⠀⢠⣾⠋⠀⠀⠀⠀⠀⣠⣄⣴⣾⣿⣿⣿⣗⠄⣤⡀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣄⠀⢿⣿⡇⢰⣿⠁⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣿⣿⠁⣿⣿⠀⠀⠀⠀⢀⣴⠞⠁⠁⠙⢿⣿⣿⣿⣿⠁⠀⢰⣶⡆⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣧⣀⣀⣴⣿⡇⠀⠐⠀⠀⠀⢹⣿⣿⣿⣿⣧⡿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣿⠆⠀⡀⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣙⣿⣶⣶⣶⠿⣹⣿⣿⣿⣾⣷⣤⣿⣿⣿⣿⣿⣿⡿⢶⣤⣤⣀⣀⣀⣤⣾⠿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣟⣿⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⣿⣿⣿⠿⣿⣧⣌⣳⡀⠀⠀⠁⣠⣿⠿⠛⠛⠻⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⣿⠟⢩⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣏⣡⣾⣿⣿⣿⣍⣳⣤⣀⢰⡿⠁⠀⠀⠀⠀⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠸⠁⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⠋⣹⣿⣿⣿⣭⡍⠻⣿⣿⣿⡶⣦⠰⠆⠸⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣆⠀⣼⣿⣿⣿⡇⠀⠀⠀⠂⠀⣸⡿⣠⣿⠃⠈⠻⣿⣿⣦⠀⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣿⣿⣿⣿⠀⠀⠀⠀⡆⠀⠟⣰⣿⠏⠀⠀⠀⠈⢻⣿⣧⠀⠀⠈⠳⢦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠠⡀⠙⢿⣿⣿⣟⣿⡀⠀⠀⠀⢿⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠋⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀⣾⣿⣷⣀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣤⣈⣿⡿⣿⣿⡇⠀⢸⣿⣿⠉⠛⠷⣶⣶⣾⡿⠿⠛⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⡄⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⡀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠙⢷⣿⣿⡦⡶⣤⣴⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⣄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠉⠉⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠈⠉⠉⠉⠀⠀⠀⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣅⢀⡀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢾⡵⡍⢲⣞⣥⠆⠀⠀⠀⠀⠀⠀⢀⡴⡉⠀⢈⠙⢶⣬⠀⠈⠀⢘⡄⠀⠀⠀⢀⢌⠔⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢘⠆⢹⠋⠀⠀⠀⠀⠀⠙⠻⣿⡀⠝⠀⢸⡇⠀⠀⠀⠠⣶⣿⡧⢀⣄⢖⣥⠎
⠀⠀⠀⠀⠀⠀⠀⢠⣷⣠⣠⢦⠆⠀⠀⠀⠀⢠⣶⣷⣾⢃⡀⣶⠛⠇⠀⠀⡀⢀⡈⣾⣰⠩⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢣⡟⠀⠀⠀⠀⠀⠁⢹⡟⠹⣦⡀⠁⠀⡀⠀⠀⣷⠈⢳⡈⠻⣼⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡀⠀⠀⣰⡄⢀⠸⣁⣤⡾⠁⠀⡀⣿⠀⠀⢻⡄⢀⢳⡄⠸⠇⡀⠀⡠⠒⢈⣁⣒⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⠟⣧⠸⢦⠋⠌⠁⢀⡼⢣⣿⠀⠀⢸⡇⢸⠀⠀⠀⠀⠈⠙⠚⠵⠷⠿⠛⠃⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣞⣈⣉⣁⠧⡀⣟⣰⣿⡏⠀⣠⡞⢁⣾⡇⠠⠀⢸⡇⠈⡇⠀⡀⢶⣤⡀⢀⠀⠀⠁⣠⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⡹⢿⣷⣿⣷⡻⠝⢩⠁⢰⠋⠀⣾⣿⠀⠆⠀⣿⠣⠀⠸⡄⠐⡼⣿⣿⣿⣿⣿⠿⢯⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠛⠋⠉⠁⠀⠀⡌⠀⠃⠀⢸⠏⠀⢸⠀⠀⠇⣠⡀⠀⠹⡄⠙⢟⡿⣏⣤⣿⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣤⣀⣀⣀⣠⣾⠀⠀⠀⠀⢎⡄⠀⠀⠀⠀⢸⣿⡍⠂⠀⠈⠢⣈⠣⢼⡁⢰⡿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡉⠛⣙⣾⣿⣿⠗⠀⠀⠀⢀⣾⡏⣄⢰⠀⣦⢸⠏⣁⣀⣉⢦⣄⡈⠑⠢⣌⣉⡇⠇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢓⣿⣻⡟⢉⠄⠀⠀⢀⡞⠉⢡⣿⠈⡆⢷⢸⠊⢹⢿⢙⡧⣉⣻⢷⣤⣤⣿⠀⢠⠓⠨⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠖⠁⠀⢀⣾⠟⣽⣶⢾⣿⣆⠘⡌⢮⣂⠌⢸⠸⢰⠁⠈⠉⠛⠻⢿⢀⢮⡛⢦⡀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠁⢀⣠⡄⡲⠛⠁⠀⡏⠇⡘⠾⠋⠁⠈⡢⠙⠦⢀⢰⡅⠀⠀⠀⠀⠀⠸⣽⡇⠉⢟⣻⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⡿⠏⠁⠀⠀⠀⠀⠙⠤⠤⠶⠙⡄⠀⢷⣦⡕⠂⠭⢑⠢⢄⠀⠀⠀⠀⠉⠋⠀⠀⡣⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢧⣀⡴⡍⢫⣢⠀⠀⠀⠀⠀⠠⠃⡼⢨⡍⠛⣓⢤⡀⠈⢲⣦⠀⠀⠀⢀⠔⣩⣤⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⣄⡀⠀⠉⠀⠘⣿⠀⠀⠀⠀⠀⣷⣼⠀⠀⠻⣿⡿⠵⠯⠓⢸⣷⠀⠀⠀⠐⡘⢏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⡷⠠⢴⣯⣕⣦⡀⠀⠀⠈⠉⠀⠀⠀⠣⣰⣾⣫⣝⢦⠘⠃⣂⠭⠀⢈⣂⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢽⠧⠀⠀⠀⠀⠀⠀⠀⢀⠜⢉⡙⢫⠞⠉⠉⠁⠀⠀⠈⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣇⠀⠀⠀⠀⠀⢠⣧⣾⣟⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣷⠀⠀⠀⠀⠈⣿⠏⡌⠀⠀⣀⡤⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⠀⠈⠒⡉⣢⠊⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠊⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠴⠒⡒⠒⢤⡀⠀⠀⠀⠀⡤⠼⠥⣄⠀⠀⠀⠀⠀⡟⣟⠀⠀⠀⠀⢀⡤⣒⣶⣿⠶⢝⣆
⠀⠀⢰⡥⠤⠤⠤⠤⠤⣽⠀⠀⠀⢺⡭⠭⠭⣭⠇⠀⠀⠀⢸⣓⠻⡄⠀⠀⢠⢫⣮⣅⡿⡿⣟⡯⡅
⠀⠀⠸⣏⣙⠾⠭⢞⣉⡿⠀⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⠀⢻⡸⢂⡇⠀⠀⢸⢸⢉⣏⠛⢽⣆⡇⡇
⠀⠀⠀⠓⠚⠢⣠⠞⠓⠃⠀⠀⠀⠀⣇⠀⢀⡇⠀⠀⠀⠀⣸⠀⠸⡇⠀⠀⠀⠣⣙⠭⠾⠶⣊⠜⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢀⡴⡟⣇⡟⡷⣄⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⢀⡠⠤⠦⠤⡀⠀⠀⠀⠀⢀⡴⠋⠻⣷⡄
⠀⠀⠸⡍⠉⠉⠉⠉⣹⠀⠀⠀⠀⢸⠛⠛⠛⢳⢤⡀⠀⠀⢯⠤⡤⠤⡠⢬⠇⠀⠀⠀⡞⠀⠀⢀⡼⠁
⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⢀⣀⣸⣄⣀⣀⣿⣊⡀⠀⠀⠘⡆⢇⢠⠇⡞⠀⠀⣠⣴⡹⠶⠒⠉
⠀⠀⠀⠘⠒⠒⠒⠚⠁⠀⠀⠀⠓⠶⠶⠶⠶⠶⠚⠁⠀⠀⠀⠙⠚⠚⠚⠁⠀⠀⠙⠚⠀⣠⣄⡀
⠀⠀⠀⠀⠀⣀⠴⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⢠⣞⣓⣞⣳⡄
⠀⠀⠀⡼⠭⠤⠤⠽⡄⠀⠀⢰⠋⠉⠛⠉⠙⠉⠉⢳⠀⠀⠀⠀⠀⣀⡞⠑⠺⡀⠀⠘⡟⢛⡻⢿⠃
⠀⠀⠀⣟⢲⡚⢲⠛⡇⠀⠀⣿⡯⢽⡯⠟⢭⣿⠽⣿⡇⠀⠀⢀⠴⣅⠈⠓⢼⠁⠀⠀⢸⡥⢒⡟
⠀⠀⠀⢸⡀⡇⡟⣸⠀⠀⠀⠙⠛⠿⠭⠭⠭⠽⠟⠛⠀⠀⠾⣙⣆⣈⣧⠴⠋⠀⠀⠀⠀⢟⣹⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⢒⣟⣲⡀⠀⠀⣠⠒⢄⣠⠒⣄⠀⠀⠀⣾⢿⠆⣜⣳⡄⠀⠀⠀⠀⠀⣴⣽⡷⠦⡀
⠀⠀⠀⢀⡴⠋⠀⡯⢽⣻⠃⠀⢸⠁⡸⠈⡇⡹⠈⡇⠀⠀⣿⠸⣤⠏⠘⢦⠀⠀⢀⡤⣪⣾⠞⠀⢀⡗
⠀⠀⢰⠋⠀⣠⠞⣠⠞⠁⠀⠀⠈⢦⠃⡰⢧⠃⡴⠃⠀⢸⠁⠀⢹⠀⠀⢸⠀⠀⢗⡿⠚⠁⠀⡠⠊
⠀⠀⠀⠑⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⢸⣀⣀⣸⣀⣀⣸⠀⠀⠈⠳⠤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢐⢳⠈⠟⠱⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠠⣬⣿⣾⠂⠀⢭⠀⠀⠀⠀⠀⢀⣤⢶⣖⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠖⠀⠠⢩⣿⠀⠀⠘⡀⠀⠀⠀⠀⢻⠒⠛⣾⢽⠳⡳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⢀⣼⠀⠋⠀⢀⠀⠳⡀⠀⠀⠀⢌⣂⣂⠏⠀⠱⢻⠵
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⣜⣿⠏⠀⠀⠀⢸⡆⠀⣜⢄⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⣀⣼⣿⣿⠃⠀⠀⠀⠀⣼⣷⡀⠘⢦⡑⠠⢀⡀⠀⠀⠀⢀⡧⢭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⢫⣤⣾⡯⢀⣼⣿⢿⣇⠀⠘⢿⢷⣄⠈⢠⠀⠀⣮⡽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⣴⣿⡿⠋⡰⡩⣿⠗⠉⣾⣗⠦⠀⠙⢿⣻⣴⣠⣜⠖⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⣛⡭⠙⠀⢚⣩⣾⣿⡄⢠⣾⡽⢿⠻⢤⣸⢯⠿⢘⣥⣾⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣷⠫⡌⠉⣀⣴⣾⡿⣛⠛⣿⣧⣼⢁⢀⠞⢠⢎⡟⡽⠿⠷⣿⡿⣿⣯⠢
⠀⠀⠀⠀⠀⠀⠀⠨⣿⡟⢠⣾⡯⣺⠏⣿⠏⣴⡿⣻⠎⢂⣂⣀⣼⣽⢤⠃⠀⠀⠀⠈⠙⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣯⣍⣶⢏⢿⡄⡨⢋⣰⢿⣿⣻⡥⡶⢮⢺⢪⢆⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠻⠽⠎⣧⢨⡙⡟⢓⣭⡾⢻⢿⠁⢿⣏⠜⠷⣺⡷⣄⡀⠀⠀⢰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⣬⣿⠰⣲⣟⠉⢨⠆⣘⣻⡀⠀⠀⠀⠀⠈⠙⠳⢮⡐⢄⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣳⣿⣧⣀⠃⠟⢃⠰⣽⠟⢫⣴⣦⣀⢥⣈⣷⣦⠀⠑⢶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢷⣼⢿⣿⣋⣑⣤⣴⣾⢻⡽⢙⣈⠑⠦⢀⠀⠀⠀⠀⠀⠘⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣔⡺⢧⣹⣧⣖⣿⣽⡯⠊⠈⣛⣷⠸⣗⡋⢄⡂⡠⠄⠀⣑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣾⣾⠭⠞⠁⠀⠀⡜⠠⣨⢇⡟⠻⠯⠿⠿⠯⠯⠶⢌⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣴⡞⡡
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣴⡦⢠⣤⣔⣒⣲⣦⣴⣯⣭⣤⣤⣤⣤⡟⠙⣧⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢩⢤⢷⠶⢿⣿⣿⣯⡿⠟⠛⠙⣉⡉⠩⠭⠭⠭⠇⣸⠧⠤⣬⣅⣀⠀⢀⣁⡛⣷⣶⣤⣀⠀⣀
⠀⠀⠀⠀⠐⠸⢴⣊⢙⣩⢗⣛⠛⣋⣩⠤⠒⠚⣉⡩⠤⠄⠔⢒⣒⡂⣺⡁⠀⠈⠒⠒⠤⠭⣙⡒⠤⣝⠩⢝⡻⣭⣛⠍⠒⢀
⠀⠀⠀⠀⣠⠞⠃⠐⡐⡀⠀⢀⡊⠋⣀⡴⠞⠉⠁⢒⡈⠉⣉⣉⣉⣁⠃⢉⠉⠉⠑⠒⠢⢤⣄⠈⠁⠂⠄⠀⠈⠑⠉⠑⠢⣀
⠀⣰⢃⡞⠁⠀⠄⠀⠀⢀⡀⠀⢀⡾⠉⠀⡠⠀⠀⣴⣶⣾⠿⡿⠕⠁⠀⠀⠽⣿⣷⣶⡦⢄⡀⠓⢤⣠⣀⠀⠀⠀⠀⠐⡆⠈⠂⠀⠀⠀⠠⣄
⠰⠃⣸⠐⠀⠘⠀⡀⠀⡏⠈⠋⠿⠀⡂⢸⠀⠀⣶⢸⠇⠁⠀⠀⠀⣀⣀⣴⣮⣮⣿⠈⠂⠀⠀⠀⠀⣈⣿⣷⣤⠀⠀⠀⠈⢣⠀⠀⠀⠀⠛⡌⢦
⠘⠀⢀⢰⢀⢰⢡⢡⠀⣇⢀⣀⡀⠀⢇⠀⠀⠀⠙⢇⡀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢁⡠⠆⠀⠈⠀⠀⢨⣽⢿⣛⠄⠀⠀⢀⠈⡷⠀⠀⠀⠀⢸⠈⣇
⠀⠀⠀⠈⢎⢧⢻⢧⠱⡈⢮⡻⣿⣦⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠈⠉⠁⠀⣀⣀⡤⠤⠶⠀⢀⡾⠉⠀⣠⣾⠏⠀⠀⢀⡄⠀⠐⢸⢄⣷
⠀⠀⠀⠀⠈⢦⠳⣙⣴⣌⠂⣙⠪⣝⡷⣦⣀⠀⠀⠐⠢⠄⠀⡀⠀⢈⢩⠉⠉⠉⠉⠉⠉⠀⠀⠀⢠⠴⠋⢀⣤⠾⠋⣀⠴⢋⠤⠋⠀⠀⢀⠎⣼⠃
⠀⠀⠀⠀⠣⣀⠑⢌⠳⣗⠑⠢⣔⠠⣙⠻⢭⣟⡶⢤⣤⡀⠀⠀⠀⠀⠬⡭⠭⠭⠄⠀⣀⣀⣤⠤⠶⠚⣋⣉⠤⢖⣫⠵⢚⣡⠔⢠⠄⠀⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠙⠦⠈⠀⠑⠂⠈⠙⠲⢭⣒⡬⢽⡓⠲⠬⣭⣽⣛⠓⠚⠛⠛⣛⣛⣩⠭⠥⠖⣒⣛⡩⠥⠖⣊⡡⠄⠚⠁⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡁⠀⠀⠈⠻⢡⡀⠀⡄⠀⠀⠒⠒⢈⠉⠩⠥⠴⡒⠊⠉⠀⠀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠈⠑⠈⠑⠊⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠒⠂⠀⠀⠰⠀⠀⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⡈⣠⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢾⡠⠄⠊⣡⠞⠁⠀⠈⠀⠀⠀⠀⠀⢧⡄⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣔⠀⠏⠀⢈⡶⠁⠀⠀⠀⠀⠀⠀⠐⠒⢦⠀⠀⢳
⠛⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣿⠁⠀⡸⠂⡼⣁⡀⠀⠀⠀⣴⠂⠀⠆⠀⢄⣠⡄⠸
⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠉⠁⠀⠀⢡⣴⣿⣿⠗⢀⠙⡄⠊⠉⠀⠀⠀⠀⠀⠀⠁
⣷⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡂⠀⢫⣿⣷⠛⣣⡛⠈⠀⠀⠀⠀⠀⢀⣀⣆⠀⠈
⢼⠗⢄⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡾⠟⠀⠀⠀⠈⠁⠀⣿⣿⣶⢾⢽⣷⡇⠀⠀⠀⣀⣠⡟⠉⡈⠀⢠
⣾⣷⣾⣷⣤⣤⣄⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡹⠃⠀⡰⠂⢠⠀⠀⠀⢠⣿⡿⢡⡟⣼⣽⡇⠀⠀⠀⠀⠹⣧⢽⢣
⣿⣿⣿⣋⣿⡿⠿⠿⣧⣾⣿⣿⡗⠠⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣤⠟⠀⠀⠀⠀⢰⣯⡇⠀⠀⠀⢹⣿⣿⣆⣽⡿⣿⡁⠀⠀⠀⠀⠀⠘⠶⢧⡀⡀
⣿⡿⠛⠉⠀⠀⢲⣶⣿⣿⣿⣿⡇⣀⡨⣿⢿⣶⣬⣯⢶⣾⡿⠋⢋⣀⣀⣀⣾⢟⣟⣮⡖⠀⠀⠀⠈⢿⣿⣿⣿⣧⡈⠷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣿⣿⣾⣿⣇⣀⡉⠻⠿⢿⡦⠰⢯⣉⡿⠿⡿⢋⣾⣿⣿⡇⠀⠀⠀⠀⠈⢻⣏⣻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣆⣿⣿⣿⣿⡿⣿⣇⡈⠁⠀⠤⣀⠒⠿⣞⠛⣾⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣧⣿⣿⣏⡳⢶⣶⠮⣯⣷⡴⠶⠏⣲⣿⠿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠙⠯⣭⣀⠈⠻⢷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠶⠿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣤⢞⣛⣡⣿⡳⠻⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣶⣷⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⢿⣿⣿⠿⠛⠫⠭⢭⣿⣿⣟⠚⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢿⣿⠟⠒⢀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡋⡳⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠻⠿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⡠⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁⡄⢀⠰⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠃⣄⠲⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣀⠀⡖⠀⠐⠀⠀⢀⣤⣴⡄⢦⡤⠄⣿⣿⡤⢖⡿⠒⢂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⢿⣦⡄⠐⠀⡸⠻⣿⡏⢸⡇⣠⣾⣿⣿⣯⡤⠀⠁
⠀⠀⠀⠀⠀⠐⠁⣰⠎⢱⠀⢠⣤⢀⣤⠿⢀⠀⠀⠙⣿⠛⠳⢬⣵⣿⡿⢻⣿⢿⡅
⠀⠀⠀⠀⢀⡄⠀⢣⠀⠘⠒⠪⠷⠚⠁⠀⢹⠀⠀⠀⠀⠳⡄⠈⠻⢿⡇⠘⠁
⠀⠀⠀⠀⡀⢿⠀⠀⠀⠐⠀⣀⣤⡼⠀⡀⠈⠀⡠⠀⠀⠠⠀⠑⠒⠦⣌⠛⠓⠶⠶⠶⠆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠠⠳⢤⠤⣴⠞⠋⠀⣀⣠⣇⣤⣏⢀⣸⡀⠀⠀⠓⠀⠀⠐⠉⠠⣸⣿⣿⣷⡀⠀⠀⠀⠠⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡴⠞⠋⢁⣈⡀⠈⠁⠆⠀⢀⡀⠅⣄⣄⣀⠀⠀⠉⠛⠛⠓⠛⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠻⢓⠄⠀⡆⠉⠀⠀⠀⠙⠻⣄⠀⠄⠀⠀⠰⠖⢢⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢒⠒⢂⠄⣠⠇⠐⠀⡍⠀⠀⠀⠀⠀⠓⠄⠈⠀⠀⠐⠀⢰⠮⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢚⣿⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢆⠀⠀⠀⡄⠀⠀⠀⡀⠀⠠⠤
⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠎⢉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠂⠀⠁⠀⠀⡰⢀⠀⠀⠋
⠀⠀⠀⠐⠒⠢⠀⢀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⢀⠖⢣⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠂⢀⠙⢁⠤⠂
⢀⠄⠀⠀⠀⠀⠠⠁⠀⢀⣀⠀⢠⡀⠀⠀⠀⠀⠊⠀⠁⢀⡤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠈⠁
⢦⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡠⠀⣀⠤⠁⠀⠀⠀⠞⠁⠀⠀⠀⠈⠓⠤⠤⠦⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⣰⣊⡑⢢⠀⠀⠀⠀⠀⣀⢤⡤⠤⣄⣠⠤⡄
⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⣠⣖⣂⣁⣀⣲⣄⠀⠀⠀⠀⣞⣁⢀⣹⣌⢱⡄⠀⠀⠀⣈⠞⠀⡞⠺⣡⡞⢾⣽
⠀⠀⠀⠀⣢⣤⠤⢤⠤⡤⠤⢤⣤⣼⡀⠀⠀⠀⠀⢧⠒⠒⠒⠒⢲⠞⠀⠀⠀⠘⢧⠶⣖⣒⠶⢲⠋⠀⠀⠀⢸⡒⠼⠼⢄⠿⠼⠚⡏
⠀⠀⠀⠀⢱⣊⣉⡲⠮⠭⢷⠭⣙⣤⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⣎⢉⣱⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠣⠤⠍⠮⡇⢙⡴⠵⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣦⠙⡾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⠔⢋⠤⡤⠤⠤⣉⢆⣴⠒⣆⠀⠀⠀⠀⣠⠔⠊⠻⡍⠙⢏⠐⠢⡀⠀⠀⡤⠒⠉⠉⠉⠙⠒⢄⠀⠀⠀⠀⠀⡴⠊⠉⠉⠲⣄
⠀⠀⠀⠀⠎⡞⢙⣚⣁⣡⢞⣕⣋⡀⣇⢸⠀⠀⠀⣜⠁⠀⠀⠀⠘⣄⣸⠦⠤⠜⠀⠘⡤⠤⠤⢤⠤⠤⠤⡞⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡆⡘⠨⠈⠁⠹⢉⠟⢲⢲⠉⠉⠀⠀⢠⠋⠣⡀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠸⡀⢇⠀⡇⢸⢠⠇⠀⠀⠀⠀⠇⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠰⡌⠳⡉⣉⣢⣀⡴⢁⡞⠀⠀⠀⠀⢸⠲⢄⣨⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⣘⡀⢃⣁⡜⠀⠀⠀⠀⣀⠇⣹⠦⠔⠋
⠀⠀⠀⠀⠀⠈⠓⠢⠤⠭⠔⠒⠉⠀⠀⠀⠀⠀⠸⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠯⣅⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡆⢠⣆⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢠⣴⡒⢒⣖⠲⠦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣧⣃⣀⣀⠀⠀⠀⠀⠀⠀⢩⠩⣇⡼⠼⡄⠀⠀⠀⠀⢀⠴⢄⡀⣠⠔⢄⡀
⠀⠀⠀⠀⢰⢛⡥⠞⠓⠦⠥⠭⡻⢄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣾⡻⣹⠀⠀⠀⠀⡈⠀⣍⠖⠒⢦⡀⠀⠀⡰⠋⠈⡆⠙⢇⢸⡀⠙⢦
⠀⠀⠀⠰⣏⡜⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⣀⢀⣱⣄⣀⣀⣤⠞⡛⢩⡁⠀⠀⠀⡞⠁⠨⠁⠀⠀⠀⢹⠀⠀⡇⠀⢠⠁⠀⢸⠀⡧⠀⢸
⠀⠀⠀⢠⣋⣀⣀⣀⣀⣀⣀⣀⣀⡸⠀⠀⠀⠘⠢⢤⣤⣄⣀⣤⠤⠴⠊⠀⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⢸⠀⠀⠱⣄⠸⠀⣀⢮⡀⠇⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⡇⠀⠀⠀⢈⠀⠀⠀⠀⠑⠎⠁⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣿⡒⢢⠀⠀⠀⠀⠀⢸⢾⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⢱⢦⡀
⠀⠀⠀⠀⠀⣀⡠⠤⣐⣵⢿⡿⠊⠉⢣⠀⠀⠀⠀⡜⣈⢘⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⣹⣳⣲⡹⠀⠀⠀⡴⠲⡤⠒⠒⡤⠐⠲⡤⠤⢤
⠀⠀⠀⢰⡯⣒⡲⣩⣓⠵⠊⠀⠀⢀⡜⠀⠀⠀⠸⡩⢍⠉⠈⡆⠀⠀⠀⠀⡰⠗⠒⠉⠁⠀⣠⠇⠀⠀⢸⣄⣈⣁⠠⠄⣁⣀⢀⣁⣀⣠⡇
⠀⠀⠀⠺⣈⠞⠉⠁⠀⠀⠀⠀⡡⠊⠀⠀⠀⠀⠀⢱⢀⠇⠸⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢮⣽⣚⡈⣉⣐⣒⢒⠮⣉⣳⢯⡽
⠀⠀⠀⠀⠘⢆⡀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠸⡄⠀⠀⠑⠤⣄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠢⠤⠒⠒⠠⠤⠁⠂⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⠤⠃⠀⠀⠀⠀⠈⠳⠴⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⣄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠦⠀⠀⢄⠈⠰⠤⠀⠒⢐⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠸⡁⢀⠄⠀⢀⠀⠀⠀⢀⠐⠀⠀⠀⡐⠊⠀⠈⠸⡀⠀⠀⠀⠀⠐⠀⠈⡀⠄
⠰⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠈⠃⠀⠋⠀⡎⣉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠑
⠀⠀⠐⠒⠒⠚⠁⠀⠀⠀⠀⠀⠊⢲⠂⢑⠤⠘⠁
⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⣀⠀⣀⡀⣀⡀⢀⡀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢰⣷⠘⣇⠁⢹⠀⣇⡀⡏⢹⢸⢹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⢸⠀⠼⠻⠴⣬⠇⢸⠀⡇⠀⢧⡼⠸⣼⠃⣧
⠀⠀⢠⡀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠌⠸⣧
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠷⠴⠆⢁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⠁⠁⠀⠉⠈⢲⡀⠀⠀⠀⠘⠟⠛⠲⢴⠿⣠⡒⠶⢅⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠦⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⡎⠱⣄⡀⢐⡀⠕⠒⢬⡧⠃⠀⠀⠀⠀⠀⠀⠀⢄⡐⠢⠀⣀
⠀⠀⢛⠀⠀⠀⠠⠈⠀⠈⠀⡀⡉⠀⠀⠀⠀⣤⠀⠐⠃⠐⠓⠒⢬⡀⢂⣤⠈⣠⠀⠀⠐⠀⠀⠀⡀⠄⠉
⠀⠀⠀⠈⠀⢁⠂⠀⠐⡀⠖⠃⠀⠀⠀⠀⠃⠠⠤⠦⣀⠐⢁⠝⢊⠀⠀⠈⠈⣀⣢

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠚⠆⠄⠀⣀⠐⠂⢄⠠⠄⠀⠀⠀⠀⠌⠂⠀⠀⣢⣠⡤⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣴⣯⣶⡄⣷⣸⢿⣄⣤⣴⣷⠆⠊⣛⣍⠱⣿⣶⡘⡒⢢⢤⣄⡆⡤⠀⡀⢁⢺⣁⣴⣹⡇
⠀⠀⠀⠀⠀⠀⢠⣴⣦⣊⣶⣷⣻⣷⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣶⣿⣽⣿⣿⣿⣿⣯⣦⣤
⠀⠀⠀⠉⠈⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠙⠋⠉⠁⠁
⠀⠀⠀⠀⠐⠀⠘⢁⣠⣴⣖⣀⣠⠀⣦⠀⠀⢠⡀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣧⣦⠈⣳⣴⡆⣯⣦⣶⢸⣯⡀⣤⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠿⠿⣿⣟⣛⣙⣿⣿⣿⠀⢀⣰⣦⣆⢀⣾⢿⡇⢰⢼⡄⠀⠀⠸⣄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠿⠉⢉⡛⠻⠆⠀⠀⠏⣿⣿⣿⣿⣷⡠⠼⠇⠀⠀⣆⣿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠀⠀⠀⢳⡶⢖⠪⡿⠿⠶⠶⣿⣁⣈⣛⣻⣦⣤⠤⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣄⢄⡀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠁⠉⠉⠉⠙⠛⠒⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⡜⠿⢷⠦⠴⣠⣴⣦⣶⣾⣿⣿⣦⠀⠈⠉⠉⠙⠛⠓⠒⠒⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠄⠹⣿⣿⣿⣿⣿⠿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠥⢄⡉⠂⡇⣑⣒⣆⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠹⠃⠳⠆⡿⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⣠⠖⠁⡠⠀⠘⠀⠀⢀⣴⣾⠃⣠⣤⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣀⣠⠇
⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠻⣤⡀⠳⣤⣀⡀⠀⣾⣿⣿⣿⣿⣽⡃⢠⡞⢻⣣⠀⠀⠀⣠⠖⠛⠉
⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡀⡈⢿⣦⣌⠚⢳⠀⣿⣿⣿⣿⣿⣿⣥⣾⣀⣴⣿⠀⠀⣶⠁⠀⠀⠀⠀⢠⠒
⣽⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⣇⠀⠘⢫⣽⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⡀⠀⣀⣠⣤⡟⢀
⠉⠛⠿⣯⣟⣿⣶⣄⠀⠀⠀⠘⢷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣠⣤⣣⣀⣉⣧⡄⠀⠘
⡄⠀⠀⠈⠛⠿⣷⣿⣛⣶⣤⠄⣰⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣽⠟⠀⡀
⣿⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡋⣱⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡿⢷⣮⢩⣿⠁⣤⡀⢨
⡿⠀⠀⠀⠀⠀⢀⣀⣴⡶⠿⣁⣸⣾⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣧⣤⣿⣿⣯⣟⣦
⣿⡀⠀⠀⠀⣤⣾⣟⠉⣷⣤⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠉⠉⠛⠤⣿⣯
⣽⣿⣿⣷⡔⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢾⣿⣿⣿⣷⣟⢻⣿⣿⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⡆⣸⣿
⠉⢉⣉⣙⣽⣾⣧⠄⠋⢉⣿⡿⣿⡿⢿⣏⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢷⣈⣦⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠊⢁⣉⣿⣿⠟⠁⠀⠀⢼⣿⡟⢿⣷⣴⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⠓⠿⠿⣷⣶⣦⣤⣤⣴⢿⡏⠁
⢀⣼⣿⡿⠁⠀⠀⠀⢀⣾⢟⢳⣾⣿⣿⣷⣿⣿⡿⢿⣏⣹⣿⣿⢷⡾⢻⡆⠀⠈⠿⣿⣿⣿⠛⠛⠂
⣧⣿⡿⠁⠀⠀⠀⣠⣿⣿⡷⢿⣟⣿⣿⣿⣿⡟⠁⣾⣿⣿⣿⠉⠾⠻⡟⣿⣄⠀⠀⠈⢹⣿
⡿⠉⠀⠀⠀⡀⢸⣿⣿⣏⣷⣾⣿⣿⣿⣿⣿⡀⠀⢉⣿⣯⣿⡇⠀⠙⢿⡿⣿⣷⡀⠀⠘⢿
⡟⠋⠛⠓⢟⣿⠿⣇⣀⣿⣿⣿⢻⣿⣿⣙⡟⠷⣤⡘⢻⡿⣿⡇⠀⠀⠀⠘⠋⣿⣛⣶⣄⡀⠉⡑⠄
⣿⢄⠀⢀⣼⣿⣄⣼⣿⠋⣿⣟⣿⣻⡇⢿⡀⠀⠀⢻⣿⣀⣿⡟⠀⠀⠀⠀⠈⠛⢿⣌⣿⡟⠀⠁
⠉⣿⡆⢸⣿⣀⣿⡿⠁⠸⢿⣿⡟⡹⢳⡾⠁⠀⢠⣾⣟⢹⣿⡇⠀⠀⠀⠀⢀⡀⠀⢻⣿⣿⣾⡃⡀
⣾⡿⢷⣾⣿⣿⠟⠁⠀⢐⠛⣿⡴⢳⣾⠃⠀⣠⣾⡟⢙⣿⠟⠀⠀⠀⢠⡖⠁⠀⠀⢸⣿⡇⠙⣿⣗⡀
⠉⣦⣾⣿⡟⠁⠀⠀⠀⠠⡿⢿⣽⠿⢷⣶⡾⠻⠋⣹⣿⣿⣸⡋⠛⠛⠛⠁⠀⠀⣰⣿⡟⠀⠀⠘⣿⣅⡀
⠰⣼⣿⠏⠀⡀⠀⠀⠀⠀⣷⡾⣿⡀⠀⠀⣀⠀⢸⡏⢹⣿⠘⢧⡀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠸⣿⡅
⢻⣿⣟⠀⠀⢿⡄⠀⢀⠀⠸⣧⣾⣷⡄⠀⠀⠳⡈⢟⣻⣿⡆⠈⣿⡀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⡗
⠘⣿⣿⡄⠀⠀⠻⣦⡀⠀⠀⠈⠳⣾⢻⢶⣄⡀⣻⠀⣽⠟⣿⣴⣿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠙⣿⣷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠙⢶⣛⣿⠟⠷⠿⣿⣿⣿⠁⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⠅
⠀⠀⠰⣿⣷⡄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⣉⣁⡀⠀⠀⠀⣽⣿⡗⠀⠀⠀⠙⣷⣄⡀⠀⠀⢀⣠⣿⠋
⣄⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠹⣦⠀⠀⢸⠁⠀⡱⠀⠀⣰⣿⡹⠇⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠛⠁
⠙⠻⠷⠾⠟⠁⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣉⣉⣤⣴⣾⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣸⣿⠀⠀⠀⡀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣻⠀⠠⡄⢏⢧⠐⡀⠙⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠠⠀⠀⣶⣿⣿⡇⢀⡀⠀⠀⠀⠣⠀⢸⡄⠈⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⢹⣿⣿⣿⣿⣇⠁⠀⠒⠒⠒⠒⠒⠛⠉⣁⡤⠒⠀⠈⠉⠉⢀⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⢳⠒⠓⠂⠀⡀⠀⡸⢦⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠈⣦⣤⣄⠀⠀⢀⡏⣠⠈⢙⡳⢦⡤⣄⣀⣀⣀⣤⡤⠤⠆⠒⠃⡀
⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣶⣤⣾⣧⡇⢸⠸⣡⣼⢇⡐⠂⠐⠀⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡼⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠙⠿⠿⠿⣿⠻⠿⠿⣿⣿⣼⣿⣇⣀⡀⣠⢼⣋⣴⡡⠇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⠀⠀⠠⡀⠀⠈⠛⠪⠿⠭⠬⠭⠭⠿⠖⠋⠁⠀⡇
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠾⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠉⠐⠒⠒⠂⠘⠑⠒⠀⠤⠤⠤⠤⠤⠤⠀⠤⠠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣥⡶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠂⠉⠉⠉⠢⡀⠀⠀⢀⣀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⡉⠀⠁⠀⢱⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⢋⢰⢆⡆⠀⣼⣡⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠀⠠⠩⠙⠳⢦⣄⣀⣀⢀⣴⣿⣦⣶⡿⣣⣾⣰⡾⠿⠷⢄
⠀⠀⠀⡠⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠛⠉⠙⢻⣿⣿⣿⣷⡴⣤⡀⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠞⢿⢡⣿⣧⡘⠯⡙⠓⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⢀⡀⠀⢈⣉⠽⢋⠀⡠⠋⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡰⠦⠃⠀⠀⢻⡿⠟⠈⠉⡀⠰⠄⠀⠀⠀⠀⠀⠄⠀⠀⠈⢳⡆⠈⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡫⠀⠀⠀⠑⠢⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠛⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠛⠋⠁⠀⣀⣀⣤⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⣏⢏⢷⣀⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⢿⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⡾⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⣛⣫⣭⡭⠭⠥⠆⠀⠀⠀⠀⠀⠚⠛⠛⠛⠿⠿⠿⠿⠿⠛⣿⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣯⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠲⠾⠿⠭⠭⠭⠭⠍⠙⠛⠛⠉⠩⠭⣭⣭⣭⣭⡭⠭⢩⡏⠀⢀⡟⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⡾⠀⠀⣼⠁⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⠶⠖⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⣾⠃⠀⢰⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⡟⢛⣶⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠲⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⡤⠶⡾⠛⠋⢩⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣽⠁⠀⣸⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢠⡟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣼⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢰⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡾⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⠈⠉⠛⠲⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠞⠋⠁⠀⣸⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠶⣭⣳⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⢖⣚⣩⡵⠞⠋
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠲⠶⠾⠿⠿⠿⠿⠿⠿⠷⠒⠛⠛⠉⠉
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣤⣤⡦⣰⡄⠀⠀⢰⡦⢦⣰⣤⣤⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⠀⣶⠓⣦⠀⠀⠀⠀⠀⣤⡀⢀⣠⡀⢠⣄⡀⣀⡀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⠀⠙⠒⣿⡄⠀⠀⣿⠀⠑⠾⠟⠛⠃⠚⠻⠟⠘⠛⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⢀⡿⠁⢈⠀⣯⠀⢰⠀⣤⢀⠀⡾⢀⣄⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠟⠀⡇⠀⠋⠀⢿⢹⢠⡇⢸⡇⠀⡁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠑⠈⠁⠁⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢓⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⠂
⠀⠀⠀⠀⠀⠀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀
⠀⢀⠤⠠⣤⣠⣇⡔⠇⠀⣀⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠤⠤⠤⣄⡀⠀⠀⢀⡠⠤⠀⠒⠂⠀⠀⠉⠀⣠⡴⢿⡀
⣤⣯⣤⡚⠀⠀⠈⡟⠉⠲⡀⠀⠀⢱⠀⠀⠀⣀⠤⢄⠀⠀⠀⢠⠖⠊⠉⠁⠀⠀⠀⠉⠘⠒⠢⣄⡙⣦⠀⡸⢤⣂⡀⠀⠀⠀⠀⣤⡼⢟⣴⣾⠇
⡇⠠⠀⠙⠶⢤⠴⠖⠒⠲⠿⣤⣤⣞⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠒⠄⠀⠀⢀⡐⠀⡂⡀⠂⠘⠏⢹⡆⢰⠆⢤⣿⣋⠐⠒⢚⣩⡴⠟⠋
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢻⠶⠇⠀⠀⠀⠀⠀⡀⠀⠀⣸⣦⣤⣄⣄⣠⣄⣠⣦⣠⣦⣶⣶⣞⣿⠀⠀⠒⢄⠉⣁⠴⠟⠋⠁
⢸⠀⡆⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣧⠀⠀⠨⣀⠀⠀⡇⠀⢾⢀⡙⠓⠛⠳⠶⠛⠷⠞⢛⣋⡭⠖⣻⠏⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠛⢆⡀
⠘⡄⠁⠀⠀⠀⠀⠀⡔⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢥⣭⡭⣭⣭⣭⣭⣭⠭⠴⠖⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠸⠀⢀⠨⡸⡄
⠀⠉⠛⠛⠛⠓⠒⠺⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣈⠀⠀⠈⠇⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡘⠲⠂⠠⢀⠉⠛⢦⣄⠀⠀⠀⠀⢷⠀⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⣠⣴⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠰⠞⠃⠀⠘⠀⠀⠀⠀⠀⠀⢀⡞⠱⠀⠀⠀⠀⠐⠢⡀⠈⠳⣄⠀⠀⠘⠇⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⢋⠉⢊⠈⢉⡏
⠀⠀⠀⠀⠀⢀⣘⠃⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡀⠀⠀⠀⠀⠈⠢⡀⠈⣆⠀⠀⠀⠃⠀⢀⡀⠸⠀⠀⠀⠀⠀⠠⡐⠠⠑⢨⠅
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠁⠀⠀⢀⣠⣶⠶⠛⠚⠋⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡏⠰⠀⠀⠀⢠⣀⣴⠾⠿⠋⠁⠀⠀⠀⠀⠀⢰⠀⠀⡈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⢀⠢⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠂⠀⠀⠀⢀⡿⠀⡀⢈⣤⡶⠛⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⢰⢬⠁
⠀⠀⠀⠀⠀⠀⠀⡆⢉⣻⣦⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⢸⣃⣴⠾⠛⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠶⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⡠⠦⠴⢤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡤⠶⠛⠿⢫⡥⠅⠀⠦⢤⡀⠀⠀⠀⠀⢀⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⢀
⠀⠘⠀⢤⠀⠈⡇⠀⠀⠀⠀⠀⣀⠠⣤⡄⢠⠶⠤⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⠚⠀⠀⠀⠀⣀⠀⢀⣿⠀⠀⣠⣤⢴⣤⣤⣤⢴⡄⢠⠀⠀⠀⠈⢳⣿⣄⠼⠶⣤
⠀⡆⠘⡆⠀⠀⣿⠀⠀⠀⣠⣾⠟⢁⡽⠓⠉⠉⠛⠛⢴⣄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣫⣽⠀⠀⠈⣽⡇⠉⢉⢻⡸⡇⣸⣤⠀⠀⠀⠀⠋⠀⠈
⠀⠃⣴⠃⠀⠀⣿⠀⠀⢰⠻⠏⡠⠊⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⣿⡀⠀⠁⣀⡠⢤⣶⠿⡿⣋⠁⣴⠼⠃⣤⠀⢸⣏⣤⣸⣄⣧⣷⣿⠃⠀⠀⠀⠀⠘
⠀⢸⠋⠆⠀⠀⡟⠀⠀⠘⢾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠻⠿⡏⠉⢀⣬⠥⠌⣻⣯⣭⠶⡞⢻⠃⠀⠘⡆⠀⠉⠉⠉⠀⣼⠁⠀⠀⠀⠀⠀⢢⠤⠬⠉
⠀⢸⣠⡇⠀⢰⡇⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠀⠒⠒⠒⠁⠀⠀⠀⣳⣟⠦⠴⣤⣾⡿⠛⠋⠀⢀⡷⠋⠀⠀⠀⢷⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⡂⣀⠰⠊
⠀⠈⣇⠀⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⣄⣀⣀⣉⣠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠸⣆⣰⠇⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠋⠀⠀⠀⠀⡀⠔⠄
⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢠⡄⠲⡀
⠀⠀⠀⢈⢧⠀⠀⠀⠠⡤⠤⠤⠤⢤⡄⣀⣀⣀⣀⣈⣐⣄⠀⠀⠀⠀⡤⢀⣤⣤⣴⠾⠿⠛⠉⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣣⠀⠈⣢⡀
⠀⠀⠀⠘⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢉⡀⠀⠙⡀⠀⠀⠔⠉⠝⠉⠁⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⢀⣀⣀⠤⠼⢧⡽⢤⣾⠿⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠐⢦⠀⠀⠀⠀⣀⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢩⠓
⠀⠀⠀⠀⢀⡤⠊⠁⠀⠠⢄⠘⢶⠂⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣫⣴⠾⠃⣤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⢠⣾⡄
⠀⠀⠀⠀⢸⡀⡀⠀⠓⠒⡢⠤⠤⠾⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠾⡋⢻⡴⠏⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢿⡾⠇⠿⣤⣤⣦⠉
⠀⠀⠀⠀⢸⣿⠩⣀⡴⠊⠀⠀⠀⠀⠀⢮⣀⡀⠀⠀⠀⠀⣤⠂⣰⣟⢻⣅⡦⠟⠉⠀⢀⣰⡿⠃⠀⠀⠀⠀⠀⣆⠚⢧⣼⡇⠨⣶⡄⠒⠉⠉⠛
⠀⠀⠀⠀⠀⠙⠢⠿⠇⠀⠀⠘⠷⠜⠀⠈⣬⡃⠀⠀⠀⠀⠙⢀⣷⡜⠋⠁⢀⢀⣶⣿⡶⠛⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠹⣿⣯⡀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣀⠀⡀⠀⠤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠻⣀⣴⣷⣉⣴⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⡉⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠶⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠂⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢾⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠦⠀⠀⠃⡀⠂⣨⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡆⠀⠀⢾⠆⡠
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⢀⣀⣐⢃⣠⣴⠾⢃⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⢿⡀⢻⣇⠀⠀⠰⢺⠃⣾⣷
⠀⠀⠀⠀⠀⣾⠁⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢶⣮⣽⣿⣿⣧⣬⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⣿⡖⠏⠉⠓⠀⠀⢼⣯⣥⠂
⠀⠀⠀⠀⠀⢉⠀⠀⠠⣿⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣿⣏⣉⣙⣛⣭⣼⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠠⠟⠋
⠀⠀⠀⠀⠀⠈⠳⢀⣰⡙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡤⣤⡿⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣠⣴⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠠⡄⠀⡀
⠀⠀⠀⠀⠀⢠⣧⣤⣴⠶⢠⣾⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠲⠦⠟⢿⣻⡆⠀⠀⠀⠀⠀⠀⠀⢠⡶⣾⣷⣶⡿⣿⣿⣿⣗⠂⡄⠐⡀⠁
⠀⠀⠀⠀⠀⠘⢩⠟⠳⠶⠷⣬⣭⣵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁⠒⠂⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣹⣯⣷⣿⣛⣻⣿⣷⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⣴⣶⡖⢢⣾⡏⠀⠀⠀⠀⠀⠀⠀⠛⢶⣌⠙⢳⣤⣿⣿⠿⣋⣽⠃⣸⢳
⠀⠀⠀⠀⠀⠀⠀⣧⡐⢿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⠬⠁⠼⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⣿⠸⣦⣾⣿⡇⠀⡿⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢷⠀⠉⠀⣉⠹⠟⠃⠘⠃⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠛⠶⠾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⣶⣬⠓⣯⣾⡻⠛⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣹⡧⠀⠀⢀⣼⣅⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢹⢻⡄
⠀⠀⠀⠀⠀⣠⠊⣿⣶⣶⡉⣭⢳⣾⣿⣖⣠⡇⠀⠀⠀⠀⠀⠀⠀⣿⡗⢩⣭⡧⠀⢠⣿⠧⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⣮⣤⡿
⠀⠀⠀⠀⠀⠛⢶⣿⣛⠻⣿⣶⣿⣤⢒⣽⡿⢋⣆⠀⠀⠀⠀⠀⠀⣶⠀⠀⢸⡇⠀⠈⡇⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⢃⠲⣼⠷⠆
⠀⠀⠀⠀⠀⠤⢂⠈⠙⠻⢿⣍⣙⠿⠼⢿⣤⡾⠛⠀⠀⠀⠀⠀⠀⣿⠀⣤⣼⡇⠀⠀⡟⢰⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡘⣟⣓⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢠⣀⡠⠈⠙⠿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠉⢹⣷⠀⠀⣷⠈⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢫⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⣸⣯⠀⠀⢹⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣦⡜⣷⣷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠲⠤
⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⣿⢡⣷⢸⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠂⡀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣇⣸⡟⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⣡⠔⠃⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠚⠛⠻⠿⣿⣿⣴⣶⡀
⠀⠀⠀⠀⠀⠐⣷⠿⠿⠿⠿⠿⢧⡾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠐⠊⠁⢀⣴⣿⣿⣿⡟⣻⠀⠀⠀⠀⠀⠀⠰⢖⣀⣀⠐⠠⠔⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⢀⡐⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⡁⠤⣳⡿⢻⣿⣽⡿⠽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢷⣦⣄⡀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣷⠾⣿⡿⠶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡻⢶⣬⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠈⠀⠠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠒⠂⠈⠁⠀⠉⠁⣀⡀⠀⡁⠀⠑⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠤⠴⠀⠀⡀⣀⠹⠿⠄⠈⢀⣠⠀⣤⠤⠁⡙⠁⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⢆⣀⡀⠀⢀⣤⠖⠀⠙⢚⣙⠀⠀⠄⠀⠠⣤⣀⡁⠀⣀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⣠⢤⣾⠁⠀⠁⠯⡿⠀⠀⠀⠀⠀⠲⢂⣾⣶⣤⠄⢠⣽⡀⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠀⠀⠀⢐⠘⠃⣹⢷⡄⠀⠀⠀⣻⣧⠀⡀⠀⠂⠉⠱⡀
⠀⠀⠀⡀⠀⠀⠀⣠⡀⡸⠮⠲⡇⠒⠼⣷⣿⠏⠀⠉⣰⣦⣺⢿⣯⢏⠛⠰⠆⠤⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⡀
⠀⠀⠠⠀⠀⠀⠀⡙⠈⢡⠄⠈⠈⡒⠄⢈⣻⠇⠀⠀⠊⠉⢼⣾⠟⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠆⡈⢹⢿⢿⡗
⠀⠀⠀⣀⠀⠚⠁⠙⠚⠣⠇⠀⡀⠷⠌⠋⢉⣇⠀⠀⠀⠀⡼⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⣤⠄⣀⡀⡀⠠
⠀⢀⣍⣻⣿⡏⢀⣓⣶⢷⣶⡏⣯⣤⣤⣶⠂⣤⢶⣾⣷⣾⣶⣀⣔⡀⠒⠀⣀⣀⣀⡀⠀⣀⣀⠀⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠈⠉⠁⠈
⠀⠸⡷⢶⠄⠻⠻⣿⣿⠏⡟⠿⠐⢚⡷⠶⣿⣟⠙⠛⠀⠛⠻⣟⣩⣐⠂⠀⣩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀⠤⢄⣀
⠀⠀⠤⠤⠤⠥⠤⠭⠝⠛⠛⣁⣘⣥⠖⣖⣵⠀⠁⠀⠁⠀⢀⡘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠉
⠀⠀⠤⠤⠦⡄⢀⠀⠀⠀⠊⠁⠀⠀⠛⠠⠉⠁⠂⠀⠀⠀⠈⠃
⠀⠀⣀⡠⠎⠁⠀⢉⣤⡍⠀⠤⠢⣀⣀
⠀⢈⣍⠁⠚⠀⠀⠘⠓⢢⣤⡴⢠⣬⡍⢉⡂⠀⠄⠀⠀⠀⠈⠉⠁⢀⠄
⠀⠈⠁⠰⠄⠀⠢⠀⠈⠁⠀⠂⠀⠒⠘⠉⠀⠉⠁⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣄⠀⠀⠀⠀⡰⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⡠⠖⣊⣉⣉⣉⣙⡧⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⣷⣿⠀⠀⠀⠀⣿⣾⡄⠀⠀⠀⠀⠀⠀⢀⣤⠀⢼⣋⣉⣉⣉⣑⠲⢄
⠀⢠⠊⡴⠛⠉⠀⠀⠉⠉⡇⠀⣆⠈⠓⢄⠀⠀⠀⠀⠀⣳⡁⠀⠀⠀⠀⢈⣞⠀⠀⠀⠀⠀⡠⠚⠁⣰⠀⢸⠉⠉⠀⠀⠉⠛⢦⠑⡄
⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠳⣄⡀⠑⠢⠄⠤⢔⡉⠀⠀⠀⠀⠀⠀⢝⡢⠤⠠⠔⠊⢀⣠⠞⡹⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⡀
⠀⠈⠌⡆⠀⠀⠀⠀⠀⠀⠙⣤⠈⠓⠬⢝⣳⠦⠦⠖⢋⡆⡀⠀⠀⠀⠀⢀⢰⡝⠲⠴⠴⣖⡋⠥⠚⠁⣤⠋⠀⠀⠀⠀⠀⠀⢰⠡⠁
⠀⠀⠀⠸⠀⠀⠀⡠⠔⢚⣉⡛⠛⠶⣤⣄⣠⣰⠤⢶⠏⠀⡇⠀⠀⠀⠀⢸⠀⠹⡷⠤⣆⣄⣠⣤⠾⠛⠛⣉⡓⠢⢄⠀⠀⠀⡇
⠀⠀⠀⠘⠀⢀⠞⡠⠊⠉⠉⠉⠓⢦⣀⠙⠒⠒⠒⠁⢀⡴⡇⠀⠀⠀⠀⠸⢦⡀⠈⠒⠒⠒⠋⣀⡴⠚⠉⠉⠉⠑⢤⠳⡀⠀⠃
⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠖⠚⠉⡠⠁⠀⣼⢇⠀⠈⢄⠉⠓⠲⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠈⡇⡇
⠀⠀⠀⠀⠀⠈⠜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢀⡼⠁⠈⢧⣀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠃
⠀⠀⠀⠀⠀⠀⠈⠪⢆⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣀⡤⠖⠉⠀⠀⠀⠀⠉⠲⢤⣀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⡴⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠔⢉⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⡉⠲⡄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠡⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⣛⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠬⢭⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣛⠳⠄⠀⠀⣤⣤⣾⣯⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠒⠒⠒⠒⠒⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⡖⠀⢰⠇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢀⠀⠀⢀⣭⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡾⠁⠀⠋⢠⠆⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠆⠸⣇⠀⠶⠀⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⢿⡆⠀⠀⠘⠈⠃⠀⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⣯⠉⠁⠀⠀⠀⣰⠃⠀⡆⠀⢀⣴⠀⠀⠀⠀⠀⢉⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣌⣋⣀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⢀⣀⣠⣤⠴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⡀⠀⠉⣉⣉⠐⠒⠓⠒⠒⠒⠒⠓⠛⠛⠉⠉⠉⠀⠀⠀⢸⡿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣀⣈⣻⠛⠃⠀⢰⡇⠠⡄⢠⣆⠀⠀⠀⠀⠼⢫⡿⠀⢸⡇⢠⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠏⠉⠙⢢⣤⠤⡄⠹⡄⢀⡄⠉⡇⠀⣠⠶⢶⡄⠀⠀⢸⣷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣨⠴⠶⣄⠀⠀⠐⠃⣠⠇⠸⠁⣼⢁⡾⠀⢈⣸⠇⠀⠀⢸⣿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠺⣧⡶⠂⠘⣷⠀⠀⠐⠋⠀⠀⠀⣉⡴⠃⠰⠟⠁⠀⣰⠆⢸⡏⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⣸⠏⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠰⠖⠛⠁⠀⢸⣇⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠻⠆⠀⠀⠀⠀⣠⡾⠏⠀⠀⠈⠉⠁⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⣸⡆⢸⣿⡛⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⢠⡾⠋⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⠛⠳⣦
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣰⡟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣦⣤⣴⠏
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢸⣿⠁⠀⠘⡄
⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠤⠦⠞
⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇
⠴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠈⠀⠒⠚⠋⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠉⠙⠲⠶⢤⣤⣍⣉⣙⣛⣛⣀⣀⣬⣤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠜⠋⠁

⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⡀⢀⡁⠀⠀⠀⠀⠀⢀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠲⢤⣀⡐⠒⠂⠀⡀⠀⠄⠒
⠀⠀⠀⠑⣂⣾⢛⣻⠗⠶⣽⢳⣖⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠎⣰⣌⣩⢥⡓⢒⡦⣟⣩⠇⢀
⠀⠀⢰⣿⢻⣿⠿⠿⢿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⢳⣶⣩⠵⠲⢿⣿⣶⣾⣷⣆⣻⠇
⠀⠀⠀⣁⠩⢵⣶⡆⠈⠁⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣄⣀⣀⣂⣤⠀⠀⠀⣠⣠⣤⡤
⠀⠀⠀⠉⠉⠉⠛⠛⠛⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢤⣖⠚⢿⣤⠿⣿⣶⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣞⠃⢿⠿⡇⢡⣜⠉⢀⣼⣿⠜⠥⣆⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⣉⡀⠴⠰⠀⠀⣐⣚⣙⣀⣐⣔⣀⣀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠈⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲
⡰⠒⠢⡄⠀⠀⣀⠀⠀⠀⠀⠸⢱⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠒⡄⠧⠴
⠑⠤⠠⠎⠀⡘⠂⠃⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣩⠆⠰⠅⠜⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⢎⣠⠇
⠀⠀⠀⢠⡏⠉⠑⢦⡤⡀⠀⠀⠀⠂⠣⡀⠀⠀⠘⢍⢧⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠁⠀⠀⠀⠀⢀⠴⠤⢔⡺⠛⢉⡭⠝⡩⠿⠽⢦⠀⡠⢤
⠀⢀⠀⠀⠙⠛⠛⠲⣄⠙⣄⣀⣀⡼⠆⣈⡉⡒⠤⠒⠃⠉⠁⠀⠈⠉⠉⠢⠴⠊⠑⢒⣁⡴⣤⠤⡝⣯⡛⠒⢒⣉⣰⡴⠋⠀⠀⡿⢀⡾⠔⠊⠉⠁⠀⠈⠉
⠀⠈⠀⠀⠀⢀⡴⠒⠈⢳⣉⠲⢷⡖⠲⣆⣏⣁⣠⠦⣀⣀⡤⠀⠀⠒⠲⠴⠂⠀⠀⠀⠠⠀⠀⡜⢵⠋⠙⠒⠋⠀⡜⠀⠀⠀⣠⠇⢸⠁
⢀⣀⠀⢠⠒⠉⡠⢄⠤⢌⡳⣧⡀⠉⠓⠏⠙⠿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠉⠢⠤⠦⠶⠤⠀⠀⣸⠁⠀⢸
⠣⠔⠁⠈⠁⠋⠀⠠⠀⠀⠳⢌⣻⣦⡀⠀⠀⠀⠀⠙⠓⢦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠦⣶⡦⣄⠀⠀⠀⠀⠙⠦⣤⡤⠤⣄⣀⣄⣠⠖⠶⠃⠀⠀⠀⠀⣀⡀⠀⠀⣸⡇⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⠀⠁⢿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣖⠈⠓⠶⠛⠛⠋⢩⠉⠛⠉⠅⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠙⠶⠤⣤⠴⠋⠳⠦⠴⠒⠐⠦⠖⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡆⠘⢆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⣄⠀⠀⠁⠒⠂⠤⠤⢤⡀⠀⠀⠀⠀⠀⠤⠤⠒⠒⠉⠀⠀⠀⠀⠀⠀⣸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠖⠂⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠂⠤⠤⠤⠤⠤⠤⠴⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡏
⠀⠀⠀⣀⡤⠤⠤⠤⠤⣿⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣷⠀⠀⠀⠀⣾⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣾⠤⠤⠤⠤⢤⣀
⢀⡴⠊⣡⠴⠶⠶⠶⠴⣾⠃⢸⠓⠦⡀⠀⠀⠀⠀⠀⠀⢻⡹⠟⠀⠀⠀⠀⠻⢏⡟⠀⠀⠀⠀⠀⠀⢀⠴⠚⡇⠘⣷⠦⠶⠶⠶⠦⣌⠑⢦
⡞⣰⠏⠁⠀⠀⠀⠀⠀⢸⡀⢸⣷⣄⠈⠳⢄⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⡠⠞⠁⣠⣼⡇⢀⡇⠀⠀⠀⠀⠀⠈⠙⣆
⡇⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢆⠙⢷⣄⡀⠙⠒⠀⢒⡭⡂⠀⠀⠀⠀⠀⠀⢸⢭⡒⠀⠒⠋⢀⣠⡾⠋⡰⠁⢐⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠘⡼⡆⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠑⠢⠭⠿⠷⠖⠚⢋⣼⠁⡄⠀⠀⠀⠀⢠⠈⣧⡙⠓⠲⠾⠯⠭⠔⠊⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢰⢧
⠀⠐⢱⠀⠀⠀⣠⠔⢊⣉⣉⠙⠛⠷⣦⣦⣴⣤⡦⠶⡿⠁⢸⡇⠀⠀⠀⠀⢸⡇⠈⢿⠶⢴⣤⣆⣴⣴⠾⠛⠋⣉⣉⡓⠢⣄⠀⠀⠀⡎⠂
⠀⠀⡜⠀⢀⡞⣡⠞⠉⠉⠉⠙⠳⣦⡈⠙⠒⠶⠒⠋⠠⣄⡿⡇⠀⢰⠆⠀⢸⢿⣠⠄⠙⠒⠶⠒⠋⢀⣴⠞⠋⠉⠉⠉⠳⣌⢳⡀⠀⢣
⠀⠀⠀⠀⢸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⠴⠤⠦⠼⠛⠁⡸⠀⠀⣼⣧⠀⠀⢇⠈⠛⠧⠴⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆⡇
⠀⠀⠀⠀⠘⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡼⠃⠘⢧⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠃
⠀⠀⠀⠀⠀⠘⢜⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢀⣠⡼⠛⠁⠀⠀⠈⠛⢧⣄⡀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣠⠔⠋⢁⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡈⠙⠢⣄⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠞⢁⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⡀⠱⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣜⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣑⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣊⠥⠚⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⠉⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢄⢀⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⡀⢀⠄⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⣨⡖⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠰⠀⠀⠸⠀⠙⠣⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⡱⢄⢀⡴⠒⠛⠛⢲⣦
⠀⠀⠀⠀⠀⠀⢊⡴⠒⠲⣦⡁⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⢢⠀⠐⠢⢌⣁⣀⠀⠀⣂⡼
⠀⠀⠀⠀⢀⠃⡟⠀⠀⠀⢈⡇⣅⠔⠋⠀⣠⠀⠀⠀⠀⠀⠈⡆⠀⢤⡀⠈⠻⣭⠉
⠀⠀⠀⠀⠀⢄⠁⠀⠀⠠⣼⢹⣁⣀⠠⠦⠬⠡⠀⣴⡀⠃⠀⠛⠀⠤⠀⠐⢦⡼⠃⢰⠤⣀⣠⡰
⠀⠀⠀⠀⠀⠀⠑⠂⠤⠖⢻⠋⣁⡥⠖⠚⠳⣶⣴⣦⣶⣴⡎⢿⡿⣖⣶⣢⣽⣶⠖⠛⢦⡀⠙
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⢋⡔⠉⣀⣤⡶⢛⡏⠈⠙⢠⣌⠀⢐⡇⠀⠉⢻⣯⣿⣄⠀⠀⢁⠀⡀
⠀⠀⠀⠀⠀⠘⠀⡠⠊⠤⢖⣴⡦⠈⢳⡦⠴⡶⠤⣀⣸⠸⡄⠀⢻⣆⠀⠀⣽⡷⣯⠁⠒⠁⡰⠃
⠀⠀⠀⠢⠔⠒⠩⠄⠇⣀⡿⠋⠀⠘⣔⡇⠀⡇⠀⢈⡿⠀⠹⣄⠀⠫⣷⣞⡿⣺⠉⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢽⢇⠀⢀⣼⡿⠇⠀⣇⠀⠸⡇⠀⠀⡟⠳⡤⠤⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⠋⣉⡩⠊⠀⠀⠸⡄⠈⣿⡀⠀⢡⡀⢂⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠻⣦⣀⣑⣤⣉⣙⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣈⣁⡥⠞⠉⠳⠦⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠈⠀⣠⠔⠈⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠆⡀⢂⠠⠤⠈⠀⠋⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠒⡀⠊⠀⠁⠀⠃⢀⡴⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠀⠀⢀⠘⢤⡀⠀⠢⠀⠈⢠⠀⠀⠀⠀⠰⡃⣀⠤⣤⣤⣶⡎⡁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠧⣀⡅⠀⢀⣅⠐⠠⠒⠣⠤⡰⠀⠀⠀⠞⢡⠿⠆⠛⣘⢋⣅⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠠⠁⠐⢀⣀⠀⡀⢺⢄⣤⡶⠃⠠⢀⠀⣀⣀⡀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢦⠀⠢⠄⠐⠒⠒⠛⠫⠛⠁⠀⠈⣉⡉⡡⠔⢁⠴⣿⣦⡥⠤⠅⠈⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠤
⠀⠴⠒⠀⠂⠂⠐⠀⠀⣀⠀⠀⠀⠴⠤⠀⣐⠒⠀⠰⠦⠶⠶⡴⠖⢚⠋⠁⠀⠀⠞⠂⠁⠙⠙⠃⠀⠀⠀⠐⠀⠐⠒⠐⠐⠒⠒⠀⠀⠁
⠀⠀⠀⠀⠂⠂⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠠⠂⠀⠀⠀⠀⠀⠐⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣠⠄⠴⡉⠉⢣⠀⡝⠛⢲⡀
⠀⠀⠀⢀⡤⢧⡀⣠⣿⣶⣿⣿⣿⣿⣿⣷⣤⡤⠤⣄
⠀⠀⢰⡋⠀⢀⣾⣿⣿⠿⠿⣿⠛⠛⢯⠀⠙⡆⣀⣠⠃
⠀⠀⢠⠟⠒⣿⣿⣿⡇⠀⠀⠈⡆⠀⣼⡤⠞⠫⡀⠀⢱
⠀⠀⠱⡄⠀⣿⣿⣿⠗⠤⣀⣠⠞⠉⠀⣇⠀⣠⠗⢴⠋
⠀⠀⠀⠙⠂⢿⣿⡿⠀⡀⠀⠑⠤⠤⠜⠁⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠉⢆
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠙⠂⠀⠀⢄⢤⣀⠴⢂⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⠈⢁⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠤⠤⣀⣠⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠰⠀⣠⠀⡄⢸⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠝⠉⠙⠶⠤⣤⣤⠤⠚⣦⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠁⠀⠀⠀⠀⠈⠲⠤⣠⣀⣀⣀⣀⠴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⢰⠓⠦⡤⠶⠦⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⢩⠀⢸⡉⠑⠦⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠈⠙⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠇
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠒⠒⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠋⠁
⠀⠀⠀⠀⡠⠊⠡⠀⠀⠀⠄⠀⠀⠒⠀⠠⡈⢳⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⣧⠉⠒⠲⠦⡤⠤⠄⠔⢶⠒⢋⣽⡞⣽⡄
⠀⠀⠀⠀⣿⣙⣓⣚⣺⣦⣤⠤⢶⡧⢾⠛⠒⢏⡹⡀
⠀⠀⠀⠀⢼⠀⣉⢹⠀⢸⠉⠉⡉⠚⠐⢅⠠⢃⡵⢇
⠀⠀⠀⠠⡛⢦⣄⣙⣤⣼⣉⣉⣥⡤⡴⠖⠚⣹⣤⡏
⠀⠀⠀⠀⠸⡖⠢⠤⢤⣌⣀⣀⣠⣤⣏⡴⢾⠉⢠⠃
⠀⠀⠀⠀⠀⠱⢄⣁⠀⠀⠉⠁⠀⠠⠂⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣷⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⠟⠉⠉⠈⠉⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⣽⠀⠀⣀⡀⢀⣀⢹⣿⣥⡀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⣿⠇⠊⠉⠁⠨⡀⢠⣿⣷⡈
⢸⣦⠀⠀⠀⢸⡀⠀⠀⢻⠀⠀⠀⢀⠄⠀⠉⢡⡄⠀⡠⠾⠚⢣⡜⠋⣍⣻⣂⡀
⠀⢿⢇⠀⠀⠘⣇⠀⢸⢸⠀⠀⠀⣾⣠⡆⣤⣾⡇⠈⠀⡀⣤⣤⣀⣀⣀⢻⣿⣷⣦⡀
⠀⠸⡎⣆⠀⢀⣿⠀⡘⢸⠀⠀⠀⣿⡟⡿⢿⠋⠹⣿⣷⣿⣿⣿⣿⣿⡏⡿⡻⢿⣿⡿⠄⣤⡀
⠀⠀⢿⠘⠶⠞⠙⢃⣁⣼⡇⠀⠀⢈⣠⣄⡄⠀⠀⠈⣿⣿⡟⠻⣿⡿⠀⠀⠀⠸⠃⠠⠾⠿⢿⣷⡀
⠀⠀⠸⠷⠖⠛⣿⡋⠉⠁⠀⠀⢠⣿⠿⠋⠀⠀⠀⠀⣿⠛⠁⠀⠻⠙⠀⠀⠀⠀⣀⡀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣆⠀⠀⢸⡿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⡇⢀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠈⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣹⠾⢧⣀⣤⡀⠀⣀⣾⠀⠀⠤⣤⣤⣶⠴⠂⠀⠹⣿⣷⡀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⡟⠀⠀⠙⣿⣿⣿⠿⠋⢸⣷⠤⠤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⣀⡀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢹⡇⠀⠀⠀⢸⣿⠗⠒⠃⢸⡿⠦⢄⠀⠀⠀⠀⠀⣼⣿⡏⠀⠹⣿⣿⠁⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⢠⡾⠋⢁⢤⣀⣀⣸⡿⡦⠴⠂⠘⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⢠⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⡀⠀⠀⠙⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⢸⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡖⠒⢲⣿⡌⡇⠀⠀⣀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⢻⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢳⣭⣄⢙⠃⠋⠙⠛⢉⣼⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⢳⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡀⠀⠀⣠⡿⠁⠀⠀⣉⣙⣿⣷⣶⣶⣶⡶⠶⠶⠶⢶⣦⣧⡀⠀⠀⠀⠀⣸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⠞⠛⠷⣤⠀⠀⠀⠀⠴⠶⠿⠟⠛⠁⢀⣴⠟⠋⠙⠻⣿⠀⠀⣰⡟⠉⠁⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠠⠴⣾⡟⠀⠰⠟⢻⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣗⡲⠭⣝⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣐⣻⡇⠀⠐⢶⣾⣷⣧⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠻⠶⢬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣾⣿⣷⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⠙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣽⣽⣽⣭⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢈⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠁⠀⠀⠀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣋⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢖⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠉⣩⣿⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣤⡆⣀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⠚⢛⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⢠⡖⠉⠁⠀⠀⠀⣠⣴⠶⠒⠤⣀⠀⠀⠀⢠⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣷⡿⣓⠏⠉⠉⠓⢾⣿⣧⣶⠴⠤⠄⠉⠒⣺⣿⠿⠒⡛⠋⢉⡒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡝⣼⠃⠀⠀⠀⠀⠀⢹⣯⡞⠉⠉⠉⠛⣩⡟⠁⣀⡧⠞⠛⠉⠛⠳⣄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⣿⠀⢀⠀⠀⠀⠀⠈⣿⡇⠀⢀⡴⢾⣿⢣⠞⠁⠀⠀⠀⠀⠀⠀⣽⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⢷⣾⠀⡀⡀⠀⠀⠊⡉⢉⣡⣴⠟⣵⣡⡴⠒⠉⠉⡉⠉⠒⠶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢈⣄⣱⠀⡀⠹⠆⠀⠈⠇⣌⠙⠛⣯⣷⣿⣷⡾⠞⣲⡗⠓⢻⣤⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠛⠛⠉⠋⠀⠳⠀⠀⠀⠀⠀⠀⠘⢛⣛⣿⣿⡛⠛⠒⠚⠛⠒⠚⠱⠿⣧⡥⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⡀⠀⠀⣀⣠⡄⢀⠄⠀⠀⠀⠀⠀⠀⢲⣤⣽⣿⣯⣥⣶⣶⣶⣶⣶⣶⣶⣖⠶⣌⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⣾⠿⠛⠛⠻⣿⣿⣇⡼⠀⠀⠀⠀⢡⣠⡀⠱⣟⠿⠛⠋⠉⠉⠁⠀⠀⢀⡼⣣⠛⠻⣎⣇⢱
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⠃⠀⠀⠀⠀⠀⠹⡿⢷⠀⠀⠀⣼⣠⣷⣝⢦⣙⠢⢄⡀⠀⠀⠀⠀⢀⣿⡾⠁⢰⢩⢯⣿⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣲⡄⢧⡀⠀⠀⠀⠀⠀⢠⣯⠏⠀⢀⡾⢿⢿⣿⣿⣷⣮⣕⣦⠈⠑⠦⣄⠀⠈⡏⢣⡀⠈⢻⡾⠇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣿⣦⣌⡉⠑⠒⣲⣦⢾⡏⠀⣰⣡⠞⠁⠀⠀⠉⠙⠚⠿⢮⣙⡢⢄⠀⠑⣦⡘⠲⠬⠭⡅⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠛⠻⢿⣿⠀⣰⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢆⠀⠙⣷⡄⠀⢰⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢽⢻⣿⠀⠀⠀⢰⢫⠭⣍⢢⠀⠀⠀⠀⠀⢱⡄⢸⣷⠀⠈⣜⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣤⡟⡇⠀⠀⠈⠳⢷⣌⣾⣇⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠈⠙⠒⢲⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⣿⠟⣠⣷⡤⠤⠤⠤⣼⡟⢣⢾⡄⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢺⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡠⠟⡞⠓⠒⠊⠛⠻⠖⠶⠶⠦⢤⡭⢟⢎⣚⡲⢤⣤⢜⣿⢋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠑⠶⠼⠦⠿⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⠂
⠀⠀⠀⠀⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠐⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠠⠴⠀⠀⠀⠀⣀⠠⢀⣀⠀⣀⡀
⠀⠀⠠⡀⠀⠈⢄⠨⡒⢄⡠⢀⠃⢱⡀⠀⠀⠀⠀⠀⣀⠠⠤⠲⣀⣀⠤⠒⠩⠔⠁⠀⠂
⡤⠀⠀⠀⠀⢀⠈⢂⠑⠒⠠⠤⠐⠂⠀⢈⠀⠀⠀⠅⠀⡀⠀⠀⠀⠐⠒⠄⠃⢄⡀⢀⣀⣀⠄⠀⠀⠀⣀
⠀⠠⡌⢁⣀⡡⠤⠤⠗⠒⠒⠦⣄⣀⡳⠚⠃⢄⣄⡠⡆⢧⠀⠀⡀⠠⠠⢤⣀⡠⢀⢀⣭⡤⠄⠈⠙⠀⠐
⠀⠀⠈⠠⢅⣀⣀⠀⠀⠀⠀⠈⠀⠀⡀⠤⢴⣆⣀⠔⡁⠀⠀⠰⠔⠒⠀⠐⠂⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠐⠒⠒⠁⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣴⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⣰⣾⠿⢧⣄
⠀⠀⠀⠀⠀⠋⠉⠀⠉⠙⢿⣿⡄⠀⠀⠀⠀⢻⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡴⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⠀⣀⠀⠠⠃⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠻⣿⣄⢛⣪⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⢠⣾⣿⠿⢿⣆⠀⢸⣿⣿⡇⠀⣠⣦⣄⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⢀⡴⠶⠃⠉⣀⣤⣿⠟⢁⠀⢀⣿⠀⠛⠛⠉⠁⣸⣿⣿⣿⣇⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠏⠀⢠⣶⣿⣿⢿⣿⠀⠀⠓⠈⠀⠀⠀⢠⢊⣩⣭⣿⠛⠹⠃⠀⠀⠰⣄⠀⠀⠀⠀⢠⠀⠀⢀⣥⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣿⠃⣿⠞⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⠃⠀⠀⠀⠀⠀⠘⣗⠀⣀⣴⣯⡀⣠⣿⡇⠀⠀⠀⣰⣿⡿⠛⠉⠉⠙⢿⣿⢃
⠀⠀⠀⠀⠀⠀⣸⡏⠀⢿⣷⣿⣿⢿⣦⣀⡀⠀⢀⠀⢦⣦⣀⡴⡏⠠⠀⡀⠀⠀⠀⡀⠘⢦⡙⢿⣿⣿⣿⣟⡀⠀⣀⣼⡿⠁⠀⠀⠀⠀⠀⠈⣿⢿⡇
⠀⠀⠀⠀⠀⣆⣸⠇⠀⠘⣿⣿⣿⣿⣧⢬⣄⣷⣴⣾⣿⡿⢋⡾⠀⠀⢀⡇⠀⠀⠀⢳⡀⠀⠻⣆⠉⠻⠟⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⣾⠇
⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡥⢀⣠⣾⠃⢰⡄⠀⠀⢡⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⠏
⠀⠀⠀⠀⠈⣻⡿⣧⣀⣀⢠⠤⢄⠈⠻⢿⡏⢀⠀⢀⡠⠀⣀⣶⣯⣽⠏⠀⣾⣷⣄⠀⠀⠛⣤⣶⣶⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⣠⣴⣿⠃
⠀⠀⠀⠀⠀⢿⣧⣼⣷⣿⣾⡟⢿⣄⣤⡜⢷⣄⣤⣾⣷⣶⣿⣴⣿⠟⠀⢸⣿⣞⣿⡆⢀⣾⡿⣿⣯⡉⠉⠛⣿⣦⢹⣿⣷⣶⣶⣾⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⢀⣾⣿⣿⣻⣿⣾⣿⠁⢹⣿⣿⣆⣀⣸⣿⣾⣿⣏⠉⠈⠉
⠀⠀⠀⠀⠀⣷⡄⠀⠀⠉⠛⠛⠻⠿⠿⠿⠟⢛⠛⠛⠉⠁⠀⠀⢀⣠⣿⣿⣷⡟⣹⣷⣾⣿⣿⡎⠙⢿⣿⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠚⠋⠁⠀⢸⣷⣶⣶⣿⣿⣿⣿⣿⣿⠛⠋⢽⣿⣿⣯⣅⣀⣀⣉⣡⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣠⣤⣤⣶⣿⠄
⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠟⠙⠛⠛⠿⣿⡿⢿⣿⠿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⢿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣰⡎⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠠⢄⣤⣤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡄⣀⣀
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠠⠤⠤⠤⠀⠀⣀⠀⠈⠀⠋⠉⠉⠙⠛⠋⠛⠂⠙⠒⠒⠲⠶⠶⢶⣮⣉⣉⠉⠉
⣥⣤⣤⣄⣷⣤⣤⣶⣿⣿⣿⡿⠿⣛⣙⠃⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠋⠍⠉
⠭⠭⣽⣯⣭⡉⠿⠿⠿⡿⠯⠽⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣄⣀⣀⣀⣀⢀⡀⠀⣀⣀⣸⣶⣷⣶⣶⣶⣶⣶
⣶⣶⣾⣿⠿⢭⣭⣭⣭⣥⣀⣀⠀⠤⠤⠤⠤⠶⠶⠿⠛⠛⠓⠒⠚⠛⠛⠛⢽⠽⠿⠿⠷⠖⠲⠶⠶⣾⣿⣏⣉⡉⠡⠤⠤
⠛⠉⠓⠂⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣶⣖⣒⣉⣭⣤⣄⣠⣤⣴⣶⣶⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣀⡀⠀⠉⠭⣽⣿⣿⣟⣛⣛⣉⣉⣀⣀⣁⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠛⢛⡛⠿⠻
⠛⠛⠩⠭⠭⠥⣤⣤⡄⠀⠶⠶⠾⠿⠿⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠤⣼⣤⠿⠭⠵⠶⠶
⢖⣶⣶⣿⣿⣿⡶⣶⠶⠶⠶⠒⠲⠶⠶⠶⢶⡖⢂⡀⠐⠂⠀⠀⣀⣀⣠⣤⡄⠁⠀⢀⣀⣉⣉⣉⣉⣙⡛⠓⠒⣒⣲⣶⣶
⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣶⠶⠶⠶⢾⣿⣿⣛⡛⠿⠿⣿⣿⣭⣍⣀⣀⠀⣀⣀⣀⣀⣈⣉⣉⣩⣤⣴⣶⣲⣶⣶⡶⠶
⣤⣤⡤⠤⠤⣴⣦⣤⣤⣤⠴⠶⠒⠒⠶⠶⠤⠀⠀⠐⠒⠒⠲⠶⠖⢺⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣭⣭⣭⣤⣤⣤⣶⣶
⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⢿⣷⠶⠶⠶⠶⠾⠛⠟⠛⠾⠿⠗⠒⠂⠀⠐⣚⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠥⠤⠤⠤⠤⠤⠤⠤⠴⠶⠾⠿⢟⣛⣛⣛⣛⣛⣿⣿⣿⡿⠯⠭⠽⠟⠛⠛⠛⠛⠉⠉⣉⣛⣉⣉⣀⣈⣉⣉⣀
⠿⠿⠿⠿⠿⠿⠾⠿⠿⠶⠾⠛⠛⠛⠋⠉⠉⢉⢁⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠉
⣒⣒⣂⣠⡤⣄⣠⣤⡤⠤⠤⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠲⠒⠒⠒⠒⠂⠛⠋⠀⠒⠀⠈⠙⠛⠓⠂
⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣄⣤⣤⣤⣤⣤⣤⣀⣀
⣀⣀⣀⣤⣤⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣭⣭⣽⣿⣿⣭⣥⣬
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⡀⠀⠈⠉⢉⣩⣭⣭⠭⠭⠴⠶⠚⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠙⠉⠛⠛⢛⣛⣛⣛⣛⡛⠻⠿⠷⢶⣶⣶⡶⠶⠶⠶⠶⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣻⣿⣿⣿⣭⣭⣍⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⠿⠟⠛⠛
⣀⣀⣀⣲⣀⣈⣭⣭⣭⣿⣿⣿⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣯⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡯⠀⠀⠀⠀⠀⠈⢿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⢛⣛⣁⣀⣀⠀⠀⠀⠉⠉⠘⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠤⠀⢰⠂⠀⠀⣀⢀⡀⠀⢀⠀⠀⠀⢸⡏⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠁⣀⠀⠀⣿⡀⠏⢢⡿⣿⡟⢠⡎⠀⠀⠀⠘⣷⢹⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠈⣿⡆⢇⢹⠀⠀⣿⣿⠀⠀⠀⢸⡇⠨⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣷⣄⢹⣇⣾⡄⡅⡀⢹⡏⠀⢸⣷⣿⠁⢠⡀⠀⠀⠀⠀⢻⡗⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢿⡸⣿⣿⣻⣧⡀⣷⢸⠇⠀⣼⣿⠇⠀⣼⣧⣤⠄⢰⡄⠚⠓⠼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠷⠛⠛⠉⢻⣿⣿⣾⡰⢠⣿⣿⣶⣦⣿⣿⣿⣴⣀⣤⣐⣴⣦⡀⠘⠿⡃⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠻⠿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠛⠉⠉⠁⠀⠀⠀⠉⠉⠙⠟⣿⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠉⠁⣀⡤⠴⠶⠶⣶⠶⡶⠖⠲⠦⠤⠤⠴⠃⠈⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢦⡨⢛⣩⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠐⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡈⠉⠘⡿⠿⣛⣋⣻⣍⣉⡋⢉⡉⠙⣛⣻⣛⡛⠛⠃⠲⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⢁⣶⣾⣿⣿⣿⣿⣿⠿⠿⠷⢶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⣈⠻⢿⣍⣍⡀⠀⡀⠆⠁⠈⠀⠀⠀⠈⠈⠉⠑⣢⣦⣠⡴⠏
⠀⠀⠀⠀⠤⠤⠶⣶⣾⣿⣿⣤⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⣴⠿⠶⠞⢛⣟⣓⣛⣛⣻⣟⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣻⣟⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣾⣿⠿⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠛⠿⠿⠿⠿⠟⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠠⢄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⠀⠈⠁⠀⠚⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠁⠀⠅⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡀⣀⠀⣤⠦⠐⣄⠤⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠌⠳⡄⡀⠀⠀⡕⠊⠀⠀⠀⠀⠀⠀⠀⠐⡢⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠘⠃⠀⢀⠀⠀⠈⠛⡠⠀⠀⠀⢀⠄⠤⢈⠴⠫⢀⠔⠢⠤⠁⢀⠀⠀⠀⠰⠆⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⠀⠀⡀⠀⠀⠀⢠⠣⡈⠢⢀⢠⠐⠁⠀⠀⠀⠤⡀⠐⠃⠀⠲⢿⠁⠂⠄⡌⠀⠠⠒⡂⠑⠃⠀⡘⠤⠃⠀⠀⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠉⠌⢊⠢⡀⠀⠀⠀⠑⢄⢡⡀⡀⢀⡞⢞⣳⠀⠀⠀⠐⢄⠱⡀⡆⠨⢰⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢸⡀⠄⠀⠀⠂⠀⠀⠺⠓⠂⠉⠀⠢⡠⠴⠀⠀⡃⢀⠃⡝⢑⠂⡰⠈⠀⠐⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⢀⠰⣀⡐⠁⠀⡠⢠⡟⡏⠅⠀⠀⠠⢈⡤⡁⠂⠄⠀⠰⠖⡐⠋⠀⡀⠔⣡⡮⠀⡑⠀⠀⠀⠠⠄⠠⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡣⠄⠠⡄⠕⠐⣬⡂⡊⡤⠋⢈⠄⠨⡐⠪⡴⠛⣁⣤⣄⡀⢤⢲⠿⠤⠤⢤⣆⣁⣼⣀⢨⣥⠀⣉⠉⠠⠔⠄⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢜⢯⡑⠞⠫⠒⠀⠐⢁⣭⡈⢀⡙⢹⡆⠀⠈⠓⢓⠈⡀⡀⠀⠠⢌⠀⢨⡼⠀⠈⣣⣰⢁⣾⡷⢎⣡⠁⡰⠀⢂
⠀⠀⠀⠀⠆⠆⠀⠀⠀⠀⠑⠩⠑⢤⣀⠀⢠⡟⠄⡽⠿⣉⡉⠀⠀⣠⡤⠗⠛⠲⣤⡤⠋⠷⠔⡉⢳⠀⠉⠈⠡⠈⡋⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⣤⠀⣎⠆⠀⠆⠐⠂⠀⠰⡙⡖⠫⠉⢉⣤⠴⠃⠂⠐⠑⢀⡤⣐⡒⠖⠠⠤⠐⠒⠀⠂⠉⣀⠀⢄⠁⠉⠠⡩⠂⠀⠛⠀⠀⠀⠀⠀⠀⣀
⡀⠀⠀⠀⣀⡆⢠⠒⠀⠀⠀⠀⠀⠀⠀⢰⡈⠀⠘⠚⠑⠲⠓⠉⠙⣻⣮⢔⣲⡭⠁⢠⠒⢒⡂⢁⠀⠂⠐⠀⠡⠈⠀⠀⠂
⠀⠀⢀⠀⠀⠀⡄⣡⠴⢄⠀⠀⠂⡠⢀⠆⠀⠂⠀⠀⢀⡄⠰⢆⢬⡁⠉⠀⠠⢀⠀⢗⠀⡆⢀⢀⠀⠀⠀⠀⠐⠀⠀⠔
⠀⠀⠀⠁⡄⢠⣅⡨⡗⠀⠦⡭⣤⠴⠻⠄⠀⠀⠀⣄⠴⢀⡾⠞⠛⠁⠒⠒⠂⠁⡀⠀⢇⡱⠈⠊⠀⣤
⠀⠀⠀⠂⠁⠪⡉⢫⡀⠀⠀⠀⠠⢄⡁⠀⠀⠀⣊⠡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠈⠜⣆⠈⠀⠀⠑⠈⡠⠔⠂⠉⠀⠀⠀⠘⠀⣀
⠀⠀⠠⠀⠀⠀⠀⠠⣨⢗⡂⠀⠀⠀⡁⠀⠀⠀⠣⠃⠀⠀⢀⡀
⠀⠀⠀⠑⠀⠀⡠⠚⠉⠋⠐⠀⡀⠀⠐⠂⠠⠤⠎⠬⠄⢒⠄
⠀⠀⢀⠔⠰⠶⡇⠀⠒⠀⠒⠂⠀⠂⠠⠆⠒⠨⠄⠒⠠⢣
⠀⠀⠈⠉⠀⠀⠐⠈⠀⠀⠘⠄⠐⠐⠠⠄⠉⢀⣘⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠶⢦⡀
⠀⠀⠀⠀⠀⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⣿⠉⠛⠳⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠞⠛⠛⠉⠁⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⢸⡇⣀⣠⡴⠶⠞⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠳⠶⢦⣤⣀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢿⡇
⠀⠀⠀⠀⠀⠘⡇⠈⠙⠳⠶⠦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉⠀⣼⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠉⠛⠶⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⠋⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠚⠛⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣽⣥⣬⣩⣯⣥⣿⣹⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⡀
⠈⢀⢈⡁
⢉⣁⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⢠⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦
⢠⡤⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠠⠤⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋
⠰⠶⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠐⠒⠘⠃⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡁
⠘⠛⠘⠃⠸⢴⣂⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡎⢆⡀
⠈⣉⢈⡃⠀⠀⠀⡴⠖⠋⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⡟⣿⣿⣿⣇⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⣰⠇
⢈⣉⢈⡁⠀⠀⠀⠙⠛⣳⠀⠔⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣷⣿⡇⢻⣿⣿⣿⣆⠀⠀⠓⠒⢦⠀⢠⡶⠛⠁
⠀⣀⢬⡁⢠⡤⡄⣰⡟⠁⠀⠀⡆⠀⢀⣼⣿⠟⣿⣿⣿⡇⣞⣿⣿⣿⢸⣿⣿⣿⣿⡄⢸⡉⠉⠉⢰⡿⠀⠀⣀
⠀⡠⢤⣽⣃⡵⠦⢼⣷⣤⣠⡊⢁⣴⣿⡿⢣⣾⡿⢃⣿⣇⣸⠇⣿⢿⡎⣿⣿⠘⣿⣷⠀⢸⡆⠀⣾⡇⡀⣸⠁
⠀⠤⢠⣼⠧⢠⣀⠜⠀⠉⡿⣿⣿⣟⠁⢠⣿⡟⠀⣼⠟⣼⣿⠀⢸⣿⣷⣽⣿⠀⢹⡟⣿⠋⠀⣼⡿⠤⣄⣀⡤⠶⢦⣄
⠀⠤⠠⡜⣆⠀⢀⠀⠀⣼⣽⡿⠛⢿⣷⣾⣿⣤⣾⣿⢾⣿⣿⠀⢸⣿⡟⢻⣿⣷⣿⣿⣾⣷⣾⠟⢠⡶⠚⡏⠀⠀⠀⢹⡆
⠀⠤⠰⠆⠈⠱⢦⣷⢾⡿⠋⠀⠀⠀⢉⣻⣿⣛⣋⣁⣼⣿⡏⠀⣼⣿⠃⠀⠻⣿⣿⡟⠉⠻⣿⣄⠈⢳⣄⠙⢆⢀⣠⡾⠁
⠐⠒⠰⠆⠀⠀⢸⠁⠈⠻⣶⣴⣶⠿⠯⠹⣿⡿⠿⠿⠟⠋⠀⠀⣿⣿⠀⠀⠀⣸⢿⣿⡄⠀⠘⢿⣦⣀⣻⣶⠞⠛⠁
⠀⠒⠐⠆⠀⠀⠘⠆⠤⠖⠛⢳⣄⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣿⠷⠂⢻⣷⣄⠀⠈⣉⣿⠟⠁⠀⠁
⠀⠒⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉
⠀⠛⠘⠃
⠈⠉⠈⠃
⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠛⠲⢦⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⡼⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡿⠃⢀⣴⡟⠁⠀⠀⢀⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢻⣄⡠⣪⠋⠀⢀⣴⠞⠋⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠆⠚⠋⠙⠲⣧⣀⣴⡟⠁⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⠀⠀⠈⠛⣋⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡛⠁⢐⡀⠰⠉⠮⠙⣹⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⣅⣠⡏⠀⠠⡄⠐⡲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢍⡿⠄⠀⠀⠀⠀⠈⠡⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡖⠱⠛⠉⠁⢘⠳⢄⠰⣄⣤⣼⡾⢿⢛⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⡴⠊⡉⠫⡌⠀⠀⠀⠀⠈⠀⠀⠈⣩⠖⠁⠀⡴⠋⠀⠈⣧⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⠊⠀⠐⢌⣲⠊⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣬⠔⣦⣀⠞⣿⡀⠀⠀⠀⢸⡄⣠⠟⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡴⣫⠞⢹⠉⠀⢸⣿⠶⠤⠀⠀⣹⠏⠠⠀⠀⢀⡧⢾⠶⠄⠀⠀⠀⠘⣆⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢊⡼⠁⠀⠘⡄⠀⣼⢻⣤⠀⢀⡼⠃⣠⠃⠀⠀⢸⠀⣿⣇⠀⠀⠀⠀⠀⢸⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⡵⢻⠀⠀⠀⠀⣧⡼⠋⠀⣿⣤⠞⢁⡴⢃⡎⠀⠀⡇⠈⠙⣿⣦⡀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⢠⠀⠀⣠⣟⠀⠀⡜⠀⢁⣴⠟⢡⡞⠀⡜⢀⡇⢀⣼⣿⢈⣿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠞⠋⠉⠛⠶⢧⣌⣉⣁⣰⡟⠀⣰⣃⣸⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉




⡿⢿⠿⡿⠿⢿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣟⣛⣛⣿⣿⣛⣿⣿⣿⣻⣿⢿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠊⠇⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣉⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣇⠀⡠⠼⠔⢣⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⣠⠔⠚⢆⢫⠀⠀⠘⡆⢰⠀⠀⠸⠀⡎⠉⠑⢢⢀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⣈⡮⣆⠀⠀⠱⠘⠀⠀⠀⡿⠀⠀⢀⣃⠏⠀⠀⢹⠂
⠀⠀⠀⠀⢀⣀⠤⣤⣴⠦⠤⠶⢾⠀⠷⠶⠦⢴⣦⣤⠧⣀⣧⠀⠸⡀⠀⠀⢻⡂⠀⢀⠇⠀⠀⡘⠉⢓⠄⢠⠃
⠀⠀⠀⢰⣅⠰⢍⣀⠀⠀⠀⠀⠘⠖⠁⠀⠀⠀⠀⣀⡩⠆⣨⡄⠀⠇⠀⠀⢸⡇⠀⠸⠀⠀⠀⡇⠀⡞⠀⡏
⠀⠀⠀⠘⡓⠮⠭⠭⢛⣛⣛⣓⣒⣓⣚⣛⣛⣛⡛⠭⠭⠵⢺⠹⡀⢸⠀⠀⢸⠇⠀⡇⠀⠀⢰⠀⢠⢁⣼
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⢇⡀⡆⠀⢸⠀⠀⡇⠀⠀⢸⢀⡼⠋⡌
⠀⠀⠀⠀⢰⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣶⠀⠀⠈⠑⠒⠚⠤⠴⠇⠐⠒⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠘⡀⠀⠀⠚⠁⠘⢃⣤⣤⣤⠘⠃⠈⠃⠀⠀⢀⠿⠀⠀⡴⠛⢶⠄⠀⠀⠀⢠⠞⠳⡦⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡿⢿⠇⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠻⠦⠞⠀⠀⠀⠀⠀⠀⡌⠀⢡⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣅⡢⡖⢈⡉⠭⠶⣞⡢⢤⣤⣤⣤⣈⡉⣀⡀⠀⠀⠠⠼⡤⢤⣐⡲⠶⠍⣉⣑⠦⠄⣤⣄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠱⣹⣉⣐⣲⣖⣂⡉⠉⣉⣒⠢⣍⡙⠛⠛⢛⣛⡻⠟⣋⣒⡢⢤⣴⣶⣊⡕⠊⠉⠁⠈⠆
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⢇⡀⣠⠞⠉⠀⠶⠀⠬⠍⣁⠙⣃⡐⢛⣒⠛⠓⠒⠚⣛⠚⠋⢻⠉⢉⣍⢀⣄⠀⠈⠙⢦⡀⢀⠆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠋⠀⠀⠀⠙⠂⠈⠶⠀⠁⠗⠈⠃⠠⡏⠰⠃⠘⠃⠴⠂⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠤⠤⢀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⠠⠤⠤⠤⠄⠒⠒⠊⠁



⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⣄⠀⣀
⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⡰⠟⡗⠚⠎⡛⡹⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢀⣄⢠
⠀⠀⠒⠚⠋⠉⠉⠀⠀⢠⡌⠈⠀⠀⠀⠐⠀⠈⠃⠀⠀⣠⣴⡶⠂⠀⠀⣀⡠⠂⣑⣀⠔⠡⣬⠀⢇⠎
⢠⣀⢄⠈⢉⣆⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠠⢾⡿⠗⠁⠀⠀⡘⠲⡇⠀⣝⡏⠀⡰⡾
⠈⠲⠃⠀⠈⢀⣀⡀⠀⠠⠀⠀⠀⠀⠃⣀⢀⡀⠀⠀⠀⠀⠀⠰⠀⢠⣅⣙⡃⣰⢾⠁⢠⣿⠁⠠⠂
⠀⠀⢀⢄⠀⡆⠄⠔⠁⠀⢠⣍⡆⠀⢘⢖⠉⠃⣠⠠⠻⣀⠠⠀⠀⢸⠃⠀⠉⠈⠉⠋⠒⡇⢀⢄⣠⡄
⠀⠒⢁⢈⠀⠃⡡⠴⠀⢀⢃⠭⡸⠀⠈⣲⠍⡆⠀⡙⣎⡁⢠⠶⣦⢸⠘⠂⠉⠐⠥⠀⣾⠀⠀⠀⠕⡁
⠀⠀⠀⢻⠈⠂⠃⠀⠀⠘⠊⠀⠓⠃⠀⠑⠒⠁⠀⠑⠐⠃⠈⠋⠁⠈⠓⠒⠒⠂⠲⠀⠃⠀⠀⢠⢰⠟
⠀⠀⠠⠒⢣⡀⠃⡑⠀⠀⠠⠫⡷⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⠞⠁
⠀⠀⠀⠀⠁⠈⢙⢤⡄⠀⠀⠁⣂⡀⡀⠀⠀⠹⠒⠇⠀⠀⠠⠀⠀⢠⡔⠀⠀⣀⡀⠠⠀⠀⠰⣿⠴⠂
⠀⠀⠀⠀⠀⠀⠣⠜⠁⠀⠀⢸⠔⠒⠊⢀⢎⢭⢳⠀⡔⡒⠄⠀⠀⠠⡀⢀⠞⠉⠙⢦⠀⢠⠶⢦⡀
⠀⠀⣼⣷⠀⠀⠠⠀⠀⠀⠀⠘⢨⠴⠂⠸⡘⠐⡸⠰⠐⠝⡘⢰⠸⠵⡘⠘⡀⠀⠀⢸⠀⠃⠀⢸⠃⠁
⠀⠀⢳⣿⡇⠀⠀⢀⣀⠠⢀⠘⠚⠀⠀⠀⠉⠉⣠⠤⢵⡮⣀⠘⠒⠈⠠⠀⠘⠢⡤⡎⠀⣀⠔⠁⠀⠸
⠀⠀⠀⠉⣴⣖⠈⠙⢷⣄⠈⣆⢤⠀⠐⠈⢀⠼⠢⡖⠚⠳⡤⣇⠠⢰⡅⠀⠀⠀⢧⠥⠀⠿⠀⠠⡂⠢
⠀⠀⠀⠀⡍⢮⣦⣠⠾⣿⠊⠡⠀⢠⣤⠀⢸⠑⠾⠛⠓⠛⠓⠺⠀⠈⠀⠀⠀⠠⡀⡄⠀⠀⡄⠀⠜⠤
⠀⠀⠀⠘⡄⠀⠈⠀⠀⣿⠀⠀⡇⠀⠉⠀⠀⡀⡆⠀⠉⠊⠀⠸⠀⠀⠀⠀⠀⣀⣥⣤⣠⡀⠁⠀⢱⡎
⠀⢀⣀⡀⠙⠂⠂⠒⠘⠛⠂⠉⠀⠀⠀⠀⠀⢟⠿⠚⡟⠛⠛⡇⠦⠀⠀⠀⠀⢠⣉⣉⣉⡁⠀⠀⢅⡸
⠀⢠⡸⣈⡵⡆⢠⣶⡐⡎⢱⠀⢔⣉⡱⠀⠀⡘⠲⠐⠓⠒⠒⠃⠀⢰⣉⡕⠀⠸⠶⠴⠴⠇⠀⠀⡔⢢
⠀⠠⠳⣦⣄⣈⣋⣀⣉⡥⠋⠀⠀⠀⠀⠀⢼⣽⠰⣿⠠⠴⠦⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠁⠀⠀⠘⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠄⠠⠄⣀⠀⠀⠀⠀⠀⠀⠈⠣⠸⠄⣜⣢⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢤⣄⣠⣼⠃⠀⠀⠀⠀⠀⠀⠆⢹⠇⠻⠇⣌⣉⡓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⢿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣀⣀⣩⣭⠭⠭⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⣛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡜⠃⠲⠐⠶⠂⠈⣆⠀⢀⡌⣷⠒⠛⠛⠓⠲⠦⣤⡀⠀⣼⠀⠀⢨⣭⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢂⢠⣌⢦⠀⠀⠀⠀⠀⠀⣹⠰⠛⣔⠳⢆⡰⠃⡀⢸⣾⡟⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠀⠀⠴⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡆⣎⢆⠳⣄⠀⣠⠖⠉⢸⣦⠦⠠⠴⠄⢁⣦⣇⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣨⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⡌⣮⡷⠞⠿⠁⠀⠀⢸⠀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡾⠁⠀⠀⢉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡜⠁⠀⠀⠀⠀⠀⠀⡘⣤⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⣀⣠⡼⢦⣀⡴⠋⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠚⠻⡄⠀⣤⣄⣀⣷⡈⠳⠇⡰⠎⠃⣦⢀⡤⡞⢿⠙⡇⢠⡟⠋⢁⣀⣤⣶⠾⠛⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢙⣶⠟⠉⠛⠛⠻⣆⡀⢉⣀⣤⠾⢿⠀⠇⠙⠀⠃⠈⠿⠛⢻⣿⣥⠶⡶⠓⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠶⠦⠤⣾⠳⣄⢀⣀⣤⠷⠞⢛⣉⣥⣤⣶⣾⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⣴⢓⣊⣩⠤⣶⡚⠋⠉⠁⠠⠤⣌⣉⣉⡙⠓⠦⣤⣀⣀⣤⠟⠀⠀⠀⠀⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡀⠀⠐⡀⢙⡹⠁⠀⠀⠀⠉⠓⠦⢤⣈⡉⠒⠪⠭⠭⣉⣛⣓⣒⣛⣳⣤⡀⠀⠀⣠⡿⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢧⡴⠤⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⠤⢤⣀⣈⣉⣉⠉⠙⣿⣯⣁⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣀⡤⠂⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢒⠠⢄⡀⠀⠀⠀⢠⡄⢠⣤⣴⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠈⠙⡄⠹⣷⡆⠀⢸⣿⣾⣿⠟⢻⣿⣿⢠⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠠⠀⣸⣆⡀⠀⣀⣠⡾⠽⢿⠟⢳⣶⣾⣿⣿⣿⡿⢂⣿⡿⣷⣤⣤⣤⣤⠶⢿⠟
⠀⠀⠀⠀⠀⣔⣈⠉⣉⣿⡉⠉⠈⠠⢆⣰⣦⣼⣿⣽⣿⣿⣿⣶⣻⣳⣷⠛⠉⠙⠛⠛⠊⠁
⠀⠀⠀⢀⠜⣁⡀⠀⠈⠁⢻⣟⡙⠛⢛⣙⣿⡿⣫⡿⢯⡷⣿⣯⢹⣿⣿⡀
⠀⠀⠀⢿⢨⠝⠀⠀⠀⠀⣊⡛⠻⠿⠿⠿⠻⠿⢿⣶⣿⣿⣽⣿⡌⢻⣾⣷⣄⠒⠂⠑⠲⢄
⠀⠀⠀⠘⣄⠀⠀⢀⣠⣔⣁⣀⣤⣶⣿⣷⣶⣦⣄⡙⠻⣿⣿⣿⣏⡀⠙⢿⣽⣷⣄⠀⠈⢊⠄
⠀⠀⠀⠀⠈⣹⠿⠛⠉⡩⢍⣉⣉⣁⢽⣿⠏⣍⡔⠍⠠⠈⢿⣿⠋⢛⠖⡀⣿⢙⠛⠛⠛⠋
⠀⠀⠀⠀⣼⠃⡠⠀⠁⠀⠀⠀⠀⠀⣰⣟⡓⣧⠋⠀⠀⠀⢔⣿⠀⠀⠀⣠⣨⣾⣿⣶⣖⡒⢒⣦
⠀⠀⠀⠀⡇⠠⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇⠁⡇⠀⠀⠀⠀⠼⣿⣶⠞⠉⡩⢤⠄⠲⡆⠠⠙⢷⠋
⠀⠀⠀⠀⢿⣄⠑⠤⣀⡀⠐⣶⣄⠀⣸⣿⣀⠒⠠⠀⠀⣸⣿⣿⠁⡴⠁⠀⠀⡆⠀⢱⡤⠇⡾
⠀⠀⠀⠀⠀⠈⠻⢮⡤⠬⠬⠤⢤⣴⠃⠹⡿⣿⣷⡿⠿⠟⢹⣇⢰⡇⠀⠀⣴⡇⠀⢸⢳⡞⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⢻⣦⣅⣰⠇⠀⠀⠀⠀⠀⠻⣎⠘⠳⢶⣟⡅⢀⡾⣸⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠾⠛⠛⠛⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣴⣶⣦⣤⣤⣤⣿⣿⣿⣷⣤⣴⡶⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢈⣉⣭⣭⣁⣉⣁⣌⣤⣀⡀⢀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠋⠉⢉⣿⠛⢻⣿⡉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡿⠿⠿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢿⡛⠿⠿⠿⠟⠛⠛⠻⢶⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⠾⠛⠛⢷⣄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡉⢻⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠈⢻⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⡟⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⣼⣶⣿⣡⡟⠀⠀⠀⠀⠀⠀⢀⣴⡾⠷⠾⠿⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⣿⣍⡙⠛⠛⠛⠛⠛⠛⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⣿⡉⢿⣦⣀⢀⣀⣀⣀⣿⠟⣿⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠙⠶⢭⣙⣛⣛⣛⣩⡥⠞⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣤⣬⣭⣭⣥⣤⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣦⠈⠉⠉⠉⠉⠉⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⣿⠀⠀⡄⠀⠀⠀⣿⡇⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡧⠀⠀⠀⣿⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⠀⢰⡇⠀⠀⠀⢸⣿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣿⠀⢸⡇⠀⢠⡄⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⢸⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⠃⠀⢸⠇⢸⡇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠀⠀⢠⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⡟⠀⣀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⠀⡏⢸⠀⠀⠀⢸⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⠀⡇⠘⠀⠀⠀⢸⣇⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢸⡟⢠⠇⠀⢀⡀⠀⢸⣿⠀⠀⢰⠞⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣀⡀⠀⢸⡇⠀⠀⠀⢸⠃⠀⢸⡇⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣴⡟⠛⠻⠇⠸⡿⠀⠀⠀⠘⠀⠀⠘⣧⠀⠘⠋⠉⣠⣄⠀⠀⠘⠋⠉⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠇⠀⢀⣤⡄⠀⠀⠀⠀⢀⡀⠀⠞⠁⠀⠲⣦⠀⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠸⣤⠀⠀⢰⡟⠁⠈⠙⠃⠠⣇⠀⠀⠀⠀⠐⠛⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣠⡄⠀⠈⠀⣀⠀⠀⣀⠀⠈⢉⣤⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠿⠛⢿⣤⣀⣠⡿⠃⠀⠻⣶⣶⠾⠛⠿⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉

⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⣄⠀⠀⠘⣿⠃⠀⢀⣾⠀⠀⠀⣠⣴⣾⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣶⣤⡀
⢹⡷⠀⠀⢹⡇⠀⠀⢹⣇⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⡀
⠸⣧⠀⠀⢸⣷⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⣿⡄⠀⠈⣿⣾⡿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡷⡼⠈⢦⢳⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⢻⣇⠀⣠⣿⣟⣀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣣⣤⣿⣤⣘⡓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠘⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠏⣤⡀⣀⡘⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⢠⣿⠏⠙⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣂⣀⣤⡍⢁⢼⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⣾⡿⢀⡴⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣿⣯⢽⣋⣒⣤⣼⣿⣿⣱⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢠⣿⡇⠯⢠⠴⠊⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⢋⡜⢡⠞⣽⣿⡿⣿⣇⢻⣿⣿⣿⣿⡳⣄⠀⠀⠀⠀⠀⠀⢹
⠀⢸⣿⠀⠘⠄⠒⣉⣼⠃⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⢻⣼⡇⣿⢸⠟⣸⢇⣯⡟⣼⠛⠀⠀⠉⠹⢎⢧⣀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⢡⣈⣡⣾⢧⡀⠀⠀⠀⠀⠀⣰⠃⢠⡀⠀⠀⠙⠹⣧⣼⡄⣿⢸⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠳⣄⠀⠀⢸
⠀⢸⣿⡄⠀⠀⠈⢻⣿⡆⠙⣦⠀⠀⣠⡶⠋⠀⢈⣷⡀⠀⠀⠀⠈⠟⠿⡷⠉⠀⠀⠀⠀⣴⢄⣿⣆⡀⠀⠀⢿⣮⢦⡀⢸
⠀⠈⣿⡇⠀⠀⠀⢸⣿⣿⡇⠈⠳⡾⠋⠀⢀⡇⣾⣿⡷⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⣿⣫⣿⣷⣭⣿⡤⠀⠀⠈⣷⣷⣼
⠀⠀⢻⣿⡀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⣀⡾⢃⣟⣼⡏⢿⣿⡶⠞⠋⢹⠀⠈⢓⠒⠲⢿⡟⣻⠏⠈⠛⠻⠶⣤⠄⠀⠙⠟
⠀⠀⠈⢿⣧⠀⠀⠀⢻⣿⢿⣟⠀⠰⢚⣩⡴⠞⠋⠀⠹⡏⠸⡇⠀⣀⣬⠓⠀⠀⡗⠠⣾⢰⠏⠀⠀⠀⠀⣰⠋⠀⢠⣶⡼
⠀⠀⠀⠈⢿⣧⠀⠀⢸⣿⡀⠛⠷⠒⠉⠁⠀⠀⠀⠀⣾⡿⣄⡇⠀⠀⡸⣆⠀⠀⠁⣰⢇⡆⠀⠀⠀⠀⣰⠇⣠⣶⣿⠏
⠀⠀⠀⠀⠈⢻⣷⡄⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡇⠈⠙⠻⢶⣧⣤⣀⣀⣰⣿⣼⡇⠀⠀⠀⠐⠓⣤⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣦⣿⣷⠀⠀⠀⠀⠀⢀⣠⣿⠐⣿⣿⣄⢲⣝⢶⣬⣙⣳⣌⡉⣀⣸⣿⡄⠀⠀⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣄⠀⢀⣤⠖⠉⠸⣿⣦⡘⢿⡌⢷⣝⢯⣙⠿⣿⣿⣿⣿⣿⣿⣿⣖⣰⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣤⣶⣄⣻⣿⣿⣦⣻⣦⡙⣷⣿⣷⣶⣭⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⠀⠀⠰⠠⠐⠀⠀⠐⠀⢺⠄⠐⠀⠠⡂⠐⠀⠉⠉⠀⡀⠀⠰⡍⠕⡀⢤⡀⠀⠀⠀⢳⠂⠀⠀⠀⠣⠘⠀⠶⠀⠀⠀⠀⢀⠀⠠⢀⡀⠘
⠀⠐⡀⠀⠀⡀⠅⠀⠀⢠⠠⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡠⣌⠉⠃⠊⢀
⠀⠀⠀⠀⠐⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠐⠏⠝⢀⡄⢲⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠎⠙⠃⠀⠀⠀⠺⠆⠁
⠀⠀⠀⠀⠄⠈⠁⠀⡠⠚⢁⠤⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠎⠕⠀⠀⠀⠉⠁⠀⠀⠠⠀⠀⠀⠂⡀⠐⢠⣀⠀⠀⠀⢀⠀⠀⢀⡠⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠈⠣⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠘⠀⠀⠀⣀⠀⠀⠂⠈⠙⠃⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠇⠀⠐⡔⢣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠂⠰⠂⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠑⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠠⠀⠚⠀⣄⠀⠂⠀⢀⠀⠀⠀⠉⠀⠀⠀⡋⡜⠃⠀⠀⠂⠀⠐⠀⣤⣄⣁⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⠈⠀⠀⠢
⠀⠗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠃⠀⠄⠀⢀⠧⡀⡮⠸⠃⠀⠀⠀⠀⠤⡁⠉⠛⠃⠀⠒⠶⠃⠀⠀⠀⠀⠢⠲⠁⠲
⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢀⠀⠐⠃⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⢼⠁⢀⠎⡁⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⡀⠀⠠⠈
⠀⣀⠀⠠⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢀⠘⠄⠄⠀⣤⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⠀⠀⠀⠂
⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠆⠀⠀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠀⠚⠠⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⡂⠠⠄⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣴⡇⠀⠀⠀⠀⣠⠊⡴⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠻⢿⣿⣿⣶⣦⣴⣶⣄⠀⠐⢦⡈⠡⠅⢀⡰⠂⢨⠀⠀⠀⠀⣸⠁⢸⠆⢀
⠀⠀⠀⠀⠀⠀⢀⣤⢤⡄⠘⡄⠀⠀⠀⠉⠉⠉⠉⠉⠻⢿⣿⣶⣿⠿⢿⡛⠉⠀⠀⠘⢦⡀⠀⠀⢻⡆⣸⡦⠂⠀⣀⠈⠉⠛⡆
⠀⠀⠀⠀⠀⠀⢸⡅⠀⣷⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⢠⡅⢠⠀⠈⠑⠒⠛⠋⠉⠀⠀⡔⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⢧⡀⠁⢄⠀⢀⠀⠀⠀⣄⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠠⡀⠀⠀⢣⠟⠀⠀⠸⡅⠀⠀⠙⠶⠤⠤⠴⠖⠚⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠗⡢⡙⠳⣄⣠⣼⡟⠀⠀⠀⢃⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠈⠓⠛⠁⠀⠀⠀⠀⠘⢻⣤⡀⠀⠀⠀⠀⠀⠀⣨⣿⡿⢻⣿⣍⡽⢿⣿⣦⣀⠀⠀⠱⣿⠲⡈⠛⠉⠁⢀⣀⡀⠀⠁⠀⠈⣀⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢒⣦⡶⠶⠶⢟⣉⣥⣾⣹⡽⠿⠇⠈⠛⢯⣿⡷⠀⠀⣿⣷⣻⣆⢺⣝⣻⣟⣿⣯⣶⣸⣯⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣤⠶⣶⣶⡌⣻⣷⡿⠾⠛⠁⠀⠀⠀⠀⠀⣸⠏⠀⢠⠿⠿⣮⣼⡘⠋⠉⠉⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠸⠋⠉⠉⠉⠁⠈⠋⢀⣴⠿⠿⣿⣲⣦⣀⡾⠁⢀⡴⠃⣀⣶⣿⢿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠙⢟⡿⠀⠀⣮⠀⣶⣭⢟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠐⡀⠀⠻⠯⠽⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⡀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣛⣛⣶⢶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⣽⢞⢀⡎⢨⢜⡜⡃⢘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⢠⠟⢽⢾⣼⡇⡏⣻⣯⣝⢲⣭⣷
⠀⠘⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣏⣚⢻⠿⣵⣆⠐⣿⣋⣿⠖⡇⣿⠄
⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⢸⣧⡉⣧⠿⢛⠳⠘⢇⡀⣴⡒⠿⣆⢣⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠋⠀⠈
⠀⠀⠀⠀⠀⢀⣼⣧⣄⠀⠀⠀⠀⠈⡇⢶⡿⣻⣭⣝⠢⠻⣿⡼⢿⠅⣠⣤⣅⠀⠀⠀⠀⠀⠀⢀⡞⠋⣽⣿
⠀⠀⠀⢀⠔⢻⣿⡀⠹⡇⠀⠀⠀⠀⠹⡀⢸⣿⡛⢿⣷⠰⠛⡫⠎⣾⣿⡂⣿⠀⠀⠀⠀⠀⠀⢸⣇⡀⣹⣛⣷
⠀⠀⠀⠀⠀⠸⡿⣿⠱⠃⠀⠀⠀⠀⠀⢣⢼⢻⣭⡋⢿⢠⢔⢥⡄⢿⣧⠙⠁⠀⠀⠀⠀⠀⠀⠈⢻⣷⢍⡬⢿
⠀⠀⠀⠀⠀⠠⢙⠿⠿⠶⣤⣀⣀⣀⠠⢜⡉⣆⣶⡄⡿⠫⡀⢸⢙⠁⢏⣄⢷⡶⣤⣀⣀⣀⣀⣠⡴⣿⠷⣬⣿⡑⣄⡀
⠀⠀⠀⠀⣀⡿⠿⠺⣞⢲⠨⣞⠋⠑⠂⣁⡀⡖⠎⠟⠡⡶⣠⣄⠾⣢⢈⣼⣎⣿⣟⠽⣛⣻⠙⠚⣳⣿⡿⠛⣿⢺⡌⣷⠄
⠀⠀⠀⡈⣯⡉⠁⠀⠈⠻⠦⣽⡜⣩⣄⣟⡿⢿⠟⣦⣿⣼⣯⣾⣿⣷⣯⣬⣷⠁⣽⢻⣯⣝⠚⠛⠋⠁⢀⣠⢏⣼⢁⡭⠆
⠀⠀⢀⣅⢜⠺⣇⠀⠀⠀⠀⠀⣀⢔⡿⠫⡄⠚⠣⠉⣻⢿⣯⢻⢿⣻⠙⣏⡝⣷⢋⠽⢴⡿⣟⡳⢲⣚⢟⠕⡈⠁⣾⠋
⠀⠀⠈⣳⢶⠟⢶⢿⡷⣶⣾⣭⣯⢔⡠⣣⡶⣤⠀⠸⠥⠈⠲⠺⣤⢟⣇⠰⢶⣹⣾⣦⡈⠻⢿⣻⣋⣍⣉⣂⡈⠙⠚
⠀⠀⠀⠛⢵⣤⣾⢦⣬⣾⠷⣚⡴⠋⡶⣁⠻⠔⢠⣾⠠⢼⣗⡄⣿⠛⢩⡾⢎⡣⢷⣀⣽⢶⣤⣀⣉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠶⠏⠀⠀⣻⣞⣑⢞⣼⣇⠷⣾⠃⢾⠸⣮⡇⣱⠀⠙⠶⣝⣳⠾⠾⠶⢶⢿⣬⣐⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣞⢹⣧⣮⠄⠚⠉⠁⠀⢸⣹⡿⣷⢳⠃⠈⢎⣷⣹⠸⡆⠀⠀⠀⠉⠉⠉⠉⠉⠓⠾⣯⣷⣄⠿⣆
⠀⠀⠀⠀⠀⠀⢠⣏⣹⡴⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⡴⢾⡄⠀⠈⠋⠳⣗⡙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢪⣳⣸⡃
⠀⠀⠀⠀⠀⠀⢸⠁⡁⣇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⡳⡀⠀⠀⠁⠢⡉⣑⣓⡂⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢹⠙⠆
⠀⠀⠀⠀⠀⠀⠘⣄⡗⢌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡙⠦⠀⠀⠀⠈⠋⠛⢿⢶⣾⣿⣿⠩⣳⡗⣶⡄⢀⣼⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣯⣾⣯⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⡀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⠃⠙⠋⠞⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁
⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠞⣧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⣶⢤⡿⠄⣽⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠤⠀⠀⠀⠀⠀⠀⣼⠉⠋⣷⢉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠙⣦⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⢀⢁⡟⠈⢳⣿⠈⢃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⠀⠀⠘⠧⠀⠟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠍⡻⢎⣹⣶⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢹⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢠⣤⣠⡟⡀⡀⠘⠷⡍⢀⣿⣷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣠⣞⣷⡛⣿⡷⡶⣿⡿⢿⡇⠀⠰⣀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡭⢻⠈⢛⠾⠿⠔⣾⠀⣾⢀⡀⠘⣿⢆⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣚⣛⣡⠞⠆⢰⢲⡬⣤⣿⠖⠀⠀⠹⣮⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⣉⣻⠿⢃⣼⠀⣠⣄⢠⣿⡄⠀⠀⠀⣷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡄⠀⠀⢀⢯⡾⣋⢴⣾⢡⣿⢀⡴⠶⣈⣷⣽⡦⠀⣀⣿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⣉⠁⠀⠀⠀⠀⠀⠀⠰⢁⢸⣇⣀⣠⢞⣿⡿⢡⡏⢳⣿⡎⢛⣝⠲⣟⣹⠻⠧⡘⠥⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠷⠟⢛⠿⠻⡜⢃⢨⣇⢸⡇⢷⣿⣿⣵⣾⡟⠷⣶⣿⢮⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠳⢆⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⢀⡀⠀⠀⠹⣮⢮⣯⢻⠿⠢⠟⠟⠫⡸⠋⠙⢿⠃⠹⣶⠖⢠⠁⠀⠀⠀⠀⠀⠀⢠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⠆⠀⠀⠀⠀⢀⡾⠁⠀⢠⡴⠿⠿⠷⣤⣀⠀⠈⢳⡏⢸⠀⠀⠀⠀⠀⠃⢀⠀⠈⠳⣀⣿⠘⣿⠀⠀⢀⣀⠀⠀⣰⠞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠰⠋⠀⠀⠀⠀⢻⣿⣷⡄⠀⡿⠁⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠻⣿⠀⠟⠀⠀⡎⠈⣷⠀⡇⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⠀⢀⣀⣀⣴⣿⣷⣤⣤⣤⠞⣿⠀⠀⡇⠀⡇⢀⡟⡸⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠒⠃⠀⠀⠀⠀⣿⣆⠀⠀⢀⣀⣀⣠⣾⣿⣿⠉⠉⠙⠻⣿⣿⣿⠟⠉⠉⠉⡏⠉⢹⡟⠀⣿⠀⠀⡇⢀⠇⣼⡟⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⡾⠋⠉⢉⣉⡀⠈⣿⣿⣦⡀⠉⠙⠛⢿⣿⣷⠶⠤⠀⠧⠀⣎⡀⠀⣿⠀⢠⠁⣼⣼⣯⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡤⠤⣤⣀⣹⣄⡀⠀⠀⠀⣹⠈⠢⣼⣿⠿⢿⣿⠗⠀⢸⣿⠀⠀⠀⢠⠀⠘⠛⠛⠶⣿⠘⢃⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣭⣭⣍⣛⣂⠄⠀⠈⠑⠢⠉⠒⠤⠶⠋⠀⠀⠈⠻⣄⡀⢿⠀⠀⣸⡿⠛⠒⠂⢞⠃⢸⠀⠀⠀⣿⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⠀⠀⠀⢠⣤⣤⣤⣶⣿⣶⣤⣍⡛⠦⢤⣿⣇⠀⠀⠀⣈⣀⣴⣤⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡼⢡⡎⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣡⡴⠤⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡑⠈⠀⠙⠀⠀⠀⠀⠈⠢⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠂⠀⠀⠀⠀⠀⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡘⠈⠀⠀⡴⠒⠶⢀⠇
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠈⠑⠲⠆⠀⠠⠀⠰⣄⠀⠁⢄⣀⣤⠀⠀⠀⠀⡜⠓⠆⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢠⡄⠀⣆⠀⠑⠼⠶⠤⠤⡤⢀⣤⠴⠊⠀⡀⠀⠊⠓⠠⠴⠂
⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⣠⣞⠀⠸⣄⡀⠠⠧⢄⠈⠀⠤⠄⣠⣃⠀⠀⠠⡞⢩⠢⡀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠢⣄⢈⠵⠒⠒⠚⠈⠐⠐⠊⠉⠓⠛⠉⠉⠉⠀⠀⠑⠢⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣆⣈⣇⢰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡟⠘⡇⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⠀⠀⠈⠙⠂⠀⠀⠀⠸⣅⡹⣇⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡉⢳⠀⠀⠁⠀⠀⠀⠀⠀⣀⢀⡆⠀⠰⡔⠑⣿⣭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠋⠀⠀⠀⠀⡀⢠⡾⣞⣿⠶⢿⠟⡇⠀⣀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡝⠪⠧⣨⠉⣃⠛⣸⣗⠀⠹⣗⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⡿⣛⡿⠇⡆⢉⣁⣹⡃⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡠⢠⠀⠀⣘⣾⡧⣾⣱⢧⡴⣒⣼⣾⡆⡀⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⣴⣿⠶⣾⣿⠟⢸⣀⡟⣦⣶⣈⣷⢭⣽⣌
⠀⠀⠀⠀⠀⠀⠐⠲⠄⠀⠀⠀⠀⣠⠔⠛⢀⡀⠀⠘⢮⣾⡿⠿⠸⠛⠫⡜⠘⢟⠑⣦⢀⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⢀⡞⠁⠠⠞⠋⠙⢶⣤⡀⠹⡄⠀⠀⠀⠀⡥⠀⠈⢣⣿⢸⠇⠀⠴⣄⢀⠋
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣸⣿⣷⣄⡁⠀⠀⢀⣠⣿⣄⣀⡠⣿⠀⠀⠀⠀⣼⡘⣰⠇
⠀⠀⠀⠀⠀⠀⠒⠓⠃⠀⠀⢸⣧⣀⣀⣀⣤⠴⣿⡏⠉⢙⣻⣿⣿⠉⠉⢉⠉⠹⠃⣿⠀⠀⢐⢠⢟⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⡌⠋⠀⠀⣆⢀⣻⣿⣦⣤⠀⢹⡿⠋⠁⠈⠀⣷⣄⣿⠠⢀⣾⣿⠟⠁
⠀⠀⠀⠀⢠⣶⣟⣒⣋⣁⠉⠙⠫⠐⠠⠴⠋⠀⠙⢧⡈⣯⠀⣸⡷⠒⠀⠖⠀⠀⠀⣿⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⠀⢶⣶⣶⣿⣷⣮⣽⣂⣿⣧⣤⣤⣤⣴⣶⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠿⠿⠿⠿⣿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⣩⣷⣶⣦⣤⣬⣉⠉⠋⠉⠛⠛⠛⠀⣀⢙⣃⠈⠉⢁⣀⣄⢾⣷⣌⣳⣤⠬⣭⣉⡉⡁⢀⡴⣢⡶⣴⣾⠳⣿⠒⣭⣿⣵⣶⣤⣒⣀
⠲⠶⠶⠄⠉⢉⣉⡀⠀⠘⠛⢀⣤⠶⠛⠉⠉⠉⣍⠛⠛⣿⠿⠿⠟⢿⣛⣿⣿⣿⣿⣿⣿⣯⣝⣳⣶⣯⠙⠛⠻⠷⠶⠮⢉⣭⣭⡟⢛
⠿⠿⠿⠿⠿⠿⠟⠛⠋⢠⣶⣿⣥⣤⠤⠤⠤⠶⠖⣶⣶⣻⣷⣤⣠⣽⢽⣿⠛⠠⢿⠏⠙⠂⠉⠠⠀⠀⠀⠀⠀⠀⠛⠛⡷⢠⡜
⣋⣹⡿⠟⣛⣋⣠⡤⢶⣖⣺⣿⡟⠛⠻⣶⣆⣧⠀⠉⢭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠠⠂⠀⣼⣧⣴⠼⣧⣴⡶⠛⠛⣿⣿⣦⣠⣭⡥
⣈⣁⣀⣬⣿⣿⣶⣶⡲⠛⠛⠳⠖⠺⠿⠿⣟⠁⠀⠀⠈⠝⣿⣷⣶⣄⠀⠀⠀⠀⢒⣀⣀⡀⠠⠦⠄⣀⣉⡹⠿⠯⢭⣉⣛⡻⢅⡀⠲
⠙⣿⣿⡏⠁⠀⠀⠀⠀⠙⠿⠦⠤⠤⣤⣤⡄⠀⠤⠶⠶⠿⠛⠛⠋⠉⠁⠀⠐⠿⠿⢿⣿⣀⣀⣴⣶⠿⠟⡀⣀⣤⣶⠾⠟⣁⣄⠙⣩
⠀⠻⣿⣏⠀⠀⠀⠀⣤⣤⣤⣤⣶⣶⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚⠃⠀⠸⢿⣿⣯⣥⡶⠶⠛⣛⣩⣴⠶⠛⠛⣑⣊⣥
⠀⠀⠉⠻⣷⣤⡀⠀⠈⠛⠛⢛⣛⣭⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⠛⠛⣉⣛⡿⠟⣠⡶⠒⣦⣤⣤⣦⣍⠩⢛⣭⣀⣀⣀⣈⣩⣭⣥
⠫⢵⡂⠤⣬⣿⡿⠃⠀⠀⠾⣿⣿⣭⣀⣀⣀⣀⣉⣹⣟⣿⣿⡿⠛⢋⣭⣬⡰⠶⠟⠋⠉⠛⣁⣉⣠⣴⣶⠿⣿⣿⣿⡿⠉⠉⠁⠚⠛
⣤⣤⣬⣿⡦⠀⢰⣶⠶⠒⠲⠶⠶⠤⢤⠭⢭⣭⣉⣉⣍⣉⡁⠀⣀⡬⠕⠒⠚⠻⠓⠒⠛⠛⠛⢿⣷⣶⣿⣿⣿⣿⣿⣷⣿⣿⠟⠛⢹
⠀⠈⠉⠉⠁⣀⣀⣉⡓⠂⠤⠀⠿⣦⣥⣤⠤⠤⠀⠐⢋⣡⣴⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⣛⠉⠡⠀⠐⠁
⠀⠀⠀⣠⣾⣿⣿⣿⠛⠛⠛⠛⠲⠶⠶⣶⣶⣿⣿⣿⣿⣿⠟⠛⠛⢻⣿⣶⡄⠀⠀⠀⠀⠀⠐⠶⠶⠶⠦⠀⠰⠄⠀⠹⡗⠀⠀⠴⠆
⡀⠀⠀⠙⠻⢿⣿⣷⣤⣄⣀⣀⣀⣤⣴⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠉⢛⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀
⠛⠟⠲⠀⠀⠀⠀⣈⣩⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣤⣤⣤⣭⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣁⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣧⣀⣀⣤⣤⣶⡶⠿⠛⠉⠉⠉⠉⠉⠙⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⢛⡛⣿⣿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠒⠀⠀⢲
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠿⠿⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⣿⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣹⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠴⠦⠤⠤⠤⠤⠤⠀⠤⠤⠔⠒⠺⠿⠿⢟⣿⣯⣥
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⡿⠟⠛⠛
⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣰⣾⡟⣹⣿⣿⣿⡏
⠀⠀⠈⠉⠙⠛⠻⠷⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢰⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣠⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⠿⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⣶⣶⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠿⠿⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠛⠛⠿⠷⠶⠶⠶⠾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⠿⠷⠦⠈⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⣾⡽⠛⢰⣶⠞⠛⢦⠀⢣⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⢀⣠⣤⣤⣤⣀⠈⠦⡉⠛⢦⡀⠀⠀⣿⢯⡠⣿⠴⣶⠀⠸⣧⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⡴⠋⠈⠉⠁⠈⠉⣙⣂⠈⢢⠘⣼⣆⠀⠙⠿⣽⣽⠞⠁⠀⢀⣿⢇⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢀⣴⠄⠈⠀⣉⠳⣄⢳⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⣸⣿⡱⠙⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⢀⡀⠀⠈⠛⢻⡆⡄⠀⠹⣾⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⣠⠾⠛⣡⠐⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠦⢿⣿⣿⣿⣧⣤⣴⣶⣻⡇⣬⠁⠊⠉⣾⠀⠈⢛⢷⣤⣠⣤⣶⣿⡟⠀⢼⠄⢊⣽⠁
⠀⠀⠀⠀⠀⠀⣴⠚⠥⣨⠿⠓⡖⢸⡟⠻⠿⢿⣿⣾⣿⣿⠇⠀⠙⢓⣿⢿⣆⢠⣀⠻⣞⣿⣿⣻⣟⠛⠀⢠⣀⡿⠃
⠀⠀⠀⠀⠀⣼⠃⠀⣼⠳⣾⣿⡿⠟⠁⢀⡴⣫⣿⣿⠿⠋⠀⢀⣤⡞⠁⣼⣾⡇⢿⣧⣙⠙⢟⣁⣤⣤⡾⠖⠋⠀⠀⢀⣀⣤⣤⡤⢄⣀
⠀⠀⠀⠀⠠⣏⡁⠠⣿⡀⠀⠀⢀⣠⡴⣫⣾⡿⠟⢁⡴⠀⢀⡿⠁⠇⢠⣿⣿⡟⡌⠛⠻⣷⣄⠉⢩⣓⠶⠶⠶⠒⠛⠙⠉⠉⢽⣿⣿⣾⣽⣆
⠀⠀⠀⠀⠀⢿⡁⠐⠻⣿⣟⠉⠉⠁⣸⢿⣋⡄⣰⣟⣀⣤⢃⡆⠀⢀⠋⡟⡼⠧⢴⡀⠀⠈⣪⡻⢶⡾⢟⡿⠿⠿⣫⡥⠖⣼⣧⠬⢽⣢⢽⣿⣇
⠀⠀⠀⠀⠀⠈⢷⣴⢀⠛⣿⡷⣤⣴⠷⣷⣿⣿⠿⣿⣿⣏⢸⣶⡄⠀⠀⡸⠁⠀⠀⢻⡀⠀⠻⣟⣿⡾⣧⡤⠂⠀⠀⠘⢿⣇⣴⣲⢾⣧⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠉⣉⣭⡿⣿⣯⡷⣮⡿⠄⠫⠽⡛⣿⣿⠀⠀⡇⠀⠀⠀⠈⡇⣆⠀⠘⣿⣿⡟⢀⡴⠿⣿⣶⣔⢻⣻⣿⡿⠯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡹⠿⠟⣩⣥⣶⣶⡿⠶⣄⠂⠀⠣⣹⣷⡄⣳⡀⠀⠀⠀⣿⣿⠀⠀⠘⢻⠀⣜⢳⣤⣾⣿⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠞⠁⣠⣾⣿⡻⠁⠹⢧⠀⢸⣏⠄⠀⣄⣿⣧⣔⢍⡒⠤⣀⣟⣿⡆⢰⣿⡏⠀⢹⣧⣼⣍⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣯⡇⠀⢠⠏⢿⣄⠁⣀⣀⣼⣷⣾⠁⠆⣰⢨⣟⣹⠻⣿⣌⠓⢬⡙⢿⣧⡈⠉⠀⣠⣿⣦⣷
⠀⠀⠀⠀⠀⠀⠀⢸⢹⠁⢀⡞⠀⠈⠻⣟⠿⡟⠉⡫⢈⢠⣧⣼⣿⣍⡓⣶⡉⣿⣧⡀⢉⢿⣿⡿⠶⣾⡿⠀⢱⡏
⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⢺⣳⠀⠀⠀⠈⢷⣈⣯⣽⡷⣾⠿⠶⠚⠛⢟⡢⣼⡏⢡⠆⠘⣧⠙⢿⡜⠃⣴⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠸⣏⣧⡀⠀⠀⠀⠀⠀⢠⡾⠃⢀⣀⠀⠀⠀⠈⣽⣷⣾⢳⢊⣿⡇⡄⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣈⠫⢷⢤⡀⠀⢀⡴⣻⡷⠐⠰⢦⡼⠶⣬⡆⢹⣾⠹⣏⣫⣸⠃⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣭⣉⣉⣩⣴⣿⠇⢅⣾⠋⠀⠀⠀⢹⡘⣟⡇⡿⣣⠿⢸⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢿⣿⠠⣧⡽⣆⠀⠀⠀⢸⡇⠛⣿⢿⢃⣴⢋⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠁⣕⡿⢻⠲⣖⣾⠃⢈⣿⣤⡞⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣻⢿⣶⣾⣿⡿⠀⡜⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⠟⠁⣰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠖⣡⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⣭⠽⠯⠿⠶⠖⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⢀⠤⠀⠠⢤⡈⣧⡀⠀⣀
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⠲⡀⠀⢀⠀⡴⡾⢉⣧⣟⢵⡱⡤⣾⠾⣀⠀⠀⠀⠀⣀⡔⠂⣄⣶
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠑⢿⢴⡞⡼⡏⣼⡸⡜⡟⢸⠟⠁⠀⠀⣈⠀⢈⢶⣿⡿⢄⡀
⠀⠱⢅⣀⣀⣀⣀⣀⣀⠠⣥⠜⡶⠀⠀⠈⠉⠁⠛⠘⠿⠇⠓⠊⠹⠀⠀⠔⠁⠀⠉⠀⠤⠭⠤⠤⠤⠙⢲
⠀⣿⣷⣾⣶⢾⣯⣿⠶⣲⣗⡿⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢘⡉⠒⠡⠌⠣⠎⠳⠉⠞⢳⡻
⠀⠳⡿⠓⠛⠪⠭⠿⠿⠿⣿⠇⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠏⠛⠛⠛⠛⠭⠭⠭⠽⠯⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢢⠅⠉⠐⠢⠤⠤⠒⡩⠡⢀⠄⢱⣀⣀
⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⢎⠉⢇⠀⠀⠤⠀⠀⠁⢉⢀⣀⠁⠤⠂⣠⠞⣠⠛
⠀⠀⣒⣓⣒⣒⣀⣀⡈⠉⢭⠭⢭⣭⣭⣭⣭⢭⠄⠀⠀⣝⣚⡳⢶⣖⣒⣒⣒⣒⣲⣦⣶⣶⢟⣒⡽⡄
⠀⠀⠖⢒⣟⣛⣿⡛⠻⠒⠛⠲⠒⠋⠍⠍⠁⠬⠇⠀⠀⠀⠣⠌⣉⣛⣁⣵⣓⣚⣛⣻⣛⠫⠽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡰⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡀⠀⠀⠀⠀⠀⣠⠒⢚⢙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢹
⠀⠰⠊⢰⡓⢤⡀⠀⠀⠀⠀⡠⣬⡄⠠⡊⡞⠀⠀⢀⣀⣀⢠⡝⣿⣥⣄⡀⠀⠀⢀⠤⣄⠀⡴⢾⣿⡷⠾
⠠⣝⡺⠒⠺⣛⡽⢄⠀⡰⠂⠓⠐⠓⢢⡸⡇⠀⠀⣿⠦⠤⠤⠩⠥⠤⠤⢿⠇⠀⣵⣁⠙⡇⢣⣷⡟⠠⠄
⠣⣤⣀⣉⢉⣵⡤⠎⠀⢗⠚⠂⠑⢊⣾⣠⢹⡆⠀⠈⣥⠔⢲⣐⠒⠂⣌⡏⠀⠀⠀⢀⣴⣡⡞⣁⠁
⠀⠰⣞⡡⢏⡞⣹⠁⠀⠈⢍⠁⠛⠉⠈⡠⠊⠀⠀⠀⢫⠌⢹⠉⢙⠀⣸⠀⠀⢸⠶⠈⠛⠏⠅⢚⡷⠐⠄
⠀⠀⠹⣿⣷⠾⡇⠀⠀⠀⠀⠈⠈⣉⡁⠀⠀⠀⠀⠀⠘⠀⣕⠈⠄⠀⠇⠀⠀⠈⠇⠒⠒⠒⠒⡹⠷⠤⠃
⠀⠀⠀⠡⡀⡸⠁⠀⠀⠀⠠⡉⠀⠈⠉⡹⠀⠀⠀⠀⠀⢠⣆⡖⢺⡞⠀⠀⠀⣤⠚⠓⠆⠲⠚⠙⢓⡆