Birthday wish Emojis & Symbols

⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⢸⡇⠐⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠀⢂⢸⡇
⠀⠀⠀⢸⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⡇
⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡇
⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⡇
⠀⠀⠀⢸⡇⡁⠀⠀⠀⠀⡇⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠠⠄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢠⢸⡇
⠀⠀⠀⢸⡇⠄⠀⠀⠀⢸⠁⠘⠁⠊⡏⡼⢨⠴⢃⠆⠃⢘⠀⠀⠀⠀⡿⠀⡆⠀⠃⢰⢀⡇⠆⡀⠍⡐⢰⢠⠁⠂⠀⠀⠰⢸⡇
⠀⠀⠀⢸⡇⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⡏⠁⢸⠈⠀⠀⡎⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘⢸⡇
⠀⠀⠀⢸⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⡇
⠀⣰⡆⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⢀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⢰⣆
⣰⣿⡇⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠁⠈⠋⠈⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⡇⢸⣿
⠙⣻⣿⣿⡁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⣿⣿⣟
⡇⠉⣩⣼⡿⠄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠐⢿⣧⣍⠉
⢁⠘⠿⢿⣵⣧⠐⡉⠙⠷⠾⡇⠀⠀⠀⠀⣠⡄⢀⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡀⢠⣄⠀⠀⠀⠀⢸⠷⠼⠋⢉⠀⣼⣮⡿⠿⠧
⠂⠀⠀⢉⣈⣠⣼⠿⢦⡀⠀⢀⣀⢀⣾⡀⣿⣧⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣿⢀⣷⡀⣀⡀⠀⢀⡴⠾⣧⣄⣁⡉
⡴⢊⠉⠁⣣⣾⡇⢀⣠⣷⡆⠙⣿⢸⣿⡇⠙⠏⢛⣡⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣬⡛⠹⠋⢸⣿⡇⣿⠋⢰⣾⣄⠀⢸⣷⣜⠈⠙⡑
⣙⠻⣆⡴⡿⠌⡵⡫⢼⣿⡘⣆⠘⠀⠙⠁⡼⣋⣿⣟⡋⠉⠁⠀⠀⠀⣤⡈⢩⣿⣿⣿⣙⢧⠈⠋⠀⠁⡰⠣⣿⡯⢙⢮⠩⠿⣦⣠⠟
⣟⠁⠻⢭⣔⣹⡧⡈⢺⡇⠀⠈⢦⠀⣰⠖⣾⠟⠛⣿⠛⠳⡀⠀⠀⣤⡹⣿⣿⣿⠟⠻⠟⠃⠳⣄⠀⣴⣁⠀⢸⡗⢉⢼⣏⣢⡽⠟⠉
⣿⣄⣀⣼⠋⠼⣿⠾⠼⠗⠚⠶⣾⣦⣽⣿⣍⣀⡀⢽⣴⡲⢒⠤⡀⠸⣿⢘⣯⡥⠂⠀⢀⣨⣿⣯⣶⣷⠶⠛⠺⡧⠷⣿⠛⠙⣧⣀⣠
⠊⠻⣇⣾⣦⡶⢇⠀⣀⣸⣟⡉⠈⣷⣜⣿⣾⣿⣇⠸⡊⠻⣾⡉⣼⣆⣘⣭⡍⣄⣘⣿⡿⣮⣜⡕⡾⠁⢉⣻⣇⣀⠀⡸⢺⣴⣷⣸⠟
⣠⢞⣻⠇⣹⡷⠛⢻⣿⡿⣿⣿⣷⣾⣿⣯⡻⠟⠉⠀⠷⢶⡞⣻⠁⢀⣱⡬⢷⣴⣪⣭⣿⣷⢍⡻⡇⠀⢸⣿⢿⣿⡟⠛⢶⣇⠼⣟⡳
⣻⣿⢓⣕⣽⡇⠀⠙⣟⣿⣿⠑⢟⣹⣿⣏⣯⡴⠒⣦⣸⣾⠒⢻⣿⣿⣿⣦⠀⣸⣿⣷⠊⠀⠀⢿⡏⠳⠋⣿⣿⣻⠋⠀⢸⣦⣪⡘⣿
⠻⠿⡿⡛⣽⣿⣆⢻⡏⠋⠁⢀⡾⠋⢱⡿⠛⠁⢈⡝⡉⣘⣧⡀⢙⡿⣿⠷⠻⣤⠟⠁⠀⢠⡀⠀⠑⢲⡀⠈⠙⢸⡟⣰⣿⣯⢻⣿⠿
⡶⣶⢾⠿⠿⡿⢿⠿⢷⣾⣿⣿⣷⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣿⣿⣶⣶⣿⣿⣶⣶⣾⢿⡿⣷⣾⡿⣿⡿⣿⡿⡷⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢀⣴⢃⣄⣀⣀⣀⣀⠀⣄⢲⣄⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣴⢀⣼⣷⠾⣟⣛⡛⠙⠛⠚⠛⠙⣛⣛⡿⢦⣿⣄⢰⣄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣼⡿⠿⠟⠶⠶⠶⠍⠙⠃⠀⠀⠀⠛⠉⠱⠶⠶⠞⠿⠷⣿⣄⢻⡆
⠀⠀⠀⠀⠀⢀⢀⣀⣤⣷⡿⣤⣭⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢫⣍⡻⣬⣷⣄⡀⡀
⠀⠀⠀⢀⡄⠒⠘⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃⠂⢠⡀
⠀⠀⠀⢉⣴⡅⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣦⡉
⠀⠀⠀⠘⣛⣱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣎⣻⠃
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢠⡚⡇⡆⡤⣄⡤⣤⢤⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠋⠻⠂⠹⠊⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⢀⣿⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢠⠠⢐⠦⣀⣆⣄⣠⠀⠀⠀⠀⠀⠀⣦⠈⣷⡀
⠀⠀⠐⢦⣿⣴⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠸⣦⣿⡴⠂
⠀⠀⠠⣤⣍⡻⣰⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣆⢟⣩⣤⠄
⠀⠀⠀⠀⠉⠙⢿⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢰⡿⠋⠉
⠀⠀⠀⠀⠈⠙⠾⣷⠃⢻⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡟⠘⣾⠷⠋⠁
⠀⠀⠀⠀⠀⠻⢷⣬⣄⣞⢰⣦⣀⡞⠉⣻⠿⠦⡀⠀⠀⠀⠀⠀⠀⢀⠴⠿⡟⠉⢳⣀⣴⡆⣻⣠⣥⠶⠛
⠀⠀⠀⠀⠀⠀⢰⡦⠾⢻⣿⠻⣦⡍⣲⣆⠀⢀⢷⢠⠟⡝⢯⠻⡐⡦⡀⠀⣰⣖⢩⣵⠟⣿⡟⢷⢴⡆
⠀⠀⠀⠀⠀⠀⠈⢷⣵⡀⠙⣷⠜⠉⠀⠙⠁⠈⠻⣁⣔⣴⣦⣣⣀⠟⠁⠈⠋⠀⠉⠣⣾⢋⢠⣮⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢻⡁⠳⣄⢀⣥⠤⠂⠤⢟⠉⣉⣻⡿⡿⠤⠀⠤⣤⡀⢠⠖⢈⡟⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⢀⣈⠀⠈⠀⠂⠀⡰⠛⡩⢏⠛⢆⠀⠀⠀⠁⢐⣁⡀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠒⠀⠀⠉⠉⠉⠀⠀⠉⠉⠋⠠⠀⠂⡀
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣟⣿⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⣠⣾⣶⣿⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⢛⠉⡉⢀⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠿⠿⠿⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣀⣀⣸⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣽⠀⣬⠀⣤⡄⡴⣶⣄⡴⣶⣄⣦⣀⣶⠄⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒⡿⡻⣿⠛⢿⢋⠙⠿⢋⠙⠿⡛⡟⡙⣿⢿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣴⢿⡇⣿⣿⠟⣿⣿⠇⢹⣿⠏⠰⣿⣿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⡁⠀⠋⡄⢸⠀⢀⣤⠀⢀⣼⠆⢀⣼⣃⠀⢈⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠛⠻⠘⠃⠂⠀⠀⠃⠀⠰⢟⠁⠀⠀⢨⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣿⣤⣤⣧⣼⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⡗⢻⣿⣿⣿
⠀⠀⠀⣶⣇⣆⠀⠰⠀⠀⠶⠦⣶⡴⢦⣆⡆⠰⣦⡛⢰⡰⡄⣢⣡⡐⠂⠀⠀⣿⣿⣿⠃⠸⢻⣿⣛⣿⣿⡍⣿⠹⢻⡟⠿⣻⣏⠙⣤⡟⢟⣿⠿⠟⢯⣿⣿
⠀⠀⠀⣿⡤⡟⠀⢭⡆⡶⠶⠄⣿⢨⡅⣿⢇⡤⢪⣅⠠⠿⡄⠸⣧⠀⠀⠀⠀⣿⣿⣿⠀⢻⢰⣷⠆⣿⢉⢉⡫⠘⡒⣿⠀⠹⣋⢕⢾⡗⣘⢻⡗⠘⣾⣿⣿
⠀⠀⠀⠭⠟⠻⡆⣻⡇⣻⢞⠁⣿⣼⡯⡿⢰⠆⠀⢸⣤⣴⣷⠀⣿⠀⠀⠀⠀⣿⣿⣯⣂⣤⣄⢿⠀⣿⢀⣠⣷⠀⠇⣖⣸⠈⣿⣿⡆⡇⠙⠸⣿⠀⣿⣿⣿
⠀⠀⠀⣭⣦⢾⠇⢺⣯⣿⢹⢆⢙⣟⡃⠶⢸⣲⣶⠞⣝⡆⠿⡆⢛⡄⠀⠀⠀⣿⣿⣿⡂⢛⢡⣾⠁⠙⢰⣧⡿⡆⢰⣿⣹⢠⣿⠛⣴⡻⣹⣠⣿⠤⢿⣿⣿
⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠉⠁⢀⣤⡪⠉⠀⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⡿⠻⣿⣾⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⣠⣶⣿⣿⣿⡆⠈⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⠟⠁⠀⠀⠀⢻⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣿⠗⠀⢀⡀⢿⣿⣿⣿⣿⡇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⣼⣿⡿⣷⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢿⣿⣿⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⡏⢰⠆⠠⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠘⣿⠀⡇⠋⠀⠀⠀⠀⢀⣴⣿⠟⢛⣉⡙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⢿⠘⠁⢀⡏⠀⡾⣰⣿⠟⠠⠞⠛⠉⠛⠆⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠆⠀⢀⣤⡀⠀⠀⠀⣼⠁⢰⠇⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠏⢠⣿⠀⠀⢿⡅⢹⠀⣀⣰⡏⢀⡿⠀⠛⠀⢸⠇⠀⠀⠉⠀⠀⠀⠀⣼⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢀⣾⠷⣄⠐⠈⠛⢾⡌⠀⣿⠋⣹⣣⣦⠀⣀⡿⢀⣤⡀⢀⠀⣠⠀⢠⡟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⡇⠘⠃⠀⢹⣆⡇⢀⠇⡿⢰⡟⠀⣿⢣⡟⡼⢩⡇⣯⢾⣡⣇⡴⣿⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣿⠁⣴⠗⠀⣸⠿⣇⡜⢸⢣⢸⣇⠀⠋⢸⡇⠷⠁⠉⠀⡈⠀⠉⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣀⣠⡟⠀⠉⠀⠘⠃⠀⠙⠂⡀⠘⠇⠀⠀⢀⣀⠀⡴⠚⢹⠇⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⣉⠉⠀⣄⠘⣿⡄⠀⣴⡆⠀⣿⠀⠀⢀⢠⡏⠙⠸⣅⣴⠟⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⣿⠀⣿⡇⡄⢻⡇⢀⡏⣴⢰⡟⠀⣿⡄⣀⣀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⢸⣿⠀⢹⣷⡇⠘⣷⠚⡇⢿⠾⣅⢄⡼⣿⠉⠹⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢸⣿⠀⣾⠘⠆⡼⢹⠀⠀⠀⠀⣰⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢀⡏⠀⠀⠑⠋⢀⡀⠀⢠⡏⠀⣠⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠞⠁⢀⡆⣠⠀⠈⠀⠀⠈⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡏⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢷⣦⠀⠀⣠⡾⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣼⠏⠀⣰⡟⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⡄⠐⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡴⢶⣿⠅⣠⡾⢳⡆⢀⣾⡗⢺⡆⣰⣿⠖⣷⠐⣿⡟⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣼⡇⢰⡏⡰⣿⢀⣼⣯⣰⡿⢡⣿⣥⣼⠏⢰⡟⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘⢧⠀⠀⠻⢧⠈⠉⠀⠉⢹⡏⠈⠉⠀⣾⠃⠉⠁⠀⣈⣉⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢿⠁⠀⠀⠸⡏⠀⠀⠀⣿⣭⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠀⢀⣤⠀⠀⣀⠀⠀⣠⠀⠀⠀⠀⠀⠂⢿⡧
⠀⠀⠀⠀⢀⣠⣴⣶⡶⠶⢤⠀⠚⢛⡛⠛⠒⠶⠶⢤⣾⣏⣴⣟⣁⣀⣀⣿⠆⢠⡿⠀⠀⠀⠆
⠀⠀⠀⠀⠸⣏⣰⣟⣀⣠⡼⢀⣀⡘⠃⣴⡦⠀⠀⣾⠃⣼⠏⣉⣭⡛⢋⣡⣤⡿⠁⠀⣠⣤⣤⠀⢀⣴⠆⣠⡄
⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⡆⢨⡟⠁⣠⢟⣿⠂⣸⠏⢰⣿⠞⣽⠋⣼⠋⢁⣿⠁⢀⣼⠟⣠⡟⠀⣾⠃⣴⡟
⠀⠀⠀⠀⠠⣿⣅⣠⣤⠞⠁⠺⠷⠚⠁⢿⡵⢾⡟⠀⢼⠃⠸⠧⠔⠷⠶⠛⠳⠶⠟⠻⠖⠹⠷⠚⠿⢎⡿⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⡾⠃⠀⣈⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⣻⣿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠂⠀⠀⠀⠀⠀⠀⠀⠳⣶⣤⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⡄⠀⠀⠀⢂⠀⠀⡇⠀⠠⠇⠀⡐⠀⠀⠀⠀⣀⣠⠤⠰⠚⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣛⣯⢶⣿⣛⣿⠀⠀⠀⡐⡀⣀⢀⠂⢂⡄⢀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⡜⣿⣟⣵⠾⠛⠉⠀⠀⠀⠈⠋⠂⠛⠈⠈⠛⠛⠚⠈⠁⠀⠀⠀⡆⡆⢲⢰⢐⡂⡄⠀⡆⠂
⠀⠀⠀⠀⠀⠀⢀⢰⡄⡷⠼⠸⠇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠃⠐⠐⠘⠁⠃⠐⠁
⠀⠀⠀⢀⡠⠆⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠁⠐
⠀⠀⠀⠀⠀⠀⠠⢁⠠⠌⠀⠀⠀⠠⠦⠭⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠈⢤⡀⣤⢠⢀⣤⢠⢩⠭⢭⡿⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠉⠉⢨⣬⣭⡉⠃⠀⠀⠀⠀⠨⠄⠠⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠐⠁⣀⠀⠀⠀⢀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠉⡋⢀⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡀⠀⠀⡶⣤⢄⣀⣀⣤⠄⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠤⠼⠽⠀⠀⠀⠀⠀⠀⠠⠄⠂⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⡄⠒⠒⢄⣀⡀⠀⢂⠀⠀⠀⢀⣐⣀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠁⠀⠀⠋⠟⠒⠀⠈⠃⢀⡀⠀⠉⢹⠛⠥⣀⣀⣀⣀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢶⣤⡈⠍⠓⠚⠒⢀⡀⣉⢉⠁⠀⠄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⣰⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢉⠲⣄⠀⠀⠀⠬⠟⢎⣀⠀⢀⠅
⠀⠀⠀⢀⡞⠀⠀⠀⢀⠇⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡼⠀⠀⠀⢀⣌⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠤⣀
⠀⠀⠀⣁⠀⠀⡀⠈⠀⠀⢠⠃⢰⠁⡞⠀⡏⢀⠇⣼⠀⡝⢸⠁⡞⠀⠀⠀⠠⢀⡇⠁⢄⣀⡀⢀⡠⠂⠂
⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠁⢠⠃⠀⠀⠀⠰⠃⠀⠀⠀⠁⡸⢸⠐⠖⠘⠍⠉
⠀⠀⣼⢠⠄⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡠⠂⢠⠃⠙
⠀⠀⢉⡞⠀⠀⡴⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢐⠀⠀⡞⠀⡀⡀
⠀⠀⢸⠁⢤⡀⠀⠠⠀⠀⠀⣸⠀⡼⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠹⠯
⠀⣠⠃⠆⠀⡈⢠⠆⢰⠐⢢⠇⢰⠗⡴⢀⠆⣸⠁⡔⢠⠆⢰⠂⡖⠀⠀⢠⠀⠀⢠
⠈⠁⠉⢉⡉⠀⠈⠁⠈⠀⠈⠀⠈⠀⠁⠈⠁⠈⠀⠁⠈⠁⠈⢠⠃⠀⠀⠀⡄⠀⠀⠁⠈
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠥
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣒⢦⣤⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⣠⣐⠀⠀⠠⠀⢀⠀⠄⠀⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠀⠀⠆
⠀⠁⠀⠀⠊⡀⢀⠈⠀⠀⠱⡞⢁⠁⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢠⣞⣁⡉⠀⠘⠄⠀⠸⡀⠀⠀⠁⠀⢀⠀⠀⢀⡠⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠦
⠀⠠⠀⠀⠀⣀⠀⠀⠀⢀⠀⠠⣈⠤⡔⠀⢠⠀⠈⠀⡀⠀⠀⠈⣴⣣⠄⡈⠅⠀⠈⡀⢀⠀⠀⠀⠄⢰⠀⠀⡄⠈⠀⣀⠀⢂⠀⠀⢀⠀⣀⠀⢀⠀⠄
⠀⡀⠀⠀⠀⠈⠁⠓⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢌⡑⢸⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠈⠁⡋⠡⠀⠂⠁⠀⠀⠀⠄⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠐⢄⡀⠀⠀⣀⠒⠀⠀⠀⡄⠤⡀⠀⠀⠐⢀⠀⢣⡀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠐
⠀⡀⠁⠀⠦⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡆⠈⠁⠠⠤⠀⠀⠁⠠⠀⠀⠀⠂⠀⠔⠀⠀⠈⠁⠀⠂⠀⠀⡀⢀⠀⠀⠠⠂⠀⠂⠀⠀⡀
⠀⠁⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⠈⠀⠠⠀⠀⠐⠀⠄⠀⢀⡀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⡀⠀⣤⣤⡤⠤
⠀⠀⢄⠀⠀⠂⠠⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⡄⠿⠀⠂⠐⠀⠀⠀⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡁⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢤⠀⠀⠀⠀⢠⡆⠀⣤⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⣿⣤⡅⠐⣋⣳⡀⣶⠶⣦⢰⠶⢦⡀⢦⠀⡴⠀⠀⠩⣅⣼⠀⢲⠀⣶⠶⠆⢹⡏⠁⣿⠶⣄⢠⠶⢼⠳⣋⣳⡄⢶⡀⢰⠄
⠀⠀⠀⠀⠀⠀⡼⠀⢽⠸⢥⠼⠇⣷⢤⠞⢸⡤⠼⠃⠘⣶⠁⠀⠀⢠⣇⠀⠧⠾⠄⣷⠀⠀⠸⣧⠀⠷⠀⢿⠡⡤⢾⠘⢧⠼⠧⠀⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⠆⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋


⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠤⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡄⢈⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠠⠊⣄⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠄⠀⡄
⠀⠀⠈⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠢⠐⠃⠀⠁⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⡀⠀⠀⠀⠠⠑⢄⡀⠁⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠇⠀⢀⠂⠒⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⢀⠐⢀⠀⠜⠄⠂⠀⠤⠀⠀⠀⠉⠁⠀⠀⠀⠠
⠀⠀⠄⠈⠉⠈⢠⠈⠉⠀⠀⠀⠀⠀⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡀⠀⣀⠀⠈⠁⠀⢀⣄⣉⣠⠠⠀⠀⠀⡀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈
⠠⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠘⡀⠀⠐⠀⠇⠀⠀⠀⠀⠰⠐⠀⠀⢃⡀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠂⠀⠀⠀⢠⡤⠦
⠀⠀⣄⠀⠀⠀⢀⠠⠐⠀⡀⠀⠈⡖⠀⠀⠀⢀⡀⢁⠂⠀⢄⡈⠠⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠁⠀⠀⠀⢀
⠀⣀⠀⠄⠀⠀⠀⣀⠀⢰⠀⠀⡞⠀⡀⠀⡈⢭⡬⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⠀⠀⠐⠀⡀⠀⠀⡀⢀
⠈⠧⠁⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠆⠤⠤⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠰⠈⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠘⡇⠀⠀⠀⠀⠀⠀⡾⠈⣧⠀⠀⠀⠀⠀⠀⠀⡾⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⡿⠀⠀⠀⠀⠀⠸⡇⠀⣽⠀⠀⠀⠀⠀⠀⠰⡇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣦⠀⠀⠀⣿⠀⠀⠀⢠⣾⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣧⣀⣀⣸⣿⣿⣁⣀⣠⣿⣀⣀⣀⣸⣿⣿⣀⣀⣀⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣄⡀⠀⠀⣀⣄⡀⠀⠀⢀⣴⠶⢦⡀⠀⢠⡾⣶⠀⠀⣰⠶⣦⠀⠀⣠⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡼⠋⠈⣿⠀⢠⡟⠈⢷⡀⠀⣾⠃⠀⠈⢿⣄⣾⠁⢸⡇⠀⣿⠀⠹⣦⣀⡿⠹⣦⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣄⣼⠃⠀⢸⡇⠀⣿⠀⠀⠀⠀⠉⠁⠀⠈⣿⢰⡏⠀⠀⠈⠉⠁⠀⠈⠻⠞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢷⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣶⢠⣄⣤⢤⣠⢤⣤⣠⠄⢰⢤⣸⣠⡤⣦⢰⢤⣀⣤⡆⣤⣤⣄⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠋⠛⠋⠹⠛⠰⠏⠀⠘⠛⠉⠉⠀⠙⠘⠈⠉⠛⠉⠛⠃⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⡠⠀⡄⡦⡄⢀⡀⢀⡀⡀⢠⡄⡆⠀⢤⠆⣠⠄⢰⢀⡤⢤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⢰⠏⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡥⣶⠀⣴⣦⠀⣶⠖⢢⣠⡾⠳⠀⠠⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⢸⡇⣿⠸⣧⠈⠃⣿⢰⣿⠻⣇⡁⠀⢀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⠄⠀⠈⠁⠀⡇⠀⣠⢄⠀⠀⠀⠈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣶⢠⡶⡆⢰⡆⠠⡆⢿⣆⣀⠀⠀⠀⠃⠀⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⠸⣇⡉⠘⠧⢸⡇⠈⠈⣿⠀⠀⠀⣰⠶⣿⠃⣰⠖⣶⢰⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣧⠀⠀⢣⣀⢿⡀⢿⡀⣿⠸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠃⠀⠀⠀⠂⠀⠀⠀⢠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⡁⣤⠄⠈⠀⠁⠀⣾⠀⠀⠀⠀⠀⣾⢡⢰⠁⠄⠀⠀⠀⠢⠞⣱⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⡇⠻⢧⣀⠀⠀⠀⣿⠀⣺⠀⢸⠂⣿⡄⢸⡦⠀⠀⢀⡾⡶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠘⠧⠀⠐⢻⡆⠀⠀⢻⠁⢻⡄⢾⠂⣿⠀⢸⡇⠀⠀⠸⣇⡈⠂⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⣡⢄⠀⠞⠀⠀⠀⠘⠃⠙⠂⠈⠓⠀⠀⠀⠈⠀⠀⡿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠢⡄⠠⠴⠦⢄⠀⠀⢰⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡘⠁⠀⠀⠀⠁⠀⢸⡇⠁⣦⠀⣦⢰⢀⢶⡆⠀⠀⣾⠃⣶⢰⣆⡴⡦⢠⠶⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠠⢼⡗⠊⢿⠐⣿⠸⠏⢸⣇⠀⠘⣧⡀⣿⠘⠟⢸⡇⢿⠀⢿⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⢄⡀⠀⠀⠀⠀⣸⠇⢠⠖⡄⠉⠀⢀⠤⠅⠀⠀⠀⡄⠀⢀⠠⠀⢁⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⢹⠀⠀⠀⣿⠀⢂⡤⠀⠃⠀⠀⠀⠀⢰⡗⠀⣀⠀⠀⠀⠃⠀⠀⠁⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⠀⣤⣄⣿⡌⢀⣤⡄⣿⣀⡘⣧⣀⡀⠀⣤⣄⡄⢸⡇⠀⣍⠀⢀⣄⡀⢠⡀⢀⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠉⢿⠀⢸⡇⢸⡇⢸⡇⢸⡇⠀⣿⠀⣿⠙⢧⢾⡇⢩⡟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠔⠉⠓⠊⠘⠆⠈⠓⠀⠙⠐⠋⠀⠘⢷⡜⠓⠘⠇⠘⢧⡀⠻⠆⠙⠷⠂⠈⠁⠘⠗⠁⠘⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠘⡆⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡄⠀⠀⠀⠀⠀⠀⠀⠹⣼⣥⠏⠀⠀⠀⠀⡰⠁⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢻⠀⠀⠀⠀⠀⠀⠀⢰⣏⣽⠀⠀⠀⠀⠸⣧⡆⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⠀⠀⠀⠀⠀⣽⣷⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⣀⣀⡀⠀⢸⢗⣻⠀⠀⠀⠀⢰⣟⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⢾⣿⣬⡿⢛⣿⣭⣼⣷⠾⢿⣦⣞⢻⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣷⣶⠚⢻⣿⣿⣇⠀⠉⠉⠁⠘⠶⠭⠥⠞⠀⠀⣭⡹⣿⠿⣷⣿⣷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠿⠋⠀⠀⣷⢬⡽⢧⣄⠀⠀⠠⣶⠀⠀⠀⣠⣾⠻⣿⣿⣆⠀⠁⠀⢀⣿⣿⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡄⠀⠀⠀⢼⡻⠶⣖⣯⠏⠀⠀⠀⠀⠀⠀⠀⠳⣝⣛⣶⣞⣻⠆⠀⠀⠀⠻⠿⠿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⣶⣳⣆⠈⠉⠉⠀⠀⠀⣴⢻⣯⣷⡄⠀⠀⠀⠉⠉⠉⠁⣰⣲⣦⣄⠘⠗⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⣤⣄⣘⠿⣛⡧⠀⠀⠰⣶⠀⠀⢿⡿⠿⣫⠇⠀⠀⣀⡀⠀⠀⢸⣉⣻⣿⡿⠀⣀⣀⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣼⣿⣿⣿⣿⡇⠀⠀⠀⣰⣶⡄⠀⠀⠈⠉⠉⠁⠀⠀⠀⠙⠃⠀⠀⠀⠈⠉⣀⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣞⣻⣴⡯⠽⣿⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⠀⢠⣶⠀⠀⣸⣿⣧⣰⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢺⣩⠟⣹⠛⣶⣿⣿⣿⣿⣧⠀⣸⣿⣿⣿⣿⠀⠀⣿⣷⣶⡄⠀⢰⣿⣿⣄⣸⣿⣦⣴⣿⣿⣿⣿⣿⣿⣷⣼⠿⣲⢦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⣿⣾⢷
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠈⠙⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⡿⣿⣿⣿⣿⣿⡿⠛⠻⡟⠋⠉⠉⢻⣯⣿⣤⣯⢿⣇
⠀⠀⠀⠀⠀⠸⣿⣆⠈⠙⢧⣀⠴⢦⡿⢷⣴⣿⣿⣿⣿⡿⢿⣿⠁⠀⠙⣿⣿⡿⠛⢦⣎⡴⠻⣿⠛⠛⢶⣤⣧⡀⠀⢺⣿⠋⠙⢿⣿⣼⡏
⠀⠀⠀⠀⠀⠀⠙⣿⢷⣄⣰⠏⠳⢾⣷⣄⠻⣿⣿⣿⣿⣧⣾⣿⣷⣤⣼⣿⣿⡋⡠⢻⠿⡍⣸⣿⣄⣀⡼⢋⣴⠍⠙⠉⠙⠀⣀⡴⢪⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡛⠶⢦⣄⣈⠁⠀⠈⠉⡉⠁⠈⠻⠿⠟⠉⠛⠛⣛⢿⣷⣾⣴⣾⠟⠁⠀⠀⠀⠛⢋⣀⣤⠴⠖⣋⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣌⣉⠛⠲⢾⣋⡉⢙⣦⣀⣀⣀⣀⣀⣀⣉⣀⣀⣈⣥⣤⣤⡴⠶⠶⠚⢛⣉⣩⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠿⠭⣭⣤⣤⣄⣀⣀⣀⣉⣉⣉⣠⣤⣤⣤⠤⠶⠶⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠰⠀⠠⠀⠀⠀⠀⠤⠘⠠⡔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠐⠀⠀⠀⡃⠀⠐⢂⠐⣁⠂⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡅⠐⠀⠢⠂⡀⠈⠀⣀⡀⠂⠀⠀⠰⢐⠮⣀⠁⠀⢀⠂⠈⠀⠀⠀⠀⠐⠒⠀⠂⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠴⠦⡤⠀⠪⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠊⠀⠠⠂⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠲⡀⣂⠁⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⡂⢲⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣰⡴⠤⠀⠀⠀⠀⠀⠀⠈⠁⠲⠆⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠢⠁⠀⠀⠀⠀⠀⠀⠂⢰⢰⡀⠒⠀⠀⠢⠀⡄⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⡄⠠⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⠸⡀⠀⠀⠀⡀⢀⢥⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠄⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠂⠀⠀⠀⠈⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠆⠀⣀⠀⠀⠒⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠴⠟⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⢀⠉⠀⠰⠠⢂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠈⠀⠀⠢⠐⠤⠈⠋⠀⠤⣄⡠⠰⢎⣱⠀⠄⠀⠈⠀⠄⠀⠀⠢⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠀⠄⠀⢀⠀⠐⠀⠀⠀⠐⢧⡶⠒⢋⠛⠈⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠀⠀⠐⠀⠀⠀⠈⠛⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⣀⡀⣀⡀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⣿⣼⡿⣿⣿⡇⠛⣿⠄⠛⢙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠉⠀⠉⠉⣀⠉⣉⠀⠀⠉⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡄⠠⣤⣀⣼⣿⢰⡟⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠟⣠⢶⠀⢰⣿⠁⢸⠃⠀⠀⠀⢀⡿⠀⠀⢀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⢠⡆⢹⣆⠀⣾⠃⢀⡞⢀⡄⢠⡾⣻⠇⢠⣿⣿⢀⣼⣏⣴⡗
⠀⠀⠀⠀⠀⠀⠀⢻⡏⣿⢺⣣⢺⡇⢠⢿⡀⠜⡁⣾⠃⣸⡵⢻⠀⣾⠟⣿⠎⠚⠋⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠇⠈⠁⠀⠁⠁⠀⠁⠀⠉⠸⠆⠁⠀⠈⠉⠀⠀⡠⠔⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣾⠏⣦⠀⠺⣦⡶⢲⡟⢰⣼⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠻⠶⠋⠀⠀⠟⠁⠘⠧⠞⠹⠇⠾⠃



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

⠀⠀⠀⠀⠀⠠⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡄⠀⡀⠀⠄⠐⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠠⠀⠀⠈⠀⣠⠚⠢⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠀⠀⠀⠀⠀⠠⠅⠂⢤⠀⠆⠀⠀⠀⡀⠈⠀⠀⠀⠄⠀⠗⠀⢂⠀⠈⠈⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠃⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⣀⡇⠴⣲⡀⣤⢤⡠⡤⣄⢠⡀⢠⠀⠐⠟⠲⠀⡅⢤⡤⡔⢾⠂⢹⣤⡀⣠⣼⠧⣲⡄⢠⠀⣠
⠀⠀⠀⠀⠸⠁⠧⠺⠬⠇⡧⠴⠃⡧⠜⠀⢳⠃⠀⠀⠤⠀⠠⠧⠼⠀⠀⠹⠄⠿⠀⠟⠤⢼⠸⠥⠧⠀⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⠀⠁⠀⠀⢀⠀⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢢⠀⠀⢀⠀⠑
⠀⠀⠐⠂⠀⡀⠓⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠃⠀⠀⡠⠄⠀⠀⠀⠀⠁⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠴⠒⠂⠀⠉⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠉⣠⠔⠊⣀⣀⣈⢉⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠞⣁⡴⢧⣄⠠⠶⠶⠤⠰⠶⣄⡀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡾⢁⠀⢀⣿⠷⠆⠀⠤⣭⠏⢴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣿⠸⠋⠀⣀⣉⣫⡥⠩⣟⣓⡉⠙⠓⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢳⠈⢸⠘⠀⡄⠀⢀⠐⢒⡂⣄⣓⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠸⠰⣇⠋⠰⠈⡀⠡⠍⠰⠸⢀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⠁⡀⡀⠃⠘⠧⠙⢳⣤⣤⣤⣤⡾⢋⡹⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠸⡀⢃⡅⢰⡘⠦⠠⠀⡿⠁⠈⢻⠧⠠⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠁⣸⣿⣄⠉⠂⡴⠀⡇⠀⠀⠨⠗⠄⠞⢃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠻⣷⣾⠁⠀⠐⢦⡴⠂⠀⣸⣾⠛⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣾⣿⡉⢦⡀⠈⠳⢦⠀⠚⠃⢠⡴⣋⣠⢊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡟⢳⡄⠁⠀⠀⠈⠛⠾⠟⢩⡾⠋⢉⡡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠘⠻⣦⡀⠠⣀⣀⠀⠠⠏⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⣄⡀⠀⠙⢦⡈⠙⠛⠃⠀⠀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠢⡄⠁⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⠀⠀⠀⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢰⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣈⣠⡿⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣿⡌⠂⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢣⣸⠀⠈⠙⠃⠀⠐⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠴⣍⡆⠀⠀⠀⠠⠀⠀⠈⠀⡏⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠉⢸⠆⠀⠀⠀⢁⡦⠀⠀⢇⡏⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡤⢿⡷⠐⣏⣠⣖⡒⠉⡁⠀⣠⠊⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡖⢠⡾⢋⠅⡼⢟⣡⣄⠄⣰⠃⡀⠀⡀⠉⠳⣄⠐⠁⠀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣮⡰⣇⠈⢧⠸⢊⣴⢋⡜⠁⣼⠃⢸⠀⠀⠈⠛⢆⠈⠢⠄⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡲⣆⠹⣿⠇⢸⢠⢺⡎⢸⢀⢸⡎⢀⡟⠀⠈⠉⠒⠄⠀⠀⡀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⡉⠟⣸⠇⠠⠟⠈⢯⠃⣟⢸⠸⡆⠸⠁⠀⠀⢀⠀⠀⠀⠴⣿⠏⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣀⢤⠞⠁⠀⠀⠓⣀⠀⠈⣦⠀⠀⠀⠈⢧⠙⠮⠧⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⣤⣦⠀⠶⠆⠛⠛⠋⠀⣤⣤⡤⠀⠙⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⢀⣄⠤⠠⠖⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⣤⣤⠄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠮⡥⠉⢡⡽⠷⡜⠁⣤⢾⣷⡈⠟⡃⣸⡷⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⢈⣧⣶⢶⡰⣟⣽⢳⣧⢻⣿⢯⣶⣷⣾⡽⣿⡿⠈⠽⠛⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣏⣏⡬⢿⣿⠛⠓⠈⠀⠀⢀⣀⣠⣤⣀⣉⡉⠁⠻⣿⣃⣴⣿⣼⠏⢤⡀
⠀⠀⠀⠀⠀⠀⣼⣃⡏⢰⣿⣶⠊⠁⠀⢀⣤⢞⡟⢋⣹⠯⣌⣿⣷⣿⣂⣦⠀⠐⡍⢻⣟⠁⢃⠷⡀
⠀⠀⠀⠀⠀⢸⡩⢮⡕⠆⣻⠁⠀⣠⡾⡹⢿⣭⡽⣶⣿⣿⡶⠟⡛⠈⠀⠁⠀⠀⠐⠀⠘⣿⣯⠚⡧
⠀⠀⠀⠀⠀⢺⣶⢄⡟⢈⣿⠀⠀⣿⣟⣷⢭⣍⡁⠻⣿⣿⣷⣋⢽⣀⡀⠀⢀⡔⠀⠈⠀⢸⡷⢾⡶
⠀⠀⠀⠀⠀⢨⡹⠾⣷⡈⠿⣦⡴⣿⡋⠀⠠⣄⠴⠷⣌⠳⣤⡘⢦⣈⠙⠓⠋⠀⠀⠃⠀⠐⡷⢶⡁
⠀⠀⠀⠀⠀⠀⢻⡄⠾⣛⠛⣫⣽⡏⠂⢀⣲⡃⠀⠀⠀⠙⠚⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⣼⡯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠨⢙⠘⠛⠛⠊⠁⠀⣤⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣸⡷⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠆⠐⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡞⣩⣹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣻⢯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⠆⠳⣿⣵⡸⠏⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣤⣴⣴⢶⣾⣾⠉⢿⣿⣣⣾⣾⣿⣿⣿⣿⣿⡶⢦⢤⣀⡀
⠀⠀⠀⠀⠈⠀⠀⢠⡤⣦⢦⣼⠿⢛⡻⠟⣷⣀⣪⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣟⡷⢼⠯⠇⢀⣦⣄
⠀⠀⠈⢀⣤⣶⠿⠿⠳⣷⣿⠝⠓⠉⠉⢁⡴⢻⡟⣿⣿⡿⠟⠋⠉⡁⠀⠠⠠⠠⠠⠡⠉⠛⠷⣤⣶⢿⣮⣛⣉⣡⡄
⠀⢀⠶⣿⠯⣍⢿⣿⠟⠉⠀⠀⠀⠀⢠⣯⣷⣮⣛⡿⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⡃⠛⠋⢩⣿⡆
⠀⣼⠲⠞⠧⠙⣼⡏⠀⠀⠀⠀⠀⠀⣾⡌⢻⣿⣿⣇⡀⠀⠀⢀⣀⣠⣤⡔⢲⣖⣶⣶⣶⡄⣀⠀⠀⠈⡿⣿⣿⡷⣿⢛
⠀⣿⠛⡿⢷⡞⢿⠃⠀⠀⠀⠀⠀⠀⢺⣵⡆⢥⡄⣿⣷⠶⢋⡽⠛⢛⣯⠒⣩⡭⣬⠉⣷⠀⣾⣗⣄⠀⣷⣮⣁⠸⢿⡞
⠀⢹⣺⢳⣿⢏⡐⣜⡦⠀⠀⠀⠀⠀⠈⢷⣶⣗⣲⢿⡶⢃⣴⣲⣮⣅⣀⡼⠿⠿⠯⢿⣯⠈⢀⣡⣥⣿⣭⣻⣭⣧⡍⣠
⠀⠈⢿⣿⣥⢾⣿⢩⢮⢀⣷⣄⡀⠀⠀⠀⠉⠻⠿⢮⢡⣼⠽⠿⠛⠉⠁⠀⠀⠀⠀⢀⣨⣿⢮⡽⢿⣿⣆⣫⣭⠟⢠⠇
⠀⠀⠀⠻⣿⢛⣏⡘⢫⡠⣽⡶⢶⣝⠒⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣯⠿⣉⡧⠔⠘⣇⢻⡟⠋⣰⠃
⠀⠀⠀⠀⠈⠙⡯⣿⣌⣱⣮⠿⣑⡛⢈⡳⢠⣾⢻⣿⠱⡴⢇⣾⣉⣻⣻⣿⣿⣿⣿⣿⣷⣯⣼⢀⡜⣿⣶⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠍⡙⠓⠾⢿⣿⣌⣡⣿⡴⢟⣙⡃⢀⣾⣟⣻⣿⣓⡿⣿⣿⣿⣿⠿⠞⢹⠌⢻⡾⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⢀⡉⠉⠁⠙⠛⠻⠿⠛⠿⠟⠟⠇⠃⠛⠉⢉⡀⠄⠒⡧⢀⣼⡃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠂⠀⠈⠈⠀⠀⠀⢜⡑⢿⢐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠃⡀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⢦⣤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢀⠶⣆⣰⣯⡿⠟⢻⣽⣿⣦⣅⠀⢀⡠⢲⣭⣵⣟⣻⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣿⢿⣁⣀⣀⣀⣀⣩⣥⡿⣸⡆⢣⣵⣟⣻⣾⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣻⣖⣎⣝⢣⠮⣝⣿⣿⡆⡾⣷⡸⣃⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⣉⡛⣩⣟⡿⠛⠉⣿⣿⢚⡷⠟⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⣀⣼⣫⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⢤⠔⠂⠉⠉⠉⠉⠀⡢⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢀⠔⢈⠤⢁⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠴⠶⠒⡄⠀⠐⠆⠠⠁⠀⠀⠀⢢⡁⠀⠇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠔⠉⢉⠀⠀⣄⡀⠀⠈⠂⣤⠀⠃⢸⡄⡀⢰⣧⠐⡄⢀⣤⣔⠚⠛⠧⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠦⠀⠙⠓⠁⠀⠀⠀⢸⠀⠀⠁⠀⠈⠓⠀⠐⠈⠀⠁⠂⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⡆⠀⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⣠⡆⠀⢀⠀⢆⠀⢠⣀⣀⣠⡄⠀⠇⠠⡀⢠⣄⣠⡴⢂⠟⠀⠀⠀⠀⠀⠀⠰⠀⡤⠁⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠱⣶⠎⠩⠃⢀⡼⠀⠈⠢⣀⠉⠁⠀⠀⠀⠀⠀⠈⠢⢌⠉⠁⠀⠀⠀⣨⠀⠀⠀⡴⠁⠘⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⢀⠈⠀⡀⠐⠊⠃⢀⠐⠚⡈⠑⠂⠀⠖⢒⡇⠀⠀⢀⠔⠉⠘⠃⣾⠀⢁⣀⠴⠊⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⣀⠀⡀⠀⠀⣄⠀⠈⢢⡇⠀⢀⡌⠁⠈⠁⠉⢩⠀⠀⠈⢢⡄⠀⠀⠀⡀⠀⠄⢁⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⠀⢇⠀⠀⠿⡈⠇⢀⠀⠘⠣⢀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⣡⠐⠄⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠒⠀⣀⠠⡀⡌⠀⠐⠀⡝⢀⡂⠀⠀⢂⠩⠀⠀⢠⠀⠀⠀⠀⢀⠀⡈⠀⠀⠠⠛⠢⢰⡆⣀⠀⡀⠀⠈
⠀⠀⠐⠀⠀⠠⠁⢃⠈⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠑⠸⠀⠀⠀⠈⠁⠀⡁⠂⠐⠀⠒⢈⠡⠔⠁⠀⡑⠢⠤⣄⡌⢉⣡⡀⠌⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡰⠀⠁⡀⠀⡀⠉⠀⠀⠀⠂⠈⠀⠀⢄⡀⠀⠀⠈⣀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠘⡁⠀⠁⠀⠀⠀⠀⠀⠀⡀⣈⠅⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠰⠀⠀⠀⠀⠑⠀⠀⠀⠀⠂⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠠⠐⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠢⠄⣀⡄⡀⡤⠒⢈⠃⠀⠀⠀⠀⣀⣀⡀⠠⠀⠠⠀⢀⠀⣀⠀⠄⠀⠀⠀⠀⠆
⠌⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠋⠙⠉⠉⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠇⠀⠘⠀⠀⠀⢠⠀⠀⠀⠀⠂⡄⠀⣀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡆⠀⠀⠀⢸⠘⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⢠⣅⡀⠀⠠⠜⠀⠀⠀⡇⠀⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢉⡀⠀⠀⠀⠀⣀⠒⠠⠤⠆⠰⠀⠀⢀⠆⠀⣠⠀⠀⢰⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠈⠁⠄⠊⠀⢠⡁⠠⠀⠁⠀⢄⣁⡢⠑⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣀⣀⣀⣿⠀⣀⣤⣦⣤⡄⢠⣄⣤⣦⡄⠀⣤⣠⣤⣤⠀⣤⡄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠋⢻⡟⢰⡟⠁⢀⣿⠁⣼⠯⣦⢸⡟⢸⡟⢶⢄⣿⢀⣿⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠿⠇⠘⠿⠶⠟⠿⢀⣿⠶⠶⠟⠁⣼⠷⠶⠾⣋⡈⠻⠶⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⣦⡀⠰⠷⠀⠀⠀⠀⠀⣠⡀⠀⢀⣿⠸⠏⠀⠀⠀⠀⠿⢰⡗⠀⠙⠻⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣤⣴⡟⠁⣾⡆⢰⣷⡶⠗⠺⣿⠿⠇⢸⣧⠶⢿⡆⢀⣴⠾⠻⣿⠇⣠⡶⠟⢷⡶⢀⣾⠀⠀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⣹⣿⢀⣿⠀⣼⡏⠀⠀⢸⣏⠀⠀⣾⠇⠀⣸⡇⢸⣇⠀⣰⣿⠀⣿⡁⢀⣾⡇⢸⣿⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠘⠋⠀⠛⠀⠀⠀⠈⠛⠛⠀⠛⠀⠀⠛⠁⠈⠛⠛⠙⠋⠀⠙⠛⠋⠛⠁⢈⠛⢋⣽⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠛⠛⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣿⣷⠀⠀⠀⣴⡟⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⢀⣿⠏⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣤⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣀⣤⣼⣟⠀⢀⣴⡶⣤⡀⠀⣼⣟⡤⣶⡄⢀⣿⢋⠴⣦⠀⣴⣿⡟⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣻⡟⠉⠉⢹⣿⠁⢰⡿⠋⣰⡟⠀⣰⣿⠋⢠⣿⠃⣾⡿⠁⣸⡿⠀⣾⡏⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⡏⠀⢿⣇⠞⣿⣇⣤⣿⢿⣽⡿⠃⣸⡿⣯⣽⠟⠁⠸⣿⡠⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠀⠀⠀⠀⠈⠻⠄⠀⠀⠘⠷⠄⠀⠁⠀⠈⠀⣾⠇⠀⠀⠀⢠⣿⠁⠀⠀⠀⢀⣀⣈⣠⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⣡⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠤⣰⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣠⣤⣤⣤⣤⣀⣀⣀⠀⠀⣠⣶⠆⢠⣾⠟⠀⠀⠈⣷⡄⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⢀⣶⡿⢛⣿⠏⠉⠉⣧⠀⠀⢀⣤⠀⠀⠈⠉⠉⠛⢻⣿⠷⣶⣿⣧⣤⣤⣤⣴⡿⠃⢠⣿⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠧⢀⣾⣏⣀⣠⡴⠋⢀⣠⣤⠉⢠⣟⣷⠀⠀⢠⣿⠃⢰⡿⢁⣤⣤⡍⢉⣡⣤⣤⣾⠃⠀⠀⣠⣶⠶⣤⠀⢀⣴⡗⠀⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉⠉⠉⢱⡄⢩⡿⠁⠀⣠⠟⣻⠇⢀⣾⠃⢀⣿⡵⢋⣿⠏⣰⡿⠋⠀⣾⠃⠀⢀⣼⡟⢁⣼⠇⠀⣼⡟⢀⣾⡟
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣀⣤⡟⠁⣿⣧⡴⠞⠁⣾⣋⣴⣿⡏⠀⢸⡟⠁⣼⣏⣠⢿⣤⣤⠾⣿⣤⣴⠿⣿⡠⠊⣿⣤⢼⣿⡠⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠁⠀⠀⠈⠁⠀⠀⠀⠉⠉⢠⣿⠁⠀⠈⠀⠀⠈⠁⠀⠀⠉⠠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠐⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠶⠶⠶⠶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠁⣀⣀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⢛⣿⣿⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣠⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠀⠀⠠⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⢶⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⣀⣀⣼⠃⠀⣄⠠⠤⢶⢀⡉⠀⠀⢀⣦⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⢿⣿⠀⢰⣿⠀⠀⠀⠋⠈⠁⠈⡤⠟⢻⣿⡇⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⡀⡙⣄⢼⣏⡀⠀⠀⠠⠑⢲⡁⠠⠾⠾⢿⡇⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠸⡇⠀⠘⣿⣦⣤⡀⠀⠨⠦⠀⠄⠀⠀⠉⠙⠁⠉⡏⣶⠂⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣭⣇⠀⢷⡀⠀⠘⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣤⣄⠀⠀⠀⢀⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⢸⣿⣤⣀⠹⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⢀⣠⡾⠟⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠄⠀⠈⠛⠷⣝⣟⠻⣷⣟⣷⣤⡀⠀⠂⠁⠀⠀⢀⣠⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠈⠛⠿⣿⣿⣏⣉⠀⠀⠀⢀⣠⣴⣿⣿⠋⠀⢀⣤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠑⢦⣀⡀⠈⠛⢿⣿⣷⣤⣀⣀⣀⣴⡿⢁⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠁⣽⣦⣤⣤⠛⣩⣿⡿⠿⠿⠛⠂⠉⡉⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠙⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠚⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠂⠀⢀⣀⠡⠠⠂⡀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⣈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠀⠐⡈⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠤⠀⠄⠁⡠⠀⠄⠀⠈⠑⠠⡄⠈⠂⠤⠐⠉⠀⠈⠀⠀⠀⠐⠁⠹⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⢀⢀⠀⠀⠀⠦
⠀⠀⠀⠀⠐⠂⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠂⠰⠊⠀⠀⢸⠁⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐
⠈⠀⠀⠀⠀⠀⠠⠼⠁⠀⡀⠀⠄⠀⠰⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠈⠧⠄
⠀⠀⢄⠰⢀⢀⠀⠀⠀⡀⠀⠀⣀⠀⡀⠀⠀⠀⠠⢀⠀⢨⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠐⢂⠀⠀⠒⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠑⢈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠂
⠀⠈⠀⠁⠈⢀⠀⠠⠀⠀⠀⡀⠐⠂⠐⡀⠀⠀⠀⡒⠒⠚⠓⢒⠂⢀⡐⠀⠐⠂⠐⠂⢢⠀⠄⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠰⠀⡆⠂⢈⠐⠂⠆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣂⠀⠀⠒⢉⠀⠂⠁⢈⡈⠀⠀⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⠘⠂⠀⠀⠘⠃⠀⠀⠐⠃⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠄⠀⠀⡠⢠⠐⡄⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢬⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠠⠐⡀⠐⣀⡖⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠠
⠀⠀⠀⠀⠀⠠⡁⣀⠅⠀⠨⢀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠁⠈⡠⠠⠈⠀⠉
⠀⠀⠀⠀⠀⠈⢒⣀⠴⠀⠣⢀⡐⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠀⠀⠰⠄
⠀⠘⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠐⠆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀
⠀⠀⠁⠂⠉⠐⠉⡀⠀⠀⠀⠀⠀⡀⠴⠐⠀⠠⣀⠀⣰⠄⠠⠰⠀⠀⢀⠄⢠⠀⠀⠠⠀⠀⠀⠀⠘⡌⣰⠢⠌⡀
⠀⠈⠀⠄⠀⠠⠁⠁⠀⠄⠀⠀⠀⠥⠐⠀⠐⢀⠀⠀⠀⢈⢁⠀⠀⠀⠈⠐⠀⢆⠁⠀⠀⠀⠀⠀⠘⠠⠈⡈⠠
⠀⠀⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠀⠃⠀⠐⠀⠐⠘⠀⠈⠀⠀⠐⠘⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠁⠀⠒

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢠⡞⠁⠐⠂⠬⢍⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣋⠭⠄⠂⠈⠙⣦
⠀⠀⠀⢸⡖⠚⢋⣉⣓⡒⠦⢝⡮⠷⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠴⠭⣞⠥⠖⣚⣋⣙⠛⠒⣿
⠀⠀⠀⠈⢷⡉⣉⠀⠨⢭⣍⣻⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣼⣋⣭⠍⠀⣈⡉⣸⠇
⠀⠀⠀⠀⠘⢧⡠⠤⠖⠒⠒⠒⠛⠦⣄⠀⠀⠙⢦⠀⠀⠀⠀⣠⠞⠁⠀⣀⡴⠞⠒⠒⠒⠒⠦⠄⣰⠏
⠀⠀⠀⠀⠀⠈⢷⣐⠊⠉⢉⣉⣉⡙⠛⠛⠒⠦⣄⡳⣐⣢⡴⣁⡤⠖⠛⠛⠛⣉⣉⣉⠉⠉⢒⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠧⣤⣤⠬⣭⣭⣭⠯⠭⢽⣏⢘⣿⠭⠭⣯⣭⣭⡭⢤⣤⡬⠿⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣁⠤⠄⠐⣶⠤⠒⠊⡝⣿⢾⡿⡑⠒⠤⢴⡒⠀⠤⢄⣉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⣉⠤⠒⢈⡏⠀⠀⣠⢾⢀⡏⡘⡇⠹⢆⡀⠀⠙⣏⠐⠢⢌⠓⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠤⠂⡩⠳⡴⢺⠁⠀⣸⢀⢃⢹⠸⠀⢻⠲⡴⠫⡁⠢⣄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⢠⠊⠀⡜⠀⠇⠀⢰⠇⠈⠃⠈⣿⠀⠈⡄⠑⡀⠈⢦⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣇⠀⡘⠀⠀⡆⢀⡞⠀⠀⠀⠀⠸⣆⠀⠇⠀⢸⠀⢈⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠶⠚⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣄⠢⣴⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠛⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⠊⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠘⣿⣿
⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣴⠒⠙⠇⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⢀⢀⣠⡴⠻⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠐⢀⡄⣴⡂⠖⡌⠁⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠙⠋⠉⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠈
⠀⠀⠈⣇⠀⠁⠈⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⠠⢤⣤⢶⡾⠋⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠈⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠡⣌⣩⣅⠞⢣⡜⢱⡇⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠘⠀⠂⢨⢇⣼⡤⢛⡁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠐⢇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣹⡆⠀⠀⠘⠆⠀⢛⡏⠰⠏⠎⡰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡔
⠀⠀⠀⠀⠀⠀⠱⡘⠿⠓⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⢹⡅⠀⣎⠵⠆⠊⠀⠈⠀⠀⣰⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢤⠶⠚⠋⠉⠦⢀⠀⠀⣴⠶⣦⠤⠒⠺⣧⠖⢫⣿⠯⢄⣈⡄⠄⠀⠅⢘⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠐⠂⢽⡀⢫⣵⣄⠀⢟⣂⡤⠕⢾⠉⠙⣇⣘⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠐⠚⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⡆⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⡐⠀⣷⠀⡴⣄⣄⣷⡘⢂
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠳⡆⢀⣄⠹⡆⢻⣴⣄⡿⡄⠻⠙⠯⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣷⣸⣟⢲⣻⡄⢿⠈⠁⠈⠁⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⡆⠿⠈⠀⠁⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⡆⠀⠀⡀⠀⢀⡀⣤⢶⡸⡼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⢻⡀⢺⡹⣼⣇⢱⣹⡶⠟⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠳⠜⠁⠙⠹⡎⠀⢻⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣦⡀⣤⡆⠀⣀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠑⠠⡀⢵⠀⠀⡤⠀⢀⠘⠿⣾⡌⢰⠃⡽⠿⠋⢰⠀⢸⡄⠀⢰⢁⡠⠐⠁
⠀⠀⠀⠀⠀⣀⡄⠀⠑⠢⣨⣸⠄⠀⠠⢃⢲⠀⠘⠿⢃⡸⡈⠻⡟⠀⡔⢂⠤⠀⠀⣆⣠⡄⠢⠡⠀⣄⡀
⠀⠀⠀⠐⠁⠀⠀⠀⢀⠐⠛⠛⣓⣐⢤⣄⠈⢳⡟⣺⣤⡞⣥⣸⡚⡶⠁⢀⣤⢔⣐⡛⠛⠓⠀⠀⠀⠀⠀⠃
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡄⠄⣔⢎⠀⠰⡁⡄⣠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠏⠔⠰⣱⠣⢣⠎⠆⠞⡜
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠏⠀⠀⠜⠁
⡇
⡇
⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠒⠒⠶⢖⣶⠖⠒⣲⠲⣶⣶⢶⣶⡶⢲⡖⠒⢶⣖⠶⠶⠒⠂⠀⠆
⠀⠀⠀⠀⠘⠠⢤⠀⡀⣀⣩⠿⢿⠁⠁⣀⠄⣰⠉⢫⡃⠴⡫⠄⣫⠛⠙⡆⠄⡀⠁⢙⡿⢿⣁⡀⡀⢠⠤⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠄⣌⠀⢠⡀⠈⡅⠀⣛⣿⠂⡟⢸⣻⣃⠀⠬⠘⣠⠀⠀⣅⠢⡈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡀⠐⠁⠄⠀⠃⠀⠁⠾⠛⢳⡼⠠⣦⠋⠛⠇⠀⠀⠀⠀⠠⠐⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣥⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡴⠶⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⡰⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⠒⠋⠉⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠬⠳⡀
⠀⠀⠀⠀⡼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡇⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢤⡀⠀⠀⣠⡇⠀⠲⣄⠀⠀⣠⡟⣡⡞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣇⢠⣀⠀⣀⣹⢦⡀⠻⣄⣴⠟⡇⠀⠀⠹⡳⡜⡝⡴⢹⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⣿⢀⣙⠻⡦⣹⣾⣌⡦⠾⠴⠴⠣⠶⣦⣄⣸⢠⡷⢁⠟⣿⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢹⡀⠉⢳⣝⣜⢿⠏⠀⠀⠀⠠⠊⠀⠈⢷⡇⢸⡇⡜⢸⣿⢡⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⢱⠛⠍⠉⢻⣾⡀⠀⠀⠀⠀⠀⠀⣀⣼⣇⣸⣷⠋⠉⠉⣹⠉⢹⡄⠀⡇⠀⢀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠉⠑⠚⠉⠉⠉⠉⠀⠀⠈⠁⠈⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⡀⡀⡀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠵⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠙⠗⡴⠷⠀⠀⠀⠀⠀⠀⠀⢠⢧⡄⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⠀⡁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⣈⠔⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡠⢂⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠡⣦⠀⠀⠀⠀⠣⡈⠄⡠⠀⠀⠀⣰⢦⠄⠀⠀⠀⠀⠀⠀⢀⠤⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢷⠼⠧⠀⠀⠀⠀⠀⠀⠉⠒⣶⠮⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⢸⠀⢀⡈⠀⣠⠄⠤⡀⠀⣆⡆⠒⠒⢄⡖⡦⠐⠒⢄⢠⠀⠀⢰⡆⠀⠀⠀⢀⠄⠠⣤⠒⢢⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡔⢉⠠⣴⢆⢃⠀⠀⢸⠀⠀⢱⠀⠁⠀⠀⠁⠀⠀⣃⡀⠀⠈⠀⠈⣀⡀⠀⢸⠀⠀⢸⠁⠀⠀⠀⠈⠢⡀⠉⢀⠌⠀⠀⠀⠀⠁⡆
⠀⠀⠀⠀⢣⠸⠙⠀⠀⠏⠀⠀⠀⠀⠀⢸⣀⢢⡀⣀⠧⡈⠀⠧⡐⣁⠜⠀⡸⢄⣊⠔⠀⠄⠠⢻⠀⠀⣠⡀⠀⠀⠈⠲⠁⠀⠀⠀⠀⣄⠚⠛⠓⣠
⠀⠀⠀⠀⠀⠉⠣⡀⠀⠆⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⢸⠀⠀⢇⠈⡢⠀⠀⠀⠀⠀⠀⠀⣠⣅⣀⠉⡁⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠙⢠⠀⠀⡏⠐⠀⡄⠀⠀⠠⡠⠔⠀⢸⠀⠀⠀⠁⢛⢀⠖⢹⠀⠀⠀⠀⡧⠤⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⡄⢒⡀⠌⠀⢀⠔⡂⠐⠀⡠⢄⣀⠤⢄⠑⠒⠊⠀⠀⠑⠒⠊⠀⠀⠀⡀⠉⠐⠐⠁⠀⠀⡆⢐⠀⡼⠖⠊⢀⠀⠀⠀⠧⢀⣀⢀⣀⡠⠄
⠀⠀⠀⠀⠀⠈⠈⠙⠀⢠⠡⡠⠃⠀⠸⣀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠈⠈⡱⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣶⣭⠈⠋⠀⠀⠀⠀⠀⠀⠶⠖⠊⠢⡀⠂⠀⠀⠤⣠⠀⠀⠶⣴⣀⡀⠀⠀⡧⠀⢄⠀⠀⠀⡠⠤⠤⣸⠀⠠⠊⠉⢢⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⡠⣄⣢⠀⢸⣴⣆⠦⠀⠀⠀⢴⠃⢦⠀⠀⠇⡄⡠⢌⠀⡆⢠⠢⡀⠘⠀⡠⠠⠠⠀⠀⢘⠀⠀⠎⠀⢀⡀⡈⢢⠀⠀⠀⢸⠀⣀⠇⠀⠀⣾
⠀⠀⠀⠀⠀⠑⠊⠀⠡⣈⠀⠀⠀⠀⠀⠘⣄⡋⢊⡠⠊⠀⢅⣙⠜⠀⠆⢈⠕⠀⠠⣀⣑⠔⠀⠀⠀⠠⣘⠟⠢⡀⠃⡈⢇⡸⠐⢄⢀⠜⠠⠔⠑⠄⠜⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠒⡄⢀⣀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⢐⡈⠲⠋⢀⠅⠀⠤⠤⠀⠤⠀⠀⠀⠄⠀⢎⡛⡝⠀⠀⠘⡀⠤⠁⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠈⠑⠲⠁⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠈⠒⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⢉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⢻⢅⠀⠀⠀⠀⠀⠀⣠⠕⣶⠂⠀⠀⠀⠀⠀⠀⠀⢨⠀⡔⠂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠟⠉⠀⠀⠀⠀⠀⠈⠗⡰⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠠⠒⣉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠚⠳⠀⠀⠀⠀⠀⠀⡔⢁⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠴⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⠔⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠒⠒⠀⠀⠐⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢀⠀⠰⡀⢠⣂⠄⣰⢠⠀⡀⠀⠈⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⢗⠙⠀⠋⠉⠈⠀⠀⠉⠀⠀⠏⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣀⣀⡀⠀⠀⣾⠋⣶⣄⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⡀⠀⢰⣦⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠰⠁⠀⠀⢸⣿⠏⠁⣨⡑⠂⠤⣀⣿⡿⠀⣄⠀⠀⣿⡆⢸⣿⠁⠀⣿⡆⢸⡿⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⢰⣿⠋⠀⣿⡆⢠⠎⣹⡧⠀⢩⡁⢠⣿⡇⠀⠀⣸⣿⠇⢰⣿⡧⠴⠟⠁⠀⠉⠓⣾⣿⡟⠋⠁⠸⣿⠁⠀⣹⣦
⠀⠀⠀⠀⠀⠀⠙⠁⣸⣿⣇⢃⡼⠛⠁⢀⣛⠋⠈⢿⣄⠀⢰⣿⡟⢀⣿⡿⢁⣀⠀⠀⣀⣤⣴⣿⡟⠀⢀⣤⡤⣭⡁⢠⣿⡿⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠈⣿⣦⠀⣾⣿⠀⠌⣼⣿⠃⣾⣿⠁⣸⣿⡧⢡⣿⠇⣴⣿⠏⣼⣿⠃⣴⣿⢋⣼⣿⠇⣿⣿⢁⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⠀⣿⣇⠎⠀⢿⣏⠔⢿⣧⠔⠹⣿⠁⣼⡿⠀⢿⡿⠎⠻⡧⠜⣿⡿⠎⢻⣿⠘⢿⡧⢊⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⣠⣾⠟⠁⣠⣬⣁⠀⠀⠀⠀⣀⣤⢄⠀⠀⠀⠀⢹⣧⣀⠄⢤⣤⠀⠀⠀⢀⣤⠴⢤⡀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠢⣄⢉⣸⣿⠀⠀⠀⣾⡏⢀⣸⡇⠀⠀⢀⡴⠻⣄⣀⣼⡿⠁⠀⠀⣾⡏⢠⣼⡗⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠉⠁⠀⠀⠀⠹⣧⣈⠛⣁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣉⡠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⠎⢠⠔⠄⠀⢀⢀⠀⡤⢄⠠⡀⢂⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠘⠠⠂⠀⠀⠇⠀⠦⠔⠀⠉⠁⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⢀⣀⣀⣀⡠⠤⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢩⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢈⠀⠀⠀⠀⣀⠤⠒⠒⠂⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡀⠀⢀⡜⠀⠀⠀⠀⡇⠀⠀⠀⣠⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠉⠉⠒⠒⠀⠀⠀⠀⢠⡇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⣒⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢰⠇⣤⠀⠀⡇⠀⡿⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠀⣸⠁⠀⢸⡇⢀⢀⠀⡼⠉⣦⠀⢸⡁⢠⡟⠠⡇⢀⡼⠁⣸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠈⢧⡀⣀⠇⠳⠀⢿⠀⣾⠶⠋⠀⢸⡇⢈⠄⠀⠘⠂⢠⡏
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡠⠤⠶⠶⢬⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡴⢢⡇⠀⡀⠀⠸⢣⠏⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠎⠀⠀⢠⠆⠀⠈⢷⠀⠠⠄⠀⠀⠀⢀⠄⠀⣼⠁⠸⠇⣠⠆⠀⢠⡏⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⡏⠀⠀⠀⣸⠀⡤⢀⠀⠀⠀⣽⠁⢰⡟⠒⠂⠉⠀⡀⢀⡿⠀⠀⢀⠀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣾⠔⠢⠴⠚⠥⣼⠁⡟⢠⡇⢠⡇⠀⣼⠀⢸⡆⢠⠏⠀⣸⡇⠀⡴⠁⢰⠇⠀⠀⠀⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠤⠤⢄⡀⠀⢯⠹⡇⢸⠃⢸⡇⡠⡏⠀⢸⠀⣿⡠⠊⢸⠁⢰⡇⡠⣿⠀⢸⠀⢰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⡇⠀⡀⠀⢹⠀⠀⠀⣿⣾⢀⡄⠉⠀⠀⠀⠈⠃⠀⠀⠀⠘⠡⠈⠉⠀⢷⣀⠜⠓⢙⡇⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠀⠀⠀⣰⠟⡈⢉⢀⠀⠀⡀⡀⠠⠀⠒⠐⠒⠐⠒⠀⢀⡀⠊⠁⠀⠀⢸⠇⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠁⠀⠂⠀⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⡀⠀⠠⠀⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣽⠇⠀⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢀⡀⠀⠀⠀⠦⠹⠴⠋
⠀⠀⠀⠀⢷⡶⠃⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠻⡆⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⣴⡀⠀⠀⠓⠚⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠉⠉⠤⠄⠈⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠟⡆⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⡰⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠐⠂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⢄⣶⣿⣿⣤⣰⣿⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣟⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⣿⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⢇⢻⠀⢹⡞⢸⡼⢪⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠃⠈⠈⠁⠀⠀⠈⠁⠋⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠠⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⡹⢀⣤⡀⠀⠉⠀⠀⠠⢀⣀⠀⠀⢠⡀⠀⠘⠁⠀⢀⠇
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠐⠋⣰⠋⠀⠀⣀⠀⠀⠀⠰⠂⡀⠉⢱⠟⠲⠦⠴⠶⠚⠁⠸⠀⠀⠀⡀
⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣰⠃⢠⡆⠀⢑⡦⢀⡼⠀⢸⡋⢠⠋⣴⠀⣴⢂⡄⢀⡴⢚⡁⠀⢸⡃
⠀⠀⠀⠸⣇⠀⠀⡀⠀⠀⠏⠀⠘⠀⠀⠘⠀⠘⠁⠐⠾⠃⠇⠘⠁⠈⠁⠺⠁⠘⠁⡘⠃⠐⠼⠃
⠀⠀⠀⠀⠈⠉⠁⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡀⠀⠀⠀⠀⠈⠙⠋⠛⠛⠀⠀⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢥⡶⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⡷⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠸⠚⡖⠀⣶⢰⠀⣾⡀⠈⠎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⠄⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣀⡤⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⣀⣿⣤⣤⣄⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠈⠷⣤⣄⠀⠈⠉⠁⠀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠐⠒⠘⢖⠀⠀⢙⡟⣠⠶⢲⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠧⠀⠀⠤⠳⣰⠟⣰⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⡀⠀⠀⠑⣄⣠⡞⠃⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠐⡄⠀⠀⠀⠙⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡈⢃⠀⠙⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢣⡈⠳⠐⠒⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠙⠁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡄⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠠⠓⢂⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡴⠘⢢⠄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣀⡞⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠉⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠄⣤⣰⢔⠒⡖⡆⠉⠲⠈⡰⡏⠰⡶⡒⢂⢤⣤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠤⠘⢞⡻⠚⢧⢍⣐⡓⢹⣢⣀⡐⣡⡨⢳⢓⠡⣰⠚⠠⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠘⢀⠛⠊⣤⡲⢰⡩⢀⣑⣅⠤⢭⡈⠓⠡⡦⣉⡁⠨⣡⠘⢗⡌⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⠀⠀⠘⣟⠵⡠⠶⢑⠄⣾⠊⣙⠲⢾⠤⠪⢅⡸⢌⡺⣄⣢⡐⢆⠸⠝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⠄⠀⠀⠙⠖⡇⢠⣒⠶⢸⣺⠊⣽⠀⠻⠜⠁⠰⢚⠆⡤⠜⡕⠋⡟⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⢀⠈⠀⠀⠀⠀⠀⣇⠈⠓⠁⢸⠓⣖⣿⠀⠀⠀⠀⠀⠙⠮⠃⡟⠍⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⡀⠁⠀⠀⠘⣄⠀⠀⢸⠰⣢⡝⠀⠀⠀⠀⠀⠀⠀⠀⠸⠱⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠻⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠠⠐⠁⠀⠀⠠⠀⠁⠀⠀⠱⡒⠂⠆⠠⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠐⠈⠀⠀⠀⠀⡀⠄⠀⠱⠐⢒⣒⠒⠒⠒⢒⣒⣒⣒⣒⡒⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⢀⠠⠀⠄⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠁⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠀⠐⠂⠀⠔⠈⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠘⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠢⢄⡄⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠼⠐⠄⠈⠶⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠰⡡⢔⡰⠐⣀⣉⢨⢁⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠃⡆⠀⢰⠁⠐⠀⢐⢀
⠀⠀⠀⠀⠀⠀⣠⠀⡈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⠀⠀⠂⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢁⠈⢖⢤⠀⠘
⠀⠀⠀⠀⠀⢁⠹⠈⠉⠁⠠⣹⠀⠀⠉⠀⠈⡀⣄⡀⠀⠀⠀⡨⢉⠃⡈⠛⠛⠀⠀⠁⠐⠂⡀⠠⡀⠆
⠀⠀⠈⡀⠀⢒⠀⣄⠀⠀⠠⠚⠀⠀⠀⡠⢚⠧⠀⠣⠤⠦⠴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠇⠀⠃
⠀⠀⠀⠈⠀⠀⠡⠌⡄⠂⠁⠀⠀⠀⠔⠃⢠⡤⡟⠒⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠁⡀⡀⠐⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠉⠀⠀⠀⠀⡠⠈⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⡠⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠁⠤⠤⠠⠄⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠆⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣈⡂⠤⣀⣈⠀⠀⠀⡀⠈⠀⠀⠀⡊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠓⠀⠀⠄⠄⢀⢀⣱⠀⢠⠴⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠄⠠⠠⠤⠀⢀
⠀⢀⣰⣶⣟⠲⢶⢖⠳⣘⣫⣶⠿⠿⠞⠛⢓⢹⠄⠂⡈⣡⢰⣺⣦⣷⣠⡄⠒⠚⠚⠇⡴⡂⢄⣃⣀⡀⢀
⠀⣠⡼⢖⣀⣤⣯⣥⠴⠂⣿⠃⠀⣀⠀⣄⣾⢻⠀⣀⠝⠨⠧⢸⡽⣏⠉⠳⢄⣄⣤⢤⡀⣤⣴⣛⣃⢼⣌⡙⣤
⢀⠏⡀⠈⠁⢈⢇⣘⣆⢀⡼⡆⠒⠉⢣⣀⢯⡘⡆⠀⠠⠤⠀⠈⢃⡷⠲⠆⠀⠀⠐⠊⠏⠁⠀⠉⠹⡀⠀⢈⣛⠁
⠊⢿⡾⠠⣿⣾⣹⡽⣝⢧⣀⣈⣀⠀⣉⡠⠀⠘⣇⠀⠐⢠⣯⠴⣟⢲⣄⢀⣐⣆⡀⢀⠶⠂⠈⠛⠂⠀⠃⣀⠉
⠀⢀⠇⠀⠀⡞⡩⠙⣶⡾⠟⠛⠻⡛⠻⣟⡣⢾⣿⣭⣶⣿⠋⠛⠉⣠⣟⠦⢌⠿⣻⣿⣾⠛⡯⡀⠠⠂⠀⠀⢀
⠀⢨⠔⠊⡰⣠⠇⢡⣿⠷⣶⡶⠀⠹⢷⡟⠙⠷⢼⣮⢻⣻⣧⠄⠞⢻⣯⣿⣃⣼⠇⠀⠈⠛⣧⣼⡁⠀⠀⠀⢨⢰⡀
⠰⠖⠶⠂⠤⠀⠀⠈⣩⡗⠈⠀⢴⡄⠀⡓⢊⠒⠶⠶⣾⡽⡈⠋⣄⣀⡏⣩⣷⡋⠀⢀⣀⣀⢸⣿⣖⡆⢸⣄⠱⣣⠂
⠀⠰⠀⠀⢘⠄⠀⠀⠀⠱⢤⣀⠤⡄⣰⡀⠙⢂⠀⠀⢪⡄⠇⡠⡤⠀⣤⢸⡂⠛⠃⢀⠁⢉⠾⣟⣿⠇⠀⠈⣄⠉
⠀⠃⣈⠉⠩⠓⠒⢲⡞⢁⠘⢿⣟⣻⠷⠖⢶⣿⣦⣐⣿⣧⣤⣀⢀⡼⠗⠛⠗⠢⡄⠛⠋⠜⠃⣁⣀⡀⠀⣀⡄⢀
⠀⢶⠉⡚⡶⠞⠶⡖⡽⠎⠃⠼⢸⣵⠴⠚⠛⠛⠿⢏⡙⠛⡛⠛⣻⠆⠀⠀⠀⠀⠙⢶⣵⣧⣼⡿⣭⣙⢷⣄⣀⠆⣃
⠀⠈⢻⠉⠀⠀⠃⠞⠀⠀⠀⠀⢈⢻⣾⣷⠄⠺⣿⡆⣿⡇⠉⣉⣿⠆⠂⠰⠶⠈⠐⢀⣏⣽⠻⠋⣹⡛⠿⠻⡆⠀⣹
⠀⠀⢩⠁⠀⠀⠀⠀⣀⡀⡵⠖⣶⠞⣇⠀⢀⣀⠀⢀⡋⠀⠘⠛⠣⡄⠷⠀⠀⠀⠀⠊⠉⠈⡆⣀⣭⣩⠀⠜⠀⠙⠃
⠀⠀⢨⡇⠤⢖⠨⠱⢠⠀⠀⠀⠀⠀⣨⣁⠠⣠⠀⡈⠀⠀⠀⠀⣰⣬⠀⠂⢀⠀⠀⠀⠀⠀⣙⢏⣁⠤⠀⠰
⠀⠀⣚⠦⣿⡴⣴⠂⠟⠀⠸⠁⠀⠀⣸⣭⠓⠻⢺⣾⡃⢤⢠⢤⣼⣿⣲⢶⠃⠘⠿⠗⢀⣶⠳⠾⠲⣄⠀⠒⠿⢻
⠀⠀⠀⡞⢿⣠⣤⠠⠒⠓⡆⠈⠀⣜⢟⣁⡈⠚⠓⢋⣷⠻⠇⡆⠨⡿⢿⠀⠀⠀⠀⠀⠀⣹⠈⠁⠰⠟⠛⡖⣺⣿⢧
⠀⠀⠀⢀⠈⠎⠘⢲⣥⠀⢈⢶⣺⢶⠊⠛⡛⡁⠸⡈⢻⠀⠀⠓⠼⠀⢸⡏⣡⠶⠄⠤⣸⠛⠟⢀⡄⠀⠀⢰⠿⠛⠈
⠀⠀⠀⠉⢠⡔⠓⠂⣶⠒⡡⡶⠀⠛⠀⠀⢀⡁⠀⢉⢠⠀⠀⠚⠻⢂⡞⠼⢿⡷⢶⣟⡹⢠⡀⠀⠀⠊⡠⠀⠆⠄
⠀⠀⠀⠀⠠⠱⡤⠀⠄⠀⡄⠀⠉⣥⠀⡠⢬⣁⣀⡠⠈⠀⠀⠤⠀⠈⠊⠉⠸⠉⠓⠛⠀⠀⠘⠃⠄⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠸⠀⠁⠈⠀⠀⠀⠀⠡⠀⠀⠀⠀⢠⠃⠀⠄
⠀⠀⠀⢠⣄⣀⠀⢪⣩⣆⢠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⡇⠰⠀⠀⠀⠐⠀⡔⠀⠁⠀⡁⠀⠆
⠀⣀⠐⢦⡀⠙⣷⣘⢳⠏⢰⢀⠏⠰⠀⠀⠀⠀⠀⡔⠡⡐⢤⠤⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⠀⠀⠈
⠀⠸⣆⠀⠙⠄⠈⣿⢼⠇⠰⣎⡴⠓⠄⢀⢔⣤⡞⠀⢀⠇⠈⡆⢠⠔⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠈⠑⢄⢸⣆⢻⣶⡆⠐⣽⠁⠀⠀⢈⠘⣿⡇⠀⢨⡆⠀⢿⢀⡟⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⢦⠻⡈⣻⢃⢣⡏⠀⠀⠀⠀⠄⠻⣷⡄⠸⣆⣀⡞⣼⢁⠇⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⡄⠀⣄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠣⣷⣿⣾⠋⠀⠀⠀⠀⠀⠀⠣⠼⡿⠿⠋⠜⡿⠑⠁⠀⠀⠀⠀⠀⠀⠈⠯⣤⠀⢳⠆⠀⢰⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⠘⠀⠀⠀⠀⠀⠀⡴⠒⠂⣴⠶⢄⡀⢳⣼⣇⣼⣿⠷⠚⠃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠑⣄⡀⠈⠷⣇⡙⢶⣍⢯⠉⣤⣤⡶⠿⢛⡋⡳
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢀⠀⠹⢦⣦⡭⣷⣶⠽⠷⠦⣤⠤⡤⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣉⣀⣀⣑⣀⣐⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⣟⡛⢻⡟⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣣⡼⠀⠀⠀⠀⠀⠀⠀⠘⢌⠝⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠭⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠭⠭⢘⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡠⠴⣉⣁⣒⠒⢺⠀⠀⠀⠀⠁⠉⠃⠀⠀⠀⠀⠑⠂⠜⠫⠄⠤⠀⠀⠀⢀⠞⠉⠀⠉⠓⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣤⢤⣈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡠⠤⠋⠉⠘⡄
⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢠⠀⠀⠀⠀⠀⢠⡤⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣀⠤⠤⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡸⠀⠀⣤⡀⠀⠘⣧⠀⢀⡹⠀⠀⠀⠀⠸⣆⠀⠀⢠⠀⠀⠀⠈⠢⣀⠀⠀⡰⠁
⠀⠀⠀⡴⠒⢤⠔⠊⢢⠀⠀⠀⣿⠗⠒⠲⡇⠀⣸⠇⢧⠀⠀⣿⠒⠉⢠⣶⠒⠢⡄⠀⢻⡄⣠⠃⠀⠀⠀⠀⠀⠀⠉⡟⣄
⠀⠀⠀⠱⡀⠀⠀⢀⡎⠀⠀⢠⣿⠀⠀⢸⠃⢰⡟⠒⠚⡆⠀⢻⡀⠀⢰⡟⠀⠀⡹⠀⠈⣿⠁⠀⠀⠠⡖⠔⡲⠀⠀⠈⢇
⠀⠀⡀⠀⠈⠢⠤⠊⠀⠀⠀⠀⠉⠀⠀⠘⠀⣿⠁⠀⠀⢱⠀⠘⠃⠀⢸⡟⠒⠋⠁⠀⠀⣿⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⢸
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠸⠇⠀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⣾⠉⠑⢆⠀⠀⢸⡇⠀⢰⡏⠙⢢⠀⠉⢹⡏⠀⢀⡄⠀⢀⡀⣿⠀⠉⢦⠀⠀⠀⠀⢶⡀⠀⠀⡄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣿⣀⣠⠇⠀⠀⣿⠁⠀⢸⣇⠤⠋⠀⠀⢸⡇⠀⢸⡇⠀⢸⠀⢹⡆⠀⢘⠄⠀⣤⠀⠘⣷⠀⡸⠀⠀⢸
⠀⠀⠲⠴⡄⠀⢿⡉⠀⠙⡆⢀⣿⠀⠀⢸⡏⠲⡄⠀⠀⢸⡇⠀⣾⠓⠒⢾⠀⢸⡇⢀⡜⠀⣼⠏⡆⠀⠸⣷⠁⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡏⠀⠈⠛⠁⠀⣼⠟⠒⡇⠀⠀⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠁⢠⢢⠀⠀⠘⠋⠀⠀⠃⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠈⠑⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡀⠀⠀⠀⠀⠀⣠⣀⣤⠀⠀⠀⠀⠀⠘⠝
⠀⠀⠀⠀⠔⠃⠀⢰⠢⣤⡀⠀⠀⠜⠁⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢃⠀⣀⣀⠀⠀⠣⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⡗⢒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠔⣒⣛⣈⡩⠄⢐⡇⠀⠀⠈⠁⠀⠀⠀⣀
⠀⠀⢠⡄⠀⠀⠀⢸⠀⢲⢀⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠤⠤⠒⠒⠉⠁⢡⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠈⣆⡀⣤⠤⣔⣲⡼⠯⠗
⠤⠊⠉⠢⣄⡀⣀⠼⠁⠀⠀⠀⠀⠀⠨⣳⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠎⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠂⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠑⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢂⡕⠉⠉⠑⡤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠀⢀⠤⠂⠁⠀⠀⠀⡠⠁⠸⠂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡠⠐⠈⠀⠀⢀⡀⠄⠐⠈⠠⠂⢀⠥⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⠀⠠⠶⠠⠬⠄⠒⠀⠈⢉⠰⠂⠁⢀⢆⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⢀⠤⠂⠁⠀⠀⢀⠤⠐⠈⠀⢀⠠⠐⠁⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡠⠊⢁⠀⠠⠐⠈⢁⠀⠠⠐⠂⠁⠀⠀⢀⠴⠄⠒⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⡀⠄⠂⠁⠀⠀⠀⣀⡀⠤⠀⠀⠁⠀⠀⡠⠊⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠔⠉⠀⢠⣊⠀⠀⢀⠀⣀⢀⡄⠀⠁⠀⠀⠀⠄⠀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠄⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠠⡤⠀⢄⣄⠀⣀⡀⠀⠄⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⣀⠈⠙⠢⢀⡀⠀⠠⠒⠂⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠓⠲⣀⠉⠉⠑⡠⠤⠊⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⢤⠄⠑⠒⠄⢀⣀⠄⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⣈⠰⠤⢄⠈⠈⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠈⠑⠠⣀⡀⠠⠈⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠑⠌⡉⠀⠉⡀⠖⠮⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠛⠃⠀⠒⠂⠉
⣿⣿⣻⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣿⣿⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⢀⣔⠒⢢⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⣀⠤⣠⣀⢀⠀⠀⠀⠀⣠⣴⠀⢤⣄⣀
⠀⠀⣘⣷⡄⢰⠉⣠⠒⠚⠢⠀⠔⠒⠢⡀⣴⣿⣯⣼⡁⠀⠀⠀⠀⢰⣿⣾⡛⠟⢷⡀⠀⠀⢰⡇⠸⣆⠀⡽⠿⢷
⠀⣾⣛⢧⣿⠜⣲⠧⠀⢀⣐⠆⠆⠀⠤⡇⢿⣯⣿⣿⢁⣤⠀⠀⢰⡸⣿⣽⣇⣉⣬⣷⠀⠀⢺⣿⣦⡈⠉⣳⣾⣿
⠀⢸⣿⡿⡟⠀⠙⣷⣾⣴⠋⠀⢴⣶⡶⠁⠘⣿⣳⡟⢛⣉⣀⣀⣸⠀⠻⣿⣯⣿⣼⠏⠀⠀⢸⣿⣿⣻⣷⣿⣿⡟
⠀⠘⣿⣿⠃⠀⠀⢿⣻⡍⠀⠀⠘⡝⠁⠀⠀⢿⣿⠇⠀⢿⣭⣼⠃⠀⠀⣠⣿⢹⣀⠀⠀⠀⠀⣇⠀⠈⡉⠈⣿
⠀⠀⢹⡇⠀⠀⠀⠈⣭⠃⢀⠀⠀⠑⠀⠀⠀⢸⣻⠀⠀⢸⣗⣿⠀⠀⠀⠉⠁⠈⢉⣴⠖⠂⠀⠻⣄⡀⣀⣠⡿
⠀⠀⢈⠁⠀⠀⣀⣀⡙⠀⣿⢯⣿⠀⡞⢻⡆⢀⣭⣤⣀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣨⣄⠀⠈⠉
⠀⠀⠈⠀⡄⢠⣿⣿⣽⡄⣿⣾⡟⠀⡃⢸⡇⣾⡏⢹⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⢦⣤⠿⠿⠿⠿⠿⠿⣶⡄
⠀⠀⠀⠀⢡⢸⣿⣿⡇⡁⣿⣽⣿⠀⡆⢸⡇⣿⡇⢈⣿⣿⠀⠀⠀⠀⠀⠀⢙⣇⣤⣶⣭⣁⡄
⠰⡟⠀⢬⣿⣾⣿⣿⡇⡅⣿⣿⣿⠀⡇⢸⡇⠻⣧⣠⣿⠏⢀⣀⣠⢤⣄⠀⢈⢻⣿⣿⣯⣿⠧⠄⣶⠀⠀⡀⡴⡄
⠀⠉⠉⠋⠉⠘⠻⠿⠓⠀⠙⠛⡏⠀⠳⠾⠃⠀⠀⠈⠀⣼⣿⣥⣿⣿⣿⠢⣀⣼⢀⣀⣘⣿⠀⣦⢸⣦⣶⣶⣶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠇⠀⠈⣻⠿⠿⣿⠁⠀⢸⣯⣻⣸⣟⢻⡬⡀
⠀⠊⠁⠉⢳⠀⢠⠖⠒⢤⡀⡠⠒⠒⢦⢀⡴⠒⠒⢆⢹⣶⣾⣿⣬⣿⡆⠀⠀⠉⡀⣠⠃⠀⠀⠘⣿⣷⠿⣿⢿⣿⠇
⠀⣷⠀⣀⣼⠆⣗⠀⠀⢰⠇⣷⠀⢀⣸⠘⣆⠀⣠⣾⠰⣟⠀⠀⢹⣯⠁⠀⠀⢞⡓⣻⡄⠀⠀⠀⠈⣿⢿⢻⣿⡇
⠀⠈⠉⠉⠉⠀⠈⠁⠉⠉⠀⠈⠉⠉⠀⠀⠈⠈⠉⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢻⣿⣻⣿⡟⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡄⠀⠀⣿⣿⣬⣿⣿⣿⣿⣞⣿⣫⣿⡟⣿⣿⣻⣿⣬⣿⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠁⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⣠⡶⠒⠀⠀⠀⣀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⡠⢊⣿⡡⠊⣼⠇⡠⢫⡟⠀⠀⠋⠀⠀⣠⣿⠃⠀⢠⣾⠏⢀⠎⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠜⢀⣾⡿⠁⣼⡏⡰⢡⣿⠃⢀⣀⠀⠀⣰⣿⡧⠆⢠⣿⢏⠔⠁⠀⣀⠀⠀⡀⠀⠀⠀⡤⠀⣀
⠀⠀⠀⠀⠀⠀⣸⣿⠁⣸⡿⣰⠃⣾⡏⢰⡿⢱⢃⡤⣿⠏⠀⢀⣾⢟⢟⣿⢃⣾⢋⠆⣸⣊⣴⡄⠘⠃⠀⣧
⠀⠀⠀⠀⠀⠀⢿⡏⠀⢿⣿⠃⢰⣿⠁⠸⣇⣼⠏⠀⢿⣀⠔⢻⣿⢫⣾⠃⢸⣏⣮⠔⠉⢱⡟⣀⠀⢀⡤⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠸⡟⠀⢀⡜⠁⠀⢀⠀⠀⠀⠈⢁⣿⠇⠀⡠⠋⠁⠀⠀⠈⠉⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠙⠁⠀⠀⠀⠸⡟⣀⠞⠁⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣤⣤⣤⣀⠀⠀⠀⣤⣤⡄⢉⣥⡄⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⢰⣿⣿⣷⠈⣿⣧⡀⣸⣿⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⣿⣯⠉⣽⣿⡇⣼⣟⣹⣿⡇⠙⢿⣉⣿⠃⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⡿⢁⣿⡿⠛⣿⣷⠀⠈⣿⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠸⠿⠇⠀⠸⠿⠀⠀⠻⠇

⠰⢶⣠⠄⢠⡔⢀⡀⠀⠀⡄⠀⠤⣄⣀⡠⠤⠤⠤⠤⢤⣤⠤⡤⠤⠤⠤⣶⣀⢲⣴⣤⣀⣴⠶⠶⠶⠒⠒⠒⢒⣶⣶⣶⡶⢶⣶⡶⠤
⠈⡈⢋⠄⠈⠑⠶⣄⠀⠼⣩⠵⢛⢉⠀⠙⠤⣏⡉⡳⡖⣀⠅⠅⠀⠀⠘⠛⠁⠀⠺⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⢒⡿⡿⡟⣡⡾
⠀⣁⠄⡠⠒⠋⠉⠒⢦⡈⠁⠂⠙⡐⢷⠀⠀⠂⠐⠁⡏⡑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⢸⢘⢉⡆
⠀⡗⡎⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠳⢤⠤⠤⢊⠔⠀⠀⠀⠀⢐⣆⢿⠀⠐⠠⡐⣴⢰⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢖⢺⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⡼⢸⡄⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢾⡎⢈⣥⠀⠕⢫⠂⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⠼⡇
⠀⣇⠁⠀⠀⠀⠀⠀⡼⠁⢸⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠇⠸⠿⢸⠀⠼⠀⠀⠇⠀⠀⠀⠀⡔⠉⠒⣄⡴⢢⠀⠘⡇
⠀⣫⣄⠀⠀⠀⣀⠜⠁⢠⠇⡆⠀⢀⡎⠀⠀⠤⠒⠂⢤⡀⠀⠀⣀⣠⠒⢶⠂⠀⠤⣶⠒⢦⡀⠀⠀⠀⠀⠀⢳⡀⠀⠘⠀⢸⠀⠈⡇
⠀⠁⠍⡱⣶⠊⠁⠀⣠⠃⢀⣧⡴⠊⠀⠀⠀⡀⣏⠆⡸⠻⠇⢠⡌⡿⠀⢸⠳⢦⡀⢸⡏⡇⢹⢤⣔⡀⢲⢸⢹⠙⢦⡀⣠⣇⡠⠌⠑
⠀⠠⠀⢈⡇⠽⠒⠚⠁⠀⡜⡞⠁⠀⠀⠀⠀⠃⣄⠙⠄⢻⠀⢰⡏⠁⣼⢸⡇⢹⡇⢈⣃⠇⡜⣴⡚⡄⡜⢼⢸⠀⢰⠉⠁⠐⢿⢡
⢀⠀⡙⠀⠧⣄⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⢰⡘⠠⠂⠾⠀⠘⠃⠀⠛⠘⠋⠘⣥⣞⡩⠞⠀⢙⣶⡷⠾⡟⡺⢄⠈⠑⠤⠔⠣⢻⡆
⢸⣎⡘⠀⡁⠀⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡻⣄⣀⢔⡽⠁⠘⠃⠀⠀⠀⠀⢸⡇
⠀⢿⡀⡄⡁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠄⠀⠀⡀⠀⠀⠀⠀⢸⠂
⠀⠐⠞⠁⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡓⠀⠖⠓⠢⠀⠀⠀⢨
⠀⣏⠚⣴⠛⠓⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⡇⠀⡔⠁⠀⠀⠀⠈⡄
⠰⣻⡄⡇⠀⠀⠀⠀⠙⢦⡤⢤⡀⣀⡤⠶⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢑⣎⢀⣘⣇⣠⠒⡂⠀⢀⠇
⠀⠭⠃⢧⣴⢚⣉⣙⣢⡞⠀⠀⡏⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠈⠙⠋⠀⠀⣀⡀⠀⠀⣀⣉⡂⠺⠊
⠀⠐⢁⠀⣿⢹⠓⠒⠚⠷⠤⡾⠯⣽⣦⢌⣁⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⠊⠈⠢⠎⠀⠸⣤⠎⠠⣄⣀⠃⠄
⠀⠀⡀⠰⡾⢾⠀⠀⠀⠀⠘⡇⠀⠀⢸⠂⠈⠀⡠⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡜⠡⠈
⠀⠀⡀⠀⠘⢸⠀⠀⠀⡇⢠⡇⠀⠀⡎⠀⡠⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠛⢒⣶⣤⠶⠶⠶⠤⠤⠈⠞⣲⠮⠑⢆
⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⢸⡇⠀⢰⠁⠁⠙⠚⠙⠒⠦⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⢀⣀⡠⢚
⠀⠀⢳⣠⣼⣿⠀⠀⠀⡇⢸⠀⠀⠸⠈⡇⢠⠀⡤⢦⣠⢄⠀⢀⣀⣀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠀⠀⡴⠃
⠀⠢⢠⡝⠃⠺⣄⣀⣀⣇⣏⡀⢀⡦⢰⠃⠸⡤⠃⠀⠀⠀⠉⠁⠀⠨⣛⣀⣀⡀⠀⠀⠤⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⡉⠂⠀⠈⢇
⠀⠀⢂⣉⣉⠙⠛⠛⠿⠏⠉⠉⠭⣀⣈⣒⢒⣚⣛⣒⠒⠂⠠⠤⠤⢼⣒⡤⢤⠤⡄⠀⠀⠀⠐⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⡀⠈⣛⠒⡒⠒⣲⠚⠛⢛⠿⢫⠏⢀⣭⠔⠒⠛⠛⣛⣛⡛⢛⠛⢡⢶⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡇
⣀⣀⣉⣈⣂⣑⣂⣉⣈⣂⣁⣉⣈⣒⣉⣈⣁⣒⣒⣉⣙⣃⣙⣈⣈⣀⣈⣑⣒⣒⣒⣒⣒⣂⣉⣉⣉⣀⣀⣀⣀⣀⣈⣉⣐⣒⣒⣉⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⠀⠀⣀⠀⠀⢸⡇⠀⠀⣾⠁⣄⢀⡤⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣿⢸⡇⣸⠇⣾⠁⣾⠃⣸⢶⣿⢀⡿⠸⣇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⡇⠹⠄⢻⡀⣿⠀⠟⢸⡇⠈⠀⠀⠀⠈⣷⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠈⢧⠀⢠⡀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠀⠀⠀⠀⠀⠇⠀⠙⠀⠀⣼⠁⠀⠀⠀⠀⢰⠇⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠁⠀⠀⠹⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡞⠀⠂⠀⠀⣤⠀⠀⣴⠋⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢸⡇⠀⠀⢀⠀⢼⠅⠀⠄⠀⢸⡇⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⢸⡇⠀⠀⠂⠀⠘⣇⠀⣀⠀⣸⠃⠀⣿⠀⢠⡀⠀⠀⡀⢰⡟⠀⢀⡀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠅⠀⠈⣷⠀⢀⠀⢠⡆⠀⢁⡟⠀⣿⠀⠀⣿⠀⢸⡇⠀⡾⠁⣸⠇⢰⠏⢰⡏⢰⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡄⠈⣧⢸⡇⠀⢸⡇⠀⢻⡀⠐⣿⠀⢸⡇⢸⡇⠀⣿⠀⢿⡀⢺⡅⠻⠅⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠃⢰⡟⠈⠓⠀⠈⠧⠀⠈⠧⠀⠙⠀⢸⡇⠈⠓⢀⠹⣎⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠙⣶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠓⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⠀⠀⠀⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠠⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠀⢹⠀⡀⠀⠀⢁
⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⢱⠀⠐⠟⠀⢠⠀⠋⠀⠀⠄⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⢸⠀⠠⡖⠀⠀⠑⠄⠀⠠⠂⠑⠀⠀⠈⠀⠀⢀⠆⠀⢳
⠀⠀⠀⠀⠀⢸⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡘⠠
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠏⠀⠀⠂⠀⠀⠀⡰⠂⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⡉⠁⠦⠁⠘⢀⠄⠂
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠧⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢠⠂⠤
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠂⠁⠉⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⣄⠲⠖⠁
⠀⠀⠀⠀⠀⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡗⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡇⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⢓⡖⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⠒⢲⠖⠒⠒⠒⠒⠒⣶⡿⠞⠉
⠀⠀⠀⣠⡶⠛⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿
⠀⢻⣄⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⠦⢤⣀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻
⢀⡤⠞⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣭
⢇⠹⡀⠀⠀⢀⡇⠀⠀⣀⠼⢄⠀⠀⠀⠀⠀⢀⠼⢇⠀⠀⠀⠀⠀⣿
⠀⠑⠢⠴⠒⠊⣧⠒⠉⠀⠀⠀⠙⢦⣀⡤⠚⠁⠀⠀⠙⢦⣀⡠⢔⡿
⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠶⣶⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⣂⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣣⣾⣀⣴⡅
⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⢀⠆
⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⡻⣿⣿⣿⣿⣿⡶⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢟⣽⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⡎⡻⣿⣿⣿⣶⣶⠶⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⢿⣿⣿⣿⠿⣿⣿⣷⢸⣿⣿⣿⣷⡝⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⣿⠏⠀⣸⣿⡿⣼⣿⣿⣿⣛⣋⣈⢻⡿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡷⢠⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣧⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⢀⣤⣤⢄⣀⣈⠉⠁⣰⣾⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣄
⠀⠀⢀⣠⣴⣾⣿⡟⢫⣍⣙⣿⢿⣿⣿⣷⡼⠛⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣟⣿⣍⠛⢻⣿⢿⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⢠⣾⣿⡟⠉⠀⣼⣿⣿⣿⠿⢿⣷⣾⣭⣭⣥⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣮⢻⡆⠊⠙⠀⠀⡿⠸⢹⣿⣿⡿⣿⣿⢻⣿⣿⣿
⢻⣿⣯⠁⣠⣾⣿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⠀⠀⠀⠜⠁⠤⠟⣿⣿⡇⣿⡏⣼⣿⣿⣿
⡞⢡⡟⢠⡛⢻⣿⠆⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⢹⡿⣿⢠⡿⢹⡏⠁
⠻⠞⠀⠀⢹⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠩⣿⣿⣿⣎⠻⡼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠃⠑⠝⠦⠓⠈⠷⠄
⠀⠀⠀⠀⢸⡋⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣶⡶⢦
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣷⣯⣿⣿⠿⢿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣧⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣀⠈⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡷⡏⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⡗⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⡏⢸⠹⠿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⣤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣿⣾⡿⣿⣿⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣘⢿⣿⣿⣿⣽⣧⣿⣿⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠻⠶⣿⣿⠻⡿⣿⣿⣷⣾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠄⠀⠀⠀⠀⠒⠀⠛⠟⠁⢸⠁⠀⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠱⠂⠀⠄⢀⡀⠀⠀⠀⠀⠀⠰⢠⠀⠀⡿⠀⠀⠀⠀⠀⣀⣠⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⡁⢠⣶⠘⠛⠏⣀⠀⡀⠀⠀⠙⡿⢦⠀⡇⠀⢀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠘⢈⡇⣺⣿⣯⠉⣴⠉⠧⠀⠀⠀⠀⠀⠀⠀⣷⣾⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠷⣌⠹⠄⠐⠃⠀⠀⠀⠀⠀⠀⣿⡷⠎⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠊⢀⠰⠋⠀⡀⠀⠀⠀⣤⠀⠀⢠⣄⣿⠂⠀⡀⠸⠿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠂⠀⠀⠀⠀⠀⣿⣧⣄⠈⢿⣿⢠⠞⢀⣀⠀⠈⠙⢻⠛⠉⠛⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠠⢀⣀⣀⢉⡙⢷⣶⠀⡿⠂⠀⢿⣿⡿⣄⠀⣸⠀⠀⠀⠀⠀⣿⣛⣧
⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⢸⡇⠀⠰⡆⠻⣝⣹⣿⠃⠈⠛⠄⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢀⠜⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⡇⠀⠂⠉⠊⠟⠳⠛⠀⠀⢀⡀⡇⠀⡀⢀⣠⡀⣸⢶⠃⠘⠃⢀⣼⣶⣵⣤⡀
⠀⠀⠀⠀⣷⡄⢀⡀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⢁⠀⠈⡿⠃⡇⠀⡃⢠⣽⣿⡏⣤⡀⠀⢀⢸⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠈⣻⣿⣧⣿⣷⡀⠸⣅⠀⠠⢾⠀⢼⠀⣀⢁⣤⡤⢀⠏⠀⠄⠸⢃⠺⣤⣼⡧⢠⠇⢀⡑⢻⠾⣯⣿⠇
⠀⠀⠀⠀⠨⡻⢿⣜⠿⣃⠘⠇⠀⠀⠀⢀⠠⠋⢇⣼⣿⣯⣷⠄⠀⠀⠀⠘⠀⢸⠅⢰⡎⢶⠺⠄⠈⠛⠋⠁
⠀⠀⠀⠀⠀⢌⣵⣬⣧⣽⣦⢷⡄⢀⣾⣿⡓⢿⡿⣿⣿⣷⠟⠀⢠⠀⠀⣿⠀⣼⠀⠸⢠⠃⢠⠀⣠
⠀⠀⠐⠀⢰⣟⣻⣿⣿⣶⣟⣱⣿⢻⣿⠟⢀⡿⠷⣿⣿⣿⡇⣠⣾⡇⠀⢻⠀⠀⣼⣿⣓⣦⣸⣿⣇⣴⢃⣤⡄
⠀⠀⠀⣇⠺⣿⡿⢿⣿⣷⣾⠿⠾⣻⣿⠄⢠⣷⣾⣄⢡⠻⢿⣿⣿⡇⠀⢸⣀⣾⠿⣷⡄⠻⣿⡿⢯⣿⣏⣞⣡⡤
⠀⠀⠀⠈⠟⠴⡿⢻⣄⡹⣸⡟⠙⠟⠁⠐⣿⣿⣿⡿⠘⡀⠀⡿⢿⣅⣠⢸⠉⡇⢰⠿⣿⡄⣠⣴⣟⣻⣽⣯⣥⡤⠄
⠀⠀⠀⠀⠀⠉⠑⠋⠘⡁⠉⣿⠀⠀⣄⠀⠈⠙⣻⣀⣀⣧⢤⣷⣼⣤⣽⠾⠶⢷⣮⠰⢒⡿⣿⣿⣤⣧⡠⡉⠐
⠀⡓⠐⢦⣜⣿⣷⣤⣄⡇⠀⣏⣾⠀⢻⣷⡀⣼⣿⢟⣽⣾⣿⣿⡏⡿⣿⣿⣛⣿⣿⣷⣻⠇⠋⡏⢻⠙⠛⠃
⠀⡇⠀⠀⠈⠉⠛⠛⠛⠛⠀⣿⠇⠀⠾⣿⣧⠟⣧⣿⡿⢿⠁⢸⣴⡇⡿⠿⣯⣭⢿⡟⠎⠀⢀⣴⣾⡿⣿⠿⣷⠆
⠀⠃

⠀⠂⠀⠀⠀⠀⠀⠃⠐⠃⠘⠃⠘⠁⠘⠀⠀⠉⠐⠇⠐⠃⠀⠀⠒⠃⠻⠀⠓⠀⠡⠀⠀⠇⠀⠓⠀⠃
⠀⠂
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⠻⣌⠀⠀⢀⠰⣾⠃⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣛⣛⣯⣟⣋⣬⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣁⣤⣄⢠⣦⣐⡎⠀⠀⣴⣯⣬⠁⠀⠈⣧⠀⠀⣿⣿⣟⣭⣭⣿⡿⣻⡦
⠀⠀⢀⡴⠖⠛⠲⣤⡀⢛⣿⡏⠙⢉⣹⡿⠁⡴⠏⠁⠀⣀⡵⠶⠴⢿⣀⠀⢾⣿⣶⣤⣿⣶⣾⡉⠁⠀⢀⡿⣦⣀
⠀⢠⡏⠀⠀⠁⠀⢈⣷⠈⡿⣿⡿⣿⣿⠇⢰⡝⠂⠀⣼⠇⠀⠀⠀⠀⢈⡄⠸⣯⣏⣻⡟⢋⣿⡏⠀⠰⣏⣆⢻⣿⢳⡀
⠀⠈⢏⠀⠀⠀⣠⣬⣟⠀⢹⣿⡷⣾⢿⠀⠈⢹⢲⡴⣯⡀⢀⠀⠀⠀⠠⣾⠀⢹⣿⣟⣛⣿⡿⠀⠴⣴⠿⠼⣿⢘⣿⣧⡄
⠀⠀⢋⡀⢀⢠⣀⢢⡼⠀⠸⣿⡷⢮⣿⠀⠀⠺⣼⣗⠀⠣⣠⡀⠤⠤⢶⡋⠀⠀⣿⢹⣿⣿⡇⠀⠼⣯⣾⣱⠚⣜⣿⣹⠃
⠀⠀⢠⡾⣷⡾⡿⡾⠀⠀⠀⠛⠓⠚⠃⠀⠀⠀⠈⢿⣿⣶⣶⣦⣴⡻⠉⠀⠀⠀⢽⢾⣤⣿⠃⠀⠀⢻⣿⣿⣾⣛⣿⡿
⠀⠀⠀⠜⣧⣻⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣧⠃⠀⠀⠀⠀⢸⣿⣩⣿⠀⠀⠀⠘⣟⣿⣹⣯⣽⠇
⠀⠀⠀⢸⣶⢋⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⣖⡏⠀⠀⠀⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⢻⣿⣙⣯⣿
⠀⠀⠀⠈⡟⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣽⣩⠁⠀⠀⠀⠀⠀⠀⠹⢿⠇⠀⠀⠀⠀⠈⣿⡟⣿⠇
⠀⠀⠀⠀⠙⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⣴⣆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢠⣶⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⣴⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣫⡖⣦⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⠵⣯⣼⣿⣿⢸⣧⡴⢞⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡔⢻⣶⣿⣿⡿⣟⠈⢷⠄⠙⠃⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣼⢋⣴⣉⣿⣿⠿⠋⣵⠄⠉⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣴⠟⣵⣧⣼⡿⢋⡅⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣿⠀⠀⠀⠀⢀⡾⢫⣾⣿⠟⠉⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⣠⡟⣱⣿⡿⣁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⣰⡟⣼⡿⢫⡄⠉⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⢸⣟⢱⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣧⠀⢰⡟⣼⠟⣥⡌⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⣿⠿⣿⣿⣶⣄⠀⠀⣿⣿⣋⣣⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡻⣤⣿⢱⠏⣦⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⢸⣿⣿⠀⠈⢻⣿⣿⣦⣼⣿⣿⣏⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡴⠛⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣦⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠛⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⢈⣿⣶⡄⠈⡳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣟⢛⡿⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⣷⣦⣤⣟⢷⣭⡻⢶⣦⣤⣤⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡋⣻⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠉⢻⣿⣿⣷⣬⡛⢶⣭⣛⠿⣍⣽⣿⠛⣿⠟⣿⠟⣿⣏⣹⣧⠼⣛⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⠈⠙⠻⠶⣮⣭⣽⣛⣓⣛⣛⣫⣭⣭⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣤
⠀⠀⠐⠒⡂⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⡀⠀⠀⣾⠢⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠤⠷⡀
⠀⠀⠈⠊⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡧⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠗⠒⠀⠀⠀⠀⢆⠊⣀⡠⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠭⠄⠒⢈⡢⠀⠀⠀⠫⡩⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠣⢄⠀⠠⠁
⠀⠐⠆⠀⠀⡀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠁⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥
⠀⠀⠀⠀⢸⡇⠀⠄⢠⡄⠀⣇⡠⢃⣀⠀⢣⠀⡀⠀⢾⠉⠂⠀⣽⠀⡖⢲⠀⢹⡏⢡⠀⠀⢿⠀⠄⠀⠀⣆⠀⡀⠀⠈
⠀⢀⡀⠀⢸⠁⢈⢀⡟⠰⠀⣷⠀⣿⠀⡁⠈⡗⠀⠀⢸⠉⠑⠀⡇⠀⡟⢅⠀⠸⠇⣸⠀⠄⢸⢀⠄⣰⠇⠘⣦⠀⠀⢠
⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡿⠈⠀⠀⠃⠀⠀⠘⠇⠊⠀⠀⠀⠃⢀⡀⠀⠀⠛⠀⠃⠈⠁⠰⠋⠁⠀⠿⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠄⡄⠀⠀⡇
⠀⢀⠀⠀⠀⠘⢲⠤⣀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⠤⢤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠈⠀⠀⠀⢰⠈⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠒⢒⡲⠭⠙⡄⠀⠀⠀⡒⠢⠔⠒⡄
⠀⢀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⣀⠀⠀⠀⠢⢀⣪⡂⠀⠀⠀⠀⠀⠀⢋⣁⡀⣤⢤⣰⠷⠀⠀⠀⠑⡀⢀⠜⠀⠀⠀⠀⠔
⠊⠀⠈⠂⠐⠊⠀⠀⠉⠁⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠈⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠒⡘⠉⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⠁⠀⠈⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠁⡠⠔⠂⠩⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠇⠎⠀⠀⣀⠀⡉⠉⠁⡀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⢠⠂⠀⠀⠀⠀⠌⠀⠀⢸⢸⢀⠀⢠⠃⡸⠁⡸⢡⠃⢠⢃⡎⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠦⡀⡏⠀⠀⠀⠀⠈⠀⠀⠀⢸⠸⠘⠂⠘⢠⠛⠀⢀⠎⠂⠀⠘⠀⡜⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣹⠙⠆⠀⠀⠀⠀⠀⠀⢄⡈⠢⠑⠒⠒⠁⢀⡤⠋⠀⡠⠂⠀⡰⠁⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠃⢀⡜⠁⠀⣀⣠⠖⠁⠀⠀⠀⠀⠀⡖⠉⠐⠀⠘⡆⠀⠀⢀⡨⠭⡀⢀⡜⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⠁⠀⠉⠓⣄⠀⠀⠐⠀⡀⠀⠔⠀⢠⠇⢀⡔⠑⠐⠀⠁⣼⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡤⠖⠒⠉⢁⡟⢂⡞⠤⣑⡀⠂⠀⠙⠊⠀⠀⠀⠀⢀⠀⠀⠀⣰⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣀⣀⣀⣀⠀⠀⣼⠁⠀⠃⣀⠀⠀⢀⡞⢀⡞⠀⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁⠀⡸
⠀⡰⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠔⠋⠉⠀⠀⠉⠳⣴⠃⢀⠞⠀⠀⡤⠀⡜⠀⡼⠂⢸⠃⠀⠀⢀⡏⠀⡀⠀⢸⠃⢠⠇⢀⡞⠀⠀⡴⠁
⢰⠁⠀⠀⠀⠀⠀⠀⢠⠊⠀⡐⠁⠀⠀⠀⠀⠀⢀⠜⢻⠀⣼⡀⠀⢰⠃⢸⡃⠸⠁⢀⡏⢰⡃⠀⣾⠀⢼⠀⠀⡇⢠⡏⠀⡼⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁⠀⠀⠀⠀⠀⢐⣁⠄⣼⢀⡈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠈⠁⠀⠁⠀⠁⢰⠃
⠈⠳⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣠⠃⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⠀⠀⠀⠀⡤⠊⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⠀⠀⠀⢠⠊⠹⣆⠀⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⢠⠎⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣆⠀⢸⣇⠀⠀⣠⠟⠀⠀⢠⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣻⠀⠀⠉⠉⠉⠀⠀⠀⠀⢾⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠴⠋
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⣴⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣶⠄⠀⠀⠀⢘⣿⠞⠁⢀⠠⠀⠐⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⠦⣀⣼⣿⠾⣿⠀⢀⡀⠀⠈⠙⣷⡌⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣴⣾⣿⠗
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⡿⠀⣾⠛⢰⡏⢀⡟⠀⣿⣠⠎⣤⣄⠀⢮⣼⡿⢀⣄⡀⠀⢀⣾⣿⣿⣦⡀⠈⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢠⣶⣦⠀⣰⡿⣿⡀⢀⡾⣇⠸⣏⣀⡼⢀⣼⡁⠀⠈⠁⠸⢿⡿⢶⣦⡀⠀⣼⣿⣿⠀⣼⣿⡏⣿⣿⡇⣸⣃⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢠⣿⢣⠏⢰⣿⠁⣾⣃⣞⣁⣽⠀⠙⠋⠀⢈⣿⣿⣿⣿⢦⣦⣄⠀⢸⣿⣇⡾⣿⣿⠇⠀⣿⣿⠀⣿⣿⢰⣿⠛⣳⣿
⠀⠀⠀⠀⠀⠀⣴⡄⢹⣧⢸⡟⠉⣠⠛⢿⡾⣉⣫⣤⡽⠶⢶⣾⠿⠿⣿⣿⣿⠟⠋⣼⣿⡿⠀⢸⣿⡿⠁⣿⡿⠀⣠⣿⣿⣴⣿⣿⡾⠻⢿⣿⡿
⠀⠀⢀⣀⡀⠈⢿⣤⣿⡟⠈⠛⠛⠁⢠⡶⠟⠋⠁⠀⠀⣰⣿⣿⣷⡀⢰⣿⡏⠀⢰⣿⣿⠇⣴⣿⣿⠁⠀⠹⢿⠾⠋⢀⣨⣽⣿⣿
⠀⣴⣿⣿⣿⣦⠀⠉⠉⠀⠀⣀⡀⠀⠀⣴⣿⣿⣦⠀⢰⣿⣿⣿⣿⠃⣼⣿⣇⢀⣾⣿⣿⣿⡟⢻⡟⠀⠀⠀⢀⣠⡶⠟⠉⢸⣿⡿
⢸⣿⡟⠁⠀⢿⠀⠀⠀⣶⣴⣿⣿⡆⢸⣿⣿⣿⡟⠀⣼⣿⠿⠛⢁⡼⠉⠻⣿⡿⠋⠈⠙⠉⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⣼⣿⡇
⣿⣿⠀⠀⠀⣀⣠⣀⠀⢹⣿⣿⣿⠁⢸⣿⡿⠋⠀⣠⡿⣿⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣰⣿⡿
⣿⡇⠀⢠⣾⣿⣿⣟⢃⡾⠸⣿⣇⣀⣼⢿⣧⣴⡾⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⣴⣿⡿⠃
⢻⣧⠀⠈⠉⣿⣿⡏⠛⠁⠀⠙⠿⠟⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣤⡄⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣶⣾⣿⡿⠋
⠈⠻⢦⣤⠶⠛⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠛⠋⠁⢰⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣈⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⠴⠒⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠃⠠⣀⣉⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠤⡀⢋⢁⠀⢲⡏⠀⠀⢀⣔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣙⠶⢤⣬⡤⠞⠋⠀⢀⡴⠊⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠊⠙⣶⣏⠁⠀⠀⠀⠀⠀⡩⠶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠀⠀⠀⣤⡀⠈⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣭⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠉⠀⠀⣀⣴⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣿⣿⣿⣿⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣧⠄⠠⣼⣿⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣧⣤⣤⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⡀⠀⠀⠀⠀⠀⢨⡿⣇⢀⡀⠀⠀⠀⠀⠀⣤⢸⠟⣡⣷⡉⣟⣿⠉⣾⣌⠹⡇⣤⠀⠀⠀⠀⠀⢀⡀⣸⢿⡅⠀⠀⠀⠀⠀⢀
⠀⠀⢻⢷⣆⢰⣤⡀⠀⠈⢬⣻⡇⡀⠀⠀⣰⡄⢿⣾⣮⠹⣿⢋⣌⣁⡙⣿⠏⣵⢷⡿⢠⣆⠀⠀⢀⢸⡟⡥⠀⠀⢀⣤⡆⣠⡾⡟
⠀⢀⣀⣓⡽⣆⢎⢻⡜⢷⣦⠀⡼⡇⢀⠀⠹⣇⣼⣿⣵⡛⢖⢻⣾⢷⡟⡲⢻⣿⣿⣧⣘⠏⠀⡀⢸⢯⠀⣴⣾⢣⡟⡱⣰⢿⣚⣀⡀
⠐⠻⠭⠉⠁⣹⡿⠛⠵⣴⣽⡃⠀⣭⣮⡇⠀⡼⠫⢵⡦⢠⣤⡜⠃⠼⢣⣤⡌⢴⡮⠝⢧⠀⢸⣵⣥⠀⢘⣯⣦⠮⠛⢿⣏⠈⠉⠭⠟
⠀⠀⠀⠀⠟⠉⢠⡴⠾⢋⣀⣽⠗⠂⢌⣇⠰⠁⠐⠋⣾⢷⠉⠀⠒⠒⠀⠉⡾⣷⠙⠂⠈⠇⣸⡡⠀⠺⣯⣀⡙⠷⢦⡄⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠘⠀⢰⢰⢂⠸⣠⠰⢐⠀⠀⠀⢰⠃⠠⠀⠀⡀⡘⠀⡀⠇⠐⡆⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⡘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣤⡀⠘⠲⣤⣌⠙⣳⡦⠀⢒⡏⢰⠀⢀⣀⢿⡶⣀⠀⣄⣠⠀⣀⢶⡿⣀⡀⠀⡆⢹⡒⠀⢴⣞⠋⣡⣤⠖⠂⢀⣤
⢠⣤⠀⢄⠈⣻⣧⣠⡶⠿⣷⡏⠀⢚⡟⡇⠀⢣⣐⠾⡧⠘⠛⢂⡖⢠⡐⠛⢃⢸⠷⣂⡜⠀⢸⢻⡓⠀⢹⣷⠿⢶⣄⣼⣟⠁⡠⠀⣤
⠀⠉⠉⡩⣷⠏⢏⣼⢃⡶⠟⠐⢱⡏⠈⠀⣰⡏⢻⣿⠶⣧⠤⣸⢷⡽⣏⠵⣼⠶⣻⡿⢹⣆⠀⠁⢹⡔⠂⠻⣾⡘⣧⡹⠹⣮⢍⠉⠉
⠀⠀⣼⣴⠏⠰⠟⠁⠀⠀⠚⣶⡇⠁⠀⠀⠹⠃⣼⢯⡟⣠⣶⣉⢋⡙⣉⣷⡄⢻⡽⣧⠘⠏⠀⠀⠈⢸⣶⠓⠀⠀⠈⠻⠇⠻⣧⣧
⠀⠀⠉⠀⠀⠀⠀⠀⠘⣥⡏⠈⠁⠀⠀⠀⠀⠀⠛⢰⣆⠹⣟⢉⣿⢿⡉⣻⠏⣰⡇⠛⠀⠀⠀⠀⠀⠈⠁⢹⣬⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠛⠛⢿⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⣿⡟⠆⠰⢻⣿⢻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠾⠁
⡶⢶⣶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⡶⣶⡶⣶⡶⡶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠐⠀⠀⠀⢀⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠒⠓⠒⠒⠈⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠾
⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⢨⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⡀⠀⠀⠀⠘⢢⣤⣠⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢄⡀⠀⠀⠠⠐⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠹⠂⠓⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠔⠉⠰⠄⠀⠀⠀⠀⠈⠓⢶⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠘⠁⠀⠀⢀⣰⠂⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠂⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⣿⣿⢟⠿⡟⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠀⡷⣀⡀⠀⢠⠄⠀⠀⠀⡀⠠⢀⣀⣤⠀⠰⣄⣰⠀⡄⢰⡆⠀⠀⣐⠷⠄⢰⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔⢁⡀⠀⡉⢀⡄⣿⢣⢠⣾⡀⢠⡤⣶⠀⣼⠊⡌⣉⠂⢠⢉⢹⣷⣠⡟⠁⠐⠃⠁⢀⠀⢀⡠⠟⢀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠙⠁⠀⠀⠙⠟⣡⡼⠀⠁⣁⢄⣤⣄⢠⠀⠀⣇⠈⠳⣾⣙⠸⣫⡟⢀⢸⡇⠹⣷⣿⡏⠹⠵⡎⢠⣾⣤⡠
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢲⠈⠉⠙⠲⠾⠟⠁⢀⣴⣿⠀⢉⢟⣼⣧⠃⠈⡀⠐⢿⡿⠟⠻⢄⣴⣎⣁⡀⠉⣍⠀⢲⣶⡿⠋⠦⠛
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⣄⡨⠒⠀⡀⠀⢀⣀⣀⣹⣿⡷⣿⢸⡇⠹⣿⡟⠁⢠⠀⠀⢶⡄⢼⣇⣠⢸⣄⣴⣿⣦⣼⠏⡼⢻⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣈⠶⡇⢰⣾⣇⢀⣼⢿⡏⠹⣟⣡⣿⠚⢃⡗⢹⣷⣶⡟⢳⣤⡟⠀⢠⣙⣧⡜⠁⣿⣿⡿⠃⣰⠆⠋⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠑⢿⡆⢻⢿⣿⣯⡿⠃⠀⠈⠉⠀⠰⣏⠁⢈⣿⣿⢁⡿⣿⠗⢠⣾⠂⢩⠁⣸⣿⡟⢡⠞⠁⣼⣶⢳⣦
⠀⠀⠀⠀⠀⠀⠈⠢⣤⣴⣷⡄⠑⢾⣧⠙⢿⣶⣦⡶⠀⢰⣄⠀⢿⡼⢻⢹⣟⣼⣇⡿⠠⣮⣽⡆⠘⠑⢿⡏⡴⠁⣠⠾⠛⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣤⢀⠹⣅⡛⢦⡀⠙⢷⡀⠙⣿⣿⣶⣿⡏⢀⡼⠁⣿⢸⣷⣿⣁⣀⡀⠀⠀⠀⠰⣶⣿⡟⠀⠀⢁⣤⠞⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠙⠳⢬⣶⣌⠻⣦⡈⢻⣿⣿⢀⡾⠁⢸⣿⢸⣿⣿⢠⡏⢧⠀⠘⣦⣄⣿⡟⣠⣤⠾⢛⠁⠣⡀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⠀⠀⠹⣿⠿⠿⠿⠾⢿⡿⣿⣷⣶⣿⣿⣾⣿⣿⣾⣷⣾⡿⠿⠿⠿⠟⠛⠛⠋⢩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠆⠉⡇⠀⠀⠘⣷⡀⣤⡶⢤⡴⣦⠀⣤⣄⣀⠀⠀⠀⠀⠀⢠⣾⠀⠀⢠⡄⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠄⠈⠀⠀⠀⠀⠘⣷⡈⠷⣌⠃⢻⠈⣇⡠⠚⠀⣠⡖⢲⠀⢸⡟⢀⣤⠞⠁⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠓⢾⡇⠉⣠⣤⠀⣿⡀⢸⠁⣸⣿⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣠⢶⡄⠀⠀⢰⡇⠘⡆⢿⣇⡸⣴⠻⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣤⠰⠃⣼⣇⡀⠀⢸⡇⠀⡇⠈⢿⣿⣯⡀⣧⢀⡴⣤⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢰⣿⡀⣰⡟⠉⢻⣦⢸⡇⢰⠁⠀⣸⠻⣎⠀⣿⣸⠀⣸⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠜⢧⣼⠏⠀⠀⠈⣿⣸⣧⠏⠀⢀⡏⠀⠘⣇⣿⣇⣠⡟⢀⡴⣦⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠸⠀⢸⡏⠀⠀⠀⠀⣿⢸⣏⠀⠀⣼⣤⡄⠀⣿⠈⠛⠋⠀⠸⣷⡎⢿⡄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⠟⡇⢠⠊⣦⢀⣿⠟⣿⣄⡴⠃⢿⣦⣴⠟⠀⠀⠟⠙⣧⡈⠀⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡏⠀⣷⣿⠀⠁⣼⠃⠀⠈⠉⠀⢄⠀⠀⠀⠀⢠⡶⣮⠠⣘⣷⠀⢸⡇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣾⠀⢸⡏⢿⣤⡼⠃⢠⠶⡀⣠⣤⡈⢣⣀⣤⣄⢸⡇⠘⣧⠈⢻⡧⣾⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⣶⡿⠁⠀⠱⣄⠘⣦⠛⡀⣿⠈⢻⠀⢻⣟⠻⣮⣷⡀⢻⡄⠈⣷⣿⡛⣆⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⢡⠟⢳⡄⢦⢸⡇⢿⡞⢻⡌⢷⣜⡆⢸⠉⢧⠹⡟⢷⣼⡇⠀⣿⠸⣧⡼⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⡷⡄⢻⡌⢿⡇⢸⡇⡆⣿⠀⠙⣷⣈⡄⠈⢷⣻⡌⢿⣧⣤⣿⠀⠉⢀⡾⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢷⣽⠈⢿⣼⠷⣼⡇⢹⣼⡇⠀⡏⠻⣷⡀⠘⣿⣷⢸⡟⠛⠋⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⣿⡀⠸⣇⠈⢿⡇⠀⡇⣀⠹⣿⣦⣸⡟⢿⠇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢛⠻⡄⢿⡑⡘⣿⣀⠙⣯⣀⣽⠆⠉⠁⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠢⣽⠈⠻⠖⠈⠉⠀⠈⠉⠁⠀⠀⠀⠀⢀⡴⠋
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠟⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠐
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣶⡆⠐⠿⠀⠀⠀⠀⣀⡀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⣤⠶⣦⡀⢿⡄⢸⡇⠀⠀⢸⣿⠾⢿⣅⢸⣿⢸⡿⠛⠀⣿⡟⢀⣿⣧⣤⡀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢸⣿⠛⢻⣧⢸⣷⣀⣸⡇⠈⢿⣿⠁⠀⠀⠸⠿⠶⠾⠋⠸⡟⢸⠇⠀⠀⣿⡅⢸⡟⠀⣸⡇⢰⡿⠛⣿⡿⠀⢀⡀
⠀⠀⠰⣷⣄⠀⣾⡏⠙⣿⡄⣿⣦⡼⠟⠈⣿⡛⠉⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠛⠃⠹⣧⣤⣿⠃⣾⠟⠛⣶⡆⣀
⢾⣦⣴⠟⢿⣦⡙⠿⠶⠛⠋⠸⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⢦⣾⡟⠀⣿⠁⣠
⠀⠹⣷⡄⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⢎⡝⣿⣆⢀⡐⠤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣼⣿⠿⠋
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠃⡎⠀⠀⠀⢸⠂⡀⢈⡐⠂⠤⣉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡍⡌⢰⠀⠀⠀⢣⡀⠳⡜⠦⡈⠐⠢⠄⡈⠑⠋⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡰⠁⢚⡜⡠⠂⠀⠀⠀⠀⠑⢄⠈⠢⡈⠐⠢⢄⡀⠉⠐⠠⢌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⣄⡔⠙⡇⣠⡡⠀⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠑⠄⡈⠑⠢⢤⣈⠉⠒⠤⣀⠙⠆⣧⢠⡴⢉⡹⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠁⣙⣂⠊⠑⢂⣼⣫⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠉⠐⠢⠤⠭⠲⣽⡟⠠⠜⠧⡴⠆⣴
⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣠⠦⣀⣍⡜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀⡀⢨⡏⢙⡂⠀⣠⡤⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣅⣰⣃⣹⣦⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⢹⡏⠙⠉⡰⠡⣸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⡟⠈⠛⠚⠥⠔⠋
⠀⠀⠀⠀⠀⡠⠖⠂⠒⠲⢤⡴⠊⠁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠮⠕⠀⠀⠀⠀⢸⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⡄⡤⠶⠖⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⣰⣏⡀⢀⣀⣀⣀⡀⠀⣀⣀⡎⠑⡟⠓⠛⢳⠚⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⠞⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠱⣠⠃⠀⠀⠀⣦⠜⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠰⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢣⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠀⠀⠀⠀⠀⠀⠘⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠴⠊⠀⠀⠀⠐⠂⠰⠆⠀⠀⠀⠉⠁⠀⠒⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠞⠁⢀⠔⠲⡄⠀⢀⡀⠀⠀⡠⢄⠀⡞⠓⡘⠣⢼⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠈⣆⣠⠇⠀⡇⠈⡆⢸⠁⢨⠀⠑⢦⡧⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠦⣤⠽⠾⠤⠄⢷⠓⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⠀⠀⠀⠀⠀⠀⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣟⠀⠀⠀⠀⠀⠀⢸⡏⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⠀⠀⣾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⢢⣄⣼⠋⠀⠀⠀⠀⠀⠀⢸⣋⣀⠤⠤⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠊⠀⠀⠀⠀⠀⠁⠀⠀⠐⢀⠐⠀⠀⣀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠦⠀⠀⠀⠀⠆⠀⠐⠃⠀⠀⠀⠀⠀⠠⡰⠈
⠀⠀⠀⠀⠀⠀⠒⢤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡄⠀⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠱⠄⠀⠀⢀⠀⠀⠀⡀⠀⢀⠀⠔⢂⡄⠐⠄⠀⠁⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠄⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⢀⠔⠊⠉⠁⠀⠈⠉⠐⠢⣀⠀⠂⠀⠠⠈⠄⠈⢋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⢃⡖⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢳⠁⠂⠈⠁⠠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠐⠠⠀⠆⠀⠀⠀⠀⠀⢣⠀⠀⡄⠉⠀⠠⠤⠀⠤
⠀⠀⠀⠀⠀⠈⠑⢢⠄⠀⠀⡀⠒⠤⡇⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢡⠀⠀⠀⡄⠀⢸⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡄⠀⠀⠀⠐⠀⠅⠚⠀⠀⠁⠀⠀⠂⠀⡄⢈⠠⠐⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠤⢀⠀⠀⡂⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠐⠀⠈⠁⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⡀⠉⠁⠒⠀⣲⠈⠁⠀⠠⠦⡀⠀⠩⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠈⠃⢠⣦⠀⠀⠄⠀⠈⠀⠀⠀⠊⠉⠀⠀⠀⡀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢂⠀⠰⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⢤⡀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣎⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⡟⢤⡄⠀⠀⠀⠀⠀⠀⠀⠁⠈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡄⠀⠀⣴⠏⠀⠀⡔⠉⢠⠆⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢒⠲⡤⢤⡀⠀⣎⠀⠀⢰⡟⠀⠀⣼⠏⠀⠀⠀⠳⢄⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠁⠰⠁⠲⢋⣀⣉⣣⣤⣿⣅⡀⣼⠏⠀⣀⡀⢀⡀⡀⢀⢀⣀⣠⠀⣠⠀⠀⠀⠀⡠⠒⠉⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠘⠀⠀⠸⣿⣛⣫⡭⣷⠟⠋⠈⣼⠇⠈⣿⡟⣴⣋⣴⢋⣾⡁⣿⣟⣡⠇⣟⣰⡟⠀⠀⠀⢰⠁⠰⡏⠉⠑⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⡤⠔⠋⠀⠀⠀⠰⠟⠀⠀⠿⠁⠛⠉⠛⢹⠋⠋⡼⠈⣩⢀⠉⢰⢇⡟⠀⠀⠈⢆⡀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡬⠙⢷⡆⠀⡀⠀⠀⠿⠀⣰⠃⣰⣃⠞⠀⡟⣼⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⣼⣧⣤⡟⠁⢀⡋⠠⣀⣈⠀⡟⢩⣏⣴⠀⣠⢶⠇⢀⢔⡖⢠⠆⡴⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣽⡏⠀⠹⣷⡀⢸⡇⡀⣽⢃⢼⣃⠾⠃⣿⢾⡷⠻⠔⠿⠺⠇⠿⣾⠁⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣿⢻⠄⠀⣿⠃⠘⠋⠀⠙⠁⠀⠁⠀⠀⡼⠃⠀⡀⠀⠀⠀⣀⣰⡧⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠇⠀⠀⣼⠏⡴⠊⣉⠉⠙⢛⣒⣲⣶⡮⢤⣞⣉⣀⣔⣚⠉⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠴⠞⠁⠀⠰⡄⠀⠀⢀⠠⠒⠋⠉⠳⢤⡀⠈⠀⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⡇⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠒⠉