Medical model of disability Emojis & Symbols

⠀⢠⣤⣤⣤⣴⡄⡰⢦⣤⣤⠆⠴⣴⣴⠦⢄⡄⢦⣦⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢸⠻⣯⠘⣿⢃⣻⢰⠿⡎⢀⢾⡎⠃⠰⠛⠱⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠄⠤⠄⢠⠀⢄⡄⡄⠀⡄⡀⡄
⠀⢘⣁⣽⠀⢃⠈⡇⢠⠖⠀⠜⢂⣄⢶⠄⣁⣀⡄⠉⠉⠁⠁⠀⠀⠀⠀⠐⣐⡐⠒⠂⢒⡒⠒⡀⠒⠂⡂⠐⠐⢀⠂⡒⠐⠂⡀
⠀⢨⠙⠻⠀⠿⣱⣿⡏⠀⠀⠴⠞⢋⣤⣾⢿⡟⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠭⢠⠁⠠⠡⣡⠅⠀⠄⡄⡄⡄⠁⠁⠀⠁
⠀⠸⢿⣦⠀⠸⠟⠋⠀⢨⠔⠒⠈⠉⠉⠁
⠀⠀⠀⠑⡆⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⢠⠤⣤⡇⠀⠀⠀⢀⣀⣀⡀⠀⡼⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⢀⠀⠶⣾⣴⣴⡶⠦⡄
⠀⢀⠶⠞⡋⠀⠀⠀⠸⠍⡙⠂⢼⡇⠀⡀⠀⠀⠐⠌⢸⣇⢤⡀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠂⠀⠀⣩⣍⠉⠉⠉⠉⠃⠀⡀⢀⡀
⠀⣠⠖⡴⠁⠸⠶⠀⠛⠂⠉⠀⠞⡧⠀⢳⠀⠀⢠⠀⠈⠻⠿⡷⠔⠢⡄⠀⢹⠃⠄⠀⡶⢺⣷⣶⣶⡿⠬⠆⠀⢀⡀⠀⠦⠀⢨⠇
⠀⠁⠀⠀⠀⠀⠀⢠⠦⣤⡀⠀⠀⢹⠀⢰⡿⢀⡜⡇⠀⢸⠀⢀⣠⣄⢄⣤⣼⠳⠶⠞⠁⠘⠀⣿⢻⠃⠀⠀⠀⠘⠉⣛⠈⣷⣿⣷⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣟⣧⡒⠅⠀⠀⣸⣶⠏⢠⡄⠀⣽⠁⢸⠀⠉⠉⢡⠓⠂⠞⠀⠐⡶⠒⠂⠀⠉⠀⢀⠀⠀⢀⣀⣙⣿⣿⠿⣻⣿⣿⡄⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣤⡄⠀⠋⡏⠀⠀⠓⠀⣿⠀⠸⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⠛⠛⠛⣸⡇
⠀⠀⣰⠄⠀⢰⣿⣿⣿⣿⣿⡇⠀⠰⢷⣤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠘⡟⠳⠛⠻⠁
⠀⠰⣯⣸⣷⣄⣿⣿⣿⢿⡿⠗⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠐⠂⠃⠀⠀⠂
⠀⠈⣠⣿⠇⠠⣍⡽⠥⠭⡯⠐⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠓⢻⣿⣿⣿⠙⠟⠿⢯⣯⠥⠿⡿⠃⠀⠀⠀⠀⠀⠠⠠
⠀⠈⠉⠑⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠑⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⢀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⠶⣶⣶⣆⣀⣀⠿⠶⡶⢶⠷⢾⠶⣲⡆⣸⢿⣗⣀⣀⣓⣺⣶⣤⣼⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⢛⡛⣛⣛⢛⣛⣛⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⠒⡒⢒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠨⠀⠠⠄⠀⠠⠀⠄⠀⠠⠀⠠⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠄⠥⠈⠀⢀⠀⡅⠀⠈⠌⠉⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡤⣤⣤⣤⣤⠄⠈⠙⣯⣤⣰⣶⣶⣶⣶⣶⣶⣶⣶⡶⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⠀⣿⣿⣻⣿⣛⣛⣟⣻⣿⣟⣻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢰⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣴⣶⣶⣤⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠙⠙⠉⠙⠉⠉⠙⠋⠙⠀⠀⠸⠛⠿⠛⠛⠛⠛⠟⠛⠛⠛⠛⠻⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠂⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣛⠳⡄⠀⠀⡄
⠀⠀⠀⠀⢀⡠⡴⣞⢹⡟⣟⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡉⠉⢛⣧⠈⣭⣴⠀⠀⠀⠀⠀⠀⠀⡴⣦⣴⠆
⠀⠀⠀⠀⣾⢰⡇⣿⣀⣃⣁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠋⡙⣦⢹⣄⣶⢿⠀⠀⠀⠀⠀⠀⣜⣘⡛⠙⡷⢦⡀
⠀⠀⠀⠀⢿⣤⠶⢻⡿⠇⢻⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⠿⡉⡾⣿⣼⣧⠇⢸⡆⠀⠀⠀⠀⠀⣿⡏⡹⢻⣦⠸⣇
⠀⠀⠀⠀⠀⠉⢲⣾⠣⣤⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡻⡯⣿⡇⣇⡴⣾⣿⣿⢦⢼⠀⠀⠀⠀⠀⠐⣿⠀⠓⣨⠹⢷⡏
⠀⠀⠀⠀⠀⠀⠀⡽⣧⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡙⢿⠠⠟⣷⢴⣾⣿⡏⠘⣤⠚⠃⠀⠀⠀⠀⠀⢦⡃⠼⣻⣦⡈⢷
⠀⠀⠀⠀⠀⣠⣼⣿⠮⠷⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠄⢸⣇⠀⢹⣾⡇⡗⠀⣰⡏⠂⠀⠀⠀⠀⠀⠀⢸⣇⣴⡿⣷⣿⣿
⠀⠀⠀⣴⡋⡽⢯⣟⡿⢛⠙⢿⣷⡀⠀⠀⠀⠀⢠⣶⡞⠏⢀⣮⠿⡇⠀⣼⡇⠇⢀⣿⣁⣰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡈⢀⣾⢧⡀
⠀⠀⣸⣿⣟⣻⣟⢮⠁⡄⢢⠀⢻⣿⡀⠀⠀⠀⠈⣻⡉⠀⣰⡯⣴⣿⣄⡘⣠⢴⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⣶⡏⣿⠅⢸⡇⠩⣧
⠀⢰⣿⣻⢿⣟⡴⡇⠀⣿⣤⡦⡤⢿⡁⠀⠀⢘⣣⣏⡄⢰⡟⠀⣿⡽⠁⠈⠁⠀⣿⣿⡇⠸⠀⠀⠀⠀⠀⠀⠀⣿⠌⠛⣠⢸⡆⠀⠩⠧
⠀⠀⢽⣿⠲⠞⢗⣽⠀⡏⢨⡧⠀⣭⡇⠀⠀⣸⣏⢰⡁⢠⠁⠀⡛⠧⣄⣰⣀⣸⠿⣿⡇⢂⠀⠀⠀⠰⡶⣄⠀⢻⣇⠙⠅⠀⣻⡀⠀⠚⢣
⠀⠀⢲⢾⣍⡀⢛⣿⣴⠇⢸⡟⠀⣨⣇⣤⡴⠓⢾⣸⡁⢸⡃⢰⢿⠷⠦⢤⠤⢴⠖⣿⡇⠘⠀⠀⠐⣷⡚⠊⢲⣾⣿⡆⢡⠀⢿⣷⣥⠀⢹
⠀⠀⡸⣶⡦⠤⠀⠱⡿⣤⣤⣟⡀⠘⢯⣴⠇⣠⣮⠇⡧⣼⢁⡾⢸⢀⡀⠀⡄⠀⠃⣿⡦⢠⡀⠀⠀⠘⣿⣦⡀⠟⠌⠻⡄⣧⡴⢋⣏⠀⢹⠄
⠀⡼⣝⣟⢱⣖⢂⠀⢹⡿⡄⢻⣶⠤⣄⠀⣾⠟⡇⢠⠀⣼⠋⠠⣜⢊⣷⡄⠀⢀⠇⡷⢹⠋⢣⠀⠀⠀⠀⠈⠹⡄⢦⡤⣿⠷⠶⠚⢹⠀⡞
⡼⣍⡮⣭⡓⢻⣏⡤⠀⠐⣇⣈⣛⡛⠻⢾⡇⠀⡇⢈⡘⢉⠣⡑⣿⠈⣟⠄⠀⠀⠧⡿⠀⣿⣦⡄⠀⠀⠀⠀⠀⠘⣦⣹⡝⣀⡀⠀⢸⣄⠻⡄
⢳⢌⡳⠆⡇⢸⠈⢹⣁⡀⠿⠉⢤⣼⠂⠀⠀⠀⡇⢺⡁⠾⡳⣘⢷⠘⠉⠆⠀⠀⢠⣽⢰⢷⡾⠁⠀⠀⠀⠀⠀⢀⢿⣟⠇⠈⣈⠓⡇⠸⡃⢻⡀
⡷⣌⡙⢀⠁⢘⡗⠀⢹⢦⣀⠄⢻⠶⢵⠀⠀⠀⠇⠈⡃⡓⡜⢼⡛⡄⠀⡇⠀⠀⢰⡕⢸⠠⢷⠆⠀⠀⡶⡄⠀⣸⡞⢮⢹⡄⠉⠉⢧⣤⣝⠳⣽
⢢⣇⠁⡤⠀⡜⠃⠀⢀⢨⡉⠛⠁⠀⠀⠀⠀⠀⠀⠀⡇⡓⢌⠺⣏⢳⠀⠃⠀⢀⣠⡅⠸⡄⠘⣤⠀⣞⠻⣧⠀⣿⢁⡷⠠⢧⠀⠘⡄⠀⠈⢳⣦
⢴⠀⠁⡀⠀⡛⠇⠀⠰⠀⠀⣾⠿⠭⢍⣉⣂⡤⠂⠀⢡⡝⢦⣙⠦⠀⢃⠀⠀⢈⢸⠅⡀⠁⡇⢯⡀⠉⢷⡽⣿⣿⢢⡋⠆⠩⢧⢂⠘⡄⠀⢮⡳
⢾⣉⣙⠆⠀⡟⠇⠀⠐⠀⠀⣾⡂⠀⣤⣒⢊⡅⣿⢹⢘⢌⣲⣭⣓⠂⢸⡆⠀⠹⡙⠀⢇⣆⣧⠸⡃⠀⢸⢁⣿⡎⠰⡇⠀⠐⠚⢧⠰⣜⡄⠈⠓
⡳⠬⠹⠀⠀⡝⡆⠀⠐⠀⠀⢣⠇⠀⣾⢯⢿⣇⣿⣶⢊⠒⣍⡛⠉⠀⢾⣇⠀⢰⡝⠄⢹⡇⡘⠖⢻⣛⡛⣼⣿⠧⡄⡄⠀⠀⠉⣽⣷⠀⠻⣆
⣙⠙⢛⠀⠀⣗⠄⠀⢀⠀⠀⣣⣿⠀⣯⡼⣾⣿⠄⣟⠰⣙⡶⢭⠁⣀⠈⣜⠀⢱⢏⠂⣿⢀⡟⢯⢽⠓⢇⢁⢿⡞⠉⠀⡷⠀⠀⠐⣞⣧⠀⠹⣦
⣈⠉⢉⠀⠀⢎⠂⠀⠘⠀⠀⢉⣹⢀⣿⣶⡏⢸⢠⡝⡓⢬⣙⡓⠀⠤⠀⢸⠀⠟⢢⠁⠚⡜⠀⢠⠀⡿⠛⢸⠐⡉⢺⠀⡇⠀⠀⠀⠠⠽⣧⡀
⢍⣉⣉⡀⡀⠀⡆⡠⠁⢤⡄⡐⡇⣾⣿⣿⣿⢸⠻⡇⠟⡲⣬⣍⡈⣓⡀⠀⠈⠳⢀⡀⡄⢡⡎⠄⠀⢸⠀⢨⣸⠈⡃⠀⡇⠀⠀⠀⠀⠐⢲⣷⡀
⢤⣀⣈⡁⠁⣴⠛⠓⠀⠙⢛⡛⢯⣿⣿⣿⣿⢐⠀⡆⠉⠉⠀⢸⣋⣽⠉⠛⢤⠞⢻⡯⣳⣾⠯⠤⠤⢼⣧⠤⣯⠐⡇⠀⠁⡀⢸⠀⠀⠀⠨⠭⢷
⣲⠤⠤⠄⠀⢈⠀⠀⠆⠐⠀⣯⠜⢿⣿⢸⡿⢸⠀⢲⠀⠀⠀⣾⣧⡏⠀⠀⠀⠀⣼⣗⣏⠀⠀⠀⠀⠀⣵⠀⠰⣌⣿⢭⠀⠁⡜⠀⠀⠀⠀⣀⣚
⠈⢙⡒⠶⠶⠾⠤⢶⠲⣤⡌⣻⣻⣾⣿⢸⣇⢸⠀⢸⠀⢀⣴⣿⣿⡇⠀⣀⣀⣠⣿⣿⣿⠁⣶⣜⣻⣤⢾⡄⠀⢈⣟⡛⠛⢶⣁⣤⣤⣤⡾⡟⠦
⠀⣸⣿⣿⠀⠀⠀⢸⣿⡿⡇⢨⣿⣿⣿⣸⣿⣚⣶⡤⠴⢿⣿⠿⠛⠃⠀⢩⡴⢴⣎⣿⣽⣦⠀⠈⠀⠀⠁⠀⠀⣿⣿⡇⠀⠀⠉⠀⠀⣻⣴⣷⡀
⣠⢾⣿⣿⣷⣤⠤⣼⣿⣧⡽⣄⡀⣠⣴⠆⠐⠒⠳⠿⠿⠋⠀⠀⠀⠀⠀⠿⣧⣀⣬⡛⠛⠛⡀⢠⢤⡒⢒⣶⣾⣿⣿⣧⣠⠔⠒⣶⣾⣿⡿⠿⠁
⠭⠭⠴⢦⣛⡛⠭⠻⣿⠏⠹⣺⡿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣤⡴⠁⠶⠈⠋⠉⠙⠋⠀⠉⠴⠏⠙⠥⠞⠛⠉
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈

⠐⠀⠀⠀⣀⠠⠀⠀⣀⣀⠤⠂⠐⠢⠄⠠⠐⠀⣠⡶⠦⠤⠀⠄⠂⠀⡐⠦⢤⡔⠺⣦⣉⠀⠀⠀⠉⠀⠀⠐⠀⠈⠁⠐⠀⠁⠀⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⢀⠔⠀⡀⠀⠰⡁⠀⠀⠈⠑⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠠⠁⠀⢊⠀⠀⠀⠀⠐⠀⠀⠀⠀⠱⡀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⢀⣃⣺⣿⠟⡛⠛⢿⣧⣴⠾⠿⠷⣶⡤⠁⠀⠀⠀⠀⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠈⣿⠈⠒⠀⣼⢿⣿⢨⠆⢠⡿⢧⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀
⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⢀⠈⠀⠀⠀⢀⠀⠀⠀⠻⠷⠶⠿⠧⠄⢿⣷⣶⡿⠁⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀
⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⡐⠁⠀⡀⠀⠀⢸⡔⠄⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤
⣾⠟⠋⠀⠀⠀⡰⡄⠀⠂⠉⠀⠀⠘⢀⠄⠒⠣⣮⡆⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⡠⣁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠁⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠐⠄⡀⠀⠄⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀⠀⠈⠉⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠀⠉⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠃⠐⠒⠂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⠑⠢⣀
⣀⣀⣀⣀⣀⣀⣀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡑⢄⠀⠀⠀⠀⠀⠀⠔⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⣀⣀⣀⣀⣀⣄⣠
⣿⣿⡌⢻⣿⣿⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠷⡤⣀⣰⣠⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⣿⣿⣧⠀⠈⢿
⠙⣿⣿⣤⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢿⣿⣧
⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⢠⢄⢠⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀
⡄⠀⠰⡀⠀⠀⠀⠀⠀⢴⠊⠑⣸⡇⠀⠀⠀⠀⠁⠀⠸⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⣃⣿⣷⠢⣀⠄⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⢀⣼⣿⣆⠀⠀⠀⠀⠀⠣⡰⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⠐⠲⠏⢦⡂⠴⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣧⡸⠃⠀⠀⠀⠀⠀⠘⣿⣿⣄⠈
⡀⠀⠹⣿⣿⡑⣄⠀⠀⠀⠀⠑⡜⣿⣧⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢰⠁⠀⡹⠋⠀⠀⠀⠀⢀⣴⣿⡄⠘⣿⣿⡆
⣿⣆⠀⠹⣿⣿⣌⠢⡀⠀⠀⠀⠈⢾⠁⠀⢀⡀⠐⠀⠀⠈⠰⠆⠀⠐⠆⠁⠀⠀⠀⠀⠀⢂⠀⢡⠔⠁⠀⠀⠀⢀⣎⠀⠙⣿⣿⣆⠹⣿⣿
⣻⣿⣷⣀⣘⣿⣿⣦⣈⢦⠀⠀⠀⢸⠀⠀⠣⠀⢀⠶⠀⡀⡀⠀⡀⠀⠀⠀⠀⣄⠆⠪⠄⠀⠀⠀⢆⠀⠀⢀⠴⠟⠛⠓⠒⠚⠛⠛⠓⠛⠛
⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⢤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠨⠀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠥⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇
⠀⠀⠀⣙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄
⠀⢰⡟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠘⣷⡘⣿⣷⡶⠶⣦⡀
⠀⡈⠿⠘⠿⠷⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⠀⠀⠀⠐⡌⠁⠀⠀⠀⠀⡘⢷⡄⠀⠀⠀⠀⠀⣀⣠
⠀⢻⠀⠀⠀⠀⠀⢈⢿⡄⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢤⣀⣀⣠⠴⢁⣀⣠⣤⣶⣶⣿⣿⣿⣿
⠀⠈⠳⢤⣀⣠⠴⠋⠀⠁⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣤⣠⡄⣤⢰⣦⣰⢰⣦⣤⡦⣤⡄⠀⢶⡴⡖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀⣀⣄⣙⣍⣉⣋⣉⣩⣉⣛⣙⣉⣋⣋⣡⣽⣤⣤⣉⣍⣉⣋⣄⣤⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠿⠿⠿⢿⠿⣿⡿⠟⡿⠿⠿⠿⣿⠿⢿⣿⡿⡿⡿⡿⠿⣿⡿⠿⢿⠿⠿⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐
⠀⠀⢀⢀⣀⣀⣀⣀⣉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣛⠛⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠀⡀⠀⣀⣀⣀⠀⢀⡀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⢀⡀⠀⠀⠀⣀⡀⢀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡄⢠⠀⣤⡀⢤⣀⣤⠤⠤⠄⣠⣠⢀⡄⢤⣄⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠄⠠⠤⠀⠤⠤⠤⠄⠀⠀⠄⠤⠤⠠⠀⠀⠤⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠁⠁
⠀⠀⠀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣖⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣛⣻⣿⣟⡛⢛⣛⢛⣛⣛⣛⡛⢛⣛⣛⠛⣛⣛⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣴⣶⣶⣦⣤⣶⣶⣶⣶⣶⣆⣶⡆⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠙⠋⠀⠿⠿⠿⠾⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣯⣭⣿⣯⣽⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡁⠀⣿⣿⣿⣽⣿⢭⣭⣿⣽⣿⣿⣿⣿⡿⣿⡅⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠒⠛⠛⠐⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣺⣶⣶⣖⣶⣶⡶⡾⣶⣶⣶⣶⣶⣢⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣻⣟⢻⣟⣿⣿⣎⣛⣟⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠟⠟⠛⠻⠶⠟⠳⠺⠻⠇⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠆⠀⣺⣿⣖⣛⣲⣟⣒⣶⣺⣿⣿⣟⣲⣏⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠷⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠂⠒⠂⠐⠂⠒⠒⠀⠂⠒⠒⠒⠒⠒⠀⠀⠀⠒⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠁⠀⠀⠃⠀⠆⠀⠀⠘⠀⠀⠀⠘⠀⠀⠁⠰⠄⠀⠀⠌⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠒⢀⣀⣒⣒⠂⢐⣂⠀⢀⣐⡒⣀⠀⣀⢂⢀⢐⢐⣲⣀⠐⣀⠐⡂⢐⠀⢂⡀



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⢶⡤⡆⠰⢢⡆⢰⣰⠀⢰⣠⡄⡶⢲⠀⡆⠀⠐⢰⠀⠀⠆⣶⠀⡆⢶⢴⠀⠀⡆⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠈⠁⡇⢸⠸⡇⡸⣿⠀⠈⢹⡇⠇⠸⠀⡇⠀⢀⢸⠀⠀⣤⢃⣱⢽⣹⣾⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠀⠀⠀⠀⠈⠉⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⣀⡤⠲⠲⠞⠋⠉⠉⠋⠛⠰⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢀
⠀⠀⠀⠀⡠⠺⠕⠃⠀⠀⠀⠀⠁⡁⠈⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠁⠀⡀⠈⠀⠁⠀⠀⠀⠁
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠁⡀⢀⠁⢀⢀⠈⠀⡀
⠀⢠⠃⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡶⢶⣶⣦⠠⢶⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠓⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⢸⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠈⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⣿⠋⡅⠃⠀⠀⠀⠀⣤⠀⣤⣤⣤⣄⠀⠀⠀⢀⣿⣗⡘⣀⣟⣀⡀
⠀⠆⠠⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣅⡄
⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠘⠛⠛⢃⣠⣄⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢠⢠⡄⠀⠀⠐⠛⠀⠀⠀⣹⣇
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⣀⣀⣈⣀⡀⠀⠀⡐⠚⠶⠖⠀⠀⠻⠷⠲⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠰⠦⠤⣄⢀⠤⠄⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡀⠂⠀⠀⢀⠀⣶⠁⢰⠰⠀⠀⠰⠶⡀⠂⠃⡄⢰⠀⠀⠀⡆⠀⠀⠓⣶⠀⣆⣀⢶⠀⡆⢰⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⠀⡈⢇⢿⠀⡟⢸⠀⠀⠀⠀⢇⠀⡄⢋⢸⠀⠀⡀⡇⠀⠀⡀⢧⣱⠿⣸⢢⡇⡇⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠠⣤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠤⠒⠩⠀⠀⠀⠀⠀⠉⠀⠉⠀⠌⠐⠄⡀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠘⠻⠞⠂⠛
⠀⠌⠀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢉⡉⠉⠉⣉⠁⠀⠀⠀⢀⢁⣈⠈⠉⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠀⠐⠀⠀⠙⠛⠉⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠐⠛⠛⠛⠀⠀⠛⠓⠛⠛⠃⠀⠀⠀⠂⠀⠘⠛⠛⠛⠂
⠘⡀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠀⠘⠛⠛⠓⠛⠃⠀⠘⠒⠛⠓⠒⠒⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀
⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉
⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⣀⡀⠀⢀⣀⣀⠤⠔⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠳⠶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠶⠶⣶⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢸⡏⠀⠀⠀⠀⣿
⣾⠛⠛⠛⠛⠛⠛⠛⣷⣄⡀⠀⠀⠀⠀⠈⣿⠟⠀⠀⠀⠀⢠⡿
⠻⠶⠶⠶⠶⠶⠶⠶⠟⠉⢻⣦⣄⡀⠀⠀⣿⠀⠐⢶⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡇⢀⣴⢿⣤⣤⣼⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⣿⡟⠁⢀⣠⣤⣤⡀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡀⠀⣿⠁⠀⠈⢿⡄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⢸⡇⠀⢿⡀⠀⠀⠘⣧⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷⠀⠀⠀⠙⠷⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣿⢀⣠⣼⣷⣤⣤⣤⣤⡈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠿⣯⣤⣤⣤⣤⣀⣨⡿⠦⣤⡈⠙⠳⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⠷⠶⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣴⡟⠀⢹⡷⢶⡄
⠀⠀⠀⠀⠀⣠⡴⠟⠋⢁⣀⣠⣤⣤⣤⣀⡈⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⣿⡍⠛⠿⠛⠁⠀⢻⡄
⠀⠀⠀⢠⡾⠋⢀⣴⠾⠛⠉⠁⢻⡅⠈⣿⡙⢳⣦⡀⠙⢷⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⣰⡟⠀⣴⠟⢷⣄⠀⠀⠀⢸⡇⠀⠛⠛⠛⠛⠻⣦⡀⠹⣿⠛⠛⠛⠛⠛⠛⣿⣦⠀⠀⠀⠘⣷
⠀⢰⡟⠀⣼⠋⠀⠀⠙⢷⣄⠀⢸⡿⠶⢶⣶⠶⠶⠶⠾⣷⠀⢹⣶⠶⠶⠶⢶⣶⠟⠹⣇⠀⠀⠀⠸⣧
⠀⣾⠃⢰⡏⠀⠀⠀⠀⠀⠙⢷⣼⣧⣴⠟⠁⠀⠀⠀⠀⢹⡇⠀⣿⠀⠀⠀⢸⡿⠀⠀⠹⣇⠀⠀⠀⢻⡆
⠀⣿⠀⢸⡿⠛⠛⠛⠛⠛⠛⢻⣧⣼⣿⠛⠛⠛⠛⠛⠛⢻⡇⠀⣿⠀⠀⠀⢸⣟⠀⠀⠀⠹⣆⠀⠀⠀⢿⡀
⠀⢹⡇⠘⣷⠀⠀⠀⠀⢀⡴⠏⢹⡏⠙⢷⣄⠀⠀⠀⠀⣼⠃⢠⡿⠛⠛⠛⢻⣿⠀⠀⠀⠀⢻⣆⠀⠀⠘⣷
⠀⠈⢿⡀⠹⣧⡀⣀⡴⠋⠁⠀⢸⡇⠀⠀⠙⢷⣄⠀⣴⠏⢀⣾⠃⠀⠀⣀⣼⣯⣄⡀⠀⠀⠀⢻⣆⠀⠀⣹⣧⣤⣄⡀
⠀⠀⠈⢷⣄⠘⠿⣏⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣹⡿⠃⢠⡾⠃⠀⢀⡾⢋⣤⣤⡉⢻⣆⠀⠀⠀⢻⣶⠟⠋⠀⠀⠈⣹⣧
⠀⠀⠀⠀⠙⢷⣄⠈⠛⠷⢦⣤⣼⣧⣤⣴⠾⠛⠉⣠⡴⠟⠁⠀⠀⢸⡇⢸⣇⣀⣿⢀⣿⠀⠀⠀⠀⠻⣦⣤⡶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⣀⣀⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠻⣦⣉⣉⣡⡾⠃
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦
⠀⠀⠀⣠⣶⣶⡾⣿⣿⣿⣿⣿⠇
⠀⢀⣾⣿⣿⠏⠀⠙⢿⡿⠿⠋
⠰⠿⠿⠛⠁⠀⢰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⣀⣤⣴⣶⣿⣧⣄
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡉⠉⠛⠛⠻⠟⠉⣽⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⣿⣟⣇⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣦
⠀⠀⠀⠀⠈⠙⣿⣿⣿⢻⣿⣿⣯⠁⠀⣠⡶⠛⡟⠛⢹⣿⣿⣿⣿⣿⣿⣧⣤⣼⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢻⣿⣿⣦⡾⠛⢦⡀⠸⡄⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠈⣿⣿⣿⡢⢤⣀⠙⢦⣱⣸⣸⢛⠟⢛⣛⠿⠛⣿⢻⡟⠛⢻⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⢹⣿⣿⣇⣀⣀⣉⣓⣿⣿⣿⣷⣊⣉⣀⣀⣀⣿⢸⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣀⡤⠔⢚⢟⢿⢿⢯⡒⠦⣄⡀⠀⣿⢸⡇⠀⠀⢹⣿⣿⣿⡆
⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⢹⣿⣿⡇⢀⠔⠁⡞⢸⠈⢆⠙⢦⡀⠈⣽⠇⣨⡷⠶⣤⡘⣿⣿⣿⣷
⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡁⠀⡼⠀⢸⠀⠘⡄⠀⣹⡾⠃⢸⡏⣷⣶⠉⣷⢿⣿⣿⣿
⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠙⠻⠷⢤⣼⣤⡴⠾⠛⠉⠀⠀⠈⠻⣯⣭⠿⠃⠀⠉⠉⠉⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣬⢨⠀⠀⢻⠾⡇⠀⠱⣿⠀⡧⡇⠀⢷⣿⡇⡇⣿⡄⡆⠀⢸⢸⡇⠀⢠⣱⡿⣸⡇⣿⢸⠀⡅⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⠀⠸⠘⢇⠀⠆⠟⠤⠛⣇⠀⠈⠸⠇⠡⠇⡇⢯⠀⠸⡈⠇⠀⠸⠆⣧⠿⢳⡟⢿⡀⠇⠇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠒⠫⠙⠛⢁⠉⡀⠉⠙⠘⠩⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡀⠀⠀⢀⡀⠀⠀⣀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⡠⠚⡕⠋⠁⠀⠀⠀⠈⠁⡁⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡀⠀⠀⢀⢈⠈⠀⡀⠈⠀⠈⠀⠀⠀⡈
⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠁⡀⠀⡀⢀⡀⡀⠁⢀
⠀⢠⠋⠀⠉⠉⠀⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠄⠉⠈⠉⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠀⠁⠀⠘⠉⠁⠀⠁⠉
⠀⡎⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⢰⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣤⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⢀⣤⣀
⢸⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠲⠶⠦⠆⠈⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠀⠁⠉
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠶⡶⡶⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣤⡄⠴⠠⡤
⠈⡄⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠂⠀⠇⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠛⠘⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠓⠘⠛⠛⠛⠣
⠀⠱⡈⠁⠉⠈⠁⠀⠀⠀⠀⢠⠀⡄⠠⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⡴⠁⢠⣤⣤⣄⠀⠀⢠⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠰⣿⡿⠃
⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠢⠀⠀⠐⠶⠷⠆⠀⠀⠀⠀⢀⣘⣀⣀⠀⠀⣐⣘⣛⡀⠀⠀⠈⠀⠀⠀⠰⠾⠗
⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣶⣦⣶⢶⡶⠀⠀⠀⠌⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⢠⣶⣤⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⡃⠀⠀⢀⠐⢳⠂⡆⡆⠀⠀⠀⠶⢴⡔⢲⢣⡄⢰⠀⠀⠐⣶⠀⠀⢸⢲⣖⠀⡆⡶⢶⡆⡆⢸⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⡁⠀⠀⡈⣷⢸⡀⣷⢷⡀⠀⠀⡇⢸⡇⠸⡠⢙⢸⠀⠀⠀⢿⠀⠀⢸⡸⣇⣾⢵⣻⢸⡇⡇⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠁⣀⣀⡈⠈⠀⠁⠁⠀⠉⠀⠀⠀⠀⠈⠀⠁⠈⠈⠁⠀⠈⠈⠀⠀⠈⠀⠉⠁⠀⠉⠈⠁⠁⠈⠀⠁
⠀⠀⠀⠀⠀⢀⡠⠔⣪⠩⠃⠀⠀⠀⠛⠀⠚⠉⡕⠢⢄
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢠⣄⠀⢦⣤⣄⣤⢠⡔
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⢀⠃⠀⠐⠒⠒⠒⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠀⠐⠂⠀⠀⠈⡄⠀⠀⢀⠰⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠴⠆⢦⡶⣤⠀⠀⠀⠀⣶⣤⣤⣴⣤⣦⡄⠄
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⢀⠠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣁⡤⡀⠀⣀⣀⣀⣀⡀⠠⠀⠀⠀⠁⠀⣀⣀⣀⣀⠐⠄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠌⣉⣉⣉⠀⠀⣀⣉⡉⠉⡁⠄⠌⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢄
⠘⡄⠀⠀⠆⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠒⠒⠒⠀⠀⠆⠀⠀⠉⠉⠙⠀⠈⠋⠙⠛⠛⠛⠁⠠⠙⠛⠛⠛⠛⠛⠀⠀⢠⣤⣤⣤⣄⠀⢤⣄⣤⣄
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠉⠁⠀⠈⠉⠈⠉
⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡁⠀⠀⡄⡜⡖⢰⣰⢰⠀⠀⠲⢶⡔⡜⠢⡆⠀⠀⢠⢲⡂⠀⢰⢲⣖⢰⣴⡇⣶⠐⠀⡇⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢱⡁⠀⠀⡘⢇⢇⢸⠞⣾⠀⠀⠇⢸⣇⢇⡄⡇⢀⠀⢸⡸⠁⠀⢸⡜⣇⡷⢿⡗⣿⠀⠀⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⣤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠤⠂⠹⠐⠀⠀⠀⠀⠉⠀⠁⠰⠉⠒⢄⡀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠢⠀⠛⠷⠓⠟⠒
⢀⠆⠀⣀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠘⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⢀⠀⠀⠀⢀⣀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠉⢉⡉⢀⠀⠀⠀⡀⡁⠀⠉⠉⠁⠀⠀⠂⠉⠋⠉⠋⠉⠙
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠋⠉⠀⠀⢀⢈⠛⠛⠙⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠛⠓⠀⠀⠘⠛⠛⠃⡀⡐⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠛⠙⠛⠃
⢸⠀⠀⠠⠤⠤⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠓⠀⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠗⠓⠂⠀⢠⣀⣀⣀⡀⠀⣀⣀⣀⡐
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠉⠉⠁
⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⠀⣀⠀⣀⣀⣀⠠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⣄⡤⠀⠦⣠⠀⡤⠀⢠⣠⡰⣴⣄⠀⠀⠀⢢⡄⠀⠐⣤⡀⡄⣦⢤⠠⢰⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡉⠀⠀⠋⣹⠃⡀⢿⢀⢷⠀⢸⠛⣄⢛⢿⠀⠀⠸⠈⡇⠀⢰⢃⣱⢧⢳⣼⠘⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⣀⣀⠀⠁⠀⠀⠁⠀⠁⠀⠀⠈⠀⠈⠀⠁⠀⠁⠁⠀⠈⠈⠁⠈⠁⠈
⠀⠀⠀⠀⠀⢀⡤⠒⠎⠛⠋⠉⠉⠉⠋⠷⠖⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⡀⠀⠀⡀
⠀⠀⠀⣠⠞⠗⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⡄⡄⠀⠄
⠀⡜⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠸⡀
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣬⡍⡄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠛⠃⠉⠙
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣤⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢠⠀⡤
⠘⡀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡜⠀⠀⠘⠛⠃⠉⠀⠀⠀⠀⠀⠙⠈⠋⠉⠛⠃⠀⠀⠀⠛⠛⠂⠛⠛⠛⠠
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠰⠶⠤⢀⢀⠠⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠀⠘⢻⡟
⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠁⠀⠀⣉⢉⠁⠀⠀⠀⠀⠶⢴⡶⠀⠰⢷⠬⠆⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠈⠉⠙⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠋⠛
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠄⢀⡀⠀⠤⠤⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⢹⣇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⡗⠀⠀⠀⣠⠦⣤⡀
⠀⠀⠀⠀⣾⠻⢷⡀⢸⠀⡜⠀⠐⢴⠂⠢⣌⣭⣤⡀⢠⣭⣅⠤⣨⡄⠀⡀⡄⠰⠀⡇⠀⠀⠐⡛⠿⠫⠃
⠀⠀⠀⠀⢃⣶⡙⠁⢸⣀⡇⠄⠀⢠⡠⡄⢰⠠⣤⡤⠀⠀⠄⠀⠀⣀⠠⠂⠀⠀⢠⣧⠀⠀⡀⢈⠉⠤
⠀⢀⡤⢁⡈⠐⠁⠐⣼⣿⠛⠑⠀⠒⠀⠀⠄⠀⠠⢉⣾⣿⣦⠀⠀⠤⠤⠄⠐⠘⠈⣿⡆⡌⡀⠀⡀
⠀⠠⠓⣺⠁⠠⠄⠒⠏⡏⢰⣦⡤⠀⢰⡳⠀⣤⠀⠘⡴⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡈⠇⢆⠁⠠⠏
⠀⣠⢠⡇⠀⠀⠀⠳⠘⣇⣘⣿⢉⣇⢘⠀⠀⢸⣀⣤⡄⣉⣢⠀⠀⢠⣴⣶⣆⠀⠀⣿⠀⠀⡦⠠⡄⢼
⠀⣿⣼⠁⠀⠀⠀⠀⠀⡇⢸⡏⠁⠂⠁⠀⠀⠀⢉⡀⣀⠁⠁⠀⠴⣿⢟⣷⣃⣀⡀⢻⠀⠀⠁⢀⠀⠘
⠀⣿⢧⠀⡀⡀⢀⠄⠸⡷⢾⡟⢢⣈⣐⢲⠀⠀⠈⠉⠰⠀⠐⠡⠳⠢⠘⣶⣋⣙⠇⠀⠀⠀⠀⢸
⠀⡏⠰⠖⠁⠀⠀⠀⡞⠁⢸⡍⠉⢹⣧⢸⣀⠀⡀⠘⠀⠐⣀⠗⣾⢿⠗⠆⠨⣏⡄⠀⠀⠀⠀⢸
⢰⠇⠀⠀⠀⡀⠁⠀⣧⠀⠸⣀⣀⡬⢽⣾⡏⣰⠀⢆⣀⡾⠷⢏⢗⠐⢚⢁⠶⡝⠁⠀⠀⠀⠀⢂
⣼⠀⠀⠀⠨⠁⠂⡄⠈⠛⠛⠛⠉⠀⠘⠛⠉⠉⠉⠀⠉⠛⠀⠀⢄⣦⠈⠀⠈⠀⠀⠀⠀⢶⠎⠈⢻⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠂⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢢⢦⠀⣶⠐⠆⠀⠖⣆⡆⠰⢴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠄⠓⠛⠚⠂⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠃⠀⠉⠁⠁⠀⠈⠀⠀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⡇⠀⠚⠀⠘⠃⠀⠀⠀⠀⠀⠀⢠⣤⢀⣠⣀⣀⣀⣀⢤⣤⣠⡶⠀⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢯⠁⠀⠀⠠⠈⠭⠀⠀⠀⠀⠀⠀⠀⠓⠋⠙⠋⠉⠉⠋⠉⠀⠈⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡼⢞⣹⠿⠷⠿⠞⠛⠻⡥⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠛⠛⠷⡏⠒⠀⣼⣿⣷⣦⣄⣀⣙⣄⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠐⠒⡖⠒⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⠤⡀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⢮⣡⡆⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⠧⠤⣰⣓⡄⠀⢠⡀⠁⠀⠀⠀⠀⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠒⠒⠒⠐⠂⠀⠒⠒⠒⢒⢾⣿⣿⣶⣶⣧⣤⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠒⠡⠈⠉⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠀⠀⢀⡀⠄⠄⠀⠄⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠒⠉⠀⠈⠐⠀⠐⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡟⣿⣿⣿⣿⣿⣿⣿⡠⠤⢄⡀⡠⠀⠂⠀⢀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢐⠂⠘⣿⢸⣿⣿⣿⣿⣿⣿⡏⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠒⠀⠀⠀⠀⠀⠀⠀⠠⡇⣻⡿⣿⡿⠟⠛⠿⠛⠁⠂⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠽⠁⢀⢂⡀⠈⢢⣀⣀⣀⣢⡤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠒⠋⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠉⠀⠀⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠁⠢⡀⠀⢂⠀⠐⠂⠐⠒⠂⠐⠂⠀⢀⠂⠀⡠⠂⠁⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠆⠀⠀⡄⠀⡄⠀⢀⠀⠀⠐⡀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢆⠀⠒⠂⠐⠒⠒⠐⠂⠀⠠⠀⠀⠀⠀⠀⠈⢹⠉⠀⠀⠀⠀⠀⢡⠀⠀⠠⠠⠤⠄⠤⠄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠠⠰⢅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠵⠠⢀⠀⠀⠀⠀⡀⠔
⠀⠀⡀⠄⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠄⠀⠘⠀⠀⠄⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠄⡀
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠀⠂⠐⠂⠂⠈⠢⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑
⡁⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠦⠤⠤⠤⠤⠶⡇⠀⠨⠤⠉⠤⠤⠬⠠⠀⠀⡷⠦⠤⠤⠤⠤⠆⠀⠀⠀⣀⠀⢀⢀⡀
⠡⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠐⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠁⠂⠀⠤⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠂⠀⢤⠄⠀⠂⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠠⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠈⠐⠴⡊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡲⠐⠈⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠁⠈⠌⠈⠉⠄⠀⢀⠁⠀⠠⠂⠁⠀⠀⠀⠀⠁⠢⡀⠀⢁⠀⠀⠈⠁⠄⠩⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠌⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠄⠀⠑⠄⡀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠤⠄⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⣀⠠⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⡀⠈⠈⡆⠙⢳⠀⠂⠐⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠈⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠒⠁⡀⢇⣀⠱⠆⢈⡰⢱⠒⢴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠉⠀⠀⠈⠈⠉⠁⠀⠁⠉⠙⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠐⠛⠒⠬⡃⠉⢉⠀⡄⠀⡇⠀⠁⠀⠀⡀⡀⠀⠀⠀⠀⠀⠘⠢⢤⠀⢠⠠⣄⠄⠠⠔⡒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠀⣄⠃⠀⠆⠀⡠⠂⠉⠀⠀⠀⠉⠂⡀⡀⠀⠀⢸⠀⡠⠊⠀⠀⠀⠀⠈⢢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⡁⠀⠀⠀⠀⠀⠀⠀⡁⡙⠀⡠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠨⠀⢫⠀⠀⠀⠀⠀⠀⠐⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠀⠀⠀⠀⠀⢀⣈⢁⠄⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⢀⠠⠘⢄⠘⡀⠀⠀⠀⠀⠀⢰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠉⠀⠀⠀⠪⠍⠠⣀⡀⠀⠀⠀⠘⡠⣀⠀⠀⠀⣀⡠⠔⠊⠀⠠⢀⠤⠤⠔⠃⠀⠀⠀⠀⠠⠎⢶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡆⠀⠀⠈⠀⠉⠀⠀⠘⢠⠐⠀⠀⠀⠄⠧⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⡰⠀⠃⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⣠⠀⢰⢀⣀⠀⢀⠀⠀⠀⡅⠀⠀⢀⠀⠀⣘⣶⣶⡖⢒⠒⣶⠓⠓⠛⠦⠞⠛⠓⠚⠓⠚⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠛⠛⡻⣉⢠⠜⠙⠢⢄⣝⠋⠉⠉⠉⠉⠙⢁⠠⠐⡡⠁⠐⠞⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡬⠔⠊⠉⠉⠀⠪⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣬⣌⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠲⠒⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⢀⠀⢀⠀⠀⠀⡇⠄⠀⠀⣠⡂⠀⡠⣀⢙⡇⡛⣋⠀⠀⡀⣀⡀⡀⠐⠜⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡶⡆⢘⢳⠀⠀⠀⢣⠂⠠⠃⢿⢿⡿⡿⠿⡿⠇⡿⠿⣿⢿⡿⡿⡧⠁⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠠⡹⣄⠀⠙⠛⠈⠙⠁⠀⢀⠎⢠⠀⠘⢠⣶⣶⣾⣳⣶⣤⣦⣷⣴⣷⣶⣴⠀⠀⢌⠦⡀⠀⠀⠀⠀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠄⡢⠤⠦⠄⠋⠁⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠈⢒⠲⠤⠜⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡈⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⠴⡄⠠⠙⡿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⠂⡀⠂⠐⣾⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠾⣠⠒⢰⣿⣿⣦⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢆⡀⠄⠉⠀⠐⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠁⠠⠀⢀⢑⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣀⠠⠐⣿⣏⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡠⢤⣀⣠⣤⣴⣶⠦⠤⢤⣤⣠⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠚⠛⠋⠉⣤⠋⢀⠀⠈⢉⣀⠄⠈⡀⠨⢿⣛⠁⠀⣸⠷⠦⠄
⠀⠀⠀⠀⠀⠀⡠⠖⢁⡴⠒⣚⡛⢶⣀⠀⠀⣿⠄⠀⣉⢫⡀⠚⠃⠀⣾⠥⠾⠛⠃⠀⠀⣲⣷⡦⢄
⠀⠀⠀⠀⢀⡶⣠⠖⢋⠀⣠⠟⠁⢀⣹⠿⠒⠶⢴⠞⢁⡜⠻⣆⢠⡟⢁⣤⠶⠖⠻⣟⠛⠃⢀⣑⣶⣷⡀
⠀⠀⠀⠀⡟⣱⠏⢀⠟⢀⡇⢀⠞⣩⠴⣏⠀⠀⢄⠀⣾⠀⠒⢈⠞⠀⢸⡇⢀⡘⠳⢻⡆⢠⡏⢹⠛⢯⡑⡄
⠀⠀⠀⢸⡖⠙⣆⠀⢀⠌⠀⢸⡇⠁⠀⠤⢼⡀⠀⣿⠃⠀⠠⠞⢀⠀⢸⣦⣿⣁⣠⣼⣆⣸⡁⢸⡆⠈⢻⣾⡄
⠀⠀⠀⠀⠁⠈⠲⠗⠤⠤⠤⠀⠙⠳⠶⠄⠈⣧⢀⡋⣀⣦⣄⣠⠾⠷⢾⣿⠀⠉⠉⠻⠟⢉⡵⠋⣠⣴⣾⣿⠳
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠲⠓⣒⠂⢲⡾⠛⠉⠀⠁⠈⠉⠁⢀⠀⠀⡿⠛⠛⣷⣶⡶⢿⣇⠐⣋⢱⣾⣷⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⣠⣤⠶⠋⠉⠙⠒⢤⡿⠶⢼⣷⠶⠙⠻⠛⢀⣰⣿⡟⣫⣼⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⠁⠀⠀⢀⣀⠀⢢⠀⠹⣦⡀⠀⢤⣤⡔⠛⢋⡛⢻⣯⠁⠠⣿⠿⠥⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣿⠈⢄⠀⠱⣀⡈⣧⡤⠾⠻⣙⡟⠋⠀⢶⡈⢦⣤⣀⠼⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣤⡔⣲⣾⣷⣶⣤⣤⣬⣕⣤⣀⣘⣿⢀⣀⡌⢀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣿⣿⣿⣭⣭⣟⣿⣽⣯⣽⣟⠿⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⠿⢿⣿⣏⣛⣻⣯⣭⣿⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠉⠛⠚⠛⠛⠛⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣒⣀⡢⢀⠀⠀⠀⠀⢘⡟⠀⠀⠀⢀⣤⣤⡭⣛⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠗⣐⣻⠿⣗⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⢿⠷⠶⠶⢿⣿⣿⣿⠇⠀⠀⠀⣠⣤⣄⣸⡆
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀⠀⠈⢿⣿⠟⠉⠉⠈⠙⢃⡄⠀⠐⣾⠁⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠈⣛⡟⠀⠀⣰⣿⣿⣟⣋⣿⠁
⠀⠀⠀⠠⡀⣾⡿⢛⣻⣿⣿⡀⠀⠀⢱⣀⠀⠀⠀⠀⠀⢻⡆⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠃⠀⢠⣇⢀⡀⢹⡟⠁
⠀⠀⠀⠀⠙⢿⣷⠋⠀⠐⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⢸⠉⠑⠒⠊⣳
⠀⠀⠀⠀⠀⠸⠛⠆⠀⠀⣸⠀⠀⠀⠲⠶⣤⣄⡀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⣠⡤⠤⠶⢾⡟⢁⣀⡀⠀⠸⡀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢉⣤⣤⣤⠟⠈⠙⢦⡀⠀⠀⠀⢻⣿⡀⠀⠀⠀⡏⢰⠠⡀⠀⠙⠛⠙⠿⠴⠶⠝⡗⢠⡞⠁
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠐⣿⣶⠿⠟⣋⣤⠶⠶⠤⣄⡙⢀⠀⠀⢹⣹⣧⠀⠀⠀⠀⠸⡄⠀⠈⠀⠀⠀⠀⠀⢠⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⣿⠁⢠⠞⠉⠀⠀⣀⣀⡀⠈⠿⣆⠀⢀⡿⠈⢧⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡀⠀⠀⢀⡴⠚⣉⣠⢤⠠⡲⠁⢀⣼⠃⠀⠈⢷⡀⠀⠀⠀⠀⣉⡛⠛⣛⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⡋⣰⠟⠋⠉⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⠉⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⡀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣤⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⠀⠀⠘⣶⡄⢈⠀⠰⠟⠐⠒⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣿⠙⠀⠐⠀⠀⢸⣷⠘⠀⣄⠸⠂⠀⠀⣄⢀⣽⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⢸⣷⣿⣿⠟⡟⠀⠆⠀⢸⣿⡌⠐⢻⠀⠓⠀⠀⣼⣿⣿⠁⢨⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣿⣿⣿⣿⡟⣠⠇⡆⢲⠀⣼⣿⣄⠀⣼⠀⡐⢰⠈⣿⣿⣿⣶⣿⠃⡿⢳⡀
⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠈⢀⠛⣿⡻⡇⠀⠃⢸⠀⣿⣿⡏⠀⢸⠀⢃⡞⠀⣿⣿⣿⣿⣿⣴⣧⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠁⣀⡤⠔⠋⠤⣀⠙⢧⣀⠨⣽⠀⣿⣿⡇⠀⢸⠃⠀⠁⠀⠃⢀⣿⡋⡛⠟⣿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡈⠀⣿⣤⣿⣿⣿⣤⣼⠀⢸⠀⠀⡠⠞⠉⠀⠙⠋⠛⠛⣿⣧
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠘⣦⡏⢿⢿⣹⠏⣿⡿⣄⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⢠⠀⠘⠂⠠⠎⠉⠒⢠⠊⠈⠁⢐⣿⡟⡋⠨⣝⣿⡯⢿⣵⣮⣿⠀⠸⠀⠀⠈⠀⠀⠀⠆⡀⢸⣿⡄
⠀⠀⠀⠀⠀⡠⠀⡁⠀⠀⡀⠀⠀⢠⠀⠀⣿⣿⠃⠠⣾⠛⠉⡛⠷⢌⠻⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢹⡻⡆
⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠁⠀⠀⠈⠀⢰⣿⡿⠂⠀⢹⠇⠟⠲⡯⠂⠑⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠈⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⢀⠀⠀⣼⣿⣥⢀⣤⡆⠙⣟⠉⠲⣤⣀⣰⣷⣆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠿⢒⣷
⠀⠄⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⠀⢰⡿⣟⠹⢹⠟⠁⠀⡏⠀⠜⣿⡏⠙⠻⠃⠀⠀⡀⠀⡢⠀⠰⠅⠀⠀⣼⠘⣄
⠀⡁⠀⠀⠀⡀⠀⠀⠀⠀⡠⠔⢁⠴⣣⣴⠟⡠⠊⠀⢠⠀⡇⠀⠀⣌⡳⣠⣷⣤⠆⡂⠀⠈⠁⠀⠀⠀⠀⢀⡟⠀⣸
⠀⠀⠀⠀⠰⡄⠀⠔⠁⠀⠀⣀⣤⠞⠁⠀⢈⡤⠀⠀⢸⡀⣡⠀⣠⣿⣿⠿⡟⢮⠙⠳⣴⡄⠀⠀⠶⠀⣀⣿⡣⣠⡟
⠀⠀⠀⠀⠀⡇⠀⢀⣠⣴⡾⢿⣴⢲⣶⣶⡟⢧⡞⠉⡣⠀⣃⠀⠉⣷⣤⠔⠚⣦⡁⠤⣈⣛⢦⡀⠀⠐⠺⣽⣿⣿⡇
⠀⠀⠀⠸⡖⠁⣠⢿⣿⠛⠀⢈⠺⠀⠈⢈⢻⡂⢄⢫⣹⠀⠂⢀⣋⣿⡡⣀⣼⠟⠇⡀⠉⠉⡟⠙⠶⣦⣾⡿⣿⡟
⠀⠀⠀⠀⠹⣶⣿⣾⡏⠀⠂⠀⠐⢁⡀⢮⣦⣿⣮⠫⠉⠀⡅⠘⣽⢏⣼⣿⠋⣤⠠⢉⡄⡀⡄⠀⣴⢭⣽⣿⣿⠇
⠀⠀⠀⠀⠀⢹⡿⣿⣷⠀⢞⢶⡀⠂⠑⢶⣿⣿⣿⡗⠂⠀⠁⢰⣿⣼⣿⣷⣾⠗⢠⡵⠁⣣⠂⢰⡏⢾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡅⢼⡦⣴⣦⣄⡀⢙⡻⣿⣿⡇⠀⣤⣿⣿⣿⣿⣯⡥⢶⠛⠀⡴⠃⠀⣾⢿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣟⠾⣿⣿⣿⣿⣿⣶⣾⣿⣦⣭⣾⣿⣿⣿⣷⡶⠯⠶⠛⢁⣰⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣭⣍⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⣁⢄⣠⣠⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢭⣿⣿⣿⣿⡿⠃⠈⠻⣯⣽⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⣰⠟⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠈⠙⣆
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⡆⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⣤⣤⣴⣶⣶⣾⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡍⣦⣀⡀⢠⠀⣀⣠⡎⡍⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡄⢉⣵⡓⢿⡟⣿⠗⣳⣍⠁⣼⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⣼⣩⢻⠳⡷⠎⢣⣾⣁⣹⣦⠋⠶⡷⢻⢫⣹⣤⡈⣧
⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣠⣤⣾⢷⣴⣯⣥⣀⣶⠿⠀⣼⣥⠺⢢⢽⡄⠼⢷⣆⣠⣭⣷⣴⢿⣦⣤⣀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⢸⣿⣿⣶⣶⣿⣿⣍⣿⣵⡿⣿⣿⣿⣿⣿⣷⣄⣿⡈⠀⠈⣸⣏⣴⣿⣿⣿⣿⣿⡿⣷⣽⣏⣹⣿⣿⣶⣾⣿⣿
⡞⢁⢱⢷⣿⡿⠯⡭⠿⢛⣽⠿⠛⠛⠛⠛⠲⢿⣿⣿⣿⣿⣵⢦⢶⣽⣿⣿⣿⣿⠷⠚⠛⠛⠛⠻⢿⣝⠻⠯⡭⠿⣿⣷⢷⢠⠙
⠑⢌⡁⠈⡻⣿⣷⣶⣚⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⣧⣿⡿⣿⣿⣿⡿⣿⣧⡟⠁⠀⠀⠀⠀⠀⠀⣠⣿⣟⣲⣶⣿⡿⡋⠀⣉⠔
⠀⠀⣨⠴⣿⣿⣟⣻⡿⢿⣿⣯⣷⣶⣦⣤⣤⣶⣾⣉⣿⣷⣿⣿⣿⣷⣿⣟⣹⣶⣦⣤⣤⣶⣶⣯⣿⣿⠿⣿⣛⣿⣿⡷⢬⡀
⠀⠀⢧⡚⠈⡟⢬⣿⣷⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠛⠉⠀⠈⠙⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣯⠜⡏⠘⣣⠇
⠀⠀⠀⠀⠀⣡⠖⣿⠟⠿⢽⣿⣿⣷⣾⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣾⣿⣿⣿⠽⠟⢿⡗⢦⡁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⢉⡉⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⣉⠉⠀⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⣛⣭⢭⣽⡯⠶⠶⠶⠾⢿⡭⠭⣭⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣉⣥⠾⠗⠛⠁⠀⢢⣾⡠⠀⠀⠀⢀⡼⠇⠀⠀⠐⢤⣈⣳⢬⣑⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠞⢋⡭⠤⠤⠶⠒⠂⢰⡾⠋⠀⠀⢀⡞⠉⠀⠀⢀⣠⠴⠞⠳⠦⢤⣀⠉⠓⢮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡽⠋⢁⣤⠞⣁⣠⠤⠤⡤⠂⠀⡞⠀⠀⠀⢀⡟⠀⠀⠐⣾⠋⠀⢀⣠⠤⠤⣄⣬⠷⠤⠤⣽⠶⣟⠦⣀
⠀⠀⠀⠀⠀⠀⢀⣼⣵⠋⡴⠚⢉⡴⠊⠁⢀⠀⠀⠀⠀⣸⣁⠀⠀⠀⢸⣇⠀⠀⠀⠈⣷⡞⠉⠀⠀⠀⠘⠄⠀⠀⠀⣿⠀⠈⠳⣌⢣⡀
⠀⠀⠀⠀⠀⢀⣼⠃⣺⣼⣁⡞⠁⠀⠀⠐⠘⢦⠀⠀⢀⡏⠀⠀⠀⣠⠞⠉⠑⠀⠀⠀⡼⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠘⣦⢷⣄
⠀⠀⠀⠀⢀⡞⢹⠞⠉⠀⠈⠑⠤⢤⡜⠀⠀⢀⡷⢄⣼⠁⠀⢀⣼⠃⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⡤⠤⠤⡀⠀⠀⠀⢠⡇⠀⢀⡿⠳⡌⢣⡀
⠀⠀⠀⠀⣸⠁⣼⠀⣀⠦⠀⠀⠀⠘⠀⣠⠊⠁⠀⠀⣿⠀⠀⠈⡇⠀⠀⠀⠀⠀⢻⠀⠀⠱⡄⠀⢸⠀⠀⠒⠻⡀⠀⠀⠉⢀⡠⠋⠀⠀⢹⣦⣷
⠀⠀⠀⡰⣹⠛⠉⣹⠇⠀⠀⠀⠀⠀⢀⡇⠀⠀⡄⠀⡟⠀⠀⠀⣧⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⢀⡇⠀⠀⠀⠀⠁⠀⠐⢲⡏⠀⠀⢀⣀⡞⠈⢿⢱
⠀⠀⢰⡇⡇⣀⣮⠀⠁⠀⠀⡖⠒⠒⠚⠇⠀⠀⢁⠀⢃⠀⠀⡀⠉⣀⣠⡴⠾⠛⠋⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⢀⠘⣦⡇
⠀⠀⠀⣷⠋⣡⠞⠢⠄⣀⡐⠃⠀⠀⠀⠀⠀⠀⠘⣆⠈⢢⣀⡿⠟⠋⠁⡤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡠⠔⠇⠠⠀⣯⠀⠀⠀⣸⡀⡸⠐⣸⡇
⠀⠀⠀⢇⢰⡇⠀⠀⢀⡔⠓⢄⡀⠀⠀⠒⠚⠃⠀⣨⡿⠛⠉⠀⠀⢀⣴⠆⠠⣤⡤⠤⠤⠴⠥⠤⠴⠐⠀⠁⠀⠀⠀⠀⢠⡏⠀⣀⣀⠀⠙⢇⠐⢠⡇
⠀⠀⠀⢸⡇⠙⠀⠀⠀⢣⠀⠀⠀⠉⠑⣤⣤⣤⠞⠁⠀⠀⢀⡠⠖⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠋⠀⠈⠉⠀⠁⠀⡿⠀⡜
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡼⠁⠀⢀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⣀⡀⠀⠀⣸⠶⠶⠶⠶⠤⠤⠴⠞⣡⠞⠁
⠀⠀⠀⠀⠹⡄⠀⠘⠦⢄⣀⢀⣀⣠⠴⣾⠁⠀⣴⠁⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣠⠤⠖⠚⠉⠀⠈⠓⠀⠀⠀⠁⠀⢀⣀⣴⣦⣤⡴⠚⠁
⠀⠀⠀⠀⠀⠙⠶⠤⢤⣤⣬⣡⣥⠤⠖⣿⠀⠀⠸⣄⠀⠀⢀⠀⠀⠀⡟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣤⣀⡀⠉⠉⠉⠑⠲⠖⠓⠀⠀⠀⢂⣤⣤⣤⣶⣶⣿⣟⣫⣽⣻⢭⣤⣶⣶⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⣠⡤⠴⠶⣾⠻⣿⣿⣿⡿⢽⣾⣵⣟⣯⣟⣻⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠛⣿⣿⣏⣩⣭⣽⣿⣷⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠻⣿⠛⠻⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠉⠉⠉⠉⠉⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠄⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣴⣿⣾⣄⣄⠀⠀⠀⢀⡀⠀⠀⠀⢠⣀⣷⣿⣦⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⣿⡿⣿⣿⣿⣾⡄⠀⠀⠀⠀⢠⣷⣿⣿⣿⢿⣿⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣿⣿⣇⣀⡙⠛⣿⣿⣦⡀⢀⣴⣿⣿⠏⢋⣀⣸⣿⣿⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠘⢉⠀⠀⣭⠙⠾⣿⣿⠇⠸⣿⣿⠿⠋⣭⠀⠀⠉⠃⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠈⢤⣤⣬⡤⠴⠋⡉⠀⠀⣉⠙⠢⢤⣥⣤⡴⠁⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠉⣡⠄⠐⠈⠀⠀⠀⠀⠁⠂⠠⣌⡉⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣀⣀⣤⣿⣇⣀⡀⠀⠀⠀⡀⠀⠀⢀⣀⣸⣿⣤⣀⣀⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣾⣩⣍⠉⠉⠀⠻⣽⣷⣼⣿⣿⣿⣿⣦⣾⣯⠟⠀⠉⠉⣩⣅⣷⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⠥⡶⠿⠀⢰⡶⡶⠿⣛⣛⣿⢿⡿⣿⣟⣛⠿⢶⢶⡆⠀⠿⢶⠬⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⣾⡿⠾⠻⠟⠻⠞⠻⠟⠿⠿⣿⡿⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⢮⠛⠛⠛⢊⣉⣈⣁⣉⡑⠛⠛⠛⡡⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢇⢦⡀⠀⠙⠛⠛⠛⢿⣿⣿⡿⠛⠛⠟⠛⠁⢠⣴⡺⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠉⣳⡘⢎⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡱⢃⡞⠉⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣏⣉⡎⠳⣿⣿⣶⣶⣶⣾⡿⣜⠷⣶⣶⣶⣾⣿⠞⢱⣉⣹⡗⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣝⡦⣀⡉⠉⠛⢿⣟⣤⠤⣛⡿⠋⠉⠉⣀⢴⣫⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢾⣿⣭⣭⡵⠶⠿⢿⣭⣭⣿⡷⠾⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢠⡞⠋⠙⠲⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⢉⠉⠉⠻⣿⣄⠀⠀⠀⠈⠉⠉⢳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⣿⣠⡶⠛⠁⠐⠻⣿⡟⠀⠀⠀⢸⡀⠀⠶⢿⡀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⣠⡼⠿⠀⠀⡄⠀⠀⣿⡇⢀⡀⠀⠈⢧⡀⠀⠀⢻⡤⠴⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣼⢋⠀⠀⠀⣴⠋⠀⠀⠀⣠⡇⠀⠈⢿⡿⠋⠀⠀⠀⠀⣿⠂⠘⢿⡀⠀⢠⡝⠷⣄
⠀⠀⠀⠀⠀⢀⣼⢿⡇⠀⠀⠀⣯⠀⠀⠀⠈⡿⠀⠀⠀⠈⡡⠔⠀⠀⠀⠀⣿⠀⠀⢸⣷⣄⡀⠹⣆⠹⣇
⠀⠀⠀⠀⢠⡎⠀⣼⠿⠿⠋⠀⣿⣦⠆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠀⠀⣿⡄⠀⠀⠀⠉⢻⣶⢿⡀⢻⡄
⠀⠀⠀⠀⡼⠀⢸⠃⠀⠀⢠⣾⠟⠁⢀⠴⠲⠶⣏⠀⠀⣿⡀⠀⢰⣇⡀⠀⠘⣷⡤⠶⠂⠀⠀⢻⡎⠻⣤⣿⡀
⠀⠀⠀⣠⠿⠿⢿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠀⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠲⠾⠷⠤⡈⠻⣆
⠀⠀⢸⡇⠀⠀⠈⠢⠀⠀⠸⣧⣀⠄⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⣼⣃⠀⠀⠀⠀⠀⠀⢤⣾⠁⠀⠀⢀⠴⠖⠶⠶⢾⣿⡆⢀⡤⠄⠀⠀⠀⠀⠈⣷⠀⠀⣠⠶⠛⠛⠻⣿⠈⣿
⠀⣾⢻⡿⠋⠑⠂⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠾⠃⠀⠀⠀⣀⣀⣠⣿⡀
⠀⣿⡈⠁⠀⣀⣤⣶⡿⠟⠷⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣀⡀⠀⣾⠁⠀⠀⠀⣠⡶⠟⠋⠉⠉⠀⣿
⢀⡼⠻⠿⠟⠋⢹⠃⠀⠀⠀⠈⠛⠦⠤⠤⠴⠶⠶⣤⣾⣿⡇⠀⠀⠘⠋⠉⠀⠀⠙⣷⠶⠶⠟⠉⠀⠀⠀⠀⠀⣠⣿
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀⢀⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⢸
⣿⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡶⠋⠀⠀⠀⣀⣴⠿⠟⠛⠒⠲⠒⠋⠀⠀⠀⠀⣼
⢸⡟⠓⠚⠛⠉⠉⠉⠛⢻⣷⣶⣄⡀⠀⠀⠀⠀⠀⠐⢤⣠⣿⡟⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉
⢸⣇⠀⠀⠀⣦⠀⠀⠀⠉⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣸⠃⠀⠀⠀⣀⡴⠂⠀⠀⠀⢀⣠⣿
⢰⣿⠶⠶⢤⣿⡄⠀⠀⠀⢀⡀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠁⠀⠀⣠⠞⠋⠛⠓⠒⠲⡶⠛⠋⠀⠀⢠
⢸⣟⢧⣄⡀⠈⠻⢦⣀⣀⣸⠇⠀⠀⠈⠻⢦⣤⣄⠀⠀⠀⢸⣄⠀⠀⠀⢀⡴⠞⠁⠀⠀⢶⡀⠀⠀⠁⠀⠀⠀⣠⡟
⠀⣻⣆⠉⠉⠛⠒⢰⡟⠉⠹⣆⠀⠀⠀⠀⠀⠈⠹⣦⣄⡀⣸⡿⠿⠶⠞⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣾⢿
⠀⢹⣿⠷⣾⡆⠀⠈⠁⠀⠀⠘⢷⣄⣀⣀⣀⠀⠀⠀⠙⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣤⣀⣠⣴⢾⡏⢁⡟
⠀⠀⠻⣆⠈⠷⣤⡀⠀⠀⣄⠀⠀⠈⠉⠉⠳⠄⠀⠀⠀⠀⣯⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⣄⠀⠈⠁⣠⡞⢀⡾⠁
⠀⠀⠀⠈⢳⣦⣀⠉⠛⠚⠻⣦⡀⠀⢷⣄⡀⠀⠀⠀⣀⣴⢿⡶⠀⢐⣈⠁⠀⠀⣀⠀⠀⣽⠶⠶⠟⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠙⣿⡛⠻⠶⡄⠈⠛⠛⠋⠉⠛⠛⠛⠛⣉⣤⣿⡅⠀⠉⠙⠛⠛⠛⠁⢀⣼⣏⣀⣤⡴⣾⡿
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⢶⣄⣀⣀⣀⣀⣤⠶⠟⠋⢉⣼⠟⠳⠦⠤⣤⣤⡴⢞⣿⠟⢉⣩⣤⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣬⣭⣿⣿⣿⣇⠀⠐⠈⠉⠻⡆⠀⠀⠀⢀⠤⠴⠋⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣭⣙⣛⠒⣋⣠⠞⠻⠶⢦⠶⠶⠶⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣤⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣀⣤⡀⣹⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣼⣿⣿⣦⡈⢳⣀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣀⣀⡞⢁⣴⣿⣿⣿⡙⡿⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⡿⠗⠀⠉⠀⠀⠀⠙⠿⠟⠉⠀⠀⠀⠉⠀⠻⢿⣿⣿⣿⠈⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡛⠉⠀⠀⢀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⢀⡀⠀⠀⠈⢻⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⠁⠀⠀⠲⣄⡙⠓⠶⠆⢸⡟⣿⡆⠴⠶⠚⢋⣠⠖⢀⠀⠈⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠻⢦⣌⣙⠛⠿⢦⢸⠀⠘⡇⠶⠟⢛⣋⣡⡴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⠸⡀⢠⢁⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡀⢀⠀⠀⠀⠀⠀⠀⠙⠃⣷⡞⠘⠁⠀⠀⠀⠀⠀⠀⢀⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⣍⣛⠷⠲⣦⡀⠀⢦⣄⠀⠘⠃⢀⣠⡔⠀⣠⡴⠞⠞⣛⡍⡙⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⣿⣿⡿⠿⣿⣿⢧⡈⠙⠀⠀⠀⠘⠉⢀⡼⣿⣿⠿⢿⣿⣷⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⡙⢯⣁⡀⠈⠻⠆⢣⠀⠀⣀⠀⠀⠀⡞⠴⠋⠀⢀⣈⡽⢫⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⠸⣧⣼⣄⣈⣍⣉⣙⠛⠀⠀⠉⠈⠀⠈⠓⣉⣉⣉⣩⣇⣤⣾⠃⣯⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⡇⠮⣭⣭⡭⠖⠀⠀⠀⣶⠃⣀⣀⠸⣦⠀⠀⠀⠲⢭⣭⣭⠔⣸⡿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⢻⡀⠀⠀⠀⠀⠀⠀⣼⠀⢾⣄⣤⡷⠀⣧⠀⠀⠀⡀⠀⠀⢠⠏⢏⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡾⠁⠀⠳⣄⠀⡡⣮⡦⣄⠈⠀⠀⢹⡏⠀⠀⠁⡀⢴⡵⢈⠀⣠⠏⠀⠘⢿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣷⣲⣄⠀⠙⢦⡑⢌⠳⢿⡷⢷⣈⣛⣗⣱⡶⢿⠿⠟⡡⢊⡼⠃⢀⣠⣶⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⣇⠀⠀⠙⠦⣍⠒⠉⠉⠙⠛⠛⠋⠉⠛⠚⣩⠞⠋⠀⠀⡸⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣄⠀⠀⠀⠈⠓⢦⡀⠀⣀⣀⠀⣀⡴⠛⠁⠀⠀⢀⣠⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢯⣷⡀⠀⠀⠀⠉⠻⠿⠿⠟⠁⠀⠀⠀⢀⣾⡽⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡺⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠟⡻⠛⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠛⠟⠻⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠠⣧⠂⠀⠀⠀⠀⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⠀⠀⠱⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⣆⢰⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠘⢷⣶⣶⣤⣖⢶⣄⣶⣶⣶⣶⣤⣶⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣰⣶⡤⣶⢲⢖⡶⣲⣶⣶⣶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⡛⢷⣿⡟⡿⢿⣌⣛⣿⣿⣿⣿⣟⢳⡄⣠⢄⣠⣄⢠⡾⣫⣽⣽⣛⣷⣯⣽⡾⣷⣿⣾⣞⣫⣾⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⢿⣷⣿⡿⣿⣾⣾⣟⣻⣿⣈⣿⣿⣿⢿⣿⠮⣿⣾⡿⣮⣋⣽⢏⣟⣧⣾⣟⣛⣿⢿⣿⣻⣶⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿⣏⣻⢟⢿⡉⠉⠉⠉⠛⢿⡿⣿⣿⣿⣿⢿⣿⠻⣶⣿⡿⠟⠉⠉⠉⢉⣽⣧⣾⣼⣷⣿⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣯⣯⣬⣷⣿⣦⣀⣀⣀⣀⣿⣷⣸⣯⢿⣪⡿⢻⣯⣾⣁⣀⣀⣀⣤⣾⠿⣻⣿⣟⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠾⣿⣿⡟⠭⣭⣵⡿⣯⡶⣿⣿⣿⣵⠟⠻⣿⡿⢻⡮⣹⣯⣛⣛⣛⡻⣿⢻⢿⣟⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣯⣼⡿⣻⣿⣥⣽⣿⡟⣉⡿⠁⠀⠀⠈⣿⣿⣿⡏⢒⡛⢿⣯⣳⣽⣿⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠿⣽⠿⠟⠉⠛⠛⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⡿⠿⠋⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⠿⡿⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠈⢉⣉⣭⡛⠃⠀⠀⠛⣫⣍⣉⠉⠀⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠻⣆⠀⠈⠸⠿⠙⢂⣀⣀⠛⠽⠿⠈⠀⢀⡞⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡏⡷⠶⠶⠚⠋⠁⠀⠈⠉⠛⠲⠶⠶⡏⣏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠒⠤⠔⠚⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣶⠞⠉⠩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠻⡝⠒⠲⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠀⠀⠀⠀⣇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢹⡀⠀⠀⠀⠀⠈⠉⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠷⢶⣄⠈⢆⣀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡄⠘⣇⠉⠉⠉⠉⠉⢁⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠘⡇⠀⠘⡄⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢿⠀⠀⠸⡄⠀⠀⡼⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⡄⠀⠀⠹⡄⡼⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⡇⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⡇⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠞⠓⠒⠚⠁⠀⠀⠀⠀⠀⣠⡤⠛⢵⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⠀⡠⡃⠀⠀⠀⠀⠀⠀⠀⡇
⠉⠓⠲⠤⣤⣀⡀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣠⡤⠴⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡆⢤⡀⠀⠠⠤⢠⠤⡤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⣻⠿⠘⢯⣭⣼⣿⣾⣓⣛⣚⡃⠀⠠⠀⢽⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠓⠀⠉⠇⡱⢊⡁⢠⣿⣿⠋⣥⠀⠉⡈⣄⠠⢞⡁⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢀⡴⢿⡦⠙⠃⠄⣥⢸⣿⣿⠺⡇⠀⠠⠇⣼⠠⠘⠃⠀⠈⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠈⠃⢠⡼⢂⠀⢐⡟⢸⣿⣷⠺⠿⠓⠛⠂⢩⠁⠇⢦⠘⢀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠄⡄⠀⣃⢘⠀⣨⢀⡌⠁⠀⢿⣿⣿⣅⡀⠀⢲⠞⠃⡆⢸⣄⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣥⣤⣄⡀⠵⣆⠀⠁⠻⣀⠘⣃⣼⣿⠁⣤⡀⠘⠏⢀⡀⠹⢩⠈⠢⡄⢠⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⢀⡀⠀⠣⢪⣣⡌⠑⠠⣄⠈⠉⢹⣿⣷⡧⡞⠛⠲⣷⡏⠀⠡⠜⡠⢦⡌⢈⣭⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡻⢂⣯⢅⡤⠄⠘⡇⠀⢳⠈⠙⣷⠟⢽⡿⢻⠃⢠⠀⢹⣆⠠⣞⣀⡀⠘⠓⠀⠀⠏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣱⣼⡀⠉⠁⠘⡃⣷⣀⠈⠟⢋⠁⠠⣾⣿⢨⡟⠁⠀⢸⢋⡞⠁⣿⠀⣀⠀⡀⠀⡄⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡛⠇⢁⠀⢾⠀⢰⠏⠘⡎⠁⢠⣞⣂⢤⣿⣯⡉⢉⡷⠆⠠⠊⠑⠀⠱⠦⠇⠀⠀⠈⠁⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠿⡧⠀⠸⠂⣸⡏⠘⢟⠀⠠⠄⠤⠆⣿⣿⣿⣯⠤⣴⠆⠀⠤⣛⣖⠲⠀⢦⠀⣀⣉⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢦⡀⠡⢀⠀⠞⢻⡆⠀⢸⡇⠀⣀⠈⠳⣾⣏⠁⠀⠀⠐⠂⠒⠀⠈⠝⠀⠀⢈⣰⠟⢉⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⠟⠳⡚⢧⠀⠘⠓⠒⠀⢿⢖⠀⠀⣷⣾⣿⣶⣟⠹⡏⢰⣄⣀⡀⢄⠰⣄⣁⣀⡀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠗⠈⢢⣉⣀⣲⢦⡤⢠⣾⡅⠀⢨⣿⣿⡯⡭⣢⠆⣻⡶⣟⠀⠘⣀⠟⠃⡄⠈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢶⡦⢁⣀⠁⢹⣄⠙⠻⣵⡦⢼⣿⣿⣿⡐⠓⠈⠁⠉⣼⡛⡿⠇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠣⠈⠁⢀⠊⠉⠠⠾⠀⠠⣶⣾⣧⠟⣽⣿⣻⠟⠒⠀⠀⠜⡿⠓⠀⡀⠀⠤⡸⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠠⢄⣼⢷⡘⠚⣡⣄⠠⣄⢀⢀⣈⣿⣿⣷⡿⢶⡀⠀⠉⣁⡄⠀⣵⣀⠀⢹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⢧⣘⣈⡝⡾⣰⣷⣮⠉⠙⠻⣿⣿⣦⡤⠤⠀⠀⡰⢿⣤⡌⠁⠈⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢿⠙⠦⢞⠋⡃⠁⡶⣶⣿⣿⠯⡤⠀⡀⠀⣢⠔⡌⢣⣤⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡘⣶⡞⠃⠈⢳⣽⣿⣿⣶⣦⡄⡠⠋⢥⡾⢇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣦⠴⠋⣸⠏⠈⠿⠾⣖⣀⣖⣈⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⡔⠀⢠⣤⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⡀⠀⠀⠀⠀⡀⢴⣧⡀⠀⠘⣏⠀⢸⡏⠀⠀⣨⡷⠄⡀⠀⠀⠀⠀⡜⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡕⣠⣴⠶⠿⢷⡄⠙⢷⠀⠀⢹⠀⢸⠀⠀⣼⠋⢀⡴⠿⠷⢶⣄⢌⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠘⣜⢧⡀⠀⠀⠘⠄⠀⢣⠀⠘⠀⠘⠀⢰⠁⠀⠊⠀⠀⠀⣰⢋⡌⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⡄⠀⠹⣦⡑⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⢤⠜⣵⠟⠀⠀⣾⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡸⣷⡀⠀⠈⢿⠇⠀⠃⠀⠀⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠁⠘⢿⠋⠀⢀⣼⡟⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠓⣹⣿⡦⠐⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⢿⡄⠀⠀⠀⠀⠀⠀⠀⠑⢴⣾⣿⡜⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠢⡀⠏⠁⠸⣿⣿⣶⣤⣦⠄⠂⠀⠀⣠⠂⠞⠁⠀⠀⠻⠀⢆⠀⠀⠈⠢⣴⣤⣴⣾⣿⡇⠀⢸⠀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⣸⣶⣄⠙⣄⠀⠀⠉⠛⠋⠉⠀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠉⠙⠛⠋⠀⠀⢠⠞⢠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠛⠻⢻⣆⠈⢦⣠⣼⣧⠀⠈⠉⠉⠉⢀⣀⣴⣄⣀⡰⠀⢣⣀⣀⣶⣄⡀⠉⠉⠉⠉⠀⣰⣷⣄⣠⢊⢰⡿⠻⡏⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣻⣿⡾⢿⡏⢿⣷⣶⣤⡬⢿⣿⣿⣿⡛⠛⠇⠀⠈⠛⠛⣿⣿⣿⡿⠭⣥⣴⣾⣿⠙⣿⢿⣾⣾⠁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣿⣿⣇⠀⠉⠛⠻⣿⣿⣄⣠⣿⡿⢛⡓⠂⠀⠀⠀⠀⠒⡛⢿⣿⣧⣀⣼⣿⠿⠛⠋⠁⢠⣿⣿⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⣾⡿⣆⠀⠀⠀⠈⠀⠠⠤⠄⠈⠉⠈⠀⠀⠀⠀⠐⠁⠈⠁⠠⠤⠤⠐⠀⠀⠀⠀⢠⠿⣯⡟⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣽⣷⡀⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⡠⢀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢁⣴⣿⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⣻⡇⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⢘⢻⡿⣿⣷⠠⣄⣀⣸⣿⠒⣶⣶⣄⠀⠀⠀⢀⣴⣶⡖⣻⣗⣀⣠⡄⢾⣿⠿⡿⠃⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠛⣾⣿⡿⠛⠻⠕⠛⠻⢿⣷⠤⢶⣿⠿⠛⠊⠿⠛⢻⣿⣷⠟⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠘⢿⡿⢂⡤⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⡠⡀⠻⣿⠏⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠊⢀⣥⣾⣏⡉⣛⠂⠀⢒⠂⠀⢛⠉⣩⣷⣮⣀⠈⠢⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢸⢿⣿⣿⣿⣿⠷⠞⠛⠛⠶⣿⣿⣿⣿⡟⡇⠀⠀⡐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣌⠘⣿⣿⠛⠑⣛⣉⠛⢉⣙⡋⠙⢿⣿⠇⣰⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣷⣼⠖⣩⠴⠖⠒⠒⠒⠒⠦⢄⡐⢯⣴⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠉⠉⠠⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠢⠉⠉⠉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⠀⠀⣰⠿⠖⠚⠒⠾⢧⡀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠉⠂⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣋⡹⡅⠋⠉⠙⢱⣴⡏⠋⠉⢻⡶⢰⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣍⣹⡄⢱⡔⠺⠘⣊⣳⣿⣯⡽⠦⣴⢾⣷⣞⠡⣾⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠱⠀⢺⣾⠇⢽⢧⠐⢩⠗⠶⣿⣿⠁⣤⣤⣹⡆⠿⢃⡟⠀⡏⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣾⠇⠦⢾⣼⠀⢾⣾⣤⡤⠶⠾⣿⡿⣆⣾⠛⠨⢹⢰⣏⠀⢠⣿⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⠇⢤⣄⣠⣤⡴⢋⣁⣴⡤⠀⢀⣿⣿⣾⠇⠰⢦⣿⡄⢹⣖⠀⠻⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢸⠀⣠⠞⠻⣆⣠⠴⠋⡉⠉⠙⠻⣿⣿⣿⡀⣶⠀⠀⢳⡾⠛⣧⠀⠩⢿⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣍⠓⠿⢤⣞⣙⠁⣤⡶⠧⣴⡆⠀⢸⣿⣬⣇⠹⡄⡰⢼⢧⡈⢾⣆⣠⣼⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠰⡏⠈⢼⣧⣬⣯⡍⠹⠶⣤⡛⠹⠅⠏⠰⣿⣿⣿⣯⡷⣌⠳⠀⣤⠄⠀⣹⠋⠀⣽⡏⢢
⠀⠀⠀⠀⠀⠀⢠⡶⢿⡐⠋⠴⠶⠶⠦⢴⣷⡜⢧⣀⠴⠾⢦⡜⣿⡻⢇⣀⣾⠶⢲⡷⠒⠀⠙⢀⠸⣵⠇⢸⠇
⠀⠀⠀⠀⠀⠀⢸⣷⣘⣟⢋⡉⢳⣼⢠⡶⢛⣛⣶⡠⠬⠤⣟⢷⣿⠀⠀⣏⢻⣦⣴⡇⢀⣤⠔⣛⡣⣌⣀⡇⣴
⠀⠀⠀⠀⠀⠀⠈⠿⡞⠙⡿⢿⠁⣇⠘⠁⢼⠙⠂⣷⠠⣤⣴⣾⣿⡀⡀⢻⡟⠉⠣⣝⠻⣎⡞⠡⡄⠈⣯⣼⢁
⠀⠀⠀⠀⠀⠀⢸⡦⣤⣿⣷⢀⡔⠈⣻⠿⠿⢦⣷⠟⡋⠍⢲⣿⣿⣻⠟⣳⣄⠓⣤⣤⣼⣁⠀⠘⠁⢰⠇⣽⣻⡀
⠀⠀⠀⠀⠀⠀⢻⠀⢘⣿⡎⣟⢦⡀⠁⠠⣆⠈⢍⣿⢦⡴⡚⢻⣿⠇⣬⡀⣾⢧⣻⣦⠟⢁⣴⣫⣴⣿⢸⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠸⡗⠀⡁⢹⡨⣤⡙⠾⠁⢺⡿⣛⣿⣌⣇⠀⣼⣿⠀⠹⢄⡼⠛⢧⠻⣠⣵⡶⣿⣿⡏⢸⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣤⠙⢦⣥⣿⣽⣷⢚⣹⢾⠫⢆⠶⠁⡼⢹⣿⠸⣵⣟⠈⠀⢨⢧⠟⠲⣼⣹⣿⠃⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣠⣤⡈⠋⡿⠶⠦⠜⢧⣌⣖⢛⣵⣿⣿⠠⠿⣿⣳⡾⠛⠛⣤⣼⡿⠋⢹⡃⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⡞⢿⡦⠈⠙⢦⡬⠉⠉⢹⣿⣿⣷⠞⡉⢁⡠⣦⣠⣀⠛⡡⣺⠾⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠋⠹⢾⡛⣷⠶⠾⣄⣠⡉⢻⢻⣿⢛⣩⠶⠿⠒⠚⠿⡌⢦⣘⠑⡿⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠴⠷⠧⠐⠢⡤⢁⡘⠸⣿⣿⣿⡿⣶⡶⠖⠀⠀⠓⠋⠙⣻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⠀⣔⣉⢻⣶⣶⣷⣬⡯⠉⢤⡀⠠⠭⡲⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣥⣤⣬⣡⡼⠟⠁⠸⣏⣘⣛⣀⣥⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡉⠀⠀⠁⢠⣤⡄⠀⠀⠀⠀⡤⣤⡄⠀⠀⠀⢛⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠻⠿⠃⠀⠀⠀⠀⠻⠿⠃⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣀⠀⠀⠁⠀⣠⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠳⣶⣶⡾⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠂⠠⢀⡀⠀⡀⠠⠔⢻⠆
⠀⠈⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠂⠸⡅⠀⠀⣤
⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⢂⣀⠙⠁⠀⠀⠀⠈⠀⢀
⠷⠀⠆⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢉⠐⠂⠰⠖⠉⠆⠀⠃
⠘⢧⠒⠀⢊⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠀⠀⠉⠲⡀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠁
⠀⠀⠀⠀⠀⠀⠻⢤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠰⠍⠀⠀⠀⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠔⠠⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡻⠗⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢀⠂⡀⣀⠀⡀⣀⡀⣀⡤⠖⠉⢡⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⣀⠀⠄⣀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⠀⠐⠄⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠺⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⠶⠟⣿⡿⠋⠁⣼⠟⠁⢀⣠⣤⣤⣉⣹⣿⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⣰⡿⠁⠶⣾⡟⠀⠀⢸⡏⠀⣴⠟⠉⠉⠉⠙⢿⡅⠀⠀⠈⢻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⢀⣀⣤⣿⡁⠀⠀⠹⠇⠀⠀⠈⠁⠀⠀⣠⣶⠟⠀⠀⠸⠇⢀⡄⠀⠈⢿⣌⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⢠⡾⠛⠉⠉⠈⣿⡄⠀⠀⠀⠀⣀⣤⣴⣶⢶⣿⡁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⢿⡄⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⣾⠃⠀⠻⣦⠀⠸⠃⠀⢀⣴⠿⠋⠉⣀⠀⠀⠈⠁⠀⠀⠀⣠⣾⠋⠀⠀⠀⣠⣾⠃⠀⢠⡾⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠛⠀⢠⣶⠾⠋⠀⠀⠀⠹⣧⠀⠀⣀⣾⠃⠀⠀⣾⠋⢀⣀⣤⣤⣴⣶⣾⠋⠁⠀⠀⢀⣾⠛⠻⣦⡀⠘⠃⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⣤⡀⠀⠀⢶⣤⣀⠀⠀⣠⣿⡷⠟⠛⠁⠀⢀⣰⣿⠟⠛⠉⠁⠀⠀⠀⠹⠇⠀⢴⡶⠟⠃⠀⠀⢸⣿⠷⣶⡀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⡇⢰⡟⠈⢿⡆⠀⠀⠈⢹⣷⠟⠋⠁⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⢺⡆⣀⣤⣤⣤⣤⣀⣀⣀⣀⣠⡴⠆⠀⣿⠀⠘⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⡇⠸⣧⠀⣼⠇⠀⠀⢰⡿⠁⠀⣤⣄⣀⣴⠟⠋⠀⠀⠀⢀⣠⣤⡿⠟⠋⠉⠀⠀⠉⠉⠙⠛⠉⠙⠷⣦⡀⠁⠀⢀⣠⣴⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⡆⠻⠿⠿⠻⣿⡇⠀⠀⠀⣹⡟⠁⠀⠀⣀⣴⠾⠛⠉⠁⠀⢠⡀⠀⣀⣤⡶⠶⠶⠶⢶⣦⣄⣈⠛⠀⠘⠻⣯⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢀⣴⠟⠛⢿⡇⠀⠀⢠⣿⠀⠀⠀⠚⠋⠁⠀⠀⣿⣶⠶⠿⣷⡾⣋⣥⡶⠶⠶⢶⣦⣄⡉⠙⠻⣦⣄⠀⠉⣰⡖⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠿⠃⠀⠀⠈⣿⡀⠀⠈⠁⢀⣴⠶⠆⠀⠀⣠⡾⢋⣴⠀⠀⣿⠻⠿⠷⠶⠶⠶⢶⣦⣽⣿⣦⡀⠀⢻⣦⣴⠟⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⢀⣀⣘⣿⣿⠶⠟⠛⠁⠀⠀⢀⣾⣿⣤⣿⠁⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣾⣇⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠙⠻⠶⣶⣦⣴⠾⠟⠁⠀⠉⠻⣧⡀⠀⠈⢹⣿⠿⠶⠶⣶⣤⣄⣀⣀⣀⣀⣼⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣤⡾⠿⣇⡀⡀⢀⣸⠋⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡈⠙⠛⢛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠈⠷⣄⡀
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠁⠀⠀⠀⠀⠈⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⣾⠉⠩⠈⣧⡀⣀⣤⣤⠴⠶⣤⣤⣤⣀⣸⣄⠀⠠⠀⠀⠀⠠⠄⠀⣠⣇⣀⣤⣤⣤⠶⠦⣤⣤⣀⢀⣼⠁⠍⠉⣷
⠀⠹⣇⠀⡠⠬⠛⠉⠆⠐⠀⠁⠀⠀⠉⠉⠉⠂⠂⠄⠤⠀⠀⠤⠠⠐⠐⠉⠉⠁⠀⠀⠈⠀⠂⠰⠉⠛⠥⢄⠀⣸⠏
⠀⠀⢻⠀⢀⡃⠀⠁⠀⢄⣀⣡⣶⣦⣥⣄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠄⠀⠀⣠⣤⣴⣶⣎⣀⡠⠀⠈⠀⠘⡀⠀⡟
⠀⠀⠸⣇⠀⡀⠐⢤⣶⡞⠋⠁⠀⠀⠀⠙⠻⣦⣤⠀⠀⠄⠠⠀⠀⣤⣴⠟⠋⠀⠀⠀⠈⠙⠳⣶⡴⠂⢀⠀⣸⠇
⠀⠀⠀⢻⡄⠄⠀⠀⠉⠛⠲⠶⣤⣤⡤⠶⠟⠉⠉⠀⠀⠂⠀⠀⠀⠉⠉⠻⠶⢤⣤⣤⠶⠖⠛⠉⠀⠀⠠⢠⡟
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠙⢷⣄⡠⠀⠀⠀⠀⠀⠀⠀⢀⠠⢢⡴⠞⠋⠙⠓⢦⡔⠄⡀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣒⡲⡂⠤⣐⣂⣭⠾⠋⠀⠀⠀⠀⠀⠀⠙⠷⣭⣐⣂⠤⢐⢖⣒⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠈⢀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠈⠀⠀⠠⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠓⡀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠠⠀⠠⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠀⠀⢀⠐⠀⠀⠜⠃⠁⠀⠀⠀⠀⢂⢀⠀⠀⠀⠂⡀⠐⠠⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠃⢀⠀⠀⠄⠂⠀⠀⠀⣨⠄⠰⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠘⠀⠊⠀⢀⡀⠀⠀⢄⠠⠠⠄⠀⠀⠤⠤⠜⠂⠠⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠈⠀⠀⠼⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠘⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠠⢀⠀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⡉⢛⣤⡽⠭⣍⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣳⠘⢋⢶⣶⣶⡆⠀⠹⢯⠁⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠛⣻⠀⠘⠘⠛⠋⠀⠀⠀⢣⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢠⣉⣒⣀⣤⣴⡆⠀⠀⣰⣇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡙⢦⣤⠶⠋⠀⣠⢾⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⢴⡞⠁⢸⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠔⠆⠳⠶⠍⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠐⣶⣾⠇⠀⢈⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠘⠯⣁⡀⠊⠀⠀⠀⣀⣀⡽⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠄⣠⠞⣿⠏⠀⣠⡟⢹⡄⠀⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠸⡋⠀⡠⠋⠢⣀⠀⠀⠀⠀⠀⣠⠊⠀⣠⢊⢴⠏⣸⣿⣤⣾⠟⠀⡿⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠈⠑⢄⡀⡠⠞⠁⠀⡔⠁⢀⣿⠀⣿⣿⣿⠏⣤⠾⣟⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠙⠆⠀⠀⠀⡆⠀⢸⡇⢰⣿⣿⠏⡼⠡⠀⢸⡦⠀⠳⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢀⡠⠖⢃⢰⣟⡇⢸⣿⠏⣸⠇⠀⠀⣸⠁⠀⣰⠻⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠒⠉⠀⠀⠘⡛⠿⠃⢸⡟⠠⡿⡄⢀⣰⠏⠀⡴⠃⠀⠘⣄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⡁⠀⠈⠁⠙⠋⢀⡜⠁⠀⠀⠀⡨⠒⠛⠁⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⢀⠀⠀⠀⠀⢠⠎⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠉⠀⠀⠀⡰⡇⢀⡴⠛⡁⠀⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠦⠁⠀⠀⠀⠀⡘⠉⠣⣀⣑⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢃⢰⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡼⢇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⣄⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢷⡶⢶⣶⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡋⣝⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢷⣤⡀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⣿⠛⠛⠓⠂⠈⠓⠀⠃⠀⠘⠃⠀⠀⠂
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣤⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠹⣆⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣷⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠰⡵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢐⡭⣗⢦⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⡀
⠐⣩⡴⣶⣶⣶⡶⣬⡑⠀⠀⠀⠀⣿⠛⢍⠉⠉⢿⡇⠀⠀⠀⠀⠀⠈⢣⢸⣿⡇⠀⠀⠀⠀⢸⡟⠉⠉⠉⠹⣿
⠸⣅⡀⣿⣷⣼⡟⢀⡽⠂⠀⠀⠀⢟⠐⠆⠻⣷⣌⡇⠀⠀⠀⠀⠀⢠⠏⡸⡽⠀⠀⠀⠀⠀⢸⡃⠲⠀⠰⠂⣿
⠀⠀⠉⠛⠛⠛⠋⢡⡤⠀⠀⠀⠀⠈⢇⠀⠧⢀⡜⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣦⡆⠀⠀⠀⠀⠱⡀⠸⠄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠁⠉⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⢸⣹⣅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣅⠀⠀⠀⠀⠀⠀⠀⣠⣬⣟⠁
⠀⠘⣿⣿⣙⡻⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⢸⢿⣿⠻⣆⠀⠀⠀⠀⠀⢸⢿⣿⡟⠷⣄⠀⠀⣀
⠀⠀⣽⣿⣿⡇⣽⣦⡄⠀⠀⠀⠀⣼⠀⠻⠿⢯⣿⡀⠀⠀⠀⠀⠀⢸⡿⣇⠈⢆⠀⠀⠀⠀⠀⢸⡿⣧⢀⣤⣤⣴⡏
⠀⢯⡟⠛⠛⠓⠛⢯⡗⠀⠀⠀⠀⠘⠦⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⡾⠁⢻⠄⠈⠦⠀⠀⠀⠀⠾⠁⡿⠉⠟⠉⠹⠇

⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣴⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠂⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄
⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠈⠿⢿⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⡟⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠤

⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠
⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢤⣀⣸⣧⡜⠉⠀⠀⠀⠀⠀⣴⣿⣷⣤⣾⣿⣦⠀⣷⠀⠀⠀⠀⢈⣿⢿⡁⠀⡀
⠀⠿⣿⣿⣿⡷⠛⠁⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⠛⠒⠀⠀⠀⠀⢿⣿⢡⢻⢟⣛⣛⡁⣋⠀⠀⠀⠀⢸⡗⢙⣿⠀⠒
⠀⠀⠛⢛⡟⠀⠀⣤⡄⠀⠀⠀⠀⠀⢠⠿⢩⡇⠉⠀⠀⠀⠀⠀⠒⠲⣿⣆⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣽⡾⣅
⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⢣⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠔⠒⠉⠁⠈⢳⠀⠀⢀⠔⠒⠉⠁⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⢀⣀⣀⠀⠻⣉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⠀⠀⡎⢀⠎⠁⠉⣉⠖⠸⡄
⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⢠⡾⠋⠁⠀⠀⠀⠱⡈⡄⠀⠀⣠⠶⠚⠲⠄⠀⠞⠉⠉⠙⠓⠀⢸⠀⣠⠃⡸⠀⠀⡜⢁⢔⠭⠒⣉⠵
⠀⢀⠴⠊⠁⠀⠀⣠⡤⠄⠈⠀⠀⣴⠞⠛⠁⠀⢣⢣⠀⠈⠀⢀⣀⡀⠀⠀⠀⣠⣤⣤⣄⠀⢸⠊⠁⡠⠃⠀⠀⠑⠯⠥⠒⠉
⠀⢸⡀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠃⠀⠀⢀⣄⠀⢟⠆⠀⠰⠛⠉⠉⠃⠀⠀⠁⠀⠀⠀⠀⡘⠉⠉
⠀⠀⠑⢄⠀⠘⠁⠀⣴⠟⠉⠁⠀⢀⢄⣰⠋⠸⠀⠘⠟⡄⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢑⠦⡀⠀⠃⠀⠀⢀⣨⡵⠛⠁⠀⢰⠀⢀⡇⠸⡀⠀⣠⠶⣖⣛⣛⡛⠛⠳⡄⢰⠁
⠀⠀⠀⠀⡌⢀⠎⠢⣄⠀⠚⢍⡁⠀⠀⢀⡠⠃⠀⢸⠁⠀⠱⣄⠛⠉⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢇⠘⠀⠀⠀⠙⠢⣄⡈⠉⠉⠁⠀⠀⣠⠎⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠈⢿⡒⠤⣀⡀⠀⠀⠀⠉⠉⠁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣈⡉⠒⢄
⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠬⢷⡞
⠀⠀⠀⠀⠀⣸⠤⠄⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣭⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣭⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣯⠁⠀⠀⠀⠀⠀⠀⢩⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣠⢖⣚⣩⣥⣴⣖⣦⣄⡙⠇⠀⠀⠀⠀⠀⠀⠟⣁⣤⣖⣶⣤⣭⣛⣒⢦⡀
⠀⠀⠀⠀⢦⣴⣾⣕⣻⠿⠿⠿⢿⠿⣿⣿⠗⠀⣀⠀⠀⠀⢀⡀⠐⢿⣿⡿⠿⠿⠿⠿⢿⣓⣽⣶⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠉⠉⠉⠀⠀⢀⣿⠀⠀⠀⠸⣇⠀⠀⠈⠉⠉⠁⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠋⢸⡇⠀⠀⠀⠀⣿⠈⠳⣄⠀⡀
⠀⠀⠀⠰⣦⣄⣀⣀⣀⣤⠤⠶⠛⠁⠈⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠈⠀⠙⠳⠦⢤⣄⣀⣀⣀⣠⡶
⠀⠀⠀⠀⢻⣷⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠘⢃⣭⣛⣛⣛⣫⣅⠛⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣱⣿⠃
⠀⠀⠀⠀⠀⠹⣷⡀⠻⣿⣦⣀⣀⣀⣠⣤⣴⣿⣿⡿⠋⠻⣿⣿⣷⣤⣤⣀⣀⣀⣠⣾⡿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⠈⠛⠛⠛⠛⠛⠛⣿⣿⣋⣀⣀⣀⣈⣻⣿⡟⠛⠛⠛⠛⠛⢋⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⠿⢿⡿⠋⠁⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠀⠔⣛⢻⣶⡄⢰⣿⣛⣳⠀⢸⠗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠉⠙⠉⠹⠃⠈⠉⠉⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠰⠋⡈⠙⢊⠁⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠤⠤⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⣠⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣧⡽⠿⠶⠒⠂⠁⡀⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⢀⡿⠈⢇⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⢸⠀⠀⠀⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠃⠸⡇⠀⠈⢆⡠⠛⣿⣿⡏⠻⣀⠆⢀⡿⠤⠼⠀⠀⠀⠀⠈⠐⠒⠒⢄
⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢣⡀⣿⣿⣷⠀⡜⢀⣼⢥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠹⣿⣿⣿⡞⢁⡟⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢘⣇⡠⡀⠀⠹⣿⡟⠀⠸⡇⠀⠀⠀⠘⠇⠀⢠⡇
⠀⠀⠀⣼⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢴⠿⠋⠀⠘⠄⠠⡏⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢦⣤⣤⠆⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣲
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡀⠀⣠⡦⣼⢧⡇
⠀⠀⠀⢢⠹⡆⠀⠀⠀⠀⠀⠈⣵⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡶⡣⠊⡰⡀⠀⠀⠀⢀
⠀⠀⠀⠈⣇⠘⠀⠀⠀⠀⠀⠀⢹⠛⠒⠦⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢀⠈⡰⠁⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⣀⣀⣸⣀⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⠁⠀⠒⠒⠶⠏⠀⠀⠈⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣈⣭⣿⡶⢶⣤⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠟⠛⢞⣛⣭⣭⣭⣶⣶⣮⣵⣶⣭⡭⢛⡻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣵⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⣥⣘⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣡⣶⡟⠛⠉⣙⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢷⣮⣛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⣼⣿⣿⣿⣿⠾⠟⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣿⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⢿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡷⢸⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢣⣽⣿⣿⣯⣥⣤⣴⣶⣿⡿⠿⣿⢟⣛⠧⠝⠣⠂⠀⠀⠀⠀⠀⠀⣀⠔⢺⣿⢿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⢰⡏⣮⡿⣿⣿⣿⣿⣏⠁⠀⠀⢠⡶⠚⠋⠈⢉⠄⠀⠀⠀⠀⠀⠄⠀⢀⠞⠁⠀⢸⣿⠘⣿⡇⢹
⠀⠀⠀⠀⠀⠀⣸⢣⣿⡇⢹⡏⢻⣿⣿⢆⣠⠖⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⢻⣦⣭⡇⢸⡇
⠀⠀⠀⠀⠀⠀⣇⢸⣿⣧⣼⣿⣾⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⠛⠛⠳⡄⠀⠀⠻⣿⡇⣸⣧⣤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⡏⠈⢿⣿⣿⣿⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⣠⠛⠛⠂⠀⠀⠀⠀⢿⣆⣥⣶⠶⢶⣬⣙⢷⡀
⠀⠀⠀⠀⠀⠀⢹⡆⣼⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠛⢠⣤⠀⠀⠀⠀⠀⢸⠟⢁⣤⡒⢤⠀⢹⣇⢿
⠀⠀⠀⠀⠀⣠⠾⢓⣼⠋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⡆⠀⠀⠀⠀⢬⡉⠀⠀⠀⠀⠀⠀⣰⠃⠀⠹⡆⠀⢸⣿⢸
⠀⠀⠀⠀⡼⢣⡾⠛⠉⠳⣌⠉⠉⠁⠀⠀⠀⠀⠀⣀⡠⠶⠛⣩⠞⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠐⢂⠙⢦⡀⠀⠀⠀⣼⢇⡟
⠀⠀⠀⢸⡇⣿⡁⠾⠉⡆⠈⠁⠒⠂⠐⠲⠶⠎⣩⣤⠔⠂⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡴⠊⠋⢁⣛⣤⠾⠃⡴⠃⠀⠀⣼⢏⡾⠁
⠀⠀⠀⢸⡟⣿⠃⣶⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢢⡄⠀⠙⢦⠜⠋⠉⠀⠀⠀⠑⢀⣠⡾⢣⡞⠁
⠀⠀⠀⠈⢷⡹⣦⡀⠂⠈⠳⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠴⠴⠤⠠⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣫⠶⠋
⠀⠀⠀⠀⠈⠳⣌⠻⣦⣀⣀⠘⠀⠻⠀⣡⡄⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⡾⣣⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠦⣭⣛⣛⡛⢿⣷⡉⣻⠌⠳⣤⡞⢉⡦⠀⠀⠀⢠⣒⣈⣶⣤⠀⠀⠀⠀⠀⠀⣠⣾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣎⢻⣄⠁⠀⠲⣄⡴⣏⠀⠀⠀⠘⠿⠿⠻⡿⠁⠀⠀⠀⠀⢀⣾⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡛⢶⣤⣀⡔⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢬⣛⡻⢤⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣝⢷⣤⣀⠀⠀⢀⣀⣀⣴⡿⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⠁⣤⡉⠉⠁⣼⠙⣧⡘⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣼⣇⠀⠈⣹⠖⠚⠓⣤⠹⣿⣿⣶⣭⣝⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣴⣿⣿⠹⠀⣠⠻⣆⠀⠀⢻⡛⠿⣿⣿⣿⣿⣿⣷⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣩⡞⣿⣿⣿⣿⡀⣷⠉⠀⠹⣧⣀⣾⡇⠀⢹⣿⡿⣿⣿⣿⣷⡜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⣿⡘⣿⣾⣿⡇⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⣿⢗⣽⣿⣿⣿⣿⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⣿⣿⣷⠈⠿⣿⣧⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⢸⣿⢻⣿⢻⣿⣷⡿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢻⢿⣿⣿⣧⠹⣷⣿⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⡟⣾⣿⢸⣿⣿⣶⢷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣿⢀⣿⣿⣿⣆⠸⣿⣇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣽⣿⣿⢼⣿⣿⣿⣿⣎⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣏⣾⣿⣿⣿⣿⣆⠹⣿⡄⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣼⡿⠟⠋⠁⢻⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⣿⣆⢨⣗⠀⠀⠀⢸⣿⣿⣿⣤⣤⠿⠋⠁⠀⠀⠀⠀⠀⢸⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠉⠉⠁⠸⣿⣿⣿⣆⠻⣷⣀⡀⠼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣷⣦⣤⣤⣤⣤⣿⣿⠷⠀⠻⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠅⢒⡀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⣛⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⣼⣦⡶⠶⠶⠶⣛⣛⣛⣯⠭⠷⠞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣛⣛⣫⣭⠴⠶⢮⣭⡵⠶⠞⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣤⡄⠀⠀⠀⣤⣄⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⣠⣦⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⢀⣴⡆⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⢷⣤⣀⣀⠀⠀⢀⣀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠈⠙⠛⢻⣶⠊⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡼⠛⠁⢸⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⣸⡿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⣿⣿⡟⠀⠀⠀⢸⣿⠋⠈⠉⠉⠀⠠⣶⣶⣾⣿⠄⠈⠻⣿⣿⡷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⣴⡆⠀⠀⠀⣿⣿⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⣿⡇⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⠀⠀⠀⠈⢃⣄⠀⠀⣿⣿⡇⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⣿⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣠⣴⣿⣿⣷⣦⡀⠀⠹⠃
⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⢿⣿⠙⠻⣿⣦⡀
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠹⣿⣿⣄⣀⡀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⣾⣿⣦⣤⣾⣿⡇⢸
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⣼⣟⠛⠛⠉⢱⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠉⠛⠛⠉⠙⠻⣿⣿⣿
⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⣄⠈⠻⠿⠀⠘⠃⣨⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣀⣴⡄⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠇⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠿⣏⣀⣴⣦⣄⣼⣿⡇⠀⠀⠀⠀⠀⣰⣿⡿⠇⠀⠀⣾⡀⠀⠀⠀⠀⢠⣿⣿
⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⡟⠈⢻⡇⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⣿⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢩⣿
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⡇⠀⠀⠀⠀⠀⢿⣿⣦⣀⡀⣿⣿⡄⠀⠀⢸⣆⣠⣿⣿
⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠀⠀⣴⣾⣿⡿⠛⠃
⣿⡃⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠙⣿⡿
⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⡇
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⢸⠃
⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠿⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸
⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡄
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠙⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⢤⣾⣿⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆⣀⣴⣶⡎⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⣴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣶⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢠⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠶⠂⠀⠒⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠓⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠸⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⣸⣿⠀⠈⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣄⠀⠀⠀⠀⢻⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠈⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢻⣄⠀⠀⠀⢸⣷⣤⡀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠙⢷⣄⠀⠸⠟⠉⠀⣶⣶⡄⠀⠀⢙⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠂⣀⣀⠀⠀⠈⢻⣷⣶⡾⠟⠁⢀⣴⣶⣶⡾⠟⠋⠘⠿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣴⠛⠛⢀⣤⣤⣴⣿⠟⠁⣤⡄⠈⠉⠉⠉⠁⠀⣤⣤⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠿⠟⠛⠛⠀⠀⠀⠈⣱⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣀⣀⣀⣀⣀⣀⣠⣴⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⠛⠁⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢠⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡏⠙⠶⠶⠆⠀⠈⠉⠙⢷⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠶⠀⠀⠠⢦⠀⠀⠀⠀⠷⣀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⣤⡀⠀⠀⣀⡀⠀⠀⠀⠀⠙⠀⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠈⢻⠁⠀⠀⠛⠁⠀⠀⠀⠀⢀⣤⣼⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠂⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣽⠖⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢤⣤⣤⡤⣤⣤⣤⡤⠀⠛⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⡄⠀⠀⠀⠀⢀⣾⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⣿⡏⢻⡷⠴⠶⠀⠉⠙⣿⠀⠀⠙⣷⢴⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢠⣿⠇⢸⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⣿⡟⠉⠲⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⢸⣿⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⣿⡇⠀⠀⢈⡿⢦⡀
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇⠀⣿⡇⠀⢠⡞⠁⠀⠻⡆
⠀⠀⠀⠀⠀⡄⠻⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠇⠀⠘⠃⠀⠀⠀⠸⠆
⠀⠀⠀⠀⡀⠋⠀⠀⢀⣴⣿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠀⢰⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠇⠀⠀⠀⢸⣿⣵⣶⡦⣼⣿⣇⠀⠀⠀⠀⣴⠀⠀⠀⡟⠀⣸⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⡿⠀⠀⡇⠀⣿⡏⠀⢸⡁⢸⡟⣿⡆⠀⠀⠀⣿⠀⢀⣾⠿⠿⢿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠃⠀⠀⡇⢸⣿⠁⠀⢸⡇⢸⠀⢻⣇⠀⠀⠀⣿⠀⣾⠄⠁⠀⠀⢼⡇⠀⢰⡆⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣷⠀⠀⠰⣇⢸⡿⠀⠀⠘⠁⢸⠃⠘⣿⡀⠀⠀⣿⠀⣸⡶⠟⠈⢻⡆⠁⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⣶
⠀⣠⠀⠀⠀⢠⡟⢻⣇⠀⠀⠀⠀⣸⠀⠀⣿⡇⠀⠀⣿⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠙
⠀⡿⠀⠀⠀⠀⡇⠈⠻⣶⣤⡀⢰⣿⣶⣾⠏⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣷
⣄⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠁⣼⡟⠉⠁⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠙
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆
⠟⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇
⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⢷⡀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠳⣴⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢃⡈⠓⣦⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣴⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠓⠀⠼⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠛⠛⠛⠛⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠑⠲⠒⠒⠶⠒⢿⠀⠀⠀⠀⣨⠿⠖⠆⣀⣀⣀⡀⢴⡞⠁
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⡴⠂⠁⠀⠀⠀⠀⠀⠀⣠⡖⠛⠋
⠀⠀⠀⠀⠉⠦⠤⠀⠀⢤⡤⠞⠋⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣤⠞⠁
⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠤⢄⡠⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢺⢀⣱⠦⣼⣤⡐⠲⡖⠚⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⡴⠁⠈⡴⠚⣿⠀⢸⡄⣹⡀⡱⣄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡈⠀⢧⠀⢀⡇⠀⣿⠀⣸⠃⠈⣅⡷⠬⢻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡡⠖⢠⠞⠀⣋⡤⠶⣿⠀⠈⠙⠒⢸⠀⠐⡚⠄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁⠒⠚⠲⡈⠁⠀⠀⢸⡄⠀⡇⠀⢆⢀⡴⠧⣜⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠞⠁⠀⠀⡇⢀⡞⠀⣾⠁⠸⣤⣄⠘⡜⢀⡄⠌⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣦⣠⡟⠛⣶⡇⠈⢷⣀⣿⡴⠖⠁⠤⠴⢧⣈⠓⡖⠛⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠈⠉⠷⣄⠀⠈⠀⠀⠙⣿⡁⢀⡤⠒⣀⣀⣈⣠⠇⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣷⡄⠀⠈⠛⠉⠛⢦⡀⣸⠋⢉⣀⡼⠉⡄⠀⠤⢠⡟⡘⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⠁⡉⠙⢶⡞⠉⠁⠀⠃⣿⡀⠀⠤⣀⣤⣿⠚⠛⢉⣄⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣹⡆⠸⡄⠳⣌⣓⡶⣿⠁⡴⢀⡼⢀⠈⣧⣠⠏⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⣳⣄⠦⠴⢦⣡⣄⣿⣤⣤⠴⠊⠁⠴⢋⣸⠄⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡓⢤⣙⡀⠰⡁⡄⢹⡀⢹⠖⢦⣤⠴⠋⢳⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡉⠓⠦⠭⣿⡗⠛⠓⢒⣤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠁⠙⠒⠚⠛⠁

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢒⡂⠀⡀⠰⠎⠩⣉⠰⠆⠒⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠉⣉⣀⣉⣀⣀⠌⡽⠀⠀⣡⠔⠛⠐⠲⠬⠓⣄⣌⠉⠲⢆⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⡡⠄⠔⠁⠀⠄⠀⢈⡹⠴⠧⢤⡞⠁⠀⠲⣧⠔⠖⠋⠉⠉⠉⢙⠮⣭⡛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡍⠀⡜⠁⠀⢠⠀⠀⠀⣇⠀⢁⠀⠀⠀⢀⡷⠆⠀⡴⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠙⠒⠮⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠼⠦⡤⠂⢀⠀⠘⠦⣀⡀⠈⠖⠁⠀⢠⠎⠑⠒⠛⢺⡇⠀⠠⢄⣺⠀⠀⠀⢸⡇⠀⢂⠀⠒⠓⢍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⣃⣀⣸⡀⠀⠀⡁⠀⠀⠄⠈⠁⠀⠠⣄⡾⠀⠀⠀⢀⠀⠻⣄⠀⠀⣿⡤⠀⠀⢸⠅⠀⠈⠲⠞⢀⠘⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⠈⡀⠤⢀⡗⢉⡀⠀⠉⠀⠀⢀⣷⡀⠀⠘⣧⠀⠈⠀⠈⢢⣀⣀⣠⠴⠃⠀⠀⠀⣸⢧⡀⠀⠀⠀⢨⠀⠀⢸⢊⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⡜⢀⣀⠀⠃⠀⠁⢀⣀⡴⠊⢹⡇⢱⡀⠀⠘⣆⠀⢀⡴⠋⠁⠀⠄⠀⠀⠀⢀⣰⠃⠀⠉⠓⠲⡖⠁⡗⠀⠨⣀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠏⡰⠉⠀⠀⠐⢤⠖⠛⠤⡀⠀⡀⢇⠀⠇⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢀⡜⢧⠀⠀⠀⠀⠘⠁⠀⣸⠀⠀⠈⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠈⡸⠀⠃⠀⠙⠒⣶⠋⠀⠀⠀⣀⠀⡇⢸⣤⡤⢤⣴⡿⠥⣤⣀⣀⣠⠼⠛⠉⠉⠁⢀⡼⠤⠤⠤⠤⢴⠋⠐⠁⠀⠀⢳⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠨⡱⠀⠀⠂⠉⠹⣅⠀⠉⠀⠀⠈⢹⡿⠋⠀⠀⢰⠃⠀⠀⠀⠈⠛⣤⣀⣀⣀⠐⠂⠙⠀⢀⣠⠤⠀⠀⡷⠤⠒⠂⢀⣞⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠄⠐⢄⡀⠈⠉⠙⢋⡡⣴⠏⠀⠀⡰⠁⠘⣆⣠⠀⠸⠀⠀⠀⠀⠀⠉⠛⠓⠚⠋⠉⠁⠀⢀⡴⠃⠀⠀⠉⠁⠈⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠉⠿⠶⠶⢶⣶⠇⠀⠀⠀⡇⠀⠢⡤⢧⣀⠀⠀⣄⣀⣠⣄⣀⡴⠦⠤⠤⣴⡶⠞⠿⠶⠶⡦⢤⣤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠉⠉⠉⠉⢻⡄⠀⠤⠒⢧⠀⠈⠀⠀⣈⣁⠔⢋⠈⠁⢀⣠⣴⡶⠶⠛⠁⣀⣉⠀⠌⢁⡰⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⠂⠀⠈⠳⣄⣀⠀⠀⠸⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⣒⣤⣄⣁⣀⣀⣀⡤⠞⠉⠉⢻⣿⣿⣶⣂⠉⠉⣀⣤⢤⠴⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠒⠿⢍⡛⠛⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠀⠀⠉⠉⠛⢶⣄⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⠉⠳⢌⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⠃
⡼⠁⠀⠈⢆⠀⠀⣀⡀⠀⠀⠀⢶⠘⠻⣆⠀⠀⢀⡤⠂⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⠀⠀⠁
⢷⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣤⣀⣄⣦⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒
⠈⢷⡀⢦⠀⣈⣆⠀⠀⠀⠀⠀⢰⣲⡀⠀⠀⢠⣤⣄⠀⠀⢄⡀⠀⠀⢘⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠏⠀⠀⠀⠀⠀⣄
⠀⠈⣷⣾⣇⠹⣿⣧⠀⠀⠀⢀⣿⢿⠆⠔⠛⠃⠊⠚⠻⣶⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠛⢉⣡⣴⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠘⣿⣿⣆⠹⣿⣆⠀⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠫⠶⡀⠀⠀⠀⠀⠀⢷⣠⣶⣾⣿⣿⣿⠶⠚⠋⠁
⠀⠀⠀⠘⣿⣿⣦⡟⡿⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⣍⠀⠀⠀⠠⣙⣦⣄⠀⠀⠀⢀⣀⡀⢠⠤⠖⠁⠀⠀⣠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⢦⣄⣠⣜⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⡀⠀⠀⠀⠀⢀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⠻⣿⣶⣌⠙⠿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢣⠀⠈⠻⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠹⢦⣄⣠⣀⡤⡤⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠾⣿⣷⣴⠿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣠⠈⢧⣀⣴⣊⡀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠏⠉⠯⣉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⢤⡤⠀⠹⢄⡉⡇
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠶⠌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⣖⠁⠀⢀⣶⢏⠷⡄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠠⡰⠖⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣿⠔⠦⢤⣶⡿⠛⠁⡰⠉⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠐⢇⠀⠀⠘⡆⠀⠀⠀⠀⠀⣠⢶⠋⡇⠀⠸⡇⢀⣾⠛⠒⠒⠉⡠⠀⢀⠤⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢀⡀⠀⡾⣀⣀⣠⠶⠤⠚⠹⡼⢸⠇⠀⠀⣿⣼⠃⠀⠀⠀⡔⠠⣞⣡⡴⡶⡶⣿⡆
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢹⠁⠈⠉⠀⠘⢉⣁⣀⣀⣀⣀⣙⡏⠀⠀⢰⢿⡿⠂⠀⠀⡐⡴⢰⠋⢀⠀⠀⢀⢀⡿
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⠛⠲⢦⣀⣀⣤⠴⠶⠬⣭⣉⢻⡇⢀⣰⢏⡾⠃⠀⠀⠌⡜⢠⡏⠔⢁⡠⠔⠉⣼⡇
⠀⠀⢠⡏⠀⠀⠀⢷⠀⠀⢸⣦⣤⢾⡍⣉⡉⠑⣞⠛⠉⠉⢻⠛⠿⠟⡻⠁⠀⠀⢀⠞⡴⠉⠁⠉⠀⠀⢀⣼⢻⡇
⠀⠀⣼⠀⠀⠀⠀⢸⠀⠀⢸⡏⠀⠈⠻⣶⣄⡀⠈⠒⠲⢤⣿⣀⣀⣰⠁⣀⣀⣰⠧⣼⣅⡀⠀⠀⢀⡴⣿⡧⣾⣀⡀
⠀⢠⠇⠀⠀⠀⠀⢸⡄⠀⠈⡇⠀⠀⠀⠀⠀⠙⠦⠤⢼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠀⠰⢋⣾⠃⣠⠇⠈⠉⠛⣦
⠀⠸⡧⠄⠀⠭⣤⠰⢇⠐⠂⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠉⣠⡾⠁⡼⠁⠀⠀⠀⢰⠇
⠀⢸⠃⠀⢒⠒⠛⣏⠈⠳⣄⠀⠈⢦⡀⠀⠀⣀⣀⡤⠾⣁⠀⢀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⡛⠋⢠⣦⣧⣄⣀⠀⢀⡞
⠀⢸⠈⠉⠉⠀⣀⠈⣆⢀⣨⠷⢦⣀⠙⠶⢋⡉⠁⠀⠠⢌⣑⡪⣭⠽⢒⣒⣒⠲⠄⠐⠊⠁⠀⣠⠎⠈⡇⠀⣹⠛⠛⠁
⠀⠀⠀⠀⠀⠉⣉⣀⣉⣐⡁⠀⠀⠈⠑⠲⠤⣼⡷⢤⠀⠀⠀⠀⣀⣀⡀⠀⠠⠤⠤⠄⢀⣀⡘⠁⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢦⣤⣄⣀⣀⢀⠀⠀⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⠀⠀⢀⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡶⠚⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡀⠀⢀⣾⡁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠾⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢖⡊⠀⢩⠟⠃⠀⠀⠀⠀⣶⠀⠀⠀⠀⣝⡠⣄⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠲⢼⡆⠀⠀⠐⣖⠚⠀⠳⣤⡄⠘⠋⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠂⠀⠀⣸⡴⢦⡏⠁⢀⡄⠀⣀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⠀⠀⠀⣄⠀⠁⠀⢀⣠⡤⠤⠭⠤⣬⣅⡀⠀⠀⠀⣤⡤⠞⠘⢓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡍⣀⢩⠟⠋⠀⠀⠀⢀⡞⠋⠙⠒⠶⢤⣄⣀⣠⠽⠷⣄⠀⢀⣏⠴⣜⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠻⠀⠠⠄⠀⢠⠞⠉⠓⠦⣄⣠⠴⠋⠉⣀⣤⠷⡛⢦⡈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⡟⠒⣦⡤⠞⠉⣀⡤⠖⠋⠁⠀⠀⢉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣞⣁⣤⡴⠿⠥⠤⠴⠶⠶⠶⠶⠶⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣒⣩⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣄⣁⣤⣤⣤⣤⠤⠤⠤⠶⠖⠛⠉⠁⠀⢸⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⣤⠀⠀⢀⣤⣴⠂⠀⠀⠀⠈⢻⢲⣄⠀⠀⠀⡴⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠂⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠱⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⡆⠀⠀⠀⠀⠀⠐⠛⠓⠀⠀⠀⢠⡆⠀⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠖⠛⠉⠉⠉⠉⠃⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢲⣤⣄⣀⣀⣀⣠⠞⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡌⠴⢋⡩⢋⡽⢋⠞⣹⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⠖⠛⢧⠻⣄⠀⠀⠈⠠⠎⡴⢣⠞⠵⣠⠏⣹⠓⡶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠳⣎⡌⠳⣌⡓⠦⢤⣄⣀⣤⠤⠶⢚⣡⢾⣡⠞⠁⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⠻⣤⣝⣛⡶⢲⡶⠶⡶⣚⣿⠵⠋⠁⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢠⠖⣀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⢀⠀⢀⠀⢀⠔⢀⡴⠀⡠⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠞⢁⠔⢁⡔⠁⣠⠆⣠⠎⣠⠞⢁⡴⠋⡴⠃⡰⠋⣠⠊⣠⠎⣠⠆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠴⠃⡴⠋⠀⠞⠁⠞⢁⠞⠁⣠⠋⢠⠞⢀⡞⠁⡼⠁⡰⠃⡴⢁⠔⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣾⡿⢿⣿⠿⣿⣦⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡿⠛⠋⠉⢀⣴⠋⠀⢀⣴⠃⠀⠸⠿⠿⠛⠛⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⣽⠃⠀⢠⡾⠟⠁⢠⣴⣟⣁⣠⠀⠀⠀⠀⠀⣴⠋⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⢠⡾⢿⡀⠀⠀⢀⣤⣤⣿⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠀⠀⣿⠀⠀⢷⠀⠀⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣼⠋⠁⠀⢀⡾⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠳⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⣷⠀⢀⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠟⠁⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠶⠶⣤⠀⠀⣿⠀⠀⢀⣴⠀⠀⠙⢷⡟⠁⣠⡼⠃⠀⢰⣧⣄⠀⠀⠀⣀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⡀⠀⠀⣾⠛⠛⠁⠀⣀⣾⡁⠀⢀⣀⣼⡷⠞⢋⡀⠀⣠⠟⠁⢹⡇⠀⠀⠉⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣇⠀⢠⡇⠀⠀⠀⣀⣽⠿⠷⠛⣋⣩⣤⠶⢾⣯⣁⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣷⣶⣶⡾⠋⣤⠶⣿⠟⠉⠁⠀⠰⡟⠁⢉⣩⣥⠶⠶⠖⠚⠓⠒⠺⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣧⡘⠃⠀⠻⠆⠀⢀⣠⡤⠶⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⣶⣶⣶⣿⢿⣿⣤⣤⣴⣟⠛⠲⢤⣤⣤⣤⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠹⣿⡆⠀⠀⢻⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣩⣍⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣠⣤⣬⣥⣤⣄⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⣉⣉⠀⠀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡘⠃⡨⢁⠘⢃⡈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠋⠉⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⡧⠀⠀⣬⠄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠐⠲⠔⠂⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⠀⠀⠀⠈⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣪⠕⢯⠑⢂⡔⠒⣹⠲⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⣤⣤⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡿⢧⡸⣤⠘⡏⢻⡟⢛⠇⢠⡼⠨⡏⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡦⢄⡡⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⡇⠳⡄⢹⣼⣿⡜⢀⡜⢀⣴⣣⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣀⠀⠀⣨⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠘⠀⣰⠁⠀⠘⢦⣻⣿⡡⠋⠀⠈⠻⠿⠃⠀⠀⡇⠀⠀⠀⠀⠀⣴⣿⣹⣿⣿⣿⣷⣾⡿⠿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠭⠭⠤⠭⠤⠤⠤⠿⠿⠥⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡏⠉⢠⣬⣻⡛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⢿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡝⢶⣆⠀⠙⠻⢿⡇⠀⢸⣿⣿⡇⠀⢀⣠⣴⣿⡿⠇⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣙⢿⣦⡀⠀⠀⠀⠈⢻⣿⣷⣿⣿⣿⠿⢋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣾⣿⣷⣾⣿⣿⣿⠩⠭⠝⠋⣁⢠⣭⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠈⠁⠉⢹⣿⣿⣿⣾⣿⣷⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣆⣀⣰⣧⢸⣟⠘⠿⠿⠃⠻⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣍⣉⣹⣿⠇⢸⣿⡄⠀⠶⠶⠖⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠉⠉⠀⢸⣿⣿⣾⣧⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣹⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣾⠉⣙⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣗⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠞⠛⠛⠛⠛⠛⠛⠷⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣶⣄⡀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣯⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀
⠀⠀⠀⠀⣶⢦⣤⣨⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠘⣦⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⢶⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡟⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠻⣇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⡿⠀⠀⠘⠋⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠛⠉⠉⠙⠃⠀⠀⠀⠀⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⣿⠀⡷⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⣿⠀⣸⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣸⡇⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠸⣧⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠛⠋⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⠶⠾⣋⣼⣿⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣭⣭⣭⣤⣶⣾⣋⣸⡇⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠉⠷⣤⣤⡟⠉⣁⣠⡿⠋⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄⠀⠀⠀⠀⠀⢠⡔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣭⣽⣟⠀⠀⠀⠀⠀⢈⣿⣭⣭⠛⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⣶⣿⡿⠋⢼⣿⡉⠈⠻⣦⡀⠀⠀⣠⡾⠋⠈⣹⣿⠀⠈⠻⣿⣶⣤⣠⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣤⠞⠛⠛⣿⠋⠉⠉⠉⠁⢀⣼⣿⠁⠀⠘⣿⢷⡀⠀⠈⠻⣤⡼⠋⠀⠀⣰⣿⡟⠀⠀⢠⡟⢿⣯⡈⠉⠉⠉⢻⠟⠛⠛⠳⣤⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⢿⡘⢷⡀⣠⡾⠛⠳⣦⡀⣼⠏⣸⠇⠀⠀⣾⠇⢸⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⢸⣧⠀⠀⢸⡇⢨⡿⠋⠀⠀⠀⠈⠻⣏⢰⡏⠀⠀⢰⡏⠀⣸⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠇⠈⢿⡀⠀⠀⢻⡏⠻⣤⣀⣀⣀⣠⡾⠋⣿⠁⠀⠀⣸⠇⠀⣿⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⣆⠀⢸⡇⠀⠀⠘⣧⠀⣼⠋⠉⠙⢻⡄⢸⠟⠀⠀⢰⡿⠀⢰⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⠉⢿⣦⣼⣿⠷⡶⣦⣿⣴⡿⠀⠀⠀⠸⣧⣿⠀⢶⣶⠾⠃⠀⠈⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣿⣶⣿⣛⡿⠷⠶⠶⠛⠛⠛⢿⣛⢯⣿⣿⠁⠀⠀⠀⠀⣿⡇⠀⠀⣿⠇⠀⠀⠀⠙⢿⣷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⢀⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣏⣿⡆⠀⠀⠀⢠⡿⠀⢠⡾⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⣸⠇⣠⡾⠁⢀⣤⡶⠶⠶⣤⣾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⢰⡏⣠⡟⠀⣰⡟⠁⠀⠀⠀⠀⠙⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⣾⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠃⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠈⠳⣦⣄⣀⣠⣤⠾⠃⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠛⠛⣷⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⢻⣇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣤⣴⠟⠉⣳⡄⠀⠀⠀⠀⠀⠸⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢻⡄
⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠉⠛⠛⠛⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇
⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡆
⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡇
⣿⣀⣀⣀⣀⣀⣀⣸⡟⠀⣿⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣸⡇⠀⢸⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠋⠙⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢶⡶⢶⠶⠶⠶⠊⢉⡹⣿⠟⢖⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⢉⡾⠁⠀⠀⠀⢻⡇⠀⠲⣤⠞⠐⢿⣟⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠂⠀⢀⡤⠂⣠⡟⠀⠀⠠⠀⠀⢀⡿⠀⠀⢸⡇⠴⠞⢹⣇⢻⡿⠿⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣴⠇⠂⠀⠀⠀⠀⠤⢾⣀⡔⠀⠉⢣⠀⠀⠀⢢⡞⠁⠀⠀⣠⠞⢻⡄⠠⠞⣿⡆⠠⡀⢸⣿⣿⡿⣷⣄⡀
⠀⠀⠀⣀⠄⠚⠁⠀⠀⠀⠴⣁⠀⠀⠀⠉⢠⠂⢀⠞⠃⠀⠀⣸⠀⠀⠀⠀⡟⠀⣼⠁⠄⠀⠙⣿⣤⣿⢾⣿⡇⠀⡈⢻⣿⣆
⠀⢀⣾⠃⠀⢀⡠⠀⢠⠂⠰⠈⠓⡀⣀⠔⠁⠀⡎⠀⠀⠀⠉⠛⢄⡀⠀⢰⡅⠀⣿⠀⢀⠔⣠⣿⣿⡏⢸⠹⣷⣹⡌⡌⢻⣿⣆
⠀⣼⡅⠀⢠⢘⠁⠀⡿⠀⢀⠀⢀⣿⠃⠀⠀⢠⣇⣀⣀⣠⣤⣤⣀⣤⣤⡾⠀⠈⣧⠀⢆⠀⠁⣿⣿⣧⡸⢰⣿⣿⣷⠈⢾⣿⣿⣦
⣾⢻⡇⠀⢠⡜⠀⠀⠃⠀⠀⠁⣿⣿⠀⣀⡤⠚⠋⢩⠉⠁⠀⠀⠀⠀⠀⢀⣤⠶⢯⣄⣀⢁⣈⣿⣇⠿⠶⣿⣿⠉⠀⣠⣿⣟⢹⣿⣆
⣿⡾⠀⠙⠻⠱⣄⡀⠀⠀⠈⠒⣿⠟⠉⠁⠀⠀⣀⣿⠀⠀⠀⠒⠉⣉⠉⠉⠀⠀⠀⠉⠛⢿⠛⠉⣠⣴⣾⣿⠟⠀⢈⣿⣿⣿⣿⣿⣿
⢿⢿⠀⠀⠀⢀⠀⠁⠂⡤⠀⢨⠃⠀⣿⣄⡀⡜⠋⠀⠀⠀⠀⠀⠀⠀⢉⠛⣻⠀⠀⢀⡀⠘⣦⣿⠿⠛⠙⣦⣹⣷⣿⣿⣿⣿⣿⣿⣿
⠈⠚⠓⡦⠀⠈⢳⡖⠉⢀⣠⡟⠀⠀⢨⠉⠉⡀⢀⠀⢠⠀⠱⣦⠐⠂⣩⡾⢋⣾⣤⣤⣴⣀⡉⢀⣴⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠱⡄⢀⣶⣴⣾⣤⣴⣿⣿⡇⠀⠀⣼⠀⠊⢀⣾⡀⠈⣀⢞⣡⣾⣿⣷⣾⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⣿⣿⣟⠻⠿⠿⠃
⠀⠀⠈⠺⢿⣟⣿⣛⣿⠿⠛⠉⣄⣀⣌⠉⣉⣥⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⢿⡉⠉⠉⠒⠺⢦⣄⠀⢀⣒⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣟⠿⢛⣡⣤⣿⠏⠙⠿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠂⣦⣴⢺⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠉⠉⠳⣍⡛⠿⠿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣌⣻⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠖⠈⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠈⠁⠀⠀⠄⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣭⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣇⠘⢿⠟⠁⢸⡟⣿⣿⢻⣟⠻⢿⣷⣶⣤⣄⣀⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠾⣿⣷⣼⣇⠛⣣⣾⡟⢱⣿⢋⣿⢏⣭⢻⣿⣿⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢈⠉⠛⠛⠿⠿⣷⣿⣿⣼⣧⠙⠿⣰⣿⣃⠸⠟⣻⣿⣿
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⡆⢻⣷⠈⣴⡆⠀⣦⣍⠉⠛⠻⠿⣾⣿⣧⣿⣦⣼⣿⣿⠇
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⡷⢀⡎⢀⡞⠛⠀⣠⠀⢀⡉⠛⠛⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⠀⣤⡀⠀⠀⠀⠈⠻⠶⠢⠿⠷⢾⠇⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢠⣇⢀⠁⣤⠀⢰⠄⢠⡶⣀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣟⠃
⠀⠀⠘⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠉⠉⠀⠻⠶⠃⠀⣶⣦⡟⠃⠀⠀⠀⠀⠀⠀⠈⠑⠞⠉⠀⢀⠀⣄
⠀⠰⣆⡀⠀⠀⠀⢠⡷⢦⡾⠁⣾⣛⡉⠀⢀⣀⠀⠀⠁⠘⠓⠀⢠⡜⠃⣤⠀⡆⠀⠀⠀⠀⢀⡘⠁⠀⣙
⠄⠀⠈⠁⠐⠒⠀⢀⣀⠘⠁⢰⣭⣍⠁⢀⣾⣿⡀⠐⣶⣄⠀⠀⠈⡇⠰⠂⡀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠁⠀⠤⠀⠉⣀⠹⠇⢠⣁⣘⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢲⣤⣉⠉⠁⠀⠀⠀⠀⠦⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠹⡦⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⠟⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣡⣼⠷⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⢀⡰⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⠁⠀⠀⠦⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢰⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⢀⣠⠆⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠉⠁⠘⠁⠈⠁⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢀⣤⣀⣀⣀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠘⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠛⠻⠟⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠠⢂⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⢂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢁⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠁⠁⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢀⡊
⠀⠀⠀⢄⠀⠘⢶⣄⠀⠻⡅⠀⠀⠀⠀⠈⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠈⢀⠀⠀⠀⠀⡽⠁⢀⣴⠞⠀⢀⠄
⠀⠀⠀⠈⠢⠀⠀⠁⠠⠄⡠⡀⠀⡀⠈⠓⠀⣂⣀⡀⠈⠀⠀⠀⠀⠀⠈⠀⣀⣀⡀⠐⠉⠀⡀⠀⡠⠀⠤⠀⠀⠀⠠⠊
⠀⠀⠀⠀⢸⠷⣤⣈⣒⣀⣠⣨⡴⠖⠛⠋⠉⠉⠉⠉⠉⠛⠲⢤⠴⠚⠋⠉⠉⠉⠉⠉⠛⠛⠶⣬⣠⣀⣀⣊⣠⡴⢿
⠀⠀⠀⠀⢸⡆⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⣾
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠛⠲⣄⡀⠨⠿⠯⠀⣀⡴⠚⠋⠉⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠙⠲⠤⣤⣤⡤⠶⠚⠛⠁⠀⠀⠙⠙⠳⠦⣤⣤⡤⠴⠚⠉⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠶⠶⠒⠛⠉⠉⠁⠀⠀⠉⠉⠙⠓⠲⠶⠶⠶⠶⠶⠚⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠑⢤⡀⠀⠀⠀⠀⠀⢈⠄⠀⢤⠈⠀⠀⢐⠂⠀⠂⠀⠀⠈⢠⠀⠀⣌⠀⠀⠀⠀⠀⠀⡠⠞⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠲⢄⠀⠀⠀⠈⠁⢀⣈⣀⠠⢤⡾⠷⠲⠿⣦⠄⢀⣸⣀⠀⠋⠀⠀⠀⣀⠔⠋⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⣿⢋⠙⠻⠄⣸⠃⠀⠀⠀⢿⡀⠼⠋⢉⢻⡇⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢢⣀⢰⣦⣿⣿⠗⠀⠀⠁⠀⠀⡀⠀⠀⠁⠀⠰⢻⣿⣵⡎⢀⣤⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣛⣿⣿⣿⠃⡀⡀⢰⠀⢀⡾⠻⣄⠀⢸⠀⠠⡈⢿⣿⣿⣟⡡⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠢⠀⢴⣽⣿⡏⠁⢀⣴⠃⡜⠀⣾⠁⠀⢹⡄⠸⡈⢧⣁⠀⠉⣿⣿⣴⠀⠠⠂⠀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⠁⠀⠜⠋⠉⢀⣾⠁⡆⢿⠀⠀⣸⠇⠀⢻⣄⠈⠉⠓⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⣀⠀⠀⡟⢀⠀⡀⠀⠀⣾⡇⠀⢡⠈⡇⠀⠏⢰⠀⠈⣿⠀⠀⠀⠀⠀⢸⡅⠀⢀⡤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⣷⢼⡄⢻⡀⠀⠘⣧⠀⠀⠇⠀⠀⠀⠃⠀⢠⡟⠀⠀⣼⠀⣾⢸⡇⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⠀⢿⡎⣧⠀⠳⣦⣀⠈⢳⡀⠀⠀⠀⠀⠀⡴⠋⢀⣤⠾⠁⢸⡏⣿⠄⢀⡀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡔⠉⢈⠉⠀⣼⡇⣿⣀⣀⡀⠙⠻⡄⠁⢠⣠⣇⣀⠐⠁⡼⠋⠁⣀⣀⣼⡙⣿⠄⠉⢉⠈⠱⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣠⠀⣸⠋⢸⡇⢹⣿⣿⣿⣷⣄⠀⣠⠿⠿⠿⠿⣦⠀⣀⣴⣿⣿⣿⣿⠀⣯⠈⢻⠀⢄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠙⠸⣯⣛⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣛⣫⠟⠘⠁⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠒⡾⡿⠀⠀⠀⠒⠺⠟⠛⠛⠳⠀⠀⠘⠛⠋⠛⠿⠒⠂⠀⠀⠼⣿⡖⠠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡄⠀⠘⠁⠛⢀⣄⣄⠈⠷⣦⣴⠂⠐⠀⠀⠀⠀⠐⠐⢶⣤⡶⠃⢀⣄⣠⠜⠁⠑⠀⠀⣏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠁⢀⣈⡇⠀⠀⠀⠂⠘⣴⠞⢷⣦⣈⠻⣦⣤⡤⡀⠀⣠⣤⣤⡞⢉⣠⣾⠿⢦⠞⠐⠂⠈⠀⢀⡇⣄⠀⠁⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠠⠀⠀⠘⠒⠠⠔⠀⠀⢘⣿⢙⣷⣤⣹⣿⣯⣾⣿⣟⢡⣴⡟⣹⣝⠀⠀⠢⠄⠀⠊⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⡀⡠⠂⢀⡅⢺⠉⠻⣷⣿⣓⣬⠉⡏⣩⣖⣻⣶⡿⠋⡻⠂⣅⠐⠢⡀⡀⠀⠀⠐⠒⠒⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⡌⠀⠁⠈⠩⠐⢤⠁⡴⠾⢻⡏⣹⣛⣟⣻⠉⣿⠿⠦⡄⢡⠖⠨⠉⠄⠀⠈⠄⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢢⡐⠀⠀⠈⣠⠙⣿⠿⠋⢉⣉⣉⣉⠙⠻⢿⠏⢠⡈⠀⠀⠀⣤⠂⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣡⠀⠤⣄⢀⠐⠃⠀⡇⠻⣶⠾⠋⠁⠀⠉⠻⢶⡾⠁⡇⠈⠀⢂⢀⡤⠄⢠⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠘⠒⠊⠁⠀⠈⠛⠀⠁⠈⠁⠘⠉⠀⠀⠉⠖⠚⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢠⠒⡀⠋⠉⠉⠙⠂⡘⢄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢀⡀⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠘⢡⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⠀⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠀⠀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡍⢀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠈⠀⠀⠐⠋⠉⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉⠙⠃⠀⠀⠀⠤⠀⠀⠀⡠⠶⠀⣀⣀⣀⣀⣀⡠⠤⠄⠀⠒⠒⠛⠛⠚⠒⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠢⢄⣀⠀⣀⣔⣀⣂⣱⡄⠀⠀⠀⠀⠀⠈⠳⢀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠒⠊⠉⠁⠁⠀⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠟⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢃⠀⠀⠀⠈⠁⠀⠀⠠⠏⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠤⠤⣀⣀⣀⣀⠀⣀⠆⠘⠀⠁⣂⣸
⠀⠀⠀⠀⠀⠀⠙⠁⣀⠀⡝⠃⠀⠠⠄⠀⢀⠂⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢂⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠙⠂⠀⠀⠀⠀⠀⠘⠀⠐⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠰⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣣⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠦⣴⠶⠖⠓⣞⠳⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⣤⠰⡎⠛⠫⢾⡱⢄⠈⠲⣕⡤⠀⠈⠳⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⣠⠄⡺⢏⠍⠃⠴⠀⠈⣠⠚⠝⢦⣐⠀⠈⠑⠠⣄⠀⠀⠀⠀⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⠔⠊⠉⠁⢠⡚⠗⣀⣊⣠⠔⠋⠀⠀⠀⠀⠈⠷⢦⡀⠀⠀⠙⠢⣔⠤⣠⠱⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡠⠞⠁⢀⠠⣔⠊⠃⢁⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠨⡓⢄⠲⣼⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡠⠊⠁⢀⠤⠊⠐⣋⡁⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⠁⠒⠂⣌⠳⡀⠀⠀⡔⢀⠱⣩⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎⡠⣐⠕⢁⠐⣵⢛⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⢛⣷⣤⡀⠈⠀⠱⠀⠐⢠⠀⠆⢡⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡎⠰⣉⠊⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⡇⠀⡇⠠⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⡀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡇⠀⡀⠀⠰⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠄⠀⣞⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡇⠀⠁⢠⢣⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣷⢽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠒⠒⠒⠒⠢⠀⠀⠀⠀⢠⣿⠀⠀⠀⡸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢸⡅⠚⣷⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⡗⡄⠀⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⢸⡂⠝⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢲⡭⣻⢱⠀⠘⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡘⡥⢚⡵⠂⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡥⣛⠭⣋⣿⢸⣿⡇⢸⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡇⡃⢛⡡⢚⠴⢪⠖⢛⠛⠲⣦⣄⣀⠀⠀⠀⢀⣀⢤⡶⡟⢣⡗⠊⢕⠺⠵⠟⡐⠛⠓⠀⡇⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠃⡇⠀⠔⡡⠒⡡⠒⣩⡆⠀⢠⠈⡩⠋⡰⠋⠙⠉⠔⠄⡐⢲⣋⠁⡈⠔⠛⠀⠹⠀⠄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⢠⠃⠀⢊⠄⠊⠔⠉⢐⡇⠀⠀⠈⠀⠊⡠⠊⠔⡁⠀⠊⡄⢪⠖⠩⠐⠀⠀⠀⠂⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡈⡄⠀⠠⠖⡡⢊⠀⣈⠇⠀⠀⠀⠀⠈⠁⠊⠔⠄⢀⢂⠄⠘⠃⢐⠌⠀⡀⠀⠀⡀⠁⢀⠃⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠎⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠒⢤⡤⣄⡈⡔⣀⠀⡌⡸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡠⠊⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠙⢶⡇⠀⡰⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠄⠀⠀⢀⠀⠀⢠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠑⢆⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠃⢀⠠⢂⡀⠐⣀⠄⢀⡀⠀⡀⠀⡀⠀⡀⠀⣀⠀⠀⠄⠀⡠⢂⠄⡀⠀⡀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠐⢊⠠⠂⢁⠔⠊⡠⠒⠁⠔⢈⠔⢊⠔⢉⡴⠊⡠⠊⢀⠔⡡⠊⡡⠊⡡⠊⡤⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠈⠠⠊⠠⠂⠡⠀⠁⠔⠁⡠⠊⠀⠖⡡⠊⠠⠊⡀⢈⠴⢁⠄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡴⠦⣤⣄⢀⣠⠤⠀⢠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠇⢀⠳⡖⠀⣻⣿⣼⠏⠀⣤⠀⠍⠻⢿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠀⡤⠊⠀⡞⠀⠈⢽⣻⣿⠄⠀⣠⠈⠒⢅⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠘⠄⠀⡄⠀⣠⠷⠒⠒⢶⣿⡇⠐⠀⢇⣠⠇⠀⠄⡃⣿⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⠋⠀⠀⠀⢀⡴⠁⠘⠂⢳⢸⣿⡧⠄⠀⠈⠁⠐⠲⣾⣀⢌⡙⠾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠐⠀⢀⠔⠉⠀⣔⠀⣤⡿⢾⣿⡇⠀⢘⡷⠒⣤⠖⠀⢁⠀⠙⠚⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠈⡇⠠⣀⡴⠀⠉⢠⡼⠆⠀⡇⣨⣿⡧⠀⣻⠇⠀⢇⠀⢸⠉⠀⣙⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⡧⠀⠇⡀⠠⠤⠴⠆⢠⠃⠠⠐⠳⠄⣿⡃⠘⠉⠀⠀⠀⠀⠈⠃⠀⡞⣩⢉⡿⣿⡄
⠀⠀⠀⠀⠀⢀⡞⠀⣆⣀⣁⣄⠀⠠⢤⣟⡀⠐⠓⡄⠻⣿⣧⣀⠀⠟⠀⠣⡀⠀⠁⣀⣠⣻⢸⣷⣿⣷
⠀⠀⠀⠀⠀⢨⠇⡀⢀⡠⠤⠀⠀⠄⠀⠈⠉⠑⠀⠈⣶⣿⣧⡄⠀⠔⠀⠀⣽⠗⢉⠉⣯⣵⡿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⢨⢂⢸⠀⢠⣀⡄⣧⠈⣆⠀⠆⡤⠊⠁⢴⣿⠀⡀⠄⡠⠇⠈⠁⣴⡿⢋⢩⣶⣰⣿⡿⣿⡇
⠀⠀⠀⠀⠀⣸⡿⠀⠓⠀⠇⠀⠈⠀⠾⠚⠦⣤⠆⠁⣼⣿⠀⡄⠀⢶⣿⣶⣶⡁⠑⢘⣆⡿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣽⠈⢆⠀⡸⣀⠀⠃⢀⡴⠃⠂⠴⠂⠀⣴⣿⠷⠋⠀⡏⠀⣦⠈⠿⠻⠿⡋⣥⣴⡿⣻⣿⣿
⠀⠀⠀⠀⠀⢹⣀⢼⣆⡀⠈⣻⣄⢀⠈⠄⠲⣄⠀⢋⣿⣿⠆⢢⠞⠀⢀⣿⠗⠚⣠⣾⠿⣟⢻⣾⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣏⠀⣈⣴⠉⡈⠉⠻⣧⢄⣀⣽⢛⠛⢿⣿⠃⣈⣨⠟⠉⣩⣬⣷⠟⣱⣿⣿⣦⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣷⢳⡄⠙⢠⠇⣀⣀⡿⢤⠄⠁⣉⢴⣿⣿⠞⠉⠁⣠⠂⣠⣿⣶⣾⣿⣿⣿⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢿⣦⢹⡞⣋⡘⢛⡅⢹⣾⡙⢦⣉⣼⣿⣿⠃⣠⠞⢆⣛⣿⡟⢰⣿⣿⣿⣛⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⣮⣽⣩⢛⣣⣤⡼⠋⠁⣨⣿⢿⣿⣿⠾⢇⡚⣿⣿⣿⡇⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣵⣾⣟⣋⣴⡛⠻⣿⣿⣿⣿⣿⠰⣦⣼⣿⣿⣿⣿⣯⣙⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠻⠯⠤⠤⠤⠤⠭⠭⠭⠽⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣭⣙⣒⣒⣒⣒⣒⣒⣒⣒⣚⣩⣬⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠁⡏⢹⠉⡏⢹⠉⡏⢹⠉⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠾⣦⣧⣼⣤⣧⣼⣤⣧⣼⣤⠷⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠿⠿⠿⠿⠿⠿⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠶⠶⢶⡶⠶⠶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠻⠶⠶⠶⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠀⠀⠀⠀⢀⡴⡖⢶⡄
⠀⠀⠀⠀⠀⢀⡴⠶⣤⣤⣄⡀⠀⠀⣿⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⣿⡀⠀⠀⣴⠟⢮⣁⣼⡇
⠀⠀⠀⠀⠀⢸⣄⣀⣸⠐⠚⣻⠀⠀⣿⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⠆⠘⣧⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠋⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣉⣸⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⢷⡀⠀⢀⡴⠟⠛⠛⢶⣄
⠀⠀⠀⢀⣤⡶⠶⠶⠶⣄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡟⠀⠀⠀⠀⠀⠙⣧
⠀⠀⢠⠟⠁⠀⠀⠀⠀⠈⢷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡶⠶⠶⢦⣤
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠘⣷⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣷
⠀⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠲⠶⠶⢦⣤⣿⡀
⢰⡇⠀⠀⣠⠶⠋⠈⣿⠀⠀⠀⣤⣀⣤⣀⣠⣄⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣲⠀⠀⠀⢹⡇
⢸⡇⠀⢰⡏⠀⠀⠀⠉⣷⠀⠀⢉⠉⠉⠀⠛⠁⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣉⣉⣀⣀⣀⣸⡇
⢸⡇⠀⠀⠻⢤⠶⢦⡤⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣤⡤⠴⢺⡇⠀⠀⠉⠉⠉⠉⠉⢹⣧
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠶⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠃⠀⢀⣠⣼⣇⡀⣀⠀⡄⠀⠀⠀⠀⣿⡀
⠀⣿⠀⠀⠀⠀⠀⣾⡖⠻⡷⠚⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣤⡤⠖⠛⠉⠁⢸⡏⠙⣿⠛⡿⠖⠀⠀⠀⢹⡇
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣧⣠⠤⠴⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢰⡟⠁⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠈⠙⢶⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠋⠉⣹⠿⢦⣄⣀⣠⣤⠤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⡄⠀⣸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⣦⣀⣠⣿⡶⠖⢿⠋⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠚⠋⠹⠇⠀⠈⠃
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢻⡆⢀⡴⠞⠳⣤⣤⠞⠁⠹⣦⡀
⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠉⠻⠷⣶⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢠⡶⠛⠿⠀⠀⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠳⠤⠿⠳⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣐⢅⡪⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡊⠅⡂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠆⠒⠒⠛⠚⠓⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⡨⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠒⠉⠉⠉⠀⠉⠉⢉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⢲⠤⠤⣍⣀⡂⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠒⠈⠀⠀⣠⠔⠋⢍⢻
⠀⠀⠀⠀⠀⢀⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠤⠒⠉⠉⠉⠉⣑⢺⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢱⠤⠏⠀⢀⠸⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⡻⠟⠛⠉⠛⠛⣲⠾⠀⠀⠀⠀⠀⣀⠈⢒⠶
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢲⠦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⠴⠒⠭⣑⡇⠀⠀⠄⠀⠀⠨⠖⠺⠄
⠀⠀⠀⢀⡔⠑⢲⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣀⣀⡠⠓⡋⠻⡀⠀⠉⠀⡀⠀⠅⠀⠀⠐⠂⠀⠀⢠
⠀⠀⠀⠀⠨⠎⠘⠂⠀⠁⠂⠀⡴⠊⡏⠉⡇⠈⣇⠈⠣⡀⡞⢄⠈⠢⣄⠀⠀⠲⠀⠀⠀⠠⠄⠐⢆⠁⡱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣼⠘⣄⣸⠞⡽⡄⠘⢄⠀⠙⡇⠈⡧⡀⢈⠓⢍⣠⠀⠀⢄⠀⠀⠀⠚⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠘⢄⡜⠁⡜⠀⡟⢄⠈⠳⣔⡇⠀⡇⠈⠢⡑⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢳⣼⣠⣴⣤⣇⣵⣾⠬⢷⡥⢷⡭⠴⣚⠫⢋⠠⢑⠢⢐⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠧⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡾⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡞⠁
⠀⢀⣤⠶⠶⠶⠶⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟
⢠⡟⠉⠢⡀⠈⠠⡀⠀⠈⠙⠶⣄⣿⠛⠒⠒⠒⠓⠛⠛⠋⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⢧⠀⠀⠈⠳⣄⠈⢦⡀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⠘⣆⠀⠀⠀⠈⠳⣄⠙⢦⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠸⣆⠈⢢⡀⠀⠄⣀⠈⠳⢄⠙⢦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠁⠀⢀⡾⠁
⠀⠘⢦⡀⠙⢦⡀⠀⠀⠀⠀⠑⢄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⢦⣀⠈⠓⠶⢤⣤⣀⣤⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⠶⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠉⢉⣽⠟⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠾⠋⠁⠠⠄⠀⢀⡤⠞⠉⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⢀⣀⣠⠴⠛⠁⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⡠⠚⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⠦⠤⢤⣄⣀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⣠⠖⠁⠀⣠⠖⠉⠀⠐⠀⠀⣠⠎
⠀⠀⠀⠀⣠⣴⡛⠛⠲⢤⣀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢴⣟⡁⢀⣠⠞⠁⠀⣀⣀⡤⠖⠋⢁⡼
⠀⠀⠀⣰⠏⠈⠙⠲⢦⣀⡈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠈⠉⠉⠉⠉⠉⢉⣀⣠⡤⠶⠋
⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⢹⣏⠑⠦⣄⡀⠀⠂⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢦⣤⢿⡆
⠀⠀⠀⠀⠻⣆⠀⠀⠉⠓⠒⠤⠤⣀⣀⣀⣀⣬⠽⠶⠒⠉⠀⢀⡿
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⠀⠀⣀⣀⣀⣤⡴⠞⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣏⡌⠀⠀⣠⠂⠀⠀⠀⠉⢛⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⠇⠈⠚⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠁⢿⡇⠀⠙⢦⡀⠀⢤⡀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠙⠓⠶⣬⣿⡀⠀⠀⠙⢦⡈⠙⠶⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠲⢄⠀⠀⠀⠀⢠⡇⠘⣷⣀⣠⡤⠔⠓⣾⢻⣷⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⢳⡀⠀⠀⠈⠳⣄⣹⡏⠈⢦⠀⢸⠃⢸⡿⠉⠛⣧⠓⢄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠙⢿⡀⠈⢧⢸⡇⣿⣧⠀⠀⠈⢧⠀⣇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣟⣦⡈⢿⣧⡟⢸⠀⠀⠀⠈⢇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⡏⢌⢿⡝⣎⣿⡇⠘⣧⣀⡀⠀⠘⣾
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⠒⠋⠀⠈⢿⠁⠀⠀⠉⠁⠘⠓⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣧⢯⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠲⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⢧⣀⠀⠀⢀⣠⠖⠋⠀⠀⠀⣠⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣼⡀⢀⡠⠤⠶⠶⠖⣛⠲⢦⣨⣻⠟⣋⣠⣄⢀⠶⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡿⠁⠀⠀⠀⠰⠶⣦⣬⠿⠋⢰⡛⡇⢧⠈⡿⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠛⠳⢦⣤⣀⠀⠀⠀⢀⡞⢰⣇⣀⡤⠖⠋⣩⠿⠋⠁⣠⠴⢮⣁⣨⠤⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⣸⠉⢻⠃⠀⢠⡴⣋⣁⡤⠖⢻⠯⣦⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⢠⠣⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⢣⠀⠀⠀⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠷⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⠀⢀⠀⠀⠀⠴⠏⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠘⢦⣅⠀⠀⠂⠀⡆⠀⠢⡆⠀⠀⠀⠀⠀⠀⠀⠀⡬⠂⠀⡄⠀⠂⠀⠀⣥⠞⠀⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠤⠀⠙⠦⠀⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠠⠞⠁⡠⠄⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⣝⣀⣉⣠⡤⠴⠚⠛⠛⠛⠒⠲⢤⠴⠒⠚⠛⠛⠚⠲⠤⣄⣈⣁⣘⡥⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠁⠀⢀⣀⣤⠤⣄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⣀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢾⡉⠀⠀⠀⠀⠈⠑⣧⠀⢠⡟⠉⠀⠀⠀⠀⢈⡹⠆⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠓⠶⠤⠤⠖⠊⠁⠀⠀⠙⠒⠦⠤⠴⠒⠋⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣀⣀⣀⡤⠤⠶⠒⠲⠦⠤⣄⣀⣀⣀⣀⡤⠖⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡄⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠃⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢢⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠸⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⢋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣼⠀⠀⢀⠄⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢱⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡄⠐⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡐⠛⢦⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠑⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠙⡆⠈⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠏⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⡸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁