⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠒⠀⠀⠀⠀⠀⠀⠑⠂⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠐⠒⠂⠁⠀⠀⠀⠀⠀⠀⠈⠰⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠪⣥⣄⣥⣴⡶⠾⠿⢿⣶⣷⡾⣿⣶⢂⣯⣍⡉⠙⠛⠻⠿⢿⣷⣶⣶⣤⣲⡔⢡⣆⢄⣶⣤⣤⣴⣶⡶⠶⠶⠶⣦⣤⣤⡀⢤⡄⠈⣲⣤⣦⣴⣴⣦⣶⣭⣭⣭⣭⣽⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⣿⣿⡟⠉⣀⠀⠤⠄⠄⢈⣟⣿⠁⣼⢸⣿⣿⡿⣟⣛⢦⠤⣀⣀⠈⢦⠀⠛⢧⡟⣿⢿⡍⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠿⢋⡟⢣⣠⣿⣷⡶⢤⣄⣀⣈⠉⠉⠉⠙⢻⡻⠉⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠉⠁⠀⢀⣀⠀⠀⠦⠦⢄⣀⠀⠈⠉⣽⣿⣿⣯⣿⣿⣿⣿⣦⣶⣍⡘⣷⡄⢸⡧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠀⣿⣿⣿⡯⠖⠀⡀⠉⠙⠛⠲⠦⢤⣷⣱⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⢀⣰⣶⣾⣿⡿⠿⠿⢶⣶⣆⣀⠉⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⡿⣿⣿⣏⠎⣀⠎⠉⠉⣹⣷⣶⣶⣆⣀⣀⠀⠀⠀⠈⠁⢶⣶⣾⣿⣿⣶⣿⣹⣶⣆⣹⣷⢸⣶⣰⢸⣿⡀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠫⠥⠤⠤⠤⠀⣀⠀⠀⣿⢿⣿⡿⢰⣿⣿⣿⣿⣿⣽⣞⡴⣆⣀⢀⠉⠉⠙⢿⣠⢇⣰⡞⠉⠀⠀⠀⠀⠀⠈⠉⠻⣿⣷⣦⣤⠄⢿⣿⣿⣿⣉⠈⠉⠀⠉⠉⠛⠛⠿⢷⣿⣿⣵⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⣀⣤⡤⠄⠒⠠⠄⡀⠉⠉⠛⠺⠅⣁⣾⣿⣿⣿⣿⣿⣿⣯⣿⣾⣬⠳⡜⡢⢄⡾⠁⢈⣁⣀⡀⠁⠀⠉⠉⢁⠀⠐⠀⠽⠅⡟⠙⢠⣾⣟⣿⣷⣯⡻⣌⢆⢠⠀⡀⠀⠀⠀⠀⣿⣿⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡡⠚⠋⠉⠉⠉⠉⠒⠢⢤⡀⠙⠲⣶⣤⣴⣾⣿⣿⣿⢯⣏⡿⣿⣿⣿⣿⣾⡿⣝⡳⣺⠔⢀⡀⠤⠓⠛⠒⠢⢤⣀⡀⠀⠂⢤⣀⣀⠀⠀⣸⣿⡟⡯⣻⢿⣽⡽⣎⣧⠳⡜⢄⠒⡠⠀⣿⡿⢧⢫⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠬⠤⠤⠀⣀⠀⠀⠀⢠⣴⡿⣷⡄⣘⡄⠀⠀⠉⠉⠙⢿⣿⣿⣶⣙⣿⣿⣿⣿⣽⡷⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣧⣄⡈⠻⠛⠛⠛⠛⠻⠶⣥⣆⠉⠻⣿⣼⡻⣜⠮⡔⢅⣸⣿⡧⣘⢞⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣉⣦⣆⡤⠒⠂⠠⣀⠈⡁⠐⠚⠫⢶⢋⣴⣿⣷⡄⢀⡄⠠⣑⢀⠈⠙⢿⣿⣷⣭⣿⡿⠋⠀⢄⣀⡀⠁⠀⠁⢉⠀⠀⠒⠂⠠⠔⣩⡿⢋⣬⣧⠀⠀⠀⠀⠀⠈⠙⢷⣤⠈⠙⢿⣭⡷⣭⢒⣸⣿⡧⠨⢧⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣾⡿⢻⢋⡉⣉⡓⠲⢦⡀⠈⠻⣶⣦⣤⣤⣿⣿⣿⣿⡿⣷⣽⡏⣖⠦⡙⠤⣀⠈⢻⠟⠉⢀⡠⠔⠒⢛⠛⠓⠦⣤⣀⠈⠑⠢⠤⣄⣀⣀⢈⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠙⢿⣾⣧⣾⣿⢃⠋⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣔⣉⣡⠤⠀⠀⣈⠙⠓⠨⠜⣗⡽⣟⠷⣢⣸⠀⠀⠀⠉⠛⠿⣯⣾⣿⣿⣾⡜⣸⠡⡍⣢⠖⠃⠀⠉⠁⠀⠀⠀⣀⣽⡴⢐⠤⢙⣿⢶⡄⢈⡋⠈⠉⠉⠛⢷⡻⡫⠿⣧⡄⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⠉⠻⣟⡟⠈⠐⣿⣼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣊⣴⠿⠿⠳⠶⢤⣤⣀⠁⠢⢤⣄⣠⢌⣶⣾⣿⣿⣦⡀⢀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⠷⠋⠀⢀⣀⡌⠳⣦⣄⡀⠀⠐⠄⡀⠀⠈⠉⠐⢥⣶⣿⣿⡄⠀⠀⠀⠀⠈⢷⣿⣷⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⢳⠇⠀⢸⣯⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢂⣁⣉⡉⠀⠒⠀⠤⠄⠀⢀⡹⣗⠦⠤⣹⠋⠉⠙⠿⣿⡿⢿⣻⣆⠆⢠⢂⡤⡄⣙⣿⠿⠟⠁⠐⢈⠁⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠈⠹⡳⠶⠶⠾⣿⣿⢿⡻⣄⡀⠀⠀⠀⠀⠙⢿⣿⠚⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⠄⢠⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣒⣭⣶⣿⣿⣯⣁⣀⣈⠁⠒⠤⡤⣤⣄⢈⣶⣾⣿⣿⣄⠀⠀⠀⠈⢷⣻⣿⣿⣥⣾⣿⣿⠿⠋⠀⠀⠐⠦⣀⠀⠀⠀⠀⡈⠁⠀⠂⠀⢄⠈⢊⣡⣤⡄⠀⠀⠀⠈⠻⣥⢋⡹⣧⠀⠀⠀⠀⠀⠀⠻⣶⡌⠳⡄⠀⠀⠀⠀⢤⣰⣿⡿⠁⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⡴⣿⠿⠛⠉⠀⠀⠀⠀⢈⠉⠿⠓⣂⣸⠛⠉⠙⠻⣿⣿⣿⢿⣄⠀⡀⢠⣨⣿⣿⣿⡿⠿⣉⢤⠦⠒⠂⠉⠉⠉⠉⠓⠢⢤⡀⠀⠑⠖⣠⣤⣄⣸⣟⣾⣿⣿⡄⠀⠀⠀⠀⠘⢯⣷⣍⣧⣀⠀⢀⣨⣶⣦⣹⣿⣧⣝⣦⣤⣖⣼⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣩⣴⠶⠶⠶⠶⠶⠶⠦⢤⣤⣵⡾⡿⣿⣿⡄⠀⠀⠀⠈⢷⣺⣿⣟⣶⣿⣿⣿⣿⣿⡏⠀⠈⣁⣉⣁⣀⠀⠀⠒⠠⠀⢀⠀⡀⠽⠓⣀⣼⠋⠁⠀⠀⠛⢗⠙⡫⠵⢦⠀⠀⠀⠀⠀⠳⣿⣾⡿⣿⣿⣿⣿⢿⠿⠿⠿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣛⢛⠻⠟⣻⣻⣶⣗⡦⣤⣄⣀⠀⠀⠛⣅⢙⣮⠽⣄⣀⣤⣶⣮⣷⣽⣿⣿⣿⣿⣿⣿⣟⣋⣛⣉⡉⠉⠓⠻⠙⠶⠦⣤⣀⣀⠈⢰⡶⡿⣯⣻⣧⠀⠀⠀⠀⠀⠱⣵⢿⡝⢧⡀⠀⠀⠀⠀⡹⣭⣿⠿⠋⠁⠠⢠⠐⢤⢠⢤⡡⣖⣲⡽⣯⢿⣻⣟⣷⣻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⢀⡨⣃⡴⢂⡵⠉⢉⡬⠭⠽⠾⡽⣿⣶⣾⣾⣿⣾⣿⣿⣿⡿⣟⡿⣿⣿⣿⡿⠛⠁⠁⢀⠄⠈⠈⠭⣯⣗⣒⣤⢤⣀⣀⠀⠀⠀⠈⠙⢏⠞⠟⣍⢵⠆⠀⠀⠀⠀⠈⢺⠻⢫⣗⡄⠀⣠⣾⣿⡿⢓⠤⡤⣋⢕⡢⢏⡺⣜⢮⡷⣯⢷⣻⣽⣟⣿⢾⣯⣟⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢒⣉⠤⣤⣤⣶⣾⣓⣮⠵⠘⠁⢀⣀⡼⢤⢃⣎⢳⡜⣶⢫⣟⣽⣿⡿⣟⣯⣿⣽⣿⠿⠛⠉⠁⠀⠀⠀⠂⠁⠀⢀⣀⠤⠃⠀⠉⡩⠩⠌⠙⣽⣷⢶⢶⣶⣄⣧⣩⣴⣾⣿⡆⠀⠀⠀⠀⠀⠹⡉⡷⣻⣴⣷⣿⠏⣄⢫⡞⡵⣭⢮⡵⣫⣗⣯⢿⣽⣯⣿⢿⣽⣾⣟⣿⡾⣯⣟⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⢟⡻⢯⣞⡩⠭⠤⠤⡤⠤⠤⢤⡐⣚⢍⢲⣉⢦⢫⡜⣧⢿⣹⣟⡾⣋⢧⣻⣿⡿⠛⠉⠀⠀⢀⡀⠔⠂⢉⡉⠤⠄⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠟⠿⣷⣿⣵⣤⣤⣄⣀⠀⠘⣕⣿⣿⡿⢁⡰⣌⢧⢻⣝⣮⢷⣛⣷⣻⣾⢿⣯⣷⣿⢿⣯⣷⣿⣻⣽⡿⣽⣻⣽⣿⣿⣿⣿⣿⡦⠀⠀ ⠀⠀⢀⣴⠿⡿⠿⢼⣯⣝⣞⣁⠀⠀⠀⣀⣀⣀⡿⢦⡽⣜⢮⡳⣎⣯⣳⡽⢾⡛⣭⢏⣷⣿⣿⠟⠉⠀⠀⢀⠔⣂⡡⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⡀⠂⠄⠂⠄⢂⠠⢀⠀⣀⠉⠋⠟⢿⠿⣾⣿⣷⡿⠇⡠⢆⡳⣬⢏⡷⡾⣭⢿⡽⣾⢿⣽⣿⢿⡽⣾⢿⣿⣽⡿⣿⣻⣿⣟⣿⡽⣿⠿⠛⠋⠉⠀⢡⠀ ⠀⣰⣏⡖⡴⣒⢥⡻⣬⢹⣿⣿⣿⣾⣿⣟⣾⣳⣟⣿⢾⣽⢳⠿⣝⡾⣭⢖⣣⣽⣾⣿⣿⠟⠁⠀⠒⠒⠒⠯⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡐⠠⢌⡐⢢⢐⡰⢌⡰⢡⠎⡜⢨⢂⡆⡡⠎⡄⠅⠂⠈⠀⠀⢀⡀⢠⡐⣧⠽⣭⡳⣝⣮⢷⡻⡽⢯⢿⡽⣿⣻⣽⣏⣟⣷⣻⢾⣽⣻⣽⠿⠞⠛⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀ ⢀⣷⣾⣹⣏⣹⡾⣱⠏⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢇⠈⣶⠶⡶⠶⣆⢉⡰⣁⠶⣀⠏⡆⢷⡈⣶⢉⣶⡈⠷⡎⡰⢇⡁⡇⠾⣀⠇⣆⢰⠰⡈⠰⢀⠰⡀⢆⡱⣈⡸⢇⡹⣎⣿⣱⢿⣹⡎⣷⣹⠿⠏⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⡳⣭⠳⣭⠳⣹⢉⡛⡘⠈⠉⠻⣁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⡇⢀⡣⡑⣌⡒⢤⡑⠈⢣⡸⣿⠷⠽⣜⣮⣳⣭⡞⣵⣺⡝⣶⣽⣲⢯⣖⡿⣝⣮⣝⡶⣳⣜⡳⣬⢳⣎⢮⣳⣭⢳⡥⡳⣜⢶⣳⢧⣟⣭⣟⡾⣵⢯⡟⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢌⡳⣜⡳⣜⢣⡕⡎⠴⣁⠆⡀⠀⠈⠱⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢆⠀⠀⠀⠈⠉⠉⠉⠓⠛⠓⠓⠛⠿⠾⠽⠿⠾⠽⠾⣵⣮⣽⢾⡳⣮⠟⠷⠯⠷⠛⠓⠛⠫⢿⣿⢾⣻⣾⡽⣯⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧ ⢌⡳⢧⡝⣮⢳⡼⣩⠳⣌⠲⣁⠆⠤⢀⠀⠈⠉⠑⠒⠒⠂⠤⠀⠠⠤⢠⣄⣀⠀⢸⠀⡡⠌⡐⢀⠂⠄⠂⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠽⠟⠋⠀⠀⠀⠀⠀⡀⠄⠒⠈⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⢫⠇ ⠸⣹⢧⣟⣾⣧⣿⣵⣳⣮⣷⡼⣜⣦⢣⢎⡰⠠⢄⡐⢠⠀⠠⢠⠀⡀⢀⠀⠀⡙⢾⡄⠣⡔⡈⠆⡘⢠⠡⡈⠄⠠⠀⠀⠀⠀⠉⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢢⣤⣤⣤⣤⣤⣤⠤⣤⢤⠖⣐⠒⣒⡖⢋⣩⢇⣸⣧⠞⠀ ⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⣴⣛⣦⣝⣦⡽⣘⢦⡳⣜⢢⢽⣰⣱⣾⠿⡶⢿⣦⣵⣌⢦⡱⢤⣉⢆⠡⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣷⣿⣾⣽⡿⠾⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡌⡭⡝⣯⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠾⠿⠿⠿⢿⣿⣿⣿⣾⣯⣿⣮⣷⣼⣰⣢⣤⣤⣤⣤⣤⣤⣄⡠⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⢀⡴⣁⠀⠀⢀⠀⠀⠀⡀⢀⡰⣀⣾⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠈⠀⠂⠑⠈⠁⠃⠙⠘⠑⠋⠙⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣀⣬⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣷⣾⣾⣯⣶⣴⣾⣦⣔⣤⣶⣦⣄⣧⣆⡔⣦⣆⡰⣠⣧⣧⣴⣶⣾⣿⣷⣭⣮⣵⣷⣦⠷⠿⠾⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠉⠃⠩⠍⠛⠼⠙⠏⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀