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