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