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