Greg Universe Emojis & Text

Copy & Paste Greg Universe Emojis & Symbols Better Than A Million PizzasIwannareadhiSummary:Wh

Better Than A Million Pizzas Iwannareadhi Summary: What if... Steven had to get his wisdom teeth removed? While waiting to be released to go home, Greg has a heartfelt conversation with a loopy Steven. Work Text: Steven had just got his wisdom teeth removed. Steven and Greg were in the hospital, with Steven in the patient chair. Steven was staring at Greg blankly, high on sedative and laughing gas. Greg was looking down at Steven. He was completely out of it. He chuckles a little bit at Steven's behavior. Steven chuckles a bit, then looks at his dad, still being kind of high from the sedative. "Hey dad, you know what's cooler than a million dollars?" Steven asked in a slurring voice. Greg smiles at his son, loving their silly little moments like these. This question was coming from the heart of a drugged-up child, so he knew it was going to be pure and sweet. Greg knew he had to take it seriously. "What's cooler than a million dollars?" Greg replied, playing along with his son's high antics. Steven thought for a while, then he got an idea and he was laughing. In his slurred voice, he says in a very high energy voice, "A million pizzas!" Greg laughed at the child-logic answer that he was absolutely certain to get as an answer. He wasn't surprised, just delighted. "A million pizzas?! You know, I bet you're right! If I could I'd give you a million pizzas, even though I know I'd never eat a million pizzas in my life. A million pizzas is better than a million dollars, I can agree with you there!" Greg says with a hearty chuckle, laughing at Steven's shenanigans. Steven then gets a brilliant idea, he has a new question to ask his dad, he looks at him with a wide, drugged-up grin. "Hey dad, you know what really is better than a million pizzas?" Greg smiles in anticipation and in preparation for what his son is about to say. "What's better than a million pizzas?" Greg asks, curious and excited to see where this question is going. Steven leans closer to his dad. "You!" He giggles then laughs, thinking that that's the best answer he's ever heard, he thinks he's so very clever with that answer. He's really proud of himself. Greg's face is washed with an incredibly warm feeling from the heart. The drugs of this child may have distorted his worldview in the present moment, making him believe that a million pizzas is just as good as a million dollars, but the simple fact that Greg holds so dearly is that Steven's simple answer, "you", was the best answer Steven knew would work, completely overwhelmed Greg with warmth, joy and pride for his child. He chuckles and hugs his kid, a true expression of love, joy, pride and affection. Steven hugs his dad too, and he may be all drugged up, but he still truly loves his dad and he can never forget how important Greg's presence, impact, and acceptance in his life is. Steven then asks another question, since he's feeling pretty good at asking questions right now. "Hey dad, wanna know something I think is pretty cool?" He asked with a smile. Greg continues the genuine hug, loving every moment of the pure, innocent, and genuine moment of affection between a parent and child. "Yes, I'd love to hear it. What do you have for me?" He asks, completely ready to hear whatever his son has to say. Steven says the next part with great pride, he's not slurring as hard as he was before, but he's still feeling a little loopy from the sedative. "I have the best D-dad in the whole w-world!" Greg hears this simple expression of affection from his son's sweet, high, and innocent lips, and he's immediately overwhelmed with emotions. The pure heart that lies within a high mind is the greatest thing of all, he thinks as a tear of pure joy rolls down his cheek. This son, this child of his, is the greatest treasure he has, and Greg is honored and privileged to be so truly lucky to have a son as kind and affectionate as Steven. He's truly blessed. Stats: Language: English Published:2023-12-01Words:673

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