---{"category_name":"medium","problem_code":"CDIGLNUM","problem_name":"Chef and Digits of Large Numbers","problemComponents":{"constraints":"- $1 \\leq T \\leq 10145$\n- $0 \\leq N \\leq 10^{100}$\n","constraintsState":true,"subtasks":"**Subtask #1 (10 points):** \n - $1 \\leq T \\leq 200$ \n - $0 \\leq N \\leq 44000000$ \n\n**Subtask #2 (90 points):** Original constraints \n","subtasksState":true,"inputFormat":"- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.\n- The first and only line of each test case contains a single integer $N$.\n","inputFormatState":true,"outputFormat":"For each test case, output in a single line the answer for given integer $N$\n","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"3\n13\n54\n198","output":"11\n48\n159","explanation":"**Test case $1$**: The only one-digit number that will not be included in the answer is $0$. The two-digit numbers that will not be included in the answer are $10, 11$ because their product of digits is less than $2! = 2$. So the answer is $= 14 - 1 - 2 = 11$. \n \n**Test case $3$**: \n- The one-digit number that will not be counted in the answer is $0$. \n- The two-digit digit numbers that will not be counted in the answer are $10, 11$, $20, 30$, $40, 50, 60,$ $70, 80, 90$ because their product of digits is less than $2! = 2$. \n- The three-digit numbers that will not be counted in the answer are $100$, $101, 102,$ $103, 104, 105$, $106, 107, 108$, $109, 110, 111,$ $112, 113, 114,$ $115, 120$,$ 121,$ $122, 130, 131,$ $140, 141, \n150,$ $151, 160, 170$, $180, 190$ because their product of digits is less than $3! = 6$. \nSo the answer is $= 199 - 1 - 10 - 29 = 159$. ","isDeleted":false}}},"video_editorial_url":"","languages_supported":{"0":"CPP14","1":"C","2":"JAVA","3":"PYTH 3.6","4":"CPP17","5":"PYTH","6":"PYP3","7":"CS2","8":"ADA","9":"PYPY","10":"TEXT","11":"PAS fpc","12":"NODEJS","13":"RUBY","14":"PHP","15":"GO","16":"HASK","17":"TCL","18":"PERL","19":"SCALA","20":"LUA","21":"kotlin","22":"BASH","23":"JS","24":"LISP sbcl","25":"rust","26":"PAS gpc","27":"BF","28":"CLOJ","29":"R","30":"D","31":"CAML","32":"FORT","33":"ASM","34":"swift","35":"FS","36":"WSPC","37":"LISP clisp","38":"SQL","39":"SCM guile","40":"PERL6","41":"ERL","42":"CLPS","43":"ICK","44":"NICE","45":"PRLG","46":"ICON","47":"COB","48":"SCM chicken","49":"PIKE","50":"SCM qobi","51":"ST","52":"SQLQ","53":"NEM"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"abhisek_12345","problem_tester":"","date_added":"2-08-2021","tags":{"0":"abhisek_12345","1":"aug21","2":"digit","3":"math","4":"medium"},"problem_difficulty_level":"Unavailable","best_tag":"Digit Dp","editorial_url":"https://discuss.codechef.com/problems/CDIGLNUM","time":{"view_start_date":1629117000,"submit_start_date":1629117000,"visible_start_date":1629117000,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=CDIGLNUM","is_proctored":false,"visitedContests":{},"layout":"problem"}---### Read problem statements in [Bengali](https://www.codechef.com/download/translated/AUG21/bengali/CDIGLNUM.pdf), [Mandarin Chinese](https://www.codechef.com/download/translated/AUG21/mandarin/CDIGLNUM.pdf), [Russian](https://www.codechef.com/download/translated/AUG21/russian/CDIGLNUM.pdf), and [Vietnamese](https://www.codechef.com/download/translated/AUG21/vietnamese/CDIGLNUM.pdf) as well.Chef and Abhishek are two friends. Abhishek really appreciates Chef's skills and wants to learn the secret formula behind Chef's tasty dishes. Chef will tell his secret formula only to acompetent person. So to check Abhishek's competency, Chef asked him to solve the following problem.Find the number of integers between $0$ and $N$ (inclusive) such that the product of digits of the integer is greater than or equal to $K!$, where $K$ is the number of digits present in the integer.**Example**: Consider $N = 1000$.- The only digit present in the integer $0$ is $0$. So the product of digit is also $0$ and $1! = 1$. So $0$ will be not counted in the answer because $0 \ngtr 1$.- The digits present in the integer $25$ are $2, 5$. So the product of digits is $(2 \cdot 5) = 10$ and $2 ! = 2$. So $25$ will be counted in the answer because $10 \geq 2$.- The digits present in the integer $11$ are $1, 1$. So the product of digits is $(1 \cdot 1) = 1$ and $2 ! = 2$. So $11$ will be not counted in the answer because $1 \ngtr 2$.- The digits present in the integer $157$ are $1, 5, 7$. So the product of digits is $(1 \cdot 5 \cdot 7) = 35$ and $3! = 6$. So $157$ will be counted in the answer because $35 \geq 6$.Since Abhishek is a lazy person, he wants your help to solve the problem.**Note**: $K!$ represents the factorial of $K$ and $K! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot (K-1) \cdot K$ .<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>