시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 128 MB42713510942.578%

문제

다항식을 계산하기 위해 고안된 계산기가 있다. 이 계산기에는 0부터 9까지의 숫자와 +, ×(곱하기), x, =의 14개의 키가 있다.

예를 들어 이 계산기를 이용하여 x^3 + x + 11을 계산하려면 x, ×, x, ×, x, +, x + 1, 1, = 을 누르면 된다. 또 x^3 + 2x^2 + 11을 계산하기 위해서는 x, +, 2, ×, x, ×, x, +, 1, 1, = 을 누르면 된다.

일반적인 계산기라면 x, +, 2, ×, x, ×, x, +, 1, 1, = 을 x + 2x^2 + 11로 인식하겠지만, 이 계산기는 추가 메모리가 없기 때문에 계산을 할 때에 계산 직전에 계산기에 저장되어 있던 값에 계산을 한다. 즉 x, +, 2, ×, x, ×, x, +, 1, 1, = 을 입력하면 계산기에는 차례로 x, x+2, x^2+2x, x^3+2x^2, x^3+2x^2+11 이 입력되는 것이다.

문제를 단순하게 하기 위해서 최고차항의 계수는 항상 1이라고 가정하자. 또 음수 계수는 고려하지 않기로 하자.

다항식이 주어졌을 때, 이 계산기로 주어진 다항식을 계산하려면 계산기를 최소 몇 번 눌러야 하는지를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 다항식의 차수 N(1 ≤ N ≤ 10,000)이 주어진다. 다음 줄에는 다항식의 계수가 최고차항부터 주어진다. 최고차항의 계수는 항상 1이며 모든 계수는 0 이상이다. 모든 계수는 1,000,000,000을 넘지 않는다.

출력

첫째 줄에 계산기를 누르는 최소 횟수를 출력한다.

예제 입력 1

3
1 0 1 11

예제 출력 1

11
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One of the most promising projects so far is the &quot;Polly Nomial&quot; project on parrot intelligence, run by Dr. Albert B. Tross and his assistants, Clifford Swallow and Perry Keet. In the ACM, parrots are trained to carry out simple polynomial computations involving integers, variables, and simple arithmetic operators.<\/p>\r\n\r\n<p>When shown a formula consisting of a polynomial with non-negative integer coe&plusmn;cients and one variable x, each parrot uses a special beak-operated PDA, or &quot;Parrot Digital Assistant,&quot; to tap out a sequence of operations for computing the polynomial. The PDA operates much like a calculator. It has keys marked with the following symbols: the digits from 0 through 9, the symbol `x&#39;, and the operators `+&#39;, `&times;&#39;, and `=&#39;. (The x key is internally associated with an integer constant by Al B. Tross for testing purposes, but the parrot sees only the `x&#39;.) For instance, if the parrot were presented with the polynomial<\/p>\r\n\r\n<p>x<sup>3<\/sup> + x + 11<\/p>\r\n\r\n<p>the parrot might tap the following sequence of symbols:<\/p>\r\n\r\n<p>x, &times;, x, &times;, x, +, x, +, 1, 1, =<\/p>\r\n\r\n<p>The PDA has no extra memory, so each &times; or + operation is applied to the previous contents of the display and whatever succeeding operand is entered. If the polynomial had been<\/p>\r\n\r\n<p>x<sup>3<\/sup> + 2x<sup>2<\/sup> + 11<\/p>\r\n\r\n<p>then the parrot would not have been able to &quot;save&quot; the value of x<sup>3<\/sup> while calculating the value of 2x<sup>2<\/sup>. Instead, a different order of operations would be needed, for instance:<\/p>\r\n\r\n<p>x, +, 2, &times;, x, &times;, x, +, 1, 1, =<\/p>\r\n\r\n<p>The cost of a calculation is the number of key presses. The cost of computing x<sup>3<\/sup> + x + 11 in the example above is 11 (four presses of the x key, two presses of `&times;&#39;, two presses of `+&#39;, two presses of the digit `1&#39;, and the `=&#39; key). It so happens that this is the minimal cost for this particular expression using the PDA.<\/p>\r\n\r\n<p>You are to write a program that finds the least costly way for a parrot to compute a number of polynomial expressions. Because parrots are, after all, just bird-brains, they are intimidated by polynomials whose high-order coefficient is any value except 1, so this condition is always imposed.<\/p>\r\n","input":"<p>Input consists of a sequence of lines, each containing a polynomial and an x value. Each polynomial a<sub>n<\/sub>x<sup>n<\/sup> + a<sub>n-1<\/sub>x<sup>n-1<\/sup> + ... + a<sub>0<\/sub> is represented by its degree followed by the non-negative coefficients a<sub>n<\/sub>, ..., a<sub>0<\/sub> of decreasing powers of x, where an is always 1. Degrees are between 1 and 100. The coefficients are followed on the same line by an integer value for the variable x, which is always either 1 or -1. The input is terminated by a single line containing the values 0 0.<\/p>\r\n","output":"<p>For each polynomial, print the polynomial number followed by the value of the polynomial at the given integer value x and the minimum cost of computing the polynomial; imitate the formatting in the sample output.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]