{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given a bracket sequence $$$s$$$ of length $$$n$$$, where $$$n$$$ is even (divisible by two). The string $$$s$$$ consists of $$$\\frac{n}{2}$$$ opening brackets \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e(\u003c/span\u003e\u0027 and $$$\\frac{n}{2}$$$ closing brackets \u0027\u003cspan class\u003d\"tex-font-style-tt\"\u003e)\u003c/span\u003e\u0027.\u003c/p\u003e\u003cp\u003eIn one move, you can choose \u003cspan class\u003d\"tex-font-style-bf\"\u003eexactly one bracket\u003c/span\u003e and move it to the beginning of the string or to the end of the string (i.e. you choose some index $$$i$$$, remove the $$$i$$$-th character of $$$s$$$ and insert it before or after all remaining characters of $$$s$$$).\u003c/p\u003e\u003cp\u003eYour task is to find the minimum number of moves required to obtain \u003cspan class\u003d\"tex-font-style-bf\"\u003eregular bracket sequence\u003c/span\u003e from $$$s$$$. It can be proved that the answer always exists under the given constraints.\u003c/p\u003e\u003cp\u003eRecall what the regular bracket sequence is:\u003c/p\u003e\u003cul\u003e \u003cli\u003e \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()\u003c/span\u003e\" is regular bracket sequence; \u003c/li\u003e\u003cli\u003e if $$$s$$$ is regular bracket sequence then \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(\u003c/span\u003e\" + $$$s$$$ + \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)\u003c/span\u003e\" is regular bracket sequence; \u003c/li\u003e\u003cli\u003e if $$$s$$$ and $$$t$$$ are regular bracket sequences then $$$s$$$ + $$$t$$$ is regular bracket sequence. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor example, \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()()\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(())()\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(())\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()\u003c/span\u003e\" are regular bracket sequences, but \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)(\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()(\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)))\u003c/span\u003e\" are not.\u003c/p\u003e\u003cp\u003eYou have to answer $$$t$$$ independent test cases.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 2000$$$) — the number of test cases. Then $$$t$$$ test cases follow.\u003c/p\u003e\u003cp\u003eThe first line of the test case contains one integer $$$n$$$ ($$$2 \\le n \\le 50$$$) — the length of $$$s$$$. It is guaranteed that $$$n$$$ is even. The second line of the test case containg the string $$$s$$$ consisting of $$$\\frac{n}{2}$$$ opening and $$$\\frac{n}{2}$$$ closing brackets.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, print the answer — the minimum number of moves required to obtain \u003cspan class\u003d\"tex-font-style-bf\"\u003eregular bracket sequence\u003c/span\u003e from $$$s$$$. It can be proved that the answer always exists under the given constraints.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\n2\n)(\n4\n()()\n8\n())()()(\n10\n)))((((())\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n0\n1\n3\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first test case of the example, it is sufficient to move the first bracket to the end of the string.\u003c/p\u003e\u003cp\u003eIn the third test case of the example, it is sufficient to move the last bracket to the beginning of the string.\u003c/p\u003e\u003cp\u003eIn the fourth test case of the example, we can choose last three openning brackets, move them to the beginning of the string and obtain \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e((()))(())\u003c/span\u003e\".\u003c/p\u003e"}}]}