{"id":792,"date":"2019-01-07T19:24:12","date_gmt":"2019-01-07T11:24:12","guid":{"rendered":"https:\/\/mnihyc.tk\/blog\/?p=792"},"modified":"2020-02-09T03:12:29","modified_gmt":"2020-02-08T19:12:29","slug":"yzoj-p2202-legend-vii-ornament","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/792","title":{"rendered":"YZOJ P2202 Legend VII &#8211; Ornament"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P2202 Legend VII &#8211; Ornament<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a131072KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #ffcc00;\">\\(5.0\\)<\/span><span style=\"color: #000000;\"><br \/>\n<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-793\" src=\"https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/\u56f33.png\" alt=\"\" width=\"1154\" height=\"245\" srcset=\"https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/\u56f33.png 1154w, https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/\u56f33-300x64.png 300w, https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/\u56f33-768x163.png 768w, https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/\u56f33-1024x217.png 1024w\" sizes=\"auto, (max-width: 1154px) 100vw, 1154px\" \/><\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6574\u6570 \\(N\\) \u548c \\(Q\\)\uff0c\u8868\u793a\u5546\u5e97\u6709 \\(N\\) \u4e2a\u88c5\u9970\u54c1\uff0c\u4e00\u5171\u6709 \\(Q\\) \u4e2a\u8be2\u95ee\u3002<\/p>\n<p>\u7b2c\u4e8c\u884c\u6709 \\(N\\) \u5bf9\u6574\u6570\uff0c\u6bcf \\(i\\) \u5bf9\u6574\u6570 \\(p_i, b_i\\) \u8868\u793a\u7b2c \\(i\\) \u4e2a\u88c5\u9970\u54c1\u7684\u4ef7\u683c\u548c\u597d\u770b\u5ea6\u3002<\/p>\n<p>\u63a5\u4e0b\u6765 \\(Q\\) \u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 \\(a, c\\)\uff0c\u5206\u522b\u63cf\u8ff0 \\(Q\\) \u4e2a\u8be2\u95ee\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u8be2\u95ee\u8f93\u51fa\u4e00\u884c\uff0c\u4e00\u4e2a\u6574\u6570\u8868\u793a\u6700\u5927\u597d\u770b\u5ea6\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">3 5\r\n2 3 1 3 1 2\r\n1 2\r\n1 1\r\n3 1\r\n3 2\r\n3 3<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">5\r\n3\r\n3\r\n3\r\n6<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e \\(30\\%\\) \u7684\u6570\u636e\uff0c\\(N \\leq 100, Q \\leq 1000\\) \u3002<\/p>\n<p>\u5bf9\u4e8e \\(100\\%\\) \u7684\u6570\u636e\uff0c\\(N \\leq 1000, Q \\leq 100000, 1 \\leq a \\leq N, c \\leq 1000\\) \u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\">\u6309\u7167\u60ef\u4f8b\uff0c\u8fd9\u9898\u53ef\u4ee5\u7528\u4e00\u79cd\u5947\u602a\u7684\u505a\u6cd5\u5361\u8fc7\u53bb\uff1a\u6b63\u53cd\u4e24\u904d\u80cc\u5305\uff0c\u7136\u540e\u5bf9\u4e8e\u6bcf\u4e2a\u8be2\u95ee<\/span> \\(O(c)\\) \u67e5\u627e\u7b54\u6848\u3002\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(Qc \\approx 10^8)\\) \uff0c\u6570\u636e\u6bd4\u8f83\u6c34\u5c31\u5361\u8fc7\u53bb\u4e86\u3002<\/p>\n<p>\u8be6\u89c1\u4ee3\u7801<\/p>\n<pre class=\"minimize:true lang:default decode:true\">#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n\r\n#define _max(_a,_b) ((_a)&gt;(_b)?(_a):(_b))\r\n\r\ninline int getnum()\r\n{\r\n\tregister char c=getchar();\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar();\r\n\tregister int a=0;\r\n\twhile(c&gt;='0' &amp;&amp; c&lt;='9')\r\n\t{\r\n\t\ta*=10;a+=c-'0';\r\n\t\tc=getchar();\r\n\t}\r\n\treturn a;\r\n}\r\n\r\nint p[1050],b[1050];\r\nint f[1050][1050],rf[1050][1050];\r\n\r\nint main()\r\n{\r\n\tregister int N=getnum(),Q=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tp[i]=getnum(),b[i]=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\tfor(register int j=0;j&lt;p[i];j++)\r\n\t\t\tf[i][j]=f[i-1][j];\r\n\t\tfor(register int j=p[i];j&lt;=1000;j++)\r\n\t\t\tf[i][j]=_max(f[i-1][j],f[i-1][j-p[i]]+b[i]);\r\n\t}\r\n\tfor(register int i=N;i&gt;=1;i--)\r\n\t{\r\n\t\tfor(register int j=0;j&lt;p[i];j++)\r\n\t\t\trf[i][j]=rf[i+1][j];\r\n\t\tfor(register int j=p[i];j&lt;=1000;j++)\r\n\t\t\trf[i][j]=_max(rf[i+1][j],rf[i+1][j-p[i]]+b[i]);\r\n\t}\r\n\tfor(register int q=1;q&lt;=Q;q++)\r\n\t{\r\n\t\tregister int a=getnum(),c=getnum();\r\n\t\tregister int ans=0;\r\n\t\t\/\/ \u53bb\u6389\u7b2c a \u4e2a\u7269\u54c1\uff0c\u91cd\u65b0\u679a\u4e3e\u5bb9\u91cf\r\n\t\tfor(register int j=0;j&lt;=c;j++)\r\n\t\t\tans=_max(ans,f[a-1][j]+rf[a+1][c-j]);\r\n\t\tprintf(\"%d\\n\",ans);\r\n\t}\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p>\n\u4f46\u662f\u6211\u4eec\u5fc5\u987b<strong>\u601d\u8003\u6b63\u89e3<\/strong>\u800c\u4e0d\u662f<span style=\"color: #ff0000;\"><strong>\u5957\u7b97\u6cd5<\/strong><\/span>\uff01<\/p>\n<p>\n\u9996\u5148\uff0c\u7531\u4e8e\u201c\u5220\u9664\u201d\u8fd9\u4e2a\u64cd\u4f5c\u4e0d\u662f\u5f88\u597d\u5b9e\u73b0\uff0c\u6240\u4ee5\u628a\u601d\u7ef4\u9006\u8f6c\u8fc7\u6765\uff0c\u8003\u8651<strong>\u201c\u589e\u52a0\u201d<\/strong>\u8fd9\u4e2a\u64cd\u4f5c\u3002<\/p>\n<p>\u63a5\u7740\uff0c\u8fd8\u53d1\u73b0\u4e00\u4e2a\u6027\u8d28\uff1a\u5982\u679c\u4e0d\u9009\u7684\u7269\u54c1 \\(a\\) \u5728\u533a\u95f4 \\([l, r]\\) \u4e2d\uff0c\u90a3\u4e48 \\(a\\) \u4e0d\u662f\u5728 \\([l, \\lfloor\\frac{l+r}{2}\\rfloor]\\) \u4e2d\u5c31\u662f\u5728 \\([\\lfloor\\frac{l+r}{2}\\rfloor+1, r]\\) \u4e2d\uff08\u5e9f\u8bdd\uff09\u3002\u8fd9\u63d0\u793a\u6211\u4eec\uff0c\u53ef\u4ee5\u7528\u5206\u6cbb\u7684\u601d\u60f3\u628a\u8fd9\u4e2a\u95ee\u9898\u5206\u6210\u591a\u4e2a\u5b50\u95ee\u9898\u6765\u89e3\u51b3\u3002<\/p>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u533a\u95f4 \\([l, r]\\) \uff0c\u5982\u679c \\(a\\) \u5728 \\([l, \\lfloor\\frac{l+r}{2}\\rfloor]\\) \u4e2d\uff0c\u90a3\u4e48\u53e6\u4e00\u4e2a\u533a\u95f4 \\([\\lfloor\\frac{l+r}{2}\\rfloor+1, r]\\) \u4e2d\u7684\u7269\u54c1<strong>\u90fd\u662f\u53ef\u4ee5\u9009<\/strong>\u7684\uff0c\u6240\u4ee5\u5bf9\u8fd9\u4e9b\u7269\u54c1\u505a01\u80cc\u5305\uff0c\u7136\u540e\u7ee7\u7eed\u5904\u7406 \\([l, \\lfloor\\frac{l+r}{2}\\rfloor]\\) \uff1b\u82e5 \\(a\\) \u5728 \\([\\lfloor\\frac{l+r}{2}\\rfloor+1, r]\\) \u4e2d\u4e5f\u662f\u540c\u6837\u3002<\/p>\n<p>\u4f46\u662f\u5f88\u660e\u663e\uff0c\u5728\u5206\u6cbb\u7684\u65f6\u5019\u9700\u8981\u4e0d\u9009 \\([l, r]\\) \u533a\u95f4\u7269\u54c1\uff0c\u5176\u4ed6\u7269\u54c1\u90fd\u9009\u65f6\u7684\u52a8\u6001\u89c4\u5212 \\(f\\) \u6570\u7ec4\u4f5c\u4e3a<strong>\u521d\u59cb\u72b6\u6001<\/strong>\uff0c\u8fd9\u6837\u624d\u80fd\u7ee7\u7eed\u5bf9\u8fd9\u4e2a\u533a\u95f4\u8fdb\u884c\u89c4\u5212\u548c\u5206\u5272\u3002\u540c\u65f6\u5fc5\u987b\u5728\u56de\u6eaf\u7684\u65f6\u5019\u628a\u8fd9\u4e2a\u6570\u7ec4\u8fd8\u539f\u3002\u5bf9\u4e8e\u6bcf\u6b21\u9012\u5f52\u548c\u56de\u6eaf\u90fd\u91cd\u65b0\u5bf9\u9664\u4e86 \\([l, r]\\) \u4e2d\u7684\u7269\u54c1\u505a\u4e00\u904d01\u80cc\u5305\u4ee3\u4ef7\u662f\u5f88\u5927\u7684\uff0c\u53ef\u4ee5\u8fbe\u5230 \\(O(N^2c)\\) \u7b49\u4e8e\u662f\u9000\u5316\u4e86\u3002<\/p>\n<p>\u6ce8\u610f\u5230\u5206\u6cbb\u7684\u9012\u5f52\u6811\u6700\u591a\u53ea\u6709 \\(log_{2}{N^2} \\approx 19\\) \u5c42\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u628a<strong>\u6bcf\u4e00\u5c42<\/strong>\u7684\u52a8\u6001\u89c4\u5212 \\(f\\) \u6570\u7ec4\u90fd<strong>\u5b58\u4e0b\u6765<\/strong>\uff0c\u5728\u5bf9\u8fd9\u4e00\u5c42\u8fdb\u884c\u89c4\u5212\u7684\u65f6\u5019\uff0c\u76f4\u63a5\u628a\u4e0a\u4e00\u5c42\u7684 \\(f\\) \u5f53\u505a\u521d\u59cb\u72b6\u6001\u5373\u53ef\u3002\u8fd9\u6837\u56de\u6eaf\u7684\u65f6\u5019\u4e5f\u4e0d\u5fc5\u8003\u8651\u5982\u4f55\u4fdd\u5b58\u5e76\u8fd8\u539f \\(f\\) \u6570\u7ec4\u4e86\u3002<\/p>\n<p>\u6700\u540e\uff0c\u5f53\u5206\u6cbb\u5230 \\(l=r\\) \u65f6\uff0c\u8fd9\u4e2a \\(a\\) \u5143\u7d20\u4e5f\u5c31\u88ab\u786e\u5b9a\u4e0b\u6765\u4e86\uff0c\u66f4\u65b0\u53bb\u6389 \\(a\\) \u7684\u7b54\u6848\u7684 \\(f&#8217;\\) \u6570\u7ec4\u5373\u53ef\u3002<\/p>\n<p>\u8fd9\u6837\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u53ea\u6709 \\(O(NclogN)\\) \u8db3\u4ee5\u901a\u8fc7\u672c\u9898\u3002<\/p>\n<p>&nbsp;<\/p>\n<pre class=\"lang:default decode:true \">#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n\r\n#define _max(_a,_b) ((_a)&gt;(_b)?(_a):(_b))\r\n\r\n\r\n#define MAXBFN 524288\r\nchar buffer[MAXBFN+1],*S,*T; \r\ninline char GetChar()  \r\n{\r\n    if(S==T)\r\n    {\r\n        T=(S=buffer)+fread(buffer,1,MAXBFN,stdin);\r\n        if(S==T)return EOF;\r\n    }\r\n    return *S++;\r\n}\r\nchar pbuf[MAXBFN+1],*pp=pbuf;\r\ninline void PutChar(const char&amp;c)\r\n{\r\n    if(pp-pbuf==MAXBFN)\r\n\t\tfwrite(pbuf,1,MAXBFN,stdout),pp=pbuf;\r\n    *pp++=c;\r\n}\r\ninline void PrintNum(long long a)\r\n{\r\n\tif(a&lt;0)\r\n\t{\r\n\t\tPutChar('-');\r\n\t\tPrintNum(-a);\r\n\t\treturn;\r\n\t}\r\n\tif(a&gt;9)\r\n\t\tPrintNum(a\/10);\r\n\tPutChar(a%10+'0');\r\n}\r\ninline int getnum()\r\n{\r\n\tregister char c=GetChar();\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=GetChar();\r\n\tregister int a=0;\r\n\twhile(c&gt;='0' &amp;&amp; c&lt;='9')\r\n\t{\r\n\t\ta*=10;a+=c-'0';\r\n\t\tc=GetChar();\r\n\t}\r\n\treturn a;\r\n}\r\n\r\n\r\nint p[1050],b[1050];\r\nint f[21][1050],ans[1050][1050];\r\n\r\nvoid Divide(register int step,register int l,register int r)\r\n{\r\n\tif(l==r)\r\n\t{\r\n\t\tfor(register int j=0;j&lt;=1000;j++)\r\n\t\t\tans[l][j]=f[step-1][j];\r\n\t\treturn;\r\n\t}\r\n\tregister int mid=(l+r)&gt;&gt;1;\r\n\t\r\n\tfor(register int j=0;j&lt;=1000;j++)\r\n\t\tf[step][j]=f[step-1][j];\r\n\tfor(register int i=l;i&lt;=mid;i++)\r\n\t\tfor(register int j=1000;j&gt;=p[i];j--)\r\n\t\t\tf[step][j]=_max(f[step][j],f[step][j-p[i]]+b[i]);\r\n\tDivide(step+1,mid+1,r);\r\n\t\r\n\tfor(register int j=0;j&lt;=1000;j++)\r\n\t\tf[step][j]=f[step-1][j];\r\n\tfor(register int i=mid+1;i&lt;=r;i++)\r\n\t\tfor(register int j=1000;j&gt;=p[i];j--)\r\n\t\t\tf[step][j]=_max(f[step][j],f[step][j-p[i]]+b[i]);\r\n\tDivide(step+1,l,mid);\r\n\t\r\n}\r\n\r\nint main()\r\n{\r\n\tregister int N=getnum(),Q=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tp[i]=getnum(),b[i]=getnum();\r\n\t\r\n\tDivide(1,1,N);\r\n\t\r\n\tfor(register int q=1;q&lt;=Q;q++)\r\n\t{\r\n\t\tregister int a=getnum(),c=getnum();\r\n\t\t\/\/printf(\"%d\\n\",ans[a][c]);\r\n\t\tPrintNum(ans[a][c]);PutChar('\\n');\r\n\t}\r\n\tfwrite(pbuf,1,pp-pbuf,stdout);\r\n\t\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P2202 Legend VII &#8211; Ornament \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236 &hellip; <a href=\"https:\/\/0.mnihyc.com\/blog\/archives\/792\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P2202 Legend VII &#8211; Ornament<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36,38,40],"tags":[],"class_list":["post-792","post","type-post","status-publish","format-standard","hentry","category-harda","category-partition","category-bagdp"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P2202 Legend VII - Ornament - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P2202 Legend VII - Ornament \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a131072KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u8f93\u5165\u683c\u5f0f \u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6574\u6570 (N) \u548c (Q)\uff0c\u8868\u793a\u5546\u5e97\u6709 (N) \u4e2a\u88c5\u9970\u54c1\uff0c\u4e00\u5171\u6709 (Q) \u4e2a\u8be2\u95ee\u3002 \u7b2c\u4e8c\u884c\u6709 (N) \u5bf9\u6574\u6570\uff0c\u6bcf (i) \u5bf9\u6574\u6570\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mnihyc.com\/blog\/archives\/792\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"YZOJ P2202 Legend VII - Ornament - mnihyc&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"YZOJ P2202 Legend VII - Ornament \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a131072KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u8f93\u5165\u683c\u5f0f \u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6574\u6570 (N) \u548c (Q)\uff0c\u8868\u793a\u5546\u5e97\u6709 (N) \u4e2a\u88c5\u9970\u54c1\uff0c\u4e00\u5171\u6709 (Q) \u4e2a\u8be2\u95ee\u3002 \u7b2c\u4e8c\u884c\u6709 (N) \u5bf9\u6574\u6570\uff0c\u6bcf (i) \u5bf9\u6574\u6570\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mnihyc.com\/blog\/archives\/792\" \/>\n<meta property=\"og:site_name\" content=\"mnihyc&#039;s Blog\" \/>\n<meta property=\"article:published_time\" content=\"2019-01-07T11:24:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-02-08T19:12:29+00:00\" \/>\n<meta name=\"author\" content=\"mnihyc\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mnihyc\" \/>\n<meta name=\"twitter:site\" content=\"@mnihyc\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"mnihyc\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mnihyc.com\/blog\/archives\/792#article\",\"isPartOf\":{\"@id\":\"https:\/\/mnihyc.com\/blog\/archives\/792\"},\"author\":{\"name\":\"mnihyc\",\"@id\":\"https:\/\/mnihyc.com\/blog\/#\/schema\/person\/61e167d6d591fdd20dcfee2cf848a751\"},\"headline\":\"YZOJ P2202 Legend VII &#8211; 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