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"NTCIR12-MathWiki-20": ["math:V!r\t=\tn\t-", "math:V!r\tO!divide\tnn\t-", "math:=\tO!divide\tn\tn", "math:=\tM!()1x1\tnu\tn", "math:=\t\u2211\tno\tn", "math:=\t=\tnn\tn", "math:O!divide\t\u2211\to\tnn", "math:O!divide\tV!i\tou\tnn", "math:O!divide\tV!n\too\tnn", "math:O!divide\tM!()1x1\ton\tnn", "math:\u2211\tV!n\to\tnno", "math:V!n\t0!\tn\tnnoo", "math:\u2211\tM!()1x1\tn\tnno", "math:\u2211\tV!x\tnw\tnno", "math:\u2211\tM!()1x1\tnn\tnno", "math:M!()1x1\tM!()1x1\tn\tnnon", "math:M!()1x1\tV!y\tnw\tnnon", "math:M!()1x1\tV!y\tw\tnnonn", "math:M!()1x1\tV!i\twb\tnnonn", "math:M!()1x1\t-\twn\tnnonn", "math:V!y\t-\tn\t2n1o2n1w", "math:V!y\tV!y\tnn\t2n1o2n1w", "math:-\tV!y\tn\t2n1o2n1w1n", "math:-\t\u0304\tna\t2n1o2n1w1n", "math:V!y\t\u0304\ta\t2n1o2n1w2n", "math:\u0304\t0!\tn\t2n1o2n1w2n1a", "math:V!y\t0!\tn\t2n1o2n1w2n", "math:V!y\tV!i\tb\t2n1o2n1w", "math:V!i\t0!\tn\t2n1o2n1w1b", "math:M!()1x1\t0!\tn\tnnonn", "math:M!()1x1\tV!x\tw\tnnon", "math:M!()1x1\tV!i\twb\tnnon", "math:M!()1x1\t-\twn\tnnon", "math:V!x\t-\tn\tnnonw", "math:V!x\tV!x\tnn\tnnonw", "math:-\tV!x\tn\t2n1o1n1w1n", "math:-\t\u0304\tna\t2n1o1n1w1n", "math:V!x\t\u0304\ta\t2n1o1n1w2n", "math:\u0304\t0!\tn\t2n1o1n1w2n1a", "math:V!x\t0!\tn\t2n1o1n1w2n", "math:V!x\tV!i\tb\tnnonw", "math:V!i\t0!\tn\t2n1o1n1w1b", "math:\u2211\tV!i\tu\tnno", "math:\u2211\t=\tun\tnno", "math:V!i\t=\tn\tnnou", "math:V!i\tN!1\tnn\tnnou", "math:=\tN!1\tn\tnnoun", "math:N!1\t0!\tn\t2n1o1u2n", "math:O!divide\t=\tn\tnn", "math:O!divide\tO!divide\tnn\tnn", "math:=\tO!divide\tn\tnnn", "math:=\tO!root\tnu\tnnn", "math:=\t\u2211\tno\tnnn", "math:=\t,\tnn\tnnn", "math:O!divide\t\u2211\to\tnnnn", "math:O!divide\tV!i\tou\tnnnn", "math:O!divide\tV!n\too\tnnnn", "math:O!divide\tM!()1x1\ton\tnnnn", "math:\u2211\tV!n\to\tnnnno", "math:V!n\t0!\tn\t4n2o", "math:\u2211\tM!()1x1\tn\tnnnno", "math:\u2211\tV!x\tnw\tnnnno", "math:\u2211\tM!()1x1\tnn\tnnnno", "math:M!()1x1\tM!()1x1\tn\t4n1o1n", "math:M!()1x1\tV!y\tnw\t4n1o1n", "math:M!()1x1\tV!y\tw\t4n1o2n", "math:M!()1x1\tV!i\twb\t4n1o2n", "math:M!()1x1\t-\twn\t4n1o2n", "math:V!y\t-\tn\t4n1o2n1w", "math:V!y\tV!y\tnn\t4n1o2n1w", "math:-\tV!y\tn\t4n1o2n1w1n", "math:-\t\u0304\tna\t4n1o2n1w1n", "math:V!y\t\u0304\ta\t4n1o2n1w2n", "math:\u0304\t0!\tn\t4n1o2n1w2n1a", "math:V!y\t0!\tn\t4n1o2n1w2n", "math:V!y\tV!i\tb\t4n1o2n1w", "math:V!i\t0!\tn\t4n1o2n1w1b", "math:M!()1x1\t0!\tn\t4n1o2n", "math:M!()1x1\tV!x\tw\t4n1o1n", "math:M!()1x1\tV!i\twb\t4n1o1n", "math:M!()1x1\t-\twn\t4n1o1n", "math:V!x\t-\tn\t4n1o1n1w", "math:V!x\tV!x\tnn\t4n1o1n1w", "math:-\tV!x\tn\t4n1o1n1w1n", "math:-\t\u0304\tna\t4n1o1n1w1n", "math:V!x\t\u0304\ta\t4n1o1n1w2n", "math:\u0304\t0!\tn\t4n1o1n1w2n1a", "math:V!x\t0!\tn\t4n1o1n1w2n", "math:V!x\tV!i\tb\t4n1o1n1w", "math:V!i\t0!\tn\t4n1o1n1w1b", "math:\u2211\tV!i\tu\tnnnno", "math:\u2211\t=\tun\tnnnno", "math:V!i\t=\tn\t4n1o1u", "math:V!i\tN!1\tnn\t4n1o1u", "math:=\tN!1\tn\t4n1o1u1n", "math:N!1\t0!\tn\t4n1o1u2n", "math:O!divide\t,\tn\tnnnn", "math:,\t0!\tn\tnnnnn", "math:O!divide\tO!root\tu\tnnnn", "math:O!divide\t\u2211\tuw\tnnnn", "math:O!root\t\u2211\tw\tnnnnu", "math:O!root\tV!i\twu\tnnnnu", "math:O!root\tV!n\two\tnnnnu", "math:O!root\tM!()1x1\twn\tnnnnu", "math:\u2211\tV!n\to\t4n1u1w", "math:V!n\t0!\tn\t4n1u1w1o", "math:\u2211\tM!()1x1\tn\t4n1u1w", "math:\u2211\tV!x\tnw\t4n1u1w", "math:\u2211\tN!2\tna\t4n1u1w", "math:\u2211\t\u2211\tnn\t4n1u1w", "math:M!()1x1\tN!2\ta\t4n1u1w1n", "math:N!2\t0!\tn\t4n1u1w1n1a", "math:M!()1x1\t\u2211\tn\t4n1u1w1n", "math:M!()1x1\tV!i\tnu\t4n1u1w1n", "math:M!()1x1\tV!n\tno\t4n1u1w1n", "math:M!()1x1\tM!()1x1\tnn\t4n1u1w1n", "math:\u2211\tV!n\to\t4n1u1w2n", "math:V!n\t0!\tn\t4n1u1w2n1o", "math:\u2211\tM!()1x1\tn\t4n1u1w2n", "math:\u2211\tV!y\tnw\t4n1u1w2n", "math:\u2211\tN!2\tna\t4n1u1w2n", "math:M!()1x1\tN!2\ta\t4n1u1w3n", "math:N!2\t0!\tn\t4n1u1w3n1a", "math:M!()1x1\tV!y\tw\t4n1u1w3n", "math:M!()1x1\tV!i\twb\t4n1u1w3n", "math:M!()1x1\t-\twn\t4n1u1w3n", "math:V!y\t-\tn\t4n1u1w3n1w", "math:V!y\tV!y\tnn\t4n1u1w3n1w", "math:-\tV!y\tn\t4n1u1w3n1w1n", "math:-\t\u0304\tna\t4n1u1w3n1w1n", "math:V!y\t\u0304\ta\t4n1u1w3n1w2n", "math:\u0304\t0!\tn\t4n1u1w3n1w2n1a", "math:V!y\t0!\tn\t4n1u1w3n1w2n", "math:V!y\tV!i\tb\t4n1u1w3n1w", "math:V!i\t0!\tn\t4n1u1w3n1w1b", "math:M!()1x1\t0!\tn\t4n1u1w3n", "math:\u2211\tV!i\tu\t4n1u1w2n", "math:\u2211\t=\tun\t4n1u1w2n", "math:V!i\t=\tn\t4n1u1w2n1u", "math:V!i\tN!1\tnn\t4n1u1w2n1u", "math:=\tN!1\tn\t4n1u1w2n1u1n", "math:N!1\t0!\tn\t4n1u1w2n1u2n", "math:M!()1x1\tV!x\tw\t4n1u1w1n", "math:M!()1x1\tV!i\twb\t4n1u1w1n", "math:M!()1x1\t-\twn\t4n1u1w1n", "math:V!x\t-\tn\t4n1u1w1n1w", "math:V!x\tV!x\tnn\t4n1u1w1n1w", "math:-\tV!x\tn\t4n1u1w1n1w1n", "math:-\t\u0304\tna\t4n1u1w1n1w1n", "math:V!x\t\u0304\ta\t4n1u1w1n1w2n", "math:\u0304\t0!\tn\t4n1u1w1n1w2n1a", "math:V!x\t0!\tn\t4n1u1w1n1w2n", "math:V!x\tV!i\tb\t4n1u1w1n1w", "math:V!i\t0!\tn\t4n1u1w1n1w1b", "math:\u2211\tV!i\tu\t4n1u1w", "math:\u2211\t=\tun\t4n1u1w", "math:V!i\t=\tn\t4n1u1w1u", "math:V!i\tN!1\tnn\t4n1u1w1u", "math:=\tN!1\tn\t4n1u1w1u1n", "math:N!1\t0!\tn\t4n1u1w1u2n", "math:O!root\t0!\tn\tnnnnu", "math:O!divide\tM!()1x1\tu\tnn", "math:O!divide\tV!n\tuw\tnn", "math:O!divide\tV!s\tun\tnn", "math:M!()1x1\tV!s\tn\tnnu", "math:M!()1x1\tV!x\tnb\tnnu", "math:M!()1x1\tV!s\tnn\tnnu", "math:V!s\tV!s\tn\tnnun", "math:V!s\tV!y\tnb\tnnun", "math:V!s\tV!y\tb\tnnunn", "math:V!y\t0!\tn\t2n1u2n1b", "math:V!s\t0!\tn\tnnunn", "math:V!s\tV!x\tb\tnnun", "math:V!x\t0!\tn\tnnunb", "math:M!()1x1\tV!n\tw\tnnu", "math:M!()1x1\t-\twn\tnnu", "math:V!n\t-\tn\tnnuw", "math:V!n\tN!1\tnn\tnnuw", "math:-\tN!1\tn\tnnuwn", "math:N!1\t0!\tn\t2n1u1w2n", "math:V!r\tV!x\tb\t-", "math:V!r\tV!y\tbn\t-", "math:V!x\tV!y\tn\tb", "math:V!y\t0!\tn\tbn"],
"NTCIR12-MathWiki-21": ["math:N!0.\t?*1*\tn\t-", "math:N!0.\tV!...\tnn\t-", "math:?*1*\tV!...\tn\tn", "math:V!...\t0!\tn\tnn"],
"NTCIR12-MathWiki-22": ["math:V!P\t?*1*\ta\t-", "math:?*1*\t0!\tn\ta", "math:V!P\t0!\tn\t-"],
"NTCIR12-MathWiki-23": ["math:?*1*\tM!()1x1\tn\t-", "math:?*1*\tO!divide\tnw\t-", "math:M!()1x1\tO!divide\tw\tn", "math:M!()1x1\tT!Frequency\twu\tn", "math:M!()1x1\tT!Frequency\two\tn", "math:O!divide\tT!Frequency\to\tnw", "math:T!Frequency\t0!\tn\tnwo", "math:O!divide\tT!Frequency\tu\tnw", "math:T!Frequency\t0!\tn\tnwu", "math:O!divide\t0!\tn\tnw", "math:M!()1x1\t0!\tn\tn"],
"NTCIR12-MathWiki-24": ["math:M!1x1\t?*2*\tb\t-", "math:?*2*\t0!\tn\tb", "math:M!1x1\t?*1*\tw\t-", "math:M!1x1\t\u23df\twb\t-", "math:?*1*\t\u23df\tb\tw", "math:\u23df\t0!\tn\twb", "math:?*1*\t0!\tn\tw", "math:M!1x1\t0!\tn\t-"],
"NTCIR12-MathWiki-25": ["math:N!1\t+\tn\t-", "math:N!1\tO!divide\tnn\t-", "math:+\tO!divide\tn\tn", "math:+\t?*1*\tnu\tn", "math:+\tN!1\tno\tn", "math:O!divide\tN!1\to\tnn", "math:N!1\t0!\tn\tnno", "math:O!divide\t?*1*\tu\tnn", "math:O!divide\t+\tun\tnn", "math:?*1*\t+\tn\tnnu", "math:?*1*\tO!divide\tnn\tnnu", "math:+\tO!divide\tn\tnnun", "math:+\t?*2*\tnu\tnnun", "math:+\tN!1\tno\tnnun", "math:O!divide\tN!1\to\tnnunn", "math:N!1\t0!\tn\t2n1u2n1o", "math:O!divide\t?*2*\tu\tnnunn", "math:?*2*\t0!\tn\t2n1u2n1u", "math:O!divide\t0!\tn\tnnunn", "math:O!divide\t0!\tn\tnn"],
"NTCIR12-MathWiki-26": ["math:V!U\tN!238\tc\t-", "math:N!238\t0!\tn\tc", "math:V!U\t+\tn\t-", "math:V!U\t?*1*\tnn\t-", "math:+\t?*1*\tn\tn", "math:+\t\u2192\tnn\tn", "math:?*1*\t\u2192\tn\tnn", "math:?*1*\t?*2*\tnn\tnn", "math:\u2192\t?*2*\tn\tnnn", "math:?*2*\t0!\tn\tnnnn", "math:V!U\tN!92\td\t-", "math:N!92\t0!\tn\td"],
"NTCIR12-MathWiki-27": ["math:?*1*\t\u2227\ta\t-", "math:\u2227\t0!\tn\ta", "math:?*1*\t\u2192\tn\t-", "math:?*1*\t?*2*\tno\t-", "math:?*1*\t?*3*\tnn\t-", "math:\u2192\t?*2*\to\tn", "math:\u2192\t\u2227\toa\tn", "math:?*2*\t\u2227\ta\tno", "math:\u2227\t0!\tn\tnoa", "math:?*2*\t0!\tn\tno", "math:\u2192\t?*3*\tn\tn", "math:\u2192\t\u2227\tna\tn", "math:?*3*\t\u2227\ta\tnn", "math:\u2227\t0!\tn\tnna", "math:?*3*\t0!\tn\tnn"],
"NTCIR12-MathWiki-28": ["math:?*1*\t=\tn\t-", "math:?*1*\t{\tnn\t-", "math:=\t{\tn\tn", "math:=\tM!2x2\tnn\tn", "math:{\tM!2x2\tn\tnn", "math:{\t?*2*\tnw\tnn", "math:M!2x2\t?*2*\tw\tnnn", "math:M!2x2\tT!if\twe\tnnn", "math:?*2*\tT!if\te\tnnnw", "math:?*2*\t?*4*\tee\tnnnw", "math:?*2*\tW!\ten\tnnnw", "math:T!if\tW!\tn\tnnnwe", "math:T!if\t>\tnn\tnnnwe", "math:W!\t>\tn\t3n1w1e1n", "math:W!\tO!divide\tnn\t3n1w1e1n", "math:>\tO!divide\tn\t3n1w1e2n", "math:>\tN!2\tnu\t3n1w1e2n", "math:>\tN!1\tno\t3n1w1e2n", "math:O!divide\tN!1\to\t3n1w1e3n", "math:N!1\t0!\tn\t3n1w1e3n1o", "math:O!divide\tN!2\tu\t3n1w1e3n", "math:N!2\t0!\tn\t3n1w1e3n1u", "math:O!divide\t0!\tn\t3n1w1e3n", "math:T!if\t?*4*\te\tnnnwe", "math:T!if\tT!if\tee\tnnnwe", "math:?*4*\tT!if\te\t3n1w2e", "math:?*4*\tW!\ten\t3n1w2e", "math:T!if\tW!\tn\t3n1w3e", "math:T!if\t\u2264\tnn\t3n1w3e", "math:W!\t\u2264\tn\t3n1w3e1n", "math:W!\tO!divide\tnn\t3n1w3e1n", "math:\u2264\tO!divide\tn\t3n1w3e2n", "math:\u2264\tN!2\tnu\t3n1w3e2n", "math:\u2264\tN!1\tno\t3n1w3e2n", "math:O!divide\tN!1\to\t3n1w3e3n", "math:N!1\t0!\tn\t3n1w3e3n1o", "math:O!divide\tN!2\tu\t3n1w3e3n", "math:N!2\t0!\tn\t3n1w3e3n1u", "math:O!divide\t0!\tn\t3n1w3e3n", "math:?*4*\t0!\tn\t3n1w2e", "math:?*2*\t0!\tn\tnnnw", "math:M!2x2\t0!\tn\tnnn"],
"NTCIR12-MathWiki-29": ["math:?*1*\t=\tn\t-", "math:?*1*\tM![]2x2\tnn\t-", "math:=\tM![]2x2\tn\tn", "math:=\t?*2*\tnw\tn", "math:=\tM![]2x1\tnn\tn", "math:M![]2x2\tM![]2x1\tn\tnn", "math:M![]2x2\t?*6*\tnw\tnn", "math:M![]2x1\t?*6*\tw\tnnn", "math:M![]2x1\t?*7*\twe\tnnn", "math:?*6*\t?*7*\te\tnnnw", "math:?*7*\t0!\tn\tnnnwe", "math:?*6*\t0!\tn\tnnnw", "math:M![]2x1\t0!\tn\tnnn", "math:M![]2x2\t?*2*\tw\tnn", "math:M![]2x2\t?*3*\twe\tnn", "math:?*2*\t?*3*\te\tnnw", "math:?*2*\t?*4*\tee\tnnw", "math:?*3*\t?*4*\te\tnnwe", "math:?*3*\t?*5*\tee\tnnwe", "math:?*4*\t?*5*\te\tnnwee", "math:?*5*\t0!\tn\t2n1w3e", "math:?*4*\t0!\tn\tnnwee", "math:?*3*\t0!\tn\tnnwe", "math:?*2*\t0!\tn\tnnw"],
"NTCIR12-MathWiki-30": ["math:V!L\tM!()1x3\tn\t-", "math:V!L\t?*1*\tnw\t-", "math:V!L\t=\tnn\t-", "math:M!()1x3\t=\tn\tn", "math:M!()1x3\t\u2211\tnn\tn", "math:=\t\u2211\tn\tnn", "math:=\t?*4*\tnu\tnn", "math:=\tV!\u221e\tno\tnn", "math:=\tO!divide\tnn\tnn", "math:\u2211\tV!\u221e\to\tnnn", "math:V!\u221e\t0!\tn\tnnno", "math:\u2211\tO!divide\tn\tnnn", "math:\u2211\tM!()1x1\tnu\tnnn", "math:\u2211\tV!exp\tno\tnnn", "math:O!divide\tV!exp\to\tnnnn", "math:O!divide\tM!()1x1\ton\tnnnn", "math:V!exp\tM!()1x1\tn\tnnnno", "math:V!exp\tN!2\tnw\tnnnno", "math:M!()1x1\tN!2\tw\t4n1o1n", "math:M!()1x1\tV!\u03c0\twn\t4n1o1n", "math:N!2\tV!\u03c0\tn\t4n1o1n1w", "math:N!2\tV!i\tnn\t4n1o1n1w", "math:V!\u03c0\tV!i\tn\t4n1o1n1w1n", "math:V!\u03c0\t?*1*\tnn\t4n1o1n1w1n", "math:V!i\t?*1*\tn\t4n1o1n1w2n", "math:V!i\t?*4*\tnn\t4n1o1n1w2n", "math:?*1*\t?*4*\tn\t4n1o1n1w3n", "math:?*4*\t0!\tn\t4n1o1n1w4n", "math:M!()1x1\t0!\tn\t4n1o1n", "math:O!divide\tM!()1x1\tu\tnnnn", "math:O!divide\t?*4*\tuw\tnnnn", "math:O!divide\t?*3*\tua\tnnnn", "math:M!()1x1\t?*3*\ta\tnnnnu", "math:?*3*\t0!\tn\t4n1u1a", "math:M!()1x1\t?*4*\tw\tnnnnu", "math:M!()1x1\t+\twn\tnnnnu", "math:?*4*\t+\tn\t4n1u1w", "math:?*4*\t?*2*\tnn\t4n1u1w", "math:+\t?*2*\tn\t4n1u1w1n", "math:?*2*\t0!\tn\t4n1u1w2n", "math:M!()1x1\t0!\tn\tnnnnu", "math:O!divide\t0!\tn\tnnnn", "math:\u2211\t?*4*\tu\tnnn", "math:\u2211\t=\tun\tnnn", "math:?*4*\t=\tn\tnnnu", "math:?*4*\tN!0\tnn\tnnnu", "math:=\tN!0\tn\tnnnun", "math:N!0\t0!\tn\t3n1u2n", "math:M!()1x3\t?*1*\tw\tn", "math:M!()1x3\t?*2*\twe\tn", "math:M!()1x3\t,\twn\tn", "math:?*1*\t,\tn\tnw", "math:,\t0!\tn\tnwn", "math:?*1*\t?*2*\te\tnw", "math:?*1*\t?*3*\tee\tnw", "math:?*1*\t,\ten\tnw", "math:?*2*\t,\tn\tnwe", "math:,\t0!\tn\tnwen", "math:?*2*\t?*3*\te\tnwe", "math:?*3*\t0!\tn\tnwee"],
"NTCIR12-MathWiki-31": ["math:?*1*\tV!x\tn\t-", "math:?*1*\tN!2\tna\t-", "math:?*1*\t+\tnn\t-", "math:V!x\tN!2\ta\tn", "math:N!2\t0!\tn\tna", "math:V!x\t+\tn\tn", "math:V!x\t?*2*\tnn\tn", "math:+\t?*2*\tn\tnn", "math:+\tV!x\tnn\tnn", "math:?*2*\tV!x\tn\tnnn", "math:?*2*\t+\tnn\tnnn", "math:V!x\t+\tn\tnnnn", "math:V!x\t?*3*\tnn\tnnnn", "math:+\t?*3*\tn\tnnnnn", "math:+\t=\tnn\tnnnnn", "math:?*3*\t=\tn\t6n", "math:?*3*\tN!0\tnn\t6n", "math:=\tN!0\tn\t7n", "math:N!0\t0!\tn\t8n"],
"NTCIR12-MathWiki-32": ["math:V!O\tM!()1x1\tn\t-", "math:V!O\t?*1*\tnw\t-", "math:M!()1x1\t?*1*\tw\tn", "math:M!()1x1\tV!log\twn\tn", "math:?*1*\tV!log\tn\tnw", "math:?*1*\tM!()1x1\tnn\tnw", "math:V!log\tM!()1x1\tn\tnwn", "math:V!log\t?*2*\tnw\tnwn", "math:M!()1x1\t?*2*\tw\tnwnn", "math:?*2*\t0!\tn\tnwnnw", "math:M!()1x1\t0!\tn\tnwnn", "math:M!()1x1\t0!\tn\tn"],
"NTCIR12-MathWiki-33": ["math:V!A\t?*1*\tn\t-", "math:V!A\tV!B\tnn\t-", "math:?*1*\tV!B\tn\tn", "math:?*1*\t=\tnn\tn", "math:V!B\t=\tn\tnn", "math:V!B\tM!()1x1\tnn\tnn", "math:=\tM!()1x1\tn\tnnn", "math:=\t?*2*\tnw\tnnn", "math:=\t?*3*\tna\tnnn", "math:M!()1x1\t?*3*\ta\tnnnn", "math:?*3*\t0!\tn\tnnnna", "math:M!()1x1\t?*2*\tw\tnnnn", "math:?*2*\t0!\tn\tnnnnw", "math:M!()1x1\t0!\tn\tnnnn"],
"NTCIR12-MathWiki-34": ["math:?*1*\tV!\u03b1\tn\t-", "math:?*1*\t=\tnn\t-", "math:V!\u03b1\t=\tn\tn", "math:V!\u03b1\t?*1*\tnn\tn", "math:=\t?*1*\tn\tnn", "math:=\tV!\u03b2\tnn\tnn", "math:?*1*\tV!\u03b2\tn\tnnn", "math:?*1*\t?*1*\tnn\tnnn", "math:V!\u03b2\t?*1*\tn\tnnnn", "math:V!\u03b2\tV!\u03b3\tnn\tnnnn", "math:?*1*\tV!\u03b3\tn\tnnnnn", "math:?*1*\t+\tnn\tnnnnn", "math:V!\u03b3\t+\tn\t6n", "math:V!\u03b3\t?*2*\tnn\t6n", "math:+\t?*2*\tn\t7n", "math:+\tV!\u03b2\tnn\t7n", "math:?*2*\tV!\u03b2\tn\t8n", "math:?*2*\t?*2*\tnn\t8n", "math:V!\u03b2\t?*2*\tn\t9n", "math:V!\u03b2\tV!\u03b3\tnn\t9n", "math:?*2*\tV!\u03b3\tn\t10n", "math:?*2*\t?*3*\tnn\t10n", "math:V!\u03b3\t?*3*\tn\t11n", "math:?*3*\t0!\tn\t12n"],
"NTCIR12-MathWiki-35": ["math:\u2200\tV!x\tn\t-", "math:\u2200\t,\tnn\t-", "math:V!x\t,\tn\tn", "math:V!x\tV!y\tnn\tn", "math:,\tV!y\tn\tnn", "math:,\t\u2208\tnn\tnn", "math:V!y\t\u2208\tn\tnnn", "math:V!y\t?*1*\tnn\tnnn", "math:\u2208\t?*1*\tn\tnnnn", "math:\u2208\tM![]1x1\tnn\tnnnn", "math:?*1*\tM![]1x1\tn\tnnnnn", "math:?*1*\tV!x\tnw\tnnnnn", "math:M![]1x1\tV!x\tw\t6n", "math:M![]1x1\t=\u0338\twn\t6n", "math:V!x\t=\u0338\tn\t6n1w", "math:V!x\tV!y\tnn\t6n1w", "math:=\u0338\tV!y\tn\t6n1w1n", "math:=\u0338\t\u2192\tnn\t6n1w1n", "math:V!y\t\u2192\tn\t6n1w2n", "math:V!y\t?*2*\tnn\t6n1w2n", "math:\u2192\t?*2*\tn\t6n1w3n", "math:?*2*\t0!\tn\t6n1w4n", "math:M![]1x1\t0!\tn\t6n"],
"NTCIR12-MathWiki-36": ["math:?*1*\t=\tn\t-", "math:?*1*\tO!root\tnn\t-", "math:=\tO!root\tn\tn", "math:=\tO!divide\tnw\tn", "math:O!root\tO!divide\tw\tnn", "math:O!root\t\u222b\twu\tnn", "math:O!root\t\u222b\two\tnn", "math:O!divide\t\u222b\to\tnnw", "math:O!divide\tN!0\tou\tnnw", "math:O!divide\tV!\u221e\too\tnnw", "math:O!divide\t?*2*\ton\tnnw", "math:\u222b\tV!\u221e\to\tnnwo", "math:V!\u221e\t0!\tn\tnnwoo", "math:\u222b\t?*2*\tn\tnnwo", "math:\u222b\tN!2\tna\tnnwo", "math:\u222b\t?*3*\tnn\tnnwo", "math:?*2*\tN!2\ta\tnnwon", "math:N!2\t0!\tn\t2n1w1o1n1a", "math:?*2*\t?*3*\tn\tnnwon", "math:?*2*\tV!d\tnn\tnnwon", "math:?*3*\tV!d\tn\t2n1w1o2n", "math:?*3*\t?*1*\tnn\t2n1w1o2n", "math:V!d\t?*1*\tn\t2n1w1o3n", "math:?*1*\t0!\tn\t2n1w1o4n", "math:\u222b\tN!0\tu\tnnwo", "math:N!0\t0!\tn\tnnwou", "math:O!divide\t\u222b\tu\tnnw", "math:O!divide\tN!0\tuu\tnnw", "math:O!divide\tV!\u221e\tuo\tnnw", "math:O!divide\t?*3*\tun\tnnw", "math:\u222b\tV!\u221e\to\tnnwu", "math:V!\u221e\t0!\tn\tnnwuo", "math:\u222b\t?*3*\tn\tnnwu", "math:\u222b\tV!d\tnn\tnnwu", "math:?*3*\tV!d\tn\tnnwun", "math:?*3*\t?*1*\tnn\tnnwun", "math:V!d\t?*1*\tn\t2n1w1u2n", "math:?*1*\t0!\tn\t2n1w1u3n", "math:\u222b\tN!0\tu\tnnwu", "math:N!0\t0!\tn\tnnwuu", "math:O!divide\t0!\tn\tnnw", "math:O!root\t0!\tn\tnn"],
"NTCIR12-MathWiki-37": ["math:O!divide\tN!1\to\t-", "math:N!1\t0!\tn\to", "math:O!divide\t-\tn\t-", "math:O!divide\tO!divide\tnn\t-", "math:-\tO!divide\tn\tn", "math:-\t?*2*\tnu\tn", "math:-\tN!1\tno\tn", "math:-\t-\tnn\tn", "math:O!divide\tN!1\to\tnn", "math:N!1\t0!\tn\tnno", "math:O!divide\t-\tn\tnn", "math:O!divide\tO!divide\tnn\tnn", "math:-\tO!divide\tn\tnnn", "math:-\t?*3*\tnu\tnnn", "math:-\tN!1\tno\tnnn", "math:-\t-\tnn\tnnn", "math:O!divide\tN!1\to\tnnnn", "math:N!1\t0!\tn\tnnnno", "math:O!divide\t-\tn\tnnnn", "math:O!divide\tO!divide\tnn\tnnnn", "math:-\tO!divide\tn\tnnnnn", "math:-\t?*4*\tnu\tnnnnn", "math:-\tN!1\tno\tnnnnn", "math:-\t-\tnn\tnnnnn", "math:O!divide\tN!1\to\t6n", "math:N!1\t0!\tn\t6n1o", "math:O!divide\t-\tn\t6n", "math:O!divide\tO!divide\tnn\t6n", "math:-\tO!divide\tn\t7n", "math:-\t?*5*\tnu\t7n", "math:-\tN!1\tno\t7n", "math:O!divide\tN!1\to\t8n", "math:N!1\t0!\tn\t8n1o", "math:O!divide\t?*5*\tu\t8n", "math:?*5*\t0!\tn\t8n1u", "math:O!divide\t0!\tn\t8n", "math:O!divide\t?*4*\tu\t6n", "math:?*4*\t0!\tn\t6n1u", "math:O!divide\t?*3*\tu\tnnnn", "math:?*3*\t0!\tn\tnnnnu", "math:O!divide\t?*2*\tu\tnn", "math:?*2*\t0!\tn\tnnu", "math:O!divide\t?*1*\tu\t-", "math:?*1*\t0!\tn\tu"],
"NTCIR12-MathWiki-38": ["math:O!divide\tV!N\to\t-", "math:O!divide\t!\ton\t-", "math:V!N\t!\tn\to", "math:!\t0!\tn\ton", "math:O!divide\tV!p\tn\t-", "math:O!divide\t?*1*\tna\t-", "math:O!divide\tM!()1x1\tnn\t-", "math:V!p\t?*1*\ta\tn", "math:?*1*\t0!\tn\tna", "math:V!p\tM!()1x1\tn\tn", "math:V!p\tN!1\tnw\tn", "math:V!p\tV!N\tna\tn", "math:M!()1x1\tV!N\ta\tnn", "math:M!()1x1\t-\tan\tnn", "math:V!N\t-\tn\tnna", "math:V!N\t?*1*\tnn\tnna", "math:-\t?*1*\tn\tnnan", "math:?*1*\t0!\tn\tnnann", "math:M!()1x1\tN!1\tw\tnn", "math:M!()1x1\t-\twn\tnn", "math:N!1\t-\tn\tnnw", "math:N!1\tV!p\tnn\tnnw", "math:-\tV!p\tn\tnnwn", "math:V!p\t0!\tn\tnnwnn", "math:M!()1x1\t0!\tn\tnn", "math:O!divide\t?*1*\tu\t-", "math:O!divide\t!\tun\t-", "math:?*1*\t!\tn\tu", "math:?*1*\tM!()1x1\tnn\tu", "math:!\tM!()1x1\tn\tun", "math:!\tV!N\tnw\tun", "math:!\t!\tnn\tun", "math:M!()1x1\t!\tn\tunn", "math:!\t0!\tn\tunnn", "math:M!()1x1\tV!N\tw\tunn", "math:M!()1x1\t-\twn\tunn", "math:V!N\t-\tn\tunnw", "math:V!N\t?*1*\tnn\tunnw", "math:-\t?*1*\tn\tunnwn", "math:?*1*\t0!\tn\t1u2n1w2n"],
"NTCIR12-MathWiki-39": ["math:V!H\t=\tn\t-", "math:V!H\tM![]1x1\tnn\t-", "math:=\tM![]1x1\tn\tn", "math:=\tO!divide\tnw\tn", "math:M![]1x1\tO!divide\tw\tnn", "math:M![]1x1\t?*3*\twu\tnn", "math:M![]1x1\t\u2202\two\tnn", "math:O!divide\t\u2202\to\tnnw", "math:O!divide\tN!2\too\tnnw", "math:O!divide\t?*2*\ton\tnnw", "math:\u2202\tN!2\to\tnnwo", "math:N!2\t0!\tn\tnnwoo", "math:\u2202\t?*2*\tn\tnnwo", "math:?*2*\t0!\tn\tnnwon", "math:O!divide\t?*3*\tu\tnnw", "math:?*3*\t0!\tn\tnnwu", "math:O!divide\t0!\tn\tnnw", "math:M![]1x1\t0!\tn\tnn", "math:V!H\t?*1*\tb\t-", "math:?*1*\t0!\tn\tb"],
"NTCIR12-MathWiki-40": ["math:O!divide\t\u2211\to\t-", "math:O!divide\tV!i\tou\t-", "math:O!divide\tV!n\too\t-", "math:O!divide\tM!()1x1\ton\t-", "math:\u2211\tV!n\to\to", "math:V!n\t0!\tn\too", "math:\u2211\tM!()1x1\tn\to", "math:\u2211\t?*1*\tnw\to", "math:\u2211\tM!()1x1\tnn\to", "math:M!()1x1\tM!()1x1\tn\ton", "math:M!()1x1\t?*2*\tnw\ton", "math:M!()1x1\t?*2*\tw\tonn", "math:M!()1x1\tV!i\twb\tonn", "math:M!()1x1\t-\twn\tonn", "math:?*2*\t-\tn\tonnw", "math:?*2*\t?*2*\tnn\tonnw", "math:-\t?*2*\tn\tonnwn", "math:-\t\u0304\tna\tonnwn", "math:?*2*\t\u0304\ta\t1o2n1w2n", "math:\u0304\t0!\tn\t1o2n1w2n1a", "math:?*2*\t0!\tn\t1o2n1w2n", "math:?*2*\tV!i\tb\tonnw", "math:V!i\t0!\tn\tonnwb", "math:M!()1x1\t0!\tn\tonn", "math:M!()1x1\t?*1*\tw\ton", "math:M!()1x1\tV!i\twb\ton", "math:M!()1x1\t-\twn\ton", "math:?*1*\t-\tn\tonw", "math:?*1*\t?*1*\tnn\tonw", "math:-\t?*1*\tn\tonwn", "math:-\t\u0304\tna\tonwn", "math:?*1*\t\u0304\ta\tonwnn", "math:\u0304\t0!\tn\t1o1n1w2n1a", "math:?*1*\t0!\tn\tonwnn", "math:?*1*\tV!i\tb\tonw", "math:V!i\t0!\tn\tonwb", "math:\u2211\tV!i\tu\to", "math:\u2211\t=\tun\to", "math:V!i\t=\tn\tou", "math:V!i\tN!1\tnn\tou", "math:=\tN!1\tn\toun", "math:N!1\t0!\tn\tounn", "math:O!divide\tO!root\tu\t-", "math:O!divide\t\u2211\tuw\t-", "math:O!root\t\u2211\tw\tu", "math:O!root\tV!i\twu\tu", "math:O!root\tV!n\two\tu", "math:O!root\tM!()1x1\twn\tu", "math:\u2211\tV!n\to\tuw", "math:V!n\t0!\tn\tuwo", "math:\u2211\tM!()1x1\tn\tuw", "math:\u2211\t?*1*\tnw\tuw", "math:\u2211\tN!2\tna\tuw", "math:\u2211\t\u2211\tnn\tuw", "math:M!()1x1\tN!2\ta\tuwn", "math:N!2\t0!\tn\tuwna", "math:M!()1x1\t\u2211\tn\tuwn", "math:M!()1x1\tV!i\tnu\tuwn", "math:M!()1x1\tV!n\tno\tuwn", "math:M!()1x1\tM!()1x1\tnn\tuwn", "math:\u2211\tV!n\to\tuwnn", "math:V!n\t0!\tn\tuwnno", "math:\u2211\tM!()1x1\tn\tuwnn", "math:\u2211\t?*2*\tnw\tuwnn", "math:\u2211\tN!2\tna\tuwnn", "math:M!()1x1\tN!2\ta\tuwnnn", "math:N!2\t0!\tn\t1u1w3n1a", "math:M!()1x1\t?*2*\tw\tuwnnn", "math:M!()1x1\tV!i\twb\tuwnnn", "math:M!()1x1\t-\twn\tuwnnn", "math:?*2*\t-\tn\t1u1w3n1w", "math:?*2*\t?*2*\tnn\t1u1w3n1w", "math:-\t?*2*\tn\t1u1w3n1w1n", "math:-\t\u0304\tna\t1u1w3n1w1n", "math:?*2*\t\u0304\ta\t1u1w3n1w2n", "math:\u0304\t0!\tn\t1u1w3n1w2n1a", "math:?*2*\t0!\tn\t1u1w3n1w2n", "math:?*2*\tV!i\tb\t1u1w3n1w", "math:V!i\t0!\tn\t1u1w3n1w1b", "math:M!()1x1\t0!\tn\tuwnnn", "math:\u2211\tV!i\tu\tuwnn", "math:\u2211\t=\tun\tuwnn", "math:V!i\t=\tn\tuwnnu", "math:V!i\tN!1\tnn\tuwnnu", "math:=\tN!1\tn\t1u1w2n1u1n", "math:N!1\t0!\tn\t1u1w2n1u2n", "math:M!()1x1\t?*1*\tw\tuwn", "math:M!()1x1\tV!i\twb\tuwn", "math:M!()1x1\t-\twn\tuwn", "math:?*1*\t-\tn\tuwnw", "math:?*1*\t?*1*\tnn\tuwnw", "math:-\t?*1*\tn\tuwnwn", "math:-\t\u0304\tna\tuwnwn", "math:?*1*\t\u0304\ta\t1u1w1n1w2n", "math:\u0304\t0!\tn\t1u1w1n1w2n1a", "math:?*1*\t0!\tn\t1u1w1n1w2n", "math:?*1*\tV!i\tb\tuwnw", "math:V!i\t0!\tn\tuwnwb", "math:\u2211\tV!i\tu\tuw", "math:\u2211\t=\tun\tuw", "math:V!i\t=\tn\tuwu", "math:V!i\tN!1\tnn\tuwu", "math:=\tN!1\tn\tuwun", "math:N!1\t0!\tn\tuwunn", "math:O!root\t0!\tn\tu", "math:O!divide\t0!\tn\t-"],
}