Re-implement functional tests in yaml + multiple fixes (#35)

Solved multiple issues: - parsing of shift expressions was wrong - integer variables were not correctly transferred to solver - improved some error messages at parsing time Co-authored-by: vargastat <tatiana.vargas@rte-france.com>
AntaresSimulatorTeam · Jun 3, 2024 · 12ccfd7 · 12ccfd7
1 parent 346d852
commit 12ccfd7
Show file tree

Hide file tree

Showing 19 changed files with 2,439 additions and 1,186 deletions.
diff --git a/grammar/Expr.g4 b/grammar/Expr.g4
@@ -17,23 +17,55 @@ grammar Expr;
 /* To match the whole input */
 fullexpr: expr EOF;
 
-shift: TIME (op=('+' | '-') expr)?;
-
-expr: '-' expr                  # negation
-    | expr op=('/' | '*') expr  # muldiv
-    | expr op=('+' | '-') expr  # addsub
-    | expr COMPARISON expr      # comparison
-    | IDENTIFIER                # identifier
-    | IDENTIFIER '.' IDENTIFIER # portField
-    | NUMBER                    # number
-    | '(' expr ')'              # expression
-    | IDENTIFIER '(' expr ')'   # function
-    | IDENTIFIER '[' shift (',' shift)* ']'  # timeShift
-    | IDENTIFIER '[' expr  (',' expr )* ']'  # timeIndex
-    | IDENTIFIER '[' shift1=shift '..' shift2=shift ']'      # timeShiftRange
-    | IDENTIFIER '[' expr '..' expr ']'      # timeRange
+expr
+    : atom                                     # unsignedAtom
+    | IDENTIFIER '.' IDENTIFIER                # portField
+    | '-' expr                                 # negation
+    | '(' expr ')'                             # expression
+    | expr op=('/' | '*') expr                 # muldiv
+    | expr op=('+' | '-') expr                 # addsub
+    | expr COMPARISON expr                     # comparison
+    | IDENTIFIER '(' expr ')'                  # function
+    | IDENTIFIER '[' shift (',' shift)* ']'    # timeShift
+    | IDENTIFIER '[' expr  (',' expr )* ']'    # timeIndex
+    | IDENTIFIER '[' shift1=shift '..' shift2=shift ']'     # timeShiftRange
+    | IDENTIFIER '[' expr '..' expr ']'        # timeRange
     ;
 
+atom
+    : NUMBER                                   # number
+    | IDENTIFIER                               # identifier
+    ;
+
+// a shift is required to be either "t" or "t + ..." or "t - ..."
+// Note: simply defining it as "shift: TIME ('+' | '-') expr" won't work
+//       because the minus sign will not have the expected precedence:
+//       "t - d + 1" would be equivalent to "t - (d + 1)"
+shift: TIME shift_expr?;
+
+// Because the shift MUST start with + or -, we need
+// to differentiate it from generic "expr".
+// A shift expression can only be extended to the right by a
+// "right_expr" which cannot start with a + or -,
+// unlike shift_expr itself.
+// TODO: the grammar is still a little weird, because we
+//       allow more things in the "expr" parts of those
+//       shift expressions than on their left-most part
+//       (port fields, nested time shifts and so on).
+shift_expr
+    : shift_expr op=('*' | '/') right_expr     # shiftMuldiv
+    | shift_expr op=('+' | '-') right_expr     # shiftAddsub
+    | op=('+' | '-') atom                      # signedAtom
+    | op=('+' | '-') '(' expr ')'              # signedExpression
+    ;
+
+right_expr
+    : right_expr op=('/' | '*') right_expr     # rightMuldiv
+    | '(' expr ')'                             # rightExpression
+    | atom                                     # rightAtom
+    ;
+
+
 fragment DIGIT         : [0-9] ;
 fragment CHAR          : [a-zA-Z_];
 fragment CHAR_OR_DIGIT : (CHAR | DIGIT);
@@ -42,9 +74,5 @@ NUMBER        : DIGIT+ ('.' DIGIT+)?;
 TIME          : 't';
 IDENTIFIER    : CHAR CHAR_OR_DIGIT*;
 COMPARISON    : ( '=' | '>=' | '<=' );
-ADDSUB        : ( '+' | '-' );
-MULDIV        : ( '*' | '/' );
-LBRACKET: '[';
-RBRACKET: ']';
 
 WS: (' ' | '\t' | '\r'| '\n') -> skip;
diff --git a/src/andromede/expression/parsing/antlr/Expr.interp b/src/andromede/expression/parsing/antlr/Expr.interp
@@ -1,23 +1,21 @@
 token literal names:
 null
-'+'
-'-'
-'/'
-'*'
 '.'
+'-'
 '('
 ')'
+'/'
+'*'
+'+'
+'['
 ','
+']'
 '..'
 null
 't'
 null
 null
 null
-null
-'['
-']'
-null
 
 token symbolic names:
 null
@@ -30,21 +28,22 @@ null
 null
 null
 null
+null
+null
 NUMBER
 TIME
 IDENTIFIER
 COMPARISON
-ADDSUB
-MULDIV
-LBRACKET
-RBRACKET
 WS
 
 rule names:
 fullexpr
-shift
 expr
+atom
+shift
+shift_expr
+right_expr
 
 
 atn:
-[4, 1, 18, 86, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 13, 8, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 5, 2, 37, 8, 2, 10, 2, 12, 2, 40, 9, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 5, 2, 49, 8, 2, 10, 2, 12, 2, 52, 9, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 70, 8, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 5, 2, 81, 8, 2, 10, 2, 12, 2, 84, 9, 2, 1, 2, 0, 1, 4, 3, 0, 2, 4, 0, 2, 1, 0, 1, 2, 1, 0, 3, 4, 97, 0, 6, 1, 0, 0, 0, 2, 9, 1, 0, 0, 0, 4, 69, 1, 0, 0, 0, 6, 7, 3, 4, 2, 0, 7, 8, 5, 0, 0, 1, 8, 1, 1, 0, 0, 0, 9, 12, 5, 11, 0, 0, 10, 11, 7, 0, 0, 0, 11, 13, 3, 4, 2, 0, 12, 10, 1, 0, 0, 0, 12, 13, 1, 0, 0, 0, 13, 3, 1, 0, 0, 0, 14, 15, 6, 2, -1, 0, 15, 16, 5, 2, 0, 0, 16, 70, 3, 4, 2, 13, 17, 70, 5, 12, 0, 0, 18, 19, 5, 12, 0, 0, 19, 20, 5, 5, 0, 0, 20, 70, 5, 12, 0, 0, 21, 70, 5, 10, 0, 0, 22, 23, 5, 6, 0, 0, 23, 24, 3, 4, 2, 0, 24, 25, 5, 7, 0, 0, 25, 70, 1, 0, 0, 0, 26, 27, 5, 12, 0, 0, 27, 28, 5, 6, 0, 0, 28, 29, 3, 4, 2, 0, 29, 30, 5, 7, 0, 0, 30, 70, 1, 0, 0, 0, 31, 32, 5, 12, 0, 0, 32, 33, 5, 16, 0, 0, 33, 38, 3, 2, 1, 0, 34, 35, 5, 8, 0, 0, 35, 37, 3, 2, 1, 0, 36, 34, 1, 0, 0, 0, 37, 40, 1, 0, 0, 0, 38, 36, 1, 0, 0, 0, 38, 39, 1, 0, 0, 0, 39, 41, 1, 0, 0, 0, 40, 38, 1, 0, 0, 0, 41, 42, 5, 17, 0, 0, 42, 70, 1, 0, 0, 0, 43, 44, 5, 12, 0, 0, 44, 45, 5, 16, 0, 0, 45, 50, 3, 4, 2, 0, 46, 47, 5, 8, 0, 0, 47, 49, 3, 4, 2, 0, 48, 46, 1, 0, 0, 0, 49, 52, 1, 0, 0, 0, 50, 48, 1, 0, 0, 0, 50, 51, 1, 0, 0, 0, 51, 53, 1, 0, 0, 0, 52, 50, 1, 0, 0, 0, 53, 54, 5, 17, 0, 0, 54, 70, 1, 0, 0, 0, 55, 56, 5, 12, 0, 0, 56, 57, 5, 16, 0, 0, 57, 58, 3, 2, 1, 0, 58, 59, 5, 9, 0, 0, 59, 60, 3, 2, 1, 0, 60, 61, 5, 17, 0, 0, 61, 70, 1, 0, 0, 0, 62, 63, 5, 12, 0, 0, 63, 64, 5, 16, 0, 0, 64, 65, 3, 4, 2, 0, 65, 66, 5, 9, 0, 0, 66, 67, 3, 4, 2, 0, 67, 68, 5, 17, 0, 0, 68, 70, 1, 0, 0, 0, 69, 14, 1, 0, 0, 0, 69, 17, 1, 0, 0, 0, 69, 18, 1, 0, 0, 0, 69, 21, 1, 0, 0, 0, 69, 22, 1, 0, 0, 0, 69, 26, 1, 0, 0, 0, 69, 31, 1, 0, 0, 0, 69, 43, 1, 0, 0, 0, 69, 55, 1, 0, 0, 0, 69, 62, 1, 0, 0, 0, 70, 82, 1, 0, 0, 0, 71, 72, 10, 12, 0, 0, 72, 73, 7, 1, 0, 0, 73, 81, 3, 4, 2, 13, 74, 75, 10, 11, 0, 0, 75, 76, 7, 0, 0, 0, 76, 81, 3, 4, 2, 12, 77, 78, 10, 10, 0, 0, 78, 79, 5, 13, 0, 0, 79, 81, 3, 4, 2, 11, 80, 71, 1, 0, 0, 0, 80, 74, 1, 0, 0, 0, 80, 77, 1, 0, 0, 0, 81, 84, 1, 0, 0, 0, 82, 80, 1, 0, 0, 0, 82, 83, 1, 0, 0, 0, 83, 5, 1, 0, 0, 0, 84, 82, 1, 0, 0, 0, 6, 12, 38, 50, 69, 80, 82]
+[4, 1, 16, 131, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 2, 3, 7, 3, 2, 4, 7, 4, 2, 5, 7, 5, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 37, 8, 1, 10, 1, 12, 1, 40, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 49, 8, 1, 10, 1, 12, 1, 52, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 70, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 81, 8, 1, 10, 1, 12, 1, 84, 9, 1, 1, 2, 1, 2, 3, 2, 88, 8, 2, 1, 3, 1, 3, 3, 3, 92, 8, 3, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 3, 4, 102, 8, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 5, 4, 110, 8, 4, 10, 4, 12, 4, 113, 9, 4, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 3, 5, 121, 8, 5, 1, 5, 1, 5, 1, 5, 5, 5, 126, 8, 5, 10, 5, 12, 5, 129, 9, 5, 1, 5, 0, 3, 2, 8, 10, 6, 0, 2, 4, 6, 8, 10, 0, 2, 1, 0, 5, 6, 2, 0, 2, 2, 7, 7, 144, 0, 12, 1, 0, 0, 0, 2, 69, 1, 0, 0, 0, 4, 87, 1, 0, 0, 0, 6, 89, 1, 0, 0, 0, 8, 101, 1, 0, 0, 0, 10, 120, 1, 0, 0, 0, 12, 13, 3, 2, 1, 0, 13, 14, 5, 0, 0, 1, 14, 1, 1, 0, 0, 0, 15, 16, 6, 1, -1, 0, 16, 70, 3, 4, 2, 0, 17, 18, 5, 14, 0, 0, 18, 19, 5, 1, 0, 0, 19, 70, 5, 14, 0, 0, 20, 21, 5, 2, 0, 0, 21, 70, 3, 2, 1, 10, 22, 23, 5, 3, 0, 0, 23, 24, 3, 2, 1, 0, 24, 25, 5, 4, 0, 0, 25, 70, 1, 0, 0, 0, 26, 27, 5, 14, 0, 0, 27, 28, 5, 3, 0, 0, 28, 29, 3, 2, 1, 0, 29, 30, 5, 4, 0, 0, 30, 70, 1, 0, 0, 0, 31, 32, 5, 14, 0, 0, 32, 33, 5, 8, 0, 0, 33, 38, 3, 6, 3, 0, 34, 35, 5, 9, 0, 0, 35, 37, 3, 6, 3, 0, 36, 34, 1, 0, 0, 0, 37, 40, 1, 0, 0, 0, 38, 36, 1, 0, 0, 0, 38, 39, 1, 0, 0, 0, 39, 41, 1, 0, 0, 0, 40, 38, 1, 0, 0, 0, 41, 42, 5, 10, 0, 0, 42, 70, 1, 0, 0, 0, 43, 44, 5, 14, 0, 0, 44, 45, 5, 8, 0, 0, 45, 50, 3, 2, 1, 0, 46, 47, 5, 9, 0, 0, 47, 49, 3, 2, 1, 0, 48, 46, 1, 0, 0, 0, 49, 52, 1, 0, 0, 0, 50, 48, 1, 0, 0, 0, 50, 51, 1, 0, 0, 0, 51, 53, 1, 0, 0, 0, 52, 50, 1, 0, 0, 0, 53, 54, 5, 10, 0, 0, 54, 70, 1, 0, 0, 0, 55, 56, 5, 14, 0, 0, 56, 57, 5, 8, 0, 0, 57, 58, 3, 6, 3, 0, 58, 59, 5, 11, 0, 0, 59, 60, 3, 6, 3, 0, 60, 61, 5, 10, 0, 0, 61, 70, 1, 0, 0, 0, 62, 63, 5, 14, 0, 0, 63, 64, 5, 8, 0, 0, 64, 65, 3, 2, 1, 0, 65, 66, 5, 11, 0, 0, 66, 67, 3, 2, 1, 0, 67, 68, 5, 10, 0, 0, 68, 70, 1, 0, 0, 0, 69, 15, 1, 0, 0, 0, 69, 17, 1, 0, 0, 0, 69, 20, 1, 0, 0, 0, 69, 22, 1, 0, 0, 0, 69, 26, 1, 0, 0, 0, 69, 31, 1, 0, 0, 0, 69, 43, 1, 0, 0, 0, 69, 55, 1, 0, 0, 0, 69, 62, 1, 0, 0, 0, 70, 82, 1, 0, 0, 0, 71, 72, 10, 8, 0, 0, 72, 73, 7, 0, 0, 0, 73, 81, 3, 2, 1, 9, 74, 75, 10, 7, 0, 0, 75, 76, 7, 1, 0, 0, 76, 81, 3, 2, 1, 8, 77, 78, 10, 6, 0, 0, 78, 79, 5, 15, 0, 0, 79, 81, 3, 2, 1, 7, 80, 71, 1, 0, 0, 0, 80, 74, 1, 0, 0, 0, 80, 77, 1, 0, 0, 0, 81, 84, 1, 0, 0, 0, 82, 80, 1, 0, 0, 0, 82, 83, 1, 0, 0, 0, 83, 3, 1, 0, 0, 0, 84, 82, 1, 0, 0, 0, 85, 88, 5, 12, 0, 0, 86, 88, 5, 14, 0, 0, 87, 85, 1, 0, 0, 0, 87, 86, 1, 0, 0, 0, 88, 5, 1, 0, 0, 0, 89, 91, 5, 13, 0, 0, 90, 92, 3, 8, 4, 0, 91, 90, 1, 0, 0, 0, 91, 92, 1, 0, 0, 0, 92, 7, 1, 0, 0, 0, 93, 94, 6, 4, -1, 0, 94, 95, 7, 1, 0, 0, 95, 102, 3, 4, 2, 0, 96, 97, 7, 1, 0, 0, 97, 98, 5, 3, 0, 0, 98, 99, 3, 2, 1, 0, 99, 100, 5, 4, 0, 0, 100, 102, 1, 0, 0, 0, 101, 93, 1, 0, 0, 0, 101, 96, 1, 0, 0, 0, 102, 111, 1, 0, 0, 0, 103, 104, 10, 4, 0, 0, 104, 105, 7, 0, 0, 0, 105, 110, 3, 10, 5, 0, 106, 107, 10, 3, 0, 0, 107, 108, 7, 1, 0, 0, 108, 110, 3, 10, 5, 0, 109, 103, 1, 0, 0, 0, 109, 106, 1, 0, 0, 0, 110, 113, 1, 0, 0, 0, 111, 109, 1, 0, 0, 0, 111, 112, 1, 0, 0, 0, 112, 9, 1, 0, 0, 0, 113, 111, 1, 0, 0, 0, 114, 115, 6, 5, -1, 0, 115, 116, 5, 3, 0, 0, 116, 117, 3, 2, 1, 0, 117, 118, 5, 4, 0, 0, 118, 121, 1, 0, 0, 0, 119, 121, 3, 4, 2, 0, 120, 114, 1, 0, 0, 0, 120, 119, 1, 0, 0, 0, 121, 127, 1, 0, 0, 0, 122, 123, 10, 3, 0, 0, 123, 124, 7, 0, 0, 0, 124, 126, 3, 10, 5, 4, 125, 122, 1, 0, 0, 0, 126, 129, 1, 0, 0, 0, 127, 125, 1, 0, 0, 0, 127, 128, 1, 0, 0, 0, 128, 11, 1, 0, 0, 0, 129, 127, 1, 0, 0, 0, 12, 38, 50, 69, 80, 82, 87, 91, 101, 109, 111, 120, 127]
diff --git a/src/andromede/expression/parsing/antlr/Expr.tokens b/src/andromede/expression/parsing/antlr/Expr.tokens
@@ -7,24 +7,22 @@ T__5=6
 T__6=7
 T__7=8
 T__8=9
-NUMBER=10
-TIME=11
-IDENTIFIER=12
-COMPARISON=13
-ADDSUB=14
-MULDIV=15
-LBRACKET=16
-RBRACKET=17
-WS=18
-'+'=1
+T__9=10
+T__10=11
+NUMBER=12
+TIME=13
+IDENTIFIER=14
+COMPARISON=15
+WS=16
+'.'=1
 '-'=2
-'/'=3
-'*'=4
-'.'=5
-'('=6
-')'=7
-','=8
-'..'=9
-'t'=11
-'['=16
-']'=17
+'('=3
+')'=4
+'/'=5
+'*'=6
+'+'=7
+'['=8
+','=9
+']'=10
+'..'=11
+'t'=13
diff --git a/src/andromede/expression/parsing/antlr/ExprLexer.interp b/src/andromede/expression/parsing/antlr/ExprLexer.interp
@@ -1,23 +1,21 @@
 token literal names:
 null
-'+'
-'-'
-'/'
-'*'
 '.'
+'-'
 '('
 ')'
+'/'
+'*'
+'+'
+'['
 ','
+']'
 '..'
 null
 't'
 null
 null
 null
-null
-'['
-']'
-null
 
 token symbolic names:
 null
@@ -30,14 +28,12 @@ null
 null
 null
 null
+null
+null
 NUMBER
 TIME
 IDENTIFIER
 COMPARISON
-ADDSUB
-MULDIV
-LBRACKET
-RBRACKET
 WS
 
 rule names:
@@ -50,17 +46,15 @@ T__5
 T__6
 T__7
 T__8
+T__9
+T__10
 DIGIT
 CHAR
 CHAR_OR_DIGIT
 NUMBER
 TIME
 IDENTIFIER
 COMPARISON
-ADDSUB
-MULDIV
-LBRACKET
-RBRACKET
 WS
 
 channel names:
@@ -71,4 +65,4 @@ mode names:
 DEFAULT_MODE
 
 atn:
-[4, 0, 18, 111, 6, -1, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 2, 3, 7, 3, 2, 4, 7, 4, 2, 5, 7, 5, 2, 6, 7, 6, 2, 7, 7, 7, 2, 8, 7, 8, 2, 9, 7, 9, 2, 10, 7, 10, 2, 11, 7, 11, 2, 12, 7, 12, 2, 13, 7, 13, 2, 14, 7, 14, 2, 15, 7, 15, 2, 16, 7, 16, 2, 17, 7, 17, 2, 18, 7, 18, 2, 19, 7, 19, 2, 20, 7, 20, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 6, 1, 6, 1, 7, 1, 7, 1, 8, 1, 8, 1, 8, 1, 9, 1, 9, 1, 10, 1, 10, 1, 11, 1, 11, 3, 11, 69, 8, 11, 1, 12, 4, 12, 72, 8, 12, 11, 12, 12, 12, 73, 1, 12, 1, 12, 4, 12, 78, 8, 12, 11, 12, 12, 12, 79, 3, 12, 82, 8, 12, 1, 13, 1, 13, 1, 14, 1, 14, 5, 14, 88, 8, 14, 10, 14, 12, 14, 91, 9, 14, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 3, 15, 98, 8, 15, 1, 16, 1, 16, 1, 17, 1, 17, 1, 18, 1, 18, 1, 19, 1, 19, 1, 20, 1, 20, 1, 20, 1, 20, 0, 0, 21, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 0, 21, 0, 23, 0, 25, 10, 27, 11, 29, 12, 31, 13, 33, 14, 35, 15, 37, 16, 39, 17, 41, 18, 1, 0, 5, 1, 0, 48, 57, 3, 0, 65, 90, 95, 95, 97, 122, 2, 0, 43, 43, 45, 45, 2, 0, 42, 42, 47, 47, 3, 0, 9, 10, 13, 13, 32, 32, 114, 0, 1, 1, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 13, 1, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 17, 1, 0, 0, 0, 0, 25, 1, 0, 0, 0, 0, 27, 1, 0, 0, 0, 0, 29, 1, 0, 0, 0, 0, 31, 1, 0, 0, 0, 0, 33, 1, 0, 0, 0, 0, 35, 1, 0, 0, 0, 0, 37, 1, 0, 0, 0, 0, 39, 1, 0, 0, 0, 0, 41, 1, 0, 0, 0, 1, 43, 1, 0, 0, 0, 3, 45, 1, 0, 0, 0, 5, 47, 1, 0, 0, 0, 7, 49, 1, 0, 0, 0, 9, 51, 1, 0, 0, 0, 11, 53, 1, 0, 0, 0, 13, 55, 1, 0, 0, 0, 15, 57, 1, 0, 0, 0, 17, 59, 1, 0, 0, 0, 19, 62, 1, 0, 0, 0, 21, 64, 1, 0, 0, 0, 23, 68, 1, 0, 0, 0, 25, 71, 1, 0, 0, 0, 27, 83, 1, 0, 0, 0, 29, 85, 1, 0, 0, 0, 31, 97, 1, 0, 0, 0, 33, 99, 1, 0, 0, 0, 35, 101, 1, 0, 0, 0, 37, 103, 1, 0, 0, 0, 39, 105, 1, 0, 0, 0, 41, 107, 1, 0, 0, 0, 43, 44, 5, 43, 0, 0, 44, 2, 1, 0, 0, 0, 45, 46, 5, 45, 0, 0, 46, 4, 1, 0, 0, 0, 47, 48, 5, 47, 0, 0, 48, 6, 1, 0, 0, 0, 49, 50, 5, 42, 0, 0, 50, 8, 1, 0, 0, 0, 51, 52, 5, 46, 0, 0, 52, 10, 1, 0, 0, 0, 53, 54, 5, 40, 0, 0, 54, 12, 1, 0, 0, 0, 55, 56, 5, 41, 0, 0, 56, 14, 1, 0, 0, 0, 57, 58, 5, 44, 0, 0, 58, 16, 1, 0, 0, 0, 59, 60, 5, 46, 0, 0, 60, 61, 5, 46, 0, 0, 61, 18, 1, 0, 0, 0, 62, 63, 7, 0, 0, 0, 63, 20, 1, 0, 0, 0, 64, 65, 7, 1, 0, 0, 65, 22, 1, 0, 0, 0, 66, 69, 3, 21, 10, 0, 67, 69, 3, 19, 9, 0, 68, 66, 1, 0, 0, 0, 68, 67, 1, 0, 0, 0, 69, 24, 1, 0, 0, 0, 70, 72, 3, 19, 9, 0, 71, 70, 1, 0, 0, 0, 72, 73, 1, 0, 0, 0, 73, 71, 1, 0, 0, 0, 73, 74, 1, 0, 0, 0, 74, 81, 1, 0, 0, 0, 75, 77, 5, 46, 0, 0, 76, 78, 3, 19, 9, 0, 77, 76, 1, 0, 0, 0, 78, 79, 1, 0, 0, 0, 79, 77, 1, 0, 0, 0, 79, 80, 1, 0, 0, 0, 80, 82, 1, 0, 0, 0, 81, 75, 1, 0, 0, 0, 81, 82, 1, 0, 0, 0, 82, 26, 1, 0, 0, 0, 83, 84, 5, 116, 0, 0, 84, 28, 1, 0, 0, 0, 85, 89, 3, 21, 10, 0, 86, 88, 3, 23, 11, 0, 87, 86, 1, 0, 0, 0, 88, 91, 1, 0, 0, 0, 89, 87, 1, 0, 0, 0, 89, 90, 1, 0, 0, 0, 90, 30, 1, 0, 0, 0, 91, 89, 1, 0, 0, 0, 92, 98, 5, 61, 0, 0, 93, 94, 5, 62, 0, 0, 94, 98, 5, 61, 0, 0, 95, 96, 5, 60, 0, 0, 96, 98, 5, 61, 0, 0, 97, 92, 1, 0, 0, 0, 97, 93, 1, 0, 0, 0, 97, 95, 1, 0, 0, 0, 98, 32, 1, 0, 0, 0, 99, 100, 7, 2, 0, 0, 100, 34, 1, 0, 0, 0, 101, 102, 7, 3, 0, 0, 102, 36, 1, 0, 0, 0, 103, 104, 5, 91, 0, 0, 104, 38, 1, 0, 0, 0, 105, 106, 5, 93, 0, 0, 106, 40, 1, 0, 0, 0, 107, 108, 7, 4, 0, 0, 108, 109, 1, 0, 0, 0, 109, 110, 6, 20, 0, 0, 110, 42, 1, 0, 0, 0, 7, 0, 68, 73, 79, 81, 89, 97, 1, 6, 0, 0]
+[4, 0, 16, 103, 6, -1, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 2, 3, 7, 3, 2, 4, 7, 4, 2, 5, 7, 5, 2, 6, 7, 6, 2, 7, 7, 7, 2, 8, 7, 8, 2, 9, 7, 9, 2, 10, 7, 10, 2, 11, 7, 11, 2, 12, 7, 12, 2, 13, 7, 13, 2, 14, 7, 14, 2, 15, 7, 15, 2, 16, 7, 16, 2, 17, 7, 17, 2, 18, 7, 18, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 6, 1, 6, 1, 7, 1, 7, 1, 8, 1, 8, 1, 9, 1, 9, 1, 10, 1, 10, 1, 10, 1, 11, 1, 11, 1, 12, 1, 12, 1, 13, 1, 13, 3, 13, 69, 8, 13, 1, 14, 4, 14, 72, 8, 14, 11, 14, 12, 14, 73, 1, 14, 1, 14, 4, 14, 78, 8, 14, 11, 14, 12, 14, 79, 3, 14, 82, 8, 14, 1, 15, 1, 15, 1, 16, 1, 16, 5, 16, 88, 8, 16, 10, 16, 12, 16, 91, 9, 16, 1, 17, 1, 17, 1, 17, 1, 17, 1, 17, 3, 17, 98, 8, 17, 1, 18, 1, 18, 1, 18, 1, 18, 0, 0, 19, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 21, 11, 23, 0, 25, 0, 27, 0, 29, 12, 31, 13, 33, 14, 35, 15, 37, 16, 1, 0, 3, 1, 0, 48, 57, 3, 0, 65, 90, 95, 95, 97, 122, 3, 0, 9, 10, 13, 13, 32, 32, 106, 0, 1, 1, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 11, 1, 0, 0, 0, 0, 13, 1, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 17, 1, 0, 0, 0, 0, 19, 1, 0, 0, 0, 0, 21, 1, 0, 0, 0, 0, 29, 1, 0, 0, 0, 0, 31, 1, 0, 0, 0, 0, 33, 1, 0, 0, 0, 0, 35, 1, 0, 0, 0, 0, 37, 1, 0, 0, 0, 1, 39, 1, 0, 0, 0, 3, 41, 1, 0, 0, 0, 5, 43, 1, 0, 0, 0, 7, 45, 1, 0, 0, 0, 9, 47, 1, 0, 0, 0, 11, 49, 1, 0, 0, 0, 13, 51, 1, 0, 0, 0, 15, 53, 1, 0, 0, 0, 17, 55, 1, 0, 0, 0, 19, 57, 1, 0, 0, 0, 21, 59, 1, 0, 0, 0, 23, 62, 1, 0, 0, 0, 25, 64, 1, 0, 0, 0, 27, 68, 1, 0, 0, 0, 29, 71, 1, 0, 0, 0, 31, 83, 1, 0, 0, 0, 33, 85, 1, 0, 0, 0, 35, 97, 1, 0, 0, 0, 37, 99, 1, 0, 0, 0, 39, 40, 5, 46, 0, 0, 40, 2, 1, 0, 0, 0, 41, 42, 5, 45, 0, 0, 42, 4, 1, 0, 0, 0, 43, 44, 5, 40, 0, 0, 44, 6, 1, 0, 0, 0, 45, 46, 5, 41, 0, 0, 46, 8, 1, 0, 0, 0, 47, 48, 5, 47, 0, 0, 48, 10, 1, 0, 0, 0, 49, 50, 5, 42, 0, 0, 50, 12, 1, 0, 0, 0, 51, 52, 5, 43, 0, 0, 52, 14, 1, 0, 0, 0, 53, 54, 5, 91, 0, 0, 54, 16, 1, 0, 0, 0, 55, 56, 5, 44, 0, 0, 56, 18, 1, 0, 0, 0, 57, 58, 5, 93, 0, 0, 58, 20, 1, 0, 0, 0, 59, 60, 5, 46, 0, 0, 60, 61, 5, 46, 0, 0, 61, 22, 1, 0, 0, 0, 62, 63, 7, 0, 0, 0, 63, 24, 1, 0, 0, 0, 64, 65, 7, 1, 0, 0, 65, 26, 1, 0, 0, 0, 66, 69, 3, 25, 12, 0, 67, 69, 3, 23, 11, 0, 68, 66, 1, 0, 0, 0, 68, 67, 1, 0, 0, 0, 69, 28, 1, 0, 0, 0, 70, 72, 3, 23, 11, 0, 71, 70, 1, 0, 0, 0, 72, 73, 1, 0, 0, 0, 73, 71, 1, 0, 0, 0, 73, 74, 1, 0, 0, 0, 74, 81, 1, 0, 0, 0, 75, 77, 5, 46, 0, 0, 76, 78, 3, 23, 11, 0, 77, 76, 1, 0, 0, 0, 78, 79, 1, 0, 0, 0, 79, 77, 1, 0, 0, 0, 79, 80, 1, 0, 0, 0, 80, 82, 1, 0, 0, 0, 81, 75, 1, 0, 0, 0, 81, 82, 1, 0, 0, 0, 82, 30, 1, 0, 0, 0, 83, 84, 5, 116, 0, 0, 84, 32, 1, 0, 0, 0, 85, 89, 3, 25, 12, 0, 86, 88, 3, 27, 13, 0, 87, 86, 1, 0, 0, 0, 88, 91, 1, 0, 0, 0, 89, 87, 1, 0, 0, 0, 89, 90, 1, 0, 0, 0, 90, 34, 1, 0, 0, 0, 91, 89, 1, 0, 0, 0, 92, 98, 5, 61, 0, 0, 93, 94, 5, 62, 0, 0, 94, 98, 5, 61, 0, 0, 95, 96, 5, 60, 0, 0, 96, 98, 5, 61, 0, 0, 97, 92, 1, 0, 0, 0, 97, 93, 1, 0, 0, 0, 97, 95, 1, 0, 0, 0, 98, 36, 1, 0, 0, 0, 99, 100, 7, 2, 0, 0, 100, 101, 1, 0, 0, 0, 101, 102, 6, 18, 0, 0, 102, 38, 1, 0, 0, 0, 7, 0, 68, 73, 79, 81, 89, 97, 1, 6, 0, 0]