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1 SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, |
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2 $ INFO ) |
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3 * |
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4 * -- LAPACK routine (version 3.0) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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6 * Courant Institute, Argonne National Lab, and Rice University |
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7 * February 29, 1992 |
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8 * |
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9 * .. Scalar Arguments .. |
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10 CHARACTER NORM |
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11 INTEGER INFO, LDA, N |
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12 DOUBLE PRECISION ANORM, RCOND |
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13 * .. |
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14 * .. Array Arguments .. |
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15 INTEGER IWORK( * ) |
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16 DOUBLE PRECISION A( LDA, * ), WORK( * ) |
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17 * .. |
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18 * |
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19 * Purpose |
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20 * ======= |
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21 * |
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22 * DGECON estimates the reciprocal of the condition number of a general |
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23 * real matrix A, in either the 1-norm or the infinity-norm, using |
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24 * the LU factorization computed by DGETRF. |
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25 * |
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26 * An estimate is obtained for norm(inv(A)), and the reciprocal of the |
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27 * condition number is computed as |
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28 * RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
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29 * |
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30 * Arguments |
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31 * ========= |
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32 * |
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33 * NORM (input) CHARACTER*1 |
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34 * Specifies whether the 1-norm condition number or the |
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35 * infinity-norm condition number is required: |
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36 * = '1' or 'O': 1-norm; |
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37 * = 'I': Infinity-norm. |
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38 * |
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39 * N (input) INTEGER |
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40 * The order of the matrix A. N >= 0. |
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41 * |
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42 * A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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43 * The factors L and U from the factorization A = P*L*U |
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44 * as computed by DGETRF. |
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45 * |
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46 * LDA (input) INTEGER |
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47 * The leading dimension of the array A. LDA >= max(1,N). |
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48 * |
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49 * ANORM (input) DOUBLE PRECISION |
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50 * If NORM = '1' or 'O', the 1-norm of the original matrix A. |
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51 * If NORM = 'I', the infinity-norm of the original matrix A. |
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52 * |
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53 * RCOND (output) DOUBLE PRECISION |
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54 * The reciprocal of the condition number of the matrix A, |
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55 * computed as RCOND = 1/(norm(A) * norm(inv(A))). |
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56 * |
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57 * WORK (workspace) DOUBLE PRECISION array, dimension (4*N) |
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58 * |
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59 * IWORK (workspace) INTEGER array, dimension (N) |
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60 * |
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61 * INFO (output) INTEGER |
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62 * = 0: successful exit |
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63 * < 0: if INFO = -i, the i-th argument had an illegal value |
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64 * |
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65 * ===================================================================== |
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66 * |
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67 * .. Parameters .. |
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68 DOUBLE PRECISION ONE, ZERO |
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69 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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70 * .. |
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71 * .. Local Scalars .. |
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72 LOGICAL ONENRM |
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73 CHARACTER NORMIN |
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74 INTEGER IX, KASE, KASE1 |
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75 DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU |
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76 * .. |
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77 * .. External Functions .. |
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78 LOGICAL LSAME |
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79 INTEGER IDAMAX |
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80 DOUBLE PRECISION DLAMCH |
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81 EXTERNAL LSAME, IDAMAX, DLAMCH |
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82 * .. |
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83 * .. External Subroutines .. |
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84 EXTERNAL DLACON, DLATRS, DRSCL, XERBLA |
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85 * .. |
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86 * .. Intrinsic Functions .. |
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87 INTRINSIC ABS, MAX |
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88 * .. |
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89 * .. Executable Statements .. |
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90 * |
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91 * Test the input parameters. |
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92 * |
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93 INFO = 0 |
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94 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) |
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95 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN |
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96 INFO = -1 |
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97 ELSE IF( N.LT.0 ) THEN |
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98 INFO = -2 |
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99 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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100 INFO = -4 |
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101 ELSE IF( ANORM.LT.ZERO ) THEN |
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102 INFO = -5 |
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103 END IF |
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104 IF( INFO.NE.0 ) THEN |
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105 CALL XERBLA( 'DGECON', -INFO ) |
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106 RETURN |
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107 END IF |
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108 * |
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109 * Quick return if possible |
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110 * |
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111 RCOND = ZERO |
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112 IF( N.EQ.0 ) THEN |
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113 RCOND = ONE |
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114 RETURN |
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115 ELSE IF( ANORM.EQ.ZERO ) THEN |
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116 RETURN |
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117 END IF |
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118 * |
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119 SMLNUM = DLAMCH( 'Safe minimum' ) |
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120 * |
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121 * Estimate the norm of inv(A). |
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122 * |
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123 AINVNM = ZERO |
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124 NORMIN = 'N' |
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125 IF( ONENRM ) THEN |
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126 KASE1 = 1 |
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127 ELSE |
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128 KASE1 = 2 |
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129 END IF |
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130 KASE = 0 |
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131 10 CONTINUE |
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132 CALL DLACON( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE ) |
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133 IF( KASE.NE.0 ) THEN |
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134 IF( KASE.EQ.KASE1 ) THEN |
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135 * |
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136 * Multiply by inv(L). |
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137 * |
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138 CALL DLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A, |
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139 $ LDA, WORK, SL, WORK( 2*N+1 ), INFO ) |
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140 * |
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141 * Multiply by inv(U). |
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142 * |
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143 CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, |
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144 $ A, LDA, WORK, SU, WORK( 3*N+1 ), INFO ) |
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145 ELSE |
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146 * |
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147 * Multiply by inv(U'). |
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148 * |
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149 CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A, |
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150 $ LDA, WORK, SU, WORK( 3*N+1 ), INFO ) |
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151 * |
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152 * Multiply by inv(L'). |
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153 * |
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154 CALL DLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A, |
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155 $ LDA, WORK, SL, WORK( 2*N+1 ), INFO ) |
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156 END IF |
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157 * |
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158 * Divide X by 1/(SL*SU) if doing so will not cause overflow. |
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159 * |
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160 SCALE = SL*SU |
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161 NORMIN = 'Y' |
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162 IF( SCALE.NE.ONE ) THEN |
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163 IX = IDAMAX( N, WORK, 1 ) |
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164 IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) |
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165 $ GO TO 20 |
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166 CALL DRSCL( N, SCALE, WORK, 1 ) |
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167 END IF |
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168 GO TO 10 |
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169 END IF |
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170 * |
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171 * Compute the estimate of the reciprocal condition number. |
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172 * |
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173 IF( AINVNM.NE.ZERO ) |
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174 $ RCOND = ( ONE / AINVNM ) / ANORM |
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175 * |
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176 20 CONTINUE |
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177 RETURN |
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178 * |
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179 * End of DGECON |
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180 * |
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181 END |
