哈儿小波分解和重构（降维和升维）实现算法
【0】README
0.1）本文旨在讲解 哈儿小波变换（分解和重构）进行数据的降维和升维；
【1】intro to 哈儿小波
1.1）定义：哈尔小波变换分为哈尔小波分解和重构。本文利用哈尔小波分解和哈尔小波重构分别对社交网络中的时间序列进行降维和升维操作，而分解降维和重构升维互为逆过程，这里以哈尔小波分解降维步骤为例进行说明。
1.2）哈尔小波分解（重构是其逆过程）：可以被看作是一系列对离散时间函数的均值和差操作。本文计算离散函数f(t)，即时间序列元素值的每两个相邻值间的均值和差。找出离散函数f(t)={9， 7， 3， 5}的哈尔小波分解过程如下表所示：
| 分辨率 级别 |
分辨率 （维度） |
均值 |
差值 |
哈尔小波 分解系数 |
降维后的 时序 |
全分辨率下的时序 |
| 2 |
4 |
{9,7,3,5} |
|
{9,7,3,5} |
|
{9,7,3,5} |
| 1 |
2 |
{8,4} |
{1,-1} |
{8,4,1,-1} |
{8,4} |
{8,8,4,4} |
| 0 |
1 |
{6} |
{2} |
{6,2,1,-1} |
{6} |
{6,6,6,6} |
A1）intro to 分辨率：哈儿小波分解和重构常应用于图像的降维和升维，这里的分辨率，你与可以理解为是图像的分辨率，分辨率越低，图像质量越不清晰，分辨率越高图片质量越清晰（数据显示更加丰富）；（干货——我们看到的图片为什么不清晰）
A2）上表中最后一列（全分辨率下的时序）：我们看到数据由 [9 7 3 5] 到 [8 8 4 4] 再到 [6 6 6 6]，显然在一个图像的某个区域内，分辨率越低，数据越不丰富，变化越不明显，这也是为什么低分辨率下数据模糊的一个原因（因为低分辨率下，数据经过降维处理了）；
【2】将上述哈尔小波分解过程用倒置二叉树表示如下：
【3】看个荔枝
对上图的分析（Analysis）：
A1）以上数据[2, 5, 8, 9, 7, 4, -1, 1]在不同分辨率下经过哈儿小波变换得到的数据如下：
分辨率3：它本身；
分辨率2：3.5， 8.5, 5.5, 0, -1.5, -0.5, 1.5, -1;
分辨率1：6， 2.75， -2.5， 2.75, -1.5, -0.5, 1.5, -1;
分辨率0：4.375， 1.625， -2.5， 2.75, -1.5, -0.5, 1.5, -1;
A2）哈儿小波变换分为哈儿小波分解和哈儿小波重构，且我们可以指定最低级分辨率（并不一定是0）；
【4】将哈儿小波变换应用到Kmeans聚类算法（干货——目的是降低聚类时间复杂度）
1）Kmeans聚类进行前：先对数据进行哈儿小波分解以降维到0分辨率（或你自己指定）（干货——聚类开始前，我们数据的分辨率是0，而维度是1，即2^0=1）；
2）Kmeans聚类过程中：聚类是一个迭代的过程，每轮迭代，我们都对数据进行哈儿小波重构进行升维（以降低聚类时间复杂度）；
如第1轮聚类后，我们将数据升维到分辨率1下；第2轮迭代后，将数据升维到分辨率2下，以此类推......；当达到全分辨率下时，我们不再进行哈儿小波变换，但可以继续聚类，直到满足聚类结束标志的条件为止；
【5】哈儿小波分解和重构源代码实现
5.1）分解和重构的源代码
public class HaarTransform{
/**
* executing haar reconstruction transform towards given array
* @param rawitem raw array
* @param curResolution current resolution
*/
public static int maxResolution;
public static void Reconstruct(double[] rawitem, int curResolution) {
double[] temp = new double[(int) pow(2, curResolution+1)];
int span;
span = (int) pow(2, curResolution);
for (int i = 0; i < span; i++)
{
temp[2*i] = rawitem[i] + rawitem[i+span];
temp[2*i+1] = rawitem[i] - rawitem[i+span];
}
System.arraycopy(temp, 0, rawitem, 0, temp.length);
}
/**
* @param rawitem is a array
* @param leastResolution is the least resolution allowed be zero.
* @param maxResolution is equals to log(full dimension)
* @return
*/
public static double[] Decompose(double[] rawitem, int leastResolution, int maxResolution) {
double[] temp = new double[rawitem.length];
int resolutionLength = ClusterData.dimension;
HaarTransform.maxResolution = maxResolution;
System.out.print("===初始分辨率为：" + maxResolution);
AlgTools.printOneDimArray(rawitem);
System.out.println("\n===哈儿小波分解数据维度（降维）===");
// you know least resolution equals to 0.
for (int i = (int)maxResolution; i > leastResolution; i--)
{
for (int j = 0; j < resolutionLength / 2; j++)
{
temp[j] = (rawitem[2*j] + rawitem[2*j+1]) / 2;
temp[resolutionLength/2+j] = (rawitem[2*j] - rawitem[2*j+1]) / 2;
}
rawitem = temp.clone();
System.out.print("===降维后的分辨率为：" + (i-1));
AlgTools.printOneDimArray(rawitem);
resolutionLength /= 2;
}
return temp;
}
}
对以上代码的分析（Analysis）：
A1）因为总共维度是128，所以最大分辨率==log128=7；
A2）上述哈儿小波分解过程中对应的变量变化如下（为了便于
更加理解分解过程）：
| 循环次数 round |
分辨率i |
分辨率级别的对应维度 resolutionLength |
j(max) |
下一分辨率级别 的维度sum |
| 1 |
7 |
128 |
63(0~63) |
64 |
| 2 |
6 |
64 |
31(0~31) |
32 |
| 3 |
5 |
32 |
15(0~15) |
16 |
| 4 |
4 |
16 |
7(0~7) |
8 |
| 5 |
3 |
8 |
3(0~3) |
4 |
| 6 |
2 |
4 |
1(0~1) |
2 |
| 7 |
1 |
2 |
0(0~1) |
1 |
===初始分辨率为：7 3.618 3.335 3.002 3.073 2.602 2.448 2.532 2.756 2.790 2.956 3.373 3.163 3.315 3.511 3.288 3.109 3.011 3.077 2.971 3.214 3.369 3.105 3.063 2.722 2.288 3.272 11.291 20.017 31.324 51.307 94.234163.889253.627372.525497.424642.902811.8281000.9981172.9371298.4281399.1901444.7701452.2061422.1691394.1541369.3461350.4861332.4741253.0821117.242946.172790.994645.383527.494437.614366.880329.590325.505353.907392.927440.781495.314556.211615.969662.322697.820712.415715.096719.292721.732721.731716.570711.313691.281662.400620.116572.862544.525524.006506.244490.833489.327490.983509.590557.346606.486656.436719.957793.370856.480916.926970.167992.306989.343969.713931.645876.140813.348743.502664.335607.390569.595548.589551.772559.155585.741615.046665.824716.634757.659804.571828.447868.492878.705886.999881.957831.100781.153724.207686.238632.322595.360546.200466.399410.905372.359357.818349.447 ===哈儿小波分解数据维度（降维）=== ===降维后的分辨率为：6 3.476 3.038 2.525 2.644 2.873 3.268 3.413 3.199 3.044 3.092 3.237 2.892 2.780 15.654 41.315129.061313.076570.163906.4131235.6831421.9801437.1881381.7501341.4801185.162868.583586.439402.247327.548373.417468.048586.090680.071713.756720.512719.150701.297641.258558.694515.125490.080500.286581.916688.196824.925943.546990.824950.679844.744703.919588.492550.181572.448640.435737.147816.509873.598884.478806.127705.222613.841506.300391.632353.632 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===降维后的分辨率为：5 3.257 2.584 3.071 3.306 3.068 3.065 9.217 85.188441.6201071.0481429.5841361.6151026.872494.343350.482527.069696.913719.831671.278536.909495.183635.056884.236970.752774.331569.337606.441776.828879.038755.674560.070372.632 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===降维后的分辨率为：4 2.921 3.188 3.066 47.203756.3341395.599760.608438.776708.372604.094565.120927.494671.834691.635817.356466.351 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===降维后的分辨率为：3 3.054 25.1351075.967599.692656.233746.307681.734641.854 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===降维后的分辨率为：2 14.094837.829701.270661.794-11.040238.137-45.037 19.940 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===降维后的分辨率为：1 425.962681.532-411.867 19.738-11.040238.137-45.037 19.940 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===降维后的分辨率为：0 553.747-127.785-411.867 19.738-11.040238.137-45.037 19.940 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===哈儿小波重构数据维度（升维）=== ===升维后的分辨率为：1 425.962681.532-411.867 19.738-11.040238.137-45.037 19.940 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===升维后的分辨率为：2 14.094837.829701.270661.794-11.040238.137-45.037 19.940 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===升维后的分辨率为：3 3.054 25.1351075.967599.692656.233746.307681.734641.854 -0.134-22.068-319.633160.916 52.139-181.187 -9.900175.502 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===升维后的分辨率为：4 2.921 3.188 3.066 47.203756.3341395.599760.608438.776708.372604.094565.120927.494671.834691.635817.356466.351 0.336 -0.118 0.002-37.986-314.714 33.984266.265-88.293-11.459 67.184-69.937-43.258102.497-85.193 61.682 93.719 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===升维后的分辨率为：5 3.257 2.584 3.071 3.306 3.068 3.065 9.217 85.188441.6201071.0481429.5841361.6151026.872494.343350.482527.069696.913719.831671.278536.909495.183635.056884.236970.752774.331569.337606.441776.828879.038755.674560.070372.632 0.219 -0.060 -0.198 0.107 -0.024 0.172 -6.437-43.873-128.543-164.635 -7.604 20.135158.289 92.096-22.934-59.021-16.842 0.681 30.019 21.784 -5.103-53.140-59.311 20.073 70.412 19.156-33.994-39.681 -5.440 50.452 53.771 19.000 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===升维后的分辨率为：6 3.476 3.038 2.525 2.644 2.873 3.268 3.413 3.199 3.044 3.092 3.237 2.892 2.780 15.654 41.315129.061313.076570.163906.4131235.6831421.9801437.1881381.7501341.4801185.162868.583586.439402.247327.548373.417468.048586.090680.071713.756720.512719.150701.297641.258558.694515.125490.080500.286581.916688.196824.925943.546990.824950.679844.744703.919588.492550.181572.448640.435737.147816.509873.598884.478806.127705.222613.841506.300391.632353.632 0.142 -0.036 0.077 -0.112 -0.083 0.105 -0.098 0.089 -0.033 -0.121 0.132 0.171 -0.492 -4.363 -9.991-34.827-59.449-72.739-94.585-62.745-22.790 15.018 12.404 9.006 67.920 77.589 58.945 35.367 2.042-19.510-27.267-29.879-17.749 -1.340 -1.220 2.580 10.016 21.142 14.169 8.881 0.753 -9.303-24.570-31.761-31.555-26.620 1.482 19.034 31.396 39.583 18.897 -1.591-13.293-25.389-20.512-11.938 -5.106 2.521 24.974 18.984 18.481 39.901 19.273 4.186 ===升维后的分辨率为：7 3.618 3.335 3.002 3.073 2.602 2.448 2.532 2.756 2.790 2.956 3.373 3.163 3.315 3.511 3.288 3.109 3.011 3.077 2.971 3.214 3.369 3.105 3.063 2.722 2.288 3.272 11.291 20.017 31.324 51.307 94.234163.889253.627372.525497.424642.902811.8281000.9981172.9371298.4281399.1901444.7701452.2061422.1691394.1541369.3461350.4861332.4741253.0821117.242946.172790.994645.383527.494437.614366.880329.590325.505353.907392.927440.781495.314556.211615.969662.322697.820712.415715.096719.292721.732721.731716.570711.313691.281662.400620.116572.862544.525524.006506.244490.833489.327490.983509.590557.346606.486656.436719.957793.370856.480916.926970.167992.306989.343969.713931.645876.140813.348743.502664.335607.390569.595548.589551.772559.155585.741615.046665.824716.634757.659804.571828.447868.492878.705886.999881.957831.100781.153724.207686.238632.322595.360546.200466.399410.905372.359357.818349.447