Linearization of the kernel functions in SVM

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SVM（Support Vector Machine）is an important classification tool, which has a wide range of applications in cluster analysis, community division and so on. SVM The kernel functions used in SVM have many forms. Here we only discuss the function of the form f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j. By introducing new variables p, q, r, u, v, w, the linearization of the function f(x,y,z) is realized by setting the correspondence x^2<-> p, y^2 <-> q, z^2 <-> r, xy<-> u, yz <-> v, zx <-> w and the function f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j can be written as g(p,q,r,u,v,w,x,y,z) = ap + bq + cr + du + ev + fw + gx + hy + iz + j, which is a linear function with 9 variables.

Now your task is to write a program to change f into g.

Input

The input of the first line is an integer T, which is the number of test data (T<120). Then T data follows. For each data, there are 10 integer numbers on one line, which are the coefficients and constant a, b, c, d, e, f, g, h, i, j of the function f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j.

Output

For each input function, print its correspondent linear function with 9 variables in conventional way on one line.

Sample Input

20 46 3 4 -5 -22 -8 -32 24 272 31 -5 0 0 12 0 0 -49 12

Sample Output

46q+3r+4u-5v-22w-8x-32y+24z+272p+31q-5r+12w-49z+12

模拟：

用的笨方法，由于没考虑那么全，导致WA了好多遍，要注意1，-1，全为0的时候结果是0，为1或-1时，只写字母就行了，1，-1不用显现出来

#include<stdio.h>long long int a[100];int main(){    int t;    scanf("%d",&t);    while(t--)    {        int sum=0;        int we;        for(int i=1;i<=10;i++)        {            scanf("%lld",&a[i]);            if(a[i]==0)            {                sum++;            }        }        for(int i=1;i<=10;i++)        {            if(a[i]!=0)            {                we=i;                break;            }        }        if(sum==10)        {            printf("0\n");        }        else        {        if(a[1]!=0)        {            if(a[1]==1)                printf("p");            else if(a[1]==-1)            printf("-p");            else                printf("%dp",a[1]);        }        if(a[2]!=0)        {            if(a[2]>1&&2>we)                printf("+%lldq",a[2]);               else if(a[2]==1&&2>we)                 printf("+q");                    else if(a[2]==1&&2<=we)                    printf("q");                    else if(a[2]==-1)                        printf("-q");                    else            printf("%lldq",a[2]);        }        if(a[3]!=0)        {            if(a[3]>1&&3>we)                printf("+%lldr",a[3]);                else if(a[3]==1&&3>we)                 printf("+r");                    else if(a[3]==1&&3<=we)                    printf("r");                     else if(a[3]==-1)                        printf("-r");                else            printf("%lldr",a[3]);        }        if(a[4]!=0)        {            if(a[4]>1&&4>we)                printf("+%lldu",a[4]);                 else if(a[4]==1&&4>we)                 printf("+u");                    else if(a[4]==1&&4<=we)                    printf("u");                     else if(a[4]==-1)                        printf("-u");                else            printf("%lldu",a[4]);        }        if(a[5]!=0)        {            if(a[5]>1&&5>we)                printf("+%lldv",a[5]);                 else if(a[5]==1&&5>we)                 printf("+v");                    else if(a[5]==1&&5<=we)                    printf("v");                     else if(a[5]==-1)                        printf("-v");                else            printf("%lldv",a[5]);        }        if(a[6]!=0)        {            if(a[6]>1&&6>we)                printf("+%lldw",a[6]);               else if(a[6]==1&&6>we)                 printf("+w");                    else if(a[6]==1&&6<=we)                    printf("w");                     else if(a[6]==-1)                        printf("-w");                else            printf("%lldw",a[6]);        }        if(a[7]!=0)        {            if(a[7]>1&&7>we)                printf("+%lldx",a[7]);                  else if(a[7]==1&&7>we)                 printf("+x");                    else if(a[7]==1&&7<=we)                    printf("x");                     else if(a[7]==-1)                        printf("-x");                else            printf("%lldx",a[7]);        }        if(a[8]!=0)        {            if(a[8]>1&&8>we)                printf("+%lldy",a[8]);                  else if(a[8]==1&&8>we)                 printf("+y");                    else if(a[8]==1&&8<=we)                    printf("y");                     else if(a[8]==-1)                        printf("-y");                else            printf("%lldy",a[8]);        }        if(a[9]!=0)        {            if(a[9]>1&&9>we)                printf("+%lldz",a[9]);                   else if(a[9]==1&&9>we)                 printf("+z");                    else if(a[9]==1&&9<=we)                    printf("z");                     else if(a[9]==-1)                        printf("-z");                else            printf("%lldz",a[9]);        }        if(a[10]!=0)        {            if(a[10]>1&&10>we)                printf("+%lld",a[10]);                  else if(a[10]==1&&10>we)                 printf("+1");                    else if(a[10]==1&&10<=we)                    printf("1");                     else if(a[10]==-1)                        printf("-1");                    else            printf("%lld",a[10]);        }        printf("\n");        }    }}

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