/*  The rows are 1..5 the columns are 1..5
    cells (1,1) (1,5) (5,1) (5,5) do not exist.
*/

#include <stdbool.h>
#include <stdio.h>

static bool exists(int r, int c) {
    return (2 <= r && r <= 4 && 1 <= c && c <= 5)
        || (2 <= c && c <= 4 && 1 <= r && r <= 5);
}

static void set(int r, int c, int k) {
    int k1;

    /* Set row r, column c, to colour k */
    printf("&x%d%d%d\n", r, c, k);
    /* The other colours are not possible for this cell */
    for (k1 = 1; k1 <= 5; k1++) {
	if (k1 != k) {
	    printf("&~x%d%d%d\n", r, c, k1);
	}
    }
    /* we _could_ note that this colour is not available
       for other cells in the same row, or column, or diagonal,
       but that should happen automatically.
    */
}

int main(void) {
    int r, r1, c, c1, k, k1;
    char ch, oc;

    oc = '(';
    for (r = 1; r <= 5; r++) {
	for (c = 1; c <= 5; c++) {
	    if (exists(r, c)) {
		/* This cell has one of five colours */
		putchar(oc);
		ch = '(';
		for (k = 1; k <= 5; k++) {
		    printf("%cx%d%d%d", ch, r, c, k);
		    ch = '|';
		}
		printf(")\n");
		oc = '&';
		/* It does not have two colours at the same time */
		for (k = 1; k < 5; k++) {
		    for (k1 = k+1; k1 <= 5; k1++) {
			printf("%c(~x%d%d%d|~x%d%d%d)\n",
			        oc, r, c, k, r, c, k1);
			oc = '&';
		    }
		}
	    }
	}
    }
    /* rows */
    for (r = 1; r <= 5; r++) {
	if (exists(r, 1)) {
	    /* This is a full row */
	    for (k = 1; k <= 5; k++) {
		/* This colour must appear in the row */
		putchar('&');
		ch = '(';
		for (c = 1; c <= 5; c++) {
		    printf("%cx%d%d%d", ch, r, c, k);
		    ch = '|';
		}
		printf(")\n");
		oc = '&';
	    }
	}
	for (k = 1; k <= 5; k++) {
	    /* This colour must not appear twice in the row */
	    ch = '(';
	    for (c = 1; c < 5; c++) {
	        for (c1 = c+1; c1 <= 5; c1++) {
	            if (exists(r, c) && exists(r, c1)) {
			printf("%c(~x%d%d%d|~x%d%d%d)\n",
			       oc, r, c, k, r, c1, k);
		        oc = '&';
		    }
		}
	    }
	}
    }
    /* columns */
    for (c = 1; c <= 5; c++) {
	if (exists(1, c)) {
	    /* This is a full column */
	    for (k = 1; k <= 5; k++) {
		/* This colour must appear in the column */
		putchar(oc);
		ch = '(';
		for (r = 1; r <= 5; r++) {
		    printf("%cx%d%d%d", ch, r, c, k);
		    ch = '|';
		}
		printf(")\n");
		oc = '&';
	    }
	}
	for (k = 1; k <= 5; k++) {
	    /* This colour must not appear twice in the column */
	    for (r = 1; r < 5; r++) {
	        for (r1 = r+1; r1 <= 5; r1++) {
	            if (exists(r, c) && exists(r1, c)) {
			printf("%c(~x%d%d%d|~x%d%d%d)\n",
			       oc, r, c, k, r1, c, k);
			oc = '&';
		    }
		}
	    }
	}
    }
    /* downwards diagonals */
    for (k = 1; k <= 5; k++) {
	for (r = 4; r >= 2; r--) {
	    putchar(oc);
	    ch = '(';
	    for (r1 = r; r1 <= 5; r1++) {
		c1 = r1 - r + 1;
		printf("%c~x%d%d%d", ch, r1, c1, k);
		ch = '|';
	    }
	    printf(")\n");
	    oc = '&';
	}
	putchar(oc);
	ch = '(';
	for (r = 2; r <= 4; r++) {
	    printf("%c~x%d%d%d", ch, r, r, k);
	    ch = '|';
	}
	printf(")\n");
	oc = '&';
	for (c = 2; c <= 4; c++) {
	    putchar(oc);
	    ch = '(';
	    for (c1 = c; c1 <= 5; c1++) {
		r1 = c1 - c + 1;
		printf("%c~x%d%d%d", ch, r1, c1, k);
		ch = '|';
	    }
	    printf(")\n");
	    oc = '&';
	}
    }
    /* upwards diagonals */
    for (k = 1; k <= 5; k++) {
	for (c = 2; c <= 4; c++) {
	    putchar(oc);
	    ch = '(';
	    for (c1 = c; c1 >= 1; c1--) {
		r1 = c - c1 + 1;
		printf("%c~x%d%d%d", ch, r1, c1, k);
		ch = '|';
	    }
	    printf(")\n");
	    oc = '&';
	}
	putchar(oc);
	ch = '(';
	for (c = 4; c >= 2; c--) {
	    printf("%c~x%d%d%d", ch, 6-c, c, k);
	    ch = '|';
	}
	printf(")\n");
	oc = '&';
	for (r = 2; r <= 4; r++) {
	    putchar(oc);
	    ch = '(';
	    for (r1 = r; r1 <= 5; r1++) {
		c1 = r - r1 + 5;
		printf("%c~x%d%d%d", ch, r1, c1, k);
		ch = '|';
	    }
	    printf(")\n");
	    oc = '&';
	}
    }
    set(1, 4, 1);
    set(3, 4, 2);
    set(5, 2, 3);
    set(5, 4, 4);
    printf(");\n");
    return 0;
}