Three companies decided to order a billboard with pictures of their logos. A billboard is a big square board. A logo of each company is a rectangle of a non-zero area. 

Advertisers will put up the ad only if it is possible to place all three logos on the billboard so that they do not overlap and the billboard has no empty space left. When you put a logo on the billboard, you should rotate it so that the sides were parallel to the sides of the billboard.

Your task is to determine if it is possible to put the logos of all the three companies on some square billboard without breaking any of the described rules.

Input

The first line of the input contains six positive integers x1, y1, x2, y2, x3, y3 (1 ≤ x1, y1, x2, y2, x3, y3 ≤ 100), where xi and yi determine the length and width of the logo of the i-th company respectively.

Output

If it is impossible to place all the three logos on a square shield, print a single integer "-1" (without the quotes).

If it is possible, print in the first line the length of a side of square n, where you can place all the three logos. Each of the next n lines should contain n uppercase English letters "A", "B" or "C". The sets of the same letters should form solid rectangles, provided that:

  * the sizes of the rectangle composed from letters "A" should be equal to the sizes of the logo of the first company, 
  * the sizes of the rectangle composed from letters "B" should be equal to the sizes of the logo of the second company, 
  * the sizes of the rectangle composed from letters "C" should be equal to the sizes of the logo of the third company, 



Note that the logos of the companies can be rotated for printing on the billboard. The billboard mustn't have any empty space. If a square billboard can be filled with the logos in multiple ways, you are allowed to print any of them.

See the samples to better understand the statement.

Examples

Input

5 1 2 5 5 2


Output

5
AAAAA
BBBBB
BBBBB
CCCCC
CCCCC


Input

4 4 2 6 4 2


Output

6
BBBBBB
BBBBBB
AAAACC
AAAACC
AAAACC
AAAACC
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/* 0 */
/***/ function(module, exports, __webpack_require__) {

	var List = __webpack_require__(1);
	var xy = List.map(parseInt, readline().split(' '));
	var Rect = (function () {
	    function Rect(width, height, label) {
	        this.width = width;
	        this.height = height;
	        this.label = label;
	    }
	    Rect.prototype.rotated = function () {
	        return new Rect(this.height, this.width, this.label);
	    };
	    return Rect;
	})();
	var rects = [];
	var label = ["A", "B", "C"];
	for (var i = 0; i < 3; i++) {
	    rects.push(new Rect(xy[2 * i], xy[2 * i + 1], label[i]));
	}
	var infinity = 100000000;
	function square(n) {
	    return List.map(function (_) { return List.replicate(n, "."); }, List.replicate(n, []));
	}
	function draw(canvas, x, y, r) {
	    for (var i = x; i < x + r.width; i++) {
	        for (var j = y; j < y + r.height; j++) {
	            canvas[i][j] = r.label;
	        }
	    }
	}
	function output(canvas) {
	    print(canvas.length);
	    print(List.map(function (s) { return s.join(""); }, canvas).join("\n"));
	}
	function fit(rect) {
	    var width = rect[0].width;
	    var height = rect[0].height;
	    if (rects[1].width > width)
	        return false;
	    height += rect[1].height;
	    if (rect[2].width + rect[1].width === width) {
	        if (rect[2].height !== rect[1].height)
	            return false;
	        if (height !== width)
	            return false;
	        var canvas = square(width);
	        draw(canvas, 0, 0, rect[0]);
	        draw(canvas, 0, rect[0].height, rect[1]);
	        draw(canvas, rect[1].width, rect[0].height, rect[2]);
	        output(canvas);
	        return true;
	    }
	    else {
	        if (rect[1].width != width || rect[2].width != width)
	            return false;
	        height += rect[2].height;
	        if (height != width)
	            return false;
	        var canvas = square(width);
	        draw(canvas, 0, 0, rect[0]);
	        draw(canvas, 0, rect[0].height, rect[1]);
	        draw(canvas, 0, rect[0].height + rect[1].height, rect[2]);
	        output(canvas);
	        return true;
	    }
	}
	var found = false;
	for (var rotation = 0; rotation < 8 && !found; rotation++) {
	    var rotated = [];
	    for (var i = 0; i < 3; i++) {
	        var should_rotate = ((rotation >> i) & 1) !== 0;
	        rotated.push(should_rotate ? rects[i].rotated() : rects[i]);
	    }
	    var p = List.range(0, 2);
	    do {
	        found = found || fit(List.apply_permutation(p, rotated));
	    } while ((p = List.next_permutation(p)) && !found);
	}
	if (!found)
	    print("-1");


/***/ },
/* 1 */
/***/ function(module, exports, __webpack_require__) {

	var Prelude_1 = __webpack_require__(2);
	function add(xs, ys) {
	    return xs.concat(ys);
	}
	exports.add = add;
	function head(xs) {
	    return xs[0];
	}
	exports.head = head;
	function last(xs) {
	    return xs[xs.length - 1];
	}
	exports.last = last;
	function tail(xs) {
	    return xs.slice(1);
	}
	exports.tail = tail;
	function init(xs) {
	    return xs.slice(0, xs.length - 1);
	}
	exports.init = init;
	function map(f, xs) {
	    var result = new Array(xs.length);
	    for (var i = 0; i < xs.length; i++) {
	        result[i] = f(xs[i]);
	    }
	    return result;
	}
	exports.map = map;
	function reverse(xs) {
	    return xs.slice().reverse();
	}
	exports.reverse = reverse;
	function intersperse(x, xs) {
	    if (xs.length == 0) {
	        return [];
	    }
	    var result = new Array(xs.length + xs.length - 1);
	    for (var i = 0; i + 1 < xs.length; i++) {
	        result[i + i] = xs[i];
	        result[i + i + 1] = x;
	    }
	    result[result.length - 1] = xs[xs.length - 1];
	    return result;
	}
	exports.intersperse = intersperse;
	function intercalate(xs, xss) {
	    return concat(intersperse(xs, xss));
	}
	exports.intercalate = intercalate;
	function foldl(f, initial, xs) {
	    var result = initial;
	    for (var i = 0; i < xs.length; i++) {
	        result = f(result, xs[i]);
	    }
	    return result;
	}
	exports.foldl = foldl;
	function foldr(f, initial, xs) {
	    var result = initial;
	    for (var i = xs.length - 1; i >= 0; i--) {
	        result = f(xs[i], result);
	    }
	    return result;
	}
	exports.foldr = foldr;
	function concat(xss) {
	    var total = sum(map(function (xs) { return xs.length; }, xss));
	    var result = new Array(total);
	    var m = 0;
	    for (var i = 0; i < xss.length; i++) {
	        var xs = xss[i];
	        for (var j = 0; j < xs.length; j++) {
	            result[m++] = xs[j];
	        }
	    }
	    return result;
	}
	exports.concat = concat;
	function sum(xs) {
	    var result = 0;
	    for (var i = 0; i < xs.length; i++) {
	        result += xs[i];
	    }
	    return result;
	}
	exports.sum = sum;
	function product(xs) {
	    var result = 1;
	    for (var i = 0; i < xs.length; i++) {
	        result *= xs[i];
	    }
	    return result;
	}
	exports.product = product;
	function maximum(xs) {
	    var result = xs[0];
	    for (var i = 1; i < xs.length; i++) {
	        if (result < xs[i])
	            result = xs[i];
	    }
	    return result;
	}
	exports.maximum = maximum;
	function minimum(xs) {
	    var result = xs[0];
	    for (var i = 1; i < xs.length; i++) {
	        if (result > xs[i])
	            result = xs[i];
	    }
	    return result;
	}
	exports.minimum = minimum;
	function replicate(n, x) {
	    var result = new Array(n);
	    for (var i = 0; i < result.length; i++) {
	        result[i] = x;
	    }
	    return result;
	}
	exports.replicate = replicate;
	function take(n, xs) {
	    return xs.slice(0, n);
	}
	exports.take = take;
	function drop(n, xs) {
	    return xs.slice(n);
	}
	exports.drop = drop;
	function splitAt(n, xs) {
	    return [take(n, xs), drop(n, xs)];
	}
	exports.splitAt = splitAt;
	function takeWhile(f, xs) {
	    for (var i = 0; i < xs.length; i++) {
	        if (!f(xs[i])) {
	            return xs.slice(0, i);
	        }
	    }
	    return xs.slice();
	}
	exports.takeWhile = takeWhile;
	function dropWhile(f, xs) {
	    for (var i = 0; i < xs.length; i++) {
	        if (!f(xs[i])) {
	            return xs.slice(i);
	        }
	    }
	    return [];
	}
	exports.dropWhile = dropWhile;
	function group(xs) {
	    if (xs.length == 0) {
	        return [];
	    }
	    var result = [];
	    var last = [xs[0]];
	    for (var i = 1; i < xs.length; i++) {
	        if (last[0] === xs[i]) {
	            last.push(xs[i]);
	        }
	        else {
	            result.push(last);
	            last = [xs[i]];
	        }
	    }
	    result.push(last);
	    return result;
	}
	exports.group = group;
	function filter(f, xs) {
	    var result = [];
	    for (var i = 0; i < xs.length; i++) {
	        if (f(xs[i]))
	            result.push(xs[i]);
	    }
	    return result;
	}
	exports.filter = filter;
	function zip(xs, ys) {
	    var n = Prelude_1.min(xs.length, ys.length);
	    var result = new Array(n);
	    for (var i = 0; i < n; i++) {
	        result[i] = [xs[i], ys[i]];
	    }
	    return result;
	}
	exports.zip = zip;
	function unzip(xs) {
	    var r1 = new Array(xs.length);
	    var r2 = new Array(xs.length);
	    for (var i = 0; i < xs.length; i++) {
	        r1[i] = xs[i][0];
	        r2[i] = xs[i][1];
	    }
	    return [r1, r2];
	}
	exports.unzip = unzip;
	function range(from, to) {
	    var result = Array(to - from + 1);
	    for (var i = from; i <= to; i++) {
	        result[i - from] = i;
	    }
	    return result;
	}
	exports.range = range;
	function copy(xs) {
	    return xs.slice(0);
	}
	exports.copy = copy;
	function apply_permutation(p, xs) {
	    var n = xs.length;
	    var result = new Array(n);
	    for (var i = 0; i < n; i++) {
	        result[i] = xs[p[i]];
	    }
	    return result;
	}
	exports.apply_permutation = apply_permutation;
	function next_permutation(p) {
	    var n = p.length;
	    if (n < 2)
	        return null;
	    var r = copy(p);
	    var k = n - 2;
	    for (; k >= 0 && r[k] >= r[k + 1]; k--)
	        ;
	    if (k < 0)
	        return null;
	    for (var i = k + 1, j = n - 1; i < j; i++, j--) {
	        var t_1 = r[i];
	        r[i] = r[j];
	        r[j] = t_1;
	    }
	    var next = k + 1;
	    for (; r[next] <= r[k]; next++)
	        ;
	    var t = r[k];
	    r[k] = r[next];
	    r[next] = t;
	    return r;
	}
	exports.next_permutation = next_permutation;


/***/ },
/* 2 */
/***/ function(module, exports) {

	function min(a, b) {
	    return a < b ? a : b;
	}
	exports.min = min;
	function max(a, b) {
	    return a < b ? b : a;
	}
	exports.max = max;
	function curry(f) {
	    return function (x) { return function (y) { return f(x, y); }; };
	}
	exports.curry = curry;
	function uncurry(f) {
	    return function (x, y) { return f(x)(y); };
	}
	exports.uncurry = uncurry;
	function id(x) {
	    return x;
	}
	exports.id = id;
	function constant(x) {
	    return function (_) { return x; };
	}
	exports.constant = constant;
	function flip(f) {
	    return function (y) { return function (x) { return f(x)(y); }; };
	}
	exports.flip = flip;
	function flip2(f) {
	    return function (y, x) { return f(x, y); };
	}
	exports.flip2 = flip2;
	function compose(g, f) {
	    return function (x) { return g(f(x)); };
	}
	exports.compose = compose;


/***/ }
/******/ ]);