Problem: Vasya has a pack of 54 cards (52 standard cards and 2 distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them.

Vasya lays out nm cards as a rectangle n × m. If there are jokers among them, then Vasya should change them with some of the rest of 54 - nm cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. in a single copy). Vasya tries to perform the replacements so that the solitaire was solved.

Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares 3 × 3, inside each of which all the cards either have the same suit, or pairwise different ranks.

Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.

Input

The first line contains integers n and m (3 ≤ n, m ≤ 17, n × m ≤ 52). Next n lines contain m words each. Each word consists of two letters. The jokers are defined as "J1" and "J2" correspondingly. For the rest of the cards, the first letter stands for the rank and the second one — for the suit. The possible ranks are: "2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K" and "A". The possible suits are: "C", "D", "H" and "S". All the cards are different.

Output

If the Solitaire can be solved, print on the first line "Solution exists." without the quotes. On the second line print in what way the jokers can be replaced. Three variants are possible:

  * "There are no jokers.", if there are no jokers in the input data.
  * "Replace Jx with y.", if there is one joker. x is its number, and y is the card it should be replaced with.
  * "Replace J1 with x and J2 with y.", if both jokers are present in the input data. x and y here represent distinct cards with which one should replace the first and the second jokers correspondingly.



On the third line print the coordinates of the upper left corner of the first square 3 × 3 in the format "Put the first square to (r, c).", where r and c are the row and the column correspondingly. In the same manner print on the fourth line the coordinates of the second square 3 × 3 in the format "Put the second square to (r, c).".

If there are several solutions to that problem, print any of them.

If there are no solutions, print of the single line "No solution." without the quotes.

See the samples to understand the output format better.

Examples

Input

4 6
2S 3S 4S 7S 8S AS
5H 6H 7H 5S TC AC
8H 9H TH 7C 8C 9C
2D 2C 3C 4C 5C 6C


Output

No solution.

Input

4 6
2S 3S 4S 7S 8S AS
5H 6H 7H J1 TC AC
8H 9H TH 7C 8C 9C
2D 2C 3C 4C 5C 6C


Output

Solution exists.
Replace J1 with 2H.
Put the first square to (1, 1).
Put the second square to (2, 4).


Input

4 6
2S 3S 4S 7S 8S AS
5H 6H 7H QC TC AC
8H 9H TH 7C 8C 9C
2D 2C 3C 4C 5C 6C


Output

Solution exists.
There are no jokers.
Put the first square to (1, 1).
Put the second square to (2, 4).

Note

The pretests cover all the possible output formats.

Solution (in PYTHON3):

Solution:
allCards = [value + suit for value in ["2","3","4","5","6","7","8","9","T","J","Q","K","A"] for suit in ["C","D","H","S"]]
n, m = map(lambda x: int(x), input().split(" "))
cards = []
for i in range(n):
    cards.append(input().split(" "))
availableCards = allCards
for arr in cards:
    for card in arr:
        if card != "J1" and card != "J2":
            availableCards.remove(card)

def joker2(i: int, j: int) -> [bool, bool, bool, set]:
    usedValues = set()
    didFoundJoker1 = False
    didFoundJoker2 = False
    for i1 in range(i, i + 3):
        for j1 in range(j, j + 3):
            if cards[i1][j1] == "J1":
                didFoundJoker1 = True
            elif cards[i1][j1] == "J2":
                didFoundJoker2 = True
            elif cards[i1][j1][0] not in usedValues:
                usedValues.add(cards[i1][j1][0])
            else:
                return [False, False, False, set()]
    res = set()
    for card in availableCards:
        if card[0] not in usedValues:
            res.add(card)

    isTrue = True
    if didFoundJoker1 or didFoundJoker2:
        isTrue = False
        for card in res:
            if isTrue: break
            for i1 in range(i, i + 3):
                if isTrue: break
                for j1 in range(j, j + 3):
                    if cards[i1][j1] not in ["J1","J2"] and cards[i1][j1][0] != card[0]:
                        isTrue = True
                        break


    return [isTrue, didFoundJoker1, didFoundJoker2, res]
ansi1, ansj1, ansi2, ansj2 = 0, 0, 0, 0
replaceJoker1 = None
replaceJoker2 = None
def joker1(i: int, j: int) -> bool:
    global replaceJoker1
    global replaceJoker2
    global ansi1, ansj1, ansi2, ansj2
    if not (i + 2 < n and j + 2 < m):
        return False
    didFound1, didFindJoker1, didFindJoker2, strings = joker2(i, j)
    if not didFound1:
        return False
    for i1 in range(n):
        for j1 in range(m):
            if (i1 > i + 2 or j1 > j + 2) and i1 + 2 < n and j1 + 2 < m:
                didFound2, didFindJoker21, didFindJoker22, strings2 = joker2(i1, j1)
                if (didFindJoker1 or didFindJoker2) and (didFindJoker21 or didFindJoker22):
                    xor = (strings2 ^ strings)
                    x1 = xor & strings
                    x2 = xor & strings2
                    if x1 and x2:
                        if didFindJoker1 and didFindJoker22:
                            replaceJoker1 = x1.pop()
                            replaceJoker2 = x2.pop()
                        else:
                            replaceJoker1 = x2.pop()
                            replaceJoker2 = x1.pop()
                        ansi1, ansj1, ansi2, ansj2 = i, j, i1, j1
                        return True
                elif didFindJoker21 and didFindJoker22:
                    if len(strings2) >= 2:
                        replaceJoker1 = strings2.pop()
                        replaceJoker2 = strings2.pop()
                        ansi1, ansj1, ansi2, ansj2 = i, j, i1, j1
                        return True
                elif didFound2 and didFindJoker1 and didFindJoker2:
                    stringsx = list(strings)
                    ansi1, ansj1, ansi2, ansj2 = i, j, i1, j1
                    for i in range(len(stringsx)):
                        for j in range(i + 1, len(stringsx)):
                            if stringsx[i][0] != stringsx[j][0]:
                                replaceJoker1 = stringsx[i]
                                replaceJoker2 = stringsx[j]
                                return True
                    continue
                elif didFound2 and didFindJoker21 and didFindJoker22:
                    stringsx = list(strings2)
                    ansi1, ansj1, ansi2, ansj2 = i, j, i1, j1
                    for i in range(len(stringsx)):
                        for j in range(i + 1, len(stringsx)):
                            if stringsx[i][0] != stringsx[j][0]:
                                replaceJoker1 = stringsx[i]
                                replaceJoker2 = stringsx[j]
                                return True
                    continue
                elif didFound2:
                    if didFindJoker1:
                        if not strings:
                            continue
                        replaceJoker1 = strings.pop()
                    if didFindJoker2:
                        if not strings:
                            continue
                        replaceJoker2 = strings.pop()
                    if didFindJoker21:
                        if not strings2:
                            continue
                        replaceJoker1 = strings2.pop()
                    if didFindJoker22:
                        if not strings2:
                            continue
                        replaceJoker2 = strings2.pop()
                    ansi1, ansj1, ansi2, ansj2 = i, j, i1, j1
                    return True

    return False

didFound = False
for i in range(n):
    if didFound:
        break
    for j in range(m):
        res = joker1(i, j)
        if res:
            print("Solution exists.")
            j1f, j2f = False, False
            for c in cards:
                for card in c:
                    if card == "J1":
                        j1f = True
                    elif card == "J2":
                        j2f = True
            if j1f and not replaceJoker1:
                replaceJoker1 = availableCards.pop()
                while availableCards and replaceJoker1 == replaceJoker2:
                    replaceJoker1 = availableCards.pop()
            if j2f and not replaceJoker2:
                replaceJoker2 = availableCards.pop()
            if replaceJoker2 and replaceJoker1:
                print(f"Replace J1 with {replaceJoker1} and J2 with {replaceJoker2}.")
            elif replaceJoker1:
                print(f"Replace J1 with {replaceJoker1}.")
            elif replaceJoker2:
                print(f"Replace J2 with {replaceJoker2}.")
            else:
                print("There are no jokers.")
            print(f"Put the first square to ({ansi1+1}, {ansj1+1}).")
            print(f"Put the second square to ({ansi2+1}, {ansj2+1}).")
            didFound = True
            break
if not didFound:
    print("No solution.")